chol.cc

Go to the documentation of this file.

/*

Copyright (C) 1994-2018 John W. Eaton
Copyright (C) 2008-2009 Jaroslav Hajek

This file is part of Octave.

Octave is free software: you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

Octave is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License
along with Octave; see the file COPYING.  If not, see
<https://www.gnu.org/licenses/>.

*/

#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif

#include "Array.h"
#include "CColVector.h"
#include "CMatrix.h"
#include "chol.h"
#include "dColVector.h"
#include "dMatrix.h"
#include "fCColVector.h"
#include "fCMatrix.h"
#include "fColVector.h"
#include "fMatrix.h"
#include "lo-error.h"
#include "lo-lapack-proto.h"
#include "lo-qrupdate-proto.h"
#include "oct-locbuf.h"
#include "oct-norm.h"

#if ! defined (HAVE_QRUPDATE)
#  include "qr.h"
#endif

static Matrix
chol2inv_internal (const Matrix& r, bool is_upper = true)
{
  Matrix retval;

  octave_idx_type r_nr = r.rows ();
  octave_idx_type r_nc = r.cols ();

  if (r_nr != r_nc)
    (*current_liboctave_error_handler) ("chol2inv requires square matrix");

  F77_INT n = octave::to_f77_int (r_nc);
  F77_INT info = 0;

  Matrix tmp = r;
  double *v = tmp.fortran_vec ();

  if (info == 0)
    {
      if (is_upper)
        F77_XFCN (dpotri, DPOTRI, (F77_CONST_CHAR_ARG2 ("U", 1), n,
                                   v, n, info
                                   F77_CHAR_ARG_LEN (1)));
      else
        F77_XFCN (dpotri, DPOTRI, (F77_CONST_CHAR_ARG2 ("L", 1), n,
                                   v, n, info
                                   F77_CHAR_ARG_LEN (1)));

      // If someone thinks of a more graceful way of doing this (or
      // faster for that matter :-)), please let me know!

      if (n > 1)
        {
          if (is_upper)
            for (octave_idx_type j = 0; j < r_nc; j++)
              for (octave_idx_type i = j+1; i < r_nr; i++)
                tmp.xelem (i, j) = tmp.xelem (j, i);
          else
            for (octave_idx_type j = 0; j < r_nc; j++)
              for (octave_idx_type i = j+1; i < r_nr; i++)
                tmp.xelem (j, i) = tmp.xelem (i, j);
        }

      retval = tmp;
    }

  return retval;
}

static FloatMatrix
chol2inv_internal (const FloatMatrix& r, bool is_upper = true)
{
  FloatMatrix retval;

  octave_idx_type r_nr = r.rows ();
  octave_idx_type r_nc = r.cols ();

  if (r_nr != r_nc)
    (*current_liboctave_error_handler) ("chol2inv requires square matrix");

  F77_INT n = octave::to_f77_int (r_nc);
  F77_INT info = 0;

  FloatMatrix tmp = r;
  float *v = tmp.fortran_vec ();

  if (info == 0)
    {
      if (is_upper)
        F77_XFCN (spotri, SPOTRI, (F77_CONST_CHAR_ARG2 ("U", 1), n,
                                   v, n, info
                                   F77_CHAR_ARG_LEN (1)));
      else
        F77_XFCN (spotri, SPOTRI, (F77_CONST_CHAR_ARG2 ("L", 1), n,
                                   v, n, info
                                   F77_CHAR_ARG_LEN (1)));

      // If someone thinks of a more graceful way of doing this (or
      // faster for that matter :-)), please let me know!

      if (n > 1)
        {
          if (is_upper)
            for (octave_idx_type j = 0; j < r_nc; j++)
              for (octave_idx_type i = j+1; i < r_nr; i++)
                tmp.xelem (i, j) = tmp.xelem (j, i);
          else
            for (octave_idx_type j = 0; j < r_nc; j++)
              for (octave_idx_type i = j+1; i < r_nr; i++)
                tmp.xelem (j, i) = tmp.xelem (i, j);
        }

      retval = tmp;
    }

  return retval;
}

static ComplexMatrix
chol2inv_internal (const ComplexMatrix& r, bool is_upper = true)
{
  ComplexMatrix retval;

  octave_idx_type r_nr = r.rows ();
  octave_idx_type r_nc = r.cols ();

  if (r_nr != r_nc)
    (*current_liboctave_error_handler) ("chol2inv requires square matrix");

