TESTING/EIG/sgqrts.f(3)

NAME
TESTING/EIG/sgqrts.f

SYNOPSIS

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

Function/Subroutine Documentation

  subroutine sgqrts (integer n, integer m, integer p, 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)

SGQRTS

Purpose:

     SGQRTS tests SGGQRF, which computes the GQR factorization of an
     N-by-M matrix A and a N-by-P matrix B: A = Q*R and B = Q*T*Z.

Parameters
    N

              N is INTEGER
              The number of rows of the matrices A and B.  N >= 0.

    M

              M is INTEGER
              The number of columns of the matrix A.  M >= 0.

    P

              P is INTEGER
              The number of columns of the matrix B.  P >= 0.

    A

              A is REAL array, dimension (LDA,M)
              The N-by-M matrix A.

    AF

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

    Q

              Q is REAL array, dimension (LDA,N)
              The M-by-M 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 SGGQRF.

    B

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

    BF

              BF is REAL array, dimension (LDB,N)
              Details of the GQR factorization of A and B, as returned
              by SGGQRF, see SGGQRF 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(N,M,P)**2.

    RWORK

              RWORK is REAL array, dimension (max(N,M,P))

    RESULT

              RESULT is REAL array, dimension (4)
              The test ratios:
                RESULT(1) = norm( R - Q'*A ) / ( MAX(M,N)*norm(A)*ULP)
                RESULT(2) = norm( T*Z - Q'*B ) / (MAX(P,N)*norm(B)*ULP)
                RESULT(3) = norm( I - Q'*Q ) / ( M*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 sgqrts.f.

Author

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