#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 complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__1 = 1;

/* Subroutine */ int chpt21_(integer *itype, char *uplo, integer *n, integer *
	kband, complex *ap, real *d__, real *e, complex *u, integer *ldu, 
	complex *vp, complex *tau, complex *work, real *rwork, real *result)
{
    /* System generated locals */
    integer u_dim1, u_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    real r__1, r__2;
    complex q__1, q__2, q__3;

    /* Local variables */
    extern /* Subroutine */ int chpr_(char *, integer *, real *, complex *, 
	    integer *, complex *);
    static real unfl;
    static complex temp;
    extern /* Subroutine */ int chpr2_(char *, integer *, complex *, complex *
	    , integer *, complex *, integer *, complex *);
    static integer j;
    extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *, 
	    integer *, complex *, complex *, integer *, complex *, integer *, 
	    complex *, complex *, integer *);
    extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer 
	    *, complex *, integer *);
    extern logical lsame_(char *, char *);
    static integer iinfo;
    static real anorm;
    extern /* Subroutine */ int ccopy_(integer *, complex *, integer *, 
	    complex *, integer *), chpmv_(char *, integer *, complex *, 
	    complex *, complex *, integer *, complex *, complex *, integer *);
    static char cuplo[1];
    static complex vsave;
    extern /* Subroutine */ int caxpy_(integer *, complex *, complex *, 
	    integer *, complex *, integer *);
    static logical lower;
    static real wnorm;
    extern doublereal clange_(char *, integer *, integer *, complex *, 
	    integer *, real *);
    static integer jp, jr;
    extern doublereal clanhp_(char *, char *, integer *, complex *, real *), slamch_(char *);
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
	    *, integer *, complex *, integer *), claset_(char *, 
	    integer *, integer *, complex *, complex *, complex *, integer *), cupmtr_(char *, char *, char *, integer *, integer *, 
	    complex *, complex *, complex *, integer *, complex *, integer *);
    static integer jp1, lap;
    static real ulp;


#define u_subscr(a_1,a_2) (a_2)*u_dim1 + a_1
#define u_ref(a_1,a_2) u[u_subscr(a_1,a_2)]


/*  -- 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   
    =======   

    CHPT21  generally checks a decomposition of the form   

            A = U S U*   

    where * means conjugate transpose, A is hermitian, U is   
    unitary, and S is diagonal (if KBAND=0) or (real) symmetric   
    tridiagonal (if KBAND=1).  If ITYPE=1, then U is represented as   
    a dense matrix, otherwise the U is expressed as a product of   
    Householder transformations, whose vectors are stored in the   
    array "V" and whose scaling constants are in "TAU"; we shall   
    use the letter "V" to refer to the product of Householder   
    transformations (which should be equal to U).   

    Specifically, if ITYPE=1, then:   

            RESULT(1) = | A - U S U* | / ( |A| n ulp ) *and*   
            RESULT(2) = | I - UU* | / ( n ulp )   

    If ITYPE=2, then:   

            RESULT(1) = | A - V S V* | / ( |A| n ulp )   

    If ITYPE=3, then:   

            RESULT(1) = | I - UV* | / ( n ulp )   

    Packed storage means that, for example, if UPLO='U', then the columns   
    of the upper triangle of A are stored one after another, so that   
    A(1,j+1) immediately follows A(j,j) in the array AP.  Similarly, if   
    UPLO='L', then the columns of the lower triangle of A are stored one   
    after another in AP, so that A(j+1,j+1) immediately follows A(n,j)   
    in the array AP.  This means that A(i,j) is stored in:   

       AP( i + j*(j-1)/2 )                 if UPLO='U'   

       AP( i + (2*n-j)*(j-1)/2 )           if UPLO='L'   

    The array VP bears the same relation to the matrix V that A does to   
    AP.   

    For ITYPE > 1, the transformation U is expressed as a product   
    of Householder transformations:   

       If UPLO='U', then  V = H(n-1)...H(1),  where   

           H(j) = I  -  tau(j) v(j) v(j)*   

       and the first j-1 elements of v(j) are stored in V(1:j-1,j+1),   
       (i.e., VP( j*(j+1)/2 + 1 : j*(j+1)/2 + j-1 ) ),   
       the j-th element is 1, and the last n-j elements are 0.   

       If UPLO='L', then  V = H(1)...H(n-1),  where   

           H(j) = I  -  tau(j) v(j) v(j)*   

       and the first j elements of v(j) are 0, the (j+1)-st is 1, and the   
       (j+2)-nd through n-th elements are stored in V(j+2:n,j) (i.e.,   
       in VP( (2*n-j)*(j-1)/2 + j+2 : (2*n-j)*(j-1)/2 + n ) .)   

