#include "blaswrap.h"
/* dgrqts.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"

/* Table of constant values */

static doublereal c_b9 = -1e10;
static doublereal c_b19 = 0.;
static doublereal c_b30 = -1.;
static doublereal c_b31 = 1.;

/* Subroutine */ int dgrqts_(integer *m, integer *p, integer *n, doublereal *
	a, doublereal *af, doublereal *q, doublereal *r__, integer *lda, 
	doublereal *taua, doublereal *b, doublereal *bf, doublereal *z__, 
	doublereal *t, doublereal *bwk, integer *ldb, doublereal *taub, 
	doublereal *work, integer *lwork, doublereal *rwork, doublereal *
	result)
{
    /* System generated locals */
    integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, bf_dim1, 
	    bf_offset, bwk_dim1, bwk_offset, q_dim1, q_offset, r_dim1, 
	    r_offset, t_dim1, t_offset, z_dim1, z_offset, i__1, i__2;
    doublereal d__1;

    /* Local variables */
    static doublereal ulp;
    static integer info;
    static doublereal unfl;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    static doublereal resid, anorm, bnorm;
    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 dggrqf_(integer *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, 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 dorgqr_(integer *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    integer *), 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   
    =======   

    DGRQTS tests DGGRQF, which computes the GRQ factorization of an   
    M-by-N matrix A and a P-by-N matrix B: A = R*Q and B = Z*T*Q.   

    Arguments   
    =========   

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

    P       (input) INTEGER   
            The number of rows of the matrix B.  P >= 0.   

    N       (input) INTEGER   
            The number of columns of the matrices A and B.  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 GRQ factorization of A and B, as returned   
            by DGGRQF, see SGGRQF 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, R and Q.   
            LDA >= max(M,N).   

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

    B       (input) DOUBLE PRECISION array, dimension (LDB,N)   
            On entry, the P-by-N matrix A.   

    BF      (output) DOUBLE PRECISION array, dimension (LDB,N)   
            Details of the GQR factorization of A and B, as returned   
            by DGGRQF, see SGGRQF for further details.   

    Z       (output) DOUBLE PRECISION array, dimension (LDB,P)   
            The P-by-P orthogonal matrix Z.   

    T       (workspace) DOUBLE PRECISION array, dimension (LDB,max(P,N))   

    BWK     (workspace) DOUBLE PRECISION array, dimension (LDB,N)   

    LDB     (input) INTEGER   
            The leading dimension of the arrays B, BF, Z and T.   
            LDB >= max(P,N).   

    TAUB    (output) DOUBLE PRECISION array, dimension (min(P,N))   
            The scalar factors of the elementary reflectors, as returned   
            by DGGRQF.   

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

    LWORK   (input) INTEGER   
            The dimension of the array WORK, LWORK >= max(M,P,N)**2.   

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

    RESULT  (output) DOUBLE PRECISION array, dimension (4)   
            The test ratios:   
              RESULT(1) = norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP)   
              RESULT(2) = norm( T*Q - Z'*B ) / (MAX(P,N)*norm(B)*ULP)   
              RESULT(3) = norm( I - Q'*Q ) / ( N*ULP )   
              RESULT(4) = norm( I - Z'*Z ) / ( P*ULP )   

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


       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;
    --taua;
    bwk_dim1 = *ldb;
    bwk_offset = 1 + bwk_dim1;
    bwk -= bwk_offset;
    t_dim1 = *ldb;
    t_offset = 1 + t_dim1;
    t -= t_offset;
    z_dim1 = *ldb;
    z_offset = 1 + z_dim1;
    z__ -= z_offset;
    bf_dim1 = *ldb;
    bf_offset = 1 + bf_dim1;
    bf -= bf_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --taub;
    --work;
    --rwork;
    --result;

    /* Function Body */
    ulp = dlamch_("Precision");
    unfl = dlamch_("Safe minimum");

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

    dlacpy_("Full", m, n, &a[a_offset], lda, &af[af_offset], lda);
    dlacpy_("Full", p, n, &b[b_offset], ldb, &bf[bf_offset], ldb);

/* Computing MAX */
    d__1 = dlange_("1", m, n, &a[a_offset], lda, &rwork[1]);
    anorm = max(d__1,unfl);
/* Computing MAX */
    d__1 = dlange_("1", p, n, &b[b_offset], ldb, &rwork[1]);
    bnorm = max(d__1,unfl);

