sdrvbd.f - Man Page

subroutine sdrvbd (nsizes, mm, nn, ntypes, dotype, iseed, thresh, a, lda, u, ldu, vt, ldvt, asav, usav, vtsav, s, ssav, e, work, lwork, iwork, nout, info)
SDRVBD

SDRVBD

Purpose:

 SDRVBD checks the singular value decomposition (SVD) drivers
 SGESVD, SGESDD, SGESVDQ, SGESVJ, SGEJSV, and DGESVDX.

 Both SGESVD and SGESDD factor A = U diag(S) VT, where U and VT are
 orthogonal and diag(S) is diagonal with the entries of the array S
 on its diagonal. The entries of S are the singular values,
 nonnegative and stored in decreasing order.  U and VT can be
 optionally not computed, overwritten on A, or computed partially.

 A is M by N. Let MNMIN = min( M, N ). S has dimension MNMIN.
 U can be M by M or M by MNMIN. VT can be N by N or MNMIN by N.

 When SDRVBD is called, a number of matrix 'sizes' (M's and N's)
 and a number of matrix 'types' are specified.  For each size (M,N)
 and each type of matrix, and for the minimal workspace as well as
 workspace adequate to permit blocking, an  M x N  matrix 'A' will be
 generated and used to test the SVD routines.  For each matrix, A will
 be factored as A = U diag(S) VT and the following 12 tests computed:

 Test for SGESVD:

 (1)    | A - U diag(S) VT | / ( |A| max(M,N) ulp )

 (2)    | I - U'U | / ( M ulp )

 (3)    | I - VT VT' | / ( N ulp )

 (4)    S contains MNMIN nonnegative values in decreasing order.
        (Return 0 if true, 1/ULP if false.)

 (5)    | U - Upartial | / ( M ulp ) where Upartial is a partially
        computed U.

 (6)    | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
        computed VT.

 (7)    | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
        vector of singular values from the partial SVD

 Test for SGESDD:

 (8)    | A - U diag(S) VT | / ( |A| max(M,N) ulp )

 (9)    | I - U'U | / ( M ulp )

 (10)   | I - VT VT' | / ( N ulp )

 (11)   S contains MNMIN nonnegative values in decreasing order.
        (Return 0 if true, 1/ULP if false.)

 (12)   | U - Upartial | / ( M ulp ) where Upartial is a partially
        computed U.

 (13)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
        computed VT.

 (14)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
        vector of singular values from the partial SVD

 Test for SGESVDQ:

 (36)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )

 (37)   | I - U'U | / ( M ulp )

 (38)   | I - VT VT' | / ( N ulp )

 (39)   S contains MNMIN nonnegative values in decreasing order.
        (Return 0 if true, 1/ULP if false.)

 Test for SGESVJ:

 (15)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )

 (16)   | I - U'U | / ( M ulp )

 (17)   | I - VT VT' | / ( N ulp )

 (18)   S contains MNMIN nonnegative values in decreasing order.
        (Return 0 if true, 1/ULP if false.)

 Test for SGEJSV:

 (19)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )

 (20)   | I - U'U | / ( M ulp )

 (21)   | I - VT VT' | / ( N ulp )

 (22)   S contains MNMIN nonnegative values in decreasing order.
        (Return 0 if true, 1/ULP if false.)

 Test for SGESVDX( 'V', 'V', 'A' )/SGESVDX( 'N', 'N', 'A' )

 (23)   | A - U diag(S) VT | / ( |A| max(M,N) ulp )

 (24)   | I - U'U | / ( M ulp )

 (25)   | I - VT VT' | / ( N ulp )

 (26)   S contains MNMIN nonnegative values in decreasing order.
        (Return 0 if true, 1/ULP if false.)

 (27)   | U - Upartial | / ( M ulp ) where Upartial is a partially
        computed U.

 (28)   | VT - VTpartial | / ( N ulp ) where VTpartial is a partially
        computed VT.

 (29)   | S - Spartial | / ( MNMIN ulp |S| ) where Spartial is the
        vector of singular values from the partial SVD

 Test for SGESVDX( 'V', 'V', 'I' )

 (30)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )

 (31)   | I - U'U | / ( M ulp )

 (32)   | I - VT VT' | / ( N ulp )

 Test for SGESVDX( 'V', 'V', 'V' )

 (33)   | U' A VT''' - diag(S) | / ( |A| max(M,N) ulp )

 (34)   | I - U'U | / ( M ulp )

 (35)   | I - VT VT' | / ( N ulp )

 The 'sizes' are specified by the arrays MM(1:NSIZES) and
 NN(1:NSIZES); the value of each element pair (MM(j),NN(j))
 specifies one size.  The 'types' are specified by a logical array
 DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type 'j'
 will be generated.
 Currently, the list of possible types is:

 (1)  The zero matrix.
 (2)  The identity matrix.
 (3)  A matrix of the form  U D V, where U and V are orthogonal and
      D has evenly spaced entries 1, ..., ULP with random signs
      on the diagonal.
 (4)  Same as (3), but multiplied by the underflow-threshold / ULP.
 (5)  Same as (3), but multiplied by the overflow-threshold * ULP.

