dgsvts3.f3

!>
!> DGSVTS3 tests DGGSVD3, 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 DOUBLE PRECISION array, dimension (LDA,M)
!>          The M-by-N matrix A.
!> 

AF

!>          AF is DOUBLE PRECISION array, dimension (LDA,N)
!>          Details of the GSVD of A and B, as returned by DGGSVD3,
!>          see DGGSVD3 for further details.
!> 

LDA

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

B

!>          B is DOUBLE PRECISION array, dimension (LDB,P)
!>          On entry, the P-by-N matrix B.
!> 

BF

!>          BF is DOUBLE PRECISION array, dimension (LDB,N)
!>          Details of the GSVD of A and B, as returned by DGGSVD3,
!>          see DGGSVD3 for further details.
!> 

LDB

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

U

!>          U is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
!> 

BETA

!>          BETA is DOUBLE PRECISION 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 DGGSVD3 for details.
!> 

R

!>          R is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (max(M,P,N))
!> 

RESULT

!>          RESULT is DOUBLE PRECISION 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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