text: /* ../netlib/dstedc.f -- translated by f2c (version 20100827). 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 "FLA_f2c.h" /* Table of constant values */
  static integer c__9 = 9;
  static integer c__0 = 0;
  static integer c__2 = 2;
  static doublereal c_b17 = 0.;
  static doublereal c_b18 = 1.;
  static integer c__1 = 1;
  /* > \brief \b DSTEBZ */
  /* =========== DOCUMENTATION =========== */
  /* Online html documentation available at */
  /* http://www.netlib.org/lapack/explore-html/ */
  /* > \htmlonly */
  /* > Download DSTEDC + dependencies */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstedc. f"> */
  /* > [TGZ]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstedc. f"> */
  /* > [ZIP]</a> */
  /* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstedc. f"> */
  /* > [TXT]</a> */
  /* > \endhtmlonly */
  /* Definition: */
  /* =========== */
  /* SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, */
  /* LIWORK, INFO ) */
  /* .. Scalar Arguments .. */
  /* CHARACTER COMPZ */
  /* INTEGER INFO, LDZ, LIWORK, LWORK, N */
  /* .. */
  /* .. Array Arguments .. */
  /* INTEGER IWORK( * ) */
  /* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) */
  /* .. */
  /* > \par Purpose: */
  /* ============= */
  /* > */
  /* > \verbatim */
  /* > */
  /* > DSTEDC computes all eigenvalues and, optionally, eigenvectors of a */
  /* > symmetric tridiagonal matrix using the divide and conquer method. */
  /* > The eigenvectors of a full or band real symmetric matrix can also be */
  /* > found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this */
  /* > matrix to tridiagonal form. */
  /* > */
  /* > 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. See DLAED3 for details. */
  /* > \endverbatim */
  /* Arguments: */
  /* ========== */
  /* > \param[in] COMPZ */
  /* > \verbatim */
  /* > COMPZ is CHARACTER*1 */
  /* > = 'N': Compute eigenvalues only. */
  /* > = 'I': Compute eigenvectors of tridiagonal matrix also. */
  /* > = 'V': Compute eigenvectors of original dense symmetric */
  /* > matrix also. On entry, Z contains the orthogonal */
  /* > matrix used to reduce the original matrix to */
  /* > tridiagonal form. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] N */
  /* > \verbatim */
  /* > N is INTEGER */
  /* > The dimension of the symmetric tridiagonal matrix. N >= 0. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] D */
  /* > \verbatim */
  /* > D is DOUBLE PRECISION array, dimension (N) */
  /* > On entry, the diagonal elements of the tridiagonal matrix. */
  /* > On exit, if INFO = 0, the eigenvalues in ascending order. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] E */
  /* > \verbatim */
  /* > E is DOUBLE PRECISION array, dimension (N-1) */
  /* > On entry, the subdiagonal elements of the tridiagonal matrix. */
  /* > On exit, E has been destroyed. */
  /* > \endverbatim */
  /* > */
  /* > \param[in,out] Z */
  /* > \verbatim */
  /* > Z is DOUBLE PRECISION array, dimension (LDZ,N) */
  /* > On entry, if COMPZ = 'V', then Z contains the orthogonal */
  /* > matrix used in the reduction to tridiagonal form. */
  /* > On exit, if INFO = 0, then if COMPZ = 'V', Z contains the */
  /* > orthonormal eigenvectors of the original symmetric matrix, */
  /* > and if COMPZ = 'I', Z contains the orthonormal eigenvectors */
  /* > of the symmetric tridiagonal matrix. */
  /* > If COMPZ = 'N', then Z is not referenced. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LDZ */
  /* > \verbatim */
  /* > LDZ is INTEGER */
  /* > The leading dimension of the array Z. LDZ >= 1. */
  /* > If eigenvectors are desired, then LDZ >= max(1,N). */
  /* > \endverbatim */
  /* > */
  /* > \param[out] WORK */
  /* > \verbatim */
  /* > WORK is DOUBLE PRECISION array, */
  /* > dimension (LWORK) */
  /* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LWORK */
  /* > \verbatim */
  /* > LWORK is INTEGER */
  /* > The dimension of the array WORK. */
  /* > If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. */
  /* > If COMPZ = 'V' and N > 1 then LWORK must be at least */
  /* > ( 1 + 3*N + 2*N*lg N + 4*N**2 ), */
  /* > where lg( N ) = smallest integer k such */
  /* > that 2**k >= N. */
  /* > If COMPZ = 'I' and N > 1 then LWORK must be at least */
  /* > ( 1 + 4*N + N**2 ). */
  /* > Note that for COMPZ = 'I' or 'V', then if N is less than or */
  /* > equal to the minimum divide size, usually 25, then LWORK need */
  /* > only be max(1,2*(N-1)). */
  /* > */
