#include "blaswrap.h"
/* drqt01.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
	on Microsoft Windows system, link with libf2c.lib;
	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
	or, if you install libf2c.a in a standard place, with -lf2c -lm
	-- in that order, at the end of the command line, as in
		cc *.o -lf2c -lm
	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

		http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"

/* Common Block Declarations */

struct {
    char srnamt[6];
} srnamc_;

#define srnamc_1 srnamc_

/* Table of constant values */

static doublereal c_b6 = -1e10;
static doublereal c_b13 = 0.;
static doublereal c_b20 = -1.;
static doublereal c_b21 = 1.;

/* Subroutine */ int drqt01_(integer *m, integer *n, 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, i__2;

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

    /* Local variables */
    static doublereal eps;
    static integer info;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    static doublereal resid, anorm;
    static integer minmn;
    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 dgerqf_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *), 
	    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 dorgrq_(integer *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    integer *);


/*  -- LAPACK test routine (version 3.1) --   
       Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..   
       November 2006   


    Purpose   
    =======   

    DRQT01 tests DGERQF, which computes the RQ factorization of an m-by-n   
    matrix A, and partially tests DORGRQ which forms the n-by-n   
    orthogonal matrix Q.   

    DRQT01 compares R with A*Q', and checks that Q is orthogonal.   

    Arguments   
    =========   

    M       (input) INTEGER   
            The number of rows of the matrix A.  M >= 0.   

    N       (input) INTEGER   
            The number of columns of the matrix A.  N >= 0.   

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

    AF      (output) DOUBLE PRECISION array, dimension (LDA,N)   
            Details of the RQ factorization of A, as returned by DGERQF.   
            See DGERQF for further details.   

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

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

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

    TAU     (output) DOUBLE PRECISION array, dimension (min(M,N))   
            The scalar factors of the elementary reflectors, as returned   
            by DGERQF.   

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

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

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

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

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


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

    /* Function Body */
    minmn = min(*m,*n);
    eps = dlamch_("Epsilon");

/*     Copy the matrix A to the array AF. */

    dlacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);

/*     Factorize the matrix A in the array AF. */

    s_copy(srnamc_1.srnamt, "DGERQF", (ftnlen)6, (ftnlen)6);
    dgerqf_(m, n, &af[af_offset], lda, &tau[1], &work[1], lwork, &info);

/*     Copy details of Q */

    dlaset_("Full", n, n, &c_b6, &c_b6, &q[q_offset], lda);
    if (*m <= *n) {
	if (*m > 0 && *m < *n) {
	    i__1 = *n - *m;
	    dlacpy_("Full", m, &i__1, &af[af_offset], lda, &q[*n - *m + 1 + 
		    q_dim1], lda);
	}
	if (*m > 1) {
	    i__1 = *m - 1;
	    i__2 = *m - 1;
	    dlacpy_("Lower", &i__1, &i__2, &af[(*n - *m + 1) * af_dim1 + 2], 
		    lda, &q[*n - *m + 2 + (*n - *m + 1) * q_dim1], lda);
	}
    } else {
	if (*n > 1) {
	    i__1 = *n - 1;
	    i__2 = *n - 1;
	    dlacpy_("Lower", &i__1, &i__2, &af[*m - *n + 2 + af_dim1], lda, &
		    q[q_dim1 + 2], lda);
	}
    }

/*     Generate the n-by-n matrix Q */

    s_copy(srnamc_1.srnamt, "DORGRQ", (ftnlen)6, (ftnlen)6);
    dorgrq_(n, n, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);

/*     Copy R */

    dlaset_("Full", m, n, &c_b13, &c_b13, &r__[r_offset], lda);
    if (*m <= *n) {
	if (*m > 0) {
	    dlacpy_("Upper", m, m, &af[(*n - *m + 1) * af_dim1 + 1], lda, &
		    r__[(*n - *m + 1) * r_dim1 + 1], lda);
	}
    } else {
	if (*m > *n && *n > 0) {
	    i__1 = *m - *n;
	    dlacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset], 
		    lda);
	}
	if (*n > 0) {
	    dlacpy_("Upper", n, n, &af[*m - *n + 1 + af_dim1], lda, &r__[*m - 
		    *n + 1 + r_dim1], lda);
	}
    }

/*     Compute R - A*Q' */

    dgemm_("No transpose", "Transpose", m, n, n, &c_b20, &a[a_offset], lda, &
	    q[q_offset], lda, &c_b21, &r__[r_offset], lda);

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

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

/*     Compute I - Q*Q' */

    dlaset_("Full", n, n, &c_b13, &c_b21, &r__[r_offset], lda);
    dsyrk_("Upper", "No transpose", n, n, &c_b20, &q[q_offset], lda, &c_b21, &
	    r__[r_offset], lda);

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

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

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

    return 0;

/*     End of DRQT01 */

} /* drqt01_ */