#include "blaswrap.h"
/* chet21.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 complex c_b1 = {0.f,0.f};
static complex c_b2 = {1.f,0.f};
static integer c__1 = 1;

/* Subroutine */ int chet21_(integer *itype, char *uplo, integer *n, integer *
	kband, complex *a, integer *lda, real *d__, real *e, complex *u, 
	integer *ldu, complex *v, integer *ldv, complex *tau, complex *work, 
	real *rwork, real *result)
{
    /* System generated locals */
    integer a_dim1, a_offset, u_dim1, u_offset, v_dim1, v_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 */
    static integer j, jr;
    static real ulp;
    extern /* Subroutine */ int cher_(char *, integer *, real *, complex *, 
	    integer *, complex *, integer *);
    static integer jcol;
    static real unfl;
    static integer jrow;
    extern /* Subroutine */ int cher2_(char *, integer *, complex *, complex *
, integer *, complex *, integer *, complex *, integer *), 
	    cgemm_(char *, char *, integer *, integer *, integer *, complex *, 
	     complex *, integer *, complex *, integer *, complex *, complex *, 
	     integer *);
    extern logical lsame_(char *, char *);
    static integer iinfo;
    static real anorm;
    static char cuplo[1];
    static complex vsave;
    static logical lower;
    static real wnorm;
    extern /* Subroutine */ int cunm2l_(char *, char *, integer *, integer *, 
	    integer *, complex *, integer *, complex *, complex *, integer *, 
	    complex *, integer *), cunm2r_(char *, char *, 
	    integer *, integer *, integer *, complex *, integer *, complex *, 
	    complex *, integer *, complex *, integer *);
    extern doublereal clange_(char *, integer *, integer *, complex *, 
	    integer *, real *), clanhe_(char *, char *, integer *, 
	    complex *, integer *, real *), slamch_(char *);
    extern /* Subroutine */ int clacpy_(char *, integer *, integer *, complex 
	    *, integer *, complex *, integer *), claset_(char *, 
	    integer *, integer *, complex *, complex *, complex *, integer *), clarfy_(char *, integer *, complex *, integer *, complex 
	    *, complex *, integer *, complex *);


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


    Purpose   
    =======   

    CHET21 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 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 )   

    For ITYPE > 1, the transformation U is expressed as a product   
    V = H(1)...H(n-2),  where H(j) = I  -  tau(j) v(j) v(j)*  and each   
    vector v(j) has its first j elements 0 and the remaining n-j elements   
    stored in V(j+1:n,j).   

    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, CHET21 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.   

    A       (input) COMPLEX array, dimension (LDA, N)   
            The original (unfactored) matrix.  It is assumed to be   
            hermitian, and only the upper (UPLO='U') or only the lower   
            (UPLO='L') will be referenced.   

    LDA     (input) INTEGER   
            The leading dimension of A.  It must be at least 1   
            and at least N.   

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

    E       (input) REAL array, dimension (N-1)   
            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.   

    V       (input) COMPLEX array, dimension (LDV, N)   
            If ITYPE=2 or 3, the columns of this array contain the   
            Householder vectors used to describe the unitary matrix   
            in the decomposition.  If UPLO='L', then the vectors are in   
            the lower triangle, if UPLO='U', then in the upper   
            triangle.   
            *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.   

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

    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 (2*N**2)   

    RWORK   (workspace) REAL array, dimension (N)   

    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.   

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


       Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --d__;
    --e;
    u_dim1 = *ldu;
    u_offset = 1 + u_dim1;
    u -= u_offset;
    v_dim1 = *ldv;
    v_offset = 1 + v_dim1;
    v -= v_offset;
    --tau;
    --work;
    --rwork;
    --result;

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

    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 = clanhe_("1", cuplo, n, &a[a_offset], lda, &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);
	clacpy_(cuplo, n, n, &a[a_offset], lda, &work[1], n);

