TESTING/EIG/cgrqts.f(3)

NAME
TESTING/EIG/cgrqts.f

SYNOPSIS

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

Function/Subroutine Documentation

  subroutine cgrqts (integer m, integer p, integer n, complex, dimension( lda, * ) a, complex, dimension( lda, * ) af, complex, dimension( lda, * ) q, complex, dimension( lda, * ) r, integer lda, complex, dimension( * ) taua, complex, dimension( ldb, * ) b, complex, dimension( ldb, * ) bf, complex, dimension( ldb, * ) z, complex, dimension( ldb, * ) t, complex, dimension( ldb, * ) bwk, integer ldb, complex, dimension( * ) taub, complex, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( 4 ) result)

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.

Author

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