    Arguments   
    =========   

    ITYPE   (input) INTEGER   
            Specifies the type of tests to be performed.   
            1: U expressed as a dense unitary matrix:   
               RESULT(1) = | A - U S U* | / ( |A| n ulp )   *and*   
               RESULT(2) = | I - UU* | / ( n ulp )   

            2: U expressed as a product V of Housholder transformations:   
               RESULT(1) = | A - V S V* | / ( |A| n ulp )   

            3: U expressed both as a dense unitary matrix and   
               as a product of Housholder transformations:   
               RESULT(1) = | I - UV* | / ( n ulp )   

    UPLO    (input) CHARACTER   
            If UPLO='U', the upper triangle of A and V will be used and   
            the (strictly) lower triangle will not be referenced.   
            If UPLO='L', the lower triangle of A and V will be used and   
            the (strictly) upper triangle will not be referenced.   

    N       (input) INTEGER   
            The size of the matrix.  If it is zero, CHPT21 does nothing.   
            It must be at least zero.   

    KBAND   (input) INTEGER   
            The bandwidth of the matrix.  It may only be zero or one.   
            If zero, then S is diagonal, and E is not referenced.  If   
            one, then S is symmetric tri-diagonal.   

    AP      (input) COMPLEX array, dimension (N*(N+1)/2)   
            The original (unfactored) matrix.  It is assumed to be   
            hermitian, and contains the columns of just the upper   
            triangle (UPLO='U') or only the lower triangle (UPLO='L'),   
            packed one after another.   

    D       (input) REAL array, dimension (N)   
            The diagonal of the (symmetric tri-) diagonal matrix.   

    E       (input) REAL array, dimension (N)   
            The off-diagonal of the (symmetric tri-) diagonal matrix.   
            E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and   
            (3,2) element, etc.   
            Not referenced if KBAND=0.   

    U       (input) COMPLEX array, dimension (LDU, N)   
            If ITYPE=1 or 3, this contains the unitary matrix in   
            the decomposition, expressed as a dense matrix.  If ITYPE=2,   
            then it is not referenced.   

    LDU     (input) INTEGER   
            The leading dimension of U.  LDU must be at least N and   
            at least 1.   

    VP      (input) REAL array, dimension (N*(N+1)/2)   
            If ITYPE=2 or 3, the columns of this array contain the   
            Householder vectors used to describe the unitary matrix   
            in the decomposition, as described in purpose.   
            *NOTE* If ITYPE=2 or 3, V is modified and restored.  The   
            subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U')   
            is set to one, and later reset to its original value, during   
            the course of the calculation.   
            If ITYPE=1, then it is neither referenced nor modified.   

    TAU     (input) COMPLEX array, dimension (N)   
            If ITYPE >= 2, then TAU(j) is the scalar factor of   
            v(j) v(j)* in the Householder transformation H(j) of   
            the product  U = H(1)...H(n-2)   
            If ITYPE < 2, then TAU is not referenced.   

    WORK    (workspace) COMPLEX array, dimension (N**2)   
            Workspace.   

    RWORK   (workspace) REAL array, dimension (N)   
            Workspace.   

    RESULT  (output) REAL array, dimension (2)   
            The values computed by the two tests described above.  The   
            values are currently limited to 1/ulp, to avoid overflow.   
            RESULT(1) is always modified.  RESULT(2) is modified only   
            if ITYPE=1.   

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


       Constants   

       Parameter adjustments */
    --ap;
    --d__;
    --e;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1 * 1;
    u -= u_offset;
    --vp;
    --tau;
    --work;
    --rwork;
    --result;

    /* Function Body */
    result[1] = 0.f;
    if (*itype == 1) {
	result[2] = 0.f;
    }
    if (*n <= 0) {
	return 0;
    }

    lap = *n * (*n + 1) / 2;

    if (lsame_(uplo, "U")) {
	lower = FALSE_;
	*(unsigned char *)cuplo = 'U';
    } else {
	lower = TRUE_;
	*(unsigned char *)cuplo = 'L';
    }

    unfl = slamch_("Safe minimum");
    ulp = slamch_("Epsilon") * slamch_("Base");

/*     Some Error Checks */

    if (*itype < 1 || *itype > 3) {
	result[1] = 10.f / ulp;
	return 0;
    }

/*     Do Test 1   

       Norm of A: */

    if (*itype == 3) {
	anorm = 1.f;
    } else {
/* Computing MAX */
	r__1 = clanhp_("1", cuplo, n, &ap[1], &rwork[1])
		;
	anorm = dmax(r__1,unfl);
    }

/*     Compute error matrix: */

    if (*itype == 1) {

/*        ITYPE=1: error = A - U S U* */

	claset_("Full", n, n, &c_b1, &c_b1, &work[1], n);
	ccopy_(&lap, &ap[1], &c__1, &work[1], &c__1);

