TESTING/EIG/sgsvts3.f(3)

NAME
TESTING/EIG/sgsvts3.f

SYNOPSIS

  Functions/Subroutines
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

Function/Subroutine Documentation

  subroutine sgsvts3 (integer m, integer p, integer n, real, dimension( lda, * ) a, real, dimension( lda, * ) af, integer lda, real, dimension( ldb, * ) b, real, dimension( ldb, * ) bf, integer ldb, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldq, * ) q, integer ldq, real, dimension( * ) alpha, real, dimension( * ) beta, real, dimension( ldr, * ) r, integer ldr, integer, dimension( * ) iwork, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 6 ) result)

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.

Author

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