  /* > If LWORK = -1, then a workspace query is assumed;
  the routine */
  /* > only calculates the optimal size of the WORK array, returns */
  /* > this value as the first entry of the WORK array, and no error */
  /* > message related to LWORK is issued by XERBLA. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] IWORK */
  /* > \verbatim */
  /* > IWORK is INTEGER array, dimension (MAX(1,LIWORK)) */
  /* > On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. */
  /* > \endverbatim */
  /* > */
  /* > \param[in] LIWORK */
  /* > \verbatim */
  /* > LIWORK is INTEGER */
  /* > The dimension of the array IWORK. */
  /* > If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. */
  /* > If COMPZ = 'V' and N > 1 then LIWORK must be at least */
  /* > ( 6 + 6*N + 5*N*lg N ). */
  /* > If COMPZ = 'I' and N > 1 then LIWORK must be at least */
  /* > ( 3 + 5*N ). */
  /* > Note that for COMPZ = 'I' or 'V', then if N is less than or */
  /* > equal to the minimum divide size, usually 25, then LIWORK */
  /* > need only be 1. */
  /* > */
  /* > If LIWORK = -1, then a workspace query is assumed;
  the */
  /* > routine only calculates the optimal size of the IWORK array, */
  /* > returns this value as the first entry of the IWORK array, and */
  /* > no error message related to LIWORK is issued by XERBLA. */
  /* > \endverbatim */
  /* > */
  /* > \param[out] INFO */
  /* > \verbatim */
  /* > INFO is INTEGER */
  /* > = 0: successful exit. */
  /* > < 0: if INFO = -i, the i-th argument had an illegal value. */
  /* > > 0: The algorithm failed to compute an eigenvalue while */
  /* > working on the submatrix lying in rows and columns */
  /* > INFO/(N+1) through mod(INFO,N+1). */
  /* > \endverbatim */
  /* Authors: */
  /* ======== */
  /* > \author Univ. of Tennessee */
  /* > \author Univ. of California Berkeley */
  /* > \author Univ. of Colorado Denver */
  /* > \author NAG Ltd. */
  /* > \date November 2011 */
  /* > \ingroup auxOTHERcomputational */
  /* > \par Contributors: */
  /* ================== */
  /* > */
  /* > Jeff Rutter, Computer Science Division, University of California */
  /* > at Berkeley, USA \n */
  /* > Modified by Francoise Tisseur, University of Tennessee */
  /* > */
  /* ===================================================================== */
  /* Subroutine */
  int dstedc_(char *compz, integer *n, doublereal *d__, doublereal *e, doublereal *z__, integer *ldz, doublereal *work, integer *lwork, integer *iwork, integer *liwork, integer *info)
  {
      /* System generated locals */
      integer z_dim1, z_offset, i__1, i__2;
      doublereal d__1, d__2;
      /* Builtin functions */
      double log(doublereal);
      integer pow_ii(integer *, integer *);
      double sqrt(doublereal);
      /* Local variables */
      integer i__, j, k, m;
      doublereal p;
      integer ii, lgn;
      doublereal eps, tiny;
      extern /* Subroutine */
      int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *);
      extern logical lsame_(char *, char *);
      extern /* Subroutine */
      int dswap_(integer *, doublereal *, integer *, doublereal *, integer *);
      integer lwmin;
      extern /* Subroutine */
      int dlaed0_(integer *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, integer *, integer *);
      integer start;
      extern doublereal dlamch_(char *);
      extern /* Subroutine */
      int dlascl_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, integer *), dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *), dlaset_(char *, integer *, integer *, doublereal *, doublereal *, doublereal *, integer *);
      extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *);
      extern /* Subroutine */
      int xerbla_(char *, integer *);
      integer finish;
      extern doublereal dlanst_(char *, integer *, doublereal *, doublereal *);
      extern /* Subroutine */
      int dsterf_(integer *, doublereal *, doublereal *, integer *), dlasrt_(char *, integer *, doublereal *, integer *);
      integer liwmin, icompz;
      extern /* Subroutine */
      int dsteqr_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *);
      doublereal orgnrm;
      logical lquery;
      integer smlsiz, storez, strtrw;
      /* -- LAPACK computational routine (version 3.4.0) -- */
      /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
      /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
      /* November 2011 */
      /* .. Scalar Arguments .. */
      /* .. */
      /* .. Array Arguments .. */
