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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