cdrvbd.f - Man Page

subroutine cdrvbd (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)
CDRVBD

CDRVBD

Purpose:

 CDRVBD checks the singular value decomposition (SVD) driver CGESVD,
 CGESDD, CGESVJ, CGEJSV, CGESVDX, and CGESVDQ.

 CGESVD and CGESDD 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 CDRVBD 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 CGESVD:

 (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 CGESDD:

 (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 CGESVDQ:

 (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 CGESVJ:

 (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 CGEJSV:

 (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 CGESVDX( 'V', 'V', 'A' )/CGESVDX( '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 CGESVDX( '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 CGESVDX( '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,
          CDRVBD 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, CDRVBD
          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 CDRVBD to continue the same random number
          sequence.

THRESH

          THRESH is REAL
          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 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 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 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 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 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 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 REAL array, dimension (max(min(MM,NN)))
          Contains the computed singular values.

SSAV

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

E

          E is REAL array, dimension (max(min(MM,NN)))
          Workspace for CGESVD.

WORK

          WORK is COMPLEX 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 REAL 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) ).
          -29: LWORK too small.
          If  CLATMS, or CGESVD 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 cdrvbd.f.