.TH "single_eig" 3 "Sun Nov 27 2022" "Version 3.11.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME single_eig \- real .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "program \fBschkee\fP" .br .RI "\fBSCHKEE\fP " .in -1c .SH "Detailed Description" .PP This is the group of real LAPACK TESTING EIG routines\&. .SH "Function Documentation" .PP .SS "program schkee" .PP \fBSCHKEE\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SCHKEE tests the REAL LAPACK subroutines for the matrix eigenvalue problem\&. The test paths in this version are NEP (Nonsymmetric Eigenvalue Problem): Test SGEHRD, SORGHR, SHSEQR, STREVC, SHSEIN, and SORMHR SEP (Symmetric Eigenvalue Problem): Test SSYTRD, SORGTR, SSTEQR, SSTERF, SSTEIN, SSTEDC, and drivers SSYEV(X), SSBEV(X), SSPEV(X), SSTEV(X), SSYEVD, SSBEVD, SSPEVD, SSTEVD SVD (Singular Value Decomposition): Test SGEBRD, SORGBR, SBDSQR, SBDSDC and the drivers SGESVD, SGESDD SEV (Nonsymmetric Eigenvalue/eigenvector Driver): Test SGEEV SES (Nonsymmetric Schur form Driver): Test SGEES SVX (Nonsymmetric Eigenvalue/eigenvector Expert Driver): Test SGEEVX SSX (Nonsymmetric Schur form Expert Driver): Test SGEESX SGG (Generalized Nonsymmetric Eigenvalue Problem): Test SGGHD3, SGGBAL, SGGBAK, SHGEQZ, and STGEVC SGS (Generalized Nonsymmetric Schur form Driver): Test SGGES SGV (Generalized Nonsymmetric Eigenvalue/eigenvector Driver): Test SGGEV SGX (Generalized Nonsymmetric Schur form Expert Driver): Test SGGESX SXV (Generalized Nonsymmetric Eigenvalue/eigenvector Expert Driver): Test SGGEVX SSG (Symmetric Generalized Eigenvalue Problem): Test SSYGST, SSYGV, SSYGVD, SSYGVX, SSPGST, SSPGV, SSPGVD, SSPGVX, SSBGST, SSBGV, SSBGVD, and SSBGVX SSB (Symmetric Band Eigenvalue Problem): Test SSBTRD SBB (Band Singular Value Decomposition): Test SGBBRD SEC (Eigencondition estimation): Test SLALN2, SLASY2, SLAEQU, SLAEXC, STRSYL, STREXC, STRSNA, STRSEN, and SLAQTR SBL (Balancing a general matrix) Test SGEBAL SBK (Back transformation on a balanced matrix) Test SGEBAK SGL (Balancing a matrix pair) Test SGGBAL SGK (Back transformation on a matrix pair) Test SGGBAK GLM (Generalized Linear Regression Model): Tests SGGGLM GQR (Generalized QR and RQ factorizations): Tests SGGQRF and SGGRQF GSV (Generalized Singular Value Decomposition): Tests SGGSVD, SGGSVP, STGSJA, SLAGS2, SLAPLL, and SLAPMT CSD (CS decomposition): Tests SORCSD LSE (Constrained Linear Least Squares): Tests SGGLSE Each test path has a different set of inputs, but the data sets for the driver routines xEV, xES, xVX, and xSX can be concatenated in a single input file\&. The first line of input should contain one of the 3-character path names in columns 1-3\&. The number of remaining lines depends on what is found on the first line\&. The number of matrix types used in testing is often controllable from the input file\&. The number of matrix types for each path, and the test routine that describes them, is as follows: Path name(s) Types Test routine SHS or NEP 21 SCHKHS SST or SEP 21 SCHKST (routines) 18 SDRVST (drivers) SBD or SVD 16 SCHKBD (routines) 5 SDRVBD (drivers) SEV 21 SDRVEV SES 21 SDRVES SVX 21 SDRVVX SSX 21 SDRVSX SGG 26 SCHKGG (routines) SGS 26 SDRGES SGX 5 SDRGSX SGV 26 SDRGEV SXV 2 SDRGVX SSG 21 SDRVSG SSB 15 SCHKSB SBB 15 SCHKBB SEC - SCHKEC SBL - SCHKBL SBK - SCHKBK SGL - SCHKGL SGK - SCHKGK GLM 8 SCKGLM GQR 8 SCKGQR GSV 8 SCKGSV CSD 3 SCKCSD LSE 8 SCKLSE ----------------------------------------------------------------------- NEP input file: line 2: NN, INTEGER Number of values of N\&. line 3: NVAL, INTEGER array, dimension (NN) The values for the matrix dimension N\&. line 4: NPARMS, INTEGER Number of values of the parameters NB, NBMIN, NX, NS, and MAXB\&. line 5: NBVAL, INTEGER array, dimension (NPARMS) The values for the blocksize NB\&. line 6: NBMIN, INTEGER array, dimension (NPARMS) The values for the minimum blocksize NBMIN\&. line 7: NXVAL, INTEGER array, dimension (NPARMS) The values for the crossover point NX\&. line 8: INMIN, INTEGER array, dimension (NPARMS) LAHQR vs TTQRE crossover point, >= 11 line 9: INWIN, INTEGER array, dimension (NPARMS) recommended deflation window size line 10: INIBL, INTEGER