#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"

/* Common Block Declarations */

struct {
    doublereal ops, itcnt;
} latime_;

#define latime_1 latime_

/* Table of constant values */

static doublereal c_b3 = -1.;
static integer c__1 = 1;

/* Subroutine */ int dlaed8_(integer *icompq, integer *k, integer *n, integer 
	*qsiz, doublereal *d__, doublereal *q, integer *ldq, integer *indxq, 
	doublereal *rho, integer *cutpnt, doublereal *z__, doublereal *dlamda,
	 doublereal *q2, integer *ldq2, doublereal *w, integer *perm, integer 
	*givptr, integer *givcol, doublereal *givnum, integer *indxp, integer 
	*indx, integer *info)
{
    /* System generated locals */
    integer q_dim1, q_offset, q2_dim1, q2_offset, i__1;
    doublereal d__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    static integer jlam, imax, jmax;
    extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *);
    static doublereal c__;
    static integer i__, j;
    static doublereal s, t;
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, 
	    integer *), dcopy_(integer *, doublereal *, integer *, doublereal 
	    *, integer *);
    static integer k2, n1, n2;
    extern doublereal dlapy2_(doublereal *, doublereal *), dlamch_(char *);
    static integer jp;
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, 
	    integer *, integer *, integer *), dlacpy_(char *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, integer *), xerbla_(char *, integer *);
    static integer n1p1;
    static doublereal eps, tau, tol;


#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]
#define q2_ref(a_1,a_2) q2[(a_2)*q2_dim1 + a_1]
#define givcol_ref(a_1,a_2) givcol[(a_2)*2 + a_1]
#define givnum_ref(a_1,a_2) givnum[(a_2)*2 + a_1]


/*  -- LAPACK routine (instrumented to count operations, version 3.0) --   
       Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab,   
       Courant Institute, NAG Ltd., and Rice University   
       September 30, 1994   

       Common block to return operation count and iteration count   
       ITCNT is unchanged, OPS is only incremented   

    Purpose   
    =======   

    DLAED8 merges the two sets of eigenvalues together into a single   
    sorted set.  Then it tries to deflate the size of the problem.   
    There are two ways in which deflation can occur:  when two or more   
    eigenvalues are close together or if there is a tiny element in the   
    Z vector.  For each such occurrence the order of the related secular   
    equation problem is reduced by one.   

    Arguments   
    =========   

    ICOMPQ  (input) INTEGER   
            = 0:  Compute eigenvalues only.   
            = 1:  Compute eigenvectors of original dense symmetric matrix   
                  also.  On entry, Q contains the orthogonal matrix used   
                  to reduce the original matrix to tridiagonal form.   

    K      (output) INTEGER   
           The number of non-deflated eigenvalues, and the order of the   
           related secular equation.   

    N      (input) INTEGER   
           The dimension of the symmetric tridiagonal matrix.  N >= 0.   

    QSIZ   (input) INTEGER   
           The dimension of the orthogonal matrix used to reduce   
           the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.   

    D      (input/output) DOUBLE PRECISION array, dimension (N)   
           On entry, the eigenvalues of the two submatrices to be   
           combined.  On exit, the trailing (N-K) updated eigenvalues   
           (those which were deflated) sorted into increasing order.   

    Q      (input/output) DOUBLE PRECISION array, dimension (LDQ,N)   
           If ICOMPQ = 0, Q is not referenced.  Otherwise,   
           on entry, Q contains the eigenvectors of the partially solved   
           system which has been previously updated in matrix   
           multiplies with other partially solved eigensystems.   
           On exit, Q contains the trailing (N-K) updated eigenvectors   
           (those which were deflated) in its last N-K columns.   

    LDQ    (input) INTEGER   
           The leading dimension of the array Q.  LDQ >= max(1,N).   

    INDXQ  (input) INTEGER array, dimension (N)   
           The permutation which separately sorts the two sub-problems   
           in D into ascending order.  Note that elements in the second   
           half of this permutation must first have CUTPNT added to   
           their values in order to be accurate.   

    RHO    (input/output) DOUBLE PRECISION   
           On entry, the off-diagonal element associated with the rank-1   
           cut which originally split the two submatrices which are now   
           being recombined.   
           On exit, RHO has been modified to the value required by   
           DLAED3.   

    CUTPNT (input) INTEGER   
           The location of the last eigenvalue in the leading   
           sub-matrix.  min(1,N) <= CUTPNT <= N.   

    Z      (input) DOUBLE PRECISION array, dimension (N)   
           On entry, Z contains the updating vector (the last row of   
           the first sub-eigenvector matrix and the first row of the   
           second sub-eigenvector matrix).   
           On exit, the contents of Z are destroyed by the updating   
           process.   

    DLAMDA (output) DOUBLE PRECISION array, dimension (N)   
           A copy of the first K eigenvalues which will be used by   
           DLAED3 to form the secular equation.   

