#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 doublereal c_b10 = 0.;
static integer c__1 = 1;
static doublereal c_b26 = 1.;

/* Subroutine */ int dspt21_(integer *itype, char *uplo, integer *n, integer *
	kband, doublereal *ap, doublereal *d__, doublereal *e, doublereal *u, 
	integer *ldu, doublereal *vp, doublereal *tau, doublereal *work, 
	doublereal *result)
{
    /* System generated locals */
    integer u_dim1, u_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Local variables */
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    static doublereal unfl, temp;
    extern /* Subroutine */ int dspr_(char *, integer *, doublereal *, 
	    doublereal *, integer *, doublereal *), dspr2_(char *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *);
    static integer j;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *);
    extern logical lsame_(char *, char *);
    static integer iinfo;
    static doublereal anorm;
    extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static char cuplo[1];
    static doublereal vsave;
    extern /* Subroutine */ int daxpy_(integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *);
    static logical lower;
    extern /* Subroutine */ int dspmv_(char *, integer *, doublereal *, 
	    doublereal *, doublereal *, integer *, doublereal *, doublereal *,
	     integer *);
    static doublereal wnorm;
    extern doublereal dlamch_(char *);
    static integer jp;
    extern doublereal dlange_(char *, integer *, integer *, doublereal *, 
	    integer *, doublereal *);
    static integer jr;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    dlaset_(char *, integer *, integer *, doublereal *, doublereal *, 
	    doublereal *, integer *);
    extern doublereal dlansp_(char *, char *, integer *, doublereal *, 
	    doublereal *);
    extern /* Subroutine */ int dopmtr_(char *, char *, char *, integer *, 
	    integer *, doublereal *, doublereal *, doublereal *, integer *, 
	    doublereal *, integer *);
    static integer jp1, lap;
    static doublereal ulp;


#define u_ref(a_1,a_2) u[(a_2)*u_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   
    =======   

    DSPT21  generally checks a decomposition of the form   

            A = U S U'   

    where ' means transpose, A is symmetric (stored in packed format), U   
    is orthogonal, and S is diagonal (if KBAND=0) or 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 - VU' | / ( 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 orthogonal 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 orthogonal matrix and   
               as a product of Housholder transformations:   
               RESULT(1) = | I - VU' | / ( n ulp )   

    UPLO    (input) CHARACTER   
            If UPLO='U', AP and VP are considered to contain the upper   
            triangle of A and V.   
            If UPLO='L', AP and VP are considered to contain the lower   
            triangle of A and V.   

    N       (input) INTEGER   
            The size of the matrix.  If it is zero, DSPT21 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) DOUBLE PRECISION array, dimension (N*(N+1)/2)   
            The original (unfactored) matrix.  It is assumed to be   
            symmetric, and contains the columns of just the upper   
            triangle (UPLO='U') or only the lower triangle (UPLO='L'),   
            packed one after another.   

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

    E       (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDU, N)   
            If ITYPE=1 or 3, this contains the orthogonal 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) DOUBLE PRECISION array, dimension (N*(N+1)/2)   
            If ITYPE=2 or 3, the columns of this array contain the   
            Householder vectors used to describe the orthogonal 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (N**2+N)   
            Workspace.   

    RESULT  (output) DOUBLE PRECISION 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.   

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


       1)      Constants   

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

    /* Function Body */
    result[1] = 0.;
    if (*itype == 1) {
	result[2] = 0.;
    }
    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 = dlamch_("Safe minimum");
    ulp = dlamch_("Epsilon") * dlamch_("Base");

/*     Some Error Checks */

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

/*     Do Test 1   

       Norm of A: */

    if (*itype == 3) {
	anorm = 1.;
    } else {
/* Computing MAX */
	d__1 = dlansp_("1", cuplo, n, &ap[1], &work[1]);
	anorm = max(d__1,unfl);
    }

/*     Compute error matrix: */

    if (*itype == 1) {

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

	dlaset_("Full", n, n, &c_b10, &c_b10, &work[1], n);
	dcopy_(&lap, &ap[1], &c__1, &work[1], &c__1);

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    d__1 = -d__[j];
	    dspr_(cuplo, n, &d__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) {
		d__1 = -e[j];
		dspr2_(cuplo, n, &d__1, &u_ref(1, j), &c__1, &u_ref(1, j + 1),
			 &c__1, &work[1]);
/* L20: */
	    }
	}
/* Computing 2nd power */
	i__1 = *n;
	wnorm = dlansp_("1", cuplo, n, &work[1], &work[i__1 * i__1 + 1]);

