Pretty-printing matrices in standard Fortran 95 using Dispmodule
Contents
1. 3 20 1 54 6 148 4 and K 3 0 12 14 0 CALL DISP K K STYLE PAD ORIENT ROW SEP ZEROAS which will display on the asterisk unit usually the screen K 3 12 14 Further examples and details can be found in the user manual 2 2 The function TOSTRING Many programming languages have built in functions that change numbers to strings It is for instance possible with Java to write System out println The square of x is x x Java also has a function Float toString that may be used instead In Matlab one may write disp The square of num2str x is num2str x x If x is 1 5 both commands display The square of 1 5 is 2 25 The function TOSTRING offers similar functionality The statement call disp The square of tostring x is tostring x x will produce the same output as the Java and Matlab commands As shown in the user manual it is possible to achieve a similar effect in Fortran using internal files and list directed output but this is cumbersome and the result is compiler dependent TOSTRING can change numeric and logical scalars and vectors into character strings and it is possible to specify how to format the string One applica tion of TOSTRING is to create variable format e g fmt F tostring w tostring d write fmt A For further examples and description see the user manual 2 3 Changing and retrieving settings for DISP an2. and g95 under Sun Solaris g95 under Suse Linux ifort It passes tests of g95 gfortran and ifort of conforming to the Fortran 95 standard 2 5 Package limitations and assumptions on the compiler Among major limitations of the module is that DISP cannot display very wide matrices as there is no provision for breaking matrices or matrix rows vertically The compilers tried can however all han dle record lengths of 1024 characters or more and since the output of DISP is intended for human reading this should not be too serious drawback Another important limitation is that displaying arrays of rank gt 3 is not supported Some minor limitations are that zeroas is not supported for complex vari ables TOSTRING cannot handle character variables and 2 byte logicals are not directly supported Among the things which the NAG matrix printing routines can do and DISP cannot is writing ma trices with special storage schemes such as triangular band or symmetric Another ability of the NAG routines missing from DISP is specifying character strings for matrix row and column labels An assumption on the compiler in the design of the package is that if A and B are real variables with IAI lt IBI and writing B with Fw d edititing does not produce w asterisks then neither does writing A One possible problem that hopefully does not occur involves compilers that automatically prepend a plus sign when writing positive numbers Every effort has been made t
3. from the author s web page www hi is jonasson Among related earlier work one can mention the Fortran 95 package Matran Stewart 2003 which contains a pretty print subroutine for items of type Matran matrix but that routine is of much more limited scope than the present one More versatile matrix printing routines are in the NAG Libraries 4 NAG 2000 and 2006 but these are not free and even if they have a few features that are absent in the current package the latter is in most respects more flexible 2 PACKAGE COMPONENTS The present package consists of one principal Fortran 95 module Dispmodule which handles the display of data types of default kind that are guaranteed to exist by the Fortran standard and several add on modules to handle data types of non default kind such as byte integers and quadruple preci sion reals The main procedures are the subroutine DISP which is used to display a scalar vector or matrix and the function TOSTRING which is used to change scalars or vectors into character strings In addition there are four subroutines to control settings for how the data are edited and one function to retrieve settings for DISP 2 1 Subroutine DISP Simple ways to call the subroutine DISP are CALL DISP X CALI DISE TITLE X CALL DISP X FMT CALL DISP TITLE X FMT where X is the item to be displayed TITLE is a character string used to label the displa
4. using a fairly versatile default format The Matlab commands A exp 3 2 3 2 disp A will display 20 0855 he 38 OL 0 0498 0 1353 It may be argued that the array programming features account for the widespread use of these lan guages for writing prototype programs which are later superseded by programs written in compiled high level languages such as C or Fortran In the 1990 s array programming in Fortran became possible with compilers for Fortran 90 and For tran 95 ISO IEC 1997 The future of Fortran is in many respects bright Reid 2003 and 2006 Metcalf et al 2003 ISO IEC 2004 However even with recent enhancements Fortran still lacks the ability to print matrices with a concise command To display a general matrix A one needs a sequence of statements such as do i 1 size A 1 write 20G12 4 A i end do which for the matrix given above will produce a rather mis aligned output 20 09 7 389 0 4979E 01 0 1353 Using an F edit descriptor an aligned display similar to the one given by Matlab is obtained but this comes at a cost as matrices with large elements can no longer be displayed Fortran also offers aster isk format for writing with default format To take an example the statement write A might display 20 085537 0 049787067 7 389056 0 13533528 However aligned output of matrices with multiple rows is not possible using this and in addition the result is compiler dependent The purpo