  F77_INT n = octave::to_f77_int (r_nc);
  F77_INT info;

  ComplexMatrix tmp = r;

  if (is_upper)
    F77_XFCN (zpotri, ZPOTRI, (F77_CONST_CHAR_ARG2 ("U", 1), n,
                               F77_DBLE_CMPLX_ARG (tmp.fortran_vec ()), n, info
                               F77_CHAR_ARG_LEN (1)));
  else
    F77_XFCN (zpotri, ZPOTRI, (F77_CONST_CHAR_ARG2 ("L", 1), n,
                               F77_DBLE_CMPLX_ARG (tmp.fortran_vec ()), n, info
                               F77_CHAR_ARG_LEN (1)));

  // If someone thinks of a more graceful way of doing this (or
  // faster for that matter :-)), please let me know!

  if (n > 1)
    {
      if (is_upper)
        for (octave_idx_type j = 0; j < r_nc; j++)
          for (octave_idx_type i = j+1; i < r_nr; i++)
            tmp.xelem (i, j) = std::conj (tmp.xelem (j, i));
      else
        for (octave_idx_type j = 0; j < r_nc; j++)
          for (octave_idx_type i = j+1; i < r_nr; i++)
            tmp.xelem (j, i) = std::conj (tmp.xelem (i, j));
    }

  retval = tmp;

  return retval;
}

static FloatComplexMatrix
chol2inv_internal (const FloatComplexMatrix& r, bool is_upper = true)
{
  FloatComplexMatrix retval;

  octave_idx_type r_nr = r.rows ();
  octave_idx_type r_nc = r.cols ();

  if (r_nr != r_nc)
    (*current_liboctave_error_handler) ("chol2inv requires square matrix");

  F77_INT n = octave::to_f77_int (r_nc);
  F77_INT info;

  FloatComplexMatrix tmp = r;

  if (is_upper)
    F77_XFCN (cpotri, CPOTRI, (F77_CONST_CHAR_ARG2 ("U", 1), n,
                               F77_CMPLX_ARG (tmp.fortran_vec ()), n, info
                               F77_CHAR_ARG_LEN (1)));
  else
    F77_XFCN (cpotri, CPOTRI, (F77_CONST_CHAR_ARG2 ("L", 1), n,
                               F77_CMPLX_ARG (tmp.fortran_vec ()), n, info
                               F77_CHAR_ARG_LEN (1)));

  // If someone thinks of a more graceful way of doing this (or
  // faster for that matter :-)), please let me know!

  if (n > 1)
    {
      if (is_upper)
        for (octave_idx_type j = 0; j < r_nc; j++)
          for (octave_idx_type i = j+1; i < r_nr; i++)
            tmp.xelem (i, j) = std::conj (tmp.xelem (j, i));
      else
        for (octave_idx_type j = 0; j < r_nc; j++)
          for (octave_idx_type i = j+1; i < r_nr; i++)
            tmp.xelem (j, i) = std::conj (tmp.xelem (i, j));
    }

  retval = tmp;

  return retval;
}

namespace octave
{
  namespace math
  {
    template <typename T>
    T
    chol2inv (const T& r)
    {
      return chol2inv_internal (r);
    }

    // Compute the inverse of a matrix using the Cholesky factorization.
    template <typename T>
    T
    chol<T>::inverse (void) const
    {
      return chol2inv_internal (chol_mat, is_upper);
    }

    template <typename T>
    void
    chol<T>::set (const T& R)
    {
      if (! R.issquare ())
        (*current_liboctave_error_handler) ("chol: requires square matrix");

      chol_mat = R;
    }

#if ! defined (HAVE_QRUPDATE)

    template <typename T>
    void
    chol<T>::update (const VT& u)
    {
      warn_qrupdate_once ();

      octave_idx_type n = chol_mat.rows ();

