root/win32/itpp-4.0.1/itpp/base/matfunc.h @ 109

/*!
 * \file
 * \brief Various functions on vectors and matrices - header file
 * \author Tony Ottosson, Adam Piatyszek, Conrad Sanderson, Mark Dobossy
 *         and Martin Senst
 *
 * -------------------------------------------------------------------------
 *
 * IT++ - C++ library of mathematical, signal processing, speech processing,
 *        and communications classes and functions
 *
 * Copyright (C) 1995-2007  (see AUTHORS file for a list of contributors)
 *
 * This program 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 2 of the License, or
 * (at your option) any later version.
 *
 * This program 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 this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 *
 * -------------------------------------------------------------------------
 */

#ifndef MATFUNC_H
#define MATFUNC_H

#include <itpp/base/mat.h>
#include <itpp/base/math/log_exp.h>
#include <itpp/base/math/elem_math.h>


namespace itpp {

  /*!
    \addtogroup matrix_functions
    \brief Functions on vectors and matrices
  */
  //!@{

  //! Length of vector
  template<class T>
  int length(const Vec<T> &v) { return v.length(); }

  //! Length of vector
  template<class T>
  int size(const Vec<T> &v) { return v.length(); }

  //! Sum of all elements in the vector
  template<class T>
  T sum(const Vec<T> &v)
  {
    T M = 0;

    for (int i=0;i<v.length();i++)
      M += v[i];

    return M;
  }

  /*!
   * \brief Sum of elements in the matrix \c m, either along columns or rows
   *
   * <tt>sum(m) = sum(m, 1)</tt> returns a vector where the elements are sum
   * over each column, whereas <tt>sum(m, 2)</tt> returns a vector where the
   * elements are sum over each row.
   */
  template<class T>
  Vec<T> sum(const Mat<T> &m, int dim=1)
  {
    it_assert((dim == 1) || (dim == 2), "sum: dimension need to be 1 or 2");
    Vec<T> out;

    if (dim == 1) {
      out.set_size(m.cols(), false);

      for (int i=0; i<m.cols(); i++)
              out(i) = sum(m.get_col(i));
    }
    else {
      out.set_size(m.rows(), false);

      for (int i=0; i<m.rows(); i++)
              out(i) = sum(m.get_row(i));
    }

    return out;
  }


  //! Sum of all elements in the given matrix. Fast version of sum(sum(X))
  template<class T>
  T sumsum(const Mat<T> &X)
  {
    const T * X_data = X._data();
    const int X_datasize = X._datasize();
    T acc = 0;

    for(int i=0;i<X_datasize;i++)
      acc += X_data[i];

    return acc;
  }


  //! Sum of square of the elements in a vector
  template<class T>
  T sum_sqr(const Vec<T> &v)
  {
    T M=0;

    for (int i=0; i<v.length(); i++)
      M += v[i] * v[i];

    return M;
  }

  /*!
   * \brief Sum of the square of elements in the matrix \c m
   *
   * <tt>sum(m) = sum(m, 1)</tt> returns a vector where the elements are sum
   * squared over each column, whereas <tt>sum(m, 2)</tt> returns a vector
   * where the elements are sum squared over each row
   */
  template<class T>
  Vec<T> sum_sqr(const Mat<T> &m, int dim=1)
  {
    it_assert((dim == 1) || (dim == 2), "sum_sqr: dimension need to be 1 or 2");
    Vec<T> out;

    if (dim == 1) {
      out.set_size(m.cols(), false);

      for (int i=0; i<m.cols(); i++)
        out(i) = sum_sqr(m.get_col(i));
    }
    else {
      out.set_size(m.rows(), false);

      for (int i=0; i<m.rows(); i++)
        out(i) = sum_sqr(m.get_row(i));
    }

    return out;
  }

  //! Cumulative sum of all elements in the vector
  template<class T>
  Vec<T> cumsum(const Vec<T> &v)
  {
    Vec<T> out(v.size());

    out(0)=v(0);
    for (int i=1; i<v.size(); i++)
      out(i) = out(i-1) + v(i);

