TESTING/EIG/zdrvbd.f(3)

NAME
TESTING/EIG/zdrvbd.f

SYNOPSIS

  Functions/Subroutines
subroutine zdrvbd (nsizes, mm, nn, ntypes, dotype, iseed, thresh, a, lda, u, ldu, vt, ldvt, asav, usav, vtsav, s, ssav, e, work, lwork, rwork, iwork, nounit, info)
ZDRVBD

Function/Subroutine Documentation

  subroutine zdrvbd (integer nsizes, integer, dimension( * ) mm, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldvt, * ) vt, integer ldvt, complex*16, dimension( lda, * ) asav, complex*16, dimension( ldu, * ) usav, complex*16, dimension( ldvt, * ) vtsav, double precision, dimension( * ) s, double precision, dimension( * ) ssav, double precision, dimension( * ) e, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer nounit, integer info)

ZDRVBD

Purpose:

     ZDRVBD checks the singular value decomposition (SVD) driver ZGESVD,
     ZGESDD, ZGESVJ, ZGEJSV, ZGESVDX, and ZGESVDQ.
     ZGESVD and ZGESDD factors A = U diag(S) VT, where U and VT are
     unitary 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 ZDRVBD 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 ZGESVD:
     (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 ZGESDD:
     (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 ZGESVDQ:
     (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 ZGESVJ:
     (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 ZGEJSV:
     (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 ZGESVDX( 'V', 'V', 'A' )/ZGESVDX( '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 ZGESVDX( '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 ZGESVDX( '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 unitary 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 sizes of matrices to use.  If it is zero,
              ZDRVBD does nothing.  It must be at least zero.

    MM

              MM is INTEGER array, dimension (NSIZES)
              An array containing the matrix 'heights' to be used.  For
              each j=1,...,NSIZES, if MM(j) is zero, then MM(j) and NN(j)
              will be ignored.  The MM(j) values must be at least zero.

    NN

              NN is INTEGER array, dimension (NSIZES)
              An array containing the matrix 'widths' to be used.  For
              each j=1,...,NSIZES, if NN(j) is zero, then MM(j) and NN(j)
              will be ignored.  The NN(j) values must be at least zero.

    NTYPES

              NTYPES is INTEGER
              The number of elements in DOTYPE.   If it is zero, ZDRVBD
              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 ISEED specifies 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.  The random number generator uses a linear
              congruential sequence limited to small integers, and so
              should produce machine independent random numbers. The
              values of ISEED are changed on exit, and can be used in the
              next call to ZDRVBD to continue the same random number
              sequence.

    THRESH

              THRESH is DOUBLE PRECISION
              A test will count as 'failed' if the 'error', computed as
              described above, exceeds THRESH.  Note that the error
              is scaled to be O(1), so THRESH should be a reasonably
              small multiple of 1, e.g., 10 or 100.  In particular,
              it should not depend on the precision (single vs. double)
              or the size of the matrix.  It must be at least zero.

    A

              A is COMPLEX*16 array, dimension (LDA,max(NN))
              Used to hold the matrix whose singular values are to be
              computed.  On exit, A contains the last matrix actually
              used.

    LDA

              LDA is INTEGER
              The leading dimension of A.  It must be at
              least 1 and at least max( MM ).

    U

              U is COMPLEX*16 array, dimension (LDU,max(MM))
              Used to hold the computed matrix of right singular vectors.
              On exit, U contains the last such vectors actually computed.

    LDU

              LDU is INTEGER
              The leading dimension of U.  It must be at
              least 1 and at least max( MM ).

    VT

              VT is COMPLEX*16 array, dimension (LDVT,max(NN))
              Used to hold the computed matrix of left singular vectors.
              On exit, VT contains the last such vectors actually computed.

    LDVT

              LDVT is INTEGER
              The leading dimension of VT.  It must be at
              least 1 and at least max( NN ).

    ASAV

              ASAV is COMPLEX*16 array, dimension (LDA,max(NN))
              Used to hold a different copy of the matrix whose singular
              values are to be computed.  On exit, A contains the last
              matrix actually used.

    USAV

              USAV is COMPLEX*16 array, dimension (LDU,max(MM))
              Used to hold a different copy of the computed matrix of
              right singular vectors. On exit, USAV contains the last such
              vectors actually computed.

    VTSAV

              VTSAV is COMPLEX*16 array, dimension (LDVT,max(NN))
              Used to hold a different copy of the computed matrix of
              left singular vectors. On exit, VTSAV contains the last such
              vectors actually computed.

    S

              S is DOUBLE PRECISION array, dimension (max(min(MM,NN)))
              Contains the computed singular values.

    SSAV

              SSAV is DOUBLE PRECISION array, dimension (max(min(MM,NN)))
              Contains another copy of the computed singular values.

    E

              E is DOUBLE PRECISION array, dimension (max(min(MM,NN)))
              Workspace for ZGESVD.

    WORK

              WORK is COMPLEX*16 array, dimension (LWORK)

    LWORK

              LWORK is INTEGER
              The number of entries in WORK.  This must be at least
              MAX(3*MIN(M,N)+MAX(M,N)**2,5*MIN(M,N),3*MAX(M,N)) for all
              pairs  (M,N)=(MM(j),NN(j))

    RWORK

              RWORK is DOUBLE PRECISION array,
                          dimension ( 5*max(max(MM,NN)) )

    IWORK

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

    NOUNIT

              NOUNIT 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  ZLATMS, or ZGESVD 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 397 of file zdrvbd.f.

Author

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