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1. After a successful Make you can use the File Save All menu command Ctrl Shift S to save the current version of all the modules together with their compiled code only modules that have been modified after the last Save are actually saved Open Modules A submodule may be opened inside the program window either by Numerit for compiling the module or when stepping into one of its functions or by the user through the Modules List window An open submodule remains open until it is closed manually using the menu command File Close Module or through the Modules List window Every open module has a tab at the bottom of the Editor pane that allows you to bring it into the Editor In addition open modules appear in boldface in the Modules List window A module remains open as long as it is not explicitly closed even if it is not currently visible in the Editor Note that a compiled library cannot be opened as a module and its source is not accessible from within the program s window To modify the code in such a module you must open it independently in its own window make the changes create a new compiled version and then click Reload in the modules list window see Modules List below When Numerit is making the program and there are open modules it uses the version of the code that is currently in the open modules Thus you may change the code in an open module without saving it and the version that is used is the one that is currently open rat
2. The command common is used to share variables between modules It allows you to specify a list of variables that you want to share between two or more modules A variable that appears in the common list of any two modules that are linked to the same program in any level is shared by these modules 1 e both actually use the same variable Note that you can only declare common variables in the main body of a module or a program and you 109 still need to use the prefix to access these variables from within a function The lists that are specified in the common instructions of two different modules need not be identical only those variables that appear in both lists will be shared For example if you put common x y z in module A common x y in module B and common y z in module C then x is shared between A and B z is shared between A and C and y is shared between A B and C const constant Syntax Operands Description delete const x c x is an identifier c is a Numeric Boolean or String constant By declaring a constant you can use the name of the constant instead of the constant itself in any Numerit instruction This is useful when you want to use the same constant in various instructions or expressions and be able to change it with a single assignment In most cases you can use a standard Numerit variable for the same purpose however the use of a declared constant ensures that it will not be modified by the program
3. Compiler internal error The program was not compiled This error should not occur normally It might occur when there is not enough memory if it persists contact technical staff Index error Internal indexing error This error should not occur normally if it persists contact technical staff Internal error Internal error This error should not occur normally if it persists contact technical staff Memory allocation failed Not enough memory to complete the operation To free memory use the free instruction inside the code whenever possible Closing other applications might also help Stack error Internal stack error This error should not occur normally if it persists contact technical staff 71 Non Fatal Errors Argument must be monotonic increasing or decreasing The specified argument is expected to be a monotonic increasing or decreasing array for example the x table that is sent to interpolation functions Array is empty An illegal operation has been performed on an empty array An empty array may be returned from a call to Loc b where b is a Boolean array whose elements are all false Some operations like sum or max cannot be performed on empty arrays since they must return a valid scalar value other operations are simply ignored Complex is illegal A Complex variable or expression is used as an argument or an operand where Complex is not allowed Check your code Degree must be an integer smaller than the numb
4. Namely the first parameter is declared as a function that returns a double value and receives one argument of type double as before the names f x a and b are optional The second and third parameters are declared as double s The Numerit callback function in this case must also expect a single scalar and return a scalar For the above example such a Numerit function looks like func sqr x x x Here we used the single line version of a Numerit function When a callback function is actually sent as an argument to a DLL function it must have a prefix So when the function integral is called the Numerit function sqr is sent to it in the following way a 0 bed c integral sqr a b A callback function may also be specified as a member of a structure For example the following declaration dfunc foo func double f double x double p double a passes the function f and the variable p as a structure to the DLL function foo When foo is called in Numerit the callback function should be specified inside the braces with the prefix namely foo ffun p x The callback process is carried out in the following way The DLL function receives an address of a function as the callback function When it needs it to evaluate a value it pushes arguments to the stack and then calls the function in the given address This call returns control to Numerit which retrieves the arguments from the stack Numerit converts the arguments to Numeri
5. else y 0 In this form there is an expression at the head x The statements of each case in the cases block are preceded by a constant or an expression followed by a colon If the value of the expression in the head x is equal to one of the constants or expressions of one of the cases the statements of this case are executed and no more cases are checked If no case matches the optionally else case is executed It is possible to specify more than one expression for a case These expressions should be separated by commas like the 1 3 1 4 case above The statements of such a case will be executed if a match to one of the expressions is found Several statements may be specified for each case They may be written in the same line separated by semicolons as in case 2 2 above or as a block on the next line as in case 5 5 To define an empty case a semicolon must be inserted as in case 6 2 above The second form of case looks like case x 4 ye l x gt 1 and x lt 3 y 2 x gt bi y 1 else y 0 Here the head is empty and each case starts with a Boolean expression which is followed by statements The expressions are evaluated one by one and the first one that yields a true and only the first is executed The optional else case is executed if no condition was satisfied This is actually a substitute for a series of if else if statements clear Syntax clear clear x y Z Operands X Y Z ar
6. float double and ptr or pointer Numerit complex arrays cannot be passed to DLL functions unlike complex scalars but a complex array can be converted to a packed array with the function PackComplex and passed as a double array to the DLL function The packed array is converted back to a Numerit complex array with the function UnpackComplex A one dimensional array is specified with a single pair of brackets For example dfunc double sum 1d double x declares a function that receives a one dimensional numeric array as an argument Since the name of the parameter is optional this could also be declared as dfunc double sum 1d double The above Numerit declaration corresponds to the following C function prototype double sum 1d double x As mentioned above in C one can also use a pointer to pass a one dimensional array so the above Numerit declaration also corresponds to the following C function prototype double sum 1d double x provided that x is indeed used as an array of double s in the function As before when the type of the array is double Numerit doesn t need to convert its values and the array is sent to the DLL function as is However if the C function requires an array of another type say int the Numerit array is converted from double Numerit s internal representation to int before it is passed to the DLL function and is converted back to double when the function returns Such a conversion will tak
7. 2x so the third column of b for example is sin x The i th element in the returned array is the coefficient of the i th basis function The second form of fitbasis allows to add a third array s which specifies relative standard deviations of the data points All the elements of s must be positive numbers A larger s i means that the corresponding data point has a larger error and consequently less weight A very small value will force the curve to go through or very close to the corresponding data point Note that in the first form of the function all the points have the same weight fitcheby Syntax fitcheby n x y fitcheby n x y Ss Operands n is an integer 92 x y and s are 1 dimensional Real expressions Description fitline Returns a 1 dimensional array with n 1 elements which are the coefficients in the linear combination of Chebyshev polynomials up to degree n that best fits the set of data points given by x and y x and y are 1 dimensional arrays of the same length and must be Real The i th element in the returned array is the coefficient of the Chebyshev polynomial Ls Note that the Chebyshev polynomials are defined on the interval 1 1 so the function fitcheby first maps the data points into this interval the smallest x is mapped to 1 and the largest x to 1 and then calculates the coefficients Thus you should use these coefficients to evaluate the fit in the interval 1 1 The second form of i
8. EX COUPON A E bin oseyecusctusdyssteestedeedvbeateassabestaseoiinutanwiearehes 71 Chapter 9 Keyboard and Mouse 75 Keyboard Shortcuts it conden Steed A idas 75 Mouse O A A e i es 77 Chapter 10 A Quick Reference to Numerit s built in functions 79 Chapter 11 A Quick Reference to Numerit s commands 83 Chapter 12 A Quick Reference to Numerit s operators 85 Chapter 13 Reference to Numerit s built in functions 87 Chapter 14 Reference to Numerit s commands 107 Numerit Software License Agreement 133 Chapter 1 Numerit Introduction Numerit is an intuitive programming environment for developing numerical computation programs and producing publication quality documents It combines the versatility of conventional programming with the powerful interface of Windows Numerit includes a specially designed program editor to make it easier for you to write your programs The editor includes special editing tools for inserting and manipulating program blocks It highlights keywords and displays comments in a distinctive color It lets you customize the fonts and the colors And It has many levels of undo redo Numerit has built in debugging tools to help you while you develop your program The program may be paused at any point during the run and may be executed line by line Variables may be inspected while the program is running with a simple mouse click Numerit includes a specially designed document editor to edit your program s output This edit
9. Editor Document View Program bar View Document bar View Status bar Panes Auto Size Ignore Compiler Warnings View Document Ruler View Document Margins View Document Whole page View Document Special characters Update Document fields Set Document Units Window Cascade Shift F5 Tile Shift F4 Minimize All Arrange Icon Horizontal Split Shift F9 Vertical Split Shift F8 Maximize Pane Shift F7 Toggle Panes Shift F6 Input Extra Editor Document Report Draft Ctrl D Message Ctrl M Help Contents F1 Search Ctrl F1 About Numerit Compile the current program Standard Edition Compile the current module Professional Edition Compile all modules that need compiling and link external functions Professional Run the current program compile make if necessary Execute the current line while stepping over functions Execute the current line while entering functions Pause the current program Stop the current program Move inspection position to the calling function Move inspection position to the called function Move to the line that will be executed next Editor Open the Inspector and show variable s content Set Clear a breakpoint at the current line pause before executing the line Clear all breakpoints Move to previous compilation or execution error or warning Move to next compilation or execution error or warning Define Editor options Define Document options Show Hide the Progra
10. The value NAN propagates through expressions namely if x becomes NAN then an expression like x 1 also yields a NAN Numeric overflow A numeric overflow occurred The program may continue to run and the result is set to INF or INF INF is an IEEE standard representation for infinity The value INF propagates through expressions namely if x becomes INF then an expression like x 1 also yields an INF Output error An error occurred while writing output to the Draft This usually indicates that the Draft is full Use the menu command Edit Clear Draft to clear the Draft or delete some text from the Draft In most cases the Draft becomes full when the output of different runs is accumulated If this accumulation is not required put the clear instruction at the head of the program s code This will clear the Draft at the beginning of each run Path not found The specified path in the directory statement was not found Singular matrix A singular or almost singular matrix has been detected Some operations e g Det cannot be completed in such a case Type error An unexpected type has been encountered during execution This error should not occur normally since types are checked during the compilation if it persists contact technical staff Undefined variable An undefined variable is used in an expression Variables must be assigned a value before they are used 73 Function didn t return a value A function that was expected t
11. 214 221 222 223 224 311 312 313 314 321 322 323 324 will be flattened to 111 112 113 114 1271 122 123 124 211 212 213 214 221 222 223 224 311 312 313 314 321 322 323 324 and passed to the DLL function as such The number of rows in the resulted flattened array is the multiplication of all the higher dimensions up to the last one 6 in the above example and the number of columns is the last dimension 4 in the above example Note that multidimensional arrays are stored in Numerit in such a way that the flattening process doesn t require an extra effort and is actually not a time consuming operation It is very important to note that in C two dimensional arrays may take two forms The first is where the array is allocated as a single contiguous block of memory of length m x n where m is the number of rows and n is the number of columns In the second form the array is allocated in two stages in the first stage an array of pointers addresses of length m is allocated and then each row of the array is dynamically allocated as a one dimensional array of length n and its address is saved in the corresponding element of the array of addresses In Numerit multidimensional arrays are allocated using the second form So multidimensional Numerit arrays can only be passed to DLL functions that expects two dimensional arrays of the second form Such an array is specified in the list of parameters of the C function w
12. In some cases a variable cannot replace a constant for example when specifying the parameters of output formats such as outprec or outwidth Constants can only be declared outside functions but can be used inside functions without the global prefix The actual constant replaces the declared name in the code at compilation time Examples const N 12 x N 0 y N 0 const NAME c data directory NAM E Syntax Operands Description dfunc delete f f isa file Deletes the file f from the disk should be previously defined by file or by binfile Syntax Operands Description 110 dfunc function prototype or dfunc block of function prototypes function prototype isa DLL function prototype Declares a function of a dynamic link library DLL The function is assumed to be a C or C function that was compiled into a standard Win32 32 bit DLL The function is searched for in the library that has been declared on a previous d11 statement For a detailed description of DLL functions in Numerit including examples see Dynamic link functions in Ch 6 The dfunc statement is used to declare functions that were compiled with cdecl calling convention A function that was compiled with the stdcall calling convention should be declared with the statement sdfunc The dfunc or sdfunc statement includes a DLL function prototype on the same line or a number of function prototypes in a subsequent
13. Same as outw Specifies a zero threshold for output numbers below the threshold appear as 0 Same as outz 83 pause pos print printin printpg randomize read readin readtab refresh repeat report return sdfunc sdfunction smessage stop system table then time to until vector wait where while wmessage write writeln writetab ynmessage yncmessage 84 Pauses the program Sets the current position in a disk file or the Input File Writes output to the Draft Writes output to the Draft and moves to a new line Writes output to the Draft and moves to a new page Initializes the random number generator Reads data from a file or a string Reads a line of text from a text file Reads tabular data from a text file Refreshes the Viewers in the Document Defines a loop with a condition test at its end Displays the Report Returns from a function Declares a dynamic link library function Same as sdfunc Displays a Stop message Stops the program Executes a system Windows command Inserts a table at the current position in the Draft Used in an if statement optional String containing the current date and time Specifies the limit in an increasing for loop Defines a loop that runs until a condition becomes true Defines a 1 dimensional array as a Vector Waits for the specified amount of time Assigns values to array elements according to a condition Defines a loop that runs while a condition is true Displays a Warn
14. Warranty The SOFTWARE is provided without warranty of any kind either express or implied including without limitation fitness for a particular purpose Defective media or documentation will be replaced at no charge provided they are returned within 90 days of the date of delivery Termination The license will terminate automatically if you fail to comply with the terms and conditions of this Agreement On termination you must destroy all copies of the SOFTWARE Limitation of liability In no event will KEDMI Scientific Computing be liable for any damages including any lost profits data or information or other indirect incidental special or consequential damages arising out of the use of or inability to use the SOFTWARE even if advised of the possibility of such damages or for any claim by any other party 133
15. as a table from a text file write Writes data to a text or binary file writeln Writes data to a text file and adds a new line character writetab Writes data to a text file as a table There are also functions that return information about files size f Returns the file size in bytes pos f Returns the current position in the file in bytes exists f Returns true if the file exists and false if it doesn t eof f Returns true if the end of file has been reached and false if not Notes 1 When writing data to a text file the format is controlled by the current setting of outwidth outprec outformat and outzero 2 When writing data to a binary file the exact representation is Number written and read as a double precision floating point number 8 bytes String written and read as a sequence of characters 1 byte each Boolean written and read as a byte 39 3 A complex number is written and read with the real part first and the imaginary part next to it as two distinct numbers 4 When reading numeric data from a text file anything that appears between the numbers is skipped actually is considered to be a delimiter except the characters minus plus and dot which cannot be used as delimiters and will cause a read error if they are not part of a number Strings should be separated by spaces unless they are read by readln Input File A Numerit program can read data from a disk file and in many cases th
16. back copy is not actually required and you can tell Numerit not to do it and save execution time This is done by adding the mark after the square brackets of the array that need not be copied back namely dfunc foo int 10 doublej int Note that with arrays that are specified in the structure without dimensions the array address is copied to the structure so the array can be directly modified by the DLL function and need not be copied back thus the is not relevant in this case Numerit does not allow you to specify a structure inside a structure If this is required you must specify the members of the inner structure as members of the same structure for example the C structure circ shown below struct coordinate double x y y struct circ struct coordinate center double radius y 1s specified as a parameter to a DLL function with a single structure namely dfunc foo double x double y double r Note that this doesn t cover all possible cases For example the following structure cannot be specified as a DLL function parameter struct circ struct coordinate center double radius Fa since a member of the structure is a pointer to another structure the above specific case can be worked around by specifying a double array i e double center instead of a pointer to coordinate but in the general case a more complex 51 structure than coordinate this cannot be done A stru
17. be C or C functions that were compiled into a standard Win32 32 bit DLL Functions in a DLL that are available to applications are called exported functions In the DLL source code which shouldn t concern you if you are just using the DLL a function is normally exported by the keyword _ declspec dllexport see also Dynamic link Libraries above Before calling a DLL function the function must be declared in Numerit This declaration serves two purposes 1 it allows Numerit to find the specified function in the DLL and 2 it specifies the function s return type and the number and types of its parameters so that Numerit can convert the variables that are sent as arguments to the actual types that are expected by the DLL function The function is searched for in the library that has been declared on a previous d11 statement The declaration in Numerit is done with the commands dfunc and sdfunc The first is used to declare functions that have been compiled with the cdecl calling convention and the second is used to declare functions that have been compiled with the stdcall calling convention other than that both commands are identical See Dynamic link Libraries above for information about calling conventions The dfunc or sdfunc statement includes a DLL function prototype that specifies the type of the function s return value and the types of the function s parameters The specified types are the C types as described in Dynamic lin
18. be written as 31 4159 12345 will be written as 12345 When outformat is set to fixed the parameter n specifies the number of digits after the decimal point and the number is always displayed in decimal format For example with outprec 4 T will be written as 3 1416 10m will be written as 31 4159 12345 will be written as 12345 0000 When outformat is set to scientific the parameter n specifies the number of digits after the decimal point and the number is always displayed in exponential format For example with outprec 4 T will be written as 3 141 6e 00 10m will be written as 3 1416e 01 12345 will be written as 1 2345e 04 outwidth outw Syntax Operands Description outwidth n or outw n n isa number Sets the width of items when writing formatted data to a file or to the Draft The parameter n defines the minimum width number of characters allocated to each item Data items that occupy less space than specified are left padded with spaces A value of 0 which is the default sets no minimum width and adds one space between the items 123 outzero outz Syntax outzero n or outz n Operands n is a number Description Sets a range of small numbers around zero that are written as 0 when writing formatted data to a file or to the Draft The parameter n specifies the negative exponent of the numbers that define the range Its default value is 15 which means that numbers in the range 107 to 107 are
19. button in the Program bar select the module and click Open Module This opens the module and brings it into the Editor At the bottom of the Editor pane there are tabs that allows you to select which of the currently open modules you want to bring into the Editor The Editor pane is also used for editing the Input File see Input File below for details To print the Editor s content use the File Print menu command or click the Print button in the Program Bar when the Editor pane is active Program Blocks Program blocks are used to group together several instructions in the program s code There are many commands that require blocks for example if for and function Unlike other languages a block in Numerit is not constructed by separate Begin and End statements but is a single entity It appears to the user as a frame which wraps the instructions on the left The block frame adjusts itself automatically to the number of instructions that are inserted into it For example if x gt 0 y x 2 if y gt 100 u x EE w uty This blocking technique allows easy manipulation of program blocks and has many advantages over conventional blocking including You get a much better view of the program s structure especially when there are several levels of nested blocks You don t have to worry about matching Begin and Ends nested blocks block indentation etc it is all done automatically Blocks may be folded which makes it possible to
20. callback structure parameters are especially useful when the DLL function is written in C and calls the callback function with arrays that are defined as classes As mentioned above array classes in C are usually defined as structures with the first member s specifying the length s and the next member specifying the address of the actual array A DLL function as a callback function As already mentioned a DLL function can be sent to another DLL function as an argument to serve as a callback function This 1s the most efficient way from an execution point of view since Numerit doesn t have to deal with the parameters of the callback function at all It just sends its address to the DLL function that calls it directly without involving Numerit in the process And since the callback function is itself a C or C function it also runs much faster than the Numerit function The drawback is of course the need to prepare in advance a C or C version of the callback function and to compile it into a DLL So if you know in advance what are the callback functions that you want to use and you know how to write and compile C functions into a DLL it is highly recommended to use this approach You can use a Numerit version of the callback function during the development stage and then when everything works as expected you can write a C version of the function and use it to save execution time When a DLL function is specified as a parameter to another DL
21. create a complex variable c from two real variables a and b write c a 1i b Strings are formed by a sequence of characters and are used for titles file names etc a String constant must appear between quotes Strings may be concatenated by the operator amp Boolean expressions may have only two values true and false The Boolean type is obtained from comparisons of Numeric String or Boolean expressions or by a direct assignment of one of the two Boolean constants true and false Booleans may form logical expressions with the operations and or xor and not File variables are defined by the commands file and binfile See the section Files for more details Kind Every variable has one of the following four kinds Scalar Array Vector and Matrix The kind is inherited upon assignment so a variable s kind changes during the run when it is assigned a value of a different kind Most operations ignore the kind Some operations are affected by the kind for example a multiplication of two matrices is not carried out on matching elements as with simple 2 dimensional arrays but according to matrix multiplication rules By default a variable s kind is Scalar or Array depending on the dimension Vectors and Matrices are explicitly defined as such or inherit the kind by assignment Expression An expression is a variable a constant a function call of a function that returns a value or any combination of these with operators
22. first module in the list and continues from top to bottom until the function is found A function may appear in more than one module but the first to be found is the one that s actually used It is possible to change the order of modules in the list and thus control which function is used see Modules List below A better control is achieved by specifying the name of the module in the calling instruction The syntax is module name function name arguments i e the module name precedes the function name with a dot between them note that the module name is not the file name see Modules List below For example if a module named MyLib contains a function MyFunc x then the instruction MyLib MyFunc x will call this specific function even if a function MyFunc also appears in another module which is located above MyLib in the list of modules In addition it is possible to call the main body of a module using the instruction module_name main for example to call the main body of MyLib you write MyLib main Calling the main body of a module may be very useful for defining global variables for the module As in any Numerit program all the functions in a module have access to the variables that are defined in the module s body using the prefix in front of the variable name see Local and Global variables in the previous chapter Thus the module s functions may share variables that are defined in the module s main body These variables are norma
23. function Either a mismatch between a and a y or a nested structure within which is not allowed Unexpected item An unexpected item has been encountered This usually indicates that a previous item is missing or incorrectly spelled Unexpected break The instruction break is allowed only inside a loop Unexpected next The instruction next is allowed only inside a loop Unexpected end of program This error occurs when the compiler is expecting more instructions but reaches the end of the program This is usually an indication for an incomplete instruction at the end of the program Unterminated String A string constant is defined between two quotes This error occurs when no terminating quote was found Wrong number of arguments in a call to name The call to the specified function contains a wrong number of arguments Check the function definition Inconsistent number of parameters rerouting funcl n1 gt func2 n2 When a function is rerouted to another function both must have exactly the same number of parameters nl and n2 are the number of parameters of each function 67 Compilation Warnings name Argument seems to be Complex must be Real The arguments of the specified function must be Real but at least one seems to be Complex name Arguments must be 1 dimensional n1 n2 The arguments of the specified function should be 1 dimensional arrays but seem to have
24. function see also Pointers below Note that the return value is always interpreted as a scalar in Numerit and the function call actually generates a Numerit scalar Parameters The parameters are listed inside the parenthesis as a list of types separated by commas one for each actual function parameter Each type can be followed by an optional parameter name and the allowed types are the same as listed above except void which can only be used for the return value 45 Unlike the return value which is always a scalar a parameter can have a much more complicated structure Numerit allows a DLL function parameter to be a scalar an array a structure or a function When you want to call a function from a DLL you must know how it expects to receive each of its parameters Note that the DLL does not provide any information about the number and types of its functions parameters So it is the responsibility of the user to supply this information accurately since there is no way to check its correctness Specifying the wrong number of parameters or a wrong type will in most cases crash the program and result in an abnormal termination of Numerit Since the DLL function prototype in Numerit is very similar to the prototype that is specified in the C header file it is not too difficult to avoid errors in the Numerit declaration You will usually copy the C function prototype to Numerit In many cases you will use the C prototype as is and in ot
25. functions a DLL may also make its global variables available to applications To distinguish DLLs from standalone executables files containing compiled dynamic link routines are named with the dll extension The dynamic link at runtime makes it possible to extend the usability of applications by adding to them functionality without making any modifications to the source code or recompiling the application Using DLLs also helps reduce memory overhead because many applications can share the same code Starting with version 1 7 Numerit supports calling of DLL exported functions as if they were Numerit built in functions Numerit also allows accessing DLL exported variables Besides extending Numerit s functionality with the large collection of available DLLs either commercially or as public domain packages the ability to call DLL functions allows Numerit users that know how to program in low level languages such as C or C to write time consuming pieces of code in the low level language and compile them into a DLL In some cases calling this code from Numerit instead of writing it in Numerit may decrease execution time by orders of magnitude In order to call DLL functions or access DLL variables you just have to declare the DLL and the functions and variables that you want to access and you can use them right away For example suppose you have a numerical analysis library DLL called numlib dll and you want to call the functions gamma x and bet
26. half the base size note that unlike the document here you cannot set tab stops manually In order to see the spaces in the equation check the Show Spaces box The space marks will not appear in the printed equation Format The Format dialog page lets you determine the current mode character attributes and row alignment Mode The Mode group lets you set the editing mode Math or Text Font name The first control in the Font group is the font name which becomes available only in the Text mode and makes it possible to select the desired font for inserting text To modify the font of an exiting text select the text and enter the desired font name Font size The second control is the font size field which is always available and lets you control the size of inserted characters and symbols To modify the size of existing items select the items and enter the desired value Base size The third control in the Font group lets you set the base size whose value which is specified in points determines the scale of the equation see Scale in the section Editing the Equation Normally the base size is taken from the current font size in the document where the equation is inserted You can change the base size value by either changing the point size at the insertion point in the document or you can break this link by resetting the check box Inherit Base Size from document in the Option dialog page and then change the value manually Note that if t
27. index 1 outside the range If y is multidimensional the returned value is a 1 dimensional array where the first element is the index in the first dimension the second element is the index in the second dimension etc locmax Syntax locmax x Operands x is an expression Description Returns the index of the maximum element in the array x If x is multidimensional the returned value is a 1 dimensional array where the first element is the index in the first dimension the second element is the index in the second dimension etc locmin Syntax locmin x Operands x is an expression Description Returns the index of the minimum element in the array x If x is multidimensional the returned value is a 1 dimensional array where the first element is the index in the first dimension the second element is the index in the second dimension etc log In Syntax log x or 1ln x Operands x is an expression Description Returns the natural logarithm of x log10 Syntax 10g10 x Operands x is an expression Description Returns the base 10 logarithm of x max Syntax max x Operands x is an expression Description Returns the maximum element of x 98 mean Syntax mean x mean x n Operands x is an expression n is an integer Description The first form returns a scalar as the mean of all the elements in x The mean is defined as the sum of elements in x divided by the number of elements The second form returns the
28. need them to restore the registration information in case it is damaged Registration Number Registration Code You can create a Registration File by clicking the item Create Registration File in the File menu This file together with the Registration Number and the Registration Code allows you to restore your registered copy in case of a damage to the registration information or to your disk Getting help Numerit comes with a context sensitive Help To get the Help contents choose Contents from the Help menu or press F1 or click the icon on the Program Bar the top tool bar To get help on a specific keyword click on it with the right mouse button or choose Search from the Help menu Ctrl F1 while the insertion cursor is on the keyword Numerit also comes with a set of sample programs that are found in the folder Samples which is located inside the Numerit folder C Program Files Numerit or as otherwise specified during the installation These samples may help you when you develop your first Numerit programs Getting in touch Web Site http www numerit com Technical Support support numerit com General Information info numerit com Comments and Suggestions feedback numerit com Your first program After you start Numerit you see an empty program window titled Program lt 1 gt On the left you see the Editor pane and on the right the Document pane The insertion cursor is inside the Editor To write your fi
29. not be manipulated or processed inside Numerit but will be transferred to another DLL function For example the following C functions are defined in a DLL where the first function allocates memory for some object whose internal structure is hidden from us and returns the address of the allocated memory block the second function receives the address of the object as a parameter uses it and returns a value and the third function frees the allocated memory obj alloc_obj int proc obj obj void free obj obj In Numerit these functions will be declared in the following way dfunc ptr alloc obj dfunc int proc obj ptr dfunc void free obj ptr And will then be used as follows p alloc obj allocate if p 0 stop allocation failed n proc obj p process free obj p free m n 1 use returned value The value of p has no meaning in Numerit although it can be tested for the success of the allocation as shown above and p is used only to transfer the address of the memory block to the functions proc_obj and free_obj The value of the integer n returned from proc_obj is numeric and can be used in subsequent Numerit operations Another use of a pointer parameter is when one needs to send a NULL pointer to a DLL function For example a DLL function that expects an array as one of its parameters may check if the array is actually sent i e the address is valid and if it receives a NULL pointer instead it wil
30. of a polynomial of degree n that best fits the set of data points given by x and y x and y are 1 dimensional arrays of the same length and must be Real The first element in the returned array is the free coefficient the second is the linear coefficient and so on Use the function poly to evaluate the polynomial not required but recommended The second form of itpoly allows to add a third array s which specifies relative standard deviations of the data points All the elements of s must be positive numbers A larger s i means that the corresponding data point has a larger error and consequently less weight A very small value will force the curve to go through or very close to the corresponding data point Note that in the first form of the function all the points have the same weight 93 fft ffts Syntax Operands Description floor fft x ffts x fft x n ffts x n x is an expression n is an integer The first and second forms return the fast Fourier transform of x over all the dimensions The third and fourth forms return the fast Fourier transform of x over the dimension n The number of elements in each transformed dimension must be an integer power of 2 With the t version the zero frequency component is the first element The ts version performs a shift after the transform so that the zero frequency component appears at the center the N 2 1 element Calling the function shifft after t is equ
31. of the file including the drive e g c data my dat Ifa full path name is not specified the current working directory is used The working directory is normally the directory where Numerit was installed but this may be changed by the operating system You can set the working directory in the program using the command directory see Chapter 14 Reference to Numerit s commands After the file is defined it is still closed A file is automatically opened the first time it is actually accessed in the program e g when reading from it or writing to it When a file is no longer needed it is a good practice to close it by the instruction close f This ensures that the file is updated in the disk and frees system resources that are associated with the file The next access to the file will open it again and set the position at the beginning Files are automatically closed at the end of the run so for short runs there is no need to close files explicitly Files in Numerit are opened for both reading and writing If the first file operation after the file is defined or is closed the one that actually opens the file is writing to the file e g write writeln writetab and the file contains data the data is first cleared and the position is set to the beginning of the file To keep the old data you must use the pos command to set the current position in the file before writing The data in the specified position will be overwritten but the rest o
32. or File Save Draft As Notes 1 Numerit s Graphs Images and Equations are converted to pictures 1 e Windows metafiles when saved in an RTF file 2 Numerit s Tables are converted to standard RTF tables However two or more tables that are inserted side by side in the same paragraph in a Numerit document will appear in different paragraphs in the RTF file 3 Numerit cannot read RTF files Document formatting The printer s page size and other properties are used while formatting a document so that it will be printed properly In most cases the displayed document looks exactly as it will look when printed However the printer properties determine the exact formatting and since the printer and the screen do not display all characters exactly the same way in some fonts some characters have different relative sizes there might be minor differences between the displayed document and the printed one For example a line may fit the current page width in the printer but appears to be too wide or too narrow on the screen The document page size is by default taken as the current printer s page size and when this page size is changed through the Printer Setup command the documents are reformatted to reflect this change It is possible to break this link by unchecking the box Printer Page Size in the Page Format dialog invoked by the menu command Format Page In such a case you may set a different page size Other formatting properties howe