    return out;
  }

  /*!
   * \brief Cumulative sum of elements in the matrix \c m
   *
   * <tt>cumsum(m) = cumsum(m, 1)</tt> returns a matrix where the elements
   * are sums over each column, whereas <tt>cumsum(m, 2)</tt> returns a
   * matrix where the elements are sums over each row
   */
  template<class T>
  Mat<T> cumsum(const Mat<T> &m, int dim=1)
  {
    it_assert((dim == 1) || (dim == 2), "cumsum: dimension need to be 1 or 2");
    Mat<T> out(m.rows(), m.cols());

    if (dim == 1) {
      for (int i=0; i<m.cols(); i++)
        out.set_col(i, cumsum(m.get_col(i)));
    } else {
      for (int i=0; i<m.rows(); i++)
        out.set_row(i, cumsum(m.get_row(i)));
    }

    return out;
  }

  //! The product of all elements in the vector
  template<class T>
  T prod(const Vec<T> &v)
  {
    it_assert(v.size() >= 1, "prod: size of vector should be at least 1");
    T out = v(0);

    for (int i=1; i<v.size(); i++)
      out *= v(i);

    return out;
  }

  /*!
   * \brief Product of elements in the matrix \c m
   *
   * <tt>prod(m) = prod(m, 1)</tt> returns a vector where the elements are
   * products over each column, whereas <tt>prod(m, 2)</tt> returns a vector
   * where the elements are products over each row
   */
  template<class T>
  Vec<T> prod(const Mat<T> &m, int dim=1)
  {
    it_assert((dim == 1) || (dim == 2), "prod: dimension need to be 1 or 2");
    Vec<T> out(m.cols());

    if (dim == 1) {
      it_assert((m.cols() >= 1) && (m.rows() >= 1),
                "prod: number of columns should be at least 1");
      out.set_size(m.cols(), false);

      for (int i=0; i<m.cols(); i++)
        out(i) = prod(m.get_col(i));
    }
    else {
      it_assert((m.cols() >= 1) && (m.rows() >= 1),
                "prod: number of rows should be at least 1");
      out.set_size(m.rows(), false);

      for (int i=0; i<m.rows(); i++)
        out(i) = prod(m.get_row(i));
    }
    return out;
  }

  //! Vector cross product. Vectors need to be of size 3
  template<class T>
  Vec<T> cross(const Vec<T> &v1, const Vec<T> &v2)
  {
    it_assert((v1.size() == 3) && (v2.size() == 3),
              "cross: vectors should be of size 3");

    Vec<T> r(3);

    r(0) = v1(1) * v2(2) - v1(2) * v2(1);
    r(1) = v1(2) * v2(0) - v1(0) * v2(2);
    r(2) = v1(0) * v2(1) - v1(1) * v2(0);

    return r;
  }


  //! Zero-pad a vector to size n
  template<class T>
  Vec<T> zero_pad(const Vec<T> &v, int n)
  {
    it_assert(n >= v.size(), "zero_pad() cannot shrink the vector!");
    Vec<T> v2(n);
    v2.set_subvector(0, v.size()-1, v);
    if (n > v.size())
      v2.set_subvector(v.size(), n-1, T(0));

    return v2;
  }

  //! Zero-pad a vector to the nearest greater power of two
  template<class T>
  Vec<T> zero_pad(const Vec<T> &v)
  {
    int n = pow2i(levels2bits(v.size()));

    return (n == v.size()) ? v : zero_pad(v, n);
  }

  //! Zero-pad a matrix to size rows x cols
  template<class T>
  Mat<T> zero_pad(const Mat<T> &m, int rows, int cols)
  {
    it_assert((rows >= m.rows()) && (cols >= m.cols()),
              "zero_pad() cannot shrink the matrix!");
    Mat<T> m2(rows, cols);
    m2.set_submatrix(0,m.rows()-1,0,m.cols()-1, m);
    if (cols > m.cols()) // Zero
      m2.set_submatrix(0,m.rows()-1, m.cols(),cols-1, T(0));
    if (rows > m.rows()) // Zero
      m2.set_submatrix(m.rows(), rows-1, 0, cols-1, T(0));

    return m2;
  }


  //! Return zero if indexing outside the vector \c v otherwise return the
  //! element \c index
  template<class T>
  T index_zero_pad(const Vec<T> &v, const int index)
  {
    if (index >= 0 && index < v.size())
      return v(index);
    else
      return T(0);
  }