array, dimension (NPARMS) nibble crossover point line 11: ISHFTS, INTEGER array, dimension (NPARMS) number of simultaneous shifts) line 12: IACC22, INTEGER array, dimension (NPARMS) select structured matrix multiply: 0, 1 or 2) line 13: THRESH Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. To have all of the test ratios printed, use THRESH = 0\&.0 \&. line 14: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 14 was 2: line 15: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 15-EOF: The remaining lines occur in sets of 1 or 2 and allow the user to specify the matrix types\&. Each line contains a 3-character path name in columns 1-3, and the number of matrix types must be the first nonblank item in columns 4-80\&. If the number of matrix types is at least 1 but is less than the maximum number of possible types, a second line will be read to get the numbers of the matrix types to be used\&. For example, NEP 21 requests all of the matrix types for the nonsymmetric eigenvalue problem, while NEP 4 9 10 11 12 requests only matrices of type 9, 10, 11, and 12\&. The valid 3-character path names are 'NEP' or 'SHS' for the nonsymmetric eigenvalue routines\&. ----------------------------------------------------------------------- SEP or SSG input file: line 2: NN, INTEGER Number of values of N\&. line 3: NVAL, INTEGER array, dimension (NN) The values for the matrix dimension N\&. line 4: NPARMS, INTEGER Number of values of the parameters NB, NBMIN, and NX\&. line 5: NBVAL, INTEGER array, dimension (NPARMS) The values for the blocksize NB\&. line 6: NBMIN, INTEGER array, dimension (NPARMS) The values for the minimum blocksize NBMIN\&. line 7: NXVAL, INTEGER array, dimension (NPARMS) The values for the crossover point NX\&. line 8: THRESH Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 9: TSTCHK, LOGICAL Flag indicating whether or not to test the LAPACK routines\&. line 10: TSTDRV, LOGICAL Flag indicating whether or not to test the driver routines\&. line 11: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 12: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 12 was 2: line 13: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 13-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path names are 'SEP' or 'SST' for the symmetric eigenvalue routines and driver routines, and 'SSG' for the routines for the symmetric generalized eigenvalue problem\&. ----------------------------------------------------------------------- SVD input file: line 2: NN, INTEGER Number of values of M and N\&. line 3: MVAL, INTEGER array, dimension (NN) The values for the matrix row dimension M\&. line 4: NVAL, INTEGER array, dimension (NN) The values for the matrix column dimension N\&. line 5: NPARMS, INTEGER Number of values of the parameter NB, NBMIN, NX, and NRHS\&. line 6: NBVAL, INTEGER array, dimension (NPARMS) The values for the blocksize NB\&. line 7: NBMIN, INTEGER array, dimension (NPARMS) The values for the minimum blocksize NBMIN\&. line 8: NXVAL, INTEGER array, dimension (NPARMS) The values for the crossover point NX\&. line 9: NSVAL, INTEGER array, dimension (NPARMS) The values for the number of right hand sides NRHS\&. line 10: THRESH Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 11: TSTCHK, LOGICAL Flag indicating whether or not to test the LAPACK routines\&. line 12: TSTDRV, LOGICAL Flag indicating whether or not to test the driver routines\&. line 13: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 14: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 14 was 2: line 15: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 15-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path names are 'SVD' or 'SBD' for both the SVD routines and the SVD driver routines\&. ----------------------------------------------------------------------- SEV and SES data files: line 1: 'SEV' or 'SES' in columns 1 to 3\&. line 2: NSIZES, INTEGER Number of sizes of matrices to use\&. Should be at least 0 and at most 20\&. If NSIZES = 0, no testing is done (although the remaining 3 lines are still read)\&. line 3: NN, INTEGER array, dimension(NSIZES) Dimensions of matrices to be