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    r__1 = -d__[j];
	    chpr_(cuplo, n, &r__1, &u_ref(1, j), &c__1, &work[1]);
/* L10: */
	}

	if (*n > 1 && *kband == 1) {
	    i__1 = *n - 1;
	    for (j = 1; j <= i__1; ++j) {
		i__2 = j;
		q__2.r = e[i__2], q__2.i = 0.f;
		q__1.r = -q__2.r, q__1.i = -q__2.i;
		chpr2_(cuplo, n, &q__1, &u_ref(1, j), &c__1, &u_ref(1, j - 1),
			 &c__1, &work[1]);
/* L20: */
	    }
	}
	wnorm = clanhp_("1", cuplo, n, &work[1], &rwork[1]);

    } else if (*itype == 2) {

/*        ITYPE=2: error = V S V* - A */

	claset_("Full", n, n, &c_b1, &c_b1, &work[1], n);

	if (lower) {
	    i__1 = lap;
	    i__2 = *n;
	    work[i__1].r = d__[i__2], work[i__1].i = 0.f;
	    for (j = *n - 1; j >= 1; --j) {
		jp = ((*n << 1) - j) * (j - 1) / 2;
		jp1 = jp + *n - j;
		if (*kband == 1) {
		    i__1 = jp + j + 1;
		    i__2 = j;
		    q__2.r = 1.f - tau[i__2].r, q__2.i = 0.f - tau[i__2].i;
		    i__3 = j;
		    q__1.r = e[i__3] * q__2.r, q__1.i = e[i__3] * q__2.i;
		    work[i__1].r = q__1.r, work[i__1].i = q__1.i;
		    i__1 = *n;
		    for (jr = j + 2; jr <= i__1; ++jr) {
			i__2 = jp + jr;
			i__3 = j;
			q__3.r = -tau[i__3].r, q__3.i = -tau[i__3].i;
			i__4 = j;
			q__2.r = e[i__4] * q__3.r, q__2.i = e[i__4] * q__3.i;
			i__5 = jp + jr;
			q__1.r = q__2.r * vp[i__5].r - q__2.i * vp[i__5].i, 
				q__1.i = q__2.r * vp[i__5].i + q__2.i * vp[
				i__5].r;
			work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L30: */
		    }
		}

		i__1 = j;
		if (tau[i__1].r != 0.f || tau[i__1].i != 0.f) {
		    i__1 = jp + j + 1;
		    vsave.r = vp[i__1].r, vsave.i = vp[i__1].i;
		    i__1 = jp + j + 1;
		    vp[i__1].r = 1.f, vp[i__1].i = 0.f;
		    i__1 = *n - j;
		    chpmv_("L", &i__1, &c_b2, &work[jp1 + j + 1], &vp[jp + j 
			    + 1], &c__1, &c_b1, &work[lap + 1], &c__1);
		    i__1 = j;
		    q__2.r = tau[i__1].r * -.5f, q__2.i = tau[i__1].i * -.5f;
		    i__2 = *n - j;
		    cdotc_(&q__3, &i__2, &work[lap + 1], &c__1, &vp[jp + j + 
			    1], &c__1);
		    q__1.r = q__2.r * q__3.r - q__2.i * q__3.i, q__1.i = 
			    q__2.r * q__3.i + q__2.i * q__3.r;
		    temp.r = q__1.r, temp.i = q__1.i;
		    i__1 = *n - j;
		    caxpy_(&i__1, &temp, &vp[jp + j + 1], &c__1, &work[lap + 
			    1], &c__1);
		    i__1 = *n - j;
		    i__2 = j;
		    q__1.r = -tau[i__2].r, q__1.i = -tau[i__2].i;
		    chpr2_("L", &i__1, &q__1, &vp[jp + j + 1], &c__1, &work[
			    lap + 1], &c__1, &work[jp1 + j + 1]);

		    i__1 = jp + j + 1;
		    vp[i__1].r = vsave.r, vp[i__1].i = vsave.i;
		}
		i__1 = jp + j;
		i__2 = j;
		work[i__1].r = d__[i__2], work[i__1].i = 0.f;
/* L40: */
	    }
	} else {
	    work[1].r = d__[1], work[1].i = 0.f;
	    i__1 = *n - 1;
	    for (j = 1; j <= i__1; ++j) {
		jp = j * (j - 1) / 2;
		jp1 = jp + j;
		if (*kband == 1) {
		    i__2 = jp1 + j;
		    i__3 = j;
		    q__2.r = 1.f - tau[i__3].r, q__2.i = 0.f - tau[i__3].i;
		    i__4 = j;
		    q__1.r = e[i__4] * q__2.r, q__1.i = e[i__4] * q__2.i;
		    work[i__2].r = q__1.r, work[i__2].i = q__1.i;
		    i__2 = j - 1;
		    for (jr = 1; jr <= i__2; ++jr) {
			i__3 = jp1 + jr;
			i__4 = j;
			q__3.r = -tau[i__4].r, q__3.i = -tau[i__4].i;
			i__5 = j;
			q__2.r = e[i__5] * q__3.r, q__2.i = e[i__5] * q__3.i;
			i__6 = jp1 + jr;
			q__1.r = q__2.r * vp[i__6].r - q__2.i * vp[i__6].i, 
				q__1.i = q__2.r * vp[i__6].i + q__2.i * vp[
				i__6].r;
			work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L50: */
		    }
		}