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      init (chol_mat.hermitian () * chol_mat + T (u) * T (u).hermitian (),
            true, false);
    }

    template <typename T>
    bool
    singular (const T& a)
    {
      static typename T::element_type zero (0);
      for (octave_idx_type i = 0; i < a.rows (); i++)
        if (a(i,i) == zero) return true;
      return false;
    }

    template <typename T>
    octave_idx_type
    chol<T>::downdate (const VT& u)
    {
      warn_qrupdate_once ();

      octave_idx_type info = -1;

      octave_idx_type n = chol_mat.rows ();

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      if (singular (chol_mat))
        info = 2;
      else
        {
          info = init (chol_mat.hermitian () * chol_mat
                       - T (u) * T (u).hermitian (), true, false);
          if (info) info = 1;
        }

      return info;
    }

    template <typename T>
    octave_idx_type
    chol<T>::insert_sym (const VT& u, octave_idx_type j)
    {
      static typename T::element_type zero (0);

      warn_qrupdate_once ();

      octave_idx_type info = -1;

      octave_idx_type n = chol_mat.rows ();

      if (u.numel () != n + 1)
        (*current_liboctave_error_handler) ("cholinsert: dimension mismatch");
      if (j < 0 || j > n)
        (*current_liboctave_error_handler) ("cholinsert: index out of range");

      if (singular (chol_mat))
        info = 2;
      else if (std::imag (u(j)) != zero)
        info = 3;
      else
        {
          T a = chol_mat.hermitian () * chol_mat;
          T a1 (n+1, n+1);
          for (octave_idx_type k = 0; k < n+1; k++)
            for (octave_idx_type l = 0; l < n+1; l++)
              {
                if (l == j)
                  a1(k, l) = u(k);
                else if (k == j)
                  a1(k, l) = math::conj (u(l));
                else
                  a1(k, l) = a(k < j ? k : k-1, l < j ? l : l-1);
              }
          info = init (a1, true, false);
          if (info) info = 1;
        }

      return info;
    }

    template <typename T>
    void
    chol<T>::delete_sym (octave_idx_type j)
    {
      warn_qrupdate_once ();

      octave_idx_type n = chol_mat.rows ();

      if (j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("choldelete: index out of range");

      T a = chol_mat.hermitian () * chol_mat;
      a.delete_elements (1, idx_vector (j));
      a.delete_elements (0, idx_vector (j));
      init (a, true, false);
    }

    template <typename T>
    void
    chol<T>::shift_sym (octave_idx_type i, octave_idx_type j)
    {
      warn_qrupdate_once ();

      octave_idx_type n = chol_mat.rows ();

      if (i < 0 || i > n-1 || j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("cholshift: index out of range");

      T a = chol_mat.hermitian () * chol_mat;
      Array<octave_idx_type> p (dim_vector (n, 1));
      for (octave_idx_type k = 0; k < n; k++) p(k) = k;
      if (i < j)
        {
          for (octave_idx_type k = i; k < j; k++) p(k) = k+1;
          p(j) = i;
        }
      else if (j < i)
        {
          p(j) = i;
          for (octave_idx_type k = j+1; k < i+1; k++) p(k) = k-1;
        }

      init (a.index (idx_vector (p), idx_vector (p)), true, false);
    }

#endif

    // Specializations.

    template <>
    octave_idx_type
    chol<Matrix>::init (const Matrix& a, bool upper, bool calc_cond)
    {
      octave_idx_type a_nr = a.rows ();
      octave_idx_type a_nc = a.cols ();

      if (a_nr != a_nc)
        (*current_liboctave_error_handler) ("chol: requires square matrix");

      F77_INT n = to_f77_int (a_nc);
      F77_INT info;

      is_upper = upper;

      chol_mat.clear (n, n);
      if (is_upper)
        for (octave_idx_type j = 0; j < n; j++)
          {
            for (octave_idx_type i = 0; i <= j; i++)
              chol_mat.xelem (i, j) = a(i, j);
            for (octave_idx_type i = j+1; i < n; i++)
              chol_mat.xelem (i, j) = 0.0;
          }
      else
        for (octave_idx_type j = 0; j < n; j++)
          {
            for (octave_idx_type i = 0; i < j; i++)
              chol_mat.xelem (i, j) = 0.0;
            for (octave_idx_type i = j; i < n; i++)
              chol_mat.xelem (i, j) = a(i, j);
          }
      double *h = chol_mat.fortran_vec ();

