/*---------------------------------------------------------------------------*
* IT++ *
*---------------------------------------------------------------------------*
* Copyright (c) 1995-2004 by Tony Ottosson, Thomas Eriksson, Pål Frenger, *
* Tobias Ringström, and Jonas Samuelsson. *
* *
* Permission to use, copy, modify, and distribute this software and its *
* documentation under the terms of the GNU General Public License is hereby *
* granted. No representations are made about the suitability of this *
* software for any purpose. It is provided "as is" without expressed or *
* implied warranty. See the GNU General Public License for more details. *
*---------------------------------------------------------------------------*/
/*!
\file
\brief Definitions of functions on vectors and matrices
\author Tony Ottosson
1.21
2003/06/17 11:48:36
*/
#ifndef __matfunc_h
#define __matfunc_h
#include "base/vec.h"
#include "base/mat.h"
#include "base/converters.h"
#include "base/scalfunc.h"
#include "base/itassert.h"
#include "base/specmat.h"
#include "base/binary.h"
#include "base/sort.h"
namespace itpp {
//! Define of absolute(x)
#define absolut(x) (((x)>0) ? (x) : (-(x)))
/*!
\defgroup 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
sum(m)=sum(m,1) returns a vector where the elements are sum over each column
sum(m,2) 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 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
sum(m)=sum(m,1) returns a vector where the elements are sum squared over each column
sum(m,2) 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
cumsum(m)=cumsum(m,1) returns a matrix where the elements are sums over each column
cumsum(m,2) 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
prod(m)=prod(m,1) returns a vector where the elements are products over each column
prod(m,2) 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;
}
//! Apply arbitrary function to a vector
template<class T, class fT>
Vec<T> apply_function(fT (*f)(fT), const Vec<T> &data)
{
Vec<T> out(data.length());
for (int i=0;i<data.length();i++)
out[i]=T(f(fT(data[i])));
return out;
}
//! Apply arbitrary functions to a matrix
template<class T, class fT>
Mat<T> apply_function(fT (*f)(fT), const Mat<T> &data)
{
Mat<T> out(data.rows(),data.cols());
for (int i=0;i<out.rows();i++)
for (int j=0;j<out.cols();j++)
//out(i,j)=static_cast<T>(f(static_cast<fT>(data(i,j))));
out(i,j)=T(f(fT(data(i,j))));
return out;
}
//! 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 = pow2(needed_bits(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;
}
/*!
\brief 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(); }
/*!
\brief Transposition of the matrix \c m
*/
template<class T>
Mat<T> transpose(const Mat<T> &m) { return m.T(); }
/*!
\brief 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(); }
/*!
\brief 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 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 <ediap@et.put.poznan.pl>
*/
template<class Num_T>
Mat<Num_T> kron(const Mat<Num_T>& x, const Mat<Num_T>& y) {
int x_rows = x.rows();
int x_cols = x.cols();
int y_rows = y.rows();
int y_cols = y.cols();
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;
}
//!@}
// -------------------- Diagonal matrix functions ---------------------------------------
/*!
\defgroup diag Diagonal matrices and functions of diagonals
*/
//!@{
/*!
\brief Returns a diagonal matrix whith the elements of the vector \c v on the diagonal and zeros elsewhere.
The size of the return matrix will be \f$n \times n\f$, where \f$n\f$ is the length of the input vector \c v.
*/
template<class T>
Mat<T> diag(const Vec<T> &v)
{
Mat<T> m(v.size(), v.size());
m = T(0);
for (int i=v.size()-1; i>=0; i--)
m(i,i) = v(i);
return m;
}
/*!
\brief Returns in the output wariable \c m a diagonal matrix whith the elements of the vector \c v on the
diagonal and zeros elsewhere.
The size of the output matrix \c m 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 Returns the diagonal elements of the input matrix \c m.
The input matrix \c m must be a square \f$n \times n\f$ matrix. The size of the output vector will be \f$n\f$.
*/
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 ---------------------------
/*!