5. 455 ENGINEERING RESEARCH INSTITUTE ox UNIVERSITY OF ICELAND Pretty printing matrices in standard Fortran 95 using Dispmodule Kristjan Jonasson Report VHI 02 2008 Reykjavik May 2008 Report VH 02 2008 Reykjav k May 2008 Kristjan Jonasson Pretty printing matrices in standard Fortran 95 using Dispmodule Engineering Research Institute University of Iceland Technical report VHI 02 2008 May 2008 Kristj n J nasson associate professor Department of Computer Science Hjardarhagi 4 IS 107 Reykjavik Iceland Email jonasson hi is The author is responsible for the opinions expressed in this report These opinions do not necessarily represent the position of the Engineering Research Institute or the University of Iceland Copyright Kristj n J nasson 2008 Engineering Research Institute University of Iceland Hjar arhagi 4 IS 107 Reykjavik Iceland ABSTRACT A standard Fortran 95 module for printing scalars vectors and matrices to external files is described The module can display variables of default kind of all intrinsic types integer real complex logical and character and add on modules are provided for data of non default kind The main module is self contained and incorporating it only requires that it be compiled and linked with a program containing a use dispmodule statement A generic interface and optional parameters are used so that the same subroutine name DISP is used to display items of diff
6. G Fortran 90 Library Manual Numerical Algorithms Group Oxford NAG 2006 NAG Fortran Library Manual Numerical Algorithms Group Oxford REID J K 2003 The future of Fortran Computing in Science and Engineering 5 4 59 67 REID J K 2006 Fortran is getting more and more powerful In Applied Parallel Computing State of the Art in Scientific Computing ed Dongarra J Madsen K and Wasniewski J Lecture Notes in Computer Science 3732 Springer 33 42 STEWART G W 2003 MATRAN A Fortran 95 Matrix Wrapper University of Maryland Department of Com puter Science Technical Report 4522
7. d TOSTRING The default settings used by DISP may be changed with the subroutine DISP_SET which with a complete list of arguments may be called with CALL DISP SET ADVANCE DIGMAX MATSEP ORIENT SEP STYLE UNIT ZEROAS All the arguments are optional and the effect of calling DISP_SET with a specified argument present is to change the default value for the corresponding argument of DISP For instance after calling CALL DISP_SET UNIT 7 subsequent DISP calls will send output to a file connected to unit 7 The only argument that is unique to DISP_SET is MATSEP matrix separator which is a character string that is used to separate items displayed with ADVANCE NO the default separator is a string with three spaces To take an example the sequence of calls CALL DISP_SET MATSEP CALL DISP 11 12 131 ADVANCE NO CALL DISP TRUE FALSE TRUE ADVANCE NO CALL DISP A B C will display cs Cs pene ea I 12 F B 13 T ue Similarly there is a function TOSTRING_SET to change default settings for TOSTRING There are also functions to return the settings to the original or factory defaults These are called DISP_SET_FACTORY and TOSTRING_SET_FACTORY The current default settings for DISP may be retrieved with the function DISP_GET which returns a structure say DS of type DISP_SETTINGS dec
8. erent data type and rank irrespective of display options The subroutine is quite versatile and hopefully can improve Fortran s competitiveness against other array programming languages The module also contains a function TOSTRING to convert numerical scalars and vectors to strings The module is distributed under a pub lic domain licence and can be freely used even in commercial packages Key Words Fortran 95 Matrix pretty printing Matrix printing Output utilities Array programming language AGRIP L st er einingu eda forritasafni skrifu u Fortran 95 sem tla er til a skrifa t lur vigra og fylki skr r eda birta essa hluti skj Einingin samt vi b tareiningum getur birt breytur af llum gagnat gum sem eru innbygg Fortran 95 heilt lur kommut lur tvinnt lur r kst r ir og t knastrengi Einingin er sj lfst og til a nota hana n gir einfaldlega a a hana og tengja vi forrit sem inniheldur use dispmodule setningu Mar gr ni og valfrj lsir stikar eru nota ir annig a sama undirforritsnafni DISP er nota til a birta st r ir af mismunandi gagnat gum og v ddum h v hva a valkostir eru nota ir vi birtinguna Einingin er fj lh f og getur ef vel tekst til b tt samkeppnish fni Fortrans gegn rum fylkjaforritunarm lum Einingin inniheldur enn fremur falli TOSTRING sem breytir talnabreytum t knastrengi Forritasafninu er dreift me opnu leyfi sem ley
9. fir frj lsa notkun jafnvel hugb na i sem er seldur CONTENTS Le Introduction ss ae a eves net ie idle ieee 4 2 Package components s gasi a a ra sina e eee E sdegecbexe 5 241 Subroutine DISP reran n a ar skra ie ieee hae ations ee 5 2 2 The function TOSTRING 21 54 a e ana e aeee enaa EE nE tag ak a a sa lb E E LN Ee tat 6 2 3 Changing and retrieving settings for DISP and TOSTRING sssseeeeseeeeerereeseerresresresresresreesesreess 6 AR BA NESE a EE E ET 7 2 5 Package limitations and assumptions on the compiler esssesessseessssesreeresreesessresteserstenresressesreses 7 R fEreNCES e e e tell een shel Leela A EEE EEE ene ae ee ee 8 1 INTRODUCTION One of the reasons for the great popularity of numerical computation systems such as Matlab Moler 2004 S plus Krause and Olson 2000 and their open source clones e g Octave Eaton 2002 Scilab Mrkaic 2001 and R Chambers 2007 stems from the ability of these systems to treat vectors and matrices as fundamental data types At the heart of these systems are languages that may be classified as array programming languages The first array programming language APL was developed in 1957 and it along with its successor J still enjoy considerable popularity Iverson 1991 A feature of all these languages is that the syntax for displaying arrays in traditional mathematical format is very simple As an example the Matlab command disp A will pretty print the matrix A
