#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"

/* Table of constant values */

static real c_b9 = -1e10f;
static real c_b19 = 0.f;
static real c_b30 = -1.f;
static real c_b31 = 1.f;

/* Subroutine */ int sgrqts_(integer *m, integer *p, integer *n, real *a, 
	real *af, real *q, real *r__, integer *lda, real *taua, real *b, real 
	*bf, real *z__, real *t, real *bwk, integer *ldb, real *taub, real *
	work, integer *lwork, real *rwork, real *result)
{
    /* System generated locals */
    integer a_dim1, a_offset, af_dim1, af_offset, r_dim1, r_offset, q_dim1, 
	    q_offset, b_dim1, b_offset, bf_dim1, bf_offset, t_dim1, t_offset, 
	    z_dim1, z_offset, bwk_dim1, bwk_offset, i__1, i__2;
    real r__1;

    /* Local variables */
    static integer info;
    static real unfl, resid;
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *);
    static real anorm, bnorm;
    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 sggrqf_(integer *, integer *, integer *, real 
	    *, integer *, real *, 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 *), sorgrq_(
	    integer *, integer *, integer *, real *, integer *, real *, real *
	    , integer *, integer *);
    static real ulp;


#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]
#define r___ref(a_1,a_2) r__[(a_2)*r_dim1 + a_1]
#define z___ref(a_1,a_2) z__[(a_2)*z_dim1 + a_1]
#define af_ref(a_1,a_2) af[(a_2)*af_dim1 + a_1]
#define bf_ref(a_1,a_2) bf[(a_2)*bf_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   
    =======   

    SGRQTS tests SGGRQF, 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) REAL array, dimension (LDA,N)   
            The M-by-N matrix A.   

    AF      (output) REAL array, dimension (LDA,N)   
            Details of the GRQ factorization of A and B, as returned   
            by SGGRQF, see SGGRQF for further details.   

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

    R       (workspace) REAL 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) REAL array, dimension (min(M,N))   
            The scalar factors of the elementary reflectors, as returned   
            by SGGQRC.   

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

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

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

    T       (workspace) REAL array, dimension (LDB,max(P,N))   

    BWK     (workspace) REAL array, dimension (LDB,N)   

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

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

    WORK    (workspace) REAL array, dimension (LWORK)   

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

    RWORK   (workspace) REAL array, dimension (M)   

    RESULT  (output) REAL 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 * 1;
    r__ -= r_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;
    --taua;
    bwk_dim1 = *ldb;
    bwk_offset = 1 + bwk_dim1 * 1;
    bwk -= bwk_offset;
    t_dim1 = *ldb;
    t_offset = 1 + t_dim1 * 1;
    t -= t_offset;
    z_dim1 = *ldb;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    bf_dim1 = *ldb;
    bf_offset = 1 + bf_dim1 * 1;
    bf -= bf_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --taub;
    --work;
    --rwork;
    --result;

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

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

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

/* Computing MAX */
    r__1 = slange_("1", m, n, &a[a_offset], lda, &rwork[1]);
    anorm = dmax(r__1,unfl);
/* Computing MAX */
    r__1 = slange_("1", p, n, &b[b_offset], ldb, &rwork[1]);
    bnorm = dmax(r__1,unfl);

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

    sggrqf_(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 */

    slaset_("Full", n, n, &c_b9, &c_b9, &q[q_offset], lda);
    if (*m <= *n) {
	if (*m > 0 && *m < *n) {
	    i__1 = *n - *m;
	    slacpy_("Full", m, &i__1, &af[af_offset], lda, &q_ref(*n - *m + 1,
		     1), lda);
	}
	if (*m > 1) {
	    i__1 = *m - 1;
	    i__2 = *m - 1;
	    slacpy_("Lower", &i__1, &i__2, &af_ref(2, *n - *m + 1), lda, &
		    q_ref(*n - *m + 2, *n - *m + 1), lda);
	}
    } else {
	if (*n > 1) {
	    i__1 = *n - 1;
	    i__2 = *n - 1;
	    slacpy_("Lower", &i__1, &i__2, &af_ref(*m - *n + 2, 1), lda, &
		    q_ref(2, 1), lda);
	}
    }
    i__1 = min(*m,*n);
    sorgrq_(n, n, &i__1, &q[q_offset], lda, &taua[1], &work[1], lwork, &info);

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

    slaset_("Full", p, p, &c_b9, &c_b9, &z__[z_offset], ldb);
    if (*p > 1) {
	i__1 = *p - 1;
	slacpy_("Lower", &i__1, n, &bf_ref(2, 1), ldb, &z___ref(2, 1), ldb);
    }
    i__1 = min(*p,*n);
    sorgqr_(p, p, &i__1, &z__[z_offset], ldb, &taub[1], &work[1], lwork, &
	    info);

/*     Copy R */

    slaset_("Full", m, n, &c_b19, &c_b19, &r__[r_offset], lda);
    if (*m <= *n) {
	slacpy_("Upper", m, m, &af_ref(1, *n - *m + 1), lda, &r___ref(1, *n - 
		*m + 1), lda);
    } else {
	i__1 = *m - *n;
	slacpy_("Full", &i__1, n, &af[af_offset], lda, &r__[r_offset], lda);
	slacpy_("Upper", n, n, &af_ref(*m - *n + 1, 1), lda, &r___ref(*m - *n 
		+ 1, 1), lda);
    }

/*     Copy T */

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

/*     Compute R - A*Q' */

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

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

    sgemm_("Transpose", "No transpose", p, n, p, &c_b31, &z__[z_offset], ldb, 
	    &b[b_offset], ldb, &c_b19, &bwk[bwk_offset], ldb);
    sgemm_("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 = slange_("1", p, n, &bwk[bwk_offset], ldb, &rwork[1]);
    if (bnorm > 0.f) {
/* Computing MAX */
	i__1 = max(1,*p);
	result[2] = resid / (real) max(i__1,*m) / bnorm / ulp;
    } else {
	result[2] = 0.f;
    }

/*     Compute I - Q*Q' */

    slaset_("Full", n, n, &c_b19, &c_b31, &r__[r_offset], lda);
    ssyrk_("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 = slansy_("1", "Upper", n, &r__[r_offset], lda, &rwork[1]);
    result[3] = resid / (real) max(1,*n) / ulp;

/*     Compute I - Z'*Z */

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

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

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

    return 0;

/*     End of SGRQTS */

} /* sgrqts_ */

#undef bf_ref
#undef af_ref
#undef z___ref
#undef r___ref
#undef q_ref


