## table of contents

single_eig(3) | LAPACK | single_eig(3) |

# NAME¶

single_eig - real# SYNOPSIS¶

## Functions¶

program

**schkee**

**SCHKEE**

# Detailed Description¶

This is the group of real LAPACK TESTING EIG routines.# Function Documentation¶

## program schkee¶

**SCHKEE**

**Purpose:**

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.

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

# Author¶

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