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1. see 10 2 4 which are in effect a set of multiple square matrices and are therefore standard Zonal Sequential Numbers Numerical Names and Zone Titles Each row and column of a square SATURN matrix has an external numerical name associated with it Thus if the matrix represents a zone to zone trip matrix the name associated with the Ith row is the numerical name of the Ith zone The sequential numbers are determined by the external zone names in increasing order i e the first row corresponds to the lowest numbered zone the second to the next lowest number etc Since zone numbers need not be sequential in SATURN i e 1 2 3 the name of the Ith zone may be much larger than The basic advantage of having a non sequential numbering system is that the user can associate informative and fixed numerical names with each zone independent of which other zones are included in the network or matrix In addition see 5 1 6 zones may have alphanumeric or text names associated with them as stored on the associated GIS files For example sequential zone 6 might be named numerically 27 and have a text title of West Ham As a convenient shorthand we refer to titles names and numbers as opposed to alohanumeric names numerical names and sequential numbers The same system of sequential and external zone numbers is also used in SATURN networks and is described in greater det
2. The Output LPX File As with other SATURN programs an output line printer file is continuously produced in order to a Keep a permanent record of useful screen output and b store outputs which are too lengthy to conveniently output to the screen Copy Transpose Re code an Input UFM File Re defining Zones General Principles These options allow one to read an external ufm file into the internal matrix either i as is ii as its transpose T becomes Tj ili aS a compressed expanded recoded matrix whereby zones are transformed iv aS an aggregated version of a stacked input matrix i e with all levels summed to create a single square matrix v as a single level from an input stacked matrix 10 13 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 4 2 5120257 Apr 15 Section 10 _SATURN vi by pasting an external square matrix into a single level of an internal stacked matrix some but not all of these options may also be applied to the internal matrix In effect the internal matrix is first copied to a scratch external matrix from which the internal matrix is re created according to the various options above Options i and ii are self explanatory indeed case i is what happens automatically when one or more input ufm matrix files are initially defined in a run of MX see 10 3 1 Case ill requires further explanation since it is the main mechanism wi
3. _SATURN l e each cell element in matrix 1 is multiplied by the corresponding cell in matrix 2 so that if say matrix 1 is a trip matrix pcus hr and matrix 2 is a skimmed time matrix hrs then the resultant matrix is a matrix of pcu hrs hr N B This is not the normal mathematical definition of matrix multiplication but one that is probably far more commonly used by network modellers MXMb5 Matrix Compression Expansion and or Reordering MXM5 mat 1 mat2 control Outputs a new matrix file mat2 ufm based on the input matrix mat1 ufm but with a different set of zone definitions Thus the existing zones may be combined together aggregated split disaggregated names changed factored etc etc according to the instructions in the control file control dat See Appendix W 3 for the formatting of control dat Similar operations may be carried out interactively as described in Section 10 4 2 and in 10 16 3 MXAGG Aggregate Matrix Levels into a Square Matrix MXAGG mstack msquare Ll L2 Outputs a square matrix msquare ufm from a stacked matrix mstack ufm by aggregating together all levels from L1 to L2 If L1 L2 are not explicitly included then all levels are aggregated See 10 2 4 and 10 4 2 MXZ2G Aggregate a Zonal Matrix into a Group to Group Matrix MXZ2G matz matg FI AZ G Compresses a zone to zone matrix matz ufm into a group to group matrix matg ufm according to the grouping of zones into groups define
4. MXBLOCK Stack a Set of Matrices horizontally MXBLOCK mat matl mat2 Mia bo 8 Outputs a stacked matrix mat ufm built from the input matrices mat1 ufm mat2 ufm etc etc in order The list of input matrices may contain up to 8 inputs and clearly must have at least two in order to make sense N B The matrices are stacked horizontally in blocks as appropriate for time periods cf MXSTACK 10 55 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 20 11 10 20 12 10 20 13 10 20 14 10 20 15 5120257 Apr 15 Section 10 _SATURN STACK Stack a Set of Matrices with sequential filenames STACK mat Outputs a stacked matrix mat ufm built from the input matrices mat1 ufm mat2 ufm etc etc The number of sub matrices n to be stacked depends on the maximum existing matrix file matn ufm and unlike MXSTACK isnot otherwise restricted STACK differs from MXSTACK only in so far as the matrices to be stacked are not explicitly named on the command line but are implied by their root name i e mat The converse of STACK is the UNSTACK procedure which creates a set of sub matrices based on a root filename STACK and UNSTACK may be conveniently used if you wish to perform the same operation e g editing the zone structure on each level of a stacked matrix UNSTACK Unstack a Stacked Matrix using sequential filenames UNSTACK mat Unstacks a stacked matri
5. The row origin zone name or sequential number NAMES T or F The ratio of the new total to the current value CSV F include a decimal point normally in col 13 RECORD SET 6 DESTINATION COLUMN FACTORS OPTIONAL Record 6A 66666 in columns 1 5 followed by Records 6B One record per column constraint formatted as SATURN MANUAL V1 1 3 l l noaa SATURN MX Interactive Matrix Manipulation i Col 1 S if the record cols 2 5 applies to a sector Cols 1 5 The column destination name or number NAMES T or F Cols 6 15 The ratio of the new total to the current 10 8 10 8 1 5120257 Apr 15 Section 10 value CSV F include a decimal point normally in col 13 Terminated by Record 6C 99999 in cols 1 5 RECORD 7 MANDATORY A final 99999 record Matrix Manipulation A number of options are available to create a new version of the internal matrix using some or all of the data currently available They are General manipulation via an equation NO Transposition A O Screen editing by cell or by sector Addition of two cost skim matrices 5 Log sum addition of two or more cost matrices OD Copying individual rows or columns 7 Manipulation of the intra zonal cells only The manipulation may be applied to the whole matrix by default or to selected areas see 10 6 Manipulation via FORTRAN Equations This option allows for a
6. see 14 1 MX mat or to enter without any specific files in mind e g to create a new ufm matrix from a text file see 10 5 use MX I To look at multiple matrix files mat1 ufm mat2 ufm it is easiest to use the MXX batch file in preference to MX E g MXX matl mat2 mat3 mat4 Selected input and or output filenames may also be set via the command line by using key words such as OUT KP and KR type MX for a full list and for name conventions In addition note that a Command Line with more than 10 words may be accommodated via the XCL option described in Section 14 8 Matrix Files General Properties DAT and UFM Files Within the SATURN Suite matrix data exists in essentially two forms first as raw data in ascii or text files and secondly as processed or binary data in unformatted files These are most easily identified by their standard file extensions dat and ufm respectively With the exception of MX when used to build matrices by converting a dat file into a ufm file all programs which involve matrices access them in their ufm format Thus for example the trip matrix file input for assignment must be a ufm file Ufm files include not only all the cell values for the matrix but also a certain number of header records which record for example basic matrix data such as the number of rows and columns in the matrix but also relevant filenames information on sec
7. the matrix column and or row sums will be included space permitting Equally the total of all cells appears in the extreme lower right hand corner Options are provided such that the row and column totals always appear on the screen display Two format modes are provided the default prints all cells with two decimal places the alternative prints integers and because each column is narrower more columns are printed at a time Alternatively under a select mode all non selected cells are left blank on the screen Not that each screen that appears is also sent to the output line printer LPX file as a permanent record Viewing Multiple or Stacked Matrices It is possible to print two or more matrices simultaneously by a set of multiple lines for each matrix row For example the first row prints cell elements in the internal matrix the second could print cell elements for the first input ufm matrix file etc etc On screen these appear as different colours Similarly with stacked matrices the different levels may be displayed interleaved as above as opposed to having the top level displayed first with lower levels beneath it Alternatively a single level of a stacked matrix may be selected for display only Post 11 1 14 buttons have been added to the menu bar to allow the display to jump to the next level up or down in addition to the existing Up and Down navigation buttons that move the dis
8. 10 See Section 10 2 3 for a more complete explanation of these terms If MPNEXT is FALSE they are set to blank by default 4 MATRIX TITLE RECORD Mandatory Cols 1 76 A title for the SATURN matrix see 10 2 6 5 MATRIX ELEMENTS Mandatory Two different standard input formats are allowed depending on the value of the LOGICAL parameter LONG But see 4 4 further non standard alternatives also exist e g CSV LONG FALSE its default FORMAT 1515 1ST CARD S The name for row 1 in cols 1 to 5 followed by the NCOLS elements in cols 6 10 11 15 etc using the subsequent cards as necessary Thus the first record contains the name plus 14 elements the second record contains elements 15 29 with the 15th element in cols 1 5 2ND CARD S As above for the second row Etc Etc b LONG TRUE 1st CARD S The name for row 1 in cols 1 to 5 followed by the NCOLS elements in cols 6 15 16 25 up to column 75 starting with cols 6 15 on any subsequent records written as F10 3 i e the decimal points must normally lie in columns 12 22 62 2nd CARD S As above for the second row Etc etc In either case the names must be in strictly increasing order but not necessarily sequential see Section 10 2 2 END OF THE DATA INPUT User Defined Format Matrix Data Files All O D Elements N B This option is rarely used Under non standard input but with all O D element
9. MX memory All three types of data are defined within a single data file and are distinguished in the normal SATURN way of appearing in 111117 22222 etc data sections following a very limited set of namelist parameters Not all data sections need appear In addition the data may be defined either for individual zones or for sectors i e aggregates of zones if these are defined elsewhere Sector factors are applied to all zones equally new sector totals and or differences are applied pro rata to constituent zones based on the totals in the current trip matrix Note that the definition of the new row and column totals is progressive in that a new row total may be defined under data set 1 incremented under 2 and factored under 3 Such a situation would probably be very unusual in practice it is expected that users would use only one of the three basic methods The precise file format is as follows RECORD SET 0 NAMELIST PARAMETERS OPTIONAL These consist of a header record amp PARAM a record defining two possible logical parameters NAMES and CSV plus an amp END record Here NAMES TRUE if the following records use zone names as opposed to sequential row column numbers Default TRUE lf CSV TRUE the data records which follow are input as comma separated variables i e with the zone name number and new total etc in any columns as long as they are separated by a comma or by one or more
10. UFM files and need not be redefined when needed All other files however would need to be user set when and as required As a matter of good practice and common sense it is proposed although this is not a rigid requirement in SATURN that all Z2G etc files should a have the same root filename and b be stored in the same folder In other words files such as mapping z2g mapping z2s mapping g2s etc would all be stored in the same folder and therefore have a common root pathname as well as a common filename The advantage of this is that the user need not define all the possible mapping files since a SATURN program could logically infer a file oath name when necessary In particular this facility is routinely used with text descriptor files of the form G2T whereby if the predicted file mapping g2t can be found it is used to add text names to groups if not group text names are simply ignored Matrix Title Every ufm matrix file has a text title of up to 76 characters associated with it Generally speaking this is defined by the user at creation e g record 4 under 10 5 1 although in some circumstances the title will be created automatically using standard titles e g when two matrices are added together the title might be 2 matrices added together MX File Structure Matrix Files The matrix files in MX can be divided into three components 1 One or more maximum 10 input UFM files stored in the e
11. all you wish to see Intrazonal cells normally identified by row equals column in a square matrix are also identified in stacked and or blocked matrices where the local row equals the local column i e both represent the same zone Matrix Graphics Graphical facilities in MX unlike P1X are relatively new and in fact do little more than duplicate facilities already in P1X see 11 6 7 2 Essentially two options are available 1 Frequency Distributions 2 Trip Length Distributions plus a parameters sub menu that services both Users who require more sophisticated graphical displays are advised to dump the matrix matrices into e g EXCEL 10 15 and use the facilities there But please advise DVV of any display forms that you would regard as essential and or specific to transport planners 10 43 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 13 10 14 5120257 Apr 15 Section 10 _SATURN The trip length distribution TFD option is only available if you have two or more matrices including the internal matrix one defines the trips and the other the costs although there are no checks whether or not the matrices you select are indeed trips and costs Recall that cost matrices are generally obtained using SATLOOK see 15 27 It is also possible to print trip length distributions from two different input trip matrices simultaneously in which case at least two external ufm files
12. all zeros However an input record may have fewer cells than the standard number of columns in which case the missing cells on the right default to zero lf desired each record may contain either n 1 or n 2 elements by including the sequential row number and or the name of the zone at the start of each record to assist in the identification of each row One potential technical problem with spreadsheet style formats is that with all elements per row held in a single record the record length may become too long lt is partly for this reason that as discussed further in Section 10 15 a spreadsheet file may contain only a subset of the columns which limits the size of each record In such cases the transfer of matrix data to and from external programs must take place in stages a necessary evil to overcome the problem of record lengths Stacked matrix files may also be input using the CSV format post 10 8 in which case the user must first interactively define the number of rows columns and levels where the number of columns equals the number of zones and the product of columns zones times levels should equal the number of rows The presumption is that the first N records contain the first level the second N records contain the second level etc etc If Zone names are explicitly included on stacked CSV records they should be identical within each level although strictly speaking they are ignored after the first leve
13. although if they do appear they will cause non fatal read errors which do not affect the final output matrix Free Format CSV Inputs Under CSV format with only items i and v included the data might consist for example of records 1 eras 0 yo nO Cor ae Indicating that cell 1 2 has a value 12 0 etc etc Alternatively using spaces and fixed columns the same data might appear as il 2 LA eG 1 5 Loe U And both data sets could be happily read as free format Note that in this case we are assuming that only sequential row and column numbers are given not their zone names i e i above but not ii Alternatively if the zone names for sequential zones 1 2 3 were 10 20 30 then only names not sequential numbers method ii could be used as in NOT AO Pili 20 OF Oy 0 SO 205 4 0 Finally belt and braces both sequential and zone names could be used as in Ore ail Oe o ye nO SO ks See Ae OA Or oA a0 Clearly in this case one would have to be careful that a sequential 1 was always followed by the name 10 whether input as a row or a column Formatted Inputs Under formatted input to repeat NOT RECOMMENDED three standard options are provided with default formats as follows Options Format i SEQUENTIAL ROWS AND COLUMNS ONLY 215 FI5 2 NAMED ROWS AND COLUMNS ONLY 216 FI5 6 3 BOTH SEQUENTIAL AND NAMED ZONES 215 216 F15 6 For example under option 2 a line 10 23 SAT