  //! Transposition of the matrix \c m returning the transposed matrix in \c out
  template<class T>
  void transpose(const Mat<T> &m, Mat<T> &out) { out = m.T(); }

  //! Transposition of the matrix \c m
  template<class T>
  Mat<T> transpose(const Mat<T> &m) { return m.T(); }


  //! Hermitian transpose (complex conjugate transpose) of the matrix \c m
  //! returning the transposed matrix in \c out
  template<class T>
  void hermitian_transpose(const Mat<T> &m, Mat<T> &out) { out = m.H(); }

  //! Hermitian transpose (complex conjugate transpose) of the matrix \c m
  template<class T>
  Mat<T> hermitian_transpose(const Mat<T> &m) { return m.H(); }



  /*!
   * \brief Returns true if matrix \c X is hermitian, false otherwise
   * \author M. Szalay
   *
   * A square matrix \f$\mathbf{X}\f$ is hermitian if
   * \f[
   * \mathbf{X} = \mathbf{X}^H
   * \f]
   */
  template<class Num_T>
  bool is_hermitian(const Mat<Num_T>& X) {

    if (X == X.H() )
      return true;
    else
      return false;
  }

  /*!
   * \brief Returns true if matrix \c X is unitary, false otherwise
   * \author M. Szalay
   *
   * A square matrix \f$\mathbf{X}\f$ is unitary if
   * \f[
   * \mathbf{X}^H = \mathbf{X}^{-1}
   * \f]
   */
  template<class Num_T>
  bool is_unitary(const Mat<Num_T>& X) {

    if ( inv(X) == X.H() )
      return true;
    else
      return false;
  }


  /*!
   * \relates Vec
   * \brief Creates a vector with \c n copies of the vector \c v
   * \author Martin Senst
   *
   * \param v Vector to be repeated
   * \param n Number of times to repeat \c v
   */
  template<class T>
  Vec<T> repmat(const Vec<T> &v, int n)
  {
    it_assert(n > 0, "repmat(): Wrong repetition parameter");
    int data_length = v.length();
    it_assert(data_length > 0, "repmat(): Input vector can not be empty");
    Vec<T> assembly(data_length * n);
    for (int j = 0; j < n; ++j) {
      assembly.set_subvector(j * data_length, v);
    }
    return assembly;
  }


  /*!
   * \relates Mat
   * \brief Creates a matrix with \c m by \c n copies of the matrix \c data
   * \author Mark Dobossy
   *
   * \param data Matrix to be repeated
   * \param m Number of times to repeat data vertically
   * \param n Number of times to repeat data horizontally
   */
  template<class T>
  Mat<T> repmat(const Mat<T> &data, int m, int n)
  {
    it_assert((m > 0) && (n > 0), "repmat(): Wrong repetition parameters");
    int data_rows = data.rows();
    int data_cols = data.cols();
    it_assert((data_rows > 0) && (data_cols > 0), "repmat(): Input matrix can "
              "not be empty");
    Mat<T> assembly(data_rows*m, data_cols*n);
    for (int i = 0; i < m; ++i) {
      for (int j = 0; j < n; ++j) {
        assembly.set_submatrix(i*data_rows, j*data_cols, data);
      }
    }
    return assembly;
  }

  /*!
   * \relates Mat
   * \brief Returns a matrix with \c m by \c n copies of the vector \c data
   * \author Adam Piatyszek
   *
   * \param v Vector to be repeated
   * \param m Number of times to repeat data vertically
   * \param n Number of times to repeat data horizontally
   * \param transpose Specifies the input vector orientation (column vector
   * by default)
   */
  template<class T> inline
  Mat<T> repmat(const Vec<T> &v, int m, int n, bool transpose = false)
  {
    return repmat((transpose ? v.T() : Mat<T>(v)), m, n);
  }