    Q2     (output) DOUBLE PRECISION array, dimension (LDQ2,N)   
           If ICOMPQ = 0, Q2 is not referenced.  Otherwise,   
           a copy of the first K eigenvectors which will be used by   
           DLAED7 in a matrix multiply (DGEMM) to update the new   
           eigenvectors.   

    LDQ2   (input) INTEGER   
           The leading dimension of the array Q2.  LDQ2 >= max(1,N).   

    W      (output) DOUBLE PRECISION array, dimension (N)   
           The first k values of the final deflation-altered z-vector and   
           will be passed to DLAED3.   

    PERM   (output) INTEGER array, dimension (N)   
           The permutations (from deflation and sorting) to be applied   
           to each eigenblock.   

    GIVPTR (output) INTEGER   
           The number of Givens rotations which took place in this   
           subproblem.   

    GIVCOL (output) INTEGER array, dimension (2, N)   
           Each pair of numbers indicates a pair of columns to take place   
           in a Givens rotation.   

    GIVNUM (output) DOUBLE PRECISION array, dimension (2, N)   
           Each number indicates the S value to be used in the   
           corresponding Givens rotation.   

    INDXP  (workspace) INTEGER array, dimension (N)   
           The permutation used to place deflated values of D at the end   
           of the array.  INDXP(1:K) points to the nondeflated D-values   
           and INDXP(K+1:N) points to the deflated eigenvalues.   

    INDX   (workspace) INTEGER array, dimension (N)   
           The permutation used to sort the contents of D into ascending   
           order.   

    INFO   (output) INTEGER   
            = 0:  successful exit.   
            < 0:  if INFO = -i, the i-th argument had an illegal value.   

    Further Details   
    ===============   

    Based on contributions by   
       Jeff Rutter, Computer Science Division, University of California   
       at Berkeley, USA   

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



       Test the input parameters.   

       Parameter adjustments */
    --d__;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    --indxq;
    --z__;
    --dlamda;
    q2_dim1 = *ldq2;
    q2_offset = 1 + q2_dim1 * 1;
    q2 -= q2_offset;
    --w;
    --perm;
    givcol -= 3;
    givnum -= 3;
    --indxp;
    --indx;

    /* Function Body */
    *info = 0;

    if (*icompq < 0 || *icompq > 1) {
	*info = -1;
    } else if (*n < 0) {
	*info = -3;
    } else if (*icompq == 1 && *qsiz < *n) {
	*info = -4;
    } else if (*ldq < max(1,*n)) {
	*info = -7;
    } else if (*cutpnt < min(1,*n) || *cutpnt > *n) {
	*info = -10;
    } else if (*ldq2 < max(1,*n)) {
	*info = -14;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("DLAED8", &i__1);
	return 0;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return 0;
    }

    n1 = *cutpnt;
    n2 = *n - n1;
    n1p1 = n1 + 1;

    if (*rho < 0.) {
	latime_1.ops += n2;
	dscal_(&n2, &c_b3, &z__[n1p1], &c__1);
    }

/*     Normalize z so that norm(z) = 1 */

    latime_1.ops = latime_1.ops + *n + 6;
    t = 1. / sqrt(2.);
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	indx[j] = j;
/* L10: */
    }
    dscal_(n, &t, &z__[1], &c__1);
    *rho = (d__1 = *rho * 2., abs(d__1));

/*     Sort the eigenvalues into increasing order */

    i__1 = *n;
    for (i__ = *cutpnt + 1; i__ <= i__1; ++i__) {
	indxq[i__] += *cutpnt;
/* L20: */
    }
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	dlamda[i__] = d__[indxq[i__]];
	w[i__] = z__[indxq[i__]];
/* L30: */
    }
    i__ = 1;
    j = *cutpnt + 1;
    dlamrg_(&n1, &n2, &dlamda[1], &c__1, &c__1, &indx[1]);
    i__1 = *n;
    for (i__ = 1; i__ <= i__1; ++i__) {
	d__[i__] = dlamda[indx[i__]];
	z__[i__] = w[indx[i__]];
/* L40: */
    }

/*     Calculate the allowable deflation tolerence */

    imax = idamax_(n, &z__[1], &c__1);
    jmax = idamax_(n, &d__[1], &c__1);
    eps = dlamch_("Epsilon");
    tol = eps * 8. * (d__1 = d__[jmax], abs(d__1));

/*     If the rank-1 modifier is small enough, no more needs to be done   
       except to reorganize Q so that its columns correspond with the   
       elements in D. */

    if (*rho * (d__1 = z__[imax], abs(d__1)) <= tol) {
	*k = 0;
	if (*icompq == 0) {
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		perm[j] = indxq[indx[j]];
/* L50: */
	    }
	} else {
	    i__1 = *n;
	    for (j = 1; j <= i__1; ++j) {
		perm[j] = indxq[indx[j]];
		dcopy_(qsiz, &q_ref(1, perm[j]), &c__1, &q2_ref(1, j), &c__1);
/* L60: */
	    }
	    dlacpy_("A", qsiz, n, &q2_ref(1, 1), ldq2, &q_ref(1, 1), ldq);
	}
	return 0;
    }

