#include "blaswrap.h"
/* zgrqts.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 doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static doublecomplex c_b3 = {-1e10,0.};
static doublereal c_b34 = -1.;
static doublereal c_b35 = 1.;

/* Subroutine */ int zgrqts_(integer *m, integer *p, integer *n, 
	doublecomplex *a, doublecomplex *af, doublecomplex *q, doublecomplex *
	r__, integer *lda, doublecomplex *taua, doublecomplex *b, 
	doublecomplex *bf, doublecomplex *z__, doublecomplex *t, 
	doublecomplex *bwk, integer *ldb, doublecomplex *taub, doublecomplex *
	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;
    doublecomplex z__1;

    /* Local variables */
    static doublereal ulp;
    static integer info;
    static doublereal unfl, resid, anorm, bnorm;
    extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *), zherk_(char *, char *, integer *, 
	    integer *, doublereal *, doublecomplex *, integer *, doublereal *, 
	     doublecomplex *, integer *);
    extern doublereal dlamch_(char *), zlange_(char *, integer *, 
	    integer *, doublecomplex *, integer *, doublereal *), 
	    zlanhe_(char *, char *, integer *, doublecomplex *, integer *, 
	    doublereal *);
    extern /* Subroutine */ int zggrqf_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, doublecomplex *, doublecomplex *, integer *, integer *)
	    , zlacpy_(char *, integer *, integer *, doublecomplex *, integer *
	    , doublecomplex *, integer *), zlaset_(char *, integer *, 
	    integer *, doublecomplex *, doublecomplex *, doublecomplex *, 
	    integer *), zungqr_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *), zungrq_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *);


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


    Purpose   
    =======   

    ZGRQTS tests ZGGRQF, 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) COMPLEX*16 array, dimension (LDA,N)   
            The M-by-N matrix A.   

    AF      (output) COMPLEX*16 array, dimension (LDA,N)   
            Details of the GRQ factorization of A and B, as returned   
            by ZGGRQF, see CGGRQF for further details.   

    Q       (output) COMPLEX*16 array, dimension (LDA,N)   
            The N-by-N unitary matrix Q.   

    R       (workspace) COMPLEX*16 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) COMPLEX*16 array, dimension (min(M,N))   
            The scalar factors of the elementary reflectors, as returned   
            by DGGQRC.   

    B       (input) COMPLEX*16 array, dimension (LDB,N)   
            On entry, the P-by-N matrix A.   

    BF      (output) COMPLEX*16 array, dimension (LDB,N)   
            Details of the GQR factorization of A and B, as returned   
            by ZGGRQF, see CGGRQF for further details.   

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

    T       (workspace) COMPLEX*16 array, dimension (LDB,max(P,N))   

    BWK     (workspace) COMPLEX*16 array, dimension (LDB,N)   

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

    TAUB    (output) COMPLEX*16 array, dimension (min(P,N))   
            The scalar factors of the elementary reflectors, as returned   
            by DGGRQF.   

    WORK    (workspace) COMPLEX*16 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. */

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

/* Computing MAX */
    d__1 = zlange_("1", m, n, &a[a_offset], lda, &rwork[1]);
    anorm = max(d__1,unfl);
/* Computing MAX */
    d__1 = zlange_("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. */

    zggrqf_(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 */

    zlaset_("Full", n, n, &c_b3, &c_b3, &q[q_offset], lda);
    if (*m <= *n) {
	if (*m > 0 && *m < *n) {
	    i__1 = *n - *m;
	    zlacpy_("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;
	    zlacpy_("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;
	    zlacpy_("Lower", &i__1, &i__2, &af[*m - *n + 2 + af_dim1], lda, &
		    q[q_dim1 + 2], lda);
	}
    }
    i__1 = min(*m,*n);
    zungrq_(n, n, &i__1, &q[q_offset], lda, &taua[1], &work[1], lwork, &info);

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

    zlaset_("Full", p, p, &c_b3, &c_b3, &z__[z_offset], ldb);
    if (*p > 1) {
	i__1 = *p - 1;
	zlacpy_("Lower", &i__1, n, &bf[bf_dim1 + 2], ldb, &z__[z_dim1 + 2], 
		ldb);
    }
    i__1 = min(*p,*n);
    zungqr_(p, p, &i__1, &z__[z_offset], ldb, &taub[1], &work[1], lwork, &
	    info);

/*     Copy R */

    zlaset_("Full", m, n, &c_b1, &c_b1, &r__[r_offset], lda);
    if (*m <= *n) {
	zlacpy_("Upper", m, m, &af[(*n - *m + 1) * af_dim1 + 1], lda, &r__[(*
		n - *m + 1) * r_dim1 + 1], lda);
    } else {
	i__1 = *m - *n;
	zlacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset], lda);
	zlacpy_("Upper", n, n, &af[*m - *n + 1 + af_dim1], lda, &r__[*m - *n 
		+ 1 + r_dim1], lda);
    }

/*     Copy T */

    zlaset_("Full", p, n, &c_b1, &c_b1, &t[t_offset], ldb);
    zlacpy_("Upper", p, n, &bf[bf_offset], ldb, &t[t_offset], ldb);

/*     Compute R - A*Q' */

    z__1.r = -1., z__1.i = -0.;
    zgemm_("No transpose", "Conjugate transpose", m, n, n, &z__1, &a[a_offset]
, lda, &q[q_offset], lda, &c_b2, &r__[r_offset], lda);

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

    resid = zlange_("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 */

    zgemm_("Conjugate transpose", "No transpose", p, n, p, &c_b2, &z__[
	    z_offset], ldb, &b[b_offset], ldb, &c_b1, &bwk[bwk_offset], ldb);
    z__1.r = -1., z__1.i = -0.;
    zgemm_("No transpose", "No transpose", p, n, n, &c_b2, &t[t_offset], ldb, 
	    &q[q_offset], lda, &z__1, &bwk[bwk_offset], ldb);

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

    resid = zlange_("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' */

    zlaset_("Full", n, n, &c_b1, &c_b2, &r__[r_offset], lda);
    zherk_("Upper", "No Transpose", n, n, &c_b34, &q[q_offset], lda, &c_b35, &
	    r__[r_offset], lda);

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

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

/*     Compute I - Z'*Z */

    zlaset_("Full", p, p, &c_b1, &c_b2, &t[t_offset], ldb);
    zherk_("Upper", "Conjugate transpose", p, p, &c_b34, &z__[z_offset], ldb, 
	    &c_b35, &t[t_offset], ldb);

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

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

    return 0;

/*     End of ZGRQTS */

} /* zgrqts_ */