TESTING/EIG/dgrqts.f(3)

NAME
TESTING/EIG/dgrqts.f

SYNOPSIS

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

Function/Subroutine Documentation

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

DGRQTS

Purpose:

     DGRQTS tests DGGRQF, 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 DOUBLE PRECISION array, dimension (LDA,N)
              The M-by-N matrix A.

    AF

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

    Q

              Q is DOUBLE PRECISION array, dimension (LDA,N)
              The N-by-N orthogonal matrix Q.

    R

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

    B

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

    BF

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

    Z

              Z is DOUBLE PRECISION array, dimension (LDB,P)
              The P-by-P orthogonal matrix Z.

    T

              T is DOUBLE PRECISION array, dimension (LDB,max(P,N))

    BWK

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

    WORK

              WORK is DOUBLE PRECISION array, dimension (LWORK)

    LWORK

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

    RWORK

              RWORK is DOUBLE PRECISION array, dimension (M)

    RESULT

              RESULT is DOUBLE PRECISION 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 dgrqts.f.

Author

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