14. an off line or batch mode without having to use MX interactively This section lists a number of such procedures which are provided as part of the standard SATURN installation MXM1 M1 Build a Matrix MXM1 mat Using as input an ascii text file mat dat in standard SATURN format it outputs a file mat ufm in binary format MXM2 Compare 2 Matrices MXM2 matl mat2 Carries out the full set of standard statistical comparisons between 2 ufm matrix files mati ufm and mat2 ufm and outputs the statistics to a line printer file mat1 lp2 See 10 9 2 MXFACTOR Factor a matrix MXFACTOR matl mat2 X LEVEL n Factors the input matrix file mat1 ufm by X to output file mat2 ufm ie gt 1 T XT If a level n is defined for a stacked matrix then the factoring is applied to that level only otherwise the factor is applied to the entire stacked matrix N B Similar to the interactive process to select a single level see 10 7 2 MXADD2 Add 2 Matrices MXADD2 matl mat2 mat3 Adds matrices mati ufm and mat2 ufm together to produce an output file mat 3 UfM i e 3 el 2 T T T MXAVER2 MXAVER2 matl mat2 mat3 Takes a 50 50 average of two matrix files mat1 ufm and mat2 ufm to produce an output file mat3 ufm where i T T 2 10 54 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 20 6 10 20 7 10 20 8 10 20 9 10 20 10 5120257 Apr 15 Section 10 _SATURN MXMSA MXMSA mati ma
15. be obtained from a corresponding network ufs file 10 3 3 If the names are pre defined this allows the input dat file to use those names instead of sequential numbers which may be more convenient for the users Within 3 and 5 above it is possible to establish the zone names by carrying out a preliminary pre pass through the dat file Matrix Units In converting matrices from one suite into another it is important to remember that different suites may have different conventions as regards units In particular recall that SATURN prefers to define trip matrices in units of pcus hr whereas other suites may use vehicles hr Thus it may be necessary having read an input data file into MX to undertake some further factoring to correct for units Cost matrices which might be in monetary units or generalised time units are another case in point 10 19 SATURN MANUAL V1 1 3 SATURN MX Interactive Matrix Manipulation 10 5 2 Standard SATURN Format Matrix Data Files MX can read in a trip matrix from a standard ascii dat file using a standard format described formally in Section 4 The detailed specification is as follows 1 RUN CARD Optional Cols 1 3 RUN Cols 5 80A title associated with the run lf omitted a default run name is used 2 NAMELIST PARAMETERS amp PARAM Mandatory See appendix A for a description of Namelist input Table 10 1 Namelist Parameters T Matrix parameters are give
16. complicated to input multiple level trip matrices as a series of simple square one purpose matrices created one at a time and then to stack the resulting ufm matrices into one large stacked matrix Spread Sheet CSV Format One record per origin A CSV Comma Separated Variables or soread sheet format is defined to be one where There is one record per origin row containing n elements for each of n columns plus optionally row and or zone names see below Each cell value is separated by a from the next value Cell values may be written as integers or with a variable number of decimal places see 10 15 2 No blanks but see below Essentially the spreadsheet format is free format with commas rather than fixed columns used to distinguish individual cell values It is the format regularly used 10 24 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 5 6 5120257 Apr 15 Section 10 _SATURN by Windows programs such as EXCEL and therefore it is frequently used by SATURN users to transfer files to and from EXCEL N B Fixed column input files may be processed as CSV files as long as there is at least one space between successive values or both commas and or spaces may be used However there may be certain instances where spaces are not recognised as CSV compatible so that the use of pure CSV formats is recommended Note that zero cell values must be included as must rows which are
17. consisting of 1 t matrices 2 a matrix mfOn followed a short 6 character matrix title with n in column 6 followed again by a longer 40 character SATURN matrix title record 4 under 10 5 1 The numerical value of n in record 2 above is user set with a default value of 1 Note that zero value cells are not output but that otherwise all cells in the matrix are considered Due to EMME conventions only matrices which are square may be processed by EMME i e stacked matrices should not be output using an EMME format CSV Outputs Alternatively users may define their own format or choose a CSV or spreadsheet style format where all the elements in a row are output to a single record with individual elements separated by commas see 10 5 5 This option is provided primarily for users who wish to dump a SATURN matrix into e g EXCEL Note however that a spreadsheet may be clever enough to read alternative SATURN outputs and that if you do try to use a spreadsheet there may be limits to the maximum number of columns which may be input in which case you may need to work with a strip of columns as described next Subsets of the matrix are selected as a rectangle within the full matrix defined by upper and lower row and column numbers You may for example choose to output all rows but only a strip of columns such that the width of each record per row does not get too long for ot
18. e g displaying elements or row column totals it is possible to optionally treat stacked matrices as though they were interleaved i e row 1 of level 1 is followed by row 1 of level 2 and row 1 of level 3 etc etc all followed by the row 2 s See 10 10 2 N B Stacking by blocks was introduced in SATURN 10 previous versions may only employ levels See Section 10 20 for various useful standard procedures e g MXSTACK UNSTACK etc for manipulating stacked matrices 10 7 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 2 5 10 2 5 1 10 2 5 2 10 2 5 3 5120257 Apr 15 Section 10 _SATURN Zonal Aggregations Groups Sectors Traffic Boroughs etc General Principles It is very often convenient with matrices based on zones of which there can be very many to represent them using aggregated spatial areas For example with a national model one might wish to combine all zones within a county into a single Spatial entity in order to obtain matrices where each cell corresponds to county to county movemenis Most commonly aggregation is based on geographically self contained areas for which several standard terms may be applied Thus we use groups as the most general terms but sectors traffic boroughs and districts are commonly used as well with certain general assumptions as to their size Thus sectors are generally very large and few in number whereas at th
19. multiple levels a single level may be dumped as a square output ufm file an operation referring to as cutting a matrix option 11 along with 12 and 13 to set the level block See 10 4 3 for the reverse procedure to paste a square input matrix into a single level The same option plus others is also available as described in 10 17 Miscellaneous UFM Output Options Options to change the matrix dimensions and units 10 2 3 and the title are available 15 Option 14 allows a matrix of 0 1 cell values to be output to represent the current state of cell selection 10 6 Thus O represents non selection 1 selection 10 50 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 17 10 18 10 18 1 5120257 Apr 15 Section 10 _SATURN Stacking and Unstacking Matrices A matrix may be stacked from two or more square input ufm files either into the internal matrix for internal analysis modification etc or else directly into an output ufm file The levels in the stacked matrix must correspond to the order of the input matrix files although optionally not all the input matrix files need be stacked Note that it is not possible to directly include the internal matrix as one of the matrices to be stacked although this may be done indirectly by first outputting the internal matrix to a ufm file and including it as an input ufm file in which case it will appear as the lowest lev
20. option put S in column 1 of a record if the entries in columns 2 to 20 refer to sectors rather than zones Again missing input fields are assumed to refer to the lowest or highest sector number as appropriate Clearly the sector option is only possible in those cases where a supplementary network or GIS file has been input in order to define sectors It will not work with free format inputs Mixed zone and sector files are also permitted records without an S in column 1 are assumed to be based on zones However zones and sectors cannot be mixed on the same line An alternative method for applying factoring at a sector to sector level is to create a UFM matrix of the sector to sector factors and then use Option 13 under UFM Outputs see 10 16 2 plus a z2s file to copy those factors into a zone to zone UFM file which may then be used to multiply the internal matrix e g using a Fortran equation 10 8 1 Note that this method is in fact potentially much more general in that the level at which the factoring is applied is not restricted to sectors as pre defined for the internal matrix but may be based on any level of aggregation e g by traffic borough district etc etc through the use of an appropriate z2s aggregation file Row and Column Specific Factoring These options are in fact specific examples of selected area factoring where the area in question is either a complete row or column A complete set of row or c
21. plus a different internal matrix are required See also 10 9 3 for non graphical methods to calculate TFDs MX can plot either to the screen or to other external devices defined in GRAF DAT The screen image may also be dumped to a bitmap file 11 3 5 by entering X when the image is on the screen Printing a complete matrix to a line printer This option prints a full listing of the cells in either the internal matrix or an external ufm file to the line printer LPX file The format includes pagination and header records and therefore is intended essentially for viewing or printing not for transfer to another program such as a spreadsheet in the latter case option 13 should be used see 10 15 If defined sector to sector matrices may also be printed Printing Dumping Row and Column Totals This option prints the row and or column totals either to the line printer LPX file or to an ascii data file with either a SATURN based format or a CSV based format In the SATURN based output the row and column totals are formatted as per that required for a trip ends control file as specified in Section 10 7 5 for matrix Furnessing i e a namelist record followed by 11111 row totals and 22222 column totals data sets CSV formatted files contain one record per zone with options to include or not a sequential row numbers b zone names per row c level numbers per row d row totals and or e column totals In addition an ex
22. set interactively in three basic ways 1 En masse via screen editing 2 Individually using keyboard inputs 3 From another matrix Under 1 the new totals may in turn be defined in three different ways a As new absolute values b As incremental changes c As factors In addition these may be set by zones or by sectors if defined Thus if one is using factors by sector an input value of 1 1 for sector 1 origins would factor the origin row totals for all zones in sector 1 by 1 1 In all three cases the defaults are no change current values change 0 factor 1 respectively Keyboard input is longer and more laborious than screen editing but is fine for changing one or two totals or for subsequent use with key files Finally trip ends from one of the external matrices may be used to set trip ends for the internal matrix an application of which is given in 10 19 1 10 32 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 7 6 5120257 Apr 15 Section 10 _SATURN Matrix Furnessing Trip Ends Set from a Control File Trip Ends for the MX Furness option may also be read from an external ascii dat file defined in one of three different ways 1 As absolute origin and or destination totals 2 As additive changes to the existing totals 3 As factors to the existing totals where the existing totals are derived from the current trip matrix i e the matrix currently within the internal
23. should follow the interactive procedures outlined in Section 10 5 preferably entering the program MX via the batch file command see 10 1 MX I At a future date the 2UFM batch files may be made sufficiently clever to detect when a ufm matrix does not pre exist and must be built totally from scratch Essentially the 2UFM procedures are the reverse of the UFM2 procedures described above the latter converts a ufm file into text the former converts a text A number of varieties of 2UFM procedures exist LINE2UFM CSV2UFM 10 57 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 20 17 10 20 18 10 20 19 5120257 Apr 15 Section 10 _SATURN EMME2UFM TBA12UFM TBA22UFM TBASAUFM following the conventions described in 10 20 13 Specifying formats and or decimal places is less important in reading from text files than in writing to them see 10 20 13 above since in general the input routines can detect whether a field is say E formatted and deal with it as appropriate Note that there are no procedures SATL2UFM or SATS2UFM as these are effectively covered by the standard matrix build procedure MXM1 See 4 1 UFMSTACK Stack a Set of Matrices based on a Control File UFMSTACK mimi leno Seen ie Outputs a stacked matrix using a set of filenames read from a text file control More specifically the first record in control gives the name of the outp
24. spaces If CSV FALSE the fixed columns with decimal points specified below must be used Default TRUE post 10 7 N B Where the specification indicates that a decimal normally appears in say column 13 out of columns 6 15 this is not a rigid requirement In fact the decimal may appear in any column as long as the whole number is contained within the columns specified Thus in the above case the user would not be restricted to a maximum of 2 decimal places in the input field RECORD SET 1 ABSOLUTE ORIGIN TOTALS OPTIONAL Record 1A 11111 in columns 1 5 followed by 10 33 SATURN MANUAL V1 1 3 Co a SATURN MX Interactive Matrix Manipulation i Records 1B One record per row constraint formatted as Col 1 ene S if the record cols 2 5 applies to a sector Cols 1 5 The row origin zone name or sequential number NAMES T or F Cols 6 15 The required new total CSV F include a decimal point normally in col 13 terminated by Record 1C 99999 in columns 1 5 RECORD SET 2 ABSOLUTE DESTINATION TOTALS OPTIONAL Record 2A 22222 in columns 1 5 followed by Records 2B One record per column constraint formatted as Col 1 S if the record cols 2 5 applies to a sector Cols 1 5 The column destination zone name or sequential number NAMES T or F Cols 6 15 The required new total CSV F include a decimal point normally in col 13 terminated by Re
25. very general matrix manipulation by defining via equations based on FORTRAN syntax the new matrix to be created Both the current internal matrix plus all input and ouput UFM files may be involved For example to average two matrices the user would type 0 5 X X while more complex matrix operations are possible for example 0 23 X e 1 10 36 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 5120257 Apr 15 Section 10 _SATURN transforms an input matrix into its corresponding negative exponential In these equations the external ufm files used for input are denoted by X1 X2 etc the internal matrix by Y and the output ufm matrix by Z as shown in Figure 10 2 For example typing 0 5 Z would take the average of the current internal matrix and the latest output ufm file and store those values as the new internal matrix Y The equation can not only use the standard arithmetic operations add subtract multiply divide and exponentiate they can also use a number of standard functions e g EXP as illustrated above The following functions are available Exp X Log X natural log SQrt X Sin X Cos X Tan X Abs X e Int X e MAX X Y MIN X Y RR X Y Uniformly distributed random variable whose mean is X and with range X 1 Y to X 1 Y RN X Y Normally distributed random variable whose mean X and whose varianc