  /*!
   * \brief Computes the Kronecker product of two matrices
   *
   * <tt>K = kron(X, Y)</tt> returns the Kronecker tensor product of \c X
   * and \c Y. The result is a large array formed by taking all possible
   * products between the elements of \c X and those of \c Y. If \c X is
   * <tt>(m x n)</tt> and \c Y is <tt>(p x q)</tt>, then <tt>kron(X, Y)</tt>
   * is <tt>(m*p x n*q)</tt>.
   *
   * \author Adam Piatyszek
   */
  template<class Num_T>
  Mat<Num_T> kron(const Mat<Num_T>& X, const Mat<Num_T>& Y)
  {
    Mat<Num_T> result(X.rows() * Y.rows(), X.cols() * Y.cols());

    for (int i = 0; i < X.rows(); i++)
      for (int j = 0; j < X.cols(); j++)
        result.set_submatrix(i * Y.rows(), j * Y.cols(), X(i, j) * Y);

    return result;
  }


  /*!
   * \brief Square root of the complex square matrix \c A
   *
   * This function computes the matrix square root of the complex square
   * matrix \c A. The implementation is based on the Matlab/Octave \c
   * sqrtm() function.
   *
   * Ref: N. J. Higham, "Numerical Analysis Report No. 336", Manchester
   * Centre for Computational Mathematics, Manchester, England, January 1999
   *
   * \author Adam Piatyszek
   */
  cmat sqrtm(const cmat& A);

  /*!
   * \brief Square root of the real square matrix \c A
   *
   * This function computes the matrix square root of the real square matrix
   * \c A. Please note that the returned matrix is complex. The
   * implementation is based on the Matlab/Octave \c sqrtm() function.
   *
   * Ref: N. J. Higham, "Numerical Analysis Report No. 336", Manchester
   * Centre for Computational Mathematics, Manchester, England, January 1999
   *
   * \author Adam Piatyszek
   */
  cmat sqrtm(const mat& A);

  //!@}



  // -------------------- Diagonal matrix functions -------------------------

  //! \addtogroup diag
  //!@{

  /*!
   * \brief Create a diagonal matrix using vector \c v as its diagonal
   *
   * All other matrix elements except the ones on its diagonal are set to
   * zero. An optional parameter \c K can be used to shift the diagonal in
   * the resulting matrix. By default \c K is equal to zero.
   *
   * The size of the diagonal matrix will be \f$n+|K| \times n+|K|\f$, where
   * \f$n\f$ is the length of the input vector \c v.
   */
  template<class T>
  Mat<T> diag(const Vec<T> &v, const int K = 0)
  {
    Mat<T> m(v.size() + std::abs(K), v.size() + std::abs(K));
    m = T(0);
    if (K>0)
      for (int i=v.size()-1; i>=0; i--)
        m(i,i+K) = v(i);
    else
      for (int i=v.size()-1; i>=0; i--)
        m(i-K,i) = v(i);

    return m;
  }

  /*!
   * \brief Create a diagonal matrix using vector \c v as its diagonal
   *
   * All other matrix elements except the ones on its diagonal are set to
   * zero.
   *
   * The size of the diagonal matrix will be \f$n \times n\f$, where \f$n\f$
   * is the length of the input vector \c v.
   */
  template<class T>
  void diag(const Vec<T> &v, Mat<T> &m)
  {
    m.set_size(v.size(), v.size(), false);
    m = T(0);
    for (int i=v.size()-1; i>=0; i--)
      m(i,i) = v(i);
  }

  /*!
   * \brief Get the diagonal elements of the input matrix \c m
   *
   * The size of the output vector with diagonal elements will be
   * \f$n = min(r, c)\f$, where \f$r \times c\f$ are the dimensions of
   * matrix \c m.
  */
  template<class T>
  Vec<T> diag(const Mat<T> &m)
  {
    Vec<T> t(std::min(m.rows(), m.cols()));

    for (int i=0; i<t.size(); i++)
      t(i) = m(i,i);

    return t;
  }

  /*!
    \brief Returns a matrix with the elements of the input vector \c main on
    the diagonal and the elements of the input vector \c sup on the diagonal
    row above.

    If the number of elements in the vector \c main is \f$n\f$, then the
    number of elements in the input vector \c sup must be \f$n-1\f$. The
    size of the return matrix will be \f$n \times n\f$.
  */
  template<class T>
  Mat<T> bidiag(const Vec<T> &main, const Vec<T> &sup)
  {
    it_assert(main.size() == sup.size()+1, "bidiag()");

    int n=main.size();
    Mat<T> m(n, n);
    m = T(0);
    for (int i=0; i<n-1; i++) {
      m(i,i) = main(i);
      m(i,i+1) = sup(i);
    }
    m(n-1,n-1) = main(n-1);

    return m;
  }

  /*!
    \brief Returns in the output variable \c m a matrix with the elements of
    the input vector \c main on the diagonal and the elements of the input
    vector \c sup on the diagonal row above.

