slaed3.c

/* slaed3.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 "clapack.h"


/* Table of constant values */

static integer c__1 = 1;
static real c_b22 = 1.f;
static real c_b23 = 0.f;

/* Subroutine */ int slaed3_(integer *k, integer *n, integer *n1, real *d__, 
	real *q, integer *ldq, real *rho, real *dlamda, real *q2, integer *
	indx, integer *ctot, real *w, real *s, integer *info)
{
    /* System generated locals */
    integer q_dim1, q_offset, i__1, i__2;
    real r__1;

    /* Builtin functions */
    double sqrt(doublereal), r_sign(real *, real *);

    /* Local variables */
    integer i__, j, n2, n12, ii, n23, iq2;
    real temp;
    extern doublereal snrm2_(integer *, real *, integer *);
    extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, real *, 
	    real *, integer *), scopy_(integer *, real *, 
	    integer *, real *, integer *), slaed4_(integer *, integer *, real 
	    *, real *, real *, real *, real *, integer *);
    extern doublereal slamc3_(real *, real *);
    extern /* Subroutine */ int xerbla_(char *, integer *), slacpy_(
	    char *, integer *, integer *, real *, integer *, real *, integer *
), slaset_(char *, integer *, integer *, real *, real *, 
	    real *, integer *);


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  SLAED3 finds the roots of the secular equation, as defined by the */
/*  values in D, W, and RHO, between 1 and K.  It makes the */
/*  appropriate calls to SLAED4 and then updates the eigenvectors by */
/*  multiplying the matrix of eigenvectors of the pair of eigensystems */
/*  being combined by the matrix of eigenvectors of the K-by-K system */
/*  which is solved here. */

/*  This code makes very mild assumptions about floating point */
/*  arithmetic. It will work on machines with a guard digit in */
/*  add/subtract, or on those binary machines without guard digits */
/*  which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. */
/*  It could conceivably fail on hexadecimal or decimal machines */
/*  without guard digits, but we know of none. */

/*  Arguments */
/*  ========= */

/*  K       (input) INTEGER */
/*          The number of terms in the rational function to be solved by */
/*          SLAED4.  K >= 0. */

/*  N       (input) INTEGER */
/*          The number of rows and columns in the Q matrix. */
/*          N >= K (deflation may result in N>K). */

/*  N1      (input) INTEGER */
/*          The location of the last eigenvalue in the leading submatrix. */
/*          min(1,N) <= N1 <= N/2. */

/*  D       (output) REAL array, dimension (N) */
/*          D(I) contains the updated eigenvalues for */
/*          1 <= I <= K. */

/*  Q       (output) REAL array, dimension (LDQ,N) */
/*          Initially the first K columns are used as workspace. */
/*          On output the columns 1 to K contain */
/*          the updated eigenvectors. */

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

/*  RHO     (input) REAL */
/*          The value of the parameter in the rank one update equation. */
/*          RHO >= 0 required. */

/*  DLAMDA  (input/output) REAL array, dimension (K) */
/*          The first K elements of this array contain the old roots */
/*          of the deflated updating problem.  These are the poles */
/*          of the secular equation. May be changed on output by */
/*          having lowest order bit set to zero on Cray X-MP, Cray Y-MP, */
/*          Cray-2, or Cray C-90, as described above. */

/*  Q2      (input) REAL array, dimension (LDQ2, N) */
/*          The first K columns of this matrix contain the non-deflated */
/*          eigenvectors for the split problem. */

/*  INDX    (input) INTEGER array, dimension (N) */
/*          The permutation used to arrange the columns of the deflated */
/*          Q matrix into three groups (see SLAED2). */
/*          The rows of the eigenvectors found by SLAED4 must be likewise */
/*          permuted before the matrix multiply can take place. */

/*  CTOT    (input) INTEGER array, dimension (4) */
/*          A count of the total number of the various types of columns */
/*          in Q, as described in INDX.  The fourth column type is any */
/*          column which has been deflated. */

/*  W       (input/output) REAL array, dimension (K) */
/*          The first K elements of this array contain the components */
/*          of the deflation-adjusted updating vector. Destroyed on */
/*          output. */

/*  S       (workspace) REAL array, dimension (N1 + 1)*K */
/*          Will contain the eigenvectors of the repaired matrix which */
/*          will be multiplied by the previously accumulated eigenvectors */
/*          to update the system. */

/*  LDS     (input) INTEGER */
/*          The leading dimension of S.  LDS >= max(1,K). */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit. */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/*          > 0:  if INFO = 1, an eigenvalue did not converge */

/*  Further Details */
/*  =============== */

/*  Based on contributions by */
/*     Jeff Rutter, Computer Science Division, University of California */
/*     at Berkeley, USA */
/*  Modified by Francoise Tisseur, University of Tennessee. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    --d__;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1;
    q -= q_offset;
    --dlamda;
    --q2;
    --indx;
    --ctot;
    --w;
    --s;