26. 5 Thus the standard SATURN format is not available as an update option since by construction it must contain all cell values The data set read need not contain all ij cell values but may be only a subset which in the case of user defined and spreadsheet formats must constitute a rectangle within the matrix as defined by upper and lower row and column numbers An update may either replace the existing cell value by the value which is read in or increment it i e add the existing and the input cell values together An advantage of updating an existing ufm matrix rather than creating one totally from scratch is that with updates the number of rows and columns plus any names see below are pre defined only certain cell values are set Sequential Numerical Zone Names The data read from an input dat file may be based on either sequential or numerical zone names 10 2 2 or indeed both as is the case with the standard SATURN formatted data files 10 5 1 With other formats e g spread sheet 10 5 5 there is no explicit mention of either row or column numbers but they are implied by the position of the entry within the data file Note that in certain cases it may be possible to pre define the numerical zone numbers before reading in the dat file Thus if the dat file updates an existing input ufm matrix the zone names will already have been obtained from the ufm file Alternatively the names may
27. A1 2 3 dumps in Tuba 1 2 3 formats By default the output text files use decimal formats with 2 decimal places 10 15 2 To change either it is necessary to change the parameters EFORM and NDPS respectively in the preferences file MX0 DAT These procedures are designed to make life easier for users who wish to transfer SATURN matrices into other suites of programs e g EXCEL in order to make use of particular facilities To transfer them back into SATURN a complementary set of procedures CSV2UFM etc are also provided see 10 20 14 below N B These procedures only work with release 10 6 and beyond of SATURN although the ufm files used and or created will work with previous releases within reason 2UFM Re build UFM Matrices from Text Files E g CSV2UFM mat re creates the binary matrix mat ufm from a csv formatted text file mat txt It therefore follows automatically the procedures described in 10 5 5 but with the proviso that the file mat ufm already exists so that it is updating rather than building Thus the new version of mat ufm takes all its structure i e the number of rows and columns the zone names etc from the old mat ufm but re sets all its cell values as read from the txt file Note therefore that these procedures are essentially restore or rebuild rather than build from scratch If you do wish to create an entirely new ufm from a csv data file you
28. External data sets once created may be used for repeated operations of the same program In a slightly different sense the MX preferences file MXO DAT may also be viewed as a control file A new version may be created from within the Files Menu Figure 10 2 MX File Structure Input External Matrices Internal Matrices External Output Matrices pe ES Note that a single run of the program may use more than one input control file each file is opened and closed as and when needed by the program Equally the input UFM files are not fixed and may be redefined during a run and more than one output file may be created but at any one time only one exists Other Input Files MX also allows the user via the Files Menu to define as an input a network ufs or a gis file 5 7 which may provide useful extra zonal information on the matrix 10 12 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 3 4 10 3 5 10 4 10 4 1 5120257 Apr 15 Section 10 _SATURN matrices being examined Thus either may supply the necessary sector definitions which see 5 1 7 or 10 2 5 3 are originally set within the node co ordinate data sets on a network dat file or the gis file Equally text names for zones are only given within gis files A further application of an input network file is to define the zone names see 10 2 2 when they have not been predefined as part of an input ufm file
29. SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 10 1 10 1 1 10 1 1 1 5120257 Apr 15 Section 10 _SATURN MX Interactive Matrix Manipulation Synopsis MX is a flexible interactive matrix manipulation program which incorporates virtually all matrix operations required by SATURN users It includes options to build matrices change them e g by factoring and analyse them The flexibility means for example that users can carry out their own trip matrix demand model procedures involving e g trip distribution constrained or otherwise modal split park and ride etc using the facilities within MX even if those procedures are not explicitly included within MX as some are see 10 20 Although MX has been constructed as a perfectly general matrix manipulation program clearly its primary use will be based on SATURN and transport planning applications Indeed the vast majority of matrices which MX handles will be origin destination trip matrices This is very often reflected in the language used in the documentation for example row and column are used interchangeably with origin and destination and sometimes cell values are referred to explicitly as trips e g when discussing distribution models Equally O D and l J will be used interchangeably when referring to individual cell locations MX includes all the facilities previously provided in earlier SATURN versions by
30. This option is particularly useful when the matrix is being input from a dat file and the zone names are not known a priori see 10 5 Post 11 1 the zone names are applied to rows within all levels of a stacked matrix previously they were only applied to rows in the base matrix Alternatively to transfer network zone names into a matrix 1 read the matrix into MX so that it becomes the internal matrix 2 input the network ufs file 3 choose to transfer the network zone names into the internal matrix if the network has the same names the choice is never presented and 4 dump the internal matrix into a ufm file Output Data Files Certain options allow data in relatively large quantities to be dumped to external ascii files created by the program For example row and column totals may be dumped in this way or the entire matrix cell by cell Various formats e g the style required by spreadsheets such as EXCEL may be selected Generally speaking the output ascii files are assigned the extension kp by default as set by the Namelist Parameter KPEXT in SAT1OKEY DAT see Appendix Y although for subsequent inputs they may need to be re christened as dat files Note however that the default value of KPEXT and therefore the default extensions used within MX may be user set either within SAT1OKEY or the Preferences File MX0O DAT Post 10 7 it is conventional to set the default extension to txt within SAT1OKEY DAT
31. URN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 5 4 3 10 5 5 5120257 Apr 15 Section 10 _SATURN iil 22 oo would imply a cell element of 6 00 for row origin 11 and column destination 22 both 11 and 22 being zone names which would need to be converted into sequential numbers Under option 1 the same line would imply the cell would be the 22nd column in the 11th row without any reference to the associated zone names Under option 3 the same cell might be specified by Li ZL 61 94 So VIII where sequential row 11 is zone 61 and sequential column 22 is zone 94 This method clearly requires internal consistency such that sequential row column 11 is always associated with zone 61 etc Reading a Stacked Matrix by Single Records A stacked matrix 10 2 4 be input via single records by either explicitly using the correct sequential row number or by including both the name of the O D zones and the level The input format must however be free format For example if a network of 100 zones has a trip matrix with three purposes i e levels then the sequential row numbers in the stacked matrix would go from 1 to 300 If the 5 and 6 sequential zones say had names 511 and 512 then an O D trip record of 23 6 trips from 511 to 512 for purpose level 3 could using purely sequential notation be written as e Cn a N Or using both zone names plus a level as OPO oy oe However users may find it less
32. after reading a dat file 10 5 The output matrix referred to as Z in Figure 10 2 may then be further used within the program The filename of the new ufm matrix may either be set interactively at the time of output or pre defined using the OUT keyword on the MX command line see 10 1 2 10 48 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 16 2 10 16 3 10 16 4 5120257 Apr 15 Section 10 _SATURN A number of different options numbered 1 through 15 in the UFM Outputs sub menu and described below control the form of the outputs Basic Outputs The most basic output is to copy the internally stored matrix data to a ufm file as is the usual option menu option 1 Alternatively the internal matrix may be output as its transpose i e Tj is output in cell i j option 2 although it is probably preferable to use methods described in 10 4 and or 10 8 4 to transpose the matrix internally prior to output Outputs Based on Transformed Zonal Structures Alternatively the output matrix may be based on a different pattern of zones by compressing expanding re coding the zones and the corresponding cells in the internal matrix options 3 to 10 Note that the options described below closely parallel those described in Section 10 4 for the transformation of the internal matrix Thus alternatively the matrix may be first transformed internally and then output as is For complex tr
33. ail in section 5 1 6 Note in particular that zone names are restricted to 5 digits i e numbers up to 99999 although a maximum of 4 is recommended in order for example not to fill up the maximum 5 column input fields as used in certain standard file formats 10 5 1 Clearly networks and matrices based on the same set of zones will have exactly the same correspondences between sequential and external numbers Logically zone names should be positive non zero numbers and whereas exceptions to this rule will be fatal errors in network building it is just about possible to have zone names equal to zero in matrices although the practice is certainly not recommended and will almost certainly be made a fatal error ASAP It is essential that users be aware of the differences between a zone s name and its sequential number In all SATURN network based programs the external names are always used in input or output However in most matrix operations it is possible to refer to either the sequential numbers or the external names in general options exist to toggle between the two systems 10 5 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 2 3 10 2 4 5120257 Apr 15 Section 10 _SATURN For square matrices rows it is assumed that the same set of numerical names and or titles applies to both rows and columns For stacked multiple level matrices if Zone names are applied to rows in the basic sq
34. ansformations e g not a straightforward compression it may be preferable to undertake the transformation before output as it may be easier to check what is happening Zonal re coding options were originally handled by the SATURN programs M3 M4 and M5 M3 and M4 were basically simplified versions of M5 which would not work with e g stacked matrices so that they have now been effectively phased out and have been given option numbers at the bottom of the list to reflect this fact In all three cases the specifications for the new zone structure must be pre coded on an input data file whose formats follow the previous M3 M4 M5 conventions given in Appendix W Option 3 M5 represents the most general form of zonal transformations in that it allows for zones to be added together compressed renamed sub divided into new zones or deleted as defined in the control file as documented in App W 3 To a large extent M5 duplicates the interactive options described in Section 10 4 2 for editing zones internally Outputs Based on Compression Options 4 through 8 are based on simpler forms of zonal transformation either a pure compression aggregation from zones to groups or conversely a pure expansion from groups to zones They follow the basic principles described in Section 10 4 4 and 10 4 5 and effectively perform the same functions but with outputs directly to an external ufm file as opposed to the internal matrix Thus optio
35. ated For example to average two matrices the user would type 0 5 X X while more complex matrix operations are possible for example 0 23X e transforms an input matrix into its corresponding negative exponential 10 2 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation _SATURN 10 1 1 3 Analysis 10 1 1 4 5120257 Apr 15 Section 10 1 STATISTICS UNIVARIATE OR COMPARISON Compare two matrices obtain a set of standard univariate statistics mean range etc for one matrix or obtain a trip length distribution 2 VIEW EDIT MATRIX ELEMENTS A flexible set of options to view the current internal matrix on the terminal Cursor control keys may be used to move through the matrix and more than one matrix may be viewed simultaneously In addition the values of cells in the internal matrix may be edited using an interactive screen editor or window 3 VIEW ROW AND COLUMN TOTALS Display row and or column totals interactively 4 MATRIX GRAPHICS Frequency and trip length distributions may be displayed graphically Output 1 PRINT MATRIX CELLS SECTORS TO THE LP FILE Produce a standard matrix listing to the line printer file intended for later analysis 2 PRINT DUMP ROW AND COLUMN TOTALS Produce a listing of row and column totals to either the line printer or a file 3 DUMP MATRIX SECTOR DATA TO A DAT FILE Output matrix file in toto to an external ascii e g dat file This
36. ating more than one GIS file which defines the sectors 10 3 3 and swapping between them Traffic Boroughs Traffic Boroughs or simply boroughs are largely a London based concept where traditionally the administrative boroughs within and around London may have been split into one or two traffic boroughs eg Wandsworth within Central London separated from the rest of Wandsworth with further definitions for areas outside London being aggregates of non London boroughs e g the whole of the North of England and Scotland might constitute a single traffic borough Within the current TfL Transport for London SATURN models there are currently 45 boroughs numbered sequentially from 1 to 45 with numbers 1 to 33 representing the 33 administrative sub areas of Greater London on a one to one basis no splits 34 to 40 adjacent or near counties and the rest large regions further afield N B Like groups there should be no borough 0 10 2 5 5 Z2G Zone to Group etc Mapping Files 5120257 Apr 15 Section 10 A set of filename conventions has been drawn up in order to identify ASCII text files which define the mapping of one set of zonal aggregates into another Thus a file with extension Z2G will contain data which specifies which Groups are to be associated with each Zone Z2S maps Zones into Sectors G2S maps groups into sectors etc etc The following letters may be used Z for zones D for districts B for boroughs an
37. ay be described as follows 1 Deletion is straightforward both the row and the column corresponding to the zone selected are removed Alternatively a range of zones e g all external zones may be removed 2 New zones are added in the rows columns corresponding to the sequential position of the new zone numbers The cell values to be inserted in these elements may be either defined uniformly by row and column e g set all row elements to 1 and all column elements to 2 or they may be copied 10 14 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 5120257 Apr 15 Section 10 _SATURN and or factored from an existing zone s row and column cells Thus you may create a new zone in a trip matrix which looks like an existing zone or under copy the new elements may be the sum of multiple zones an average of multiple zones or a weighted sum of multiple zones Alternatively the cell values in the new rows and or columns may be set either a from an external data source via the update options described in Section 10 5 1 2 b via matrix manipulation equations to selected rows columns 10 8 2 described in 10 8 1 or c by screen editing 10 10 4 Compression aggregates two or more existing zones i e rows and columns into a single larger zone many to one by adding cell elements together whereas renaming basically copies one zone into another with a different name one to one Since
38. be useful as a means of creating fixed or frozen matrices for input to SATALL or SATME2 Note that the 0 1 definitions may optionally be reversed if desired such that non selection equals 1 and selection equals 0 Matrix Factoring General Principles Three general forms of matrix factoring are allowed and operate only on the internal matrix 1 Factoring Individual Cells within Selected Areas I E JE where f is a user defined factor and the cells which are factored may either constitute the entire matrix or a selected subset i e an area 2 Row or Column Specific Factoring T Al Or Ti B where Aj B are row column specific factors set by the user 10 28 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 7 1 1 5120257 Apr 15 Section 10 _SATURN 3 Singly or Doubly Constrained Furnessing 1 ABT where the row and or column balancing factors are chosen such that Lep m ij j DF 0 where the row and column sums O and Dj are user input Under a singly constrained model only one set of constraints is applied as under 2 under doubly constrained both are Note that singly constrained Furnessing is effectively equivalent to row column factoring the only difference being that the required trip ends are defined under Furness as opposed to the trip end factors e g O as opposed to O 0i All three forms are available through a combination of interactiv