    If the number of elements in the vector \c main is \f$n\f$, then the
    number of elements in the input vector \c sup must be \f$n-1\f$. The
    size of the output matrix \c m will be \f$n \times n\f$.
  */
  template<class T>
  void bidiag(const Vec<T> &main, const Vec<T> &sup, Mat<T> &m)
  {
    it_assert(main.size() == sup.size()+1, "bidiag()");

    int n=main.size();
    m.set_size(n, n);
    m = T(0);
    for (int i=0; i<n-1; i++) {
      m(i,i) = main(i);
      m(i,i+1) = sup(i);
    }
    m(n-1,n-1) = main(n-1);
  }

  /*!
    \brief Returns the main diagonal and the diagonal row above in the two
    output vectors \c main and \c sup.

    The input matrix \c in must be a square \f$n \times n\f$ matrix. The
    length of the output vector \c main will be \f$n\f$ and the length of
    the output vector \c sup will be \f$n-1\f$.
  */
  template<class T>
  void bidiag(const Mat<T> &m, Vec<T> &main, Vec<T> &sup)
  {
    it_assert(m.rows() == m.cols(), "bidiag(): Matrix must be square!");

    int n=m.cols();
    main.set_size(n);
    sup.set_size(n-1);
    for (int i=0; i<n-1; i++) {
      main(i) = m(i,i);
      sup(i) = m(i,i+1);
    }
    main(n-1) = m(n-1,n-1);
  }

  /*!
    \brief Returns a matrix with the elements of \c main on the diagonal,
    the elements of \c sup on the diagonal row above, and the elements of \c
    sub on the diagonal row below.

    If the length of the input vector \c main is \f$n\f$ then the lengths of
    the vectors \c sup and \c sub must equal \f$n-1\f$. The size of the
    return matrix will be \f$n \times n\f$.
  */
  template<class T>
  Mat<T> tridiag(const Vec<T> &main, const Vec<T> &sup, const Vec<T> &sub)
  {
    it_assert(main.size()==sup.size()+1 && main.size()==sub.size()+1, "bidiag()");

    int n=main.size();
    Mat<T> m(n, n);
    m = T(0);
    for (int i=0; i<n-1; i++) {
      m(i,i) = main(i);
      m(i,i+1) = sup(i);
      m(i+1,i) = sub(i);
    }
    m(n-1,n-1) = main(n-1);

    return m;
  }

  /*!
    \brief Returns in the output matrix \c m a matrix with the elements of
    \c main on the diagonal, the elements of \c sup on the diagonal row
    above, and the elements of \c sub on the diagonal row below.

    If the length of the input vector \c main is \f$n\f$ then the lengths of
    the vectors \c sup and \c sub must equal \f$n-1\f$. The size of the
    output matrix \c m will be \f$n \times n\f$.
  */
  template<class T>
  void tridiag(const Vec<T> &main, const Vec<T> &sup, const Vec<T> &sub, Mat<T> &m)
  {
    it_assert(main.size()==sup.size()+1 && main.size()==sub.size()+1, "bidiag()");

    int n=main.size();
    m.set_size(n, n);
    m = T(0);
    for (int i=0; i<n-1; i++) {
      m(i,i) = main(i);
      m(i,i+1) = sup(i);
      m(i+1,i) = sub(i);
    }
    m(n-1,n-1) = main(n-1);
  }

  /*!
    \brief Returns the main diagonal, the diagonal row above, and the
    diagonal row below int the output vectors \c main, \c sup, and \c sub.