tested\&. line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs These integer parameters determine how blocking is done (see ILAENV for details) NB : block size NBMIN : minimum block size NX : minimum dimension for blocking NS : number of shifts in xHSEQR NBCOL : minimum column dimension for blocking line 5: THRESH, REAL The test threshold against which computed residuals are compared\&. Should generally be in the range from 10\&. to 20\&. If it is 0\&., all test case data will be printed\&. line 6: TSTERR, LOGICAL Flag indicating whether or not to test the error exits\&. line 7: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 7 was 2: line 8: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 9 and following: Lines specifying matrix types, as for NEP\&. The 3-character path name is 'SEV' to test SGEEV, or 'SES' to test SGEES\&. ----------------------------------------------------------------------- The SVX data has two parts\&. The first part is identical to SEV, and the second part consists of test matrices with precomputed solutions\&. line 1: 'SVX' in columns 1-3\&. line 2: NSIZES, INTEGER If NSIZES = 0, no testing of randomly generated examples is done, but any precomputed examples are tested\&. line 3: NN, INTEGER array, dimension(NSIZES) line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs line 5: THRESH, REAL line 6: TSTERR, LOGICAL line 7: NEWSD, INTEGER If line 7 was 2: line 8: INTEGER array, dimension (4) lines 9 and following: The first line contains 'SVX' in columns 1-3 followed by the number of matrix types, possibly with a second line to specify certain matrix types\&. If the number of matrix types = 0, no testing of randomly generated examples is done, but any precomputed examples are tested\&. remaining lines : Each matrix is stored on 1+2*N lines, where N is its dimension\&. The first line contains the dimension (a single integer)\&. The next N lines contain the matrix, one row per line\&. The last N lines correspond to each eigenvalue\&. Each of these last N lines contains 4 real values: the real part of the eigenvalue, the imaginary part of the eigenvalue, the reciprocal condition number of the eigenvalues, and the reciprocal condition number of the eigenvector\&. The end of data is indicated by dimension N=0\&. Even if no data is to be tested, there must be at least one line containing N=0\&. ----------------------------------------------------------------------- The SSX data is like SVX\&. The first part is identical to SEV, and the second part consists of test matrices with precomputed solutions\&. line 1: 'SSX' in columns 1-3\&. line 2: NSIZES, INTEGER If NSIZES = 0, no testing of randomly generated examples is done, but any precomputed examples are tested\&. line 3: NN, INTEGER array, dimension(NSIZES) line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs line 5: THRESH, REAL line 6: TSTERR, LOGICAL line 7: NEWSD, INTEGER If line 7 was 2: line 8: INTEGER array, dimension (4) lines 9 and following: The first line contains 'SSX' in columns 1-3 followed by the number of matrix types, possibly with a second line to specify certain matrix types\&. If the number of matrix types = 0, no testing of randomly generated examples is done, but any precomputed examples are tested\&. remaining lines : Each matrix is stored on 3+N lines, where N is its dimension\&. The first line contains the dimension N and the dimension M of an invariant subspace\&. The second line contains M integers, identifying the eigenvalues in the invariant subspace (by their position in a list of eigenvalues ordered by increasing real part)\&. The next N lines contain the matrix\&. The last line contains the reciprocal condition number for the average of the selected eigenvalues, and the reciprocal condition number for the corresponding right invariant subspace\&. The end of data is indicated by a line containing N=0 and M=0\&. Even if no data is to be tested, there must be at least one line containing N=0 and M=0\&. ----------------------------------------------------------------------- SGG input file: line 2: NN, INTEGER Number of values of N\&. line 3: NVAL, INTEGER array, dimension (NN) The values for