39. calibration exercise carried out by trial and error Economic Evaluation Rule of a Half The classical rule of a half for calculating the consumer benefit of network trip matrix 1 compared to network trip matrix 2 may be written as Equation 10 1 C S T T C C ij This may be calculated by inputting the 4 relevant trip matrices T T C C as input files 1 to 4 respectively recalling that cost matrices may be calculated as described in Section 15 27 4 and then creating the internal matrix via the equation 0 5 X X X X The consumer benefits may then be viewed per cell per origin destination or in to using master options 8 and 9 Note that to dump the total benefit into an external file e g as part of a iterative process involving forecasts for a series of future years you may make use of the facilities described in 10 14 More simply the R O H calculations are available as part of a standard batch file see 10 20 8 10 53 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 20 10 20 1 10 20 2 10 20 3 10 20 4 10 20 5 5120257 Apr 15 Section 10 _SATURN Useful Matrix Batch Files As explained in Sections 3 5 14 5 and 14 7 it is possible via the use of command line options to set up standard batch procedures using interactive programs such as MX to carry out certain standard bread and butter operations such as adding two matrices together in
40. compression is essentially similar to that of defining sectors to be aggregates of zones it may sometimes be more convenient to perform this step via sector definition for example with sectors it is possible to view both the zonal and the sectoral matrices within the same run The zones to be compressed may either be in a block of sequential zone numbers e g zones 4 5 6 and 7 or mixed e g zones 1 5 7 and 8 They may either be aggregated into a zone with a completely new number e g zones 4 to 7 go into zone 40 or an existing zone e g zones 4 to 7 all go into zone 4 in which case the original zone 4 effectively stays where it was Renaming is straight forward the row and column elements are moved to the new sequential positions In effect renaming is an alternative form of compression the difference being that with renaming a single zone is converted into another single zone with compression several zones are converted into one Renaming and compression are therefore included within the same menu structure with the first two many into one being effectively compression and the next two one into one being effectively renaming The Split function may be used to divide a single zone into a set of 2 or more sub zones with separate factors by row and column Normally at the end of the process the old zone has been deleted However the new sub zones may in fact contain the original zone number so that this func
41. cord 2C 99999 in cols 1 5 RECORD SET 3 CHANGES TO ORIGIN TOTALS OPTIONAL Record 3A 33333 in columns 1 5 followed by Records 3B One record per row and or column constraint formatted as Col 1 S if the record cols 2 5 applies to a sector Cols 1 5 The row origin zone name or sequential number NAMES T or F Cols 6 15 The difference of the new total from the current value CSV F include a decimal 5120257 Apr 15 10 34 Section 10 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 5120257 Apr 15 Section 10 Terminated by Record 3C 99999 in cols 1 5 SATURN point normally in col 13 RECORD SET 4 CHANGES TO DESTINATION TOTALS OPTIONAL Record 4A 44444 in columns 1 5 followed by Records 4B One record per column constraint formatted as Col 1 Cols 1 5 Cols 6 15 Terminated by Record 4C 99999 in cols 1 5 S if the record cols 2 5 applies to a sector The column destination zone name or sequential number NAMES T or F The difference of the new total from the current value CSV F include a decimal point normally in col 13 RECORD SET 5 ORIGIN ROW FACTORS OPTIONAL Record 5A 55555 in columns 1 5 followed by Record 5B One record per row constraint formatted as Col 1 Cols 1 5 Cols 6 15 Terminated by Record 5C 99999 in cols 1 5 S if the record cols 2 5 applies to a sector
42. culations The resulting T values are stored in the internal matrix use main menu option 14 to permanently store them in a ufm matrix file if desired similarly to carry out a singly constrained trip distribution model set MCUBC 1 see 7 10 2 Note that these functions are not applicable directly to multiple user class models where the matrices are not square but stacked by levels to represent the different user classes To undertake demand calculations by user class it is necessary to treat each user class separately with its own square matrix Blocked Matrices Matrices which are stacked by blocks see 10 2 4 are currently only used to represent multiple time periods and therefore the demand calculations available within MX reflect this Thus the one model available is the incremental logit model of time period choice as described in Section 17 12 and 10 20 7 The MX Box of Clever Tricks The section lists a number of matrix operations which can be carried out using MX but which may not be readily apparent Basic Trip Distribution Models using Furness We demonstrate here how MX may be used to run a basic doubly constrained trip distribution model of the form 2C IT A B 0 D e where A and B are row and column balancing constraints to satisfy the row and column totals O and Dj lt requires as input a skimmed cost matrix ufm file say input as the first matrix file plus optionally but most conveniently an existing tr
43. d S for sectors plus more generally N for node where the files are being used in networks as in FILN2G see 5 1 7 In addition T represents text so that a G2T file would consist of a series of group names followed by a text description of that group e g 1 Otley All such files except the to text 2T files have the same general very simple format described as follows 10 9 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 5120257 Apr 15 Section 10 _SATURN They consist of a series of text records terminated by a 99999 record where each record consists of two integers in free format i e including CSV specifying a zone followed by its group where we use the terms zone and group to denote the first and second quantities as in a Z2G file but the same specifications apply equally to all such files Note that numerical names must always be used for both the zone and the group not sequential numbers although very often names are in fact sequential Records need not be in numerical order of zones i e the first number given does not have to be always increasing although this is generally the most convenient way to create such files Duplication i e assigning the same zone to two different groups is not allowed although it may not always be checked A hyphen in front of a zone name negative numbers may be used to indicate a range of zones Thus two success
44. d either by the optional file FILZ2G or using the pre defined zone to group mapping in matz ufm see 10 2 5 5 and 10 16 4 MXZ2B Aggregate a TFL Zonal Matrix into Traffic Boroughs MXZ2B matz matb Compresses a zone to zone matrix matz ufm into a borough to borough matrix matb ufm whereby the grouping of zones into traffic borough follows the naming conventions used by TfL See section 5 1 7 2 and 10 2 5 4 MXG2Z Expand De compress a group matrix back to a zonal matrix MXG2Z matg matz FILZ2G Expands de compresses a group to group matrix matg ufm into a zone to zone matrix matz ufm based on the the grouping of zones into groups defined either by the file FILZ2G optional or using the pre defined zone to group mapping in matg recommended The assumption is that matg ufm has 10 59 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 20 25 5120257 Apr 15 Section 10 SATURN previously been compressed from a zone to zone matrix using MXZ2G according to the same zonal groupings in FILZ2G Note MXG2Z sets all intrazonals to zero See also 10 2 5 5 and 10 16 5 MXDIVIDE Divide one matrix by another cell by cell MXDIVIDE Moel mat2 mat3 Divides each cell in mat1 ufm by the corresponding cell in mat2 and outputs file mat3 ufm i e 1 T3 a J T2 ij If T 0 then the output value is always taken as 1 0 MXDIVIDE may be used for example to establish the gro
45. e Y The upper case letters above indicate the minimum number which must be used to denote a function thus E X EX X once EXP X all have the same affect Note that numerical values may be used within the equation written either as integers or reals i e without or with decimal points Open and close brackets may be used as part of the expression always in pairs and follow standard FORTRAN syntax rules They may be used to clarify the order of calculation which again follows standard FORTRAN rules e g operations within brackets always precede operations outside For example in the expression X X 10 37 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 8 2 10 8 3 10 8 4 5120257 Apr 15 Section 10 _SATURN the variables X1 and X2 are always added together prior to exponentiation This would not be the same as X X Users are advised if in doubt to carry out several steps with very simple equations which create temporary data columns For example by first calculating Art A which might be stored in data column 4 followed by Xa would have the same effect as above although the final result might not be in the same data column Partial Manipulation over Selected Areas The use of selected sub areas of the matrix may be very usefully applied in this context Suppose you wish to add 50 of the trips for origin 6 from the second input ufm file to the int
46. e commands and or data from external ascii control files The choice of the form and the mode of control is made both in the top menu within FACTOR and in the next sub menu e g if you choose Furness at the top menu the choice of single double constraints and or input mode is made at the next menu Note as well that under doubly constrained Furness it is implicitly assumed that the sum of all the row totals should equal the sum of all the column totals If this condition is not satisfied various options to correct are offered e g factoring up all row constraints so that they equal the column totals Since factoring in transport applications is mostly applied to trip matrices the documentation below refers for simplicity to origins and destinations and trip ends instead of row totals or column totals although the actual factoring operations are applicable to any type of matrix Zero sum Rows and or Columns Note that if a row and or column of the matrix to be factored contains all zeros then equally the factored matrix row column will also be all zeros under both singly and doubly constrained However confusion may arise if a row column contains a very small number of very small valued cells e g 0 0001 This may arise as a combination of rounding errors or if one matrix is subtracted from another The problem is that the row column sum may be printed as 0 00 rounding down which is therefore diffic
47. e contains optionally the sequential row and or column numbers their corresponding zone names and the 10 45 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation _SATURN cell values with a large number of decimals for maximum accuracy In addition with stacked matrices the level and or block value may also be included e g as the third value on a record if only the sequential row column numbers names are included the fifth if both numbers and names are given Single line records may be either formatted i e output within fixed columns or free format CSV i e output with each item separated by a comma The fixed column widths are set large enough that spaces will certainly exist between each item so that the formatted output may be effectively re read in MX see Section 10 5 4 as though it were free format At this stage therefore and as far as subsequently re inputting files back into MX goes the choice is not particularly important although for inputs the free format choice is strongly recommended 10 5 4 In Release 10 8 20 an extra option has been provided to suppress the final record which by default consists of 99999 and which can be awkward if the ascii file is being input to other suites of programs 10 15 1 3 EMME 2 Formats 10 15 1 4 5120257 Apr 15 Section 10 Output in EMME 2 format follows the conventions specified in 10 5 5 In particular two header records are included
48. e file Names are then re set to the equivalent sequential values 10 30 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 7 3 1 10 7 4 5120257 Apr 15 Section 10 _SATURN Similarly for stacked matrices the row and column numbers may be based either on the full matrix or for a particular level within the stacked matrix For example if one had 3 10x10 matrices stacked so that the internal matrix has 30 rows and 10 columns and one wished to factor rows 3 to 5 of level 2 then one could either specify them as Sequential rows 13 to 15 if a level were unset or rows 3 to 5 if the level were pre defined as 2 Note that if the option to use zone names rather than sequential numbers has been pre selected then the only way to define rows within levels other than the first is to pre define the level Row or column numbers left blank or equal to zero are assumed to be either 1 or the maximum row column number as appropriate Hence all blanks in columns 1 to 20 implies the whole matrix is to be factored To terminate the file put 99999 in columns 1 to 5 or strictly any number or name greater than the number of rows Alternatively the input data may be free format again a user set option in which case each of the five inputs must be separated by blanks or commas Factoring Based on Sectors Etc A modification of the above procedure uses SECTORS in place of ZONES to define the area to be factored To use this
49. e following i sequential row and column numbers li low and column zone names iii the matrix level in the case of a stacked matrix iv the block if stacked by blocks v the cell value Of these either i and ii or both are mandatory iii and iv are generally not used and v is mandatory Choices for the contents are defined interactively by the user prior to input The records may either be read formatted i e in pre defined fixed columns or free format CSV i e with each record separated from its neighbours by one or more spaces and or commas Note that fixed column data may also be read as though it were free format provided that there is always at least one space between adjacent entries but the converse is not true It is strongly recommended that the free format input option is selected With 10 6 it is now the default Note that the form and contents of the input data must be fully and correctly specified by the user interactively prior to reading in the data otherwise input errors will almost certainly result Although optionally more than one record per ij pair may appear and the inputs are added together This may be useful for eg aggregating survey data 10 22 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 5 4 1 10 5 4 2 5120257 Apr 15 Section 10 _SATURN For the moment header records etc cannot be explicitly included with single records
50. e other extreme districts may contain say only 4 or 5 zones each Very often the different aggregates may sit inside one another like Russian dolls although this is not essential Thus a group of adjacent zones might be aggregated into districts adjacent districts into boroughs and adjacent boroughs into sectors However aggregates of zones need not be entirely spatial one might also wish to define groups based on common characteristics e g all Zones which are predominantly industrial all high household income zones etc etc The following sections described the properties generally ascribed to groups sectors etc followed by a discussion of how the mapping from one level to another is set within SATURN Groups Group is the most general term applied to any user set aggregation of zones and may be used at any level of aggregation e g 5 000 zones could be aggregated into 5 groups or 500 into 250 As with nodes and zones groups have numerical names which need not be sequential although in some applications there may be an upper limit e g 999 on the maximum group name Again as with nodes and zones a proper group cannot have a name of zero although if a zone has not been allocated to an explicit group then it is assigned to group O which in certain applications will result in a fatal error Sectors Sectors play a very traditional role within SATURN and have fairly restricted properties T