33. outzero Note If this is the first file operation the one that actually opens the file the old data in the file is first cleared and the position is set to the beginning of the file To keep the old data you must use the pos command to set the current position in the file before writing see the section Files Syntax Operands Description writetab f x y Z f isa text file X Y Z are expressions Writes the content of x y z to the file f should be previously defined by file Any number of items may be specified The items are written line by line as a table at the current position in the file namely the first elements of x y z are written to the first line the second elements of x y z are written to the next line and so on The format of the written data is controlled by the current setting of outwidth outprec outformat and outzero Note If this is the first file operation the one that actually opens the file and the file contains data the data is first cleared and the position is set to the beginning of the file To keep the old data you must use the pos command to set the current position in the file before writing see the section Files Note If this is the first file operation the one that actually opens the file the old data in the 131 file is first cleared and the position is set to the beginning of the file To keep the old data you must use the pos command to set the curren
34. size of the array it needs to pass to the callback function The argument of a callback function can also be a structure In this case Numerit assumes that the DLL function pushes the address of the structure to the stack as an argument However since Numerit doesn t have structures the actual callback Numerit function will receive the structure members as separate variables For example the following declaration dfunc foo func double int double 1 double tells us that the DLL function foo receives two parameters the first is a callback function of the form func double int double 1 and the second is a double scalar When foo will call the callback function it will pass to it the address of a structure whose members are a scalar of type int and an array of type double whose length is specified in the previous integer scalar The Numerit callback function that cannot work directly with structures will actually receive two arguments a scalar and an array This conversion from a single structure sent by the DLL function to the two arguments that are actually sent to the Numerit callback function is carried out internally by Numerit All you have to do is to make sure that the number of arguments of the callback function matches the number of members in the structure sent by the DLL function plus of course any other arguments that are sent in addition to the structure 54 Note that when the array size is specified inside a st
35. that is derived from the file name The fields Name and File at the top always reflect the name and file name of the currently selected module These fields allow you to specify and modify both the module s name and file name manually Note that the actual name and file name are not modified while you are editing them in the Name and File fields but only when you press the Enter key If you don t press the Enter key after entering the name or file name the list will not be updated and the names you entered will be ignored Opening and Closing Modules To open a module in the Editor pane select it and click the button Open Module If you try to open a module that does not exist on the disk Numerit gives you an option to create a new module of the specified name To close a module select it and click the button Close Module An open module appears in boldface in the list For each open module there is a tab at the bottom of the Editor pane which allows you to bring it into the Editor When you close a module its tab is removed You may also close a module using the menu command File Close Module which closes the module that is currently displayed in the Editor A module remains open as long as it is not explicitly closed even if it is not currently visible in the Editor Note that when a module is open Numerit is using its current open version when running the program rather than the disk version see Open Modules in the section Modules above Note that
36. the Table Viewer displays variables as a table each variable in a column the Graph Viewer displays variables as a Y X graph and the Image Viewer displays a two dimensional array as an image each array element represents either intensity or color From the point of view of document editing a Viewer behaves like a single character and as such it is just part of the text Whenever the program pauses or stops the Viewers are updated if the variables listed in them have new values It is also possible to explicitly update the viewers while the program is running by the command refresh in the program s code This make it possible to display data in real time as it is changing All Viewers have default parameters that define their appearance e g size color etc These parameters may be modified in the Viewer editing dialog by double clicking the Viewer It is possible to freeze the current value of a Viewer s variables so that further changes in the variables will not affect the Viewer This is done by checking the Freeze Data box in the Viewer s dialog Variable Viewer The Variable Viewer displays a scalar variable Numeric String or Boolean as a formatted text according to user s specifications Inserting a new Viewer or double clicking an existing one opens a dialog in which the variable s Name the Width in characters and the numeric Format are specified A numeric format specifies how a number is displayed It consists of a Format
37. toas 7 Phe sStatus Barts 23 2 st Sica ee ca eg se ea ee ee etn Be eee Se A 8 The Program Wind atte 9 Printing programs and COCuMentts cccccescescceceseeeseeseeeseeseeeseescesecseceseceeesecsecseseaecseceaeeseeaecseeeaecaeeesecsaeesecesesaeseseseeseaeeeeeneeesaeeess 9 Chapter 3 The Editor 11 A A cea desabice casa viet need abs O oxtaeesedid sate we canes coke A stents om eee teense etinnemetes 11 PrOGTAMEBIOCKS oia a di see ey DO ceo Fa a ee ie 11 Highlighting ikeen nener oe eetecuie e ES 11 Comments tr cd to Nod 12 A NON 12 Editor Options iii sg ca 12 Chapter 4 The Document 13 Introduction teoria dead cen ene ae tens dae eel lor do a te Mac Nate ters Me Ales tt a dla ae tia 13 II O AU 13 A Benet oe sci E E EE E EEE E E clad tesadeude bonite Aadecttesees 13 Rich Text Format RTE Jetra nbs Seb hae Cea asa A GOVE PN REIN ERO OIE SEN BORE ice 13 Documenttormatting E ate Ae ee ek Hea Ra he le a eae ea ole tn ee 14 Pr Formaatti ienn e Persie aa A eee Bee o a 14 Paragraph Formatting onrein irria a EREE ias 14 Character Formato ct o ree e de dd de a Mace E 15 Paragraph Sl A A A A A a Oia 15 Fhe Rulet m e ected a eE eset ane ce ae en ae cae A Wl Se AR eee 16 Character Mapes sci dsc sce cdevschciveydecsieieesgavevlessaed cout E A cies ORE ati 16 Td Rd 5 750 versie sevnveses cateeseuyaceveerestighastl revel sects cebteectnoig A OTE caedt esa lib A EE E A ET 16 Spelling Checken e eerste eae sa 16 Personal Dictionaries icc ccciccachdssge
38. type which may be either Auto Decimal or Scientific and a Precision which is a number When there is not enough room for the specified numeric format width too small the viewer displays asterisks instead of the number Auto is a free format that uses the precision to determine the number of significant digits that appear after the decimal point In this format with a precision of 2 for example the number 0 0348 is displayed as 0 035 3 and 5 are the first two significant 18 digits the number 3 412 is displayed as 3 41 and the number 3 004 is displayed as 3 Decimal and Scientific are fixed formats of the form 99 99 and 99 99x10 respectively Both use the precision as the number of digits that must appear after the decimal point even if not significant When a Variable Viewer is used for displaying a String or a Boolean variable the Format and Precision fields are ignored and the only relevant field is the Width However you must note that although the width is specified in characters the resulted Viewer s width does not always fit the displayed string even if the number of characters is correct and you might have to adjust the width by increasing or decreasing the specified number of characters The reason is that the actual width of the Viewer in pixels is independent of the content of the variable and is determined before this content is known So Numerit uses an average character size of the font at the Viewer s position to d
39. void which can only be used for ret_type Functions that belong to the same DLL that was declared in a previous statement can be grouped together into a single dfunc block namely dll mylib dl1 dfunc void set int n double x double sqr double x nlib pow2 A scalar parameter A scalar parameter is specified by its type and an optional name A scalar can be sent to the function in two ways by value or by reference When a variable is sent to a DLL function by value the function reads the value from the stack but has no access to the variable itself When a variable is sent to the function by reference the function has full access to the variable itself it can read its value and also modify it A scalar is sent by value when the parameter is specified with only the type e g double x A scalar is sent by reference when the parameter is specified with a type and the address mark e g doubles x A scalar can also be sent as an argument to a function that expects a one dimensional array see below In such a case the scalar will be sent by reference and will actually be treated as an array with one element An array parameter An array parameter is specified by its type an optional name and square brackets One dimensional arrays are specified with a single pair of brackets e g double x A scalar can be sent as an argument to a function that expects a one dimensional array In su
40. when it is opened When the Report is saved as a separate document it is saved together with the current data that is shown in its Viewers When it is saved as part of the program the Viewers are saved only with the names of the variables that are specified in them and the variables data is not saved unless the Viewers are in the Freeze Data mode You can save the Report as a Rich Text Format file see section below which is a portable format that is recognized by most word processors This allows you to continue editing the document in your favorite word processor When the Report is saved its previous version on the disk if exists is kept as a backup with the character added as the last character of the file name leaving the extension unchanged The Draft When the Report Draft item is unchecked or the button released the Draft is brought into the Document pane The Draft is mostly used as an output sheet for the program s output statements e g print graph table etc After the program sends its output to the Draft it can be edited like any other document But the Draft is considered to be a temporary storage for text and as such it is not saved with the program on the disk It can however be saved as a separate document using the menu command File Save Draft As In this case its is saved as a file of type drf Numerit automatically identifies this file as a document when it is opened The Draft is cleared either throug
41. write f x y Z f isa file or a string X Yr Z are expressions Writes the content of x y Zz to the file f If f isa file it should be previously defined by file or by binfile if it is a string it should be defined as such e g Any number of items may be specified The items are written one after another at the current position in the file or at the beginning of the string If isa text file or a string the format of the written data is controlled by the current setting of outwidth outprec outformat and outzero If f isa binary file the data is written in its binary form Note If this is the first file operation the one that actually opens the file the old data in the file is first cleared and the position is set to the beginning of the file To keep the old data you must use the pos command to set the current position in the file before writing see the section Files Syntax Operands Description writetab writeln f x y Z writeln f f isa text file X Y Z are expressions Writes the content of x y z to the text file and adds a new line character at the end f should be previously defined by file Any number of items may be specified The items are written one after another at the current position in the file If no items are specified only a new line character is written The format of the written data is controlled by the current setting of outwidth outprec outformat and
42. y len nor x to y lenn Operands x Y d n are scalar expressions n is an integer Description Defines a 1 dimensional array ranging from x to y The first form a x y defines an array with 101 elements namely the interval between the elements is one hundredth the full range The second form a a to y defines an array with interval 1 between the elements The third form a x y by dora x to y by 4 defines an array with interval d between the elements The fourth form a x y len n or a x to y len n defines an array with n elements read Syntax read f Xx y Z read input x y Z Operands f isa file or a string X Y Z are variables Description Reads data from a file or a string or the Input File into the specified variables If isa file it should be previously defined by file a text file or by binfile a binary file Any number of variables may be specified The variables are read one after another from the current position in the file or from the beginning of the string Since each variable consumes data which fits its type and size the variables should be defined before the read namely their type and size should be known when they are read Reading into an undefined variable defines it as a Real scalar by default When reading numeric data from a text file a string or the Input File any character or group of characters may be used as a delimiter between the numbers except the characters min
43. 1 The program is run one line at a time i e stepping 2 The program has at least one breakpoint set 3 The inspector is open and is in Watch mode The Inspector The Inspector is a utility for inspecting program s variables Each program has its own inspector To open the Inspector Position the insertion point on a variable s name in the Editor Choose Inspect from the Run menu or press F12 or Click the right mouse button on a variable s name in the Editor The inspector window is displayed and the variable s name appears in the Name field When pointing to an empty space inside the Editor pane the Name field is empty and you can type any variable name in it The Inspector looks for a variable of the specified name that belongs to the function at the cursor position The Inspector displays the variable s attributes type number of dimensions etc and its content When the variable is dimensioned its content is displayed as a list When it has two or more dimensions you choose along which dimension the list is displayed by selecting one of the radio buttons that appear under the title Dim The index of the first element in the list is specified in the fields that appear under the title Index The window which displays the variable content has two scroll bars The vertical scroll bar is used for scrolling the window up and down along the dimension that is currently selected for viewing The horizontal scroll bar is used for scrolli
44. 1 dimensional Boolean array is true same as loc index of scalar in an array same as loc Integral of an expression Cubic splines interpolation Inverse of a square matrix Length of variable Linear interpolation Linear system solution using LU decomposition Linear system solution using singular value decomposition Natural logarithm same as log indices where a 1 dimensional Boolean array is true same as index index of scalar in an array same as index index of maximum element in an array index of minimum element in an array Natural logarithm same as In Base 10 logarithm Maximum element of an array Mean of elements in array Mean of elements in array over dimension n Minimum element of an array Convert a number to String Test for an odd number Packs a complex array Packs a complex array Phase of a complex number same as arg angle Polynomial evaluation Position in a file Product of elements Same as prod x Product of elements over dimension n Same as prod x n Random number Real part Zero of an expression same as root Rounded value Rounded value with accuracy 10 Secant Hyperbolic secant Sign Shift of a fast Fourier transform Shift of a fast Fourier transform over dimension n Sine Hyperbolic sine Size of file Sorting an array Square root Standard deviation Standard deviation over dimension n Delete characters in string Inserts string into string Length of string Lowercase of
45. 67 2 is 1300 rounded to hundreds and ceil 1234 567 2 is 1234 57 rounded to hundredths conj Syntax conj x Operands x is an expression Description Returns the complex conjugate of x 89 COS Syntax cos x Operands x is an expression Description Returns the cosine of x cosh Syntax cosh x Operands x is an expression Description Returns the hyperbolic cosine of x cot Syntax cot x Operands x is an expression Description Returns the cotangent of x coth Syntax coth x Operands x is an expression Description Returns the hyperbolic cotangent of x CSC Syntax csc x Operands x is an expression Description Returns the cosecant of x csch Syntax csch x Operands x is an expression Description Returns the hyperbolic cosecant of x defint Syntax defint exp x y defint exp X Y tol Operands exp is a formal expression of one variable x and y are Real expressions tol isa number Description Returns the definite integral of the expression exp from x to y exp has one dummy 90 variable over which the integration is done It is represented by the dollar character x and y must have the same dimensions The integration is carried out between every two matching pairs of x and y If for example x and y are 1 dimensional then the i th element of the result is the integral of the expression from x i to y i The integral is calculated by an iterative process adaptive Simpson s rule which termi
46. ATT A AAA AAA AA AAA E A A A eee 35 E A E O NS 35 Arrays initialization with lists and ranges cceccesceescesseeseeseeeseeseeeseeseessecsecesecssensecaceeseceaecsecssesseeesecseeesecseeeaesseeeseceseeaeenseseenseeaes 35 NN 36 Dimensions ai ee AAA AA ista 36 Minimum and maximum A aaa 36 SUDAN A A A e o os em APA ino as ted eee ete 37 Vectors and MACS 00 A A o tai 37 A cases cst obec Ta E A E We cue death aa gaec ts Pettiaus tondlannadeaueaaeen 38 SNS Seoni a e e e edo a Mache 38 Pl tato 39 O teetiste stole AEE N EE cet Nass tet alae cities Maces E AE E TERE E bs slate 40 User Defined FUNCIONS oise aran NE a A E R E A aE E E a sda cuetavae E a 40 Type of arguments andthe teturi dd ci 41 Arguments by reference or by value ii A sa 41 AAA E E E a AT 41 Local and Global variabl s uta dato 41 Calling a function from another fUNCtION ceceeccescesseeseeseeeseeseceseeseeesecsecesecsecsaecseeeaeceeeaecaeesseceeesesesecaesesecseeeeeeseaeeseteesstneeee 42 Function TEO a nr a e a e T A 42 Dinamica Ed A dia 43 Calling Convention neyin ae Seeds hs A SN Re Eases EE LE a On EES 43 TYPOS A E ak a oho Sad ETA A ed es Had AN Ea a 43 Erro as aes ants tne ae ak ees 44 Dynamiclink Functions saan tess eee eae eee o Oe eS 45 Return types nero E A A AA AE E AAA ais 45 Patameter ut a elo ee e do dl la alo edo dad o al do do AT 46 O NN 46 AcSCalar A a A 47 Anarray PATA iii a ia id A A A TR 48 ASA eee 50 A Boolean A ita 50 AUSTTUCIUTE PATEAR A AD
47. An expression has a specific type and kind and usually appears at the right side of an assignment or as an argument to a function Dummy Variable A dummy variable is designated by the character dollar It is actually a placeholder for a real variable Expressions that contain a dummy variable are called formal expressions and are not evaluated when they are specified but are sent as arguments to functions that evaluate them by replacing the dummy variable with real values Formal Expression A formal expression is an expression that contains at least one dummy variable which is represented by the character dollar Such an expression is sent to a function as an argument see for example Integ and is evaluated inside this function by replacing the dummy variable with actual values The other variables and constants in the formal expression are used with their current values The dimension of the value that is returned when the formal expression is evaluated must be the same as that of the dummy variable in this expression This will normally be the case if the expression consists of ordinary operations that involve the dummy variable Make sure that this dimension relation is also kept when the formal expression calls a user defined function Such a function should not set a specific dimension to the returned value but rather inherit the dimension of the dummy variable sent to it as an argument 34 Note that while a formal expression is eva
48. B R G and B must be integers between 0 to 255 where R specifies the weight of red G the weight of green and B the weight of blue in the pixel s color The RGB check box allows you to directly specify a color for each pixel and easily create true color images When you define the color image array you must make sure that the values of R G and B are integers between 0 and 255 you can use the round or floor functions to create integers You can also read an image from a bitmap file and convert it to an image array in the Image Viewer RGB format using Numerit s bitmap function To manipulate the different colors of the RGB color image after it has been defined by the program or read from a bitmap file you may need to extract the values of each basic color namely to inverse the operation that defines the image array This is achieved by defining the following functions in Numerit func red z floor z 65536 func green z floor z mod 65536 256 func blue z floor z mod 256 where z is the image array Each function returns a two dimensional array of the same dimensions as the image array containing integer values between 0 to 255 Remember that when you modify the values of elements in these arrays you must make sure that they remain in the range 0 to 255 and that they are integers by using the round or floor functions before you sum them up to create the new image array Reconstruction of the image array may be done by defining the f
49. E 50 A funchon parametersc i icf Soest e io a a o a 52 A DEL sftunction as a callback nc ii A ac 55 iii Chapter 7 Executing and Debugging 57 Running the ias 57 Moduless0s estais ede tts Maceo Ph ae el haat A eae dl A a to Ma Ades ots Ahi Pee chat ie e 2 salts e siesta sl tt 57 Compiled Libri a A a O aia 58 LO o hg A a a a E O 58 Makati E A NN 58 Open Module Ssi et ad est talado ad 58 Saving MA ee eee 59 Usitig Modules ita 59 Modules List art ol ees dot eco Satta ll ial dr ed bes cles el ear bras ede Les tical 59 Adding and Removing Modales ais 59 Submodules Listin da a OE aie Aa ARA AA dada 60 Module Namie and Fille Nava asl eile ee sctecseae EE E aea r Ea AE a A aa aea Eana Eoo esaa EO EN e aaia Toas 60 Op ning and Closine Modules a e a a n sat stbeeeds 60 Modules Directory nmr nenn a ee Ree A ae eS ee 60 Reload eini erann areni ai RA atin iets AA pie teal ain nie eee ay 60 Reorderits the lis tes its seottn chitestd seat Maeiates Sarita eh a gees ish hes 98 add otis Ue che Meee hans a oc Joh Wonks ote abe 61 Extra Modulos A id aia Ma Ais We oe a DT ee i 61 Debugtih genron ciara ited Asie he av cidade acaba ese eaves AeA ei ate ihe E as a cee E se Aaa 61 The Inspector E as Pes eke T Aah AS ea ete ke a AR SS eS Oe a 62 NumR n Th sNumerit Execution e sere deta de 63 Chapter 8 Errors and Warnings 65 TOC da 65 Compilation Es ia 66 Compilation WM dadas 68 Compilation Not 0 led 70 Link EOS 3 453 A AAA A A A A AS ene ladent 71
50. L function its type in the function declaration should be ptr or pointer You can declare two versions of the same DLL function where the first receives a Numerit function as an argument and the second receives a DLL function as an argument Returning to the function integral discussed above the first version that expects a Numerit function for the integrand can be declared as dfunc integ num func double f double double a double b integral and the second version that expects a DLL function for the integrand as dfunc integ dll ptr f double a double b integral Since the second version doesn t involve any argument passing to Numerit Numerit doesn t need to know the returned type or parameters types of the callback function To use the second version a C function such as sqr should be compiled into a DLL and declared in Numerit for example dfunc double sqr double 55 In the instruction that calls the function integ_d11 the callback function is specified as an argument the same way as a Numerit function is specified namely using the prefix c integ dll sqr a b And since the first parameter of integ_ dll is a ptr Numerit will send to it the address of the DLL function sqr Note that here again it is the user s responsibility to make sure that the DLL callback function matches in types and number of parameters the expected callback function 56 Chapter 7 Executing and Debugging Running the program After typin
51. Numerit Version 1 7 User s Manual Do your numerical computations the easy way Go directly to the final publication quality document Write powerful programs with minimum effort Use superior tools to edit and debug your programs Numerit 1 7 User s Manual Copyright 2012 KEDMI Scientific Computing All rights reserved No part of this manual may be reproduced or transmitted in any form or by any means electronic mechanical photocopying recording or otherwise without the express written permission of KEDMI Scientific Computing All products and names mentioned in this document are trademarks of their respective companies Contents Chapter 1 Numerit 1 IO UC roda 1 Nim OS a 1 NUM Un soi AAA AAA A AAA ta 1 System Toque da o e Mae E oa 1 AA NN 2 A Ae eh eae este ee eee es ee es ee 2 Getting an touche ae iret E a ec ee ee a Me Oe he de 2 Your first PEO A de Ds nated ie Sei e te ed Da do 2 Chapter 2 The Desktop 3 a a ee ee 3 The Men Baleer girri cased avert ccssenseeachene tees deen EE aga 3 Pl o a Mie den a tes eh aaltd net O o e le cee tent 3 RN OURAN 4 Sr e e e e de e a e ed Sted 4 RU A A AAA A AA A AAA AA LA ge eae 5 Op E cases ce ed nia 5 Mi o aa oe 5 Heel piscsscenzescevzuceseetevescescceigey R EEE N A Ava 5 INS S EATE AAE ET ET EE O ATTE T A A 6 OPIN trols E A sue ce E E E A ET N A T 6 A O E E AE E E 6 DPh Program Bar EEA A E ETTA aaah eee ee ae ee E 7 The Document Ba A ovata dent
52. Page menu command To change one of the paragraph indents first line left or right point to the marker with the mouse and drag it to the new position To move the left indent with the first line indent together point to the area between the markers above the left indent marker and drag them to the new position This is equivalent to setting the indents with the Format Paragraph menu command To seta tab stop at a certain position select the tab type in the Document Bar point with the mouse to the lower part of the ruler and drag the tab stop marker to the position To remove a tab stop point to its marker and drag 1t out of the ruler This is equivalent to setting tab stops with the Format Paragraph menu command The Ruler may be hidden by unchecking the item View Document Ruler in the Options menu Character Map The menu command Tools Character Map or the corresponding button in the Document Bar opens a character map for the current font This allows you to insert extended characters not found on most keyboards into the document The character map also allows inserting symbols and other characters e g Greek whose key positions are not known to you Undo Redo Operations in the document may be undone For example a deleted text may be recovered or a formatting operation may be reversed This is done by the menu command Edit Undo Ctrl Z or the Undo button in the Program Bar Numerit keeps a list of recent operations This
53. a a b and read the value of the variable pi_ half from this library All you have to do is declare the library and then the functions and variables dll numlib dl1 dfunc double gamma double dfunc double beta double double dvar double pi half and call them note that in Numerit a DLL variable is accessed as 1f it is a function x 1 y gamma x a 0 5 Di Lio c beta a b pi2 pi_half When you declare a function you specify its name and the types of its return value and parameters see Types below When you declare a variable you specify its name and type See Dynamic link Functions below and also the commands d11 dfunc and dvar in Chapter 14 Reference to Numerit s commands for a detailed description of these instructions Calling Convention Numerit assumes that the functions in the DLL are C or C functions that were compiled into a standard Win32 32 bit DLL Functions written in other languages may also be called if their argument passing mechanism matches the C convention pushed on the stack from right to left and they support the same parameter types Two calling conventions are supported the cdecl standard C calling convention and the stdcall calling convention The second is more efficient since it relies on the called function itself to clean up the stack after execution When a function is compiled into a DLL with the stdcall calling convention it must be declared in Numerit with sdfunc instea
54. a 3 dimensional Real array with 10 elements in each dimension Note that in this case the array is defined using its last index rather than the number of elements If the assigned value is not 0 and the array does not exist only the specified element is set to the given value while the other elements are 0 if the array exists all the other elements remain unaltered Moreover you must be aware of the fact that if arrays do not start with index 1 by setting firstindex to a different value the last index is not equal to the number of elements Arrays initialization with lists and ranges An array may also be defined by assigning different values to its elements For a 1 dimensional array this is done by specifying its elements as a list of numbers or strings or Boolean constants separated by commas for example x 1 1 2 5 3 6 or x red green blue It is possible to put a 1 dimensional array instead of one of the numbers in this list and thus merge 1 dimensional arrays into one array For example if x is defined as above then y 1 2 x 3 defines y as Ty 2y br PAS A 09 38 One dimensional Numeric arrays may also be defined by using one of the range statements e g x 0 to 10 A range enclosed in parenthesis may also be specified in a list that defines a 1 dimensional array So for example the following definition is legal x 0 to 10 15 20 to 30 For arrays of higher dimensions you must use blocks For example a 2 dimensional 3x3 arra
55. a dialog which allows you to specify the titles text and the font The left and right axes titles are written in a 90 degrees orientation 1 e along the vertical axis It is possible to show the left and right titles at 0 degrees orientation i e same as the bottom title by checking the Upright checkbox next to the title The title may be entered as a simple text or as a formatted title see Formatted Titles below for details Axes Each axis of the graph in a Graph Viewer may be customized The button Axes in the graph edit dialog opens a dialog the allows you to specify which of the axes will be shown and for each axis its position line width and color 20 By default all the axes are shown in the minimum and maximum positions i e at the ends of the scales Tick marks The tick marks on each axis of the graph in a Graph Viewer may be customized The spacing between the tick marks is set in the scale specification The size line width and type of the major and the minor ticks may be specified by clicking the button Ticks in the graph edit dialog The type of the ticks on each axis may be set to either in facing inside out facing outside or cross crossing the axis Tick labels may appear next to each major tick The type of the labels is set by clicking the button Labels Tick labels Each major tick mark in a graph may be labeled by a number which identifies the value it represents The labels may be
56. a variable in the Color Table field the values of the image array are drawn differently depending on this variable The first option is to specify a scalar variable whose value is a positive integer smaller or equal to 256 In such a case the interpretation is very similar to the default interpretation the only difference is that the number of levels is taken as the value of this variable Thus if the value of this scalar variable is 256 the result is equivalent to the default interpretation See the sample program image bw num The second option is to specify a one dimensional array in the Color Table field In this case an internal table is created by dividing the range that is defined by the minimum and maximum values of the image array to N equidistant values where N is the number of elements of the specified color table The position 1 to N of the value of each element in this table is used as an index to the color table and the pixel is drawn in the color specified at that position The specified color must be an integer between 0 to 255 where 0 is drawn in black 255 is drawn in white and any integer between these values is drawn in a corresponding gray Thus the value of each element in the image array is actually a pointer to the color table In this case if the color table consists of 256 elements ranging from 0 to 255 the result is equivalent to the default interpretation i e when no variable is specified in the Color Table field See th
57. age Breaks a loop Specifies an increment Defines conditional execution of statements Clears a variable a file or the Draft Gives access to the computer internal clock Closes a file Declares common variables in modules Declares a constant Deletes a file Declares a dynamic link library function Same as dfunc Declares a dynamic link library variable Sets the current working directory Declares a dynamic link library Used in various loop statements optional Specifies the limit in a decreasing for loop Displays the Draft Used in if case and where statements for optional execution Opens a dialog to select a file name for opening Defines a text file Sets the starting index of arrays Defines a loop with a running counter Frees the memory occupied by a variable Frees a dynamic link library Opens a dialog to select a file name for saving Starts a function definition Same a func Transfers execution to a labeled line Inserts a graph at the current position in the Draft Defines conditional execution of statements Gets input from the user Specifies an array length Defines an infinite loop Defines a 2 dimensional array as a Matrix Opens a menu of options for user selection Displays a message Causes a jump to the next loop round Displays a OK Cancel message Specifies the format of numbers on output Same as outf Specifies the precision of numbers on output Same as outp Specifies the width allocated to items on output
58. also be 2 dimensional and 1 dimensional arrays respectively rather than a matrix and a vector in which case the returned value is a 1 dimensional array If M has m rows and n columns then the system represents m linear equations in n unknowns so the returned solution vector has n elements When m lt n there are fewer equations than unknowns and there is no unique solution to the system When m gt n there are more equations than unknowns and linsolsvd returns a least squares solution In log Syntax ln x or log x Operands x is an expression Description Returns the natural logarithm of x 97 loc index Syntax loc b or index x y loc x y or index x y Operands b isa 1 dimensional Boolean array x is a scalar expression y is an expression Description The first form returns an array of indices where b is true Note that this is applicable only to 1 dimensional arrays For example if you need to operate on the positive elements of a 1 dimensional array x and leave the other elements intact you define an index array i loc x gt 0 and operate on x i Ifall the elements of b are false the returned array is empty namely the value returned by length i is 0 The second form returns the index of the scalar x in the array y Note that the returned index is the first that s found namely if x appears in y in different locations only the first is returned If x does not appear in y the returned index is the last
59. alue is also Real in the range 88 nm 2 to 1 2 atan2 Syntax Operands Description atanh Syntax Operands Description azeryo aroot atan2 y x y and x are Real expressions Returns the inverse tangent of y x x and y must be Real and the returned value is in the range T to T atanh x x is an expression Returns the inverse hyperbolic tangent of x Syntax azero y x or aroot y x Operands x and y are 1 dimensional Real expressions Description Returns the value of x which corresponds to the zero of y Both x and y must be 1 dimensional Real arrays The search for zero starts from the first element of y When a sign change is detected the zero crossing position is calculated by cubic splines interpolation of y VS X bessj Syntax bessj n x Operands n is an integer x is a Real expression Description Returns the Bessel function of the first kind of order n of x x must be Real bessy Syntax bessy n x Operands n is an integer x is a positive Real expression Description Returns the Bessel function of the second kind of order n of x x must be Real and positive ceil Syntax ceil x ceil x n Operands x is an expression n is an integer Description The first form returns the rounded up value of x nearest integer value not smaller than x The second form returns the rounded up value of x with accuracy 10 namely n determines which digit is rounded For example ceil 1234 5
60. an expression Description Returns the length of x namely the number of elements in each dimension If x is multidimensional the returned value is an array linterp Syntax linterp y x Xx Operands y X and xx are Real expressions y and x are 1 dimensional Description Returns the linear interpolation of y x at xx y and x are 1 dimensional arrays of the same length All the arguments must be Real x should be monotonic increasing or decreasing linsol Syntax linsol M b Operands M isa matrix b isa vector Description Returns the vector x that solves the linear system Mx b Misa non singular square matrix and b is a vector whose number of elements is equal to the number of rows of M M and b may be Complex M and b may also be 2 dimensional and 1 dimensional arrays respectively rather than a matrix and a vector in which case the returned value is a 1 dimensional array linsol uses LU decomposition to solve the system The function linsolsvd which uses the singular value decomposition may be used for solving systems where the number of equations is different from the number of unknowns linsolsvd Syntax linsolsvd M b Operands M is a Real matrix b is a Real vector Description Returns the vector x that solves the linear system Mx b using singular value decomposition M is a matrix not necessarily square and b is a vector whose number of elements is equal to the number of rows of M M and b should be Real M and b may
61. an return values in two ways 1 The C style by using return 2 The Pascal style by assigning a value to the function s name A function with no parameters must still be called with parenthesis just as it is defined i e y When you want to return more than one variable from a function you can send variables as arguments to the function and the function may assign values to them Local and Global variables Variables that are defined in the function are local to the function and are not available to other functions or to the main program A local variable may have any name and there is no conflict between variables of the same name in other functions or in the main program Local variables exist only while the function is active however for efficiency considerations Numerit does not free and does not initialize the local variables when exiting a function so that repeated calls to the same function will not create and destroy variables which is a time consuming operation especially with large variables So when the function is called again its local variables are already defined as they were on the last call and with the same value If there is a shortage in memory or if you want to make sure that you start with new variables on every call e g when variables have different dimensions on different calls use the ree command to free local variables before you return from the function or when you enter the function If you onl
62. an the first element Apply again to restore the original array The first form shifts all the dimensions The second form shifts the dimension n Note shifft may either return the shifted x and keep x unchanged when specified as part of an expression or on the right side of an assignment e g y shifft x or may shift x itself when specified as a statement i e shifft x The second method is recommended if the original x is not needed since it uses less memory sin Syntax sin x Operands x is an expression Description Returns the sine of x sinh Syntax sinh x Operands x iS an expression Description Returns the hyperbolic sine of x size Syntax size f Operands f isa file Description Returns the file size in bytes should be previously defined by file or by binfile sort Syntax sort x Operands x isa l dim expression Description Returns a sorted version of the 1 dimensional array x sqrt Syntax sqrt x Operands x is an expression Description Returns the square root of x stdev Syntax stdev x stdev x n Operands x is an expression n is an integer Description The first form returns a scalar as the standard deviation of all the elements in x The 102 standard deviation is defined as the square root of the variance of the elements in x See var below for the definition of the variance The second form returns the standard deviation of elements of x over the dimension n The returned val
63. andling to report about errors in a DLL function back to Numerit In such a case when the DLL function returns to Numerit the error handling mechanism of Numerit stops the currently running Numerit program and reports about the error This is done the same way it is done when an error occurs in the Numerit code namely a dialog box pops up and shows the error message and the message is also shown in the Message pane To allow this option you need to add the following code in your DLL typedef void stdcall ErrorHandler int errcode char message _ declspec dllexport ErrorHandler NumeritError NULL The first line defines the type ErrorHandler as the type of a function with two parameters that is called using the stdcall calling convention The first parameter is an integer that receives the error code and the second is a string that receives the error message The second line defines an exported pointer to a function of type ErrorHandler This pointer NumeritError is set by Numerit to its internal error handler so that you can call it in your DLL code to report errors back to Numerit Note that it is important to initialize it to NULL so that you will be able to check if it is actually set see below When you need to report an error to Numerit you call NumeritError with the error code and an optional message If the error code is positive and corresponds to one of Numerit s execution errors see Errors and Warnings the message t
64. annot have more than 64 characters This error occurs when a longer name has been specified Number of dimensions cannot exceed n m An array of dimension m was defined but the maximum number of dimensions is n 66 String too long The maximum length of a string constant is 1024 characters This error occurs when a longer string is defined Syntax error The compiler found an unidentified syntax error This usually does not occur but if it does it means that the compiler cannot supply more information about the error Type mismatch in a call to name argument n type gt parameter name type2 The n th argument in a call to the specified function was of type type which does not match the corresponding parameter s type type2 Type mismatch in assignment typel lt type2 A variable of type type was assigned an expression of a different type type2 Type mismatch in comparison typel lt gt type2 Expressions of different types cannot be compared In comparison operations e g x gt y the operands must have the same type Undefined label name An undefined label has been specified in a goto statement Undefined function name A call to an undefined function has been encountered Unexpected y Unexpected f Unterminated Missing Unmatched structure marks or nested structures These messages indicate an error in the specification of a structure in a DLL declaration or a call to a DLL
