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.

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.

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