/*     If there are multiple eigenvalues then the problem deflates.  Here   
       the number of equal eigenvalues are found.  As each equal   
       eigenvalue is found, an elementary reflector is computed to rotate   
       the corresponding eigensubspace so that the corresponding   
       components of Z are zero in this new basis. */

    *k = 0;
    *givptr = 0;
    k2 = *n + 1;
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
	latime_1.ops += 1;
	if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {

/*           Deflate due to small z component. */

	    --k2;
	    indxp[k2] = j;
	    if (j == *n) {
		goto L110;
	    }
	} else {
	    jlam = j;
	    goto L80;
	}
/* L70: */
    }
L80:
    ++j;
    if (j > *n) {
	goto L100;
    }
    latime_1.ops += 1;
    if (*rho * (d__1 = z__[j], abs(d__1)) <= tol) {

/*        Deflate due to small z component. */

	--k2;
	indxp[k2] = j;
    } else {

/*        Check if eigenvalues are close enough to allow deflation. */

	s = z__[jlam];
	c__ = z__[j];

/*        Find sqrt(a**2+b**2) without overflow or   
          destructive underflow. */

	latime_1.ops += 10;
	tau = dlapy2_(&c__, &s);
	t = d__[j] - d__[jlam];
	c__ /= tau;
	s = -s / tau;
	if ((d__1 = t * c__ * s, abs(d__1)) <= tol) {

/*           Deflation is possible. */

	    z__[j] = tau;
	    z__[jlam] = 0.;

/*           Record the appropriate Givens rotation */

	    ++(*givptr);
	    givcol_ref(1, *givptr) = indxq[indx[jlam]];
	    givcol_ref(2, *givptr) = indxq[indx[j]];
	    givnum_ref(1, *givptr) = c__;
	    givnum_ref(2, *givptr) = s;
	    if (*icompq == 1) {
		latime_1.ops += *qsiz * 6;
		drot_(qsiz, &q_ref(1, indxq[indx[jlam]]), &c__1, &q_ref(1, 
			indxq[indx[j]]), &c__1, &c__, &s);
	    }
	    latime_1.ops += 10;
	    t = d__[jlam] * c__ * c__ + d__[j] * s * s;
	    d__[j] = d__[jlam] * s * s + d__[j] * c__ * c__;
	    d__[jlam] = t;
	    --k2;
	    i__ = 1;
L90:
	    if (k2 + i__ <= *n) {
		if (d__[jlam] < d__[indxp[k2 + i__]]) {
		    indxp[k2 + i__ - 1] = indxp[k2 + i__];
		    indxp[k2 + i__] = jlam;
		    ++i__;
		    goto L90;
		} else {
		    indxp[k2 + i__ - 1] = jlam;
		}
	    } else {
		indxp[k2 + i__ - 1] = jlam;
	    }
	    jlam = j;
	} else {
	    ++(*k);
	    w[*k] = z__[jlam];
	    dlamda[*k] = d__[jlam];
	    indxp[*k] = jlam;
	    jlam = j;
	}
    }
    goto L80;
L100:

/*     Record the last eigenvalue. */

    ++(*k);
    w[*k] = z__[jlam];
    dlamda[*k] = d__[jlam];
    indxp[*k] = jlam;

L110:

/*     Sort the eigenvalues and corresponding eigenvectors into DLAMDA   
       and Q2 respectively.  The eigenvalues/vectors which were not   
       deflated go into the first K slots of DLAMDA and Q2 respectively,   
       while those which were deflated go into the last N - K slots. */

    if (*icompq == 0) {
	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    jp = indxp[j];
	    dlamda[j] = d__[jp];
	    perm[j] = indxq[indx[jp]];
/* L120: */
	}
    } else {
	i__1 = *n;
	for (j = 1; j <= i__1; ++j) {
	    jp = indxp[j];
	    dlamda[j] = d__[jp];
	    perm[j] = indxq[indx[jp]];
	    dcopy_(qsiz, &q_ref(1, perm[j]), &c__1, &q2_ref(1, j), &c__1);
/* L130: */
	}
    }

/*     The deflated eigenvalues and their corresponding vectors go back   
       into the last N - K slots of D and Q respectively. */

    if (*k < *n) {
	if (*icompq == 0) {
	    i__1 = *n - *k;
	    dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
	} else {
	    i__1 = *n - *k;
	    dcopy_(&i__1, &dlamda[*k + 1], &c__1, &d__[*k + 1], &c__1);
	    i__1 = *n - *k;
	    dlacpy_("A", qsiz, &i__1, &q2_ref(1, *k + 1), ldq2, &q_ref(1, *k 
		    + 1), ldq);
	}
    }

    return 0;

/*     End of DLAED8 */

} /* dlaed8_ */

#undef givnum_ref
#undef givcol_ref
#undef q2_ref
#undef q_ref