65. ant Optimize to call instead of the empty function Merit the functions Merit and MyMerit will normally have one or more parameters To do so you write optlib Merit gt MyMerit optlib Optimize You may even omit the opt1lib from these instructions and write y p Merit gt MyMerit Optimize and Numerit will find the functions Merit and Optimize in the module opt lib provided that functions of the same names are not defined elsewhere in the Main module or in one of the other modules A function may be rerouted as many times as necessary to different functions To return a function to its initial state you reroute 1t to itself for example Merit gt Merit The functions Merit and MyMerit in this example may have any number of parameters as long as it s the same for both They may return a value or modify the value of the parameters sent to them In other words the rerouting mechanism is general enough to allow any type of information exchange between the function that acts as a client and the function that acts as a server It allows you to compile a module and replace its functions at runtime according to your needs without recompiling the whole module 42 Dynamic link Libraries A dynamic link library DLL is a collection of routines functions that can be called by applications It is actually a separately compiled executable that is linked at runtime to the programs that use it In addition to
66. are sent in addition to the structure When the array size is specified inside a structure as the number of a parameter 1 e with the prefix the numbering is done from the beginning of the specific structure and not from the beginning of the parameter list e g in func double int double 1 int double 1 1 is used in both structures to specify that the length is the first member in each of them A DLL function as a callback function A DLL function can be sent to another DLL function as an argument to serve as a callback function In such a case Numerit sends the address of the callback function as an argument to the DLL function that calls it directly without involving Numerit in the process When a DLL function is specified as a parameter to another DLL function its type in the function declaration should be ptr or pointer It is the user s responsibility to make sure that the DLL callback function matches in types and number of parameters the expected callback function The callback function must also be declared with dfunc or sdfunc and is specified as an argument the same way as a Numerit function is specified namely using the prefix directory Syntax directory s Operands s isa string Description Sets the working directory from this point on to s For example directory c data 113 dil Files that are defined after this statement without specifying their full path name in the file
67. array with two elements 1 and 2 which are zeros of the given expression obtained by taking 0 and 3 as initial guesses The expression can be just a function call for example y root fun x where fun x is any Numerit function built in or user s round Syntax round x round x n Operands x is an expression n is an integer Description The first form returns the rounded value of x the nearest integer value The second form returns the rounded value of x with accuracy 10 namely n determines which digit is rounded For example round 1234 567 2 is 1200 rounded to hundreds and round 1234 567 2 is 1234 57 rounded to hundredths Tie breaking when rounding 0 5 this function rounds away from zero for example 1 5 is rounded to 2 and 1 5 is rounded to 2 sec Syntax sec x Operands x is an expression Description Returns the secant of x sech Syntax sech x Operands x is an expression Description Returns the hyperbolic secant of x sign Syntax sign x Operands x is an expression Description Returns the sign of x i e 1 if x is positive and 1 if x is negative The sign of 0 is O The sign of a complex number z is z z 101 shifft Syntax shifft x shifft x n Operands x is an expression n is an integer Description Performs a shift of a fast Fourier transform so that the zero frequency component appears at the center the N 2 1 element rather th
68. arrays the same way they work with scalars Most array operations are performed without the use of loop statements but a wide variety of loop types is still available In addition the language provides many functions for data analysis including line and polynomial fitting linear and cubic splines interpolation multidimensional fast Fourier transform numerical integration and differentiation root finding solution of linear algebraic equations matrix vector arithmetic special functions and more Some of the basic concepts in the language are described below Identifier An identifier is a name that is used for designating a variable or a function A legal identifier consists of a sequence of letters and digits but must start with a letter The underscore character _ is considered a letter The number of characters in an identifier cannot exceed 64 Type Every variable or constant has one of the following four types Numeric String Boolean and File Different types cannot be mixed in expressions and a variable cannot change its type during the run The Numeric type is divided into two sub types Real and Complex Real and Complex may be mixed and a Complex is automatically created when necessary There are some cases where only a Real is acceptable especially as a parameter in some built in functions A complex number is specified as a sum of a real number and an imaginary number e g 2 1i 3 41 etc j may be used instead of i To
69. at expects a parameter of type char or unsigned char This is true for Boolean scalars as well as Boolean arrays A structure parameter Structures in C are objects that include several variables of different types that are grouped together Unlike C Numerit doesn t support structures but it allows you to group together several variables and send them as a single structure to a DLL function Numerit actually creates a structure at runtime and sends its address to the DLL function by reference A structure is declared in the dfunc statement with braces surrounding a list of types for example the parameter int double double represents a structure whose first member is an integer and the second and third members are double s An array can be specified as a member of a structure with a size or without it If the size is specified e g int 10 double the array s elements are copied to the structure when the structure is created If the size is not specified e g int double the array s address is copied to the structure The same is true with two dimensional arrays namely when you specify an array without its size e g int the address of an array 1s copied to the structure To copy the actual array elements you must specify the size in both dimensions e g int 4 5 On return Numerit copies back the values of arrays that were specified with size If this is not required you can save execution time and instr
70. at the string variable is of the right dimension readtab Syntax readtab f x y Z readtab input x y zZ Operands f isa file X Y Z are variables Description Reads data from a text file or from the Input File into the specified variables should 126 be previously defined by file Any number of variables may be specified The variables may be scalars 1 dimensional arrays or 2 dimensional arrays For scalars readtab has no special meaning and they are read from the first line of the file 1 dimensional arrays are read one element per line namely the first line is read into the first elements of each array the second line is into the second elements and so on 2 dimensional arrays are read one row per line namely the first line is read into the first row the second line is read into the second row and so on The variables must already be defined namely their type and size should be known before they are read Each variable consumes from the file data which fits its type and size So each 1 dimensional array consumes one item per line and the number of items consumed by each 2 dimensional array is equal to its number of columns If the number of items read from a file s line is smaller than the number of items in the line the unread items in the line are skipped So it is possible to read only the first few columns of data from a file which contains many columns An example Suppose the data in a file is arranged i
71. at the bottom of the Editor pane that will allow you to move to other modules and back to the Extra module with a simple click The code you put in the Extra module is saved when you save the program so the next time you open the program this code is loaded into the Extra module the Extra code is saved inside the program file and not separately Note that the Extra code is executed only when you bring the Extra module to the Editor and run it namely when you press Run while the Extra module is visible In addition to providing a way to continue the program of the Main module after it was ended the Extra module has other uses For example you can use it for debugging Suppose that you run a program and at some point while the program is still running you want to pause it and examine the value of some variables After you pause the program you can open the Extra module and print or plot the values of any of the main program s variables or the result of any operation you do with these variables Since the Extra module has full access to all the variables and functions of the Main module you can put in it any code that you would put in the Main module You can for example pause the main program write a code in the Extra module that changes the value of some of the program s variables run the Extra code and then resume the execution of the main program with the new values Debugging When a program produces errors or does not behave as expecte
72. ation unless an explicit request by refresh is encountered Thus when only the final result is needed refresh is not required since the Viewers will be updated at the end of the run But for displaying intermediate results a refresh is required Note that by using the refresh command inside a loop where variables that are displayed by a Viewer are constantly changed an animated view of these variables is produced Syntax Description report repeat Statements while Condition repeat Statements until Condition Defines a loop in which the statements are repeatedly executed as long as the condition that follows the while is true or until the condition that follows the until becomes true Since the test is done at the end of the loop the statements in the loop are always executed at least once When there is only one statement in the loop it may appear on the same line for example x 1 repeat x 2 while x lt 10 Otherwise a block should used for example x 5 repeat println x 2 x 5 until x gt 25 Syntax Description reseterror report Displays the Report in the Document pane When the program encounters the command report it checks the Document pane and if it is displaying the Draft it is switched to the Report This allows the program to send output to both the Report and the Draft and to control which of them is currently displayed Syntax Description reseterror Resets the error code to 0 so tha
73. b Bold b0 Bold off Italic i0 Italic off u Underline u0 Underline off g Greek font g0 Default font sb Subscript s0 Subscript Superscript off sp Superscript sO Subscript Superscript off upN Shift baseline up by N half points N is a positive integer dnN Shift baseline down by N half points N is a positive integer n New line Notes Subscript and superscript commands shift the text and also shrink its size Both commands are turned off by the same control word sO that restores normal text 24 upN and dnN are not turned on and off but rather define a new baseline for the text So for example to restore the baseline to its previous position after a up10 command put a dn10 command Note that up or dn that are not followed by an integer are ignored There is only one level of subscript and superscript so a second sp for example is ignored and the text remains at the same level of superscript you can still use upN and dn commands to get higher levels of subscript and superscript but without further shrinkage of the font size Remember the commands b i lu g sb and sp remain in effect until turned off So for example if you write X sp2 Y sp2 the result is X rather than X Y which should be written as X sp2 s0 Y sp2 s0 Note that the first space after sO in this example is ignored and interpreted as a delimiter of the 1s0 sequence so you must put a second space to see a space be
74. back to normal when the key is pressed again or when the character is deleted Besides being the best way for entering a long comment this is also very useful while debugging the program when you want to comment out portions of the code Comments are displayed in a distinctive color to make the program more readable This color may be set by the menu command Options Editor Undo Redo Operations in the editor may be undone For example a deleted text may be recovered This is done by the menu command Edit Undo Ctrl Z or the Undo button in the Program Bar Numerit keeps a list of recent operations This makes it possible to restore the editor to its state before each of these operations took place Undone operations may be redone by the menu command Edit Redo Ctrl Shift Z or the Redo button in the Program Bar Thus it is possible to move back and fourth through the operation list New operations are inserted at the current position in the list so operations that were made after this point are lost The size of the operation list may be set with the menu commands Options Editor The maximum size is 99 operations the default is 25 operations When the list becomes full the oldest operations are pushed out Some editing operations are grouped into one operation in the list For example when deleting successive characters they are all restored at once Before undoing or redoing an operation the cursor position is checked and if it is not wher
75. be set graphically When the image is selected a single click you can mark a rectangle inside the image and the scales will automatically be set to fit this rectangle To cancel the operation before releasing the mouse button press the Esc key To restore the previous settings after the mouse button is released press Undo Titles Each axis of the image in an Image Viewer may have a title The button Titles in the image edit dialog opens a dialog to specify the titles text and font The left and right axes titles are written in a 90 degrees orientation 1 e along the vertical axis It is possible to show the left and right titles at O degrees orientation i e same as the bottom title by checking the Upright checkbox next to the title The title text may be entered as a simple text or as a formatted title see Formatted Titles below Formatted Titles The Table Graph and Image viewers allow you to add titles to the columns in Tables and to axes and legends in Graphs and Images These titles have a default font type and font size and if entered as simple text are displayed using these default settings The default font and size may be modified by the user In addition you can embed instructions inside the text of the title to control some of its formatting and character attributes These instructions are entered as control words A control word consists of a backslash followed by a sequence of lowercase alphabetic characters and digits Th
76. ber of a structure you can do it with the array size or without it If you do specify the size the array s elements are copied to the structure when the structure is created If you don t specify the array size its address is copied to the structure For example in the following declaration dfunc foo int 10 double int the structure consists of 10 int values and one double value and corresponds to the C structure 50 struct int n 10 double x a while in the following declaration dfunc foo int double int the structure consists of an address to an int array and a double value and corresponds to the following C structure struct int n double x F The same is true with two dimensional arrays namely when you specify an array without its size e g int the address of an array is copied to the structure To copy the actual array elements you must specify the size in both dimensions e g int 4 5 Since the structure itself is passed to the DLL function by reference it is expected that the DLL function can modify the values of the structure s members including arrays that are specified with dimensions However when Numerit sends such an array as a structure member it actually sends a copy of the Numerit array rather than the array itself so it copies the array s elements back to the Numerit array after the function returns If you know that the DLL function does not modify the array this
77. block The format of such a prototype is ret_type name parameters actual_name where ret_ type is optional and is the function s return type name is the name that the function will have in Numerit parameters is the list of parameter types that the function expects to receive and actual _ name is the actual name of the function in the library The colon and the actual_name that follows it may be omitted if the actual function s name is name i e the name that you want to use when you call the function from Numerit is the same as its name in the library Note that if name or actual name is not found in the library Numerit will look for it using the name preceded by an underscore since many compilers attach an underscore to global names For example if name or actual_name is foo then Numerit first searches for the function foo and if it is not found Numerit searches for the function foo If ret_ type is specified it must be one of the following void char uchar or unsigned char short ushort or unsigned short int uint or unsigned int float double complex ptr or pointer void is specified when the function doesn t return a value If ret_ type is omitted it is assumed to be void The parameters are listed inside the parenthesis as a list of types separated by commas one for each actual function parameter Each type can be followed by an optional parameter name and the allowed types are the same as listed above except
78. bute after insertion select the text and change the size or the attribute in the Format dialog page Hats Hats are symbols such as bars arrows or dots that are inserted above characters To insert a hat move the insertion point after the character to which you add the hat open the Hats dialog page in the Equation Editor s control panel and click on the desired symbol Up to four hats may be inserted above the same character When more hats are added they replace the upper hat The button Remove is used to remove the upper hat from the character on left Spaces The Equation Editor spaces the items as necessary while you insert them However there are cases when you want to control the exact spacing To do that open the Spaces dialog page and click on one of the spaces in the list or press the corresponding key combination When a space is inserted manually it replaces the automatic space that usually appears around operators like etc and templates The automatic spacing mechanism may be disabled by unchecking the box in the Options dialog page The various spaces that may be inserted in the equation are of different sizes which are related to the current value of the base size When this value is changed the spaces are scaled accordingly see Scale in the section Editing the Equation Besides spaces you may also insert a tab This will align the inserted items to the closest tab stop The distance between tab stops is equal to
79. ccdevceviecbscea dis casey E cease AEA A dacs ncapey AEE E EEE stdeagvcss oecad F EE ERER 17 Auto numbered MOS 17 EUA A A cg os ase bape goa coat vat a See das E A we a ees Sas aes EA 17 Di A eee 18 Nonbreaking space Line break and Page break eccceceseeseeseeeseeseceneeseeeseesecesecseeeseccessecaecaeseaeeseceaecseeesecseeeaeeneesaeenseeaeentaeeee 18 MI liada 18 EI EATA EE rad cts acond Tn rd do ai E E O e o e o TO An 19 E eee a savas Sevens aes E aeee eSB asa vas sea codices E N Cob ee ibs TATAN Saas EE a bak va Gia ee ane 19 Graph Viewers ic incisive i hese ia ses EA a etic ees assis a avd ds Lav nd eed dh Cea bes a A E EE E 19 A Big or cee A O ROO TN 19 ME tadas 20 SU A a O 20 TACO in aida 20 Sl A A AAA A IA cada 20 Mt ad AEE A a a ESAE 21 AR A A e Se ado 21 A A O E 21 Tick abel ticas 21 AS A e a Rates 21 Lependas tieso oi Petts healt E lero ala rn e A EE a o cg 21 EI O O A 21 A AAN ON 22 Color Tablet A A A AAA AA A BOR ER a PEs 22 o ONO 22 SP NN 23 Zoom and Window Zi A ia iaa da picadas 23 Sl rl tcl Bae Ut rca le ln ee ld lo ia tte 23 RS IAN 23 A O nr OO SO a AS 23 Tica ii A AA se 24 O O OO OA 24 Sal NT SE A A oa 24 Ti a AAA AA AAA AA AAA A A A TE 24 Formatted Pitlesss o a o e e e a ee sate 24 PU E a A aid 25 DOME OPIO a iS 25 Chapter 5 The Equation Editor 27 Tntrod cfi om is A EA EA AA E CRT TREN TR 27 Equation A AE IS BGI ESS E AR 27 Editing the Equ aaa 27 O i 27 SC a o A e ks e e o A e a 27 Moa ic BE 27 Di
80. ce it is possible to change the default fonts Note that this is only related to the Math mode since in the Text mode the font is explicitly set in the Format dialog page The third parameter is the space between rows in a stack of blocks This is given as a percentage of the base size and its default value is 20 The next parameter is the maximum length of a variable s name This is used in the Math mode to determine when to italicize a word and when not to italicize it By default this parameter is set to 4 so names that are 4 letters long or less are considered to be variable names and are italicized while longer names are considered to be words and are not italicized Note that function names are identified the most common names and are not italicized even when they are short When you want to insert normal text regardless of words length do it in the Text mode The last parameter is a check box that specifies whether to do auto spacing or leave all the spacing to the user This box is normally set to allow the Equation Editor to automatically add spaces around operators and templates 31 32 Chapter 6 Writing Programs Writing the program A new program is created by opening a Program window using the menu command File New Ctrl N An existing program is loaded from the disk by the command File Open Ctrl O Each Program occupies a window which has its own Editor that is used for writing the program s code and two documents the Rep
81. ch a case the scalar will be sent by reference This is actually equivalent to sending an array with one element Multidimensional arrays are specified with two pairs of square brackets e g double x All numeric types are allowed except complex A complex array should be converted to a packed array with the function PackComplex and passed as a double array to the DLL function The packed array is converted back to a Numerit complex array with the function UnpackComplex Numerit arrays with more than two dimensions are flattened to two dimensions and are passed to the DLL function as two dimensional arrays See Dynamic link functions for details about the structure of two dimensional arrays that are sent as arguments to DLL functions A string parameter Strings are treated in C as one dimensional arrays of characters When a DLL function has a parameter that is a one dimensional array of type char you can send to it a Numerit String as an argument Note that although in Numerit a string is considered to be a scalar when sent as an argument to a DLL function it is sent as an array of char s A one dimensional array of strings can be sent as an argument to a function that expects a two 111 112 dimensional array of char s A Boolean parameter In Numerit a Boolean variable namely a variable that can have only one of two values true or false occupies one byte So you can only send it as an argument to a DLL function th
82. changing the name in the variable s name field or by clicking the right mouse button on a new variable and it will replace the current one When the Watch check box is set the Inspector is updated whenever the watched variable changes its value If the Watch check box is not set the update is done manually by clicking the button Update When the program pauses inside a function it is possible to move the inspection point back to the calling statement and inspect variables at that point The inspection point is marked by a dashed horizontal line unless it coincides with the execution point which is marked by a solid horizontal line At the bottom of the Inspector s window you can see the name of the function whose variable is currently displayed and the name of the function where the program was paused the execution point Note that when you right click on a variable s name the Inspector looks for the variable in the function that is currently at the cursor position In order to uniquely identify this function the program must be compiled Therefore when you open the Inspector after the program is modified Numerit first compiles the modified program and only then opens the Inspector 62 NumRun The Numerit Executor NumRun is an environment that allows execution of Numerit programs outside the Numerit environment It can execute compiled Numerit programs or Numerit executables which do not include the source code Numerit executables are creat
83. ck for example ifa gt b a b b 0 else b a a 0 input Syntax input tx x ty Y tz Z Operands X Y Z are variables tx ty tz are optional strings Description Opens a dialog for user s input into the variables The dialog is opened for each variable in turn If a string precedes the variable it is used as the title for its dialog otherwise the variable s name is the title Only scalars and 1 dimensional variables may receive user s input The input for a 1 dimensional variable is a list of items separated by spaces If the variable is defined as complex before execution of the Input command the values are read as pairs of real and imaginary values i e RIRI The variables should normally be defined before Input is executed namely their type and size should be known before they are read Input into an undefined variable defines it as a Real scalar or 1 dimensional array according to the number of values entered len Syntax len Description Used in a range definition to specify the number of elements loop Syntax loop Statements Description Defines an infinite loop The statement or block of statements that follow it are executed 120 until the loop is broken by a break or a goto statement For example x 0 loop x 1 if x gt 4 break print x matrix Syntax matrix x matrix y x matrix y m n v Operands x is a 2 dimensional array y is an identifier m and n are integers and v is a scalar ex
84. cription 114 downto Used to specify the lower limit of a decreasing for loop draft Syntax Description dvar Syntax Operands Description draft Displays the Draft in the Document pane When the program encounters the command draft it checks the Document pane and if it is displaying the Report it is switched to the Draft This allows the program to send output to both the Report and the Draft and to control which of them is currently displayed dvar variable prototype or dvar block of variable prototypes variable prototype isa DLL variable prototype Declares a variable of a dynamic link library DLL A DLL may contain exported variables in addition to functions Numerit allows you to access such variables and read or set their value Note that a DLL variable is treated in Numerit as if it is a function and not a variable So to read or set its value you must call it like a function namely with parenthesis A variable prototype has one of the following forms type name actual variable name or name type actual_ variable name or amp name actual variable name The name is the name that will be used to access the variable in Numerit and actual variable name is the actual name of the variable in the library The colon and the actual variable name that follows it may be omitted if the actual variable s name is name 1 e the name that you want to use when you access the variable from Numerit is the sa
85. cture may also include a member that is a function see A function parameter below As mentioned above the Numerit structure parameter can also be used for sending variables to DLL functions that expect C objects For example in most C implementations an array is declared as a class whose data part consists of the array length and address such as the following simple array class class array int len double x public array int n x new double len n array delete x int size return len double amp operator int bi Such an array appears in a C function parameter list as double sumld array amp a The DLL function sum1d is declared in Numerit as dfunc double sumld int double and is called with a Numerit array x in the following way 1 to 10 sumld length x x X S A function parameter In many situations C functions receive other functions as arguments For example a function that calculates the integral of another function will normally receive the function that it integrates as an argument Numerit allows you to send Numerit functions as arguments to DLL functions It also allows you to send a DLL function as an argument to another DLL function Such functions are referred to as callback functions since they are called from the called DLL function Notes 1 A Numerit built in function e g sin cannot be specified directly as a callback function If this is requir
86. customized by clicking the button Labels in the graph edit dialog For each axis the labels may be shown or hidden Their numeric format may be set to Auto default Decimal or Scientific see the section Variable Viewer for details on the numeric format In addition a factor that multiplies the label values may be specified for each axis its default value is 1 It is possible to hide the labels that appears near axes Namely in the bottom and top axes the labels that appear near the left and right axes may be skipped and in the left and right axes the labels that appear near the top and bottom axes may be skipped By default the left and bottom axes are labeled and the labels at the right and top axes are hidden Grids Grids extend the tick marks across the graph The button Grids in the graph edit dialog opens a dialog which allows you to define the grids You may select a horizontal grid and or a vertical grid For each grid it is possible to specify if the gridlines pass through major and or minor tick marks The line style of the grid its line width and its color may also be set Legend It is possible to specify a legend label for each graph trace in a Graph Viewer This is done in the same table where the trace s variables are entered Only traces that are defined with legend label will appear in the legend A legend will be displayed by default if at least one trace has a legend label A legend may be hidden even if legend labels a
87. d in needs debugging Usually debugging is done by pausing the program and inspecting the variables and the output in the Report or the Draft There are several ways to pause a program The first is by using the menu command Run Pause or the Pause button in the Program Bar while the program is running This will pause the program after completing the execution of the current line of code When a better control is required the program may be run one line at a time In this mode the program pauses after each line There are two commands that allow stepping through the program both are invoked from the Run menu or by buttons in the Program Bar The first command is Step Over F8 which executes all the instructions in the current line and pauses before the next line The second command is Step Into F7 which executes the instructions in the current line and steps into functions when they are called If no functions are called in the line the two commands are equivalent Another way to pause a program is to put breakpoints at specific lines and run the program normally Run Run or F9 When a line with a breakpoint is encountered the program pauses just before the line is executed A breakpoint is set or reset by the menu command Run Breakpoint F4 or by clicking the left mouse button at the left edge of the line where the mouse cursor changes its shape into a right pointing arrow A line with a breakpoint is highlighted To set a breakpoint inside a mo
88. d international treaty provisions Use of Evaluation Edition You may use the Evaluation Edition of the SOFTWARE free of charge on one or more computers Use of Professional Edition or Standard Edition You may install and use the Professional Edition or Standard Edition of the SOFTWARE on a single computer provided that you have obtained a license for it Under no circumstances may you use the SOFTWARE on more than one computer at a time unless you have obtained a site license If you have obtained a site license you may install and use the licensed Professional Edition or Standard Edition of the SOFTWARE on more than one computer provided that your site license is covering the number of people that use the SOFTWARE simultaneously You may make a copy of the software for backup purposes only Your Registration Code and Registration File should be kept confidential and you may not transfer them to third parties Restrictions You may not reverse engineer decompile or disassemble the SOFTWARE You may not remove any component copyright notices or proprietary notices from the SOFTWARE You may not rent or lease the SOFTWARE but you may transfer your rights under this License on a permanent basis provided you transfer the SOFTWARE and all documentation and media and you do not retain any copies and the recipient agrees to the terms of this License If the SOFTWARE is an upgrade any transfer must include all prior versions of the SOFTWARE Limited
89. d of dfunc This tells Numerit that it doesn t have to take care of the stack after the function returns It is very important to use the correct declaration otherwise Numerit might terminate abnormally Types Unlike low level languages such as C Numerit does not distinguish between different types of numeric variables The standard numeric variable in Numerit is a double precision floating point number A complex number consists of two such double precision numbers real and imaginary A double precision number occupies eight bytes in memory Low level languages such as C support other numeric types that occupy less bytes In 32 bit implementations the different numeric types in C are char A single byte signed integer unsigned char A single byte unsigned integer short A two byte signed integer unsigned short A two byte unsigned integer 43 int A four byte signed integer unsigned int A four byte unsigned integer long A four byte signed integer equivalent to int in 32 bit implementations unsigned long A four byte unsigned integer unsigned int in 32 bit implementations float A four byte floating point number double An eight byte floating point number In many implementations there is also an additional floating point type long double that occupies more than eight bytes Another type that is supported in many implementations is complex that consists of two double s packed together so it occupies 16 bytes When a DLL function is
90. d when an error is detected at run time There are two types of errors A fatal error stops the program for example where there is not enough memory to continue A non fatal error pauses the program In most cases you should stop the program after such an error and correct it Non fatal errors may also be handled by the program which can trap the error check it and decide how to proceed This is done with the help of three commands HideError ShowError ResetError and the system variable errval See more details and an example in the description of the command HideError in Chapter 14 Reference to Numerit s commands 65 Compilation Errors typel used as type2 An expression of type typel is used where an expression of type type2 is expected name Nested formal expression is not allowed The specified function requires a formal expression as an argument and cannot be itself part of another formal expression Common variables cannot be declared inside a function Common variables can only be declared in the main body of a program Constants cannot be declared inside a function Constants can only be declared in the main body of a program Declaration of DLL function must be preceded by a dll statement A declaration of a DLL function has been encountered before a dll statement The declarations of DLL functions must be preceded by a dll statement that defines the library where the functions should be found Different r
91. data that the graph displays By clicking the button Scale in the graph edit dialog it is possible to set a specific range for each scale and to select it as linear or logarithmic In addition the interval between the major tick marks and tick labels is set in the field By and the number of sub divisions between the major tick marks is specified in the field Sub Divisions Next to the field By there is an Auto checkbox When checked it instructs Numerit to adjust the interval between tick marks automatically even when the X and Y scales are set manually When the scale is logarithmic the specified interval between major tick marks the field By is used as the ratio between two successive labels and must be a power of 10 if set differently it will be forced to such a value The number of sub divisions in this case may be 1 2 or 9 other values will be forced to one of these When the check box Automatic is not set the scales remain fixed regardless of changes in the displayed data The scales limits may be set graphically When the graph is selected a single click you can mark a rectangle inside the graph and the scales will automatically be set to fit this rectangle To cancel the operation before releasing the mouse button press the Esc key To restore the previous settings after the mouse button is released press Undo Titles Each axis of the graph in a Graph Viewer may have a title The button Titles in the graph edit dialog opens
92. declared in Numerit the types of its parameters must be specified so that Numerit will know what are the arguments types that the function expects Since different types have different sizes and representations it is very important to specify the correct types so that Numerit will be able to convert the variables that are sent as arguments to the actual types that are expected by the DLL function The types that are specified in the DLL function or variable declaration in Numerit i e in the dfunc sdfunc or dvar instructions are the same types as shown in the list above namely the C types including complex The type long double is not supported in Numerit so DLL functions that expect a long double argument cannot be called from Numerit In Numerit unsigned types can be abbreviated by attaching u to the beginning of the type namely uchar is equivalent to unsigned char ushort is equivalent to unsigned short uint is equivalent to unsigned int and ulong is equivalent to unsigned long and to unsigned int Numerit also allows you to pass pointers between different DLL functions pointers have no meaning inside Numerit In such a case you can declare a parameter of type ptr or pointer In 32 bit implementations such as the current version of Numerit this is actually equivalent to an unsigned int See Dynamic link Functions below for information about the use of pointers Error Handling If you write your own DLL you can use Numerit s error h
93. dimensional Real expressions Description Returns an array which is the derivative of y with respect to x using cubic splines interpolation Both x and y must be 1 dimensional Real arrays ainteg Syntax ainteg y x Operands y and x are 1 dimensional Real expressions Description Returns an array which is the integral of y with respect to x using cubic splines interpolation Both x and y must be 1 dimensional Real arrays angle arg phase Syntax Operands Description aroot azero angle x orarg x or phase x x is an expression Returns the argument or phase of x The argument is the angle in radians of x in the complex plane Syntax aroot y x or azero y x Operands x and y are 1 dimensional Real expressions Description Returns the value of x which corresponds to the zero of y Both x and y must be 1 dimensional Real arrays The search for zero starts from the first element of y When a sign change is detected the zero crossing position is calculated by cubic splines interpolation of y vs x asin Syntax asin x Operands x is an expression Description Returns the inverse sine of x If x is in the range 1 to 1 the returned value is Real in the range 1 2 to 7 2 asinh Syntax asinh x Operands x is an expression Description Returns the inverse hyperbolic sine of x atan Syntax atan x Operands x is an expression Description Returns the inverse tangent of x If x is Real the returned v
94. dimensions n1 and n2 name Argument must be 2 dimensional n The argument of the specified function should be a 2 dimensional array but seems to be n dimensional name must be m dimensional n The specified variable seems to be an n dimensional array but should be m dimensional name must be a scalar n The specified variable seems to be an n dimensional array but should be a scalar name seems to be a scalar and cannot be indexed The specified variable seems to be a scalar and cannot be referenced with an index name seems to n dimensional but its index does not match The specified variable seems to be n dimensional but is referenced with an index of a different dimension name Formal expression cannot have dimensions n The formal expression sent as an argument to the specified function seems to be n dimensional but should be a scalar name First argument must be 2 dimensional The first argument of the specified function should be 2 dimensional It seems to have a different dimension name Second argument must be 1 dimensional The second argument of the specified function should be 1 dimensional It seems to have a different dimension name Fitted arrays must be 1 dimensional n Fitting can only be done to a set of points represented as 1 dimensional arrays It seems that an n dimensional expression was specified name Order must be a scalar The order of the fitting polynomials should be an intege
95. dingly When a caption or equation is deleted from the text the references to it are no longer valid If the caption was cut moved to the clipboard it is considered to be temporary missing as long as it is still in the clipboard and all references to it are shown as question marks When the caption is inserted back pasted from the clipboard its new position is calculated its number is updated and the references to it are updated according to the new number If the caption was deleted not cut or is no longer available clipboard was changed the references to it are cleared and replaced by empty fields only a place holder Automatic field update may be disabled by unchecking the menu item Options Update Document fields The fifth field type Page number displays the page number of the page on which it appears and is especially useful in the header and the footer Date A date is inserted in the text by the menu command Insert Date The date may be inserted as either a text or a field As a text the date is inserted as a sequence of characters as if you typed it in You may modify it and edit it as a normal text When inserted as a field the date appears as a single object which cannot be edited but is controlled by the system In this case the date is linked to the system clock and is updated whenever the system date changes Use the first method when you want to keep the inserted date unchanged and the second method when you want
96. document relative to other captions Whenever a caption is inserted or removed all the captions are renumbered automatically according to the new order It is possible to refer to captions in the text by inserting a number field a Figure number a Table number or a Reference number The fields are also renumbered when captions are inserted or removed so a number field that refers to a specific caption will always refer to the same caption Captions are inserted by commands in the Insert menu Equations Numerit supports two types of equations which are both created and edited by its built in Equation Editor The first type is a numbered equation which occupies a whole line and is inserted by the menu command Insert Equation or the Equation button in the Document Bar The second type is an unnumbered equation which is inserted inside the line by the menu command Insert Expression The Equation Editor is invoked by either selecting one of the menu commands to insert a new equation or by double clicking an existing equation in the document Numbered equations are centered in the line and are automatically numbered according to their position in the document relative to other equations Whenever a numbered equation is inserted or removed all the equations are renumbered automatically It is possible to refer to a numbered equation in the text by inserting an Equation number field The number fields are also renumbered when equations are inserted