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    r__1 = -d__[j];
	    cher_(cuplo, n, &r__1, &u[j * u_dim1 + 1], &c__1, &work[1], n);
/* 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;
		cher2_(cuplo, n, &q__1, &u[j * u_dim1 + 1], &c__1, &u[(j - 1) 
			* u_dim1 + 1], &c__1, &work[1], n);
/* L20: */
	    }
	}
	wnorm = clanhe_("1", cuplo, n, &work[1], n, &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) {
/* Computing 2nd power */
	    i__2 = *n;
	    i__1 = i__2 * i__2;
	    i__3 = *n;
	    work[i__1].r = d__[i__3], work[i__1].i = 0.f;
	    for (j = *n - 1; j >= 1; --j) {
		if (*kband == 1) {
		    i__1 = (*n + 1) * (j - 1) + 2;
		    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 = (j - 1) * *n + 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 = jr + j * v_dim1;
			q__1.r = q__2.r * v[i__5].r - q__2.i * v[i__5].i, 
				q__1.i = q__2.r * v[i__5].i + q__2.i * v[i__5]
				.r;
			work[i__2].r = q__1.r, work[i__2].i = q__1.i;
/* L30: */
		    }
		}

		i__1 = j + 1 + j * v_dim1;
		vsave.r = v[i__1].r, vsave.i = v[i__1].i;
		i__1 = j + 1 + j * v_dim1;
		v[i__1].r = 1.f, v[i__1].i = 0.f;
		i__1 = *n - j;
/* Computing 2nd power */
		i__2 = *n;
		clarfy_("L", &i__1, &v[j + 1 + j * v_dim1], &c__1, &tau[j], &
			work[(*n + 1) * j + 1], n, &work[i__2 * i__2 + 1]);
		i__1 = j + 1 + j * v_dim1;
		v[i__1].r = vsave.r, v[i__1].i = vsave.i;
		i__1 = (*n + 1) * (j - 1) + 1;
		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) {
		if (*kband == 1) {
		    i__2 = (*n + 1) * 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 = j * *n + 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 = jr + (j + 1) * v_dim1;
			q__1.r = q__2.r * v[i__6].r - q__2.i * v[i__6].i, 
				q__1.i = q__2.r * v[i__6].i + q__2.i * v[i__6]
				.r;
			work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L50: */
		    }
		}

		i__2 = j + (j + 1) * v_dim1;
		vsave.r = v[i__2].r, vsave.i = v[i__2].i;
		i__2 = j + (j + 1) * v_dim1;
		v[i__2].r = 1.f, v[i__2].i = 0.f;
/* Computing 2nd power */
		i__2 = *n;
		clarfy_("U", &j, &v[(j + 1) * v_dim1 + 1], &c__1, &tau[j], &
			work[1], n, &work[i__2 * i__2 + 1]);
		i__2 = j + (j + 1) * v_dim1;
		v[i__2].r = vsave.r, v[i__2].i = vsave.i;
		i__2 = (*n + 1) * j + 1;
		i__3 = j + 1;
		work[i__2].r = d__[i__3], work[i__2].i = 0.f;
/* L60: */
	    }
	}

	i__1 = *n;
	for (jcol = 1; jcol <= i__1; ++jcol) {
	    if (lower) {
		i__2 = *n;
		for (jrow = jcol; jrow <= i__2; ++jrow) {
		    i__3 = jrow + *n * (jcol - 1);
		    i__4 = jrow + *n * (jcol - 1);
		    i__5 = jrow + jcol * a_dim1;
		    q__1.r = work[i__4].r - a[i__5].r, q__1.i = work[i__4].i 
			    - a[i__5].i;
		    work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L70: */
		}
	    } else {
		i__2 = jcol;
		for (jrow = 1; jrow <= i__2; ++jrow) {
		    i__3 = jrow + *n * (jcol - 1);
		    i__4 = jrow + *n * (jcol - 1);
		    i__5 = jrow + jcol * a_dim1;
		    q__1.r = work[i__4].r - a[i__5].r, q__1.i = work[i__4].i 
			    - a[i__5].i;
		    work[i__3].r = q__1.r, work[i__3].i = q__1.i;
/* L80: */
		}
	    }
/* L90: */
	}
	wnorm = clanhe_("1", cuplo, n, &work[1], n, &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);
	if (lower) {
	    i__1 = *n - 1;
	    i__2 = *n - 1;
/* Computing 2nd power */
	    i__3 = *n;
	    cunm2r_("R", "C", n, &i__1, &i__2, &v[v_dim1 + 2], ldv, &tau[1], &
		    work[*n + 1], n, &work[i__3 * i__3 + 1], &iinfo);
	} else {
	    i__1 = *n - 1;
	    i__2 = *n - 1;
/* Computing 2nd power */
	    i__3 = *n;
	    cunm2l_("R", "C", n, &i__1, &i__2, &v[(v_dim1 << 1) + 1], ldv, &
		    tau[1], &work[1], n, &work[i__3 * i__3 + 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;
/* L100: */
	}

	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;
/* L110: */
	}

/* 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 CHET21 */

} /* chet21_ */