#include "blaswrap.h"
/*  -- translated by f2c (version 19990503).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include "f2c.h"

/* Common Block Declarations */

struct {
    char srnamt[6];
} srnamc_;

#define srnamc_1 srnamc_

/* Table of constant values */

static doublereal c_b4 = -1e10;
static doublereal c_b9 = 0.;
static doublereal c_b14 = -1.;
static doublereal c_b15 = 1.;

/* Subroutine */ int dqrt02_(integer *m, integer *n, integer *k, doublereal *
	a, doublereal *af, doublereal *q, doublereal *r__, integer *lda, 
	doublereal *tau, doublereal *work, integer *lwork, doublereal *rwork, 
	doublereal *result)
{
    /* System generated locals */
    integer a_dim1, a_offset, af_dim1, af_offset, q_dim1, q_offset, r_dim1, 
	    r_offset, i__1;

    /* Builtin functions   
       Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);

    /* Local variables */
    static integer info;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    static doublereal resid, anorm;
    extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, doublereal *,
	     integer *);
    extern doublereal dlamch_(char *), dlange_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *);
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    dlaset_(char *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *);
    extern doublereal dlansy_(char *, char *, integer *, doublereal *, 
	    integer *, doublereal *);
    extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    integer *);
    static doublereal eps;


#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]
#define af_ref(a_1,a_2) af[(a_2)*af_dim1 + a_1]


/*  -- LAPACK test routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    DQRT02 tests DORGQR, which generates an m-by-n matrix Q with   
    orthonornmal columns that is defined as the product of k elementary   
    reflectors.   

    Given the QR factorization of an m-by-n matrix A, DQRT02 generates   
    the orthogonal matrix Q defined by the factorization of the first k   
    columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),   
    and checks that the columns of Q are orthonormal.   

    Arguments   
    =========   

    M       (input) INTEGER   
            The number of rows of the matrix Q to be generated.  M >= 0.   

    N       (input) INTEGER   
            The number of columns of the matrix Q to be generated.   
            M >= N >= 0.   

    K       (input) INTEGER   
            The number of elementary reflectors whose product defines the   
            matrix Q. N >= K >= 0.   

    A       (input) DOUBLE PRECISION array, dimension (LDA,N)   
            The m-by-n matrix A which was factorized by DQRT01.   

    AF      (input) DOUBLE PRECISION array, dimension (LDA,N)   
            Details of the QR factorization of A, as returned by DGEQRF.   
            See DGEQRF for further details.   

    Q       (workspace) DOUBLE PRECISION array, dimension (LDA,N)   

    R       (workspace) DOUBLE PRECISION array, dimension (LDA,N)   

    LDA     (input) INTEGER   
            The leading dimension of the arrays A, AF, Q and R. LDA >= M.   

    TAU     (input) DOUBLE PRECISION array, dimension (N)   
            The scalar factors of the elementary reflectors corresponding   
            to the QR factorization in AF.   

    WORK    (workspace) DOUBLE PRECISION array, dimension (LWORK)   

    LWORK   (input) INTEGER   
            The dimension of the array WORK.   

    RWORK   (workspace) DOUBLE PRECISION array, dimension (M)   

    RESULT  (output) DOUBLE PRECISION array, dimension (2)   
            The test ratios:   
            RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )   
            RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )   

    =====================================================================   


       Parameter adjustments */
    r_dim1 = *lda;
    r_offset = 1 + r_dim1 * 1;
    r__ -= r_offset;
    q_dim1 = *lda;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    af_dim1 = *lda;
    af_offset = 1 + af_dim1 * 1;
    af -= af_offset;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    --tau;
    --work;
    --rwork;
    --result;

    /* Function Body */
    eps = dlamch_("Epsilon");

/*     Copy the first k columns of the factorization to the array Q */

    dlaset_("Full", m, n, &c_b4, &c_b4, &q[q_offset], lda);
    i__1 = *m - 1;
    dlacpy_("Lower", &i__1, k, &af_ref(2, 1), lda, &q_ref(2, 1), lda);

/*     Generate the first n columns of the matrix Q */

    s_copy(srnamc_1.srnamt, "DORGQR", (ftnlen)6, (ftnlen)6);
    dorgqr_(m, n, k, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);

/*     Copy R(1:n,1:k) */

    dlaset_("Full", n, k, &c_b9, &c_b9, &r__[r_offset], lda);
    dlacpy_("Upper", n, k, &af[af_offset], lda, &r__[r_offset], lda);

/*     Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k) */

    dgemm_("Transpose", "No transpose", n, k, m, &c_b14, &q[q_offset], lda, &
	    a[a_offset], lda, &c_b15, &r__[r_offset], lda);

/*     Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) . */

    anorm = dlange_("1", m, k, &a[a_offset], lda, &rwork[1]);
    resid = dlange_("1", n, k, &r__[r_offset], lda, &rwork[1]);
    if (anorm > 0.) {
	result[1] = resid / (doublereal) max(1,*m) / anorm / eps;
    } else {
	result[1] = 0.;
    }

/*     Compute I - Q'*Q */

    dlaset_("Full", n, n, &c_b9, &c_b15, &r__[r_offset], lda);
    dsyrk_("Upper", "Transpose", n, m, &c_b14, &q[q_offset], lda, &c_b15, &
	    r__[r_offset], lda);

/*     Compute norm( I - Q'*Q ) / ( M * EPS ) . */

    resid = dlansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);

    result[2] = resid / (doublereal) max(1,*m) / eps;

    return 0;

/*     End of DQRT02 */

} /* dqrt02_ */

#undef af_ref
#undef q_ref



.