      /* .. */
      /* ===================================================================== */
      /* .. Parameters .. */
      /* .. */
      /* .. Local Scalars .. */
      /* .. */
      /* .. External Functions .. */
      /* .. */
      /* .. External Subroutines .. */
      /* .. */
      /* .. Intrinsic Functions .. */
      /* .. */
      /* .. Executable Statements .. */
      /* Test the input parameters. */
      /* Parameter adjustments */
      --d__;
      --e;
      z_dim1 = *ldz;
      z_offset = 1 + z_dim1;
      z__ -= z_offset;
      --work;
      --iwork;
      /* Function Body */
      *info = 0;
      lquery = *lwork == -1 || *liwork == -1;
      if (lsame_(compz, "N"))
      {
          icompz = 0;
      }
      else if (lsame_(compz, "V"))
      {
          icompz = 1;
      }
      else if (lsame_(compz, "I"))
      {
          icompz = 2;
      }
      else
      {
          icompz = -1;
      }
      if (icompz < 0)
      {
          *info = -1;
      }
      else if (*n < 0)
      {
          *info = -2;
      }
      else if (*ldz < 1 || icompz > 0 && *ldz < max(1,*n))
      {
          *info = -6;
      }
      if (*info == 0)
      {
          /* Compute the workspace requirements */
          smlsiz = ilaenv_(&c__9, "DSTEDC", " ", &c__0, &c__0, &c__0, &c__0);
          if (*n <= 1 || icompz == 0)
          {
              liwmin = 1;
              lwmin = 1;
          }
          else if (*n <= smlsiz)
          {
              liwmin = 1;
              lwmin = *n - 1 << 1;
          }
          else
          {
              lgn = (integer) (log((doublereal) (*n)) / log(2.));
              if (pow_ii(&c__2, &lgn) < *n)
              {
                  ++lgn;
              }
              if (pow_ii(&c__2, &lgn) < *n)
              {
                  ++lgn;
              }
              if (icompz == 1)
              {
                  /* Computing 2nd power */
                  i__1 = *n;
                  lwmin = *n * 3 + 1 + (*n << 1) * lgn + (i__1 * i__1 << 2);
                  liwmin = *n * 6 + 6 + *n * 5 * lgn;
              }
              else if (icompz == 2)
              {
                  /* Computing 2nd power */
                  i__1 = *n;
                  lwmin = (*n << 2) + 1 + i__1 * i__1;
                  liwmin = *n * 5 + 3;
              }
          }
          work[1] = (doublereal) lwmin;
          iwork[1] = liwmin;
          if (*lwork < lwmin && ! lquery)
          {
              *info = -8;
          }
          else if (*liwork < liwmin && ! lquery)
          {
              *info = -10;
          }
      }
      if (*info != 0)
      {
          i__1 = -(*info);
          xerbla_("DSTEDC", &i__1);
          return 0;
      }
      else if (lquery)
      {
          return 0;
      }
      /* Quick return if possible */
      if (*n == 0)
      {
          return 0;
      }
      if (*n == 1)
      {
          if (icompz != 0)
          {
              z__[z_dim1 + 1] = 1.;
          }
          return 0;
      }
      /* If the following conditional clause is removed, then the routine */
      /* will use the Divide and Conquer routine to compute only the */
      /* eigenvalues, which requires (3N + 3N**2) real workspace and */
      /* (2 + 5N + 2N lg(N)) integer workspace. */
      /* Since on many architectures DSTERF is much faster than any other */
      /* algorithm for finding eigenvalues only, it is used here */
      /* as the default. If the conditional clause is removed, then */
      /* information on the size of workspace needs to be changed. */
      /* If COMPZ = 'N', use DSTERF to compute the eigenvalues. */
      if (icompz == 0)
      {
          dsterf_(n, &d__[1], &e[1], info);
          goto L50;
      }
      /* If N is smaller than the minimum divide size (SMLSIZ+1), then */
      /* solve the problem with another solver. */
      if (*n <= smlsiz)
      {
          dsteqr_(compz, n, &d__[1], &e[1], &z__[z_offset], ldz, &work[1], info);
      }
      else
      {
          /* If COMPZ = 'V', the Z matrix must be stored elsewhere for later */
          /* use. */
          if (icompz == 1)
          {
              storez = *n * *n + 1;
          }
          else
          {
              storez = 1;
          }
          if (icompz == 2)
          {
              dlaset_("Full", n, n, &c_b17, &c_b18, &z__[z_offset], ldz);
          }
          /* Scale. */
          orgnrm = dlanst_("M", n, &d__[1], &e[1]);
          if (orgnrm == 0.)