    The input matrix \c m must be a square \f$n \times n\f$ matrix. The
    length of the output vector \c main will be \f$n\f$ and the length of
    the output vectors \c sup and \c sup will be \f$n-1\f$.
  */
  template<class T>
  void tridiag(const Mat<T> &m, Vec<T> &main, Vec<T> &sup, Vec<T> &sub)
  {
    it_assert(m.rows() == m.cols(), "tridiag(): Matrix must be square!");

    int n=m.cols();
    main.set_size(n);
    sup.set_size(n-1);
    sub.set_size(n-1);
    for (int i=0; i<n-1; i++) {
      main(i) = m(i,i);
      sup(i) = m(i,i+1);
      sub(i) = m(i+1,i);
    }
    main(n-1) = m(n-1,n-1);
  }


  /*!
    \brief The trace of the matrix \c m, i.e. the sum of the diagonal elements.
  */
  template<class T>
  T trace(const Mat<T> &m)
  {
    return sum(diag(m));
  }

  //!@}


  // ----------------- reshaping vectors and matrices ------------------------

  //! \addtogroup reshaping
  //!@{

  //! Reverse the input vector
  template<class T>
  Vec<T> reverse(const Vec<T> &in)
  {
    int i, s=in.length();

    Vec<T> out(s);
    for (i=0;i<s;i++)
      out[i]=in[s-1-i];
    return out;
  }

  //! Row vectorize the matrix [(0,0) (0,1) ... (N-1,N-2) (N-1,N-1)]
  template<class T>
  Vec<T> rvectorize(const Mat<T> &m)
  {
    int i, j, n=0, r=m.rows(), c=m.cols();
    Vec<T> v(r * c);

    for (i=0; i<r; i++)
      for (j=0; j<c; j++)
        v(n++) = m(i,j);

    return v;
  }

  //! Column vectorize the matrix [(0,0) (1,0) ... (N-2,N-1) (N-1,N-1)]
  template<class T>
  Vec<T> cvectorize(const Mat<T> &m)
  {
    int i, j, n=0, r=m.rows(), c=m.cols();
    Vec<T> v(r * c);

    for (j=0; j<c; j++)
      for (i=0; i<r; i++)
        v(n++) = m(i,j);

    return v;
  }

  /*!
    \brief Reshape the matrix into an rows*cols matrix

    The data is taken columnwise from the original matrix and written
    columnwise into the new matrix.
  */
  template<class T>
  Mat<T> reshape(const Mat<T> &m, int rows, int cols)
  {
    it_assert_debug(m.rows()*m.cols() == rows*cols, "Mat<T>::reshape: Sizes must match");
    Mat<T> temp(rows, cols);
    int i, j, ii=0, jj=0;
    for (j=0; j<m.cols(); j++) {
      for (i=0; i<m.rows(); i++) {
        temp(ii++,jj) = m(i,j);
        if (ii == rows) {
          jj++; ii=0;
        }
      }
    }
    return temp;
  }

  /*!
    \brief Reshape the vector into an rows*cols matrix

    The data is element by element from the vector and written columnwise
    into the new matrix.
  */
  template<class T>
  Mat<T> reshape(const Vec<T> &v, int rows, int cols)
  {
    it_assert_debug(v.size() == rows*cols, "Mat<T>::reshape: Sizes must match");
    Mat<T> temp(rows, cols);
    int i, j, ii=0;
    for (j=0; j<cols; j++) {
      for (i=0; i<rows; i++) {
        temp(i,j) = v(ii++);
      }
    }
    return temp;
  }

  //!@}


  //! Returns \a true if all elements are ones and \a false otherwise
  bool all(const bvec &testvec);
  //! Returns \a true if any element is one and \a false otherwise
  bool any(const bvec &testvec);

  //! \cond

  // ----------------------------------------------------------------------
  // Instantiations
  // ----------------------------------------------------------------------

#ifdef HAVE_EXTERN_TEMPLATE

  extern template int length(const vec &v);
  extern template int length(const cvec &v);
  extern template int length(const svec &v);
  extern template int length(const ivec &v);
  extern template int length(const bvec &v);

  extern template double sum(const vec &v);
  extern template std::complex<double> sum(const cvec &v);
  extern template short sum(const svec &v);
  extern template int sum(const ivec &v);
  extern template bin sum(const bvec &v);

  extern template double sum_sqr(const vec &v);
  extern template std::complex<double> sum_sqr(const cvec &v);
  extern template short sum_sqr(const svec &v);
  extern template int sum_sqr(const ivec &v);
  extern template bin sum_sqr(const bvec &v);

