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  (M's and N's)
    !> and a number of matrix  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  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  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  are specified by a logical array
    !> DOTYPE( 1:NTYPES ); if DOTYPE(j) is .TRUE., then matrix type
    !> 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  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  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  if the , 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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