sgsvts3.f - Man Page

subroutine sgsvts3 (m, p, n, a, af, lda, b, bf, ldb, u, ldu, v, ldv, q, ldq, alpha, beta, r, ldr, iwork, work, lwork, rwork, result)
SGSVTS3

SGSVTS3

Purpose:

 SGSVTS3 tests SGGSVD3, which computes the GSVD of an M-by-N matrix A
 and a P-by-N matrix B:
              U'*A*Q = D1*R and V'*B*Q = D2*R.

Parameters

M

          M is INTEGER
          The number of rows of the matrix A.  M >= 0.

P

          P is INTEGER
          The number of rows of the matrix B.  P >= 0.

N

          N is INTEGER
          The number of columns of the matrices A and B.  N >= 0.

A

          A is REAL array, dimension (LDA,M)
          The M-by-N matrix A.

AF

          AF is REAL array, dimension (LDA,N)
          Details of the GSVD of A and B, as returned by SGGSVD3,
          see SGGSVD3 for further details.

LDA

          LDA is INTEGER
          The leading dimension of the arrays A and AF.
          LDA >= max( 1,M ).

B

          B is REAL array, dimension (LDB,P)
          On entry, the P-by-N matrix B.

BF

          BF is REAL array, dimension (LDB,N)
          Details of the GSVD of A and B, as returned by SGGSVD3,
          see SGGSVD3 for further details.

LDB

          LDB is INTEGER
          The leading dimension of the arrays B and BF.
          LDB >= max(1,P).

U

          U is REAL array, dimension(LDU,M)
          The M by M orthogonal matrix U.

LDU

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

V

          V is REAL array, dimension(LDV,M)
          The P by P orthogonal matrix V.

LDV

          LDV is INTEGER
          The leading dimension of the array V. LDV >= max(1,P).

Q

          Q is REAL array, dimension(LDQ,N)
          The N by N orthogonal matrix Q.

LDQ

          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= max(1,N).

ALPHA

          ALPHA is REAL array, dimension (N)

BETA

          BETA is REAL array, dimension (N)

          The generalized singular value pairs of A and B, the
          “diagonal” matrices D1 and D2 are constructed from
          ALPHA and BETA, see subroutine SGGSVD3 for details.

R

          R is REAL array, dimension(LDQ,N)
          The upper triangular matrix R.

LDR

          LDR is INTEGER
          The leading dimension of the array R. LDR >= max(1,N).

IWORK

          IWORK is INTEGER array, dimension (N)

WORK

          WORK is REAL array, dimension (LWORK)

LWORK

          LWORK is INTEGER
          The dimension of the array WORK,
          LWORK >= max(M,P,N)*max(M,P,N).

RWORK

          RWORK is REAL array, dimension (max(M,P,N))

RESULT

          RESULT is REAL array, dimension (6)
          The test ratios:
          RESULT(1) = norm( U'*A*Q - D1*R ) / ( MAX(M,N)*norm(A)*ULP)
          RESULT(2) = norm( V'*B*Q - D2*R ) / ( MAX(P,N)*norm(B)*ULP)
          RESULT(3) = norm( I - U'*U ) / ( M*ULP )
          RESULT(4) = norm( I - V'*V ) / ( P*ULP )
          RESULT(5) = norm( I - Q'*Q ) / ( N*ULP )
          RESULT(6) = 0        if ALPHA is in decreasing order;
                    = ULPINV   otherwise.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 207 of file sgsvts3.f.