  extern template vec cumsum(const vec &v);
  extern template cvec cumsum(const cvec &v);
  extern template svec cumsum(const svec &v);
  extern template ivec cumsum(const ivec &v);
  extern template bvec cumsum(const bvec &v);

  extern template double prod(const vec &v);
  extern template std::complex<double> prod(const cvec &v);
  extern template short prod(const svec &v);
  extern template int prod(const ivec &v);
  extern template bin prod(const bvec &v);

  extern template vec cross(const vec &v1, const vec &v2);
  extern template cvec cross(const cvec &v1, const cvec &v2);
  extern template ivec cross(const ivec &v1, const ivec &v2);
  extern template svec cross(const svec &v1, const svec &v2);
  extern template bvec cross(const bvec &v1, const bvec &v2);

  extern template vec reverse(const vec &in);
  extern template cvec reverse(const cvec &in);
  extern template svec reverse(const svec &in);
  extern template ivec reverse(const ivec &in);
  extern template bvec reverse(const bvec &in);

  extern template vec zero_pad(const vec &v, int n);
  extern template cvec zero_pad(const cvec &v, int n);
  extern template ivec zero_pad(const ivec &v, int n);
  extern template svec zero_pad(const svec &v, int n);
  extern template bvec zero_pad(const bvec &v, int n);

  extern template vec zero_pad(const vec &v);
  extern template cvec zero_pad(const cvec &v);
  extern template ivec zero_pad(const ivec &v);
  extern template svec zero_pad(const svec &v);
  extern template bvec zero_pad(const bvec &v);

  extern template mat zero_pad(const mat &, int, int);
  extern template cmat zero_pad(const cmat &, int, int);
  extern template imat zero_pad(const imat &, int, int);
  extern template smat zero_pad(const smat &, int, int);
  extern template bmat zero_pad(const bmat &, int, int);

  extern template vec sum(const mat &m, int dim);
  extern template cvec sum(const cmat &m, int dim);
  extern template svec sum(const smat &m, int dim);
  extern template ivec sum(const imat &m, int dim);
  extern template bvec sum(const bmat &m, int dim);

  extern template double sumsum(const mat &X);
  extern template std::complex<double> sumsum(const cmat &X);
  extern template short sumsum(const smat &X);
  extern template int sumsum(const imat &X);
  extern template bin sumsum(const bmat &X);

  extern template vec sum_sqr(const mat & m, int dim);
  extern template cvec sum_sqr(const cmat &m, int dim);
  extern template svec sum_sqr(const smat &m, int dim);
  extern template ivec sum_sqr(const imat &m, int dim);
  extern template bvec sum_sqr(const bmat &m, int dim);

  extern template mat cumsum(const mat &m, int dim);
  extern template cmat cumsum(const cmat &m, int dim);
  extern template smat cumsum(const smat &m, int dim);
  extern template imat cumsum(const imat &m, int dim);
  extern template bmat cumsum(const bmat &m, int dim);

  extern template vec prod(const mat &m, int dim);
  extern template cvec prod(const cmat &v, int dim);
  extern template svec prod(const smat &m, int dim);
  extern template ivec prod(const imat &m, int dim);
  extern template bvec prod(const bmat &m, int dim);

  extern template vec diag(const mat &in);
  extern template cvec diag(const cmat &in);
  extern template void diag(const vec &in, mat &m);
  extern template void diag(const cvec &in, cmat &m);
  extern template mat diag(const vec &v, const int K);
  extern template cmat diag(const cvec &v, const int K);

  extern template mat bidiag(const vec &, const vec &);
  extern template cmat bidiag(const cvec &, const cvec &);
  extern template void bidiag(const vec &, const vec &, mat &);
  extern template void bidiag(const cvec &, const cvec &, cmat &);
  extern template void bidiag(const mat &, vec &, vec &);
  extern template void bidiag(const cmat &, cvec &, cvec &);

  extern template mat tridiag(const vec &main, const vec &, const vec &);
  extern template cmat tridiag(const cvec &main, const cvec &, const cvec &);
  extern template void tridiag(const vec &main, const vec &, const vec &, mat &);
  extern template void tridiag(const cvec &main, const cvec &, const cvec &, cmat &);
  extern template void tridiag(const mat &m, vec &, vec &, vec &);
  extern template void tridiag(const cmat &m, cvec &, cvec &, cvec &);