10. lared in Dispmodule with these settings The settings may be re applied to DISP by calling DISP_SET DS The user manual contains details 2 4 Testing The package contains a test program Test_Dispmodule which applies modern testing techniques to ascertain the correctness of Di spmodule The test program calls all the procedures of the module and all arguments are tried Testing of all possible data types for X is allowed for For arguments that have a limited range of allowed values all these values are tried In addition all the examples given in the user manual and in this paper are tested It is however impossible to test all possible combinations of X data type arguments and argument values so one must be content with a partial test accompa nied by examination of the source code of the module s and the test program There is a parameter declared at the beginning of the test program to control the verbosity level or amount of output It has three possible settings minimal output a short report and a detailed report including the result of all DISP and TOSTRING invocations In all cases the report ends with OK if all tests are passed Further instructions for operation of the test program are given in the user man ual The package has been tested successfully with recent versions of the following compilers under Microsoft Windows gfortran g95 f95 from NAG and ifort from Intel under Ubuntu Linux gfortran
11. o use SS editing to suppress potential plus signs but no compiler that defaults to SP editing is known to the author The feature of writing matrices side by side with ADVANCE NO is implemented by allocating memory for the blocks waiting to be written out To avoid memory leaking care must be taken to clear the output queues on each unit by calling DISP with ADVANCE YES in effect before exiting the program REFERENCES CHAMBERS J M 2007 Software for Data Analysis Programming with R Springer Verlag New York EATON J W 2002 GNU Octave Manual Network Theory Limited Bristol ISO IEC 1997 Information Technology Programming Languages Fortran Part 1 Base Language ISO IEC 1539 1 1997 ISO Geneva ISO IEC 2004 Information Technology Programming Languages Fortran Part 1 Base Language ISO IEC 1539 1 2004 ISO Geneva IVERSON K E 1991 A personal view of APL IBM Systems Journal 30 4 582 593 JONASSON K 2008 Dispmodule User Manual Report VHI 01 2008 Engineering Research Institute University of Iceland KRAUSE A AND OLSON M 2000 The Basics of S and S PLUS second ed Springer Verlag New York METCALF M REID J K AND COHEN M 2004 Fortran 95 2003 explained Oxford University Press MOLER C 2004 Numerical Computing with MATLAB SIAM Philadelphia MRKAIC M 2001 Scilab as an econometric programming system J Appl Econometr Systems 16 4 553 559 NAG 2000 NA
12. se of the current subroutine package is to remedy this deficiency by providing a module written in standard Fortran that will with minimal fuss display a vector or a matrix with sensible de fault format At the same time the module offers considerable flexibility in controlling the format of the output much more than Matlab s disp It is possible to specify the edit descriptor the displayed items may be labelled rows and columns may be numbered and the output may be directed to a file to the screen or even when calling Fortran from Matlab to the Matlab command window Several matrices vectors may be written side by side The package is especially useful for debugging purposes and for preliminary display of numerical results but it is general enough that it may in many cases be used for final display of such results It uses a generic interface and has optional parameters so that the same subroutine name DISP is used to display items of different data types and ranks with or without labels and using default or specified format in Fortran terminology scalars have rank 0 vectors rank 1 matrices rank 2 etc All the intrin sic data types of Fortran are supported i e integer real both single and double precision complex logical and character The module is accompanied by documentation in a comprehensive user manual Jonasson 2008 in four different formats plain text html pdf and Microsoft Word The package may be downloaded
13. yed item and FMT is an edit descriptor to control the display Assume that a exp i j 1 and b exp i i j 1 3 Then examples of calls are CALL DISP A A which will write out A 2 718 7 389 20 086 7 389 20 086 54 598 20 086 54 598 148 410 CALL DISP B which displays 2 71828E 00 2 71828E 00 2 71828E 00 7 38906E 00 5 45981E 01 2 98096E 03 2 00855E 01 8 10308E 03 5 32048E 11 and CALL DISP A 1 2 F0 5 which displays 2 71828 7 38906 20 08554 7 38906 20 08554 54 59815 A call with a complete list of arguments is CALL DISP TITLE X FMT FMT IMAG ADVANCE DIGMAX LBOUND ORIENT SEP STYLE TRIM UNIT ZEROAS All the arguments are optional and the purpose data type and possible values of each argument are given in Table 1 in the user manual Not all arguments are compatible with all data types or ranks of X It is for instance only possible to specify FMT_IMAG for complex X and ORIENT for vectors Argument association for ar guments after or starting with FMT will usually be realized with argument keywords e g CALL DISP A A UNIT 3 ZEROAS Examples demonstrating some of the possibilities are CALL DISP MATRIX A STYLE UNDERLINE amp NUMBER UNIT 8 DIGMAX 4 which with the matrix A given above will send the following to a formatted file on unit 8 MATRIX 1 2 3 1 A 7 4 20 1 2 7 4 20 1 54 6
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