Parameters

NSIZES

          NSIZES is INTEGER
          The number of matrix sizes (M,N) contained in the vectors
          MM and NN.

MM

          MM is INTEGER array, dimension (NSIZES)
          The values of the matrix row dimension M.

NN

          NN is INTEGER array, dimension (NSIZES)
          The values of the matrix column dimension N.

NTYPES

          NTYPES is INTEGER
          The number of elements in DOTYPE.   If it is zero, SDRVBD
          does nothing.  It must be at least zero.  If it is MAXTYP+1
          and NSIZES is 1, then an additional type, MAXTYP+1 is
          defined, which is to use whatever matrices are in A and B.
          This is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
          DOTYPE(MAXTYP+1) is .TRUE. .

DOTYPE

          DOTYPE is LOGICAL array, dimension (NTYPES)
          If DOTYPE(j) is .TRUE., then for each size (m,n), a matrix
          of type j will be generated.  If NTYPES is smaller than the
          maximum number of types defined (PARAMETER MAXTYP), then
          types NTYPES+1 through MAXTYP will not be generated.  If
          NTYPES is larger than MAXTYP, DOTYPE(MAXTYP+1) through
          DOTYPE(NTYPES) will be ignored.

ISEED

          ISEED is INTEGER array, dimension (4)
          On entry, the seed of the random number generator.  The array
          elements should be between 0 and 4095; if not they will be
          reduced mod 4096.  Also, ISEED(4) must be odd.
          On exit, ISEED is changed and can be used in the next call to
          SDRVBD to continue the same random number sequence.

THRESH

          THRESH is REAL
          The threshold value for the test ratios.  A result is
          included in the output file if RESULT >= THRESH.  The test
          ratios are scaled to be O(1), so THRESH should be a small
          multiple of 1, e.g., 10 or 100.  To have every test ratio
          printed, use THRESH = 0.

A

          A is REAL array, dimension (LDA,NMAX)
          where NMAX is the maximum value of N in NN.

LDA

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,MMAX),
          where MMAX is the maximum value of M in MM.

U

          U is REAL array, dimension (LDU,MMAX)

LDU

          LDU is INTEGER
          The leading dimension of the array U.  LDU >= max(1,MMAX).

VT

          VT is REAL array, dimension (LDVT,NMAX)

LDVT

          LDVT is INTEGER
          The leading dimension of the array VT.  LDVT >= max(1,NMAX).

ASAV

          ASAV is REAL array, dimension (LDA,NMAX)

USAV

          USAV is REAL array, dimension (LDU,MMAX)

VTSAV

          VTSAV is REAL array, dimension (LDVT,NMAX)

S

          S is REAL array, dimension
                      (max(min(MM,NN)))

SSAV

          SSAV is REAL array, dimension
                      (max(min(MM,NN)))

E

          E is REAL array, dimension
                      (max(min(MM,NN)))

WORK

          WORK is REAL array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The number of entries in WORK.  This must be at least
          max(3*MN+MX,5*MN-4)+2*MN**2 for all pairs
          pairs  (MN,MX)=( min(MM(j),NN(j), max(MM(j),NN(j)) )

IWORK

          IWORK is INTEGER array, dimension at least 8*min(M,N)

NOUT

          NOUT is INTEGER
          The FORTRAN unit number for printing out error messages
          (e.g., if a routine returns IINFO not equal to 0.)

INFO

          INFO is INTEGER
          If 0, then everything ran OK.
           -1: NSIZES < 0
           -2: Some MM(j) < 0
           -3: Some NN(j) < 0
           -4: NTYPES < 0
           -7: THRESH < 0
          -10: LDA < 1 or LDA < MMAX, where MMAX is max( MM(j) ).
          -12: LDU < 1 or LDU < MMAX.
          -14: LDVT < 1 or LDVT < NMAX, where NMAX is max( NN(j) ).
          -21: LWORK too small.
          If  SLATMS, or SGESVD returns an error code, the
              absolute value of it is returned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 363 of file sdrvbd.f.