51. ead as is or transformed in various ways e g by adding new zones or aggregating existing zones Using a simple trick this also allows the zonal structure of the internal matrix to be edited 3 BUILD UPDATE THE INTERNAL MATRIX FROM A DAT FILE Construct a matrix from an external ascii data file This may be either in a standard SATURN format or in one set by the user e g to facilitate matrix transfer from other suites of programs or from a spreadsheet program In particular this function may be used in conjunction with the dump facility under 13 below to transfer a SATURN matrix file into say EXCEL edit it and re read it within MX Under Update the matrix may be only partially set e g within a selected area from the input dat file or an existing matrix may be incremented Matrix Changes 1 SELECT Certain options such as factoring may be applied only to selected areas or cells of the matrix this option defines those areas 2 FACTORING These options include not only simple factoring of all or part of the matrix but also Furness factoring by row or column totals both singly and doubly constrained Factor definitions may be either interactive or read in from pre prepared control files 3 MATRIX MANIPULATION E G USING FORTRAN EQUATIONS This option allows for a very general matrix manipulation by defining via equations based on FORTRAN syntax the new matrix to be cre
52. el The output stacked ufm file may be stacked either in levels or in blocks as selected by the user see 10 2 4 A procedure to stack matrices using a pre prepared bat file MXSTACK is described in 10 20 9 Conversely if the internal matrix is itself a stacked matrix with L levels it may be subdivided into a set of L individual square ufm output matrix files For example an internal matrix of 40 rows and 10 columns could give 4 10 x 10 output matrices one per level Alternatively post 10 9 20 a single level may be selected for output as a Square matrix an operation referring to as cutting a matrix See 10 4 2 for the reverse paste procedure to input a single level In Version 10 7 an option has been added to allow the output unstacked matrices to take their filenames from a root filename Thus if the root filename were mat ufm then the output files are mat1 ufm mat2 ufm etc etc This is a slightly more convenient procedure than having to explicitly define a filename for each output matrix The same convention is also used by a bat file UNSTACK see 10 20 12 and it is also used by the reverse procedure STACK 10 20 11 to stack a set of square matrices mat1 ufm mat2 ufm etc etc into a stacked matrix mat ufm We also note here although strictly it should be included within 10 4 that if a stacked ufm matrix is input to MX options exists to read only a single level into an internal S
53. ell value conditions as AND conditions Note that a single level may equally be selected for factoring using the LEVEL parameter in the batch file MKFACTOR see 10 20 3 Selected Area Cell Factoring Input Control File The Selected Area Factoring option within MX factors an area defined by an upper and lower row i e origin plus a left hand and right hand column i e destination by a specific factor They therefore define a rectangular sub area within the full matrix square And indeed it may help users to draw a map of the matrix and its sub areas a bit like a Venn diagram in order to help visualise what is included in each sub area whether there are overlaps allowed etc etc The external control file defines areas plus factors formatted as follows one record per area to be factored Cols 1 5 Upper row Cols 6 10 Lower row Cols 11 15 Left hand column Cols 16 20 Right hand column Cols 21 30 Factor decimal normally in column 28 Format F10 2 Certain options for the definition of the row and column factors may be selected interactively before the file is processed N B Mixing interactive and file input control is not ideal but it works and given how infrequently this method is probably used it doesn t seem worth introducing major changes requests to DVV Thus rows and columns may be defined as either names or sequential numbers via an option set interactively prior to processing th
54. ernal matrix To do so first use the select procedures to select row 6 all columns then use the equation Y 0 5X The selection of single rows and or columns may also be very usefully applied to setting the row column values for newly created zones see 10 4 2 Using Row and or Column Totals Equations may also make use of the row and column totals in either the current internal matrix or any of the external ufm files Thus the equation ROW 1 COL 1 Y would imply that each new cell element equals the product of the row and column totals of the first input ufm file divided by its current internal matrix value Syntax rules are that either ROW or ROW 0 implies the row total from the internal matrix ROW n is the total from the n th ufm input matrix Ditto COL COL 0 and COL n Matrix Transposition Very simply the I J cell in the internal matrix becomes the J I and vice versa Note however a special case of matrix transposition whereby a matrix stacked by blocks 10 2 4 may be transposed by block rather than by cell Thus the sub matrices in Figure 10 1 b would be moved into the positions in Figure 10 1 a 10 38 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 8 5 10 8 6 10 8 7 5120257 Apr 15 Section 10 _SATURN This is a useful trick since at the moment MX is better equipped to display information relating to sub matrices by level rather than by block e g pr
55. fm matrix file allows one to set a flat matrix with user set numbers of rows and columns 10 26 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 6 10 6 1 10 6 2 5120257 Apr 15 Section 10 _SATURN Select Options Certain options within MX for example matrix comparison or matrix manipulation 10 8 operate either on the whole matrix or optionally on certain selected cells The select facility defines those cells Selection is based on Location e g select rows 1 to 5 and or Value e g select only those cells whose value is greater than 10 Selection by Location Location selection essentially defines a rectangular area defined by lower and upper rows and or lower and upper columns where everything in between is either in or out Alternatively if sectors have been defined the limits for both rows and columns may be defined by sector numbers e g you may select origins rows in sector 1 to all destinations columns in sectors 2 to 6 Post release 10 8 with stacked matrices e g multiple user class matrices the selected area definitions may be further refined to either apply to all levels separately or to a particular level In these situations one has to be careful in specifying areas to distinguish between sequential row column numbers and zone names Suppose for example that you have a basic 10x10 matrix with 3 levels so that the fu
56. he LPX file 10 40 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 9 3 10 10 10 10 1 5120257 Apr 15 Section 10 _SATURN 3 You may analyse the whole matrix or selected portions of it 4 The matrices used may be either external ufm files either input or output or the internal matrix but clearly you need at least two available matrices before this option will appear 5 In addition if the internal matrix is stacked i e it contains multiple basic Square matrices then the comparison may be made between any two of the internal levels 6 Graphical scatterplots of one matrix vrs the other are available In earlier versions of SATURN this function was provided by a separate program M2 hence the name Note that this function is also available through a standard batch file MXM2 see 10 20 2 Trip Length Distributions A trip length distribution TLD calculates the number of trips from one trip matrix within length bands defined by another matrix Length here refers to any one of properties such as distance time generalised cost etc and should more properly be referred to by the generic title cost Thus if length or cost is a time matrix then the TLD lists the number of ij trips in the time band 0 20 seconds 20 40 seconds etc where the width of each band is user set The output appears in the line printer LPX file both as a tabular distribution plu
57. her packages to handle In such cases it might be preferable to dump say a 200 x 200 matrix as 10 200 x 20 strips each as 10 46 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation _SATURN separate files Although clearly it is much more convenient to deal with one rather than 10 files so only use this as a last resort Note that the number of decimal places used in CSV outputs may be an issue for both numerical precision and record lengths see 10 15 2 below More precisely the maximum record length allowed is 16384 characters If the required length exceeds this the output record is truncated and produces a Non fatal Error message in the LP file which may escape your notice 10 15 1 5 TUBA Formats TUBA the current standard UK software for evaluation provides three different text formats for matrices all three of which were added in release 10 5 and enhanced under release 10 6 For example the number of decimal places can now be user set under all 3 formats and the latest value stored within the preferences file as NDPS However the output units are fixed so that e g a matrix of distances is always output as kilometres whereas SATURN would normally use metres Note that TUBA format 1 CSV format is effectively the same as that output under option 4 above and the same caveats apply Formats 2 and 3 are very similar to the SATURN single record outputs option 3 Under formats 2 and 3 zone names a
58. hey represent a very high level of zonal aggregation as described in section 5 1 7 such that the maximum number of zones is 20 or strictly 21 since sector 0 is regarded as a valid sector number unlike nodes zones groups etc Sectors are common to both matrices and networks Like the alphanumeric zone names sector definitions may be obtained externally from either an associated GIS file see Block 8 App Z 10 8 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 2 5 4 _SATURN a network ufs file See 6 8 an explicit zone to sector Z2S file 10 2 5 5 below hierarchy rules based on either TfL conventions or by a parameter IROCKY see 5 1 7 and Table 10 1 in 10 5 2 below or alternatively set within MX using a sub option of the Files menu Generally speaking the number of sectors should be small enough that the entire sector to sector matrix may be viewed within a single screen or page so that an intuitive feel for the matrix may be obtained Looking at individual cells in say a 200 x 200 matrix provides very little useful information Most options within MX may be applied either at the basic zone to zone cell level or provided that sectors have been defined at the sector to sector level At present only one set of sector definitions is allowable within MX at any one time i e multiple groups are not allowed They could however be handled somewhat awkwardly by cre
59. ilar to viewing a block of cells except that aggregate sector to sector cells are displayed Options allow either sector numbers of sector titles to appear over rows and columns On exit from the screen edit cell values in the internal matrix are replaced by those on the screen Instructions as to how to use screen editing different between 16 and 32 bit versions are given in Section 19 9 Note in particular under 32 bit that the screen constitutes a formatted data set so that changing the position of any data item on a line or adding deleting lines may lead to cells being mixed up on return Note as well that under 32 bit the row and column integer headers are for information only and may not be edited Viewing Row and Column Totals Basically this option lists all row and column totals the grand total of all cells plus the total of the intrazonal diagonal cells to the screen with a series of options as below 1 alphanumeric text names are available they may be included 2 afrom more than one matrix may be included e g from one or more of the external ufm files in which case they appear in different colours See 10 10 2 3 and column totals from stacked matrices may be shown interleaved e g the row totals for row 1 for level 1 level 2 etc etc are given together as opposed to appearing on lines 1 n 1 2n 1 etc Alternatively the grand totals plus intras may be displayed on their own faster if this is
60. inting cell values or row column totals interleaved Screen Editing On screen editing of individual cell values follows the same procedures as described under 10 10 4 Alternatively screen editing can be performed at the sector to sector level there being two options for converting a sector to sector cell value into its constituent zone to zone cells Cel ij IJ TYT where ij refers to zones within sectors and J Thus under 1 all tj cell values equal the sector IJ values this would be appropriate if the matrix elements are e g costs which apply equally to all cells within a sector Under option 2 ij cells are factored by a sector to sector constant Fu such that the new ij elements sum to the new J values This would be more appropriate for e g trio matrices where the elements are additive Adding Cost Skims via a Park n Ride Zone A transport specific matrix problem is to calculate the cost from zone i to zone j via some intermediate zone k where e g k represents a park n ride site so that Ij A B Aix therefore represents the cost from the origin to the park and ride zone and B the subsequent cost to get from k to the final destination Log sum Addition of Cost Matrices A common operation within logit models is to combine two or more sets of o d cost matrices at a common level in a hierarchical demand model into a single composite perceived cost matrix via a log
61. ip matrix as the second file the latter is used below as a convenient method of obtaining the trip ends O and Dj Thus first create the cost matrix Cj as the internal matrix which it will automatically become if the first input ufm matrix is the cost file Then transform it into the negative exponential assuming B 0 01 via the matrix manipulation equation see 10 8 1 10 52 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 19 2 5120257 Apr 15 Section 10 _SATURN go Next enter the matrix factoring option and choose first option 3 to factor all rows by factors you select to be the row totals i e origins O from the trip matrix ufm file see 10 7 4 Thus the internal matrix now becomes 0 01 O e l Repeat with option 4 to factor all columns by the column totals Dj to give 0 01C O D e Alternatively and probably more conveniently the above three steps could be reduced to a single step via the FORTRAN equation ROW 2 COL 2 e assuming as above that the input trip matrix is the second ufm file Finally choose the matrix Furnessing 10 7 5 and set the trip ends again from the second ufm input file Requesting the doubly constrained Furness option solves the original equations Goodness of fit statistics comparing the distributed trip matrix the internal matrix Y to the assumed observed trip matrix X2 may be obtained under the Statistics Option and a
62. ive records 2 1 zo a would indicate that all zone names in the range 10 through 19 would be assigned to group 2 and that zone 9 would be assigned to group 1 Note that 19 need not necessarily be a valid zone name itself it simply represents an upper limit in which case the true upper limit would be the maximum zone name lower than 19 The lower value of the range is the previous upper limit plus one If a negative number is used to indicate an interval the absolute value of the negative number must be greater than the absolute of the previous number in the list If as above a positive number is used e g 9 to set the previous line that zone name must exist Therefore it is recommended that you use either all intervals negative numbers or include all zone names in the Z2 file using the philosophy that the point of using intervals is for the process not to fail and the point of using a zone by zone list is that you want the process to warn you about missing elements by failing Errors occur and are noted if a record does not consist of two integers if a zone cannot be identified excluding negative values above and if some zones are not assigned to groups These may or may not result in the operation being rejected Blank records are allowed and ignored as are comments i e records with a in column 1 In order to process a Z2G file the zone names and their number must already be Known within MX but the set of group
63. l SATURN format as described in 10 5 1 to a set of newer more flexible formats where to a certain extent the users may define their own format The latter facility is intended to simplify the transfer of matrix data from other suites of programs such as EXCEL into SATURN The format selection is made from the following choices Standard SATURN formatted input file User defined format with all O D data included Non zero elements only with l J indicators one record per cell Spreadsheet or Comma Separated CSV Format one record per row EMME 2 Format Tuba Formats 1 2 and 3 These are defined more precisely in Sections 10 5 1 to 10 5 6 respectively and correspond closely to the dump formats in 10 15 A further option allows the user to have a preliminary look at the input file prior to selecting a format option or defining sub options Note that these options are part of the standard interactive matrix building procedures within MX whereby an input data file is nominated various options are selected and subsequently an output ufm file is created as described in 10 16 Alternatively ufm matrices can be built from data files using the more batch like procedure MXM1 as described in section 4 Note however that the formats of the input data files 1 to 6 above are the same in both cases We may further note that if an all new matrix is to be built interactively from data inputs i e with
