## 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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