      // Calculate the norm of the matrix, for later use.
      double anorm = 0;
      if (calc_cond)
        anorm = xnorm (a, 1);

      if (is_upper)
        F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 ("U", 1), n, h, n, info
                                   F77_CHAR_ARG_LEN (1)));
      else
        F77_XFCN (dpotrf, DPOTRF, (F77_CONST_CHAR_ARG2 ("L", 1), n, h, n, info
                                   F77_CHAR_ARG_LEN (1)));

      xrcond = 0.0;
      if (info > 0)
        chol_mat.resize (info - 1, info - 1);
      else if (calc_cond)
        {
          F77_INT dpocon_info = 0;

          // Now calculate the condition number for non-singular matrix.
          Array<double> z (dim_vector (3*n, 1));
          double *pz = z.fortran_vec ();
          OCTAVE_LOCAL_BUFFER (F77_INT, iz, n);
          if (is_upper)
            F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 ("U", 1), n, h,
                                       n, anorm, xrcond, pz, iz, dpocon_info
                                       F77_CHAR_ARG_LEN (1)));
          else
            F77_XFCN (dpocon, DPOCON, (F77_CONST_CHAR_ARG2 ("L", 1), n, h,
                                       n, anorm, xrcond, pz, iz, dpocon_info
                                       F77_CHAR_ARG_LEN (1)));

          if (dpocon_info != 0)
            info = -1;
        }

      return info;
    }

#if defined (HAVE_QRUPDATE)

    template <>
    void
    chol<Matrix>::update (const ColumnVector& u)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      ColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, w, n);

      F77_XFCN (dch1up, DCH1UP, (n, chol_mat.fortran_vec (), n,
                                 utmp.fortran_vec (), w));
    }

    template <>
    octave_idx_type
    chol<Matrix>::downdate (const ColumnVector& u)
    {
      F77_INT info = -1;

      F77_INT n = to_f77_int (chol_mat.rows ());

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      ColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, w, n);

      F77_XFCN (dch1dn, DCH1DN, (n, chol_mat.fortran_vec (), n,
                                 utmp.fortran_vec (), w, info));

      return info;
    }

    template <>
    octave_idx_type
    chol<Matrix>::insert_sym (const ColumnVector& u, octave_idx_type j_arg)
    {
      F77_INT info = -1;

      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT j = to_f77_int (j_arg);

      if (u.numel () != n + 1)
        (*current_liboctave_error_handler) ("cholinsert: dimension mismatch");
      if (j < 0 || j > n)
        (*current_liboctave_error_handler) ("cholinsert: index out of range");

      ColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, w, n);

      chol_mat.resize (n+1, n+1);
      F77_INT ldcm = to_f77_int (chol_mat.rows ());

      F77_XFCN (dchinx, DCHINX, (n, chol_mat.fortran_vec (), ldcm,
                                 j + 1, utmp.fortran_vec (), w, info));

      return info;
    }

    template <>
    void
    chol<Matrix>::delete_sym (octave_idx_type j_arg)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT j = to_f77_int (j_arg);

      if (j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("choldelete: index out of range");

      OCTAVE_LOCAL_BUFFER (double, w, n);

      F77_XFCN (dchdex, DCHDEX, (n, chol_mat.fortran_vec (), n, j + 1, w));

      chol_mat.resize (n-1, n-1);
    }

    template <>
    void
    chol<Matrix>::shift_sym (octave_idx_type i_arg, octave_idx_type j_arg)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT i = to_f77_int (i_arg);
      F77_INT j = to_f77_int (j_arg);

      if (i < 0 || i > n-1 || j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("cholshift: index out of range");

      OCTAVE_LOCAL_BUFFER (double, w, 2*n);

      F77_XFCN (dchshx, DCHSHX, (n, chol_mat.fortran_vec (), n,
                                 i + 1, j + 1, w));
    }

#endif

    template <>
    octave_idx_type
    chol<FloatMatrix>::init (const FloatMatrix& a, bool upper, bool calc_cond)
    {
      octave_idx_type a_nr = a.rows ();
      octave_idx_type a_nc = a.cols ();

      if (a_nr != a_nc)
        (*current_liboctave_error_handler) ("chol: requires square matrix");