  extern template double trace(const mat &in);
  extern template std::complex<double> trace(const cmat &in);
  extern template short trace(const smat &in);
  extern template int trace(const imat &in);
  extern template bin trace(const bmat &in);

  extern template void transpose(const mat &m, mat &out);
  extern template void transpose(const cmat &m, cmat &out);
  extern template void transpose(const smat &m, smat &out);
  extern template void transpose(const imat &m, imat &out);
  extern template void transpose(const bmat &m, bmat &out);

  extern template mat transpose(const mat &m);
  extern template cmat transpose(const cmat &m);
  extern template smat transpose(const smat &m);
  extern template imat transpose(const imat &m);
  extern template bmat transpose(const bmat &m);

  extern template void hermitian_transpose(const mat &m, mat &out);
  extern template void hermitian_transpose(const cmat &m, cmat &out);
  extern template void hermitian_transpose(const smat &m, smat &out);
  extern template void hermitian_transpose(const imat &m, imat &out);
  extern template void hermitian_transpose(const bmat &m, bmat &out);

  extern template mat hermitian_transpose(const mat &m);
  extern template cmat hermitian_transpose(const cmat &m);
  extern template smat hermitian_transpose(const smat &m);
  extern template imat hermitian_transpose(const imat &m);
  extern template bmat hermitian_transpose(const bmat &m);

  extern template bool is_hermitian(const mat &X);
  extern template bool is_hermitian(const cmat &X);

  extern template bool is_unitary(const mat &X);
  extern template bool is_unitary(const cmat &X);

  extern template vec rvectorize(const mat &m);
  extern template cvec rvectorize(const cmat &m);
  extern template ivec rvectorize(const imat &m);
  extern template svec rvectorize(const smat &m);
  extern template bvec rvectorize(const bmat &m);

  extern template vec cvectorize(const mat &m);
  extern template cvec cvectorize(const cmat &m);
  extern template ivec cvectorize(const imat &m);
  extern template svec cvectorize(const smat &m);
  extern template bvec cvectorize(const bmat &m);

  extern template mat reshape(const mat &m, int rows, int cols);
  extern template cmat reshape(const cmat &m, int rows, int cols);
  extern template imat reshape(const imat &m, int rows, int cols);
  extern template smat reshape(const smat &m, int rows, int cols);
  extern template bmat reshape(const bmat &m, int rows, int cols);

  extern template mat reshape(const vec &m, int rows, int cols);
  extern template cmat reshape(const cvec &m, int rows, int cols);
  extern template imat reshape(const ivec &m, int rows, int cols);
  extern template smat reshape(const svec &m, int rows, int cols);
  extern template bmat reshape(const bvec &m, int rows, int cols);

  extern template mat kron(const mat &X, const mat &Y);
  extern template cmat kron(const cmat &X, const cmat &Y);
  extern template imat kron(const imat &X, const imat &Y);
  extern template smat kron(const smat &X, const smat &Y);
  extern template bmat kron(const bmat &X, const bmat &Y);

  extern template vec repmat(const vec &v, int n);
  extern template cvec repmat(const cvec &v, int n);
  extern template ivec repmat(const ivec &v, int n);
  extern template svec repmat(const svec &v, int n);
  extern template bvec repmat(const bvec &v, int n);

  extern template mat repmat(const vec &v, int m, int n, bool transpose);
  extern template cmat repmat(const cvec &v, int m, int n, bool transpose);
  extern template imat repmat(const ivec &v, int m, int n, bool transpose);
  extern template smat repmat(const svec &v, int m, int n, bool transpose);
  extern template bmat repmat(const bvec &v, int m, int n, bool transpose);

  extern template mat repmat(const mat &data, int m, int n);
  extern template cmat repmat(const cmat &data, int m, int n);
  extern template imat repmat(const imat &data, int m, int n);
  extern template smat repmat(const smat &data, int m, int n);
  extern template bmat repmat(const bmat &data, int m, int n);

#endif // HAVE_EXTERN_TEMPLATE

  //! \endcond

} // namespace itpp

#endif // #ifndef MATFUNC_H