97. double n where n is a global variable This method is useful when the array s length is under the control of the Numerit program and in most cases will also be sent as an argument to the DLL function Two dimensional arrays should be specified with both dimensions e g func double double 3 5 Any combination of the above three methods is allowed in such a case e g func double f int double 3 1 The values of array elements are copied back to the DLL function argument when the callback function completes its calculation If these values are not required by the DLL function it is possible to skip this copy operation and save execution time by adding the mark after the square brackets of the array e g func double f int double 1 The argument of a callback function can also be a structure The parameters in the declaration in such a case are specified inside braces e g func double f int double 1 In this case Numerit assumes that the DLL function pushes the address of the structure to the stack as an argument 1 e that the structure is sent by reference Note however that since Numerit doesn t have structures the actual callback Numerit function will receive the structure members as separate variables The user must make sure that the number of arguments of the callback function matches the number of members in the structure sent by the DLL function plus of course any other arguments that
98. dule in Numerit Pro open the module through the Modules List window or make it visible by clicking its tab if it s already open see Open Modules in the section Modules above and set the breakpoint Note that in order to keep the breakpoint active the module must remain open but not necessarily visible during the run when the module is closed the breakpoint is removed The menu command Run Clear Breakpoints clears all the breakpoints The last method for pausing a program is by putting the instruction pause inside the program s code This will pause the program before the next instruction is executed When the program pauses inside a function it is possible to move the inspection point back to the calling statement and inspect the variables at that point This is done by the menu command Run Calling Function Ctrl lt or by clicking the Calling Function button in the Program bar The menu command Run Called Function Ctrl gt or the Called Function button return the inspection point to its original position This back and forth movement can be performed through all levels of function calls 61 and across modules When the inspection point is not at the current Pause position it is marked by a dashed horizontal line as opposed to a solid line at the actual Pause position Note that during debugging the program runs slower than normal Numerit enters the debugging mode automatically when it identifies one of the following situations
99. e The returned value is a String that contains the selected file name including the full path The parameter t specifies the title of the dialog box The parameter fn specifies the default file name that appears in the dialog box The parameter ft specifies the list of file types that will be available for the user The first string in each row of ft is a description of the file type the second string is a filter that specifies the file types that should be displayed in the dialog box when each description is selected For example st Documents txt Data Wk dat TALE k x file f fsavedlg Save As mydoc st write f a b c function func Syntax function name parameters expression function name parameters block Description A function is defined by the declaration function or func followed by the function s name the parameter list inside parentheses which are empty when there are no parameters and the function s body A function definition may appear anywhere in the program even after the statement that calls it but only at the top level namely it cannot appear inside a block There are two possible forms 1 Single line The function header is followed on the same line by an equal sign and an expression which will be evaluated and returned when the function is called For example function foo a x a x 2 2 Multiline The function header is followed on the next line by a block of statements F
100. e button Axes the bars are drawn on both sides of the axis depending on the Y value Line attributes in the Line group Checking the Show Box will result in data points being connected by lines The Style field determines which type of line will be drawn solid dashed etc The Width field specifies the line width in mm The color field specifies the line s color Symbol attributes in the Symbol group Available for the Line and Step trace types only Checking the Show Box will result in a symbol appearing at each data point The Style field specifies which symbol will be used Circle Diamond etc The Size field specifies the size of the symbol in mm The Color field specifies a color for the symbol With closed shape symbols e g Circle or Square this color is used to fill the shape while the line color is used to frame it With open shapes e g Cross Star this color is used to draw the symbol itself e Fill attributes in the Fill group Available for the Bar trace type only Checking the Show box will define a fill for the bars of the bar graph The Style field defines the fill pattern and the Color field specifies the fill color Note that if the variable that is specified for a given trace is two dimensional all its rows are drawn with the same trace attributes Scale The scales of the graph in a Graph Viewer are by default set to automatic mode In this mode the X and Y scales are linear and are dynamically adjusted to the
101. e condition and the statement s that follow it The then is redundant and is actually ignored by the compiler time Syntax time Description Returns the current time and date as a string For example s time The string s looks like Mon Jan 01 2001 10 15 08 to Syntax to Description Used to define a range see range for syntax and description or to specify the upper limit of an increasing for loop until Syntax until Condition do Statements Description Defines a loop in which the statements are repeatedly executed until the condition becomes true The keyword do is optional but is redundant When there is only one statement in the loop it may appear on the same line for example x 0 until x 100 x 5 Otherwise a block should be used for example i 10 until i gt 25 foe San i 1 129 vector Syntax vector x vector y x Operands x isa l dimensional array Description Converts x into a vector The first form changes the kind of x itself while the second form defines a new variable y and copies the content of x into it wait Syntax wait x Operands x is a scalar expression Description Waits for the specified amount of seconds before executing the next instruction x may be any expression that yields a Real value Note that the accuracy of the delay is machine dependent where Syntax where Condition Assignments where Condition Assignments else Assignments Description Used for conditional as
102. e dimensional and two dimensional arrays They are created by the declarations vector and matrix For example vector v 3 0 creates a vector with 3 elements and matrix m 3 3 0 creates a matrix with 3 rows and 3 columns When a variable is a vector or a matrix we say that its kind is Vector or Matrix as opposed to the Array kind Vectors and matrices obey the matrix vector arithmetic rules When a vector multiplies a matrix from left vector matrix it is taken as a row vector and its length must match the number of rows in the matrix When the matrix is on the left matrix vector the vector is taken as a column vector and its length must match the length of the matrix row 37 When multiplying two matrices the length of the left matrix row must match the number of rows of the right matrix The multiplication of an NxM matrix N rows M columns by an MxK matrix produces an NxK matrix A square matrix can be raised to an integer power positive or negative Raising a square matrix to a positive power n is equivalent to multiplying the matrix n times Raising a square matrix to a negative power n is equivalent to multiplying the matrix n times and taking the inverse of the result Raising a square matrix to the power 0 returns the identity matrix Multiplication of two vectors is carried out as a scalar product so their lengths must match and the result is a scalar Operations that involve matrices or vectors with regular arrays are perfor
103. e first space that follows the control word is ignored and is used as a delimiter of the sequence Any characters following the first space including spaces will appear in the title The control properties of most control words except upN dnN and n see below have two states When such a control word ends with 0 zero it turns off the property For example b turns on Bold whereas 1b0 turns off Bold Note however that the control words sb and sp that define subscript and superscript attributes are both set off by the control word 1s0 so the sequences sb0 and sp0 do not exist if entered the 0 is interpreted as part of the subscript or superscript text The space delimiter may be omitted in many cases if the character that follows the control word cannot be interpreted as part of it Take for example the control word b that turns on the Bold attribute The sequence bXY displays XY bold XY and so does the sequence b XY where the space after the b is ignored In this case the space is not required since bX cannot be interpreted as a valid control word sequence The sequence b01 on the other hand displays a normal rather than a bold 01since the control word is interpreted as 1b0 bold off and the 0 is not displayed In order to display a bold 0 you must put a space delimiter after the b So b 01 displays 01 bold 01 In case of a doubt always put a space after the control word The following control words are defined
104. e is set from 1 to N where N is the number of elements of the image in the corresponding dimension When the X scale or Y scale are set manually the image is displayed in the given range relative to the maximum range as specified in the X and Y fields of the main dialog In such a case the image magnification see Zoom in Image Viewer is set to a value that fits the specified range while trying to keep the viewer s window as close as possible to its current size In addition the interval between the major tick marks and tick labels is set in the field By and the number of sub divisions between the major tick marks is specified in the field Sub Divisions Next to the field By there is an Auto checkbox When checked it instructs Numerit to adjust the interval between tick marks automatically even when the X and Y scales are set manually When the Image scale is set manually bottom field the values of the image that exceed the higher scale value are clipped to this value and the values of the image below the lower scale value are clipped to this value This allows you to map the whole color dynamic range from black to white to a limited range of image values When the image is drawn in RGB mode see above the Image scale is set to the range 0 to 16777215 the maximum available value in this mode and cannot be modified When the check box Automatic is not set the scales remain fixed regardless of changes in the displayed data The scales limits may
105. e it was when the operation took place it is first moved to that position and only the next undo redo command will actually undo redo the operation Editor Options The Editor command in the Options menu opens a dialog in which some of the Editor properties may be customized The font may be selected from a list of the available fixed pitch fonts this font is also used in the Message pane The font size may be set Note that some fonts may not be scaled Language keywords may appear in bold text by checking the Bold keywords box The number of undo levels may be set The default is 25 the maximum is 99 Colors of normal text keywords comments and the background may be selected When the OK button is clicked the selected options are applied immediately to all the currently open programs and become the default options from now on When Numerit is closed these options are saved and will be used in next sessions of Numerit 12 Chapter 4 The Document Introduction Every program has two output documents the Draft and the Report The two documents allow two different approaches for displaying the program s output The Draft is used as a scrolling output sheet to which the program sends output as if it was a printer while the Report is a document in which the user embeds objects that display the value of program variables in different forms e g tables graphs When the program is running the Draft accumulates output while the Rep
106. e loop next loop round or for i 1 tom for j 1 ton if a i 2 b j 2 gt max val break 2 exit both loops if b j lt 0 next 2 exit this loop and go to next i println a i b j 121 ocmessage Syntax Operands Description ocmessage t s t and s are strings Opens an OK Cancel message window where the string t is the window s title and the string s is the message text The user must click either the OK or the Cancel buttons to continue program execution ocmessage returns 1 if the user clicked OK and 0 if the user clicked Cancel For example if ocmessage AppName OK to save x 1 write f x outformat outf Syntax Operands Description 122 outformat fmt or outf fmt or outformat fmt or outf fmt fmt can be auto fixed scientific or sci point left right Sets the format of numbers when writing data to a file or to the Draft The parameter fmt can be one of the following auto the output format is determined automatically according to the data fixed floating point output in fixed point notation scientific orsci floating point output in scientific notation point forces a decimal point left adjust the output to the left of the output field as defined by outwidth right adjust the output to the right of the output field as defined by outwidth Note that specifying outformat without a parameter is equivalent to outformat auto and resets all the other flags Each
107. e place for example when calling the following C function void qsort int x tas which is declared in Numerit as dfunc void gsort int x The conversion is of course a time consuming operation especially with large arrays and should be avoided if possible Note however that although passing double arrays is more efficient in many cases the actual execution of the function is the dominant time consuming process and the conversion time is negligible so one should not make too much effort to use double arrays in a DLL function if using other types of arrays is more natural This is especially true when the function is already written and changing types of arrays requires making modifications to existing code Note you can send a scalar as an argument to a function that expects a one dimensional array In such a case the scalar will be sent by reference This is actually equivalent to sending an array with one element 48 A multidimensional array parameter is declared in Numerit with two pairs of square brackets for example dfunc double sum 2d double x Note that this declaration is used whenever a multidimensional Numerit array not only two dimensional needs to be passed to a DLL function Arrays with more than two dimensions are flattened to two dimensions before they are passed to the DLL function For example the following three dimensional 3x2x4 array 111 112 113 114 121 122 123 124 211 212 213
108. e sample program image bw num The third option is to specify a two dimensional array in the Color Table field In this case the color table must have three columns and any number of rows i e a N x 3 array As before an internal table is created by dividing the range that is defined by the minimum and maximum values of the image array to N equidistant values where N is the number of rows of the specified color table The position 1 to N of the value of each element in this table is used as an index to the color table and the pixel is drawn in the color specified at that position The color is specified as three integers one in each column of value between 0 to 255 The drawn color is a combination of the three basic colors Red Green and Blue where the weight of each basic color is determined by the value in the corresponding column of the color table first column is Red second column is Green and third column is Blue As in the previous option here too the value of each element in the image array is actually a pointer to the color table See the sample program image color num RGB Next to the Color Table field there is a check box entitled RGB When this box is checked the Color Table field is disabled and ignored In this mode values of image array elements are interpreted as colors rather than pointers to a color table Each element in the image array is constructed with the following formula 2 R 2 G B i e 65536 R 256 G
109. e the Document Pressing the function key F12 is equivalent to pressing the right mouse button 77 78 Chapter 10 A Quick Reference to Numerit s built in functions Language keywords that return a value or modify variables value abs x abs2 x acos x acosh x acot x acoth x adefint y x a b aderiv y x ainteg y x angle x arg x aroot y x asin x asinh x atan x atan2 y x atanh x azero y x bessj n x bessy n x ceil x ceil x n conj x cos x cosh x cot x coth x csc x csch x defint exp x y tol deriv exp x det M dim x eof x erf x even x exists x exp x fitbasis b y s fitcheby n x y s fitline x y s fitpoly n x y S fft x ffts x floor x floor x n gamma x gammaln x ident n ifft x Absolute value Absolute value squared Inverse cosine Inverse hyperbolic cosine Inverse cotangent Inverse hyperbolic cotangent Definite integral of array by interpolation Derivative of array by interpolation Integral of array by interpolation Angle of a complex number same as arg phase Argument of a complex number same as angle phase Zero of array by interpolation same as azero Inverse sine Inverse hyperbolic sine Inverse tangent Inverse tangent of y x Inverse hyperbolic tangent Zero of array same as aroot Bessel function of the first kind of order n Bessel function of the second kind of order n Rounded up value Rounded up value with accurac
110. e variables Description The first form clears the Draft document The second form clears all the elements of the specified variables set the value to 0 or clear the strings Note that the variables are still defined and occupy the same amount of memory as before To free the memory occupied by variables use free If the variable is of type File this command clears all the file s data and puts the current position at the beginning of the file clock Syntax clock Description Returns the processor time elapsed since the beginning of the program invocation in miliseconds This can be used to determine the time interval between two events For example the following code t clock statements delta t clock t sets delta_t to the time it takes to execute the statements between the two calls to clock close Syntax close f Operands f isa file Description Closes the file f should be previously defined by file or by binfile common Syntax common x y Z Operands X Y Z are identifiers variables names Description Variables that are defined in the main body of a program can be accessed by all the functions in this program using the prefix see Local and Global variables in the section User Defined Functions in Chapter 6 This makes it possible for functions to share variables either as predefined constants or for transferring information between them However these variables are not accessible to different modules of the same program
111. ed by the menu command File Create Numerit Executable Inside NumRun the program s code is not visible to the user and the output documents cannot be edited In order to make a program executable by NumRun you must save the program after it is compiled so that the compiled code is included in the saved file or create a Numerit executable If your program includes modules you must create a Numerit executable in order to allow NumRun to execute it A Numerit executable has the extension nex as opposed to the num extension of a Numerit program Users of Numerit may develop programs and distribute them to customers The customers can download NumRun from http www numerit com download htm for free and use it to run the programs No royalties are charged from users that develop Numerit programs and distribute or sell them 63 64 Chapter 8 Errors and Warnings Introduction The Message pane located at the bottom of the Program window is used for displaying compilation and execution errors and warnings Errors and warnings are listed in the Message pane along with the line numbers to which they refer When pointing to a specific message in the Message pane the message is highlighted and so is the corresponding line in the Editor To edit this line press the Enter key or move to the Editor and make it the active pane the insertion point will move to the highlighted line To move the insertion point to the next or previous error without goi
112. ed its previous version on the disk if exists is kept as a backup with the character added as the first character of the file name Before a program is executed it is compiled either by the user or by Numerit see Chapter 7 When a program or a module is saved the compiled code is saved too but only if it is updated 1 e the program or module has not been modified after compilation When a program and all its modules are saved together with their compiled code the program is ready to run right after it s read from the disk without compilation The command File Save does not save the modules that are linked to the program The menu command File Save All Ctrl Shift S saves the program and all its open modules that have not been saved yet including their source code and their compiled code this is normally done after a Make or Run see Chapter 7 The language Numerit s programming language is a high level language that is based on conventional programming paradigm like popular programming languages i e BASIC C FORTRAN or PASCAL 33 In addition to the versatility that such languages provide Numerit s programming language offers many enhancements that make it much more powerful and easy to learn and use Variables are defined by assignment with the right type and the right dimensions Complex numbers are automatically created when necessary Operators and functions built in as well as user defined work with multidimensional
113. ed a user defined function must be defined that calls the built in function e g func sinf x sin x 2 When a Numerit function is called from a DLL it should be called using the cdecl convention namely the default C calling convention See Dynamic link Libraries above for information about calling conventions A Numerit function is declared as a parameter of a DLL function by declaring it as function or func in the list of parameters of the function and by specifying its own list of parameters This list specifies the types of the parameters of the callback function The allowed types are the same as the types that can be specified in a DLL function declaration except a function parameter namely a callback function does not accept another function as an argument For example the following C code defines a function sqr that receives a double scalar and returns its value squared The function integral receives the function sqr as an argument and returns the integral Whenever the function integral needs to evaluate the value of its integrand at a specific point in the given range it calls sqr with an argument and gets a value back double sqr double x return x x 52 typedef double integrand double double integral integrand f double a double b calculate integral of f from a to b The function integral will be declared in Numerit as follows dfunc integral func double f double x double a double b
114. een reached false otherwise should be previously defined by file or by binfile The second form checks for end of file in the Input file 91 erf Syntax erf x Operands x is an expression Description Returns the error function of x exists Syntax exists f Operands f isa file Description Returns true if the file exists false otherwise should be previously defined by file or by binfile even Syntax even x Operands x is an expression Description Returns true if the expression is an even integer false otherwise exp Syntax exp x Operands x is an expression Description Returns the exponential e to the x fitbasis Syntax fitbasis b y fitbasis b y s Operands b is a 2 dimensional Real expression y and s are 1 dimensional Real expressions Description Returns a 1 dimensional array whose elements are the coefficients in the linear combination of basis functions represented by b that best fits the set of data points given by y b is a user supplied 2 dimensional Real array with number of rows that is equal to the number of data points and number of columns that is equal to the number of basis functions The i th column of the array b is the value of the i th basis function evaluated at x where x is an array of x coordinates that correspond to the given y For example when fitting a Fourier series to the set of data points the first five base functions are 1 cos x sin x cos 2x sin
115. ely to all the currently open programs and become the default colors from now on Default settings are applied to new programs only When Numerit is closed the options are saved and will be used in next sessions of Numerit 25 26 Chapter 5 The Equation Editor Introduction Numerit s Equation Editor is invoked when a new equation is inserted or when an existing equation in the document is double clicked The Equation Editor is actually a dialog window so clicking the OK button closes the dialog and inserts or updates the currently edited equation in the document and clicking the Cancel button closes the dialog without updating the document Note that when you click Cancel all editing operations are lost after your confirmation The Equation Editor s window consists of two parts a control panel at the top and a display pane at the bottom The left side of the control panel contains buttons that are used for performing various editing actions The right side consists of a set of dialog pages that are accessed through a corresponding set of tabs at the bottom of the panel These pages are used for inserting templates and special symbols into the equation and for controlling the equation appearance The equation is edited in the display pane by typing characters and inserting templates or symbols from the control panel The Equation Editor formats the equation automatically as items are added to the equation It controls the position of i
116. er fn specifies the default file name that appears in the dialog box The parameter ft specifies the list of file types that will be available for the user The first string in each row of ft is a description of the file type the second string is a filter that specifies the file types that should be displayed in the dialog box when each description is selected For example Ss Documents txt Data dat AL We A file f fopendlg Open mydoc st read f a b c firstindex Syntax firstindex n Operands n is a number Description Sets the starting index of arrays Valid values are integers in the range 32000 to 32000 The default value of n is 1 Different values of firstindex may be set in different points of the same program The specified value will be in effect until a new value is set for Syntax for var exp to exp by value do statements for var exp downto exp by value do statements Description free Syntax Operands Description freedil Syntax Operands Description Defines a loop that is controlled by a variable which goes between two limits The first form is used when the control variable should be increased while looping and the second form is used when the control variable should be decreased while looping The default step is 1 and a different value may be specified with the keyword by followed by a constant or a variable s name The keyword do is optional but is red
117. er of data points When fitting polynomials to a set of data points FitPoly and FitCheby the first parameter is the degree and must be an integer smaller than the number of data points When fitting a basis of functions FitBasis to a set of data points the number of basis functions must be smaller than or equal to the number of data points Dimension error Wrong dimension or dimension mismatch in operation Division by zero A division by zero is a numeric error The program may continue to run and the result of the operation is set to INF or INF INF is an IEEE standard representation for infinity The value INF propagates through expressions namely if x becomes INF then an expression like x 1 also yields an INF End of file The end of file was reached while reading from the file File Open error File not found or couldn t been opened File Position error File position could not been set This usually occurs when the specified position is invalid or larger than the file size File Read error An error occurred while reading from the file File Write error An error occurred while writing to the file Possible reason the disk is full Index not integer A non integer value was specified as an array index Index out of range The specified array index is either smaller than the first index which is 1 or the value set by the instruction firstindex or greater than the index of the last element of the array Kind error A
118. ervices of another function Server to fulfill its task Suppose that you have different versions of Server say Serverl Server2 Server3 etc and you want to control which specific version is used by Client in a specific call Client doesn t know in advance what are and will be the possible Server functions so you can t simply send it a flag to tell it which function to call What you really want is to somehow reassign Server to the actual version that you want Client to call so that when it calls Server it actually calls the specific version that was assigned to Server A more specific example is an optimization function Suppose that you have developed a general optimization function Optimize that calls a merit function Merit during the optimization process to evaluate the optimized function at a specific point You want to be able to use the same Optimize function with different Merit functions even functions that you will create in the future Numerit offers a solution to this problem with function rerouting In your Client function you call the function Server The function Server is anormal Numerit function which is defined by the instruction function with any number of parameters During the run Client calls Server and the instructions of Server are executed However Numerit allows you to reroute the function Server to another function say Server1 at runtime so that when
119. es and the titles Note that in these dialogs there are two small buttons labeled All next to the standard OK and Cancel buttons Clicking such a button accepts or cancels the current setting and closes all the dialogs The OK and Cancel button themselves return you back to the previous level the main dialog so you can continue with other settings The image customization dialogs are Axes Each axis of the image in an Image Viewer may be customized The button Axes in the image edit dialog opens a dialog to specify which of the axes will be shown and for each axis its position line width and color By default all the axes are shown in the minimum and maximum positions 1 e at the ends of the scales Tick marks The tick marks on each axis of the image in an Image Viewer may be customized The spacing between the tick marks is set in the scale specification The size line width and type of the major and the minor ticks may be specified by clicking the button Ticks in the image edit dialog The type of the ticks on each axis may be set to either in facing inside out facing outside or cross crossing the axis Tick labels may appear next to each major tick The type of the labels is set by clicking the button Labels Tick labels Each major tick mark in an image may be labeled by a number which identifies the value it represents The labels may be customized by clicking the button Labels in the image edit dialog For each axis the
120. es the same Undo Redo mechanism that is used in the document only that here the operations are undone or redone immediately when the buttons are clicked regardless of the insertion cursor position The Equation Editor keeps a list of the recent 25 operations The Undo and Redo buttons make it possible to move back and fourth through the operations list and restore the edited equation to its state before or after each of these operations took place New operations are inserted at the current position in the list so operations that were made after this point are lost Shortcut keys for Undo and Redo Ctrl Z and Ctrl Shift Z respectively Help The third button in the first row shows the Equation Editor Help topic Shortcut key F1 Cut The first button in the second row cuts the currently selected items This deletes the selected items and copies them to the clipboard See Copy below for available formats Shortcut key Ctrl X Copy The second button in the second row copies the selected items to the clipboard The information is sent to the clipboard in two formats an internal format for use by the Equation Editor and a Metafile picture for use by other Windows applications Shortcut key Ctrl C 28 Paste The third button in the second row pastes data from the clipboard to the current insertion position Shortcut key Ctrl V Scale up The first button in the third row scales the view up This does not affect the size of the equation in
121. et a window whose dimensions are as close as possible to 256 x 256 pixels So if for example the image size is 100 x 100 pixels Numerit will choose a zoom value of 3 and will display a 300 x 300 pixels image If the drawn image is not defined yet the zoom value is set to 1 and the window size is set to 256 x 256 pixels When the image array is defined or changed and the option Fixed is not checked the zoom value is adjusted to keep the viewer window size as close as possible to its current size If the option Fixed is checked the zoom value will remain fixed and the size will change as necessary You may set any zoom value between 1 99 to 99 Pressing the Reset button will return the zoom setting to the initial value i e making the size as close as possible to 256 x 256 pixels When the image dimensions or scales are changed during the run Numerit does not update the Viewer s window size immediately and waits for the next program pause or stop to do it This may result in a temporary mismatch between the displayed image and the size of the Viewer s window you can manually pause the program and resume execution if you want to readjust the window size Style The fields inside the Style frame allow you to set the border thickness and a shadow for the viewer window Customization Dialogs The buttons at the middle of the dialog box are used to open customization dialogs for defining the axes the tick marks the tick labels the grids the scal
122. etermine the actual width but since most fonts are proportional i e different characters have different widths the final string might come out shorter or longer than the Viewer s width Table Viewer The Table Viewer displays up to 16 columns of data each corresponding to one program variable The displayed variables may be of any type numeric or string and can be either scalars or one dimensional A row of a two dimensional array may be specified with a dot followed by a number e g x 2 represents the second row of x and is treated as a one dimensional variable Note that in this case the specified row is shown as a column in the table To display a column of x as a column in the table define the transpose of x Inserting a new Viewer or double clicking an existing one opens a dialog in which the variables names are specified in addition to other parameters that define the appearance of the Table Viewer The variables are entered in a four column table Each line of this table represents a column in the Table Viewer The specified parameters are the variable s name the column title the column width in characters and the number of padding spaces Numeric data is aligned to the right and the specified padding spaces are inserted to the right of the number Strings are aligned to the left and the specified padding spaces are inserted to the left of the string The column title may be entered as a simple text or as a formatted title see For
123. eturn types in function name The type of the value that is returned from a function must be unique When more than one return instructions are specified in a function they must return values of the same type Function with no return value is used in expression A function that does not return a value was used as 1f 1t does namely inside an expression or in an assignment Illegal constant xxx The specified constant cannot be evaluated When an item starts with a digit it is assumed to be a numeric constant This error occurs if it is not a legal constant e g contains letters Illegal parameter A global variable prefix cannot be used with a parameter name in a function definition Incomplete instruction This error occurs when the compiler identifies a beginning of a valid instruction but cannot find the rest of it Insufficient memory to complete compilation There is not enough memory to complete the compilation Close other programs to free memory and try again Loc Arguments are of different types The arguments of the function Loc must be of the same type Multiple declaration of constant name The specified constant has already been declared Multiple declaration of function name The specified function name is already used in a previous function definition Multiple declaration of label name The specified line label is already used Line labels must be unique Name too long The name of a variable or function c
124. ever Server is called itis Serverl1 that is actually executed Thus if you have a set of server functions and you want to control which of them is actually called by the function Client all you have to do is to reroute the function Server to one of them before you call Client The function Server itself may do some default action or may even be empty if it s never actually used but serves only as a model The rerouting operation is very simple you just write the instruction Server gt Serverl before calling Client We use here the names Client and Server but you can of course use any other name In fact any Numerit function can be rerouted to any other Numerit function provided that their parameter lists are identical same number of parameters and same parameters types Note that in the rerouting instruction you should only specify the functions names without the parameters or the parentheses You can also reroute a function in one module to a function in another module if you are running Numerit Pro Returning to the optimization example mentioned above you may build an optimization module called opt1ib for example where you define a function Optimize which calls a function Merit The function Merit is defined in the module optlib as an empty function and just serves as a model The module can be compiled without errors In your main module you have a specific merit function MyMerit which you w
125. f the data in the file will remain untouched Be careful when you overwrite existing data replace it with matching data so that the rest of the data in the file will not be damaged To append data to the file first move the current position to the end by the instruction pos f 1 and then write the data It is possible to explicitly clear the file s content by the instruction clear f where f is the file variable This also moves the current position to the beginning Note that writing to the file after closing it will first clear its content as described above When a file variable is redefined e g with a new name or even with the same name and the file is open it is closed before the new definition takes place When a file variable is freed by the free command the file is closed and is no longer available to the program unless it is defined again A file may be deleted from the disk by the instruction delete f The commands fopendlg and fsavedlg open Windows standard dialogs for selecting a file or specifying a new file name This is a useful tool to allow the user to control the names of the files that are read or written by the program There are several commands that allow you read from files and write to files see Chapter 14 Reference to Numerit s commands for details read Reads data into variables from a text or binary file readin Reads lines of data into a string variable from a text file readtab Reads data into variables
126. for integer x this is equivalent to the factorial of x 1 gammaln Syntax gammaln x Operands x is an expression Description Returns the logarithm of the gamma function of x This function may be used with large values of x where the gamma function overflows ident Syntax ident n Operands n is an integer Description Returns an n xn Identity matrix ifft Syntax ifft x iffts x ifft x n iffts x n Operands x is an expression n is an integer Description The first and second forms return the inverse fast Fourier transform of x over all the dimensions The third and fourth forms return the inverse fast Fourier transform of x over the dimension n The number of elements in each transformed dimension must be an integer power of 2 The ifft version is the inverse of fft namely it assumes that the zero frequency component is the first element The iff ts version is the inverse of ffts namely it assumes that the zero frequency component appears at the center the N 2 1 element so it performs a shift before the inversion Calling the function shifft before ifft is equivalent to calling iffts Notes ifft and iffts may either return the transform of x and keep x unchanged when specified as part of an expression or on the right side of an assignment e g y ifft x or may be applied on x itself when specified as statements e g ifft x The second method is recommended if the original x is not needed since it use
127. fore the Pictures A picture may be inserted in the document by loading it from a disk file using the menu command Insert Picture or by pasting it from the clipboard Two types of pictures are supported Bitmap and Metafile A picture that is loaded from a disk file may be kept in the document in two forms The first is embedding the picture itself in the document The second is inserting a link to the disk file by keeping only the file name in the document If the second form is chosen then the picture file must exist in the same location on the disk in order to be displayed by the document A picture that is pasted from the clipboard is always saved inside the document equivalent to the first form above Double clicking a picture opens a dialog which allows to set a new size for the picture or restore the original size It is also possible to change the picture size by dragging its borders when it is selected use single click to select Document Options The Document command in the Options menu opens a dialog in which some of the Documents properties may be customized Default setting of various parameters may be set These will be applied to new documents only Parameters of current documents are set explicitly in each document The number of undo levels may be set The default is 25 the maximum is 99 Foreground background and fields colors may be selected When the OK button is clicked the selected colors are applied immediat
128. functions Arguments by reference or by value A function may return a value or modify the arguments sent to it Normally a variable that is sent as an argument to a function is sent by reference namely the function receives the variable itself and not a copy of it and can change its value however the function itself does not care how the variable is sent and there is no need to specify if a parameter is by reference or by value when the function is defined This is determined when the function is called In order to send a variable by value a copy rather than the variable itself it should be preceded by a when sent as an argument e g y f x this tells the system to send a temporary copy of x to the function f Sending arguments by reference is more efficient Sending a variable by value is only required when you know that the function modifies the argument and you want to protect the variable i e keep its original value There are cases where temporary arguments are automatically constructed by the system 1 the argument is an expression e g y atb 2 the argument is an indexed variable e g y f a 3 3 the argument is a constant e g y 3 Temporary arguments can be modified by the function but since they are temporary they are actually local variables of the function Returning from a function Functions that do not return a value cannot appear in expressions or assignments Functions c