      F77_INT n = to_f77_int (a_nc);
      F77_INT info;

      is_upper = upper;

      chol_mat.clear (n, n);
      if (is_upper)
        for (octave_idx_type j = 0; j < n; j++)
          {
            for (octave_idx_type i = 0; i <= j; i++)
              chol_mat.xelem (i, j) = a(i, j);
            for (octave_idx_type i = j+1; i < n; i++)
              chol_mat.xelem (i, j) = 0.0f;
          }
      else
        for (octave_idx_type j = 0; j < n; j++)
          {
            for (octave_idx_type i = 0; i < j; i++)
              chol_mat.xelem (i, j) = 0.0f;
            for (octave_idx_type i = j; i < n; i++)
              chol_mat.xelem (i, j) = a(i, j);
          }
      float *h = chol_mat.fortran_vec ();

      // Calculate the norm of the matrix, for later use.
      float anorm = 0;
      if (calc_cond)
        anorm = xnorm (a, 1);

      if (is_upper)
        F77_XFCN (spotrf, SPOTRF, (F77_CONST_CHAR_ARG2 ("U", 1), n, h, n, info
                                   F77_CHAR_ARG_LEN (1)));
      else
        F77_XFCN (spotrf, SPOTRF, (F77_CONST_CHAR_ARG2 ("L", 1), n, h, n, info
                                   F77_CHAR_ARG_LEN (1)));

      xrcond = 0.0;
      if (info > 0)
        chol_mat.resize (info - 1, info - 1);
      else if (calc_cond)
        {
          F77_INT spocon_info = 0;

          // Now calculate the condition number for non-singular matrix.
          Array<float> z (dim_vector (3*n, 1));
          float *pz = z.fortran_vec ();
          OCTAVE_LOCAL_BUFFER (F77_INT, iz, n);
          if (is_upper)
            F77_XFCN (spocon, SPOCON, (F77_CONST_CHAR_ARG2 ("U", 1), n, h,
                                       n, anorm, xrcond, pz, iz, spocon_info
                                       F77_CHAR_ARG_LEN (1)));
          else
            F77_XFCN (spocon, SPOCON, (F77_CONST_CHAR_ARG2 ("L", 1), n, h,
                                       n, anorm, xrcond, pz, iz, spocon_info
                                       F77_CHAR_ARG_LEN (1)));

          if (spocon_info != 0)
            info = -1;
        }

      return info;
    }

#if defined (HAVE_QRUPDATE)

    template <>
    void
    chol<FloatMatrix>::update (const FloatColumnVector& u)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      FloatColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (float, w, n);

      F77_XFCN (sch1up, SCH1UP, (n, chol_mat.fortran_vec (), n,
                                 utmp.fortran_vec (), w));
    }

    template <>
    octave_idx_type
    chol<FloatMatrix>::downdate (const FloatColumnVector& u)
    {
      F77_INT info = -1;

      F77_INT n = to_f77_int (chol_mat.rows ());

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      FloatColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (float, w, n);

      F77_XFCN (sch1dn, SCH1DN, (n, chol_mat.fortran_vec (), n,
                                 utmp.fortran_vec (), w, info));

      return info;
    }

    template <>
    octave_idx_type
    chol<FloatMatrix>::insert_sym (const FloatColumnVector& u,
                                   octave_idx_type j_arg)
    {
      F77_INT info = -1;

      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT j = to_f77_int (j_arg);

      if (u.numel () != n + 1)
        (*current_liboctave_error_handler) ("cholinsert: dimension mismatch");
      if (j < 0 || j > n)
        (*current_liboctave_error_handler) ("cholinsert: index out of range");

      FloatColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (float, w, n);

      chol_mat.resize (n+1, n+1);
      F77_INT ldcm = to_f77_int (chol_mat.rows ());

      F77_XFCN (schinx, SCHINX, (n, chol_mat.fortran_vec (), ldcm,
                                 j + 1, utmp.fortran_vec (), w, info));

      return info;
    }

    template <>
    void
    chol<FloatMatrix>::delete_sym (octave_idx_type j_arg)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT j = to_f77_int (j_arg);

      if (j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("choldelete: index out of range");

      OCTAVE_LOCAL_BUFFER (float, w, n);

