#include "blaswrap.h"
/* zrqt02.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 doublecomplex c_b1 = {-1e10,-1e10};
static doublecomplex c_b9 = {0.,0.};
static doublecomplex c_b14 = {-1.,0.};
static doublecomplex c_b15 = {1.,0.};
static doublereal c_b23 = -1.;
static doublereal c_b24 = 1.;

/* Subroutine */ int zrqt02_(integer *m, integer *n, integer *k, 
	doublecomplex *a, doublecomplex *af, doublecomplex *q, doublecomplex *
	r__, integer *lda, doublecomplex *tau, doublecomplex *work, integer *
	lwork, doublereal *rwork, doublereal *result)
{
    /* System generated locals */
    integer a_dim1, a_offset, af_dim1, af_offset, q_dim1, q_offset, r_dim1, 
	    r_offset, i__1, i__2;

    /* Builtin functions   
       Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);

    /* Local variables */
    static doublereal eps;
    static integer info;
    static doublereal resid, anorm;
    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 *);
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *), 
	    zlaset_(char *, integer *, integer *, doublecomplex *, 
	    doublecomplex *, doublecomplex *, integer *);
    extern doublereal zlansy_(char *, char *, integer *, doublecomplex *, 
	    integer *, doublereal *);
    extern /* Subroutine */ int 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   
    =======   

    ZRQT02 tests ZUNGRQ, which generates an m-by-n matrix Q with   
    orthonornmal rows that is defined as the product of k elementary   
    reflectors.   

    Given the RQ factorization of an m-by-n matrix A, ZRQT02 generates   
    the orthogonal matrix Q defined by the factorization of the last k   
    rows of A; it compares R(m-k+1:m,n-m+1:n) with   
    A(m-k+1:m,1:n)*Q(n-m+1:n,1:n)', and checks that the rows 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.   
            N >= M >= 0.   

    K       (input) INTEGER   
            The number of elementary reflectors whose product defines the   
            matrix Q. M >= K >= 0.   

    A       (input) COMPLEX*16 array, dimension (LDA,N)   
            The m-by-n matrix A which was factorized by ZRQT01.   

    AF      (input) COMPLEX*16 array, dimension (LDA,N)   
            Details of the RQ factorization of A, as returned by ZGERQF.   
            See ZGERQF for further details.   

    Q       (workspace) COMPLEX*16 array, dimension (LDA,N)   

    R       (workspace) COMPLEX*16 array, dimension (LDA,M)   

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

    TAU     (input) COMPLEX*16 array, dimension (M)   
            The scalar factors of the elementary reflectors corresponding   
            to the RQ factorization in AF.   

    WORK    (workspace) COMPLEX*16 array, dimension (LWORK)   

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

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

    RESULT  (output) DOUBLE PRECISION array, dimension (2)   
            The test ratios:   
            RESULT(1) = norm( R - A*Q' ) / ( N * norm(A) * EPS )   
            RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )   

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


       Quick return if possible   

       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 */
    if (*m == 0 || *n == 0 || *k == 0) {
	result[1] = 0.;
	result[2] = 0.;
	return 0;
    }

    eps = dlamch_("Epsilon");

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

    zlaset_("Full", m, n, &c_b1, &c_b1, &q[q_offset], lda);
    if (*k < *n) {
	i__1 = *n - *k;
	zlacpy_("Full", k, &i__1, &af[*m - *k + 1 + af_dim1], lda, &q[*m - *k 
		+ 1 + q_dim1], lda);
    }
    if (*k > 1) {
	i__1 = *k - 1;
	i__2 = *k - 1;
	zlacpy_("Lower", &i__1, &i__2, &af[*m - *k + 2 + (*n - *k + 1) * 
		af_dim1], lda, &q[*m - *k + 2 + (*n - *k + 1) * q_dim1], lda);
    }

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

    s_copy(srnamc_1.srnamt, "ZUNGRQ", (ftnlen)6, (ftnlen)6);
    zungrq_(m, n, k, &q[q_offset], lda, &tau[*m - *k + 1], &work[1], lwork, &
	    info);

/*     Copy R(m-k+1:m,n-m+1:n) */

    zlaset_("Full", k, m, &c_b9, &c_b9, &r__[*m - *k + 1 + (*n - *m + 1) * 
	    r_dim1], lda);
    zlacpy_("Upper", k, k, &af[*m - *k + 1 + (*n - *k + 1) * af_dim1], lda, &
	    r__[*m - *k + 1 + (*n - *k + 1) * r_dim1], lda);

/*     Compute R(m-k+1:m,n-m+1:n) - A(m-k+1:m,1:n) * Q(n-m+1:n,1:n)' */

    zgemm_("No transpose", "Conjugate transpose", k, m, n, &c_b14, &a[*m - *k 
	    + 1 + a_dim1], lda, &q[q_offset], lda, &c_b15, &r__[*m - *k + 1 + 
	    (*n - *m + 1) * r_dim1], lda);

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

    anorm = zlange_("1", k, n, &a[*m - *k + 1 + a_dim1], lda, &rwork[1]);
    resid = zlange_("1", k, m, &r__[*m - *k + 1 + (*n - *m + 1) * r_dim1], 
	    lda, &rwork[1]);
    if (anorm > 0.) {
	result[1] = resid / (doublereal) max(1,*n) / anorm / eps;
    } else {
	result[1] = 0.;
    }

/*     Compute I - Q*Q' */

    zlaset_("Full", m, m, &c_b9, &c_b15, &r__[r_offset], lda);
    zherk_("Upper", "No transpose", m, n, &c_b23, &q[q_offset], lda, &c_b24, &
	    r__[r_offset], lda);

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

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

    result[2] = resid / (doublereal) max(1,*n) / eps;

    return 0;

/*     End of ZRQT02 */

} /* zrqt02_ */