129. g in the program s code the program is ready to run This is done by the menu command Run Run F9 or the Run button in the Program Bar The program s code is first compiled and its syntax is checked If invalid instructions are found a notification window pops up and a list of errors is displayed in the Message pane Numerit Pro also verifies that all the modules that are linked to the program are compiled If all the modules are compiled and there are no compilation errors Numerit Pro links external functions from the modules to the main program see Modules below If one or more functions are not found a notification window pops up and a list of link errors is displayed in the Message pane If there are no errors the program is executed Any modification in the Editor will cause a re compilation of the program when it is run again If the program s code is not modified it can be run again without compilation It is possible to compile the program without running it e g for syntax checking by the menu command Run Compile In Numerit Pro this is done with the menu command Run Compile Module which is used to compile the Main module or any other module of the program It is also possible to compile all the uncompiled modules and link external functions without running the program by the menu command Run Make see Modules below Besides error messages the compiler also issues warnings when it detects suspicious situations for example when a variable
130. g in which the name of the two dimensional array variable is specified in addition to other parameters that define the appearance of the image Image Dialog Controls X Y The X field allows you to specify the name of a one dimensional array whose minimum and maximum values define the range of the X axis scale Note that only the minimum and maximum values are used and all the other elements are ignored so it is sufficient to specify only two elements in the array Similarly the Y field allows you to define a scale for the Y axis If no variable is specified in the X or Y field the scale is taken from 1 to the number of elements in the corresponding dimension of the image array If the variable that is specified in one of these fields is not valid e g a scalar a 2 d array etc the scale is not drawn Color Table The Color Table field allows you to change the default interpretation of the data in the image array The default interpretation if no variable is specified in the Color Table field is to create an internal table by dividing the range that is defined by the minimum and maximum values of the image array to 256 equidistant values The position 0 to 255 of the value of each 21 element in this table is used as the color of the drawn pixel where 0 is drawn in black 255 is drawn in white and any integer between these values is drawn in a corresponding gray from a very dark gray to a very light gray When you specify a name of
131. get an overview of the program without the details of inner blocks A group of instructions may be easily put inside a block by selecting it and inserting a block A whole block may easily be commented by a single key press Commenting out a group of instructions is very simple just select it insert a block and comment the block If such a block is also folded it becomes almost invisible Blocks are inserted by the menu command Edit Block Ctrl or by the Block button in the Program Bar The shortcut key ctrl is the most useful way for inserting blocks The same command is used to insert a block around a selected group of instructions and to insert an empty block when no text is selected A block frame may be deleted by pressing Delete in front of it Blocks are folded and unfolded by using the menu command Edit Fold Ctrl Shift F or by clicking the right mouse button while pointing to the block A block is commented by putting a comment character in front of its frame Deleting this character or pressing the same key again restores the block to normal Blocks may be split and joined By pressing Enter in front of a block frame the block splits to two at the point of insertion By deleting the line between two blocks they are joined together and form a single block Highlighting In order to make it easier to work with the editor and make the program s code more readable the editor s normal text language keywords and c
132. h the Edit Clear Draft menu command or by the instruction clear in the program s code The output remains in the Draft until it is explicitly erased so one can accumulate the results of several runs It is a good practice to clear the Draft when this information is no longer needed If such accumulation is not required it is better to put a clear instruction at the top of the program s code so that each run will first clear the old data You can save the Draft as a Rich Text Format file see section below which is a portable format that is recognized by most word processors This allows you to continue editing the document in your favorite word processor When the Draft is saved its previous version on the disk if exists is kept as a backup with the character added as the last character of the file name leaving the extension unchanged Rich Text Format RTF As mentioned above you can save a document Report or Draft as a Rich Text Format RTF document The RTF specification provides a format for text and graphics interchange that can be used with different output devices operating environments and operating systems So you can save your program s output document as an RTF file and continue the editing in your favorite word processor such as Microsoft Word without losing formatting or character attributes information 13 To create an RTF file select the Rich Text Format type in the Save As dialog of the commands File Save Report As
133. hat corresponds to the given error code will be displayed and the second argument message will be ignored and can actually be NULL If the error code is negative Numerit will display the specified error message second argument For example NumeritError 12 NULL NumeritError 1 Argument must be greater than 1 The first call will display the message File Read error while the second call will display the specified message Note that it is important to export the function pointer NumeritError so that Numerit can find it when it loads the DLL and set it to the actual error handler Numerit will first look for the pointer using the name NumeritError and if this is not found it will look for it using the name _NumeritError since many compilers attach an underscore to global names If both attempts fail error reporting is not enabled so before you call the error handler function you must check that the pointer is actually set and is not NULL for example if x lt 1 if NumeritError NumeritError 1 Argument must be greater than 1 return 0 44 Note that earlier versions of some compilers use the keyword export instead of _declspec dllexport to export functions and variables from a DLL and some compilers may use other keywords as well Dynamic link Functions Numerit allows you to call dynamic link library DLL functions as if they were Numerit built in functions The DLL functions are assumed to
134. he check box is set and the font size in the document is modified by either selecting the text and setting a new font size or by changing the style the base size of all the equations in the range will be updated Attributes The Attributes group has three controls Italic Bold and Underline In the Text mode each of the controls has two possible states Set and Not Set In the Math mode the Underline control is not available the Bold control has two possible states Set and Not Set and the Italic control has three possible states Set Not Set and Auto The Auto state means that the Equation Editor is responsible for italicization see Math and Text modes 30 Alignment The last group of controls in the Format page is the Alignment group The controls in this group are used for specifying the alignment type for stack of blocks that are generated by splitting a block with the Enter key Any block may be split to several rows of blocks that can be aligned in various ways Options The Options dialog page lets you define several parameters for the currently edited equation These parameters also become the defaults when inserting new equations Existing equations keep their parameters and are not affected by the new setting The first two parameters are the name of the fonts that are used for normal characters and for Greek characters Normally in Windows these are the Times New Roman font and the Symbol font however if there is a better choi
135. he end of the string are deleted Note that this function does not return a value but rather operates on the string itself strins s p t Inserts the string t into s at position p The position of the first character in s is 0 If p is greater than the length of s the string t is appended to s Note that this function does not return a value but rather operates on the string itself strtonum s Converts the string s to a number and returns its value numtostr x Converts the value of the numeric expression x to a string and returns the string In addition to these functions there are commands for reading and writing from and to strings similar to files read Reads data into variables from a String write Writes data to a String 38 Files Numerit supports two types of files for input and output of data a text file which contains information as a formatted text and a binary file which contains information in binary representation Text files are used when the data they contain should be displayed printed or transferred to other applications Binary files are used when the full precision of the data should be maintained and are usually more compact Files are defined as variables of type File in the program s code by the instructions file f file name fora text file or binfile f file name fora binary file f is the variable and the file s name is specified as a string The file s name may contain the full path name
136. he specified callback function in number and types of arguments a mismatch will result in unpredictable results When the DLL function is called the callback function should be sent to it as an argument with a prefix e g foo f A callback function may also be specified as a member of a structure for example dfunc double foo func double f double x double p Here too when foo is called the callback function is specified inside the braces with the prefix e g foo p When a Numerit function is called back by a DLL function the arguments that are sent by the DLL function are converted to Numerit variables and are then sent to the Numerit function When the argument is an array Numerit must know its size in order to carry out the conversion That s why an array parameter in the declaration of a callback function must also include its length This can be done in one of the following three ways 1 The array has a fixed known size In such a case the size of the array should be specified inside the square brackets e g func double f double 3 2 One of the arguments before the array is used to specify the length In such a case the number of this argument is specified instead of the actual length by adding the prefix to the number e g func double f int double 1 tells Numerit to take the length from the first argument 3 The array s length is taken from a global variable e g func double f
137. he tolerance argument seems to be Complex It must be a real scalar UnPackComplex Argument must be a Real Complex array The first argument of UnpackComplex must be a Real array and the second argument if specified must be a Complex array Vector must be 1 dimensional n A vector must be 1 dimensional but was defined as n dimensional Compilation Notices Parameter name is not used The specified parameter appears in the function header but is not used inside the function This is allowed but is usually an indication of an error Variable name is not used The specified variable was defined but not used anywhere in the program This is allowed but is usually an indication of an error 70 Link Errors Unresolved function name n Numerit couldn t find the specified function in the current program or in any of its modules n is the number of parameters Different number of parameters rerouting funcl n1 gt func2 n2 When a function is rerouted to a function in another module both must have exactly the same number of parameters nl and n2 are the number of parameters of each function Cannot open DLL name The specified dynamic link library DLL could not be opened Either the library doesn t exist or is not in the DLL search path Unresolved DLL function name or Unresolved DLL variable name The specified function or variable was not found in the specified dynamic link library Execution Errors Fatal Errors
138. header Insert a numbered Reference caption header Insert a numbered Equation Insert an Expression Insert a Picture from disk Insert a Date in a specific format Insert a new page force a page break Insert a new line within the same paragraph force a line break Nonbreaking space Ctrl Shift Spacebar Insert a nonbreaking space Format Character Change character appearance Bold Font size etc Paragraph Change paragraph appearance Alignment Indentations Tabs etc Style Change paragraph style Normal Title etc Page Change page appearance Size Margins etc Define Style Change definition of styles Tools Document Spelling Check spelling of the document from the current position Word Spelling Ctrl W Check spelling of the word at the current position Dictionary Edit personal dictionaries Character Map Open a character map for the current font The Program Bar The Program Bar is the main tool bar It is located below the menu bar at the top of the Desktop The buttons in the Program Bar give faster access to some of the menu commands and are arranged in six groups each matches a set of menu commands These buttons are relevant to the program as a whole and to both the Editor and the Document panes The buttons are also used as indicators for various states For example when the program is running the Run button gt is depressed and shown as DP Note that the buttons Modules and Save Module are onl
139. her cases you ll have to make some adjustments see below Pointers Before entering into a detailed description of typed parameters it is important to clarify how Numerit refers to C pointers Numerit has to deal with C pointers only when a pointer is specified as a return value or as a parameter of a DLL function In C a pointer may represent different objects a scalar an array a structure etc The actual interpretation of the pointer is done in the function itself Since there are no pointers in Numerit you must know how a parameter that is declared as a pointer in C is actually interpreted in the function before you can specify its type in the dfunc statement If the return value is a pointer you must specify it as ptr or pointer If a parameter is a pointer the type you specify depends on the interpretation of the pointer For example if it represents a scalar that is sent by reference you must declare it with a type and an ampersand e g doubles and if it represents a one dimensional array you should declare it with a type and square brackets e g double see a more detailed description of each of these cases below When the pointer represents an address to an object that is not supported by Numerit it should be declared as ptr or pointer The use of a ptr parameter is mainly to transfer an object s address from one DLL function to another The value of such an address will normally be returned from a DLL function and will
140. her than the one on the disk A Numerit program may be open simultaneously in several windows either as an independent program if opened with the File Open menu command or as a submodule of another program if opened through the Modules List window All the versions of the program refer to the same file As long as the file is not saved each version of it is independent of the others and each program ignores the changes in the source code of other programs and uses its own copy When the file is saved either as an independent program or as a module a message is sent to all the programs that use this file If a program uses this file as a submodule there are two possible cases 1 if the submodule is not open the file is listed in the Modules List but is closed Numerit will use the disk version when the program is executed and 2 if the submodule is open Numerit will display a message asking you to either reload the module from the disk or to ignore the disk version and continue with the current source code Note that if you continue with the current version and save it it will rewrite the disk version If the file is open as a program in its own window not a submodule and is saved by another program as a program or as a module the current version will continue to be used but when you ll try to save it Numerit will issue a warning to remind you that the same file was also saved by another program If you confirm the Save it will rewrite the disk
141. hift H Set character Height point size in the Document Ctrl I Set Italic text in the Document Ctrl J Justify a paragraph in the Document Ctrl L Align a paragraph to the Left in the Document Ctrl M Show the Message pane Ctrl N Create a New program Ctrl O Open an existing program Ctrl P Print the current program or document Ctrl Q Insert an equation at the current position Ctrl R Align a paragraph to the Right in the Document Ctrl S Save the current program module or Input File Ctrl T Set a paragraph style in the Document Ctrl U Set Underline text in the Document Ctrl V Paste from the clipboard to the current position Ctrl W Check spelling of the Word at the current position in the Document Ctrl X Cut the selected text to the clipboard Ctrl Y Delete the current line in the Editor Ctrl Z Undo the last editing operation Ctrl Shift Z Redo the last undone operation Fl Display Help Contents Ctrl F1 Search for a keyword and display its help topic F2 Repeat the last Replace operation Shift F2 Search and Replace text F3 Repeat the last Find operation Shift F3 Find text F4 Set Clear a breakpoint at the current line Ctrl F4 Close the current program Altt F4 Exit Numerit Shift F4 Tile Program windows FS Stop the current program Shift F5 Cascade Program windows F6 Pause the current program Shift F6 Move between the Editor and the Document panes in the current Program window F7 Step Into execute the current line while e
142. his is actually equivalent to sending the variables of the structure as argument one after another so Numerit doesn t provide special means for sending structures by value A structure is declared in the dfunc statement with braces surrounding a list of types For example the following structure struct person i int age double height weight y may appear for example in a C parameter list as void insert struct person p int n but will be declared in Numerit as dfunc void insert int a double h double w int n The void and the names a h w and n are of course optional and the above declaration is equivalent to dfunc insert int double double int This declaration tells Numerit that the first parameter it passes to the DLL function is a structure whose first member is an int and second and third members are double s The function also has a second parameter which is an int a simple integer In the Numerit instruction that calls the DLL function the relevant variables should also be grouped together with braces for example age 25 weight 80 height 180 n 1 insert age height weight n Note that C expands the notion of structures to classes however the data structure of class objects is in most cases the same as that of simple structures so the same syntax of sending structures can be used for sending arguments to DLL functions that expect class objects When you specify an array as a mem
143. ically This is especially useful when you write a multi module program for someone else without knowing in advance where it will be installed Reload When you open a program with modules Numerit searches for the modules and creates the modules tree remember that each module may have submodules of its own At this stage Numerit doesn t care if a module file is not found only when you run the program Numerit tries to find all the modules and compile the uncompiled ones If then a module is not found Numerit issues an error message In some rare situations you may want to force a reload of all the modules For example if Numerit already loaded all the modules and found no errors it will not try to reload the modules again each time you run the program to save time In such a case if you replace a module s file on the disk with a new file outside the Numerit environment Numerit will keep using the currently loaded version You may then click the button Reload to force Numerit to reload the modules and thus to update the replaced module This situation is rare since normally you will modify modules inside the Numerit environment and Numerit will be aware of these modifications Another case is when you modify the source of a compiled library see above and recreate the library In such a case you must click Reload in order to load the new version of the compiled library 60 Reordering the list When Numerit looks for functions in the modules it s
144. if a module doesn t exist displayed in red opening it will first create a new module of the specified name on the disk after confirmation Modules Directory At the bottom of the Modules window you may see the Directory field where you can specify the modules directory This allows you to use short file names i e not including the full path for modules in the list If you want to add a module that is not in the specified directory you must put its full file name in the list including the path Note that when you add a module using the top Browse button and the module is inside the specified modules directory Numerit automatically puts its short file name in the list If you change the modules directory the short file names will remain which means that Numerit will now search for the modules in the new directory So if you rename the modules directory in Windows you only need to change the modules directory in the Directory field and not each individual module in the list A module file name that is specified with its full path name will always refer to the same file regardless of the modules directory The Auto checkbox next to the Directory field allows you to specify that the modules directory is not set by you manually but rather is taken as the directory of the main program This allows you to move the program and the modules from one directory to another or from one computer to another and the modules directory will be updated automat
145. ify the word that appears in the Replacement field In this case clicking the button Check Replacement will check the modified replacement Personal Dictionaries Personal dictionaries contain words that do not appear in the standard dictionary Words are added to a personal dictionary by either clicking the buttons Add or Add Correction during a spelling check or by opening the dictionary using the Tools Dictionary menu command This opens a dialog for specifying the current personal dictionary It also lets you add new words or remove existing entries from the dictionary During a spelling check Numerit is looking in the currently open personal dictionary in addition to the standard dictionary A word that appears in the dictionary without a correction next to it is considered a correctly spelled word a word that has a correction will be replaced by the correction when checked Auto numbered Captions Graphs and tables are usually accompanied by captions It is possible to insert caption headers 1 e Figure nn or Table nn where nn is a number anywhere in the document normally under graphs and above tables It is also possible to insert a caption header for a reference anywhere in the document references are normally inserted as a list at the end of the document A reference header is just a number The relevant caption s text is typed in by the user next to the header The headers are automatically numbered according to their position in the
146. iled and saved its functions may be called from any program Besides modularity Numerit and Numerit Pro are identical So users of the Standard Edition can use this manual knowing that they are limited to single module programs NumRun In addition to Numerit we also provide the program NumRun which allows execution of compiled Numerit programs outside the Numerit environment See the section NumRun The Numerit Executor Users of Numerit may develop programs and distribute them to customers The customers can download NumRun from http www numerit com download htm for free and use it to run the programs No royalties are charged from users that develop Numerit programs and distribute or sell them System requirements To use Numerit you need e A Pentium or higher computer e Windows 98 2000 XP Vista 7 Registration Every copy of Numerit has its own Registration Number When you invoke the Evaluation Edition of Numerit you may see the Registration Number of your copy on the opening dialog window In order to register your evaluation copy and upgrade it to the commercial edition visit our web site at http www numerit com fill out the order form and submit it After processing your order we will send you a Registration Code that matches your Registration Number Click the button Registration Code in the opening dialog and enter the Registration Code Please keep both your Registration Number and the Registration Code safe you will
147. ine in the Editor or Start a new line within the same paragraph in the Document Start a new page in the document force a page break Insert a tab Move to the next Program window Move between the Editor and Document panes in the current Program window Insert a nonbreaking space Delete a character on left Delete the current character or the current selection Toggle Insert Overwrite mode Move to the beginning of the current line Move to the beginning of the Editor or the Document Move to the end of the current line Move to the end of the Editor or the Document Move up one screen page Scroll Left Move down one screen page Scroll Right Move up one line Scroll Up Move down one line Scroll Down Move one character to the left Move one word to the left Move one character to the right Move one word to the right Mouse Operations The left mouse button is used for Moving the cursor around Selecting menu commands e Selecting text Selecting objects Resizing frames Setting the Document s ruler Setting breakpoints Clicking buttons Double clicking with the left mouse button on a Viewer opens the Viewer s edit dialog The right mouse button is used for Folding blocks in the Editor when pointing to a block Displaying help on keywords when pointing to a keyword in the Editor Opening the Inspector when pointing to a variable or to an empty space in the Editor Opening the Insert Field menu when insid
148. ing message Writes output to a file or a string Writes output to a text file and moves to a new line Writes tabular output to a text file Displays a Yes No message Displays a Yes No Cancel message Chapter 12 A Quick Reference to Numerit s operators Operators are listed in order of precedence highest to lowest Operators in each group have the same precedence Operator Meaning Types A power Numeric outer power Numeric factorial Numeric multiplication Numeric outer multiplication Numeric division Numeric outer division Numeric mod modulo Numeric addition Numeric outer addition Numeric subtraction Numeric outer subtraction Numeric amp concatenation String gt greater than All lt less than All gt greater than or equal All lt less than or equal All equal All lt gt not equal All in element in array All not logical NOT Boolean and logical AND Boolean or logical OR Boolean xor logical exclusive OR Boolean assignment All increase by Numeric decrease by Numeric multiply by Numeric divide by Numeric concatenate to String gt function rerouting Function 85 86 Chapter 13 Reference to Numerit s built in functions abs Syntax abs x Operands x is a numeric expression Description Returns the absolute value of x If x is complex the returned value is the square root of the sum of squares of the real part and
149. ion Returns a version of the string s where all upper case characters have been replaced with lower case characters strpos Syntax strpos s t Operands s and t are strings or arrays of strings Description Returns the position of the substring t in the string s The position of the first character in s is 0 If the substring is not found in s the returned value is 1 strsub substr Syntax Operands Description strsub s p n or strsub s p s is a string p and n are integers Returns a substring of s with length n starting at position p The position of the first character in s is 0 If the third parameter n is omitted the substring from position p to the end of the string is returned s p and n may also be arrays 103 strtonum Syntax Operands Description strtonunm s s is a string or array of strings Converts the string s to a number and returns its value strupp strupper Syntax Operands Description substr strsub strupp s or strupper s s is a string or array of strings Returns a version of the string s where all lower case characters have been replaced with upper case characters Syntax substr s p n or substr s p Operands s is a string p and n are integers Description Returns a substring of s with length n starting at position p The position of the first character in s is 0 If the third parameter n is omitted the substring from position p to the end of the string is re
150. ion it is sent as an array of char s And as with other types of arrays what is actually sent is the address of the array so the DLL function may modify its content A one dimensional array of strings can be sent as an argument to a function that expects a two dimensional array of char s namely char or char 49 A Boolean parameter In Numerit a Boolean variable namely a variable that can have only one of two values true or false occupies one byte So you can only send it as an argument to a DLL function that expects a parameter of type char or unsigned char This is true for Boolean scalars as well as Boolean arrays Note that in other languages e g C Boolean variables are defined as integers namely variables of type int so if you want to pass an argument to a DLL function that expects such a Boolean variable you must use int in the DLL function declaration and send to it a numeric variable as an argument rather than a Numerit Boolean Such a numeric variable should be defined as 0 for false and 1 for true A structure parameter Structures in C are objects that include several variables of different types that are grouped together Unlike C Numerit doesn t support structures but it allows you to group together several variables and send them as a single structure to a DLL function Such a structure is sent by reference namely only the address of the structure is sent C also allows to send structures by value but t
151. is assigned a value but is not used by the program For a complete list of compilation errors and warnings see the chapter Errors and Warnings A program may be paused or stopped any time using the Pause or Stop commands in the Run menu or the corresponding buttons in the Program Bar When a program pauses or stops it does so after completing all the instructions in the current code line When a program pauses a marker horizontal line appears above the line which will be executed next when the run is resumed It is possible to run the program one line at a time by either the Run Step Over menu command F8 which executes the line without tracing into functions or by the Run Step Into F7 command which executes the line while tracing into functions when they are called during the execution of the line Both commands have corresponding buttons in the Program Bar After the execution of each line the program is in the Pause state This mode of execution is very useful for debugging Other debugging aids are the Inspector and breakpoints See the section Debugging below for more details When errors occur during the run a notification window pops up and displays the error A corresponding error message is also sent to the Message window and the erroneous line appears in the Editor Some execution errors do not allow the program to continue Fatal errors and stop it Other errors non fatal just pause the program so it may continue to run Non fatal err
152. is is a convenient way to define parameters for the program However in some cases it is desired to modify the parameters from run to run and doing that with a disk file requires opening the file making the modifications and saving the file before running the program In order to shorten this procedure Numerit allows you to open an Input File in the Editor pane and read data from this file directly Reading from the Input File is similar to reading from an ordinary text file and the same instructions can be used namely read readln readtab and pos only that input should be specified instead of a File variable For example to read the two variables x and y from the Input File write read input x y The instruction pos input should be followed by two numeric parameters that set the current position in the Input File to the specified line and column the next read will start at this position For details on these commands see Chapter 14 Reference to Numerit s commands The menu command File New Input File opens an empty Input File or clears the Input File pane if a file is already open The menu command File Open Input File opens a disk file and copies its content to the Input File pane The menu commands File Save Input File and File Save Input File As save the current Input File as an ordinary text file on the disk When the program is saved the name of the current input file is also saved and this file is opened again as the Input File the next ti
153. is used before it is defined The specified variable is probably used before it was defined It is illegal to use a variable before a value is assigned to it Loc Wrong dimensions in arguments n1 n2 The first argument of the function Loc must be a scalar and the second argument an array n1 n2 are the actual dimensions found Locmin Locmax Argument must be an array The argument of the function Locmin or Locmax must be an array but seems to be a scalar 69 Looks like a numeric type mismatch typel lt gt type2 The numeric type of the expression involved in the operation must be the same both Real or both Complex Matrix must be 2 dimensional n A matrix must be 2 dimensional but was defined as n dimensional Operands of outer operation should be 1 dimensional Two expressions that are involved in an outer operation e g x y should be 1 dimensional They can also be scalars but then the outer operation is the same as the corresponding standard operation PackComplex Argument must be a Complex Real array The first argument of PackComplex must be a Complex array and the second argument if specified must be a Real array Poly First argument must be 1 dimensional n The first argument of the function poly which specifies the coefficients array must be 1 dimensional but seems to be n dimensional Tolerance must be a scalar The tolerance argument must be a scalar Tolerance seems to be Complex must be Real T
154. it to always reflect the current date In both cases you may select the format of the inserted date from a list Nonbreaking space Line break and Page break Nonbreaking spaces are inserted between two words that you want to keep together so that they will not be separated at the end of line To insert a nonbreaking space press Ctrl Shift Spacebar A line break is inserted in a paragraph to end the current line and start a new line without starting a new paragraph To insert a line break press Shift Enter A page break is inserted to force a new page regardless of Numerit s mechanism of dividing the text into pages which tries to fit as much text as possible on each page according to the current page size and margins setting To insert a page break press Ctrl Enter Nonbreaking spaces and line breaks are not visible normally They become visible when the item View Document Special characters in the Options menu is checked or when the corresponding button in the Document Bar in clicked The page break 1s always visible None of these marks are shown on the printed page Viewers Viewers are objects that are inserted in a document for displaying program variables There are currently four types of Viewers the Variable Viewer the Table Viewer the Graph Viewer and the Image Viewer The menu command Insert Viewer F11 opens a menu of Viewers The Variable Viewer displays a scalar variable Numeric Staring or Boolean as a simple formatted text
155. ith either two pointer operators e g double x or with one pointer operator and a square bracket e g double x In both cases the declaration in Numerit is the same with two square bracket namely x which is actually not a legal specification in C As before if you copy the function declaration from a C header file you must change the s and s to s When a DLL function expects a parameter as a contiguous array with two or more dimensions it can only be called with a Numerit one dimensional array So this parameter must be specified in the Numerit declaration as a one dimensional array namely with a single In the C declaration such a multidimensional array is specified as x n or x m n or even x m n where m and n are numbers and in general all the dimensions except the first must be specified The size of the Numerit one dimensional array must be equal to the multiplication of all the dimensions of the target array and the interpretation of the elements is left to the user remember that in C elements of multidimensional arrays are stored row wise A string parameter Strings are treated in C as one dimensional arrays of characters When a DLL function has a parameter that is a one dimensional array of type char namely char or char you can send to it a Numerit String as an argument Note that although in Numerit a string is considered to be a scalar when sent as an argument to a DLL funct
156. ith the type of error and a list of optional replacements Possible errors are Word not in dictionary Capitalization one or more letters in the word need capitalization and Abbreviation an error in an abbreviation The word shown in the Replacement field is the one that appears at the top of the list The list is ordered according to similarity to the misspelled word Selecting a word from the list copies it to the Replacement field Double clicking a word in the list selects it and also substitutes it for the misspelled word in the document You may do one of the following Click Ignore to skip the current word Click Ignore All to ignore all the occurrences of that word during the current check Click Replace to replace the word with the one that appears in the Replacement field Click Replace All to replace every occurrence of the word with the specified replacement during the current check 16 Click Add to add the misspelled word to the personal dictionary The word will be treated as correctly spelled from now on until it is explicitly removed from the personal dictionary Click Add Correction to add the word and the specified replacement to the personal dictionary The specified replacement will replace the word from now on every time the word will be checked until it is explicitly removed from the personal dictionary Click Undo to move to the last visited word and undo the last replacement It is possible to manually mod
157. ivalent to calling ffts Notes fft and ffts may either return the transform of x and keep x unchanged when specified as part of an expression or on the right side of an assignment e g y t x or may be applied on x itself when specified as statements e g fft x The second method is recommended if the original x is not needed since it uses less memory No normalization is performed on the transform There are two common methods to normalize the transform 1 divide the transform by the multiplication of the number of elements in each of the transformed dimensions and leave the inverse transform as is or 2 divide both the transform and the inverse by the square root of the above normalization factor Both methods ensure that after performing a transform and its inverse we return to the original array The functions ifft and iffts are the inverse transforms of fft and ffts respectively Syntax Operands Description gamma floor x floor x n x is an expression n is an integer The first form returns the rounded down value of x nearest integer value not greater than The second form returns the rounded down value of x with accuracy 10 namely n determines which digit is rounded For example floor 1234 567 2 is 1200 rounded to hundreds and floor 1234 567 2 is 1234 56 rounded to hundredths Syntax Operands Description 94 gamma x x is an expression Returns the gamma function of x
158. k Libraries above For example the following statement dfunc double sqr double x declares a DLL function sqr that accepts one parameter of type double a double precision floating point number and returns a value of type double The DLL function is called just like a Numerit function for example the following code calls the function sqr that was declared above x 1 5 y sqr x A DLL function may either return a value as the function sqr above or not The following statement declares a function that doesn t return a value but has two parameters the first of type int integer and the second of type double dfunc void set int n double x For the exact syntax of a DLL function declaration see the command d unc in Chapter 14 Reference to Numerit s commands Return type A function return type must be of one of the following void char uchar or unsigned char short ushort or unsigned short int uint or unsigned int float double complex and ptr or pointer The specified type should match of course the actual return type of the function For more information about types in DLL function declarations see Dynamic link Libraries above The type void is used to specify that the function does not return a value If the type is omitted it is assumed to be void When the return type is ptr or pointer it represents an address of a variable or an object and cannot be used in Numerit but can be transferred to another DLL
159. l array which is the product of the rows of M while prod M 2 returns a 1 dimensional array which is the product of the columns of M rand Syntax rand x Operands x is an expression Description Returns a random number between 0 to x If x is an array the result is also an array of the same size If for example x is a 1 dimensional array then the i th element of the result is a random number between 0 and x i real Syntax real x Operands x is an expression Description Returns the real part of x root zero Syntax root exp x or zero exp x root exp x tol or zero exp x tol Operands exp isa formal expression of one variable x is the initial guess tol isa number Description Returns the zero of the expression exp exp has one dummy variable over which the 100 search for the zero is done It is represented by the dollar character x is the initial guess from which the search starts If the expression has several zeros the returned value is usually but not necessarily the closest to the initial x x must be real but may have any dimension When x is multidimensional root returns an array of the same dimension as x whose elements are the zeros that were obtained by taking the corresponding elements in x as initial guesses A tolerance may be specified as a third argument If not specified it is taken as 107 For example the following x 0 3 z root S 2 3 S 2 x defines z asa 1 dimensional
160. l perform a different operation When you declare such a function in Numerit you must specify an array in the parameter list and since Numerit checks that the argument you send is indeed an array when you call the function this does not allow you to send a NULL value namely 0 which is a scalar The solution to this is to declare two versions of the same function with two different Numerit names one version with an array parameter and the other version with a pointer parameter see the command d unc in Chapter 14 Reference to Numerit s commands for the exact 46 syntax of naming DLL functions Both versions will refer to the same DLL function but since they have different Numerit names you can call the first when you send an array and the other when you send a NULL pointer For example in the following declarations note that here we use an array parameter which is described in detail later dfunc fool double a foo dfunc foo0 ptr foo both fool and foo0 refer to the same DLL function foo but the first is called with an actual array and the second with 0 for example x 1 to 10 fool x foo0 0 A pointer parameter may also be used to transfer an address of one DLL function as an argument to another DLL function more details below A scalar parameter A scalar parameter is specified by its type and an optional name When the function is called Numerit checks that the argument sent is actually a scalar A scalar can be
