text: /* 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_ */
  