#include "blaswrap.h"
/* sqrt01.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 real c_b6 = -1e10f;
static real c_b11 = 0.f;
static real c_b16 = -1.f;
static real c_b17 = 1.f;

/* Subroutine */ int sqrt01_(integer *m, integer *n, real *a, real *af, real *
	q, real *r__, integer *lda, real *tau, real *work, integer *lwork, 
	real *rwork, real *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 real eps;
    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;
    static integer minmn;
    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 sgeqrf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *), slacpy_(char *, integer 
	    *, integer *, real *, integer *, real *, integer *), 
	    slaset_(char *, integer *, integer *, real *, real *, real *, 
	    integer *);
    extern doublereal slansy_(char *, char *, integer *, real *, integer *, 
	    real *);
    extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *);


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


    Purpose   
    =======   

    SQRT01 tests SGEQRF, which computes the QR factorization of an m-by-n   
    matrix A, and partially tests SORGQR which forms the m-by-m   
    orthogonal matrix Q.   

    SQRT01 compares R with Q'*A, 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) REAL array, dimension (LDA,N)   
            The m-by-n matrix A.   

    AF      (output) REAL array, dimension (LDA,N)   
            Details of the QR factorization of A, as returned by SGEQRF.   
            See SGEQRF for further details.   

    Q       (output) REAL array, dimension (LDA,M)   
            The m-by-m orthogonal matrix Q.   

    R       (workspace) REAL array, dimension (LDA,max(M,N))   

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

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

    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( 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;
    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 = slamch_("Epsilon");

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

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

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

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

/*     Copy details of Q */

    slaset_("Full", m, m, &c_b6, &c_b6, &q[q_offset], lda);
    i__1 = *m - 1;
    slacpy_("Lower", &i__1, n, &af[af_dim1 + 2], lda, &q[q_dim1 + 2], lda);

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

    s_copy(srnamc_1.srnamt, "SORGQR", (ftnlen)6, (ftnlen)6);
    sorgqr_(m, m, &minmn, &q[q_offset], lda, &tau[1], &work[1], lwork, &info);

/*     Copy R */

    slaset_("Full", m, n, &c_b11, &c_b11, &r__[r_offset], lda);
    slacpy_("Upper", m, n, &af[af_offset], lda, &r__[r_offset], lda);

/*     Compute R - Q'*A */

    sgemm_("Transpose", "No transpose", m, n, m, &c_b16, &q[q_offset], lda, &
	    a[a_offset], lda, &c_b17, &r__[r_offset], lda);

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

    anorm = slange_("1", m, n, &a[a_offset], lda, &rwork[1]);
    resid = slange_("1", m, n, &r__[r_offset], 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", m, m, &c_b11, &c_b17, &r__[r_offset], lda);
    ssyrk_("Upper", "Transpose", m, m, &c_b16, &q[q_offset], lda, &c_b17, &
	    r__[r_offset], lda);

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

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

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

    return 0;

/*     End of SQRT01 */

} /* sqrt01_ */