    /* Function Body */
    *info = 0;

    if (*k < 0) {
	*info = -1;
    } else if (*n < *k) {
	*info = -2;
    } else if (*ldq < max(1,*n)) {
	*info = -6;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SLAED3", &i__1);
	return 0;
    }

/*     Quick return if possible */

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

/*     Modify values DLAMDA(i) to make sure all DLAMDA(i)-DLAMDA(j) can */
/*     be computed with high relative accuracy (barring over/underflow). */
/*     This is a problem on machines without a guard digit in */
/*     add/subtract (Cray XMP, Cray YMP, Cray C 90 and Cray 2). */
/*     The following code replaces DLAMDA(I) by 2*DLAMDA(I)-DLAMDA(I), */
/*     which on any of these machines zeros out the bottommost */
/*     bit of DLAMDA(I) if it is 1; this makes the subsequent */
/*     subtractions DLAMDA(I)-DLAMDA(J) unproblematic when cancellation */
/*     occurs. On binary machines with a guard digit (almost all */
/*     machines) it does not change DLAMDA(I) at all. On hexadecimal */
/*     and decimal machines with a guard digit, it slightly */
/*     changes the bottommost bits of DLAMDA(I). It does not account */
/*     for hexadecimal or decimal machines without guard digits */
/*     (we know of none). We use a subroutine call to compute */
/*     2*DLAMBDA(I) to prevent optimizing compilers from eliminating */
/*     this code. */

    i__1 = *k;
    for (i__ = 1; i__ <= i__1; ++i__) {
	dlamda[i__] = slamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
/* L10: */
    }

    i__1 = *k;
    for (j = 1; j <= i__1; ++j) {
	slaed4_(k, &j, &dlamda[1], &w[1], &q[j * q_dim1 + 1], rho, &d__[j], 
		info);

/*        If the zero finder fails, the computation is terminated. */

	if (*info != 0) {
	    goto L120;
	}
/* L20: */
    }

    if (*k == 1) {
	goto L110;
    }
    if (*k == 2) {
	i__1 = *k;
	for (j = 1; j <= i__1; ++j) {
	    w[1] = q[j * q_dim1 + 1];
	    w[2] = q[j * q_dim1 + 2];
	    ii = indx[1];
	    q[j * q_dim1 + 1] = w[ii];
	    ii = indx[2];
	    q[j * q_dim1 + 2] = w[ii];
/* L30: */
	}
	goto L110;
    }

/*     Compute updated W. */

    scopy_(k, &w[1], &c__1, &s[1], &c__1);

/*     Initialize W(I) = Q(I,I) */

    i__1 = *ldq + 1;
    scopy_(k, &q[q_offset], &i__1, &w[1], &c__1);
    i__1 = *k;
    for (j = 1; j <= i__1; ++j) {
	i__2 = j - 1;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
/* L40: */
	}
	i__2 = *k;
	for (i__ = j + 1; i__ <= i__2; ++i__) {
	    w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
/* L50: */
	}
/* L60: */
    }
    i__1 = *k;
    for (i__ = 1; i__ <= i__1; ++i__) {
	r__1 = sqrt(-w[i__]);
	w[i__] = r_sign(&r__1, &s[i__]);
/* L70: */
    }

/*     Compute eigenvectors of the modified rank-1 modification. */

    i__1 = *k;
    for (j = 1; j <= i__1; ++j) {
	i__2 = *k;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    s[i__] = w[i__] / q[i__ + j * q_dim1];
/* L80: */
	}
	temp = snrm2_(k, &s[1], &c__1);
	i__2 = *k;
	for (i__ = 1; i__ <= i__2; ++i__) {
	    ii = indx[i__];
	    q[i__ + j * q_dim1] = s[ii] / temp;
/* L90: */
	}
/* L100: */
    }

/*     Compute the updated eigenvectors. */

L110:

    n2 = *n - *n1;
    n12 = ctot[1] + ctot[2];
    n23 = ctot[2] + ctot[3];

    slacpy_("A", &n23, k, &q[ctot[1] + 1 + q_dim1], ldq, &s[1], &n23);
    iq2 = *n1 * n12 + 1;
    if (n23 != 0) {
	sgemm_("N", "N", &n2, k, &n23, &c_b22, &q2[iq2], &n2, &s[1], &n23, &
		c_b23, &q[*n1 + 1 + q_dim1], ldq);
    } else {
	slaset_("A", &n2, k, &c_b23, &c_b23, &q[*n1 + 1 + q_dim1], ldq);
    }

    slacpy_("A", &n12, k, &q[q_offset], ldq, &s[1], &n12);
    if (n12 != 0) {
	sgemm_("N", "N", n1, k, &n12, &c_b22, &q2[1], n1, &s[1], &n12, &c_b23, 
		 &q[q_offset], ldq);
    } else {
	slaset_("A", n1, k, &c_b23, &c_b23, &q[q_dim1 + 1], ldq);
    }


L120:
    return 0;

/*     End of SLAED3 */

} /* slaed3_ */