161. l vs x1 and y2 vs x2 witha legend Note The command graph actually inserts a Graph Viewer in the Draft As any other Viewer this may also be edited to change its attributes It can also be copied from the Draft to the Report The data in this Viewer is frozen namely the graph shows the data as it was at the moment when it was created Further changes to the variables that appear in the Viewer will not affect the displayed data Note that unlike manually inserted Viewers here the arguments may be expressions and not only variables hideerror Disables the automatic execution error handling While this command is in effect may be canceled by showerror the system doesn t pause the program on execution errors Instead the program continues to run and the user is responsible for handling errors Use this command with care Put it before an operation check the error code right after the operation by checking the value of the system variable errval and resume automatic error handling using showerror If after checking the error code you decide to handle the error you will normally reset the error flag using reseterror before you resume automatic error handling For example suppose we call the function integ and we want to change the tolerance parameter when the process doesn t converge In this case the execution error is Not converging and the value of errval is 3 See table of execution error codes Normally this will
162. labels may be shown or hidden Their numeric format may be set to Auto default Decimal or Scientific In addition a factor that multiplies the label values may be specified for each axis its default value is 1 It is possible to hide the labels that appears near axes Namely in the bottom and top axes the labels that appear near the left and right axes may be skipped and in the left and right axes the labels that appear near the top and bottom axes may be skipped By default the left and bottom axes are labeled and the labels at the right and top axes are hidden Grids Grids extend the tick marks across the image The button Grids in the image edit dialog opens a dialog to define the grids You may select a horizontal grid and or a vertical grid For each grid it is possible to specify if the gridlines pass through major and or minor tick marks The line style of the grid its line width and its color may also be set Scale The scales of the image in an Image Viewer are by default set to automatic mode In this mode the X and Y scales are set to the maximum range of the variables specified in the X and Y fields in the main dialog see above and the Image scale the range of image values that are displayed is dynamically adjusted to the data of the image array By clicking the button Scale in 23 the image edit dialog it is possible to set a specific range for each scale If no variables are specified in the X or Y field the scal
163. lied to the current paragraph only where the insertion point is A paragraph s format information is copied with the paragraph mark at the end of the paragraph Note that when a paragraph is formatted the current page width is used This is normally taken from the current setting of the printer so that when the document is printed the paragraph will be aligned properly in the page The page width may be manually set to a different value using the menu command Format Page Character Formatting Character formatting determines the appearance of characters It may be set by the menu command Format Character Except for the Color all the parameters may also be set in the Document Bar The dialog fields are Font and Font size Attributes Bold Italic and Underline Subscript and superscript Color When a new character format is set while text is selected it is applied to the selected text otherwise it will affect the next characters that will be typed Paragraph Styles It is possible to set a style to a paragraph The style includes the default paragraph format settings and the default character format settings for the text in the paragraph The style may be set by the menu command Format Style or in the Document Bar There are eight available styles The first is the Normal style which is the default style The second is the Main Title style which may be used for titles The third is the Sub Title style which may be u
164. lly defined by calling the main body of the module once before the module s functions are called To share variables between modules use the instruction common Modules List Every program in Numerit Pro owns a list of modules The list is initially empty and you can add as many modules as necessary to it To open the list select the menu command File Modules or click the Modules button in the Program bar The Modules window displays the list of modules that are currently linked to the program The lines in the list may appear in either the default color normally black or in a strong color normally bold black or in an error color red The normal color represents an existing module that is not open in the editor The strong color represents an open module see Open Modules above and Opening and Closing Modules below The error color represents a module that either doesn t exist or is not a valid Numerit program Opening a module that doesn t exist creates a new module of the specified name after confirmation Adding and Removing Modules To add a module to the list select an empty line in the list and click the top Browse button next to the File field This opens a window that allows you to select a Numerit program remember that any Numerit program may serve as a module or a Numerit compiled library You must point to an empty line in the list when you add a module To insert an empty line above the current line click the button Insert To
165. logs to customize the graph This includes the scales the titles the axes the tick marks the tick labels the grids and the legend The Trace dialog is used for editing each individual trace The other dialogs refer to the whole graph Note that in these dialogs there are two small buttons labeled All next to the standard OK and Cancel buttons Clicking such a button accepts or cancels the current setting and closes all the dialogs The OK and Cancel button themselves return you back to the previous level the main dialog so you can continue with other settings Trace Each graph trace in a Graph Viewer may be customized by pointing to its line in the graph edit dialog and clicking the button Trace This opens a dialog where various properties may be specified Trace Type Line Step or Bar In the Line type points are connected with straight lines In the Step type points are connected with steps namely a vertical line is drawn from the point to the Y position of the next point and a horizontal line is then drawn from this position to the next point In the Bar type a bar is drawn on each point to the height that represents the Y value The width of the bars is determined by the system according to the graph width the number of bars and the number of bar traces Bars are drawn from the bottom axis Normally the bottom axis is at the minimum Y value and the bars are drawn upward If the axis position is not at the minimum may be set by th
166. luated the program is busy and does not respond to external events This means that the other programs are temporarily put on hold and that user action is not processed Normally a single evaluation takes a very short time so this effect is not noticed however if the expression contains a call to a user defined function and this function takes a long time to complete it looks like the program is stuck To interrupt the process in such a case press Esc Arrays Arrays are variables that have dimensions An array may have up to 8 dimensions and may be of type Numeric String or Boolean Array definition An array is defined using the following syntax thy AN EA Where x is the array s name m n the number of elements in each dimension and v the initial value that is set to all the array s elements The type of v defines the type of the array For example the instruction 37351 1 defines x as a 2 dimensional 3x3 Real array with all its elements set to 1 the instruction zZ 2 2 2 0 01 defines z as a 3 dimensional 2x2x2 Complex array with all its elements set to 0 and the instruction Siig defines s as a 1 dimensional String array with 7 empty strings If the array already exists the array definition instruction redefines it with the newly specified size and initialization Another way to define an array is to assign a value to its last element assuming it s not defined yet For example if x is not defined than x 10 10 10 0 defines
167. m bar Show Hide the Document bar Show Hide the Status bar Resize panes automatically when changing the active pane Ignore compiler warnings and notices Show Hide the Ruler in the current document Show Hide the top bottom margins in the current document Show the whole page of the current document Show special characters spaces tabs etc Update fields figure numbers equation numbers etc Set the measurement units inch cm Cascade Program windows on the desktop Tile Program windows on the desktop Minimize all Program windows Arrange icons of minimized windows Split the current program horizontally Split the current program vertically Maximize the current pane Toggle between the Editor and the Document panes Select the Input file for editing Select the Extra module for editing Professional Edition Select an open module for editing Select the Report or the Draft for editing Check to show the Report in the Document pane Uncheck to show the Draft Show the Message pane Show contents of online help Search for help on keyword Show version number copyright registration info etc The following menus appear when editing the document Insert Viewer F11 Field F12 Figure caption Table caption Reference caption Equation Expression Picture Date Page break Ctrl Enter Line break Shift Enter Insert a Viewer Insert a Field Insert a numbered Figure caption header Insert a numbered Table caption
168. makes it possible to restore the document to its state before each of these operations took place Undone operations may be redone by the menu command Edit Redo Ctrl Shift Z or the Redo button in the Program Bar Thus it is possible to move back and fourth through the operation list New operations are inserted at the current position in the list so operations that were made after this point are lost The size of the operation list may be set with the menu command Options Document The maximum size is 99 operations the default is 25 operations When the list becomes full the oldest operations are pushed out Some editing operations are grouped into one operation in the list For example when deleting successive characters they are all restored at once Before undoing or redoing an operation the cursor position is checked and if it is not where it was when the operation took place it is first moved to that position and only the next undo redo command will actually undo redo the operation Spelling Check To check the spelling of the document use the Tools Document Spelling menu command or the corresponding button in the Document Bar This checks the document from the current position to the end of the document To check the spelling of the word at the current position use the Tools Word Spelling Ctrl W menu command or the corresponding button in the Document Bar If a misspelled word is found a dialog opens and displays the misspelled word w
169. matted Titles below for details The first row in the Table Viewer is normally row 1 which corresponds to the first element of the specified variables However it is possible to start from any other row by specifying its number in the field First row In addition the number of rows in the Table must be specified in the field Number of rows so that the Viewer s size can be determined If the variables that appear in the Table Viewer have already been computed it is possible to find the maximum number of rows by clicking the button Calculate next to the Number of rows field Note that a Table Viewer is a single object and as such cannot be split between pages If you need to display a long table you must change the page height accordingly menu command Format Page The other controls in the dialog are the numeric format which is specified for each column the font the border the background the shadow and the grids For details on the numeric format see the section Variable Viewer Graph Viewer The Graph Viewer displays up to 16 traces inside the same frame each corresponding to one or two program variables Inserting a new Viewer or double clicking an existing one opens a dialog the graph edit dialog in which the variables names are specified in addition to other parameters that define the appearance of the graph Traces Table The traces are specified in a four column table Each line of this table represents one trace The first colu
170. maximum of the two Missing elements in the shorter array are considered to be zeros These virtual zeros behave like true zeros so that a division by such an array for example will generate a division by zero error Minimum and maximum index The first index in each dimension is by default 1 It can be set to another value by the command firstindex for example the instruction firstindex 0 will set the first index to 0 from now on The maximum index is shifted by the same amount The maximum number of elements that may be specified in each dimension is about 500 000 000 but in reality the amount of 36 free memory limits the size of arrays A 2 dimensional array of 1000010000 elements for examples requires about 800 MB of free memory Note that when all the physical memory of the computer is used up the system allocates more space from the virtual memory taken from the disk so working with very large arrays might degrade the performance significantly Sub Arrays Array elements are accessed with indices A simple index like x 2 1 3 extracts one element a scalar from an array However it is possible to extract sub arrays from a given array by using indices that are themselves 1 dimensional arrays For example the following code x 10 20 30 40 50 60 70 80 90 100 i 2 5 8 y x i defines y as a l dimensional array with elements 20 50 80 The index may also be specified by using a range directly must appear inside parenthese
171. me as its name in the library Note that if name or actual variable name is not found in the library Numerit will look for it using the name preceded by an underscore since many compilers attach an underscore to global names For example if name or actual_ variable name is xglb then Numerit first searches for the variable xg1b and if it is not found Numerit searches for the variable _xglb The type must be one of the following char uchar or unsigned char short ushort or unsigned short int uint or unsigned int float double complex ptr or pointer The first form should be used when you want to read the value of the variable The second form should be used when you want to set the value of the variable The third form should be used when you want to get the address of the variable rather than its value Note that this address has no use in Numerit but might be required by some DLL functions as an argument Such an argument must be specified as type ptr or pointer in the DLL function prototype If you want to both read and set the value of a variable you must use two separate declarations with different name s see example below You can declare more than one DLL variable with a single dvar instruction followed by a block of variable prototypes Examples The following code declares four dvar s dparam flag set _flag and x addr The first is used to read the value of the DLL variable dparam of type double the sec
172. me the program is opened If the input file and the program file are in the same directory the name of the input file is saved without the full path and it is assumed that it resides in the same directory as the program This allows you to move the program and input file from one directory to another or from one computer to another and when the program is opened it can find and open the input file This is especially useful when you write a program with an input file for someone else without knowing in advance where it will be installed Note that when the Input File is displayed in the Editor pane the shortcut key combination Ctrl S is interpreted as a File Save Input File When a file is saved its previous version on the disk if exists is kept as a backup with the character added as the first character of the file name Note that the Input File pane can be used as an ordinary text editor for editing text files So even if you prefer to read data from disk text files rather than directly from the Input File you can still use it to open edit and save these files The Input File also exists in NumRun the package that executes compiled Numerit programs outside the Numerit environment See the section NumRun The Numerit Executor This allows users that run Numerit programs with NumRun to easily modify program input parameters User Defined Functions Functions let you execute the same piece of code many times and with different parameters A f
173. mean of elements of x over the dimension n The returned value has one dimension less than x For example if M is a 2 dimensional array than mean M 1 returns a 1 dimensional array which is the mean of the rows of M while mean M 2 returns a 1 dimensional array which is the mean of the columns of M min Syntax min x Operands x is an expression Description Returns the minimum element of x numtostr Syntax numtostr x Operands x iS an expression Description Converts the value of the numeric expression x to a string and returns the string odd Syntax odd x Operands x is an expression Description Returns true if the expression is an odd integer false otherwise packcomplex Syntax Operands Description packcomplex z packcomplex z x z is a Complex array x is a Real array This function packs a complex array into a real array of twice the length of the complex array where the real and imaginary parts of each complex number are placed in alternate neighboring elements If the array s dimension is greater than 1 only the last dimension is doubled and all the other dimensions are the same The main use of packed arrays is as parameters to DLL functions The first form accepts a complex array and returns the packed array as a real array The second form receives both arrays as arguments where the second argument is the packed array whose type must be Real and whose length must be twice that of the complex array
174. med as regular array operations element by element The kind of the result is inherited from the first operand namely matrix array yields a matrix while array matrix yields an array It is possible to convert an array to a vector or a matrix by explicit declarations For example if v is a 1 dimensional array the statement vector v converts it into a vector Similarly 2 dimensional arrays may be converted to matrices by the command matrix The opposite conversion is also possible namely vectors and matrices may be converted to regular arrays by the command array Several functions are available for doing matrix analysis like Det Inv Trace and Svd Outer operations Outer operations operate on 1 dimensional arrays and produce 2 dimensional arrays The 1 3 element of the result is the outcome of the operation on the i th element of the first operand and the j th element of the second operand Outer operations are defined for the five basic operators addition subtraction multiplication division and power They are specified by putting the corresponding operator inside parenthesis For example if x and y are 1 dimensional arrays of lengths N and M respectively then x y produces an NxM array whose i j elementis x i y j Using an outer operation is much faster than using Numerit s loops to perform the same operation Notes 1 If x and y are defined as vectors the result is a matrix 2 If either x or y isa scalar the outer
175. mn is for the Y variable and the second column is for the X variable The third column may specify an Error variable which defines the size of error bars peak to peak The fourth column is used for a text which will appear as a label in the legend for this trace A legend will be displayed by default if at least one of the legend labels is specified only the traces for which labels are specified will appear in the legend The displayed variables can be either scalars one dimensional or two dimensional A two dimensional array is considered as one trace although all of its rows are drawn If it is specified with a dot followed by a number only the specified row is drawn e g x 2 represents the second row of x When both the Y and the X variables are two dimensional each row of Y is drawn versus the corresponding row of X If they don t have the same number of rows the number of rows in Y is taken and if there are not enough rows in X its last row will be used for the rest of Y s rows The same applies when the Error variable is two dimensional Size The default size of the graph window is 3 x 2 inch It may be changed by specifying the width and the height in the graph edit dialog or by selecting the Viewer with a single click and dragging the borders 19 Style The Style controls allow you to customize the border the background and the shadow of the graph window Customization Dialogs From the graph edit dialog you open other dia
176. n The last dimension is along the row from left to right For example in the 3 dimensional array above the element x 2 4 3 is the third element in the fourth row of the second block with value 243 The number of dimensions of an array is obtained by the built in function dim The length in each dimension is obtained by the built in function Length which for a multidimensional array returns a dimensional array of lengths All the operations and functions are performed on variables of any dimension Operations that involve two variables e g addition or multiplication are done on matching elements in both operands so the operands must have the same number of dimensions and of course the same type There are two exceptions to this rule 1 Scalars may be involved in expressions with arrays of any dimension In such a case the operation is carried out between the scalar and each of the array s elements 2 Outer operations take two 1 dimensional arrays and produce a 2 dimensional array whose elements are combinations of each element of the first operand with each element of the second operand In may cases outer operations may be used instead of two dimensional loops which are much slower The number of dimensions is inherited upon assignment thus assignment of a 3 dimensional array into a 1 dimensional variable redefines it as 3 dimensional When two arrays are involved in an operation the length in each dimension of the result is the
177. n the following way 10 20 30 40 50 11 31 41 51 32 42 52 We may define 4 variables p q r s where p is a 1 dim array with 2 elements q isa scalar r isa 3x2 2 dim array and s is a 1 dim array with 3 elements After the read p contains the first column i e 10 11 q is 20 r contains the next two columns and s contains the last column i e 50 51 52 When reading numeric data from a text file any character or group of characters may be used as a delimiter between the numbers except the characters minus plus and refresh dot which must be part of a number Strings should be separated by spaces use readln to read a whole line including spaces as a single string Note It s the user s responsibility to make sure that data is read from the file in the same way it was written to it namely that the file is indeed a text file and that the variables are of the right type and size Syntax Description repeat refresh Refreshes Viewers When the program encounters the command refresh it scans the documents the Draft and the Report looking for Viewers that need refreshing A Viewer is refreshed 1 e updated and redrawn if at least one of the variables that it displays has been changed since the last refresh Viewers are automatically checked for refresh when the program pauses or stops However during the run they are not checked even if the variables they display get new values this check is a time consuming oper
178. nates when the relative error of two successive iterations is smaller than some tolerance The tolerance may be specified in the fourth argument If not specified it is taken as 10 For example assuming that the variables a b c x y are known z defint a 2 b sin S c x y calculates the integral of the expression from x to y where represents the integration variable The expression used as the integrand can be just a function call for example z defint fun x y where fun x is any Numerit function built in or user s deriv Syntax deriv exp x Operands exp isa formal expression of one variable x is an expression Description Returns the derivative of the expression exp at x exp has one dummy variable over which the differentiation is done It is represented by the dollar character For example assuming that the variables a b c x are known z deriv a 2 b sin c x calculates the derivative of the expression at x with respect to The derived expression can be just a function call for example y deriv fun x where fun x is any Numerit function built in or user s det Syntax det x Operands x is a square matrix Description Returns the determinant of the matrix x dim Syntax dim x Operands x is an expression Description Returns the number of dimensions of x eof Syntax eof f eof input Operands f isa file Description Returns true if the end of file has b
179. ncluding other templates Each block has a baseline which determines the vertical position of items in it The insertion cursor has a small horizontal bar which shows the position of the active block s baseline Scale The equation scale is determined by the base size whose value is specified in points in the Format dialog page By default the base size is taken from the current font size in the document where the equation is inserted and this is the normal size of characters and symbols in the equation In many templates some of the blocks have smaller size e g limits in an integral When the base size is changed all other sizes are scaled accordingly so as to keep the same proportions in the equation Note that changing the view scale does not affect the actual size of the equation so in order to obtain an enlarged equation for presentation purposes for example one must set a new value to the equation s base size this can be easily done by selecting the equation in the document and setting the font size Movement To move from one block to another click with the mouse on the required block or move the insertion point with the keyboard s arrow keys While you move between blocks the Equation Editor surrounds the currently active block with a gray frame to make it clear to which block you are currently inserting items Display refresh The equation display pane is refreshed constantly while you insert new items It is also possible however t
180. never one of the Editor or the Document panes becomes active and it is smaller than the other the two panes swap sizes so that the active pane takes the larger size This makes 1t easy to work with the Editor and the Document panes without the need for manual resizing It is possible to disable panes auto sizing by unchecking the menu item Options Panes Auto Size The pane sizes are saved with the program and are restored when the program is loaded from disk Printing programs and documents To print the program s code or the document use the menu command File Print or the Print button in the Program Bar This opens a dialog for entering the print specifications The program s code is printed when the Editor pane is the active pane The document is printed when the Document pane is the active pane The menu command File Printer Setup opens a dialog for selecting a specific printer from a list of currently installed printers The button Properties in the dialog opens a dialog usually supplied by the printer s vendor for changing the settings of the selected printer 10 Chapter 3 The Editor Introduction The program is written and edited in the Editor pane by Numerit s program editor The editor was especially designed to help you edit and debug your program In Numerit Pro the Editor pane is used for editing the Main module as well as other modules of the program To edit a module open the Modules dialog menu command File Modules or the Modules
181. ng back to the Message pane use the menu commands Run Next Error Ctrl Shift gt and Run Previous Error Ctrl Shift lt Pressing F1 inside the Message pane displays a help topic for the currently highlighted error or warning Compilation messages are issued when the program is compiled There are three types An Error is issued when the compiler detects an error that does not allow the program to run Such an error must be corrected before that program may run A Warning is issued when the compiler detects a situation that is most likely but not necessarily an error Such a situation involves in most cases variable s dimensions which may be modified at run time So for example when the compiler detects that a 2 dimensional array is used where a 1 dimensional array is expected it cannot be sure that this is actually an error Another situation is when the compiler detects that a variable is used in an expression before it has been assigned a value In this case it cannot be sure if at run time the variable will not be initialized by a call to a function When warning are issued the program may still run but if these warnings are actually errors which is most likely the program will stop due to execution errors A Notice alerts you to a possible programming error and is issued when a variable or a function parameter is defined but is never used in the program A notice has no effect on the program Execution errors are issue
182. ng the window to the left or to the right when the displayed data is too wide to fit the window mainly long strings Note that when displaying a multidimensional array scrolling to the left or to the right will not display different columns of the array but rather shift the currently displayed list so as to fully view its data if it s wider than the window To see different columns you should select the appropriate indices in the index fields under the Index title For example if you inspect a 2 dimensional array M you see two index fields that allow you to select the index of the first element in the list By default the first element is M 1 1 and the list shows the first column because the first dimension is selected in the Dim radio buttons and this dimension is along the rows of the array from the top row downward To display the next column increase the index in the second index field This will start the list from M 1 2 which is the first element of the second column Increasing the second index field to 3 will start from element M 1 3 and display the third column and so on To see the rows you should follow a similar procedure but select the second dimension for viewing in the Dim radio buttons Then increasing the first index will display each row in turn The Inspector runs in the background and may remain open while the program is running It may also remain open when you change the name of inspected variable This is done by either
183. not very recommended from a programming style point of view but may be more convenient and more efficient when you want to modify many variables by a function or when there are many functions that should receive the same variables as arguments Global variables are not accessible to different modules of the same program To share variables between modules use the command common Calling a function from another function All the functions that are defined inside the same program may call each other In Numerit Pro it is also possible to call functions that are defined in other programs See the section Modules in Chapter 7 41 Functions may call themselves directly or indirectly This process is called recursion Recursive functions must contain a proper termination to avoid an infinite loop The use of recursive calls should be done with care If not terminated correctly the repeated call to the same function will exhaust system resources especially the memory A proper termination is a conditional statement that skips the recursive call You must ensure that the condition is indeed satisfied some time Recursion may be direct function calls itself directly or indirect function A calls function B which calls function A Function rerouting In many situations it is desirable to allow reassignment of functions at runtime Consider for example the following case you have a function Client that performs a certain operation and needs the s
184. ns unless one is a scalar Expecting a scalar n An n dimensional expression is detected where a scalar is expected Expressions in Range definition cannot have dimensions When defining a range all the parameters must be scalars but one of the specified parameters seems to be an array FFT IFFT Shifft Argument should be an array The argument of the functions FFT x IFFT x FFTS x IFFTS x Shifft x Transform Shift of x over all the dimensions should be an array FFT IFFT Shifft First argument should be an array The first argument of the functions FFT x n IFFT x n FFTS x n IFFTS x n Shifft x n Transform Shift of x over dimension n should be an array FFT IFFT Shifft Second argument should be a scalar The second argument of the functions FFT x n IFFT x n FFTS x n IFFTS x n Shifft x n Transform Shift of x over dimension n should be an integer scalar FitBasis Basis must be 2 dimensional n The basis sent to the function FitBasis should be represented by a 2 dimensional array but an n dimensional expression was detected Integ Argument must be 1 dimensional n The second argument of the function Integ which specifies the array where the integral is evaluated must be 1 dimensional but an n dimensional expression was detected Interp Linterp Wrong dimensions in arguments n1 n2 n3 The arguments of the function Interp or Linterp must have matching dimensions It looks like name
185. nsidered to be the Main module The modules that are listed in its modules list are the submodules A submodule is itself a Numerit program and as such may have submodules of its own A submodule of a submodule is not accessible to the Main module but it may also be declared as a submodule of the Main module if necessary Numerit makes sure that only one copy of this submodule is actually loaded 57 Compiled Library As mentioned above a submodule is an ordinary Numerit program whose functions are made available to the main program Normally a program that serves as a submodule is added to the modules list with its source namely the program itself num is specified in the list In some cases it might be desired to add a compiled version of the program to the list This allows for example to develop a library of functions and distribute it to Numerit users without providing the source code To create a compiled version of a program use the menu command File Create Library The resulted file with the default extension nlb includes only the compiled code of the program without the source code or the Report Note do not confuse between compiled libraries and Numerit executables Executables are also compiled programs but are intended to be run by NumRun see NumRun The Numerit Executor Numerit compiled libraries can only be used by Numerit Pro Linking When a function is called by an instruction in the Main module either in the body o
186. nsional Real expression tol isa number Returns the integral of the expression exp at x exp has one dummy variable over which the integration is done It is represented by the dollar character x must be a 1 dimensional array The 1 th element of the result is the integral of the expression from the first element of x to x i The integral is calculated by an iterative process adaptive Simpson s rule which terminates when the relative error of two successive iterations is smaller than some tolerance The tolerance may be specified in the third argument If not specified it is taken as 107 For example assuming that the variables a b c are defined constants y integ a 2 b sin c x calculates the integral of the expression at x where represents the integration variable The expression used as the integrand can be just a function call for example y integ fun x where fun x is any Numerit function built in or user s interp y x XX y X and xx are Real expressions y and x are l dimensional Returns the cubic splines interpolation of y x at xx y and x are l dimensional arrays of the same length All the arguments must be Real x should be monotonic increasing or decreasing Boundary conditions are set with zero second derivative inv Syntax inv x Operands x is a square matrix Description Returns the inverse of the matrix x length Syntax length x Operands x is
187. nted by the dollar character x is the initial guess from which the search starts If the expression has several zeros the returned value is usually but not necessarily the closest to the initial x x must be real but may have any dimension When x is multidimensional zero returns an array of the same dimension as x Whose elements are the zeros that were obtained by taking the corresponding elements in x as initial guesses A tolerance may be specified as a third argument If not specified it is taken as 10 For example the following x 0 3 z zero S 2 3 2 x defines z asa 1 dimensional array with two elements 1 and 2 which are zeros of the given expression obtained by taking 0 and 3 as initial guesses The expression can be just a function call for example y zero fun x where fun x is any Numerit function built in or user s Chapter 14 Reference to Numerit s commands array Syntax array x array y x Operands x is a vector or a matrix Description Converts x into an array The first form changes the kind of x itself while the second form defines a new variable y and copies the content of x into it beep Syntax beep Description Generates a beep binfile Syntax binfile f s or binfile f s Operands f is an identifier s isa string Description Defines f asa binary file the string s specifies the file name For example binfile f c bin dat bitmap Syntax bitmap s Operands
188. ntering into functions Shift F7 Maximize the current pane in the current Program window F8 Step Over execute current line without entering to functions Shift F8 Split the current Program window vertically F9 Run or resume running of the current program Ctrl F9 Compile Make the current program 75 Press Shift F9 F10 F11 F12 Ctrl Ctrl Ctrl Ctrl Ctrl gt Ctrl lt Ctrl Shiftt gt Ctrl Shiftt lt Enter Shift Enter Ctrl Enter Tab Ctrl Tab Shift Tab Ctrl Shift Spacebar Back Space Delete Insert Home Ctrl Home End Ctrl End Page Up Ctrl Page Up Page Down Ctrl Page Down Up Arrow Ctrl Up Arrow Down Arrow Ctrl Down Arrow Left Arrow Ctrl Left Arrow Right Arrow Ctrl Right Arrow 76 To Split the current Program window horizontally Make the menu bar active Insert a Viewer in the current document Invoke a right mouse button operation Increase the font size in the Document Decrease the font size in the Document Insert a block around the selected text or insert an empty block if not text is selected in the Editor or Set subscript text in the Document Set superscript text in the Document Move inspection position to the calling function Move inspection position to the called function Find the next error in the Editor Find the previous error in the Editor Start a new line in the Editor or Start a new paragraph in the Document Move to the beginning of the next l
189. o refresh the display without inserting items by pressing the Esc key though this is normally not needed 27 Modes Usually you will edit the equation in the Math mode In this mode the Equation Editor automatically defines the appropriate font for each item and controls its position If you want to insert a normal text or a character of a specific font you may change to the Text mode Spacing The Equation Editor spaces the items as necessary while you insert them However you may insert spaces of different sizes from the Spaces dialog page You may also insert a tab when you want to ensure alignment of the text to a specific position See Section Spaces below for more details Selection To copy equation items to the clipboard or to modify their attributes they must be selected Items are selected by either pressing the mouse button and dragging or by holding down the Shift key and pressing one of the arrow keys It is not possible to move out of the active block when selecting items To select a whole block double click inside it To select the whole equation double click anywhere in the area outside the blocks or press Ctrl A Action Buttons The Equation Editor s control panel contains buttons that are used for performing various editing actions At the upper left corner of the panel there are two shift controls and underneath them three rows of buttons Shift controls The items in the equation are automatically positioned while
190. o return a value has terminated without returning a value Variable capacity exceeded Arrays are limited in the number of elements that they may have in each dimension This error indicates that too many elements have been defined in one dimension Execution Errors Codes Numeric overflow Division by zero Not converging Numeric error Argument must be monotonic increasing or decreasing Complex is illegal Degree must be an integer smaller than the number of data points Dimension error 9 End of file 10 File Open error 11 File Position error 12 File Read error 13 File Write error 14 Index not integer 15 Index out of range 16 Kind error 17 Length is not a power of 2 18 Length mismatch 19 Matrix must be square 20 Must be positive 21 Negative value not allowed 22 Non integer order 23 Output error 24 Singular matrix 25 Type error 26 Undefined variable 27 Function didn t return a value 28 Variable capacity exceeded 29 Array is empty 30 Path not found 31 Must be integer CANN un 74 Chapter 9 Keyboard and Mouse Keyboard Shortcuts Press To Ctrl A Select All Ctrl B Set Bold text in the Document Ctrl C Copy the selected text to the clipboard Ctrl D Toggle the Document pane between the Report and the Draft Ctrl E Center a paragraph in the Document Ctrl F Find text Ctrl Shift F Fold Unfold a block in the Editor Ctrl G Set Greek font in the Document Ctrl H Search and Replace text Ctrl S
191. o the specified values by adding or removing rows and columns Note that when removing rows the last row and the last column are removed first and when expanding the array rows and columns are added at the bottom and on the right side respectively The third templates row includes various types of sums products and labeled arrows The last two rows includes various types of integrals Symbols Symbols are inserted from the Symbols dialog page of the Equation Editor s control panel To insert a symbol at the current position in the equation click on it with the mouse Symbols may have any font size and also Italic and Bold attributes When a symbol is inserted its size and attributes are determined by the current setting in the Format dialog page To change a symbol s size or attribute after insertion select it and change the size or the attribute in the Format dialog page 29 Greek Letters Greek letters may be inserted in two ways 1 Click the Greek button in the Equation Editor s control panel or Ctrl G When this button is pressed Greek letters are typed with the keyboard Releasing the button restores the keyboard to English 2 Insert Greek letters from the Greek dialog page in the Equation Editor s control panel Greek letters may have any font size and also Italic and Bold attributes When a Greek letter is inserted its size and attributes are determined by the current setting in the Format dialog page To change the size or attri
192. of the flags can be reset individually by putting a minus sign in front of it e g to reset the fixed flag write outformat fixed To set more than one flag you need to call outformat once for each flag for example outformat fixed outformat left The default format is auto In this setting numbers are printed according to their value and the current precision and are adjusted to the right of the output field Note that the exact form of the displayed numbers depends on the setting of outprec see outprec below for more details Some examples the following code a 1234 56789 outw 10 outp 4 outf fixed println a outf sci println a outf auto println a will produce 1234 5679 outprec outp 1 2346e 03 1235 See more examples in the description of outprec Syntax Operands Description outprec n or outp n n isa number Sets the precision of numbers when writing formatted data to a file or to the Draft The interpretation of n depends on the current setting of outformat The default value of n is 4 When outformat is not set or is set to auto n defines the number of significant digits that are displayed If the displayed number is equal to or greater than 10 it will be displayed in exponential format For example With outprec 4 T will be written as 3 142 10 7 will be written as 31 42 12345 will be written as 1 234e 04 With outprec 6 T will be written as 3 14159 10m will