the matrix dimension N\&. line 4: NPARMS, INTEGER Number of values of the parameters NB, NBMIN, NS, MAXB, and NBCOL\&. line 5: NBVAL, INTEGER array, dimension (NPARMS) The values for the blocksize NB\&. line 6: NBMIN, INTEGER array, dimension (NPARMS) The values for NBMIN, the minimum row dimension for blocks\&. line 7: NSVAL, INTEGER array, dimension (NPARMS) The values for the number of shifts\&. line 8: MXBVAL, INTEGER array, dimension (NPARMS) The values for MAXB, used in determining minimum blocksize\&. line 9: IACC22, INTEGER array, dimension (NPARMS) select structured matrix multiply: 1 or 2) line 10: NBCOL, INTEGER array, dimension (NPARMS) The values for NBCOL, the minimum column dimension for blocks\&. line 11: THRESH Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 12: TSTCHK, LOGICAL Flag indicating whether or not to test the LAPACK routines\&. line 13: TSTDRV, LOGICAL Flag indicating whether or not to test the driver routines\&. line 14: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 15: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 15 was 2: line 16: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 17-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path name is 'SGG' for the generalized eigenvalue problem routines and driver routines\&. ----------------------------------------------------------------------- SGS and SGV input files: line 1: 'SGS' or 'SGV' in columns 1 to 3\&. line 2: NN, INTEGER Number of values of N\&. line 3: NVAL, INTEGER array, dimension(NN) Dimensions of matrices to be tested\&. line 4: NB, NBMIN, NX, NS, NBCOL, INTEGERs These integer parameters determine how blocking is done (see ILAENV for details) NB : block size NBMIN : minimum block size NX : minimum dimension for blocking NS : number of shifts in xHGEQR NBCOL : minimum column dimension for blocking line 5: THRESH, REAL The test threshold against which computed residuals are compared\&. Should generally be in the range from 10\&. to 20\&. If it is 0\&., all test case data will be printed\&. line 6: TSTERR, LOGICAL Flag indicating whether or not to test the error exits\&. line 7: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 17 was 2: line 7: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 7-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path name is 'SGS' for the generalized eigenvalue problem routines and driver routines\&. ----------------------------------------------------------------------- SXV input files: line 1: 'SXV' in columns 1 to 3\&. line 2: N, INTEGER Value of N\&. line 3: NB, NBMIN, NX, NS, NBCOL, INTEGERs These integer parameters determine how blocking is done (see ILAENV for details) NB : block size NBMIN : minimum block size NX : minimum dimension for blocking NS : number of shifts in xHGEQR NBCOL : minimum column dimension for blocking line 4: THRESH, REAL The test threshold against which computed residuals are compared\&. Should generally be in the range from 10\&. to 20\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 5: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 6: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 6 was 2: line 7: INTEGER array, dimension (4) Four integer values for the random number seed\&. If line 2 was 0: line 7-EOF: Precomputed examples are tested\&. remaining lines : Each example is stored on 3+2*N lines, where N is its dimension\&. The first line contains the dimension (a single integer)\&. The next N lines contain the matrix A, one row per line\&. The next N lines contain the matrix B\&. The next line contains the reciprocals of the eigenvalue condition numbers\&. The last line contains the reciprocals of the eigenvector condition numbers\&. The end of data is indicated by dimension N=0\&. Even if no data is to be tested, there must be at least one line containing N=0\&. ----------------------------------------------------------------------- SGX input files: line 1: 'SGX' in columns 1 to 3\&. line 2: N, INTEGER Value of N\&. line 3: NB, NBMIN, NX, NS, NBCOL, INTEGERs These integer parameters determine how blocking is done (see ILAENV for details) NB : block size NBMIN : minimum block size NX : minimum