sgqrts.f3

!>
!> SGQRTS tests SGGQRF, which computes the GQR factorization of an
!> N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.
!> 

N

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

M

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

P

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

A

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

AF

!>          AF is REAL array, dimension (LDA,N)
!>          Details of the GQR factorization of A and B, as returned
!>          by SGGQRF, see SGGQRF for further details.
!> 

Q

!>          Q is REAL array, dimension (LDA,N)
!>          The M-by-M orthogonal matrix Q.
!> 

R

!>          R is REAL array, dimension (LDA,MAX(M,N))
!> 

LDA

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

TAUA

!>          TAUA is REAL array, dimension (min(M,N))
!>          The scalar factors of the elementary reflectors, as returned
!>          by SGGQRF.
!> 

B

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

BF

!>          BF is REAL array, dimension (LDB,N)
!>          Details of the GQR factorization of A and B, as returned
!>          by SGGQRF, see SGGQRF for further details.
!> 

Z

!>          Z is REAL array, dimension (LDB,P)
!>          The P-by-P orthogonal matrix Z.
!> 

T

!>          T is REAL array, dimension (LDB,max(P,N))
!> 

BWK

!>          BWK is REAL array, dimension (LDB,N)
!> 

LDB

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

TAUB

!>          TAUB is REAL array, dimension (min(P,N))
!>          The scalar factors of the elementary reflectors, as returned
!>          by SGGRQF.
!> 

WORK

!>          WORK is REAL array, dimension (LWORK)
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK, LWORK >= max(N,M,P)**2.
!> 

RWORK

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

RESULT

!>          RESULT is REAL array, dimension (4)
!>          The test ratios:
!>            RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP)
!>            RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP)
!>            RESULT(3) = norm( I - Q'*Q ) / ( M*ULP )
!>            RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )
!> 

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