cgsvts3.f - Man Page

subroutine cgsvts3 (m, p, n, a, af, lda, b, bf, ldb, u, ldu, v, ldv, q, ldq, alpha, beta, r, ldr, iwork, work, lwork, rwork, result)
CGSVTS3

CGSVTS3

Purpose:

 CGSVTS3 tests CGGSVD3, 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 COMPLEX array, dimension (LDA,M)
          The M-by-N matrix A.

AF

          AF is COMPLEX array, dimension (LDA,N)
          Details of the GSVD of A and B, as returned by CGGSVD3,
          see CGGSVD3 for further details.

LDA

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

B

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

BF

          BF is COMPLEX array, dimension (LDB,N)
          Details of the GSVD of A and B, as returned by CGGSVD3,
          see CGGSVD3 for further details.

LDB

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

U

          U is COMPLEX array, dimension(LDU,M)
          The M by M unitary matrix U.

LDU

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

V

          V is COMPLEX array, dimension(LDV,M)
          The P by P unitary matrix V.

LDV

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

Q

          Q is COMPLEX array, dimension(LDQ,N)
          The N by N unitary 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 CGGSVD3 for details.

R

          R is COMPLEX 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 COMPLEX 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 206 of file cgsvts3.f.