dimension for blocking NS : number of shifts in xHGEQR NBCOL : minimum column dimension for blocking line 4: THRESH, REAL The test threshold against which computed residuals are compared\&. Should generally be in the range from 10\&. to 20\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 5: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 6: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 6 was 2: line 7: INTEGER array, dimension (4) Four integer values for the random number seed\&. If line 2 was 0: line 7-EOF: Precomputed examples are tested\&. remaining lines : Each example is stored on 3+2*N lines, where N is its dimension\&. The first line contains the dimension (a single integer)\&. The next line contains an integer k such that only the last k eigenvalues will be selected and appear in the leading diagonal blocks of $A$ and $B$\&. The next N lines contain the matrix A, one row per line\&. The next N lines contain the matrix B\&. The last line contains the reciprocal of the eigenvalue cluster condition number and the reciprocal of the deflating subspace (associated with the selected eigencluster) condition number\&. The end of data is indicated by dimension N=0\&. Even if no data is to be tested, there must be at least one line containing N=0\&. ----------------------------------------------------------------------- SSB input file: line 2: NN, INTEGER Number of values of N\&. line 3: NVAL, INTEGER array, dimension (NN) The values for the matrix dimension N\&. line 4: NK, INTEGER Number of values of K\&. line 5: KVAL, INTEGER array, dimension (NK) The values for the matrix dimension K\&. line 6: THRESH Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 7: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 7 was 2: line 8: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 8-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path name is 'SSB'\&. ----------------------------------------------------------------------- SBB input file: line 2: NN, INTEGER Number of values of M and N\&. line 3: MVAL, INTEGER array, dimension (NN) The values for the matrix row dimension M\&. line 4: NVAL, INTEGER array, dimension (NN) The values for the matrix column dimension N\&. line 4: NK, INTEGER Number of values of K\&. line 5: KVAL, INTEGER array, dimension (NK) The values for the matrix bandwidth K\&. line 6: NPARMS, INTEGER Number of values of the parameter NRHS line 7: NSVAL, INTEGER array, dimension (NPARMS) The values for the number of right hand sides NRHS\&. line 8: THRESH Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 9: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 9 was 2: line 10: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 10-EOF: Lines specifying matrix types, as for SVD\&. The 3-character path name is 'SBB'\&. ----------------------------------------------------------------------- SEC input file: line 2: THRESH, REAL Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. lines 3-EOF: Input for testing the eigencondition routines consists of a set of specially constructed test cases and their solutions\&. The data format is not intended to be modified by the user\&. ----------------------------------------------------------------------- SBL and SBK input files: line 1: 'SBL' in columns 1-3 to test SGEBAL, or 'SBK' in columns 1-3 to test SGEBAK\&. The remaining lines consist of specially constructed test cases\&. ----------------------------------------------------------------------- SGL and SGK input files: line 1: 'SGL' in columns 1-3 to test SGGBAL, or 'SGK' in columns 1-3 to test SGGBAK\&. The remaining lines consist of specially constructed test cases\&. ----------------------------------------------------------------------- GLM data file: line 1: 'GLM' in columns 1 to 3\&. line 2: NN, INTEGER Number of values of M, P, and N\&. line 3: MVAL, INTEGER array, dimension(NN) Values of M (row dimension)\&. line 4: PVAL, INTEGER array, dimension(NN) Values of P (row dimension)\&. line 5: NVAL, INTEGER array, dimension(NN) Values of N (column dimension), note M <= N <= M+P\&. line 6: THRESH, REAL Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 