sgrqts.f - Man Page

subroutine sgrqts (m, p, n, a, af, q, r, lda, taua, b, bf, z, t, bwk, ldb, taub, work, lwork, rwork, result)
SGRQTS

SGRQTS

Purpose:

 SGRQTS tests SGGRQF, which computes the GRQ factorization of an
 M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.

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,N)
          The M-by-N matrix A.

AF

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

Q

          Q is REAL array, dimension (LDA,N)
          The N-by-N 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 SGGQRC.

B

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

BF

          BF is REAL array, dimension (LDB,N)
          Details of the GQR factorization of A and B, as returned
          by SGGRQF, see SGGRQF 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(M,P,N)**2.

RWORK

          RWORK is REAL array, dimension (M)

RESULT

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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 175 of file sgrqts.f.