      F77_XFCN (schdex, SCHDEX, (n, chol_mat.fortran_vec (), n,
                                 j + 1, w));

      chol_mat.resize (n-1, n-1);
    }

    template <>
    void
    chol<FloatMatrix>::shift_sym (octave_idx_type i_arg, octave_idx_type j_arg)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT i = to_f77_int (i_arg);
      F77_INT j = to_f77_int (j_arg);

      if (i < 0 || i > n-1 || j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("cholshift: index out of range");

      OCTAVE_LOCAL_BUFFER (float, w, 2*n);

      F77_XFCN (schshx, SCHSHX, (n, chol_mat.fortran_vec (), n,
                                 i + 1, j + 1, w));
    }

#endif

    template <>
    octave_idx_type
    chol<ComplexMatrix>::init (const ComplexMatrix& a, bool upper, bool calc_cond)
    {
      octave_idx_type a_nr = a.rows ();
      octave_idx_type a_nc = a.cols ();

      if (a_nr != a_nc)
        (*current_liboctave_error_handler) ("chol: requires square matrix");

      F77_INT n = to_f77_int (a_nc);
      F77_INT info;

      is_upper = upper;

      chol_mat.clear (n, n);
      if (is_upper)
        for (octave_idx_type j = 0; j < n; j++)
          {
            for (octave_idx_type i = 0; i <= j; i++)
              chol_mat.xelem (i, j) = a(i, j);
            for (octave_idx_type i = j+1; i < n; i++)
              chol_mat.xelem (i, j) = 0.0;
          }
      else
        for (octave_idx_type j = 0; j < n; j++)
          {
            for (octave_idx_type i = 0; i < j; i++)
              chol_mat.xelem (i, j) = 0.0;
            for (octave_idx_type i = j; i < n; i++)
              chol_mat.xelem (i, j) = a(i, j);
          }
      Complex *h = chol_mat.fortran_vec ();

      // Calculate the norm of the matrix, for later use.
      double anorm = 0;
      if (calc_cond)
        anorm = xnorm (a, 1);

      if (is_upper)
        F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 ("U", 1), n,
                                   F77_DBLE_CMPLX_ARG (h), n, info
                                   F77_CHAR_ARG_LEN (1)));
      else
        F77_XFCN (zpotrf, ZPOTRF, (F77_CONST_CHAR_ARG2 ("L", 1), n,
                                   F77_DBLE_CMPLX_ARG (h), n, info
                                   F77_CHAR_ARG_LEN (1)));

      xrcond = 0.0;
      if (info > 0)
        chol_mat.resize (info - 1, info - 1);
      else if (calc_cond)
        {
          F77_INT zpocon_info = 0;

          // Now calculate the condition number for non-singular matrix.
          Array<Complex> z (dim_vector (2*n, 1));
          Complex *pz = z.fortran_vec ();
          Array<double> rz (dim_vector (n, 1));
          double *prz = rz.fortran_vec ();
          F77_XFCN (zpocon, ZPOCON, (F77_CONST_CHAR_ARG2 ("U", 1), n,
                                     F77_DBLE_CMPLX_ARG (h), n, anorm, xrcond,
                                     F77_DBLE_CMPLX_ARG (pz), prz, zpocon_info
                                     F77_CHAR_ARG_LEN (1)));

          if (zpocon_info != 0)
            info = -1;
        }

      return info;
    }

#if defined (HAVE_QRUPDATE)

    template <>
    void
    chol<ComplexMatrix>::update (const ComplexColumnVector& u)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      ComplexColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, rw, n);

      F77_XFCN (zch1up, ZCH1UP, (n,
                                 F77_DBLE_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 n,
                                 F77_DBLE_CMPLX_ARG (utmp.fortran_vec ()),
                                 rw));
    }

    template <>
    octave_idx_type
    chol<ComplexMatrix>::downdate (const ComplexColumnVector& u)
    {
      F77_INT info = -1;

      F77_INT n = to_f77_int (chol_mat.rows ());

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      ComplexColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, rw, n);

      F77_XFCN (zch1dn, ZCH1DN, (n,
                                 F77_DBLE_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 n,
                                 F77_DBLE_CMPLX_ARG (utmp.fortran_vec ()),
                                 rw, info));

      return info;
    }

    template <>
    octave_idx_type
    chol<ComplexMatrix>::insert_sym (const ComplexColumnVector& u,
                                     octave_idx_type j_arg)
    {
      F77_INT info = -1;