\defgroup reshaping Reshaping of vectors and matrices
*/
//!@{
//! 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_assert1(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_assert1(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;
}
//!@}
/*!
\defgroup upsample Upsampling of vectors and matrices
*/
//!@{
//! Repeat each element in the vector norepeats times in sequence
template<class T>
Vec<T> repeat(const Vec<T> &v, int norepeats)
{
Vec<T> temp(v.length()*norepeats);
for(int i=0; i<v.length(); i++) {
for(int j=0;j<norepeats;j++)
temp(i*norepeats+j)=v(i);
}
return temp;
}
//! Repeats each column norepeats times in sequence
template<class T>
Mat<T> repeat(const Mat<T> &m, int norepeats)
{
Mat<T> temp(m.rows(), m.cols()*norepeats);
for (int j=0; j<m.cols(); j++) {
for (int i=0;i<norepeats;i++) {
temp.set_col(j*norepeats+i, m.get_col(j));
}
}
return temp;
}
//! Upsample a vector by incerting \a (usf-1) zeros after each sample
template<class T>
void upsample(const Vec<T> &v, int usf, Vec<T> &u)
{
it_assert1(usf >= 1, "upsample: upsampling factor must be equal or greater than one" );
u.set_size(v.length()*usf);
u.clear();
for(long i=0;i<v.length();i++)
u(i*usf)=v(i);
}
//! Upsample a vector by incerting \a (usf-1) zeros after each sample
template<class T>
Vec<T> upsample(const Vec<T> &v, int usf)
{
Vec<T> u;
upsample(v,usf,u);
return u;
}
//! Upsample each column by incerting \a (usf-1) zeros after each column
template<class T>
void upsample(const Mat<T> &v, int usf, Mat<T> &u)
{
it_assert1(usf >= 1, "upsample: upsampling factor must be equal or greater than one" );
u.set_size(v.rows(),v.cols()*usf);
u.clear();
for (long j=0;j<v.cols();j++)
u.set_col(j*usf,v.get_col(j));
}
//! Upsample each column by incerting \a (usf-1) zeros after each column
template<class T>
Mat<T> upsample(const Mat<T> &v, int usf)
{
Mat<T> u;
upsample(v,usf,u);
return u;
}
//! Upsample each column by a factor of \a (usf-1) by linear interpolation
template<class T>
void lininterp(const Mat<T> &m, int usf, Mat<T> &u)
{
it_assert1(usf >= 1, "lininterp: upsampling factor must be equal or greater than one" );
long L = (m.cols()-1)*usf+1;
u.set_size(m.rows(),L);
for (long i = 0; i < m.rows(); i++){
for (long j = 0; j < L-1; j++)
u(i,j) = (m(i,j/usf) + (j % usf)/((double)usf)*(m(i,(j+usf)/usf)-m(i,j/usf)));
u(i,L-1) = m(i,m.cols()-1);
}
}
//! Upsample each column by a factor of \a (usf-1) by linear interpolation
template<class T>
Mat<T> lininterp(const Mat<T> &m, int usf)
{
Mat<T> u;
lininterp(m,usf,u);
return u;
}
//! Upsample by a factor of \a (usf-1) by linear interpolation
template<class T>
void lininterp(const Vec<T> &v, int usf, Vec<T> &u)
{
it_assert1(usf >= 1, "lininterp: upsampling factor must be equal or greater than one" );
long L = (v.length()-1)*usf+1;
u.set_size(L);
for (long j = 0; j < L-1; j++) {
u(j) = (v(j/usf) + (j % usf)/((double)usf)*(v((j+usf)/usf)-v(j/usf)));
}
u(L-1) = v(v.length()-1);
}
//! Upsample by a factor of \a (usf-1) by linear interpolation
template<class T>
Vec<T> lininterp(const Vec<T> &v, int usf)
{
Vec<T> u;
lininterp(v,usf,u);
return u;
}
//!@}
} //namespace itpp
#endif // __matfunc_h
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