64. l has been read in On the other hand sequential row numbers if contained should go right the way through from 1 to the total number of rows N B CSV formats may also be used as inputs to MXM1 see 4 4 EMME Format EMME input formats follow the rules laid down by the package of that name for punched output files and consist of in our version at least variable number of header records a set of cell records each including values from a single origin row plus one or more destinations columns On input the header records are ignored by SATURN They are identified by having an alphabetic character normally c a or t in the first character whereas the data records which follow may be identified by having blanks in their first characters per record The cell records consist of 10 25 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 5 7 10 5 8 5120257 Apr 15 Section 10 _SATURN The row number name see below in columns 1 5 Upto 10 pairs of numbers written as destination zone cell value For example 1 Pi pO ee Se en Ove SP ale would define the cell values for ij pairs 1 2 1 3 1 5 Any missing values 1 1 1 4 etc would be assigned default values of zero In addition spaces may be allowed between the and the cell values and the cell values may be either integer or real Note the zones may be referenced either by their seque
65. ll matrix has 30 rows and 10 columns and that the zone names are simply 1 to 10 You might using sequential numbers select all rows from 5 to 25 even though rows 5 and 25 both have the same zone name i e 5 but clearly they are in different levels Alternatively you could define row limits by zone name e g zones 5 to 7 in which case this could either be applied to all levels to include sequential rows 5 to 7 15 to 17 and 25 to 27 or you could choose to apply it only to a single level e g level 2 rows 15 to 17 only In addition with levels it is possible to select either a single level in its entirety or else a range of levels in their entirety So that in the above example if you were to select level 2 only this would be equivalent to selecting rows 11 through 20 but with no further selection rules l e if you select level 2 then there is no possibility to add extra restrictions on columns A slightly different form of location definition is to select intrazonal or diagonal cells Alternatively you may select cells outside the defined locations For example you may select an area perform an operation on those cells only return to Select and toggle to select the outside cells and perform a different operation on those cells Selection by Value Selection by value requires the user to define A matrix which could be the internal matrix or an external ufm file 10 27 SATURN MANUAL V1 1 3 MX In
66. ls were 5 no trips would be lost The losses may become significant in very large matrices where a large number of cells have been in filled with very small values Thus extra decimal points may be needed for extra precision although this may also depend both on the format used and on the units of the matrix For example 10 47 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 15 2 1 10 15 3 10 16 10 16 1 5120257 Apr 15 Section 10 _SATURN assuming decimalised outputs if a matrix contains inter zonal travel times which are of the order of 30 minutes in units of seconds 2 decimal places may give ample precision 80 minutes would be output as 1800 00 seconds but if the units were hours then 30 minutes becomes 0 50 on output and any O D cell less than say 0 01 hours 86 seconds might be rounded down and output as 0 00 under 2 decimals Increasing the number of decimals avoids such problems On the other hand using a large number of decimal places may create problems in certain circumstances e g CSV outputs see above where the length of an individual record may exceed 16384 characters and be truncated Compromises on the number of decimals may sometimes be necessary However we note that trailing zeros and or the decimal point are truncated Thus 10 10 becomes 10 1 on output as CSV 10 00 becomes simply 10 etc etc Thus increasing the number of decimal points does not necessarily i
67. may be either in the standard SATURN format or in a format set by the user e g so as to be able to export a matrix to a spreadsheet See also 3 above for the reverse operation 4 DUMP RE CODE THE INTERNAL MATRIX TO A UFM FILE The internal matrix file may be output in to to an external binary UFM file for use in other SATURN programs This is the normal way to save a new matrix As in option 2 the matrix file may be output as is or transformed in various ways e g by recoding zones 5 STACKING AND UNSTACKING UFM FILES A set of externally input square matrices may be combined together and output as a single stacked matrix file see 10 2 4 or alternatively if the internal matrix is itself a stacked matrix it may be split into a full set of output individual matrices or a single matrix from a single level 6 MATRIX DEMAND CALCULATIONS A prototype set of formal transport demand model steps such as distribution or modal split are carried out using a combination of input 10 3 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 1 2 10 2 10 2 1 5120257 Apr 15 Section 10 _SATURN trip and cost matrices These parallel the standard elastic demand options within SATEASY see sections 7 4 to 7 10 and demand calculations by time period see 17 12 Launching MX from a Command line Batch file To invoke MX to look at a matrix file mat ufm use a batch command line
68. n 4 and 5 aggregate zones into groups defined either option 4 via an input Z2G file or option 5 using a pre defined zone group mapping as carried by the ufm file or as previously introduced within this particular run of MX For example the Z2G file might have been set by the parameter FILZ2G during the matrix build see Table 10 1 in section 10 5 2 and the necessary information stored in the ufm file 10 49 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 16 5 10 16 6 10 16 7 5120257 Apr 15 Section 10 _SATURN Option 6 aggregates zones to groups using a hierarchical set of rules based on zone numbers plus parameters IROCKY and NBASE see 10 4 4 while option 7 aggregates zones to sectors following the current definitions of sectors Finally option 8 first introduced in release 11 2 9 outputs a compressed or aggregated matrix but following a specific set of rules within the TfL SATURN zone naming conventions see 5 1 7 2 Thus the output matrix is aggregated into a traffic borough to traffic borough format Note that in order to make use of this option the internal matrix must be recognised as a IfL based matrix most easily done by toggling option 16 within Main Menu 1 10 1 1 1 although it is also possible to declare a matrix as a TfL matrix at the point of its creation see the parameter TFL in Table 10 1 in 10 5 2 Outputs Based on Expansion Groups to Zones Options 9 and 10 introd
69. n on the following record Parameter Type Default Interpretation NROWS INTEGER 0 Defines the size of the matrix to be built NCOLS INTEGER ie Defines the size of the matrix to be built 1 records 5 below 1 signifies SATURN formats either long or short See 4 4 for the currently limited alternatives 4 for CSV IROCKY INTEGER The sector corresponding to a zone may be derived by dividing the zone number by IROCKY a very bad spelling of HIERARCHY If 0 it does not apply See 5 1 7 LONG LOGICAL F T The long input formats apply see the matrix element records below MPNEXT LOGICAL F T The rules for hierarchical node and zone numbers as used in TfL networks are assumed to operate E g the first digit in a 4 digit Zone number gives its sector See 5 1 7 2 and 6 8 GISFIL TEXT this matrix 5 7 FILZ2S TEXT Blank The filename of a file listing the sectors per zone see 10 2 5 3 FILZ2G TEXT The filename listing groups per zone see 10 2 5 5 KROPT INTEGER Defines the formats for the matrix elements and 6 for TUBA 1 The filename of the GIS file associated with 3 THE MATRIX PARAMETER RECORD optional MPNEXT T 5120257 Apr 15 10 20 Section 10 SATURN MANUAL V1 1 3 oo SATURN MX Interactive Matrix Manipulation l Cols 1 8 The units of the matrix elements e g time Cols 9 16 The dimensions of the elements e g minutes 10 5 3 5120257 Apr 15 Section
70. names and their total number are only Known and fully specified after the Z2G file has been processed Note that the Z2G format also corresponds to a simplified version of the Records 2 used by the batch file MXM5 see Appendix W 3 10 10 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation _SATURN 10 2 5 6 Z2G Data within UFM Files 10 2 6 10 2 7 10 3 10 3 1 5120257 Apr 15 Section 10 Once a Z2G file has been set and processed data such as the zone to group mappings the names of the groups etc are included within the header records of any output UFM files such that any future applications of those UFM files will allow immediate access to the zone to group information which in turn allows certain operations such as aggregation to groups to be carried out automatically See for example MXZ2G section 10 20 22 Z2G etc Filenames Extensions and Folders lt is clearly simplest if a file containing zone to group mappings has an extension Z2G to indicate its function and if a Z2G filename is given e g on a command line without an extension Z2G will be added automatically However for example a namelist parameter record FILZ2G my_z2qg file dat is perfectly acceptable And FILZ2G my_z2g_file would have Z2G added A Z2S file may be defined by the parameter FILZ2S in a matrix dat file see 10 5 2 as may a Z2G file via FILZ2G so that these filenames are then embedded within the
71. ncrease the size of the CSV output records proportionately Note that the default number of decimal places is now 5 but it may be re set via the namelist parameter NDPS used in the MX preferences file mx0 dat E Formats E formats avoid problems when matrix cells contain both very large and very small values For example take 2 cells with values 12345 67 and 0 000123456 7 Under E formats with 7 decimal places they would be output as 0 1234567E 06 and 0 1234567E 03 whereas under decimal outputs they would become 12345 670000 and 0 0001235 In this case decimal outputs lose precision with the smaller outputs while E formats do not For maximum precision minimum loss of accuracy it is recommended that users choose E formats with 7 decimal places as this corresponds roughly to the numerical precision of single precision real variables on the computer Lack of precision may be a serious problem if a matrix is being dumped to text in order to export it to say EXCEL manipulate it and then return it to MX For one way transfers precision may be less of an issue Sector to Sector Outputs Secior to sector data may also be output in the same manner as individual O D cells Output UFM Matrices General Principles To save the internal matrix output it to a binary ufm matrix file This is the normal procedure by which a ufm matrix file is created Thus the M1 or MXM1 procedure described in Section 4 uses this output option
72. ned matrix would consist of 80 rows and 20 columns Rows 1 to 20 correspond to matrix 1 21 to 40 to matrix 2 etc In the latter case the combined matrix would consist of 20 rows and 80 columns such that columns 1 20 consist of matrix 1 21 40 matrix 2 These are illustrated in Figure 10 1a and 10 1b respectively 10 6 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 5120257 Apr 15 Section 10 _SATURN Figure 10 1 Stacked matrices b Horizontal stacking by blocks We use the term level to refer to the different sub matrices when stacked vertically and block when stacked horizontally We also use the term base matrix to refer to the basic square matrix from which the levels and or blocks are built up and whose length width dimension would normally correspond to the number of zones in a corresponding network Stacked matrices by level are only used within the multiple user class assignment options of SATURN so that the four matrices above might correspond to four separate user classes See Section 7 3 2 for further details Horizontally stacked matrices by block are used to represent multiple time periods as used within SATURN s dynamic assignments see 17 4 3 At the moment it is not possible to stack by both levels and blocks at the same time e g to create a single trip matrix file which is both multiple user class and multiple time period But it will come For some operations in MX
73. ntial number or by their numerical name see 10 2 2 as an option selected by the user The standard EMME 2 default is to use zone names not sequential numbers Due to EMME conventions only matrices which are square may be processed by EMME i e stacked matrices may not be created using an EMME format TUBA Formats Tuba input formats follow the rules laid down by the evaluation package TUBA see 15 41 and Appendix C of the TUBA User Manual where three separate formats are specified 1 One record per origin CSV 2 One record per cell CSV Origin Destination Cell value 3 One record per cell fixed columns user class plus multiple time periods Thus Tuba Format 1 is very similar to that of CSV described in Section 10 5 5 while 2 and 3 are similar to that in 10 5 4 Note that Tuba Format 3 is presumably intended to deal with multiple time periods whereas as implemented in SATURN only one cell value is generally output It may therefore not be much use as of yet to serious Tuba users but it could be extended as and when required Creating a Flat Matrix An option exists within MX to create a flat or uniform matrix i e one in which all cells have the same value This is done by entering the program in a purely interactive mode i e with no input dat or ufm file most easily done by a command line MX I The first menu in addition to offering the option to define an input dat or u
74. o save the instructions input interactively e g which zones to copy which to delete etc in the form of a control file as required by the MXM5 procedure see 10 20 20 and Appendix W 3 Editing Stacked Matrices If either the input ufm matrix or the internal matrix assuming it has already been created are stacked i e contain multiple levels of a basic square matrix see 10 2 4 then various additional operations become possible Thus firstly a square internal matrix may be created by summing together all the various sub matrices contained in the stacked ufm matrix file The same operation may also be carried out using an external procedure mxagg See 10 20 21 Secondly and similarly a square internal matrix may be created from a single level of the input stacked ufm file Thirdly if the internal file is a stacked matrix but the nominated input ufm matrix is square that matrix may be used to over write or paste a particular internal sub matrix without any changes being made to any of the other sub matrices The paste operation may often be usefully combined with the cut operation see 10 16 6 whereby a square matrix is extracted from a stacked matrix edited in some fashion and then pasted back into the original matrix Pure Zonal Aggregation Compression into Groups A matrix which is defined in terms of zone to zone cells may be compressed or aggregated into a matrix of g
75. olumn specific factors needs to be defined These may be either set interactively by screen editing or they may be taken to be the row column totals from an input matrix the most common example of the latter being to multiply rows in a matrix 10 31 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 7 5 5120257 Apr 15 Section 10 _SATURN of probabilities by origin totals or columns of probabilities by destination totals see 10 19 1 lf the matrix is stacked e g for multiple user classes then the screen edit format sub divides the data displayed on the screen by level if all levels are being edited together Alternatively it is possible to set row origin factors for Level 1 and then apply the same factors to all levels or to set factors and apply them to rows for a single level only The latter options are new in release 10 8 while the former correct potential pre 10 8 errors Finally options were added in 10 9 23 to apply column factoring to a single selected level from a stacked matrix At the moment there are no options to read in factors from an external dat file although this can be done with only slight inconvenience using selected area factoring 10 7 3 For example a control file IL IL O O TO 2 2 O O RERS O O ili 1 a i 1 O O IO would factor row 1 by 1 50 row 2 by 1 75 column 1 by 1 20 etc Matrix Furnessing Trip Ends Set Interactively New trip ends i e row and column totals may be