		i__2 = j;
		if (tau[i__2].r != 0.f || tau[i__2].i != 0.f) {
		    i__2 = jp1 + j;
		    vsave.r = vp[i__2].r, vsave.i = vp[i__2].i;
		    i__2 = jp1 + j;
		    vp[i__2].r = 1.f, vp[i__2].i = 0.f;
		    chpmv_("U", &j, &c_b2, &work[1], &vp[jp1 + 1], &c__1, &
			    c_b1, &work[lap + 1], &c__1);
		    i__2 = j;
		    q__2.r = tau[i__2].r * -.5f, q__2.i = tau[i__2].i * -.5f;
		    cdotc_(&q__3, &j, &work[lap + 1], &c__1, &vp[jp1 + 1], &
			    c__1);
		    q__1.r = q__2.r * q__3.r - q__2.i * q__3.i, q__1.i = 
			    q__2.r * q__3.i + q__2.i * q__3.r;
		    temp.r = q__1.r, temp.i = q__1.i;
		    caxpy_(&j, &temp, &vp[jp1 + 1], &c__1, &work[lap + 1], &
			    c__1);
		    i__2 = j;
		    q__1.r = -tau[i__2].r, q__1.i = -tau[i__2].i;
		    chpr2_("U", &j, &q__1, &vp[jp1 + 1], &c__1, &work[lap + 1]
			    , &c__1, &work[1]);
		    i__2 = jp1 + j;
		    vp[i__2].r = vsave.r, vp[i__2].i = vsave.i;
		}
		i__2 = jp1 + j + 1;
		i__3 = j + 1;
		work[i__2].r = d__[i__3], work[i__2].i = 0.f;
/* L60: */
	    }
	}

	i__1 = lap;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = j;
	    i__3 = j;
	    i__4 = j;
	    q__1.r = work[i__3].r - ap[i__4].r, q__1.i = work[i__3].i - ap[
		    i__4].i;
	    work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L70: */
	}
	wnorm = clanhp_("1", cuplo, n, &work[1], &rwork[1]);

    } else if (*itype == 3) {

/*        ITYPE=3: error = U V* - I */

	if (*n < 2) {
	    return 0;
	}
	clacpy_(" ", n, n, &u[u_offset], ldu, &work[1], n);
/* Computing 2nd power */
	i__1 = *n;
	cupmtr_("R", cuplo, "C", n, n, &vp[1], &tau[1], &work[1], n, &work[
		i__1 * i__1 + 1], &iinfo);
	if (iinfo != 0) {
	    result[1] = 10.f / ulp;
	    return 0;
	}

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = (*n + 1) * (j - 1) + 1;
	    i__3 = (*n + 1) * (j - 1) + 1;
	    q__1.r = work[i__3].r - 1.f, q__1.i = work[i__3].i + 0.f;
	    work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L80: */
	}

	wnorm = clange_("1", n, n, &work[1], n, &rwork[1]);
    }

    if (anorm > wnorm) {
	result[1] = wnorm / anorm / (*n * ulp);
    } else {
	if (anorm < 1.f) {
/* Computing MIN */
	    r__1 = wnorm, r__2 = *n * anorm;
	    result[1] = dmin(r__1,r__2) / anorm / (*n * ulp);
	} else {
/* Computing MIN */
	    r__1 = wnorm / anorm, r__2 = (real) (*n);
	    result[1] = dmin(r__1,r__2) / (*n * ulp);
	}
    }

/*     Do Test 2   

       Compute  UU* - I */

    if (*itype == 1) {
	cgemm_("N", "C", n, n, n, &c_b2, &u[u_offset], ldu, &u[u_offset], ldu,
		 &c_b1, &work[1], n);

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    i__2 = (*n + 1) * (j - 1) + 1;
	    i__3 = (*n + 1) * (j - 1) + 1;
	    q__1.r = work[i__3].r - 1.f, q__1.i = work[i__3].i + 0.f;
	    work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L90: */
	}

/* Computing MIN */
	r__1 = clange_("1", n, n, &work[1], n, &rwork[1]), r__2 = (
		real) (*n);
	result[2] = dmin(r__1,r__2) / (*n * ulp);
    }

    return 0;

/*     End of CHPT21 */

} /* chpt21_ */

#undef u_ref
#undef u_subscr



.