cgrqts.f - Man Page

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

CGRQTS

Purpose:

 CGRQTS tests CGGRQF, 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 COMPLEX array, dimension (LDA,N)
          The M-by-N matrix A.

AF

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

Q

          Q is COMPLEX array, dimension (LDA,N)
          The N-by-N unitary matrix Q.

R

          R is COMPLEX 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 COMPLEX array, dimension (min(M,N))
          The scalar factors of the elementary reflectors, as returned
          by SGGQRC.

B

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

BF

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

Z

          Z is REAL array, dimension (LDB,P)
          The P-by-P unitary matrix Z.

T

          T is COMPLEX array, dimension (LDB,max(P,N))

BWK

          BWK is COMPLEX 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 COMPLEX array, dimension (min(P,N))
          The scalar factors of the elementary reflectors, as returned
          by SGGRQF.

WORK

          WORK is COMPLEX 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 174 of file cgrqts.f.