/*     Factorize the matrices A and B in the arrays AF and BF. */

    dggrqf_(m, p, n, &af[af_offset], lda, &taua[1], &bf[bf_offset], ldb, &
	    taub[1], &work[1], lwork, &info);

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

    dlaset_("Full", n, n, &c_b9, &c_b9, &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);
	}
    }
    i__1 = min(*m,*n);
    dorgrq_(n, n, &i__1, &q[q_offset], lda, &taua[1], &work[1], lwork, &info);

/*     Generate the P-by-P matrix Z */

    dlaset_("Full", p, p, &c_b9, &c_b9, &z__[z_offset], ldb);
    if (*p > 1) {
	i__1 = *p - 1;
	dlacpy_("Lower", &i__1, n, &bf[bf_dim1 + 2], ldb, &z__[z_dim1 + 2], 
		ldb);
    }
    i__1 = min(*p,*n);
    dorgqr_(p, p, &i__1, &z__[z_offset], ldb, &taub[1], &work[1], lwork, &
	    info);

/*     Copy R */

    dlaset_("Full", m, n, &c_b19, &c_b19, &r__[r_offset], lda);
    if (*m <= *n) {
	dlacpy_("Upper", m, m, &af[(*n - *m + 1) * af_dim1 + 1], lda, &r__[(*
		n - *m + 1) * r_dim1 + 1], lda);
    } else {
	i__1 = *m - *n;
	dlacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset], lda);
	dlacpy_("Upper", n, n, &af[*m - *n + 1 + af_dim1], lda, &r__[*m - *n 
		+ 1 + r_dim1], lda);
    }

/*     Copy T */

    dlaset_("Full", p, n, &c_b19, &c_b19, &t[t_offset], ldb);
    dlacpy_("Upper", p, n, &bf[bf_offset], ldb, &t[t_offset], ldb);

/*     Compute R - A*Q' */

    dgemm_("No transpose", "Transpose", m, n, n, &c_b30, &a[a_offset], lda, &
	    q[q_offset], lda, &c_b31, &r__[r_offset], lda);

/*     Compute norm( R - A*Q' ) / ( MAX(M,N)*norm(A)*ULP ) . */

    resid = dlange_("1", m, n, &r__[r_offset], lda, &rwork[1]);
    if (anorm > 0.) {
/* Computing MAX */
	i__1 = max(1,*m);
	result[1] = resid / (doublereal) max(i__1,*n) / anorm / ulp;
    } else {
	result[1] = 0.;
    }

/*     Compute T*Q - Z'*B */

    dgemm_("Transpose", "No transpose", p, n, p, &c_b31, &z__[z_offset], ldb, 
	    &b[b_offset], ldb, &c_b19, &bwk[bwk_offset], ldb);
    dgemm_("No transpose", "No transpose", p, n, n, &c_b31, &t[t_offset], ldb, 
	     &q[q_offset], lda, &c_b30, &bwk[bwk_offset], ldb);

/*     Compute norm( T*Q - Z'*B ) / ( MAX(P,N)*norm(A)*ULP ) . */

    resid = dlange_("1", p, n, &bwk[bwk_offset], ldb, &rwork[1]);
    if (bnorm > 0.) {
/* Computing MAX */
	i__1 = max(1,*p);
	result[2] = resid / (doublereal) max(i__1,*m) / bnorm / ulp;
    } else {
	result[2] = 0.;
    }

/*     Compute I - Q*Q' */

    dlaset_("Full", n, n, &c_b19, &c_b31, &r__[r_offset], lda);
    dsyrk_("Upper", "No Transpose", n, n, &c_b30, &q[q_offset], lda, &c_b31, &
	    r__[r_offset], lda);

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

    resid = dlansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);
    result[3] = resid / (doublereal) max(1,*n) / ulp;

/*     Compute I - Z'*Z */

    dlaset_("Full", p, p, &c_b19, &c_b31, &t[t_offset], ldb);
    dsyrk_("Upper", "Transpose", p, p, &c_b30, &z__[z_offset], ldb, &c_b31, &
	    t[t_offset], ldb);

/*     Compute norm( I - Z'*Z ) / ( P*ULP ) . */

    resid = dlansy_("1", "Upper", p, &t[t_offset], ldb, &rwork[1]);
    result[4] = resid / (doublereal) max(1,*p) / ulp;

    return 0;

/*     End of DGRQTS */

} /* dgrqts_ */