193. ollowing Numerit function func RGB r g b 65536 round r 256 round g round b where r g and b are the basic color arrays Note that the functions red green blue and RGB are not internal functions of Numerit and you must define them as Numerit functions if you want to use them see the sample program image rgb num Orientation The Orientation field has four options 0 90 180 and 270 The image is rotated clockwise by the specified value The scales are rotated with the image so if at the default orientation 0 the horizontal scale is defined by the variable in the X field from left to right and the vertical scale by the variable in the Y field from bottom to top in a 90 orientation the vertical 22 scale is defined by X from top to bottom and the horizontal scale by Y from left to right note however that the tick labels are still drawn as specified in the Labels dialog which by default is on the left and bottom axes see below Below the Orientation field there are two check boxes Flip Horizontal and Flip Vertical that allow flipping of the image in the horizontal and the vertical directions The scales are also flipped Zoom and Window Size The Zoom field inside the Window Size frame allows you to set a magnification factor for the image When you select this factor you can see the actual size of the window in pixels and in inches or cm Initially Numerit sets a zoom value so as to g
194. omments are all displayed in different colors You can set these colors by using the menu command Options Editor Language keywords may also be displayed in bold face to make them more distinguishable 11 Comments Comments may be inserted anywhere in the code and are ignored when the program runs A comment starts with the comment character and is terminated either at the end of the line or by a second comment character on the same line Thus several comments may appear on the same line each enclosed between two comment characters Since the end of line is considered to be a closing comment character the number of comment characters in a line may be odd and the last comment is terminated at the end of line To convert all the text from some point to the end of the line into a comment regardless of the comment characters that appear after this point insert two successive comment characters This ensures that everything from that point to the end of the line is a comment This is useful while debugging the program to comment out a line of code or a portion of it even when it includes comments inserting a single comment character will start a comment that will be terminated by the next comment character in the line and will not comment out the whole text that follows it To enter a multiline comment put it in a block and comment the whole block A whole block is commented by putting the comment character in front of it The block goes
195. ond and third are used to read and set the value of the same DLL variable nlib control_word of type int and the fourth returns the address of the DLL variable x_ global 115 dvar double dparam dvar int flag nlib control word dvar set_flag int nlib control word dvar amp x addr x global The following code reads the value of the DLL variable dparam and puts it in the Numerit variable dp dp dparam The following code reads the value of the variable nlib control word c flag and the following code sets its value to 7 set _flag 7 The following code reads the address of the DLL variable x_ global xa x addr else Syntax else Description May appear at the end of if where or case statements It is followed by statements that are executed if no condition was satisfied file Syntax file f sor file f s Operands f is an identifier s isa string Description Defines f asa text file the string s specifies the file name For example file f c txt dat fopendlg Syntax fopendlg t fn ft Operands t and fn are strings ft is a string array with two columns and any number of rows Description Opens a dialog box that allows the user to specify a file for opening The user can select a 116 disk drive a directory path and a file name The returned value is a String that contains the selected file name including the full path The parameter t specifies the title of the dialog box The paramet
196. operation is interpreted as the corresponding standard operation Strings In Numerit a string is a variable of type String it is not an array of characters As with any other variable you can define an array of strings of any dimension Strings may be concatenated by the operators amp and amp In addition Numerit provides various functions for manipulating strings These functions also accept an array of strings as an argument strlower s or strlow s Returns a version of the string where all upper case characters have been replaced with lower case characters strupper s or strupp s Returns a version of the string where all lower case characters have been replaced with upper case characters strlen s Returns the length of the string strlen s n Sets the length of the string s to n expands or shrinks as necessary strpos s t Returns the position of the substring t in the string s The position of the first character in s is O If the substring is not found in s the returned value is 1 strsub s p n or substr s p n Returns a substring of s with length n starting at position p The position of the first character in s is 0 If the third parameter n is omitted the substring from position p to the end of the string is returned strdel s p n Deletes n characters of s starting at position p The position of the first character in s is 0 If the third parameter n is omitted the characters from position p to t
197. or example func foo a x y a x 2 return y A function s name may be any valid identifier and the parameter list consists of identifiers that are separated by commas See section User Defined Functions in Chapter 6 for more details goto Syntax goto label Description Transfers the execution point to a labeled line whose label is specified graph Syntax graph yl xl el tl y2 x2 e2 t2 Operands y1 y2 are scalars or 1 dim expressions 118 x1 x2 are optional scalars or 1 dim expressions el e2 are optional scalars or 1 dim expressions t1 t2 are optional strings Description hideerror Syntax Description Inserts a graph at the current position in the Draft Each group of four arguments y x e t represents a trace in the graph Up to 16 traces may be specified for the same graph The first argument in each group y is drawn vs the second argument x the third argument e represents sizes of error bars the fourth argument t is a legend label for the trace Except for the first argument in each trace y any of the other arguments may be omitted When an argument is omitted and there are no more arguments in the group the colons that follows it may also be omitted When the x argument is not specified the index of the y argument is used instead Some valid forms of graph graph yl y2 draws y1 and y2 vs the index graph yl x y2 x draws yl and y2 vs x graph yl x1 tracel y2 x2 trace2 draws y
198. or binfile statements will be opened in this directory Syntax Operands Description do dlls s isa string Declares the dynamic link library DLL where the succeeding DLL functions and DLL variables are searched for For example dll my dl1 dfunc void set int n double x dfunc double sqr double x dvar double x glb dll other dll dfunc int mode dvar int flag dvar param int The library my dll will be searched for the functions set sqr and the variable x_glb while the library other dll will be searched for the function mode and the variables flag and param The string s may specify the full path of the DLL e g dll c lib my dl1 or only its name namely dll my dl1 In the first case Numerit will look for the DLL only in the given directory In the second case it will look for it in the following directories in the given sequence 1 The Numerit directory where Numerit was installed 2 The current Numerit program directory 3 The 32 bit Windows system directory e g c windows system372 4 The Windows directory e g c windows 5 The directories that are listed in the PATH environment variable Syntax Description downto do An optional do may appear after the condition of a while until or for loops to separate between the condition and the statement s that follow it The do is redundant and is actually ignored by the compiler Syntax Des
199. or has all the tools and features you expect from an advanced scientific word processor It has a built in equation editor It automatically numbers figure captions table captions equations and references and also updates all references to these numbers in the document It lets you insert graphs and tables that are directly linked to your program s variables and automatically refreshes them each time you run the program The program s output document may be saved as an RTF file which allows you to continue the editing in your favorite word processor e g Microsoft Word Numerit s high level programming language is easy to learn powerful and versatile It supports multidimensional arrays up to eight dimensions complex numbers and user defined functions It has many built in functions for data analysis including line and polynomial fitting linear and cubic splines interpolation multidimensional fast Fourier transform numerical integration and differentiation root finding solution of linear algebraic equations matrix vector arithmetic special functions gamma erf Bessel and more Numerit s Editions Numerit is currently offered in two editions the Standard Edition and the Professional Edition Numerit Pro Numerit Pro allows linking of several Numerit programs modules into a single program In the Standard Edition a program may have only one module Numerit Pro lets you build libraries of reusable functions once a library is comp
200. or removed so a number field that refers to a specific equation will always refer to the same equation Fields A field is a code that is inserted in the document and displays a number that is related to some other object in the document There are five types of fields Figure number Table number Reference number Equation number and Page number All are inserted through the menu command Insert Field F11 In the text we refer many times to figure numbers table numbers reference numbers and equation numbers e g See Fig 3 or In Eq 5 etc Instead of writing these numbers as normal text it is possible to insert a field as a place holder for entering the number The inserted field is automatically linked to the figure caption the table caption the reference caption or the equation whose number is entered When captions or equations are inserted removed or moved their number is automatically updated according to their new position in the document and following this all the fields that refer to them are also automatically updated For example suppose we refer to Figure 3 in different places in the text and another figure actually a figure caption is inserted before it The caption header Figure 3 will first be converted to Figure 4 caption renumbering and then all 17 references to Figure 3 in the text will be converted to references to Figure 4 field update All the higher numbers will be also updated accor
201. ors may also be handled by the program which can trap the error check it and decide how to proceed This is done with the help of three commands HideError ShowError ResetError and the system variable errval See more details and an example in the description of the command HideError in Chapter 14 Reference to Numerit s commands See the chapter Errors and Warnings for a complete list of execution errors When the menu item Options Panes Auto size is set the Document pane becomes active whenever the program is executed in order to make it larger for displaying the output This does not happen when panes auto sizing is not enabled or while stepping through the program If the program sends output to the Draft by print graph etc and the Report has no viewers in it the Draft is brought into the Document pane to display the output If the Report has viewers in it it is not replaced by the Draft Modules In Numerit Pro you can link external modules to a program When program A is declared as a module of program B all the functions of A are available to B This makes it possible to create programs that serve as libraries of reusable functions Every program in Numerit Pro has a list of modules attached to it This list which is initially empty is opened by the menu command File Modules or by clicking the Modules button in the Program bar See Modules List for details about the list and how to edit it The code of the program itself is co
202. ort and the Draft that display the program s output Several programs may be open at the same time and run concurrently The program s code consists of a main body and functions When the program is running the instructions in the main body are executed in order Functions are declared by the function statement Instructions in the main body and in functions may call any function that is defined inside the program In the Standard Edition of Numerit a program can only call functions that are defined inside the program itself In Numerit Pro on the other hand it is possible to call functions of other programs as well See the section Modules in Chapter 7 for details The program s code is normally written one statement a line The end of line terminates the statement but it is possible to continue a long statement into the next line by putting a backslash at the end of line It is also possible to put several statements on the same line and separate them by a semicolon Lines may be labeled Labels allow to jump from one statement to another using the goto command Too many goto statements and labeled lines tend to complicate the program but in some cases the use of a goto is better than other alternatives and even simplifies the code A labeled line consists of a label name or number followed by a colon and the instructions for example L1 x 10 L2 y 20 x y 45 x 25 Saving the program The menu command File Save or the Sa
203. ort s content remains unchanged and only the embedded objects are updated with new values The Report and the Draft are both edited in the Document pane The Document pane is actually a word processor with all the standard features plus special features that were especially designed for technical reports To print the Document s content use the File Print menu command or click the Print button in the Program Bar when the Document pane is active This will print the Report or the Draft whichever is currently displayed in the Document pane The Report The Report is brought into the Document pane by either selecting the Report tab at the bottom of the Document pane or by checking the Report Draft item in the Window menu or clicking the Report Draft button in the Program Bar Various objects 1 e graphs tables pictures equations may be inserted into the Report by commands in the Insert menu Output objects like graphs and tables are linked to the program s code and display the value of the program s variables These objects are called Viewers Viewers are updated whenever the program pauses stops or reaches a refresh instruction The report is an integral part of the program It is saved on disk and is loaded from the disk together with the program The report may also be saved as a separate document by the menu command File Save Report As In this case its is saved as a file of type rep Numerit automatically identifies this file as a document
204. ow the whole page in the window EE Insert an equation at the current position Ctrl Q co co cc EE Open a character map for the current font Check spelling of the document from the current position Check spelling of the word at the current position Ctrl W BE The Document Bar may be hidden by unchecking the item View Document bar in the Options menu The Status Bar The status bar is used for displaying information about the current status of the program It is located at the bottom of the Desktop and is divided into five fields Editor 3 4 Insert Modified Running The first field at the left shows the current position in the program Editor Report etc The second field shows the position in the Editor line no column no or the Document page no number of pages whichever is currently active The third field shows the current Insert mode Insert Overwrite The fourth field shows the Modified state When the item Modified appears in the status bar it means that the text in the currently active pane i e the program s code in the Editor pane or the report or the draft in the Document pane has been modified since the last save The last field shows the Run state Running Pause etc When the cursor is pointing to a menu command or to a button in one of the tool bars the status bar displays a help message for that command The status bar may be hidden by unchecking the item View Stat
205. pause the program and display the error message In the following code we disable automatic error handling before computing the integral and check the error code right after 1t If there is no error errval is 0 or if the error is other than Not converging we go directly to the command showerror which resumes automatic error handling and generates an error message if the value is nonzero If the error code is 3 we reset it to 0 reseterror increase the tolerance and try again If the second attempt also fails the error code is again 3 and will be displayed when automatic error handling is resumed x 0 10 tol le 9 HideError y integ sin x tol if errval 3 ResetError tol le 6 y integ sin x tol ShowError 119 if Syntax if Condition then Statements if Condition then Statements else Statements Description Used for a conditional execution of statements In the first form the statements are executed if the condition is true In the second form the first group of statements is executed if the condition is true otherwise the second group that follows the else is executed The keyword then may follow the condition but it is redundant The condition is a Boolean expression with no dimensions scalar If there is only one statement to execute it may appear on the same line right after the condition for example ifa gt b a b else a b If there are several statements to execute they must be put in a blo
206. pression Description The first form converts the 2 dimensional array x to a matrix by changing its kind The second form defines y as a matrix and copies the content of the 2 dimensional array x into it The third form defines an mxn matrix y and initializes its elements to the value v menu Syntax menu i j S Operands i and j are integers s is a string array Description Opens a menu box that presents to the user a list of options When the user clicks one of the options the menu is closed and the number of the option is returned If the user clicks outside the menu box the returned value is 0 i and j specify the position in pixels of the menu box relative to the top left corner of the program window s is an array of strings that specifies the options presented to the user For example s Monday Tuesday Wednesday Thursday Friday n menu 10 10 s message Syntax message t s Operands t and s are strings Description Opens a message window where the string t is the window s title and the string s is the message text The user must click the OK button to continue program execution next Syntax next next n Operands n is a number Description Used for jumping directly to the next loop round The second form is followed by a number which specifies how many nested loops not rounds should be skipped For example n length b i 0 loop i 1 if i gt n break if b i lt 0 next ali sqrt b i end th
207. r in one of the functions and this function is not found in the program s code Numerit looks for the function in the modules that appear in the program s list of modules The search is conducted from top to bottom until the function is found This process is called Linking and is carried out before the program is executed It is redone whenever the Main module or one of the submodules is modified If a function is not found in any module an error is issued and the program cannot run Making Before external functions are linked to the Main module Numerit verifies that all the submodules in all levels are compiled If it finds an uncompiled module it opens it and compiles it note that from now on until the module is closed Numerit will use the open version of it rather than its disk version see Open Modules below After compiling all the modules that need compilation Numerit links the external functions in each module and the program is ready to run This process of compiling and linking is called Making It is possible to Make a program without running it using the menu command Run Make Ctrl F9 If during the compilation Numerit finds errors in a module it brings it into the Editor and lists the errors in the Message pane You can correct the errors and try to run the program again Numerit will use the corrected version of the module rather than its disk version so you don t have to save the module after the modifications see Open Modules below
208. r scalar An index item cannot be n dimensional In an index each item can be either a scalar or a 1 dimensional expression but a higher dimension n was detected For example in x 1 3 i and j must be either scalars or 1 dimensional arrays BessX Order must be a scalar The first argument of a Bessel function is the order and should be an integer scalar Defint Arguments must have the same dimension n1 n2 The arguments that define the limits in the function Defint should have the same dimensions but seem to have different dimensions n1 n2 Dimension greater than 1 n An n dimensional expression was detected where a 1 dimensional expression was expected 68 Dimension mismatch n1 lt gt n2 An indexed variable whose index defines an item with dimension nl is assigned an expression which seems to be of a different dimension n2 For example if i is a 1 dimensional array then x i y is valid only if y is also a 1 dimensional array Dimension mismatch in comparison n1 lt gt n2 An expression of dimension nl was compared to an expression with a different dimension n2 In comparison operations e g x gt y the operands must have the same dimensions Dimension mismatch in for loop The limits and the step in a for loop may be arrays but if they are they must have the same dimensions Dimension mismatch in operation n1 lt gt n2 Two expressions that are involved in an operation e g x y must have the same dimensio
209. re specified To customize the legend click the button Legend in the graph edit dialog There are two type of legends Vertical and Horizontal In a vertical legend the traces are listed vertically top to bottom In a horizontal legend the traces are listed side by side left to right The legend s style border color font etc and position may also be set The legend may be inside or outside the graph It may be positioned at one of the corners or at the center of one of the sides The position may be fine tuned by specifying a vertical and or horizontal shift in millimeters positive or negative The legend text may be entered as a simple text or as a formatted title see Formatted Titles below for details Image Viewer The Image Viewer displays a two dimensional array as an image By default the value of each element in the array is interpreted as the intensity of the image The array is drawn from left to right and from bottom to top Namely each row of the array is drawn as a raw in the image from left to right where the first row is drawn at the bottom of the image and the last row at the top of the image The maximum value of the array is displayed in white and the minimum value in black The other values are mapped linearly between these two values and are displayed in 256 levels of gray The user can control many of the default properties of the Image Viewer Inserting a new Viewer or double clicking an existing one opens a dialo
210. real array The first form accepts a real array and returns the complex array The second form receives both arrays as arguments where the second argument is the complex array whose length must be half that of the real array this form may be used if the function is called many times with the same arrays to save memory allocation of the complex array on each call var Syntax var x var x n Operands x is an expression n is an integer Description The first form returns a scalar as the variance of all the elements in x The variance is defined as 105 zero root Syntax Operands Description 106 N LI X xy where N is the length of x x may have any dimension i l Note that we divide by N rather than N 1 so if you need a variance with a denominator of N 1 you should multiply the result by the appropriate factor The second form returns the variance of elements of x over the dimension n The returned value has one dimension less than x For example if M is a 2 dimensional array than var M 1 returns a 1 dimensional array which is the variance of the rows of M while var M 2 returns a 1 dimensional array which is the variance of the columns of M zero exp x or root exp x zero exp x tol or root exp x tol exp isa formal expression of one variable x is the initial guess tol isa number Returns the zero of the expression exp exp has one dummy variable over which the search for the zero is done It is represe
211. remove a module or an empty line from the list select it and click the button Remove Note that there is always an empty line at the end of the list that is available for adding a new module You can also add a module or change the name of a listed module manually without using the button Browse Just type the file name of the module in the File field and press the Enter key you must press the Enter key after entering or modifying the name otherwise the operation is ignored Submodules List If the added module has submodules of its own you ll see a plus sign preceding its file name in the list Double clicking the line displays the list of submodules double clicking the first line of the submodules list which is marked by two dots and 59 an up arrow returns you to the parent s modules list Note that a submodule s list cannot be modified you must open the module as a program using File Open in order to modify its modules list Module Name and File Name Each module has a name in addition to its filename This name is displayed at the left column of the Modules window A module is known to Numerit only by its name This name is used both in the program code when you want to call a function from a specific module instead of letting Numerit search for it in the list see section Modules above and as a tab title to identify the module when several modules are open When you add a new module to the list Numerit creates a name for it
212. rit as dfunc void set doubles x Note that if you copy the function declaration from a C header file you must change the s to amp s wherever the is used for sending a scalar by reference 47 A real not complex Numerit scalar can be sent as an argument when the expected function type in the C function is char unsigned char short unsigned short int unsigned int float double or a pointer A complex Numerit scalar can be sent as an argument only when the expected C type is complex representing two double values real and imaginary Since the internal representation of variables in Numerit is as double precision floating point numbers Numerit needs to convert the scalar to the expected type before it passes it to the function and then to convert it back if passed by reference after the function returns The conversion is not required with parameters of type double and complex Thus passing a double parameter is more efficient than passing an integer parameter i e char short or int A scalar can also be sent as an argument to a function that expects a one dimensional array see below In such a case the scalar will be sent by reference and will actually be treated as an array with one element An array parameter An array parameter is specified by its type an optional name and square brackets The allowed types are char uchar or unsigned char short ushort or unsigned short int uint or unsigned int
213. rphan lines i e do not allow the first line of a paragraph to be the last line on the page moves the whole paragraph to the next page Paragraph Formatting Paragraph formatting determines the appearance of paragraphs It may be set by the menu command Format Paragraph Some parameters may also be set in the Ruler or by buttons in the Document Bar The dialog fields are Alignment Left Center Right Justified May also be set by buttons in the Document Bar Indentations From left specifies the amount of indentation from the left margin From right specifies the amount of indentation from the right margin First line specifies the amount of indentation of the first line from the left margin May also be set in the Ruler Spacing between paragraphs and line spacing within paragraphs Before specifies the amount of space before the first line of the paragraph After specifies the amount of space after the last line of the paragraph Line spacing specifies the vertical space between lines Tab stops Left aligned Centered Right aligned May also be set in the Ruler and by buttons in the Document Bar Pagination options Keep with next do not insert a page break between the paragraph and the next paragraph and Keep together do not insert a page break inside the paragraph 14 When anew paragraph format is set while text is selected it is applied to all the paragraphs inside the selection otherwise it is app
214. rst program enter the following two lines x O0 10 graph sin x x Press F9 to run Numerit will plot the graph on the Document pane Introduction Chapter 2 The Desktop The Desktop is Numerit s workplace namely the main window which consists of the Menu bar the Tool bars the Status bar and the Program windows Hg Numerit Pro Menu File Edit Search Insert Format Tools Bun Options Window Help Preso Co ce Ea at e raja oae Document Normal 7 Courier New y 10 Jp Eek EEE EH Program lt 1 gt EA Program lt 2 gt println Hello World x pD graph sin x x The Menu Bar Draft Page 1 1 Insert Modified OL 15 x olx Draft The menu bar is located at the top of the Desktop It toggles between two states one is used for program editing and the other is used for document editing The following menus are common to both states Some menu items are applicable only to the program editor and are designated by Editor and some are only applicable to the document and are designated by Document File New Ctrl N Open a new Program Open Ctrl 0 Open a Program or a Document Close Ctrl F4 Close the current Program Close All Close all Programs Save Ctrl S Save the current Program Save As Save the current Program under a new name Save Report As Save the current Program s Report as a Document Save Draft As Save the current Program s Draft as a Doc
215. ructure as the number of a parameter 1 e with the prefix the numbering is done from the beginning of the specific structure and not from the beginning of the parameter list For example in the following declaration dfunc foo func double int double 1 int double 1 double the DLL function foo calls the callback function with two arguments each representing a structure of two members where the first member provides the size of the second array member In both structures we see 1 as the number of parameter that provides the size because the number of parameter is counted from the beginning of each structure In general parameters of a callback function are counted locally inside structures and globally when specified outside a structure The corresponding Numerit callback function in the above case will have four parameters for example func bar m x n y where x and y are arrays whose lengths are m and n respectively In another example we can see how a structure specifying a two dimensional array is sent to a callback function dfunc foo func double int int double 1 2 double The callback function will now receive a structure with two integer scalars and an address of a two dimensional array whose length is given by the two integers The Numerit callback function will look like func bar m n x where x is a two dimensional array whose number of rows given in m and number of columns in n Note that the above
216. s so y x 4 to 7 defines y asa 1 dimensional array with elements 40 50 60 70 If x is a 2 dimensional array then the code x Td K3 217227223 3132733 i 1 2 J Lia y x i j defines y as the following 2 dimensional array 12 13 22723 Here again you can use a range directly so the code y x i 1 to 2 defines y as a 2 dimensional array given by Ta 12 21 22 It is also possible to extract sub arrays with less dimensions For example y x i 1 same index variable for both indices defines y as the 1 dimensional array 11 22 taken from the diagonal of x Or another example if x is the 3 dimensional array that was defined before then the following code y Slay 2 31 where one index is a scalar defines y as a 2 dimensional array given by 122 123 222 223 The opposite assignment is also possible namely z i 2 3 y defines z as a 3 dimensional array in which the elements in the positions specified by i and j are taken from y Or x i i 1 2 setsx 1 1 tol and x 2 2 to2 For such assignments to be valid the effective dimensions of both sub arrays must match It is possible to extract all the elements in a specific dimension by using asterisk as the index for example y x 2 defines y asa 1 dimensional array by extracting all the elements in the second row of x and x 2 3 4 defines x as a 2x2 array with 3 4 in its second column Vectors and Matrices Vectors and matrices are special cases of on
217. s command For example 128 system dir Opens a Windows command window and executes the dir command displays a list of files and sub directories in a directory In order to keep the command window open add amp amp pause to the command for example system dir amp amp pause table Syntax table x1 t1 x2 t2 Operands x1 x2 are scalars or 1 dim expressions t1 t2 are optional strings Description Inserts a table at the current position in the Draft Each group of two arguments x t represents a column in the table Up to 16 columns may be specified for the same table The first argument in each group x is the column s data and the second argument t is a column s title If the second argument which is optional is not specified the variable s name is used as the column s title Note The command table actually inserts a Table Viewer in the Draft As any other Viewer this may also be edited to change its attributes It can also be copied from the Draft to the Report The data in this Viewer is frozen namely the table shows the data as it was at the moment when it was created Further changes to the variables that appear in the Viewer will not affect the displayed data Note that unlike manually inserted Viewers here the arguments may be expressions and not only variables then Syntax then Description An optional then may appear after the condition of an if statement to separate between th
218. s isa string Description Returns a two dimensional array containing a bitmap image The string s specifies the bitmap file name For example b bitmap c images mypicture bmp The bitmap file is converted to the Image Viewer RGB format so that it can be displayed using the Image Viewer See the section Image Viewer subsection RGB This format allows you to manipulate each of the three color components of the image red green and blue break Syntax break break n Operands n is a number Description Used for breaking a loop It stops the loop and transfers the execution point to the first statement after the loop block The second form is followed by a number which specifies how many nested loops to exit For example n length b i 0 107 loop it 1 if i gt n break end the loop if b i lt 0 next next loop round afi sqrt b i or for i 1 tom for j 1 ton if a i 2 b j 2 gt max val break 2 exit both loops if b j lt 0 next 2 gt exit this loop and go to next i println a i b j by Syntax by Description Used in a range definition to specify an interval and in a for loop to specify the step case Syntax case expression cases block case conditional cases block Description Used for a conditional execution of statements The first form looks like the following 108 example case x 8 5 y X 2 2 a xti y a x 1 1 3 1 4 y x 1 545s a x 1 b x 1 y a 2 b 2 G2 i
219. s less memory No normalization is performed on the inverse transform See fft for more details imag Syntax imag x Operands x is an expression Description Returns the imaginary part of x 95 Index loc Syntax Operands Description index b or loc b index x y or loc x y b isa 1 dimensional Boolean array x is a scalar expression y is an expression The first form returns an array of indices where b is true Note that this is applicable only to 1 dimensional arrays For example if you need to operate on the positive elements of a 1 dimensional array x and leave the other elements intact you define an index array i loc x gt 0 and operate on x i Ifall the elements of b are false the returned array is empty namely the value returned by length i is 0 The second form returns the index of the scalar x in the array y Note that the returned index is the first integ Syntax Operands Description interp Syntax Operands Description 96 that s found namely if x appears in y in different locations only the first is returned If x does not appear in y the returned index is the last index 1 outside the range If y is multidimensional the returned value is a 1 dimensional array where the first element is the index in the first dimension the second element is the index in the second dimension etc integ exp x integ exp x tol exp isa formal expression of one variable x isa l dime
220. se the size of the array should be specified inside the square brackets for example dfunc integ 3d func double f double 3 double a double b Now when the callback function is called by integ_ 3d Numerit will know that the argument sent to it represents an array It will create a Numerit array of length 3 and copy to it the content of the array that was sent as an argument Note that the arrays a and b are sent to the DLL function and do not require specification of the length 53 In some cases the DLL function expects the callback function to modify the array it sends to it That s why before returning to the DLL function the Numerit array is copied back to the C array Since this is not always required the user may let Numerit know that a back copy is not required to save time by adding the mark after the square brackets of the array that need not be copied back namely dfunc integ 3d func double f double 3 double a double b This tells Numerit that the values of the array elements are not needed by the calling function and can be discarded If a two dimensional array is sent as an argument to a callback function all the lengths must be specified for example dfunc foo func double double 3 5 Note that here as with multidimensional arrays that are sent to a DLL function multidimensional arrays are expected be allocated by rows and not as a single block of memory although the syntax here resembles the s
221. sed for subtitles The forth is the Caption styles which may be used for figure and table captions The last four styles are Userl User2 User3 and User4 and may be used for any purpose When a new style is set while text is selected it is applied to all the paragraphs inside the selection Any style may be re defined i e its paragraph and character settings may be modified by using the menu command Format Define Styles This menu command also lets you save on disk the current set of eight styles or load from disk a set of previously saved styles When a set of styles is saved in the main Numerit directory under the name DEFAULT STY it is used as the default set of styles from now on deleting this file restores the original default set When a style is re defined all the paragraphs of that style in the document are reformatted 15 The Ruler At the top of the Document pane there is a ruler which provides quick setting for some of the document s parameters It also contains a scale which shows dimensions in the current unit of measurement which is either inch or centimeter and is set by the menu command Options Set Document Units first line indent right margin left margin a E left indent tab right indent To change the document margins point with the mouse at the left margin or left to it or at the right margin or right to it and drag it to the new position This is equivalent to setting the margins with the Format
222. sent to the function in two ways by value or by reference When a variable is sent to a DLL function by value its value is copied to the function s stack and the function reads the value from the stack but has no access to the variable itself When a variable is sent to the function by reference its address is copied to the function s stack and the function has full access to the variable itself it can read its value and also modify it A C function receives a scalar variable as a by value parameter when it is specified with only the type for example in the function void foo int n double x atte the parameters n and x are passed by value The same rule is used to specify a scalar parameter by value in the DLL function declaration namely the above DLL function will be declared in Numerit as dfunc void foo int n double x A C function receives a variable by reference when the parameter is specified with a type and an address mark an ampersand for example void set double x x 1 23 or when it is specified as a pointer for example void set double x RS LS Numerit does not distinguish between the two and when specifying a scalar parameter by reference in Numerit you should always use the ampersand syntax even when the C function expects a specifying double will generate an error So the above equivalent DLL functions will be declared in Nume
223. signment of array elements The condition should be a Boolean array followed by a single assignment or by a block of assignments for example where x gt y x y or where x gt y a x bey Cc y x The assignments take place only in elements where the condition array is true The other elements of the assigned variable remain unchanged The assigned variables should have the same dimensions as the condition array The where statement may be followed by an else with a single assignment or a block of assignments which will take place in the elements where the condition array is false For example after the following code is executed i 1 2 3 4 where i gt 1 and i lt 4 x i else x 1 the value of x is 1 2 3 1 while Syntax while Condition do Statements Description Defines a loop in which the statements are repeatedly executed as long as the condition is 130 true The keyword do is optional but is redundant When there is only one statement in the loop it may appear on the same line for example x 0 while x lt 10 x x 1 Otherwise a block should be used for example x 0 while x lt 5 print x E 2 wmessage Syntax Operands Description write Syntax Operands Description writeln wmessage t s t and s are strings Opens a Warning message window where the string t is the window s title and the string s 1s the message text The user must click the OK button to continue program execution
224. splay e es ee ES es Dn BE eR ees 28 A Seah PRT ET BERRI I ES BOE VE INE Ec RE RRR OE RR 28 SPACING reek re A clea ete Moot oa oh oth te 28 NO 28 Action Button Sisip e EEEE EE A dias 28 Shiticontrols pis de a e da A oth ATE A TAEAE 28 NOR ii dedo 28 Hei a Sa ol auth a esta aed as St aoe Be eee e ee ds dd 28 CUB sees ned AA AS BAG SEIN AAA A ARRON BEE 28 E a E E EE EA ENEA ad rta stevie E 29 RN ee 29 ad 29 Scale Ow a oe cosa ito E OE NE A EE e eae 29 Hi a N ANIE E E ti A A GINA rt ee 29 Math and Text Mods A Gua Cosel cv A a ii sia 29 A iS her T 29 o ANN 30 AUS os src id adi sere haune ENS 30 SPACeS xcs dais 30 OMA A A a at seats aster dee aes Aree seed eee ee ty na eee O ea 30 IMOde ices RN OR tert tert NA 30 Font jame nenori dea sescdectbede i ai EEE ES ARE E lua coven cobby tide AE AG EA dusvlca dua coop E E TE S E 30 Font Sieniniai r a AA AAA SRE aa eR E T N SE ce id 30 ETIA E E ET T A A E N E T E E 30 ATI DUES te Taass ae e kien Me a a ea as do 31 Alignment goiania A a ee 31 OP it sealed logan etnies AA A E E A dasa readies 31 Chapter 6 Writing Programs 33 Writing the 018023 T 1a 0 DEPE o e a e AE a o o ad ees 33 SI O 33 TE LATA A oi Beveled eee lng nolan 34 TA Siti fesse esse E EE cece Naa Saeed ON ON isc alee ded ca aoa cesta cette OO RON ora Ded Crapo aa 34 TIP as aida reta sonda iO a 34 A ANNA 34 EXPTE des 34 Duimmy Variables anta drid o tano ete Eonia ta dr lee Ar les e o o Ot og dd ae 34 Eorma Expression de a e fetos 34
225. state in the Math mode The Text mode is used for inserting normal text or a character of a specific font In this mode the Equation Editor behaves like a word processor and you control the font and its attributes Note that by inserting a template or a symbol while in Text mode the mode at the insertion point is converted to Math Templates Most of the editing activity in the Equation Editor involves inserting templates and filling in the template s empty blocks The Template page in the Equation Editor s control panel lets you choose from a variety of templates To insert a template click on it with the mouse The templates at the top row offer various combinations of parenthesis and brackets They enclose one or two blocks and adjust their own size to the size of the enclosed blocks The second row includes various types of fractions radicals superscript subscript overscript underscript overbars underbars and two types of arrays a normal size array and a small size array The dimensions and elements alignment of the inserted array are defined in the array definition panel located at the right side of the Template page This panel is also used to modify the size and alignment of existing arrays To do this click on one of the array s elements and make it the active block This will turn the X sign between the dimension specifiers into a button and will display the dimensions in red Clicking the button X sets the dimensions of the array t