      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT j = to_f77_int (j_arg);

      if (u.numel () != n + 1)
        (*current_liboctave_error_handler) ("cholinsert: dimension mismatch");
      if (j < 0 || j > n)
        (*current_liboctave_error_handler) ("cholinsert: index out of range");

      ComplexColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (double, rw, n);

      chol_mat.resize (n+1, n+1);
      F77_INT ldcm = to_f77_int (chol_mat.rows ());

      F77_XFCN (zchinx, ZCHINX, (n,
                                 F77_DBLE_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 ldcm, j + 1,
                                 F77_DBLE_CMPLX_ARG (utmp.fortran_vec ()),
                                 rw, info));

      return info;
    }

    template <>
    void
    chol<ComplexMatrix>::delete_sym (octave_idx_type j_arg)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT j = to_f77_int (j_arg);

      if (j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("choldelete: index out of range");

      OCTAVE_LOCAL_BUFFER (double, rw, n);

      F77_XFCN (zchdex, ZCHDEX, (n,
                                 F77_DBLE_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 n, j + 1, rw));

      chol_mat.resize (n-1, n-1);
    }

    template <>
    void
    chol<ComplexMatrix>::shift_sym (octave_idx_type i_arg,
                                    octave_idx_type j_arg)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT i = to_f77_int (i_arg);
      F77_INT j = to_f77_int (j_arg);

      if (i < 0 || i > n-1 || j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("cholshift: index out of range");

      OCTAVE_LOCAL_BUFFER (Complex, w, n);
      OCTAVE_LOCAL_BUFFER (double, rw, n);

      F77_XFCN (zchshx, ZCHSHX, (n,
                                 F77_DBLE_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 n, i + 1, j + 1,
                                 F77_DBLE_CMPLX_ARG (w), rw));
    }

#endif

    template <>
    octave_idx_type
    chol<FloatComplexMatrix>::init (const FloatComplexMatrix& a, bool upper,
                                    bool calc_cond)
    {
      octave_idx_type a_nr = a.rows ();
      octave_idx_type a_nc = a.cols ();

      if (a_nr != a_nc)
        (*current_liboctave_error_handler) ("chol: requires square matrix");

      F77_INT n = to_f77_int (a_nc);
      F77_INT info;

      is_upper = upper;

      chol_mat.clear (n, n);
      if (is_upper)
        for (octave_idx_type j = 0; j < n; j++)
          {
            for (octave_idx_type i = 0; i <= j; i++)
              chol_mat.xelem (i, j) = a(i, j);
            for (octave_idx_type i = j+1; i < n; i++)
              chol_mat.xelem (i, j) = 0.0f;
          }
      else
        for (octave_idx_type j = 0; j < n; j++)
          {
            for (octave_idx_type i = 0; i < j; i++)
              chol_mat.xelem (i, j) = 0.0f;
            for (octave_idx_type i = j; i < n; i++)
              chol_mat.xelem (i, j) = a(i, j);
          }
      FloatComplex *h = chol_mat.fortran_vec ();

      // Calculate the norm of the matrix, for later use.
      float anorm = 0;
      if (calc_cond)
        anorm = xnorm (a, 1);

      if (is_upper)
        F77_XFCN (cpotrf, CPOTRF, (F77_CONST_CHAR_ARG2 ("U", 1),
                                   n, F77_CMPLX_ARG (h), n, info
                                   F77_CHAR_ARG_LEN (1)));
      else
        F77_XFCN (cpotrf, CPOTRF, (F77_CONST_CHAR_ARG2 ("L", 1),
                                   n, F77_CMPLX_ARG (h), n, info
                                   F77_CHAR_ARG_LEN (1)));

      xrcond = 0.0;
      if (info > 0)
        chol_mat.resize (info - 1, info - 1);
      else if (calc_cond)
        {
          F77_INT cpocon_info = 0;

