TESTING/EIG/sdrvbd.f(3)

NAME
TESTING/EIG/sdrvbd.f

SYNOPSIS

  Functions/Subroutines
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

Function/Subroutine Documentation

  subroutine sdrvbd (integer nsizes, integer, dimension( * ) mm, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, real thresh, real, dimension( lda, * ) a, integer lda, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldvt, * ) vt, integer ldvt, real, dimension( lda, * ) asav, real, dimension( ldu, * ) usav, real, dimension( ldvt, * ) vtsav, real, dimension( * ) s, real, dimension( * ) ssav, real, dimension( * ) e, real, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer nout, integer info)

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.

Author

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