226. stration file for restoring the registered version in case of a damage Restore your registered version after a damage End the session and exit Numerit Undo the last editing action Redo the last undone action Cut the selected text delete and copy to the clipboard Copy the selected text to the clipboard Insert text from the clipboard to the current position Insert text from the clipboard in a specific format Document Delete the selected text Delete the current line Editor Select the whole text not including headers footers Clear the Draft text Block the selected text or insert a new block Editor Fold Unfold the current block Editor Find the specified text Find the specified text same as Ctrl F Repeat the last Find operation Replace the specified text by another text Replace the specified text by another text same as Ctrl H Repeat the last Replace operation Move to the top of the Editor Move to the bottom of the Editor Move to the specified line in the Editor Editor Move to the line that will be executed next Editor Move to the specified page in the Document Document Run Compile Ctrl F9 Compile Module Make Ctrl F9 Edition Run F9 Step Over F8 Step Into F7 Pause F6 Stop F5 Calling Function Ctrl lt Called Function Ctrl gt Go to Execution Point Inspect F12 Breakpoint F4 Clear Breakpoints Previous Error Ctrl Shift lt Next Error Ctrl Shift gt Options
227. string Lowercase of string Position of substring in string Extract substring from string Convert string to number strupp s strupper s substr s p n sum x sum x n svd M tan x tanh x trace M transp x transpose x trunc x trunc x n unpackcomplex z unpackcomplex z x var x var x n zero exp x Uppercase of string Uppercase of string Extract substring from string Sum of elements of array Sum of elements of array over dimension n Singular value decomposition of a matrix Tangent Hyperbolic tangent Trace of a square matrix Transpose of a multidimensional array Same as transp Integer part Integer part with accuracy 10 Unpacks a complex array Unpacks a complex array Variance Variance over dimension n Zero of an expression same as root 81 82 Language keywords that define objects perform operations on objects or control program execution array beep binfile bitmap break by case clear clock close common const delete dfunc dfunction dvar directory dll do downto draft else fopendlg file firstindex for free freedll fsavedlg func function goto graph if input len loop matrix menu message next ocmessage outf outformat outp outprec outw outwidth outz outzero Chapter 11 A Quick Reference to Numerit s commands Converts Vector or Matrix into a simple Array Generates a beep Defines a binary file Reads a bitmap file and converts to Im
228. t position in the file before writing see the section Files ynmessage Syntax ynmessage t s Operands t and s are strings Description Opens a Yes No message window where the string t is the window s title and the string s is the message text The user must click either the Yes or the No buttons to continue program execution ynmessage returns 1 if the user clicked Yes and 1 if the user clicked No For example if ynmessage AppName Stop program 1 stop yncmessage Syntax ynemessage t s Operands t and s are strings Description Opens a Yes No Cancel message window where the string t is the window s title and the 132 string s is the message text The user must click either the Yes No or Cancel buttons to continue program execution yncmessage returns 1 if the user clicked Yes 1 if the user clicked No and 0 if the user clicked Cancel For example the following may be a test inside a loop rc yncmessage AppName Continue with current item if rc 0 break else if rc lt 0 next Numerit Software License Agreement Acceptance KEDMI Scientific Computing grants you a non exclusive license to use Numerit a software and accompanying documentation SOFTWARE Exercising your rights to use the SOFTWARE indicates your acceptance of the terms of this Agreement Copyright All intellectual property rights in the SOFTWARE are owned by KEDMI Scientific Computing and are protected by international copyright laws an
229. t the last execution error will be ignored by the system See the command hideerror for more details 127 return Syntax return return expression Description Used to return from a function May appear anywhere in the function The first form is used to return from a function without a value not required at the end of the function The second form is used to return from a function with a value Note that since the first form does not return a value the function call in this case cannot be part of an expression but must be in a statement of its own sdfunc Syntax sdfunc function prototype or sdfunc block of function prototypes Operands function prototype isa DLL function prototype Description Declares a function of a dynamic link library DLL The sdfunc statement is used to declare functions that have been compiled with the stdcall calling convention Other than that sdfunc is equivalent to dfunc showerror Syntax showerror Description Resumes the automatic execution error handling See the command hideerror for more details smessage Syntax smessage t s Operands t and s are strings Description Opens a Stop message window where the string t is the window s title and the string s is the message text The user must click the OK button to continue program execution stop Syntax stop Description Stops the program system Syntax system s Operands s is a string Description Executes a system Window
230. t variables according to the types that are specified in the callback function declaration in the dfunc statement The Numerit function is then called with these variables as arguments and returns a value The value is converted to the type that should be returned by the callback function again according to the dfunc declaration and is returned to the calling DLL function As before it is very important to provide an accurate description of the expected callback function including the return type the number of parameters and the types of the parameters It is also important that the Numerit function will match the expected callback function Any error here will result in unpredictable results Numerit has no way to verify how many arguments and of what type were actually sent by the DLL function in the callback process so it must rely on the information that is specified in the declaration of the callback function that appears inside the declaration of the DLL function A somewhat more complex situation exists when the argument of the callback function is not a scalar but an array Since Numerit must convert the argument to a Numerit variable before the callback function is executed it must know the exact size of the array and of course its type That s why an array parameter in the declaration of a callback function must also include its length This can be done in one of the following three ways 1 The array has a fixed known size In such a ca
231. tarts with the first module in the list and searches down Functions with the same name may appear in two or more modules but only the first that is found is the one that s actually used Thus the order of modules in the list might be important You can change the position of a module in the list by selecting it and clicking the Up or Down arrows at the bottom right corner of the Modules window next to the title Move Extra Module The Extra module is intended to be used when you run a program and then need to execute some extra code without changing the program or rerunning it It is available only in Numerit Pro The code in the Extra module is executed as if it was part of the Main program For example you run a program that computes a lot of data and then realize that after the long run you didn t save some of the data in a file You can add the code to save the data in the Extra module and run it The code will be considered as a continuation to the code of the Main module You can then copy the code to the main program for the next run or leave it in the Extra module for optional execution Note that in Numerit when a program has ended its variables are still defined and that s why the Extra module can use them The variables are initialized only when the program is run again To open the Extra module select File Open Extra Module To close the Extra module select File Close Extra Module When the Extra module is open you will see an Extra tab
232. tax trace x Operands x is a square matrix Description Returns the trace sum of diagonal elements of the square matrix x transpose transp Syntax transpose x or transp x Operands x is an expression Description Returns the transpose of x If x is a scalar or 1 dimensional the operation has no effect If x is 2 dimensional the rows and columns are interchanged If x has a higher dimension the operation is generalized in the following way each dimension is shifted forward and the last dimension moves to the first position e g a 3x5x7 array is converted to a 7X3x5 array trunc Syntax trunc x trunc x n Operands x is an expression n is an integer Description The first form returns the integer part of x The second form returns the truncated value of x with accuracy 10 namely n determines from which digit the value is truncated For example trunc 1234 567 2 is 1200 truncated to hundreds and trune 1234 567 2 is 1234 56 truncated to hundredths The function trunc behaves like floor with positive numbers and like ceil with negative numbers namely it always rounds toward 0 unpackcomplex Syntax unpackcomplex x unpackcomplex x z Operands x is a Real array z is a Complex array Description This function unpacks a packed complex array represented as a real array back into a complex array reversing the operation of packcomplex The length of the complex array is half the length of the
233. tcheby allows to add a third array s which specifies relative standard deviations of the data points All the elements of s must be positive numbers A larger s i means that the corresponding data point has a larger error and consequently less weight A very small value will force the curve to go through or very close to the corresponding data point Note that in the first form of the function all the points have the same weight Syntax Operands Description fitpoly Syntax Operands Description fitline x y fitline x y s x y and s are 1 dimensional Real expressions Returns a 1 dimensional array with two elements such that the straight line a 1 a 2 x is the best linear fit to the set of data points given by x and y x and y are l dimensional arrays of the same length and must be Real The second form of fitline allows to add a third array s which specifies relative standard deviations of the data points All the elements of s must be positive numbers A larger s i means that the corresponding data point has a larger error and consequently less weight A very small value will force the straight line to go through or very close to the corresponding data point Note that in the first form of the function all the points have the same weight fitpoly n x y fitpoly n x y s n is an integer x y and s are 1 dimensional Real expressions Returns a 1 dimensional array with n 1 elements which are the coefficients
234. tems the space between them and the font of the typed characters When characters are typed or symbol are inserted their attributes are determined by the current setting in the Format dialog page To change the size or attribute after insertion select the characters and set new values in the Format dialog page Equation Structure An equation is constructed from blocks of items The currently active block the one with the insertion cursor has a gray frame around it A block may be split to two stacked blocks one above the other by pressing the Enter key inside the block When a new equation is inserted it has a single empty block which is the root block A multiline equation is created by splitting the root block as many times as necessary The rows are aligned according to the Alignment setting in the Format dialog page An empty block appears as a filled gray rectangle when it is not the active block Blocks are usually created when inserting templates Each template has a set of blocks which are placed by the Equation Editor in default positions You may adjust the position of blocks by the Shift controls in the Equation Editor s control panel Editing the Equation Blocks Items are inserted into the currently active block of the equation by typing and by inserting templates and symbols from the Equation Editor s control panel While inserting templates the Equation Editor creates empty blocks which are place holders for other items i
235. the document The maximum scale is 4 times the equation s true scale Scale down The second button in the third row scales the view down This does not affect the size of the equation in the document The minimum scale is the equation s true scale Greek The third button in the third row lets you type Greek letters from the keyboard Releasing this button restores the keyboard to English Note that Greek letters may also be inserted from the Greek dialog page in the Equation Editor s control panel Shortcut key Ctrl G Math and Text Modes The mode is selected in the Format dialog page Most of the equation editing is done in the Math mode In this mode the Equation Editor automatically defines the appropriate font for each item and controls its position Variables appear in italics and spaces are automatically inserted around operators In addition functions names e g sin cos etc are not italicized and so are long names which are assumed to be words rather than variable names the maximum variable name length is set by default to 4 but may be set to any other value in the Options dialog page It is possible to force the characters Italic and Bold attributes see Format The Italic check box has three possible states Set Not Set and Auto When the check mark in the box has a gray background the state is Auto and then the Equation editor is responsible for italicizing the characters according to the above rule this should be the normal
236. the equation is edited The shift controls allow you to make adjustments to the position of specific items in the equation when you are not satisfied with the automatic positioning Each shift control consists of two positioning buttons which surround a display field that shows the shift value in screen pixels relative to the default position The upper control is used for horizontal adjustment and the lower control is used for vertical adjustment To shift a whole block make it the active block and use the shift controls to move it To shift items inside a block select the items with the mouse or the keyboard and then use the shift controls to move the selected items When nothing is selected the shift controls display the shift values of the active block When items are selected the shift controls display the shift values of the selected items a control becomes disabled when not all the selected items have the same shift Note that the shift is performed in screen pixels at the current scaling so by scaling the view up you get a finer positioning grid When the equation is printed these shifts are translated to physical distances which match as closely as possible the distances shown on screen Shortcut keys for the positioning buttons Ctrl LeftArrow Ctrl RightArrow Ctrl DownArrow and Ctrl UpArrow Undo Redo The left button in the first row of buttons is the Undo button and the button next to it is the Redo button The Equation Editor us
237. the imaginary part abs2 Syntax abs2 x Operands x is a numeric expression Description Returns the square of absolute value of x If x is complex the returned value is the sum of squares of the real part and the imaginary part acos Syntax acos x Operands x is an expression Description Returns the inverse cosine of x If x is in the range 1 to 1 the returned value is Real in the range 0 to 7 acosh Syntax acosh x Operands x is an expression Description Returns the inverse hyperbolic cosine of x acot Syntax acot x Operands x is an expression Description Returns the inverse cotangent of x If x is Real the returned value is also Real in the range 1 2 to 7 2 acoth Syntax acoth x Operands x is an expression Description Returns the inverse hyperbolic cotangent of x adefint Syntax adefint y x adefint y x a b Operands y and x are 1 dimensional Real expressions a and b are scalars Description The first form returns a scalar which is the definite integral of y with respect to x using cubic splines interpolation The integration is carried out from the first element of x to its last element Both x and y must be 1 dimensional Real arrays The second form returns the definite integral from a to b If a or b are outside the x 87 range they are clipped to this range in other words the array y is considered to be 0 outside the range aderiv Syntax aderiv y x Operands y and x are 1
238. this form may be used if the function is called many times with the same arrays to save memory allocation of the real array on each call phase angle arg Syntax Operands Description phase x or angle x or arg x x is an expression Returns the phase or argument of x The phase is the angle in radians of x in the complex plane 99 poly Syntax poly c x Operands c isa 1 dimensional expression and x is an expression Description Evaluates a polynomial with the given coefficients c at x c must be 1 dimensional and x may have any dimension Both may be Real or Complex The degree of the evaluated polynomial is n 1 where n is the number of coefficients The first element of c is the free coefficient the second element is the linear coefficient etc poly c x is equivalent to c 1 c 2 x c 3 x c 4 x but is much more efficient pos Syntax pos f Operands f isa file Description Returns the current position in the file in bytes product prod f should be previously defined by file or by binfile Syntax product x or prod x product x n or prod x n Operands x is an expression n is an integer Description The first form returns a scalar as the product of all elements of x The second form returns the product of elements of x over the dimension n The returned value has one dimension less than x For example if M is a 2 dimensional array than prod M 1 returns a 1 dimensiona
239. turned s p and n may also be arrays sum Syntax sum x sum x n Operands x is an expression n is an integer Description The first form returns a scalar as the sum of all elements of x The second form returns the sum of elements of x over the dimension n The returned value has one dimension less than x For example if M is a 2 dimensional array than sum M 1 returns a 1 dimensional array which is the sum of the rows of M while sum M 2 returns a 1 dimensional array which is the sum of the columns of M svd Syntax svd M Operands M is a Real matrix Description Returns the singular value decomposition of a Real matrix M M may also be a 2 dimensional array rather than a matrix Assuming that M is an mxn matrix m rows n columns its singular value decomposition is given as a multiplication of three matrices M U W V where U is an mxn matrix W is a diagonal nxn matrix and V is the transpose of an nxn matrix The matrices U and V are each orthogonal svd returns a matrix with m n 1 rows and n columns The first m rows form the matrix U the next n rows form the matrix V and the last row consists of the diagonal elements of W To learn how to extract the sub matrices see Sub Arrays in the section Arrays tan Syntax tan x Operands x is an expression Description Returns the tangent of x 104 tanh Syntax tanh x Operands x is an expression Description Returns the hyperbolic tangent of x trace Syn
240. uct Numerit to skip the copy operation by adding the mark after the square brackets of the array e g int 10 double Numerit does not allow you to specify a structure inside a structure If this is required you must specify the members of the inner structure as members of the same structure when possible A function parameter Numerit allows you to send user defined Numerit functions as arguments to DLL functions Such functions are referred to as callback functions since they are called from the called DLL function you can also send a DLL function as an argument to another DLL function see A DLL function as a callback function below Note that the Numerit callback function should be called from the DLL using the cdecl convention A Numerit function is declared as a parameter of a DLL function by declaring it as function or func in the list of parameters of the function and by specifying its own return type and list of parameters types for example in dfunc double foo func double f double x the function f is declared as a parameter of the DLL function foo The callback function f is declared as a function that receives and returns a double scalar The allowed types of the callback function parameters are the same as the types that can be specified in a DLL function declaration except a function parameter namely a callback function does not accept another function as an argument The Numerit function should match t
241. ue has one dimension less than x For example if M is a 2 dimensional array than stdev M 1 returns a dimensional array which is the standard deviation of the rows of M while stdev M 2 returns a 1 dimensional array which is the standard deviation of the columns of M strdel Syntax strdel s p n or strdel s p Operands s is a string p and n are integers Description Deletes n characters of s starting at position p The position of the first character in s is 0 If the third parameter n is omitted the characters from position p to the end of the string are deleted Note that this function does not return a value but rather operates on the string itself s p and n may also be arrays strins Syntax strins s p t Operands s and t are strings p is an integer Description Inserts the string t into s at position p The position of the first character in s is 0 If p is greater than the length of s the string t is appended to s Note that this function does not return a value but rather operates on the string itself s pand t may also be arrays strlen Syntax strlen s or strlen s n Operands s is a string or array of strings n is an integer Description The first form returns the length number of characters of the string s The second form sets the length of the string s to n expands or shrinks as necessary strlow strlower Syntax strlow s or strlower s Operands s is a string or array of strings Descript
242. ument Save All Ctrl Shift S Save the current program and modules Professional Edition Modules Open the Modules window Professional Edition Close Module Close the current module Professional Edition Save Module Ctrl S Save the current module Professional Edition Save Module As Save the current module under a new name Professional Edition Open Extra Module Open the Extra module Professional Edition Close Extra Module New Input File Open Input File Close Input File Save Input File Ctrl S Save Input File As Print Ctrl P Printer Setup Create Executable Create Library Create Registration File Restore Registration Info Exit Alt F4 Edit Undo Ctrl Z Redo Ctrl Shift Z Cut Ctrl X Copy Ctrl C Paste Ctrl V Paste Special Delete Del Delete Line Ctrl Y Select All Ctrl A Clear Draft Block Ctrl Fold Ctrl Shift F Search Find Ctrl F Find Shift F3 Find Again F3 Replace Ctrl H Replace Shift F2 Replace Again F2 Go to Top Ctrl Home Go to End Ctrl End Go to Line Go to Execution Point Go to Page Close the Extra module Professional Edition Create a new input file Open an input file Close the current input file Save the current input file Save the current input file under a new name Print the currently visible Editor s or Document s content Set up printer parameters Create a Numerit executable for NumRun Create a Numerit library Create a regi
243. unction is defined by the declaration unction or unc followed by the function s name the parameter list inside parentheses which are empty when there are no parameters and the function s body A function definition may appear anywhere in the program even after the statement that calls it but only at the top level namely it cannot appear inside a block of another function or another command i e if or for There are two possible forms 1 Single line The function header is followed on the same line by an equal sign and an expression which will be evaluated and returned when the function is called For example function foo a x a x 2 2 Multiline The function header is followed on the next line by a block of statements For example function foo a x y a x 2 return y A function s name may be any valid identifier and the parameter list consists of identifiers that are separated by commas 40 Type of arguments and the return value The function receives arguments and may return a value Since the language is type sensitive it determines the type of the arguments and the return value during compilation so it is not possible to call the function once with an argument of one type and then with a different type However other variable attributes kind and number of dimensions may change from call to call thus the same function automatically works with variables of different dimensions and kinds just like the built in
244. undant and is ignored by the compiler The control variable starts from the first limit and terminates the loop when it passes the second limit The limits and the step may have dimensions In such a case the control variable is an array whose first element is used for controlling the loop 1 e testing for termination When there is only one statement in the loop it may appear on the same line for example for i 1 to 100 x i i 2 Otherwise a block should be used for example for i 1 downto 2 by 2 bee e if i gt 50 print x i free x y Z X Y Z are variables Free the memory occupied by the specified variables The memory is returned to the operating system so that more memory becomes available to the program If the variable is a file this command also closes the file The specified variables become undefined but still keep their type Numeric Boolean String or File So if they are assigned a new value it must be of the same type freedll s freedll s is a string Frees the Dynamic link library DLL whose name is specified in the string s or free all open DLLs if no name is specified For example freedll my dll 117 fsavedlg Syntax Operands Description fsavedlg t fn ft t and fn are strings ft is a string array with two columns and any number of rows Opens a dialog box that allows the user to specify a file for saving The user can select a disk drive a directory path and a file nam
245. us plus and dot which must be part of a number This actually means that any character that cannot be interpreted as part of a number is filtered out during the read So for example you may put any comments that do not include digits in a text file and 125 when you read numbers from the file these comments will be automatically skipped When reading strings they should be separated by spaces use read1n to read a whole line including spaces as a single string Note It s the user s responsibility to make sure that data is read from the file in the same way it was written to it namely that the file was defined the same way text or binary and that the variables are of the right type and size readin Syntax readin f readin input readin f s readln input s Operands f isa text file s is a String variable Description Reads a line or lines of text from a text file or from the Input File should be previously defined by file The first two forms skip one line in the file regardless of the text in that line The third and fourth forms read text lines into the String variable s The number of lines read depends on the dimensions of s If s has no dimensions one line is read into it If s is a string array lines are read one by one into its elements If s is undefined it is automatically defined as a simple string and one line is read into it Note It s the user s responsibility to make sure that the file is indeed a text file and th
246. us bar in the Options menu The Program Window A new program is created by opening a Program window using the menu command File New or Ctrl N An existing program is loaded from the disk by the command File Open or Ctrl O Each Program window is divided into panes The two main panes are the Editor pane and the Document pane The Editor pane is where the program s code is written and the Document pane is where the program s output is displayed In addition there is a third pane the Message pane at the bottom of the program window This pane is used for displaying errors and warnings EA Program lt 2 gt println Hello World x 0 10 graph sin xj x Main Report 4 Draft It is possible to arrange the panes in two configurations The first vertical shown above puts the Editor pane on the left and the Document pane on the right The second horizontal puts the Document pane at the top and the Editor pane below it The Message pane is always at the bottom To change configuration use either the commands in the Window menu or the corresponding buttons in the Program Bar The panes may be resized by changing the position of the separators between them pressing the mouse button and dragging There are two such separators one between the Editor and the Document panes and one above the Message pane When the configuration is changed or when the active pane is maximized the separators are relocated automatically Whe
247. variable or expression with an unexpected kind was encountered Length is not a power of 2 The length of the array that is transformed by the functions FFT and IFFT must be an integer power of 2 72 Length mismatch Some operations require equal lengths of the operands This error occurs when the lengths are different Matrix must be square A non square matrix was specified as an argument to a function that expects a square matrix e g Det Inv Must be integer Some functions and operations expect an integer argument e g when a matrix is raised to a power n n must be an integer This error occurs when the argument is not an integer Must be positive Some functions expect a positive argument e g the standard deviation argument sent to the fitting functions This error occurs when this argument was not positive Negative value not allowed Some functions do not accept negative arguments e g Bessy Non integer order Bessel functions can only be evaluated for integer orders Not converging Some functions like Integ Deriv and Root use an iterative process This error occurs when the process does not converge This might indicate that the specified tolerance is too small Numeric error An error occurred as a result of an invalid numerical operation e g 0 0 log 0 etc The program may continue to run and the result of the operation is set to NAN NAN or NAN is an IEEE standard representation for Not A Number
248. ve button in the Program bar saves the program including its code the Report and the name of the current Input File if exists The menu command File Save As renames the program and then saves it under the new name In Numerit Pro the menu command File Save Module or the Save Module button in the Program bar saves the code source and compiled of the module that is currently visible in the Editor The menu command File Save Module As saves a copy of the currently visible module under a new name Note that unlike the File Save As command in this case the open module itself is not renamed and its original name is kept This is done so because the module may appear as a sub module in different levels of the modules list So if you want to continue working with the new module file you must change the module s name in the modules list manually otherwise you are still working with the original module see the section Modules List in Chapter 7 for details on the sub modules tree The shortcut key combination Ctrl S is used to save the program a module or the Input File Its interpretation depends on what is currently displayed in the Editor pane When the Main module 1 e the program s code is displayed it is interpreted as a File Save command when a sub module is displayed it is interpreted as a File Save Module command and when the Input File is displayed in the Editor pane Ctrl S is interpreted as a File Save Input File When a file is sav
249. ver are still taken from the current printer e g characters sizes Page Formatting Page formatting determines the appearance of the page It may be set by the menu command Format Page The dialog fields are Page size Normally the document is formatted according to the current setting of the printer page So in order to change the printer page size or orientation use the menu command File Printer Setup It is possible however to unlink the page size from the printer s page by unchecking the Printer page size box in the Page formatting dialog If this case the page width and height may be set to any value Margins Each of the top bottom left and right margins may be set Note that the top and bottom margins are normally hidden To make them visible check the menu item Options View Document Margins Header and Footer A header is displayed at the top margin and a footer at the bottom margin of every page To specify a different Header or Footer for odd and even pages or for the first page check the appropriate boxes In addition a space above the Header and below the Footer may be specified To edit the header or the footer make the top and bottom margins visible check the menu item Options View Document Margins and move into the header or the footer Pagination options Avoid Widow lines i e do not allow the last line of a paragraph to be the first line on the page moves at least two lines to the next page and Avoid O
250. version 58 Saving Modules You may save a modified module using the File Save Module menu command or the Save Module button in the Program bar When a module is saved only its source code and compiled code are updated in the file remember that as a Numerit program the module also has a Report document which is ignored when it is used as a module If you save the module using the menu command File Save Module As a copy of the module is saved under a new name but you continue to work with the original module This is done so because the module may appear as a sub module in different levels of the modules list If you want to continue working with the new module file you must change the module s name in the Modules List window manually Note that when a module is displayed in the Editor pane the key combination Ctrl S is interpreted as a Save Module command when the Main module is displayed the Ctrl S combination saves the whole program including the Report document and the modules list but not including the modules themselves To save the program and all its open modules that have not been saved yet use the menu command File Save All Ctrl Shift S Using Modules Calling a module s function is not different from calling a function that is defined inside the program When Numerit encounters a call to a function and cannot find the function in the Main module the program itself it looks for it in the submodules The search starts with the
251. written as 0 The instruction outzero 0 disables this feature pause Syntax pause Description Pauses the program before executing the next instruction pos Syntax pos fn pos input m n Operands f isa file m n are numbers Description The first form sets the current position in the file to n in bytes To move the current position to the beginning of the file use pos f 0 to move it to the end of the file use pos f 1 or any other negative value If n is greater than the file size the current position moves to the end of the file The second form sets the current position in the Input File to the line m and column n To move the current position to the beginning of the Input File use pos input 0 0 Subsequent read or write operations will start from the new position f should be previously defined by file or by binfile print Syntax print x y Z Operands X Y Z are expressions Description Writes the content of x y z to the Draft document Any number of items may be specified The items are written one after another into the current paragraph at the current position in the Draft The format of the written data is controlled by the current setting of outwidth outprec outformat and outzero Subsequent print commands send output to the same paragraph Use println to send output to different paragraphs printin Syntax println x y Z println Operands X YrZ are expressions Description Writes the content of
252. x y z to the Draft document and then moves the current 124 position in the Draft to a new line starting a new paragraph Any number of items may be specified The items are written one after another at the current position in the Draft If no items are specified the current position in the Draft is moved to a new line The format of the written data is controlled by the current setting of outwidth outprec outformat and outzero printpg Syntax printpg x y Z printpg Operands X Y Z are expressions Description Writes the content of x y z to the Draft document and then moves the current position in the Draft to a new page Any number of items may be specified The items are written one after another at the current position in the Draft If no items are specified the current position in the Draft is moved to a new page The format of the written data is controlled by the current setting of outwidth outprec outformat and outzero randomize Syntax randomize randomize x Operands x is an expression Description Initializes the random number generator The first form initializes the generator with a random value The second form initializes the generator with the seed x The seed is an integer between 1 and 2 that determines which sequence of random numbers will be generated by the function rand the same seed will always generate the same sequence range Syntax Racy x to y x y by dor x to y by d x
253. y 10 Complex conjugate Cosine Hyperbolic cosine Cotangent Hyperbolic cotangent Cosecant Hyperbolic cosecant Definite integral of an expression Derivative of an expression Determinant of square matrix Dimension of variable End of file detection Error function Test for an even number Existence of file Exponent function Fit a basis of functions to a set of data points Fit Chebyshev polynomials to a set of data points Fit a straight line to a set of data points Fit a polynomial to a set of data points Fast Fourier transform Shifted fast Fourier transform Rounded down value Rounded down value with accuracy 10 Gamma function Logarithm of gamma function Identity matrix n x n Inverse fast Fourier transform 79 iffts x imag x index b index a x integ exp x tol interp y x xx inv x length x linterp y x xx linsol M b linsolsvd M b In x loc b loc a x locmax x locmin x log x log10 x max x mean x mean x n min x numtostr x odd x packcomplex z packcomplex z x phase x poly c x pos x prod x product x prod x n product x n rand x real x root exp x round x round x n sec x sech x sign x shifft x shifft x n sin x sinh x size x sort x sqrt x stdev x stdev x n strdel s p n strins s p t strlen s strlow s strlower s strpos s t strsub s p n strtonum s 80 Shifted inverse fast Fourier transform Imaginary part indices where a
254. y available in Numerit Pro Use To Invoke 0O E E m 8 File New Open Modules Save Save Module Print K AE C Edit Undo Redo Cut Copy Paste Block D EY Search Find Find Again Replace Replace Again gt gt gt b J 4 1 Run Run Step Over Step Into Pause Stop Calling Function Called Function m1 Ale 28 l al Window Vertical Horizontal Split Maximize Pane Toggle Panes Message Report Draft Y Help Contents The Program Bar may be hidden by unchecking the item View Program bar in the Options menu The Document Bar The Document Bar is used for operations that are related to document editing It is located below the Program Bar at the top of the Desktop and is active only when editing a document The buttons in the Document Bar are also used as indicators for various states For example when editing a bold text in the document the Bold button PB is depressed and shown as Use To Noma 2 Select a style for the current paragraph Ctrl T Times NewRoman y Select a font 12 z 3 Select a character height point size 5 El E g Toggle bold italic underline Greek attribute Ctrl B I U G Set subscript superscript attribute Ctrl Ctrl E Align paragraph left center right justified Ctrl L E R J gt gt EQ Set left center right aligned tab Show Hide paragraph marks and other special characters Sh
255. y is defined by the following statement x Dida 12713 21422 23 31 32 33 35 and a 3 dimensional 2x4x3 array is defined by x 111 112 113 121 122 123 131132133 141 142 143 211 212 213 221 222 223 231 232 233 241 242 243 Arrays of higher orders are analogously defined with higher levels of blocks These definitions determine both the size of the array and the value of its elements The length number of elements in a specific dimension is determined by the longest list along this dimension For example if in a definition of a 2 dimensional array one row has 3 elements while the others have and 2 elements the length in this dimension is set to 3 and the missing elements in the other rows are set to 0 Thus the definition x 11 12 DV play 23 31 Yields the following 3x3 array 11 12 0 21722723 31 0 0 Dynamic length A length of an array is dynamically expanded when a value is assigned to an element with index that is greater than the length For example if x is a 1 dimensional array with 10 elements then the statement x 20 1 will expand the array and set element no 20 to 1 This applies to any dimension of the array Dimensions The leftmost dimension of an array is the first dimension the next is the second and so on When defining an initialized array whose dimension is greater than 1 the first dimension is along the leftmost higher level block the second is along the next level of blocks and so o
256. y want to make sure that values from the last call are cleared and that you start with an initialized variable on every call use the clear command either when you exit the function or when you enter the function This is normally needed with local variables that are arrays For example a statement a 1000 0 inside a function defines a local variable a as an array with all its elements set to 0 On the first call a is not defined yet so the assignment statement also allocates a memory for it On the next call the memory will already be allocated so the same statement will only set the 1000th element which is a much simpler operation but the other elements in a will have the same values they had when the function was last exited So by putting a clear a command after the assignment you make sure that all the elements are 0 If you want to make sure that the array is both initialized and has the right size use array definition instead of assignment e g a 1000 0 This will make sure that the array size is indeed 1000 in case it has been changed and that all its elements are set to 0 A function has access to the variables of the main program globals This is done by preceding the variable s name by namely when the variable x appears inside a function it refers to the variable x of the main program Note that the function may modify the values of the global variables so this is another method to return values from a function this method is
257. yntax of an array that was allocated as a single block 2 The second method to transfer the array length is to use one of the arguments before the array to specify the length In such a case the number of the argument is specified instead of the actual length inside the square brackets This is done by adding the prefix to the number for example the declaration dfunc integ nd func double f int double 1 double a double b tells Numerit that the length of the array is sent in the first argument which is int A two dimensional array in such a declaration can look like this dfunc foo func double int int double 1 2 Here the argument of the callback function is a two dimensional array where the number of rows is sent in the first argument and the number of column in the second argument A combination of methods 1 and 2 is also possible for example dfunc foo func double int double 3 1 3 The third method to transfer an array length is to use a global variable for the length For example n 0 dfunc integ nd func double f double n double a double b int n The global variable n will be assigned a value before the DLL function is called and this value will be used for the length of the array This method is useful when the length parameter n is under the control of the Numerit program and in the above example it is also sent as a parameter to the DLL function last parameter so that it will know the

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