76. or from SATURN into say a spreadsheet such as EXCEL The output ASCII file may be either defined interactively by the user or else set as a command line parameter see 10 1 2 using the keyword KP as in MX matri IE EIJ ea exc Note that the KP option may be usefully used to set the filename when a matrix is dumped using a KEY or KEY VDU file to generate the necessary commands as in MX moc teak FE EI aae T EVDO te ump Output Formats The output data file may be written in a number of different formats Standard SATURN format 2 varieties MN A user defined format Q Non zero values only one line per record D EMME 2 format TUBA formats 1 2 and 3 O O A spreadsheet comma separated CSV format In addition under formats 2 3 and 4 above the output may be based on either i the entire matrix or ii a selected subset of cells N B These formats mirror the matrix input formats described in Section 10 5 SATURN Formats In case 1 the user may choose one of the two standard SATURN formats LONG T or F which effectively differentiate between an output with three decimal places per cell or output with no decimals i e integer In both cases the zone name is included as the first element in each block Full specifications are given in 10 5 1 10 15 1 2 One Cell per Record 5120257 Apr 15 Section 10 In case 3 one record per non zero cell each lin
77. out any existing ufm matrices being involved then it will be necessary to initiate a run of MX using the command line MX I which see 10 1 calls mx exe without a normal initial matrix The Numbers of Rows and or Columns Before matrix cells can be input it is necessary to Know in advance the number of rows and columns generally the same in the matrix so that the values can be stored in their correct cell positions as they are read in A similar problem is to establish the zonal names in advance see below With SATURN formats 1 above this information is contained in the initial Namelist records see 10 5 1 With other formats this information must be supplied interactively by the user in some cases a pre read of the data file establishes the names see below 10 18 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 100 12 10 9 13 10 5 1 4 5120257 Apr 15 Section 10 _SATURN Updates It is also possible to use input from an ascii file to update all or part of the current internal matrix presumably read from an existing ufm matrix rather than writing it from scratch The choice between build and update is made immediately on entering the top menu under Build Update Matrix update data may use only some of the standard data input format conventions described below i e user defined records 10 5 3 individual cell records 10 5 4 and spreadsheets 10 5
78. play immediately up or down Viewing Single Rows and Columns This format lists e g all elements in row 1 all elements in column 6 etc with at the end both row and column totals for that particular zone i e printing row 1 will give both the total of all elements in row 1 plus the total of all elements in column 1 As under 10 10 2 more than one matrix can be printed simultaneously but it is not possible to print say row 1 from matrix 1 with row 2 from matrix 2 Nor can think of any reason why you should want to Screen Editing the Internal Matrix Under screen editing all elements in the current block of the internal matrix are dumped to the screen and may be altered as desired On exit from the screen edit cell values in the internal matrix are replaced by those on the screen Instructions as to how to use screen editing different between 16 and 32 bit versions are given in Section 19 9 Note in particular under 32 bit that the screen constitutes a formatted data set so that changing the position of any data item on a line or adding deleting lines may lead to cells being mixed up on return 10 42 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 10 5 10 11 10 12 5120257 Apr 15 Section 10 _SATURN Note as well that under 32 bit the row and column integer headers are for information only and may not be edited Viewing Sector to Sector Matrices This display is sim
79. quare matrix or to sum all the levels into a single aggregate square matrix Use the latter option e g to obtain a total trip matrix from a set of stacked say trip purpose matrices Matrix Demand Calculations Matrix oased demand models allow the user to carry out e g mode split or distribution calculations provided that all necessary cost and trip matrices are input along with essential parameter values The result of these calculations is always a trip matrix Different models require different shapes of trip matrices i e square or stacked by blocks and these are described separately Square Matrices The matrix demand models included within MX effectively mirror those models that are included under the elastic or variable demand assignment models for a 10 51 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 18 2 10 19 10 19 1 5120257 Apr 15 Section 10 _SATURN single user class described in Sections 7 4 to 7 10 They also use the same parameter names for example setting MCGILL 2 see 7 7 1 in the demand model sub menu requests an incremental power law model of the form Lg T c Cy where three input ufm matrices must be defined Tj cj and cj and the power p set These are also defined within the sub menu with the matrices being equated to external input files 1 2 3 etc Once all the necessary parameters have been defined choose 1 Do It Now to perform the cal
80. re automatically used as opposed to sequential numbers N B if the input matrix ufm file does not contain the correct zone names only sequential numbers the zone names must be added from a network ufs file see 10 3 3 In addition post 11 1 cells with zero values may optionally be output under Tuba 3 By default they are excluded and including them is definitely not recommended it may create extremely large files but there may be circumstances under which it is necessary 10 15 1 6 Automatic Matrix Dumping 10 15 2 5120257 Apr 15 Section 10 Note that the output options effectively mirror the input options described in section 10 5 so that data may be conveniently dumped under these procedures and re input undumped See 10 20 13 and 10 20 14 for a list of useful batch procedures to dump undump Output Options The number of decimal places Under certain options the user has the choice of the number of decimals to be used and whether or not the data is output in decimal format or E formats e g 1 23 as opposed to 0 123E 01 These choices relate to questions of precision and or rounding errors Problems of a loss of precision may arise if an insufficient number of decimal places are not used due to rounding errors For example a trip matrix cell value 10 12345 would be output as 10 12 if the output format specifies 2 decimal places in effect 0 00345 trips are lost If the number of decima
81. roup to group cells by adding together all the appropriate zonal cells Mathematically Tij XY T iel jE where and J represent the rows and columns of an aggregated matrix and j are zonal rows and columns and i denotes the fact that zone i is contained within group l Note that this form of aggregation is appropriate for say a matrix of trips where it is natural to add trips together but it would not be appropriate to a matrix of say zone to zone distances where ideally the group to group distance should be some form of weighted average of the zone to zone distances The rules for compression aggregation may be specified via a number of different formats 1 an explicit mapping of zones into groups 2 hierarchical numerical rules and 3 specific TfL numbering conventions for traffic boroughs These are described in further detail below The conversion from zones into groups may be either set explicitly by an external Z2Q file or by pre defined zone to group data 10 16 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 4 5 10 4 6 5120257 Apr 15 Section 10 _SATURN Hierarchical aggregation uses two parameters NBASE and IROCKY to create new aggregated zones based on the current set of zone names by applying the formula new NBASE old IROCKY Generally speaking IROCKY will be 10 or some power of ten on the basis that the first digit in a Zone name equals a sector of
82. s average lengths per origin and various totals Graphical plots of a trip length distribution can be obtained either here or under the Matrix Graphics options see 10 12 Viewing and or Editing Matrix Elements Elements in either the internal matrix and or any of the external ufm matrices may be displayed on the screen in a number of basic formats 1 A block of cells i e covering a range of rows and columns to fill the screen ii All elements in a single row or column iii AS a complete aggregated sector to sector matrix if sectors have been defined Viewing a Block of Cells Depending on the options selected this option displays on the screen all matrix cell values from a block covering approximately 15 rows down the screen and 7 columns across the screen Within this option it is possible to move around within the matrix by using either the cursor keys or the keys U D L and R for Up Down Left and Right The Home and End keys move up to upper left or lower left The above options all move the upper left hand corner of the display Alternatively the cell in the upper left hand corner may be explicitly set via a location sub menu 10 41 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 10 2 10 10 3 10 10 4 5120257 Apr 15 Section 10 _SATURN lf the area currently on screen includes the bottom and or the right hand side of
83. s included data must be ordered by destination within origin i e a complete set of destination data for origin 1 on one or more records followed by the records for origin 2 etc etc All NROWS NCOLS elements must be included User set sub options allow a A fixed number of initial records to be skipped before origin 1 data e g to allow for header records b A fixed number of initial numerical data entries within each origin set to be skipped e g to allow for zone names purpose codes etc C A FORTRAN style Format of the origin data sets e g 1015 for 10 INTEGER data entries per record 5 columns each 10 21 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 5 4 5120257 Apr 15 Section 10 _SATURN d The number of rows and columns i e zones if not already specified An example of such a data file with two header records 8 rows and a single column header entry per origin and format 615 might be Jonesville observed trips Wee Weuleneys 1S s O 6 2 3 l O 1 5 10 6 O Za S il O 1 5 Thus the first Zone is zone 5 with I j elements 0 6 5 the second is zone 10 with elements 6 0 5 Whether or not the numerical entries are real or not i e have decimals or not is determined by the format which follows standard FORTRAN rules Non zero matrix elements only one O D cell per record Here each non zero O D entry occupies a single line or record giving some possibly all of th
84. sector totals Reboot Returning to the Original Matrix lf the zone structure has been transformed using any of the above options then the original matrix matrices are effectively lost having been replaced by the new structure The reboot command allows the original command line to be re processed and the original matrix matrices to be restored at the cost of losing the new restructured matrix data The idea is that if you input a zonal matrix and then compress it to a group matrix 10 4 4 in order to view the matrix in terms of group to group you may return to the original zone to zone version This therefore gets around a feature of MX whereby you cannot store a zonal matrix and a group matrix in internal memory at the same time now you may swap between them By contrast sector to sector versions of the basic matrix may be stored at the same time as the full version and both may be viewed within the same program however there are severe restrictions on the size of sectors 10 17 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 5 10 5 1 1 5120257 Apr 15 Section 10 _SATURN Matrix Input and or Updating from a DAT File The internal matrix may be built in whole or in part see Updates below by reading data from an input ASCII data file for which the default extension is dat The input dat file must be formatted with a set of possible options ranging from the traditiona
85. some sort NBASE generally 1 is included so that a new zone name of zero is not permitted whereas the very similar use of IROCKY to define sectors explicitly does not use NBASE since a sector 0 is permitted The specific aggregation of a TfL SATURN matrix from zones to traffic boroughs follows the rules used by TfL see 5 1 7 2 to include the definition of a traffic borough within a zone number specifically using the first two digits Note that the MXZ2G and similar does include any intra zonal trips in the aggregation Expanding a Matrix Groups to Zones A matrix which has previously been compressed from zones into say groups may be transformed back into a zonal matrix but with very specific rules which differ from the rules applied for compression or aggregation 10 4 4 Thus under compression zonal cells are added to create group cells by contrast under expansion all zone to zone cells take the same corresponding group to group cell value i e group to group values are replicated Mathematically Tj Ty V icl jes i j This could logically be applied to a matrix of say OD costs or factors but not to a trip matrix where the group to group trips would need to be factored down when disaggregated to a zonal level Note that MXG2Z sets the intra zonal trips to zero This may have implications in later calculations if your original zonal matrix had values in the intra zonals as MXZ2G would have included these in any intra
86. sum See for example equation 7 27 in section 7 6 3 In principle a log sum of two or more matrices may be achieved by using the Fortran Equation options above although the equations tend to be rather long winded and easy to mistype hence the need for an explicit option To carry out a log sum the user must a identify those matrices to be combined presumably cost matrices but no explicit check is possible and b a value for the parameter beta The composite matrix is created as the internal matrix 10 39 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 8 8 10 8 9 10 9 10 9 1 10 9 2 5120257 Apr 15 Section 10 _SATURN Copying Individual Rows and or Columns Options here allow the user to copy cells from one row or column into another row or column with options for factoring and or furnessing the newly created rows columns Manipulation of Intra zonal Cells Two options are currently available for the manipulation of intra zonal cells specifically Setting a fixed value for all intra zonal cells Creating intra zonal values based on the minimum of all other cells in a row More specifically option 2 has been created in order to set intra zonal costs equal to 0 5 times the minimum cost from that origin to any destination excluding those O D cells which have zero cost Statistical Analysis Three separate forms of statistical analysis are described below They may be applied either a
87. t the cell by cell or sector by sector level For more complicated analysis users are advised to dump the matrix matrices into ascii files 10 15 and to transfer the data into proper statistical packages such as SPSS or SAS or into spreadsheets such as EXCEL Univariate Analysis of a Single Matrix This option produces a set of standard unvariate statistics mean standard deviation etc of either a set of individual cells or else a set of row and column totals These may be based on either the internal matrix or any of the external ufm files Equally they may refer to the whole matrix or selected sub areas see 10 6 The same set of univariate statistics per matrix may also be printed in a table covering all external ufm matrices plus optionally the internal matrix or equally a table of univariate statistics covering all levels of a single matrix may equally be displayed Comparison of Two Matrices M2 These options compare two matrices either cell by cell row total by row total or column total by column total or combinations thereof and print copious comparison statistics and tables e g of absolute differences to the line printer file LPX with summary statistics to the screen Various options are provided 1 You may list all elements whose absolute differences exceed a specified value the list appears in the LPX file 2 You may list the 10 largest absolute differences this appears both on screen and in t
88. t2 mat3 n Use the Method of Successive Averages to combine together two matrices mat1 ufm and mat2 ufm to produce an output matrix mat3 ufm where T 1 1 n T 1 n T The rationale behind the method of successive averages is explained in Section 7 2 2 MXKK MXKK TIJO CIJO CIJ TIJ BETA Produces a new multiple time period trip matrix TlJ ufm based on the incremental logit model formulation of KK Chin See 17 12 Note that each matrix above must be blocked by time periods see 10 2 4 MXROH Rule of a Half MXROH TDN TDS CDN CDS BEN Calculates the economic benefits according to the rule of a half see 10 19 2 from a do something scenario with trip matrix TDN UFM and minimum cost matrix CDS UFM compared with the do nothing scenario represented by the trip matrix TDN UFM and cost matrix CDN UFM The outputs are a matrix BEN UFM anda one line text file BEN DAT Note that MXROH works equally well with multiple user class networks MXSTACK Stack a Set of Matrices vertically MXSTACK mat matl Mele 2 Mia oes Outputs a stacked matrix mat ufm built from the input matrices mat1 ufm mat2 ufm etc etc in order The list of input matrices may contain up to 8 inputs and clearly must have at least two in order to make sense N B The matrices are stacked vertically in levels as appropriate for user classes cf MXBLOCK To stack more than 8 matrices see either STACK 10 20 11 or UFMSTACK 10 20 17