          // Now calculate the condition number for non-singular matrix.
          Array<FloatComplex> z (dim_vector (2*n, 1));
          FloatComplex *pz = z.fortran_vec ();
          Array<float> rz (dim_vector (n, 1));
          float *prz = rz.fortran_vec ();
          F77_XFCN (cpocon, CPOCON, (F77_CONST_CHAR_ARG2 ("U", 1), n,
                                     F77_CMPLX_ARG (h), n, anorm, xrcond,
                                     F77_CMPLX_ARG (pz), prz, cpocon_info
                                     F77_CHAR_ARG_LEN (1)));

          if (cpocon_info != 0)
            info = -1;
        }

      return info;
    }

#if defined (HAVE_QRUPDATE)

    template <>
    void
    chol<FloatComplexMatrix>::update (const FloatComplexColumnVector& u)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      FloatComplexColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (float, rw, n);

      F77_XFCN (cch1up, CCH1UP, (n, F77_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 n, F77_CMPLX_ARG (utmp.fortran_vec ()), rw));
    }

    template <>
    octave_idx_type
    chol<FloatComplexMatrix>::downdate (const FloatComplexColumnVector& u)
    {
      F77_INT info = -1;

      F77_INT n = to_f77_int (chol_mat.rows ());

      if (u.numel () != n)
        (*current_liboctave_error_handler) ("cholupdate: dimension mismatch");

      FloatComplexColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (float, rw, n);

      F77_XFCN (cch1dn, CCH1DN, (n, F77_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 n, F77_CMPLX_ARG (utmp.fortran_vec ()),
                                 rw, info));

      return info;
    }

    template <>
    octave_idx_type
    chol<FloatComplexMatrix>::insert_sym (const FloatComplexColumnVector& u,
                                          octave_idx_type j_arg)
    {
      F77_INT info = -1;
      F77_INT j = to_f77_int (j_arg);

      F77_INT n = to_f77_int (chol_mat.rows ());

      if (u.numel () != n + 1)
        (*current_liboctave_error_handler) ("cholinsert: dimension mismatch");
      if (j < 0 || j > n)
        (*current_liboctave_error_handler) ("cholinsert: index out of range");

      FloatComplexColumnVector utmp = u;

      OCTAVE_LOCAL_BUFFER (float, rw, n);

      chol_mat.resize (n+1, n+1);
      F77_INT ldcm = to_f77_int (chol_mat.rows ());

      F77_XFCN (cchinx, CCHINX, (n, F77_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 ldcm, j + 1,
                                 F77_CMPLX_ARG (utmp.fortran_vec ()),
                                 rw, info));

      return info;
    }

    template <>
    void
    chol<FloatComplexMatrix>::delete_sym (octave_idx_type j_arg)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT j = to_f77_int (j_arg);

      if (j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("choldelete: index out of range");

      OCTAVE_LOCAL_BUFFER (float, rw, n);

      F77_XFCN (cchdex, CCHDEX, (n, F77_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 n, j + 1, rw));

      chol_mat.resize (n-1, n-1);
    }

    template <>
    void
    chol<FloatComplexMatrix>::shift_sym (octave_idx_type i_arg,
                                         octave_idx_type j_arg)
    {
      F77_INT n = to_f77_int (chol_mat.rows ());
      F77_INT i = to_f77_int (i_arg);
      F77_INT j = to_f77_int (j_arg);

      if (i < 0 || i > n-1 || j < 0 || j > n-1)
        (*current_liboctave_error_handler) ("cholshift: index out of range");

      OCTAVE_LOCAL_BUFFER (FloatComplex, w, n);
      OCTAVE_LOCAL_BUFFER (float, rw, n);

      F77_XFCN (cchshx, CCHSHX, (n, F77_CMPLX_ARG (chol_mat.fortran_vec ()),
                                 n, i + 1, j + 1, F77_CMPLX_ARG (w), rw));
    }

#endif

    // Instantiations we need.

    template class chol<Matrix>;

    template class chol<FloatMatrix>;

    template class chol<ComplexMatrix>;

    template class chol<FloatComplexMatrix>;

    template Matrix
    chol2inv<Matrix> (const Matrix& r);

    template ComplexMatrix
    chol2inv<ComplexMatrix> (const ComplexMatrix& r);

    template FloatMatrix
    chol2inv<FloatMatrix> (const FloatMatrix& r);

    template FloatComplexMatrix
    chol2inv<FloatComplexMatrix> (const FloatComplexMatrix& r);
  }
}