    } else if (*itype == 2) {

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

	dlaset_("Full", n, n, &c_b10, &c_b10, &work[1], n);

	if (lower) {
	    work[lap] = d__[*n];
	    for (j = *n - 1; j >= 1; --j) {
		jp = ((*n << 1) - j) * (j - 1) / 2;
		jp1 = jp + *n - j;
		if (*kband == 1) {
		    work[jp + j + 1] = (1. - tau[j]) * e[j];
		    i__1 = *n;
		    for (jr = j + 2; jr <= i__1; ++jr) {
			work[jp + jr] = -tau[j] * e[j] * vp[jp + jr];
/* L30: */
		    }
		}

		if (tau[j] != 0.) {
		    vsave = vp[jp + j + 1];
		    vp[jp + j + 1] = 1.;
		    i__1 = *n - j;
		    dspmv_("L", &i__1, &c_b26, &work[jp1 + j + 1], &vp[jp + j 
			    + 1], &c__1, &c_b10, &work[lap + 1], &c__1);
		    i__1 = *n - j;
		    temp = tau[j] * -.5 * ddot_(&i__1, &work[lap + 1], &c__1, 
			    &vp[jp + j + 1], &c__1);
		    i__1 = *n - j;
		    daxpy_(&i__1, &temp, &vp[jp + j + 1], &c__1, &work[lap + 
			    1], &c__1);
		    i__1 = *n - j;
		    d__1 = -tau[j];
		    dspr2_("L", &i__1, &d__1, &vp[jp + j + 1], &c__1, &work[
			    lap + 1], &c__1, &work[jp1 + j + 1]);
		    vp[jp + j + 1] = vsave;
		}
		work[jp + j] = d__[j];
/* L40: */
	    }
	} else {
	    work[1] = d__[1];
	    i__1 = *n - 1;
	    for (j = 1; j <= i__1; ++j) {
		jp = j * (j - 1) / 2;
		jp1 = jp + j;
		if (*kband == 1) {
		    work[jp1 + j] = (1. - tau[j]) * e[j];
		    i__2 = j - 1;
		    for (jr = 1; jr <= i__2; ++jr) {
			work[jp1 + jr] = -tau[j] * e[j] * vp[jp1 + jr];
/* L50: */
		    }
		}

		if (tau[j] != 0.) {
		    vsave = vp[jp1 + j];
		    vp[jp1 + j] = 1.;
		    dspmv_("U", &j, &c_b26, &work[1], &vp[jp1 + 1], &c__1, &
			    c_b10, &work[lap + 1], &c__1);
		    temp = tau[j] * -.5 * ddot_(&j, &work[lap + 1], &c__1, &
			    vp[jp1 + 1], &c__1);
		    daxpy_(&j, &temp, &vp[jp1 + 1], &c__1, &work[lap + 1], &
			    c__1);
		    d__1 = -tau[j];
		    dspr2_("U", &j, &d__1, &vp[jp1 + 1], &c__1, &work[lap + 1]
			    , &c__1, &work[1]);
		    vp[jp1 + j] = vsave;
		}
		work[jp1 + j + 1] = d__[j + 1];
/* L60: */
	    }
	}

	i__1 = lap;
	for (j = 1; j <= i__1; ++j) {
	    work[j] -= ap[j];
/* L70: */
	}
	wnorm = dlansp_("1", cuplo, n, &work[1], &work[lap + 1]);

    } else if (*itype == 3) {

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

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

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    work[(*n + 1) * (j - 1) + 1] += -1.;
/* L80: */
	}

/* Computing 2nd power */
	i__1 = *n;
	wnorm = dlange_("1", n, n, &work[1], n, &work[i__1 * i__1 + 1]);
    }

    if (anorm > wnorm) {
	result[1] = wnorm / anorm / (*n * ulp);
    } else {
	if (anorm < 1.) {
/* Computing MIN */
	    d__1 = wnorm, d__2 = *n * anorm;
	    result[1] = min(d__1,d__2) / anorm / (*n * ulp);
	} else {
/* Computing MIN */
	    d__1 = wnorm / anorm, d__2 = (doublereal) (*n);
	    result[1] = min(d__1,d__2) / (*n * ulp);
	}
    }

/*     Do Test 2   

       Compute  UU' - I */

    if (*itype == 1) {
	dgemm_("N", "C", n, n, n, &c_b26, &u[u_offset], ldu, &u[u_offset], 
		ldu, &c_b10, &work[1], n);

	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    work[(*n + 1) * (j - 1) + 1] += -1.;
/* L90: */
	}

/* Computing MIN   
   Computing 2nd power */
	i__1 = *n;
	d__1 = dlange_("1", n, n, &work[1], n, &work[i__1 * i__1 + 1]), d__2 = (doublereal) (*n);
	result[2] = min(d__1,d__2) / (*n * ulp);
    }

    return 0;

/*     End of DSPT21 */

} /* dspt21_ */

#undef u_ref