7: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 8: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 8 was 2: line 9: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 9-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path name is 'GLM' for the generalized linear regression model routines\&. ----------------------------------------------------------------------- GQR data file: line 1: 'GQR' in columns 1 to 3\&. line 2: NN, INTEGER Number of values of M, P, and N\&. line 3: MVAL, INTEGER array, dimension(NN) Values of M\&. line 4: PVAL, INTEGER array, dimension(NN) Values of P\&. line 5: NVAL, INTEGER array, dimension(NN) Values of N\&. line 6: THRESH, REAL Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 7: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 8: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 8 was 2: line 9: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 9-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path name is 'GQR' for the generalized QR and RQ routines\&. ----------------------------------------------------------------------- GSV data file: line 1: 'GSV' in columns 1 to 3\&. line 2: NN, INTEGER Number of values of M, P, and N\&. line 3: MVAL, INTEGER array, dimension(NN) Values of M (row dimension)\&. line 4: PVAL, INTEGER array, dimension(NN) Values of P (row dimension)\&. line 5: NVAL, INTEGER array, dimension(NN) Values of N (column dimension)\&. line 6: THRESH, REAL Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 7: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 8: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 8 was 2: line 9: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 9-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path name is 'GSV' for the generalized SVD routines\&. ----------------------------------------------------------------------- CSD data file: line 1: 'CSD' in columns 1 to 3\&. line 2: NM, INTEGER Number of values of M, P, and N\&. line 3: MVAL, INTEGER array, dimension(NM) Values of M (row and column dimension of orthogonal matrix)\&. line 4: PVAL, INTEGER array, dimension(NM) Values of P (row dimension of top-left block)\&. line 5: NVAL, INTEGER array, dimension(NM) Values of N (column dimension of top-left block)\&. line 6: THRESH, REAL Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 7: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 8: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 8 was 2: line 9: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 9-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path name is 'CSD' for the CSD routine\&. ----------------------------------------------------------------------- LSE data file: line 1: 'LSE' in columns 1 to 3\&. line 2: NN, INTEGER Number of values of M, P, and N\&. line 3: MVAL, INTEGER array, dimension(NN) Values of M\&. line 4: PVAL, INTEGER array, dimension(NN) Values of P\&. line 5: NVAL, INTEGER array, dimension(NN) Values of N, note P <= N <= P+M\&. line 6: THRESH, REAL Threshold value for the test ratios\&. Information will be printed about each test for which the test ratio is greater than or equal to the threshold\&. line 7: TSTERR, LOGICAL Flag indicating whether or not to test the error exits for the LAPACK routines and driver routines\&. line 8: NEWSD, INTEGER A code indicating how to set the random number seed\&. = 0: Set the seed to a default value before each run = 1: Initialize the seed to a default value only before the first run = 2: Like 1, but use the seed values on the next line If line 8 was 2: line 9: INTEGER array, dimension (4) Four integer values for the random number seed\&. lines 9-EOF: Lines specifying matrix types, as for NEP\&. The 3-character path name is 'GSV' for the generalized SVD routines\&. ----------------------------------------------------------------------- NMAX is currently set to 132 and must be at least 12 for some of the precomputed examples, and LWORK = NMAX*(5*NMAX+5)+1 in the parameter statements below\&. For SVD, we assume NRHS may be as big as N\&. The parameter NEED is set to 14 to allow for 14 N-by-N matrices for SGG\&. .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.