text: #include "clapack.h"
  
  /* Table of constant values */
  
  static integer c__1 = 1;
  
  /* Subroutine */ int slaed9_(integer *k, integer *kstart, integer *kstop, 
  	integer *n, real *d__, real *q, integer *ldq, real *rho, real *dlamda, 
  	 real *w, real *s, integer *lds, integer *info)
  {
      /* System generated locals */
      integer q_dim1, q_offset, s_dim1, s_offset, i__1, i__2;
      real r__1;
  
      /* Builtin functions */
      double sqrt(doublereal), r_sign(real *, real *);
  
      /* Local variables */
      integer i__, j;
      real temp;
      extern doublereal snrm2_(integer *, real *, integer *);
      extern /* Subroutine */ int 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 *);
  
  
  /*  -- LAPACK routine (version 3.1) -- */
  /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
  /*     November 2006 */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  SLAED9 finds the roots of the secular equation, as defined by the */
  /*  values in D, Z, and RHO, between KSTART and KSTOP.  It makes the */
  /*  appropriate calls to SLAED4 and then stores the new matrix of */
  /*  eigenvectors for use in calculating the next level of Z vectors. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  K       (input) INTEGER */
  /*          The number of terms in the rational function to be solved by */
  /*          SLAED4.  K >= 0. */
  
  /*  KSTART  (input) INTEGER */
  /*  KSTOP   (input) INTEGER */
  /*          The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP */
  /*          are to be computed.  1 <= KSTART <= KSTOP <= K. */
  
  /*  N       (input) INTEGER */
  /*          The number of rows and columns in the Q matrix. */
  /*          N >= K (delation may result in N > K). */
  
  /*  D       (output) REAL array, dimension (N) */
  /*          D(I) contains the updated eigenvalues */
  /*          for KSTART <= I <= KSTOP. */
  
  /*  Q       (workspace) REAL array, dimension (LDQ,N) */
  
  /*  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) 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. */
  
  /*  W       (input) REAL array, dimension (K) */
  /*          The first K elements of this array contain the components */
  /*          of the deflation-adjusted updating vector. */
  
  /*  S       (output) REAL array, dimension (LDS, K) */
  /*          Will contain the eigenvectors of the repaired matrix which */
  /*          will be stored for subsequent Z vector calculation and */
  /*          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 */
  
  /*  ===================================================================== */
  
  /*     .. 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;
      --w;
      s_dim1 = *lds;
      s_offset = 1 + s_dim1;
      s -= s_offset;
  
      /* Function Body */
      *info = 0;
  
      if (*k < 0) {
  	*info = -1;
      } else if (*kstart < 1 || *kstart > max(1,*k)) {
  	*info = -2;
      } else if (max(1,*kstop) < *kstart || *kstop > max(1,*k)) {
  	*info = -3;
      } else if (*n < *k) {
  	*info = -4;
      } else if (*ldq < max(1,*k)) {
  	*info = -7;
      } else if (*lds < max(1,*k)) {
  	*info = -12;
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("SLAED9", &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 = *n;
      for (i__ = 1; i__ <= i__1; ++i__) {
  	dlamda[i__] = slamc3_(&dlamda[i__], &dlamda[i__]) - dlamda[i__];
  /* L10: */
      }
  
      i__1 = *kstop;
      for (j = *kstart; 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 || *k == 2) {
  	i__1 = *k;
  	for (i__ = 1; i__ <= i__1; ++i__) {
  	    i__2 = *k;
  	    for (j = 1; j <= i__2; ++j) {
  		s[j + i__ * s_dim1] = q[j + i__ * q_dim1];
  /* L30: */
  	    }
  /* L40: */
  	}
  	goto L120;
      }
  
  /*     Compute updated W. */
  
      scopy_(k, &w[1], &c__1, &s[s_offset], &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]);
  /* L50: */
  	}
  	i__2 = *k;
  	for (i__ = j + 1; i__ <= i__2; ++i__) {
  	    w[i__] *= q[i__ + j * q_dim1] / (dlamda[i__] - dlamda[j]);
  /* L60: */
  	}
  /* L70: */
      }
      i__1 = *k;
      for (i__ = 1; i__ <= i__1; ++i__) {
  	r__1 = sqrt(-w[i__]);
  	w[i__] = r_sign(&r__1, &s[i__ + s_dim1]);
  /* L80: */
      }
  
  /*     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__) {
  	    q[i__ + j * q_dim1] = w[i__] / q[i__ + j * q_dim1];
  /* L90: */
  	}
  	temp = snrm2_(k, &q[j * q_dim1 + 1], &c__1);
  	i__2 = *k;
  	for (i__ = 1; i__ <= i__2; ++i__) {
  	    s[i__ + j * s_dim1] = q[i__ + j * q_dim1] / temp;
  /* L100: */
  	}
  /* L110: */
      }
  
  L120:
      return 0;
  
  /*     End of SLAED9 */
  
  } /* slaed9_ */
  