          {
              goto L50;
          }
          eps = dlamch_("Epsilon");
          start = 1;
          /* while ( START <= N ) */
  L10:
          if (start <= *n)
          {
              /* Let FINISH be the position of the next subdiagonal entry */
              /* such that E( FINISH ) <= TINY or FINISH = N if no such */
              /* subdiagonal exists. The matrix identified by the elements */
              /* between START and FINISH constitutes an independent */
              /* sub-problem. */
              finish = start;
  L20:
              if (finish < *n)
              {
                  tiny = eps * sqrt((d__1 = d__[finish], f2c_abs(d__1))) * sqrt(( d__2 = d__[finish + 1], f2c_abs(d__2)));
                  if ((d__1 = e[finish], f2c_abs(d__1)) > tiny)
                  {
                      ++finish;
                      goto L20;
                  }
              }
              /* (Sub) Problem determined. Compute its size and solve it. */
              m = finish - start + 1;
              if (m == 1)
              {
                  start = finish + 1;
                  goto L10;
              }
              if (m > smlsiz)
              {
                  /* Scale. */
                  orgnrm = dlanst_("M", &m, &d__[start], &e[start]);
                  dlascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &m, &c__1, &d__[ start], &m, info);
                  i__1 = m - 1;
                  i__2 = m - 1;
                  dlascl_("G", &c__0, &c__0, &orgnrm, &c_b18, &i__1, &c__1, &e[ start], &i__2, info);
                  if (icompz == 1)
                  {
                      strtrw = 1;
                  }
                  else
                  {
                      strtrw = start;
                  }
                  dlaed0_(&icompz, n, &m, &d__[start], &e[start], &z__[strtrw + start * z_dim1], ldz, &work[1], n, &work[storez], & iwork[1], info);
                  if (*info != 0)
                  {
                      *info = (*info / (m + 1) + start - 1) * (*n + 1) + *info % (m + 1) + start - 1;
                      goto L50;
                  }
                  /* Scale back. */
                  dlascl_("G", &c__0, &c__0, &c_b18, &orgnrm, &m, &c__1, &d__[ start], &m, info);
              }
              else
              {
                  if (icompz == 1)
                  {
                      /* Since QR won't update a Z matrix which is larger than */
                      /* the length of D, we must solve the sub-problem in a */
                      /* workspace and then multiply back into Z. */
                      dsteqr_("I", &m, &d__[start], &e[start], &work[1], &m, & work[m * m + 1], info);
                      dlacpy_("A", n, &m, &z__[start * z_dim1 + 1], ldz, &work[ storez], n);
                      dgemm_("N", "N", n, &m, &m, &c_b18, &work[storez], n, & work[1], &m, &c_b17, &z__[start * z_dim1 + 1], ldz);
                  }
                  else if (icompz == 2)
                  {
                      dsteqr_("I", &m, &d__[start], &e[start], &z__[start + start * z_dim1], ldz, &work[1], info);
                  }
                  else
                  {
                      dsterf_(&m, &d__[start], &e[start], info);
                  }
                  if (*info != 0)
                  {
                      *info = start * (*n + 1) + finish;
                      goto L50;
                  }
              }
              start = finish + 1;
              goto L10;
          }
          /* endwhile */
          /* If the problem split any number of times, then the eigenvalues */
          /* will not be properly ordered. Here we permute the eigenvalues */
          /* (and the associated eigenvectors) into ascending order. */
          if (m != *n)
          {
              if (icompz == 0)
              {
                  /* Use Quick Sort */
                  dlasrt_("I", n, &d__[1], info);
              }
              else
              {
                  /* Use Selection Sort to minimize swaps of eigenvectors */
                  i__1 = *n;
                  for (ii = 2;
                          ii <= i__1;
                          ++ii)
                  {
                      i__ = ii - 1;
                      k = i__;
                      p = d__[i__];
                      i__2 = *n;
                      for (j = ii;
                              j <= i__2;
                              ++j)
                      {
                          if (d__[j] < p)
                          {
                              k = j;
                              p = d__[j];
                          }
                          /* L30: */
                      }
                      if (k != i__)
                      {
                          d__[k] = d__[i__];
                          d__[i__] = p;
                          dswap_(n, &z__[i__ * z_dim1 + 1], &c__1, &z__[k * z_dim1 + 1], &c__1);
                      }
                      /* L40: */
                  }
              }
          }
      }
  L50:
      work[1] = (doublereal) lwmin;
      iwork[1] = liwmin;
      return 0;
      /* End of DSTEDC */
  }
  /* dstedc_ */
  