89. teractive Matrix Manipulation 10 6 3 10 7 10 7 1 5120257 Apr 15 Section 10 _SATURN An operation e g less than greater than or equal etc A critical value Thus you could select cells in the second input trip matrix whose values are gt 10 Note that tests such as EQ or NE also imply equality within some plus minus limits which also need to be specified The principles apply equally to link selection within P1X or SATDB see 11 6 1 for further details Note that selection by value is not permanent when applied to the internal matrix Thus if you select all internal matrix cells gt 10 0 factor just those cells by 0 5 and then carry out another operation with selection by value the cells to be selected in the second operation will be those whose current value is 10 0 i e those cells who were originally gt 20 0 In order to fix a selection by value using the internal matrix you should copy it into a ufm file and add it as an input matrix and base your selection on that file so that the values do not change N B This is the opposite of link selection in SATDB P1X etc where links once selected are permanently branded Output of a Selected Matrix Note that it is possible to create an output ufm matrix see 10 16 7 which records the current state of cell selection Thus by default an output value of 1 indicates that that cell is selected O that it is not This may
90. the separate programs M1 through M7 plus many new ones The original historical program names tend to live on within e g batch files names and some internal options within MX See 10 9 2 10 20 and Appendix W MX operates essentially on a single internal matrix stored in RAM although operations involving up to 10 external matrices are also permitted More details are given in 10 3 In operational terms MX is an interactive menu based program largely but not exclusively text based see 19 6 and the general principles outlined in Section 19 3 apply Uses of MX A more detailed description of each of the main options listed in the Master Menu follows These may be subdivided into Input Changing matrices Analysis Output Input 1 FILES MENU The FILES option allows the user to define new input matrices 10 3 1 to request basic information on these files e g matrix title and to introduce a supplementary 10 1 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 1 1 2 5120257 Apr 15 Section 10 _SATURN network UFS or GIS file 10 3 3 to supply e g sector definitions 10 2 5 3 or zone names 10 3 3 and to declare a matrix as following TfL zone name conventions 5 1 7 2 COPY TRANSPOSE RE CODE AN INPUT UFM FILE REDEFINE ZONES Transfer an external input matrix into the internal memory where it can be manipulated analysed etc etc The matrix may be either r
91. thin MX by which the structure of the zones may be edited i e the number of rows and columns may be altered as opposed to editing individual cells It also differs from i and ii in that the changes may be applied to each level of a stacked matrix whereas the first two methods apply only to square matrices Cases iv to vi apply to various operations involving stacked matrices as described in more detail below Section 10 4 3 General Zonal Editing Zonal editing must generally start with an external ufm file which once the mapping of old zones into new has been fully defined is copied into the appropriate cells of the new internal matrix It is however also possible to edit the internal matrix in situ in which case the program automatically copies the internal matrix into temporary external ufm file from whence it is recopied edited into the new internal matrix Thus with respect to the original zone definitions on the input ufm file the new matrix may 1 delete old zones in both rows and columns 2 create totally new zones whose sequential position is determined by their name 3 compress the existing zones into larger zones i e aggregate or add zones together 4 rename existing zones and therefore potentially change their sequential position 5 split i e disaggregate and or copy old zones into new zones In greater detail these five sets of fundamental operations m
92. tion effectively duplicates renaming split a zone 100 into a different zone and copying split a zone 100 into itself and 100 into the new zone Use whichever seems most convenient Note that certain options plus factors leave the total number of elements in the matrix unchanged so that these operations are suitable for matrices such as trip matrices but probably not for matrices such as distance matrices where if a block of zones were to be aggregated together one would wish to average the cell elements not add them together Thus if you wanted to aggregate four zones from a trip matrix choose factors of 1 0 if it were a distance matrix choose 0 25 To a large extent the above functions mirror those available under M5 see Section 10 16 3 and as a distinct batch file MXM5 see 10 20 20 which dump the internal matrix to an output ufm file Thus to aggregate a matrix from zones into say districts one could either aggregate on input as here and produce a new ufm by simple output or else read in the zonal matrix and aggregate to districts 10 15 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 4 3 10 4 4 5120257 Apr 15 Section 10 _SATURN on output One difference is that the input options use only interactive input commands whereas the outputs use control files Although through the use of key files both can be run equally well in a purely batch mode From version 10 7 it is possible t
93. tors and post 11 3 details of any zone to group aggregations which may have been specified via Z2G files see 10 2 5 5 For virtually all transport based applications the matrices are square number of rows equals number of columns and the rows columns are associated with zones SATURN follows the general convention that rows are associated with origins and columns with destinations Thus in a trip matrix the seventh element in the third row represents the number of trips from zone 3 to zone 7 Each row is stored in a separate record within a ufm file 10 4 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 2 2 5120257 Apr 15 Section 10 _SATURN Note that with SATURN 9 5 matrix ufm files are held in a zipped format which is invisible to the user and whose objective is to minimise the size of the files For example if a matrix row consists entirely of zeros the zipped format records this with a single marker rather than n number of columns distinct values A number of other similar tricks are employed This means that for example an observed trip matrix 95 of whose cells might be zero only requires marginally more than 5 of a full matrix In theory MX can handle both square and non square matrices however for the reason above MX is very seldom used in practice with non square matrices so some caution is advised if you do wish to work with non square The exception is stacked matrices
94. tra header record may be included with titles for each column included CSV output is probably preferable if the user wishes to manipulate the data for example using a spreadsheet as opposed to simply printing data or transferring it elsewhere within MX Various options include whether or not to print Zone names or sequential numbers see 10 2 2 the source of the matrix internal or external ufm whether or not zero values are included and whether in the case of stacked matrices whether row column totals from a single level or from the full matrix are output A further option allows the sum of all elements in the matrix to be output as a single line to an ascii file in which case the data line may be appended i e added to an existing file The append option is useful e g as part of a set of runs over several forecast years when it is desired to create a file for input to a spreadsheet containing matrix totals by forecast year 10 44 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 15 10 15 1 10 15 1 1 _SATURN Note that if the output file has the extension CSV the default then the output format is automatically in CSV such that commas are added at the end of each numerical field Dumping a Matrix to an ASCII DAT Text File This option writes the cell values of the internal matrix into a user specified ASCII text file It is used typically to transfer matrix data between suites
95. uare matrix see 10 2 4 it is generally assumed that the same zone names will be applied to upper levels as well although this is not mandatory For example if the row names are identical to sequential row numbers then this would not be the case Matrix Dimensions and Units Since it is expected that SATURN matrices will include a large number of different types of matrices e g trip matrices distance matrices cost matrices it is very useful for the user to define the sort of elements held in the matrix file For example it makes the output much more legible when totals from a trip matrix are clearly marked trips costs are shown as being in pounds etc etc This is done within SATURN by defining a series of parameters which specify the elements stored on each matrix file Thus we store information on the dimensions of the elements e g whether they are times distances costs etc their units e g minutes miles pounds etc These are either defined on the input data files 10 5 1 as up to 8 characters or may be interactively defined within MX under Matrix Manipulation 10 8 or UFM Output 10 16 7 Stacked Matrices Levels and Blocks Stacked matrices are special forms of matrix files in which say four square matrices of size 20 by 20 are stored together as a single matrix file Stacking may take place either vertically or horizontally Thus in the former case the combi
96. uced in 11 2 6 allow an aggregated matrix e g a matrix which has been defined at the level of say group to group cells to be expanded disaggregated into a matrix of zone to zone cells where the relationship between groups and zones may either by set by a Z2G file or preferably via the existing zone group mappings Note that in this case the zone to group mapping is used in reverse in order to define which zones are within each group We note that under expansion the value in an individual group to group cell is copied into each and every corresponding zone to zone cell so that the sum of all the zone to zone cells will be considerably greater than the sum of the group to group cells Hence this option is not suitable for a matrix of quantities such as a trip matrix whereas it would be suitable for a qualitative matrix of say group to group distances or group to group factors N B The use of the terms group and zone above is purely nominal they are simply referring to two different levels of spatial aggregation The same procedures could equally well be used to transform a matrix defined in terms of boroughs into one defined by districts or from boroughs into zones etc etc see Section 10 2 5 for a discussion on different levels of aggregation and their names Output Options for Stacked Matrices If the internal matrix is stacked with
97. ult to distinguish from a true 0 00 and in this case the factored row column will not contain all Zeros In release 10 9 a row column sums less than 0 01 are printed with extra decimal places e g 0 000012 rather than 0 00 and b warning messages are printed under Furness to warn of very small row column sums 10 29 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 7 2 10 7 3 5120257 Apr 15 Section 10 _SATURN Selected Area Cell Factoring Interactive Control The user needs to define interactively A factor An area of the matrix over which the factor is to be applied where the area to be factored is defined via the SELECT procedures see 10 6 Note that the area may actually be defined in terms of cell values so that it need not be a block of cells By default the selected area to be factored will be the entire matrix so that in the case of a stacked matrix all levels are included by default However a short cut select procedure may also be used with stacked matrices whereby a single square level and or block of the full matrix is directly pre selected to be factored as opposed to the more long winded but equivalent process of explicitly identifying the row and column limits associated with a specific level block Note that having nominated a particular sub matrix the selection may be further refined by setting e g internal zone limits and or c
98. ut matrix to be stacked while each following record lists a sub matrix to be stacked The number of matrices to be stacked is therefore dictated only by the number of records in the file Thus it is not otherwise restricted by the number of matrices 8 that MX can store internally unlike MXSTACK 10 20 9 since each matrix to be stacked is read copied and then closed immediately If the second parameter is QUIET then the program runs in quiet mode see 14 9 UFMUNSTACK Unstack a Matrix based on a Control File UFMUNSTACK Core r o Ouine Unstacks a matrix into a set of sub matrices using a set of filenames read from a text file control As with UFMSTACK the first record in control gives the name of the ufm matrix to be unstacked while each following record lists a sub matrix The number of sub matrices should be equal to the number of levels in the stacked matrix but is not otherwise restricted If the second parameter is QUIET then the program runs in quiet mode see 14 9 Clearly UFMUNSTACK is the converse of UFMSTACK and the same control file may be used for both MXDOT2 Take the dot product of two matrices MXDOT2 matl MENEZ mat3 Takes the dot product of matrices mat2 ufm and mat1 ufm together to produce an output file mat 3 ufm i e 10 58 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 20 20 10 20 21 10 20 22 10 20 23 10 20 24 5120257 Apr 15 Section 10
99. wth factors of one trip matrix relative to another 10 60 SATURN MANUAL V11 3 MX Interactive Matrix Manipulation 10 21 5120257 Apr 15 Section 10 Revision 10 9 10 10 9 12 10 9 17 10 9 22 10 9 24 11 1 09 11 2 01 11 2 05 11 3 03 11 3 07 11 3 10 11 3 12 Version Control JOB NUMBER 5120257 DOCUMENT REF Section 10 doc Purpose Description SATURN v10 9 Release DVV SATURN v10 9 Release Full DVV Web release Jun 10 DVV Web release Dec 10 DVV SATURN v10 9 Release Full DVV SATURN v11 1 Release Full DVV SATURN v11 2 Release Full DVV SATURN v11 3 10 Release DVV SATURN v11 3 12 Release DVV 10 61 Checked DG DG NP AG AG AG JS SN DAS DAS DAS _SATURN SATURN Date 04 09 09 22 10 09 22 06 10 06 12 10 06 05 11 31 03 12 07 12 12 17 03 13 30 04 14 26 09 14 22 01 15 20 04 15
100. x mat ufm into its various components mati ufm mat2 ufm etc etc up to the number of sub matrices stacked in mat ufm The sub matrices may be re combined into a stacked matrix using STACK above MXSUB2 Subtract one matrix from another MXSUB2 matl mat2 iment gt Subtracts matrix mat2 ufm from mat1 ufm together to produce an output file mat 3 ufm i e T T T ij ij ij MXWEIGHT Weighted Average of Two Matrices MXWEIGHT matl mat2 matos I Takes a weighted average of two matrix files mat1 ufm and mat2 ufm to produce an output file mat3 ufm where 3 l 2 T n Ela As opposed to MXAVER2 which takes a fixed 50 50 average UFM2 Dump UFM Matrices to Text Files E g UFM2CSV mat text dumps a binary matrix mat ufm into a csv formatted text file text or if the second parameter is not included into a default value mat ixt It therefore follows automatically the procedures described in 10 15 1 option 4 A number of varieties of UFM2 exist essentially one for each of the various output options described in 10 15 1 Thus 10 56 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 20 16 5120257 Apr 15 Section 10 _SATURN UFM2SATL dumps in SATURN long format UFM2SATS dumps in SATURN short format UFM2LINE dumps single records for non zero cells UFM2CSV dumps as CSV Comma Separated Variables UFM2EMME dumps in EMME 2 format UFM2TB
101. xternal memory i e on the hard disk 2 An internal matrix stored entirely in core memory RAM 10 11 SATURN MANUAL V1 1 3 MX Interactive Matrix Manipulation 10 3 2 10 3 3 5120257 Apr 15 Section 10 SATURN 3 A single output UFM matrix copied at the user s request from the internal matrix to the hard disk These are illustrated in Figure 10 2 where the external files used for input are denoted X1 X2 etc up to Xn the matrix in internal memory is denoted by Y and the output matrix is Z Thus for example two input matrices X1 and X2 may be added to create a new internal matrix Y which is then dumped to the output file Z See 10 8 1 By default when one or more ufm files are input then initially the first input matrix is copied directly into the internal RAM Thus the command MX mat would cause the matrix file mat ufm to be read into the internal memory Changes are applied only to the internal matrix whereas the majority of viewing or analysis operations can use both internal and external files Control Files In addition to the matrix files described above certain options within MX may make use of external input data and or control files e g to define the row and or column totals to Furness a trip matrix While this data may be defined interactively it is very often easier for the user to prepare large data sets off line with an editing program

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