#include "blaswrap.h"
/* dqlt02.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_b4 = -1e10;
static doublereal c_b10 = 0.;
static doublereal c_b15 = -1.;
static doublereal c_b16 = 1.;

/* Subroutine */ int dqlt02_(integer *m, integer *n, integer *k, doublereal *
	a, doublereal *af, doublereal *q, doublereal *l, integer *lda, 
	doublereal *tau, doublereal *work, integer *lwork, doublereal *rwork, 
	doublereal *result)
{
    /* System generated locals */
    integer a_dim1, a_offset, af_dim1, af_offset, l_dim1, l_offset, q_dim1, 
	    q_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;
    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 *), dorgql_(integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, integer *);
    extern doublereal dlansy_(char *, char *, integer *, doublereal *, 
	    integer *, doublereal *);


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


    Purpose   
    =======   

    DQLT02 tests DORGQL, which generates an m-by-n matrix Q with   
    orthonornmal columns that is defined as the product of k elementary   
    reflectors.   

    Given the QL factorization of an m-by-n matrix A, DQLT02 generates   
    the orthogonal matrix Q defined by the factorization of the last k   
    columns of A; it compares L(m-n+1:m,n-k+1:n) with   
    Q(1:m,m-n+1:m)'*A(1:m,n-k+1:n), 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 DQLT01.   

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

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

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

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

    TAU     (input) DOUBLE PRECISION array, dimension (N)   
            The scalar factors of the elementary reflectors corresponding   
            to the QL 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( L - Q'*A ) / ( M * norm(A) * EPS )   
            RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )   

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


       Quick return if possible   

       Parameter adjustments */
    l_dim1 = *lda;
    l_offset = 1 + l_dim1;
    l -= l_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 */
    if (*m == 0 || *n == 0 || *k == 0) {
	result[1] = 0.;
	result[2] = 0.;
	return 0;
    }

    eps = dlamch_("Epsilon");

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

    dlaset_("Full", m, n, &c_b4, &c_b4, &q[q_offset], lda);
    if (*k < *m) {
	i__1 = *m - *k;
	dlacpy_("Full", &i__1, k, &af[(*n - *k + 1) * af_dim1 + 1], lda, &q[(*
		n - *k + 1) * q_dim1 + 1], lda);
    }
    if (*k > 1) {
	i__1 = *k - 1;
	i__2 = *k - 1;
	dlacpy_("Upper", &i__1, &i__2, &af[*m - *k + 1 + (*n - *k + 2) * 
		af_dim1], lda, &q[*m - *k + 1 + (*n - *k + 2) * q_dim1], lda);
    }

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

    s_copy(srnamc_1.srnamt, "DORGQL", (ftnlen)6, (ftnlen)6);
    dorgql_(m, n, k, &q[q_offset], lda, &tau[*n - *k + 1], &work[1], lwork, &
	    info);

/*     Copy L(m-n+1:m,n-k+1:n) */

    dlaset_("Full", n, k, &c_b10, &c_b10, &l[*m - *n + 1 + (*n - *k + 1) * 
	    l_dim1], lda);
    dlacpy_("Lower", k, k, &af[*m - *k + 1 + (*n - *k + 1) * af_dim1], lda, &
	    l[*m - *k + 1 + (*n - *k + 1) * l_dim1], lda);

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

    dgemm_("Transpose", "No transpose", n, k, m, &c_b15, &q[q_offset], lda, &
	    a[(*n - *k + 1) * a_dim1 + 1], lda, &c_b16, &l[*m - *n + 1 + (*n 
	    - *k + 1) * l_dim1], lda);

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

    anorm = dlange_("1", m, k, &a[(*n - *k + 1) * a_dim1 + 1], lda, &rwork[1]);
    resid = dlange_("1", n, k, &l[*m - *n + 1 + (*n - *k + 1) * l_dim1], 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_b10, &c_b16, &l[l_offset], lda);
    dsyrk_("Upper", "Transpose", n, m, &c_b15, &q[q_offset], lda, &c_b16, &l[
	    l_offset], lda);

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

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

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

    return 0;

/*     End of DQLT02 */

} /* dqlt02_ */