#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 real c_b4 = -1e10f;
static real c_b10 = 0.f;
static real c_b15 = -1.f;
static real c_b16 = 1.f;

/* Subroutine */ int sqlt02_(integer *m, integer *n, integer *k, real *a, 
	real *af, real *q, real *l, integer *lda, real *tau, real *work, 
	integer *lwork, real *rwork, real *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 integer info;
    static real resid;
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    static real anorm;
    extern /* Subroutine */ int ssyrk_(char *, char *, integer *, integer *, 
	    real *, real *, integer *, real *, real *, integer *);
    extern doublereal slamch_(char *), slange_(char *, integer *, 
	    integer *, real *, integer *, real *);
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *), slaset_(char *, integer *, 
	    integer *, real *, real *, real *, integer *), sorgql_(
	    integer *, integer *, integer *, real *, integer *, real *, real *
	    , integer *, integer *);
    extern doublereal slansy_(char *, char *, integer *, real *, integer *, 
	    real *);
    static real eps;


#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define l_ref(a_1,a_2) l[(a_2)*l_dim1 + a_1]
#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   
    =======   

    SQLT02 tests SORGQL, 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, SQLT02 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) REAL array, dimension (LDA,N)   
            The m-by-n matrix A which was factorized by SQLT01.   

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

    Q       (workspace) REAL array, dimension (LDA,N)   

    L       (workspace) REAL array, dimension (LDA,N)   

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

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

    WORK    (workspace) REAL array, dimension (LWORK)   

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

    RWORK   (workspace) REAL array, dimension (M)   

    RESULT  (output) REAL 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 * 1;
    l -= l_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 */
    if (*m == 0 || *n == 0 || *k == 0) {
	result[1] = 0.f;
	result[2] = 0.f;
	return 0;
    }

    eps = slamch_("Epsilon");

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

    slaset_("Full", m, n, &c_b4, &c_b4, &q[q_offset], lda);
    if (*k < *m) {
	i__1 = *m - *k;
	slacpy_("Full", &i__1, k, &af_ref(1, *n - *k + 1), lda, &q_ref(1, *n 
		- *k + 1), lda);
    }
    if (*k > 1) {
	i__1 = *k - 1;
	i__2 = *k - 1;
	slacpy_("Upper", &i__1, &i__2, &af_ref(*m - *k + 1, *n - *k + 2), lda,
		 &q_ref(*m - *k + 1, *n - *k + 2), lda);
    }

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

    s_copy(srnamc_1.srnamt, "SORGQL", (ftnlen)6, (ftnlen)6);
    sorgql_(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) */

    slaset_("Full", n, k, &c_b10, &c_b10, &l_ref(*m - *n + 1, *n - *k + 1), 
	    lda);
    slacpy_("Lower", k, k, &af_ref(*m - *k + 1, *n - *k + 1), lda, &l_ref(*m 
	    - *k + 1, *n - *k + 1), 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) */

    sgemm_("Transpose", "No transpose", n, k, m, &c_b15, &q[q_offset], lda, &
	    a_ref(1, *n - *k + 1), lda, &c_b16, &l_ref(*m - *n + 1, *n - *k + 
	    1), lda);

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

    anorm = slange_("1", m, k, &a_ref(1, *n - *k + 1), lda, &rwork[1]);
    resid = slange_("1", n, k, &l_ref(*m - *n + 1, *n - *k + 1), lda, &rwork[
	    1]);
    if (anorm > 0.f) {
	result[1] = resid / (real) max(1,*m) / anorm / eps;
    } else {
	result[1] = 0.f;
    }

/*     Compute I - Q'*Q */

    slaset_("Full", n, n, &c_b10, &c_b16, &l[l_offset], lda);
    ssyrk_("Upper", "Transpose", n, m, &c_b15, &q[q_offset], lda, &c_b16, &l[
	    l_offset], lda);

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

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

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

    return 0;

/*     End of SQLT02 */

} /* sqlt02_ */

#undef af_ref
#undef q_ref
#undef l_ref
#undef a_ref


