TESTING/EIG/sgrqts.f(3)

NAME
TESTING/EIG/sgrqts.f

SYNOPSIS

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

Function/Subroutine Documentation

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

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.

Author

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