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/*!
* \file
* \brief Polynomial functions
* \author Tony Ottosson
*
* -------------------------------------------------------------------------
*
* IT++ - C++ library of mathematical, signal processing, speech processing,
* and communications classes and functions
*
* Copyright (C) 1995-2008 (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
*
* -------------------------------------------------------------------------
*/
#include <itpp/signal/poly.h>
#include <itpp/base/converters.h>
#include <itpp/base/algebra/eigen.h>
#include <itpp/base/specmat.h>
#include <itpp/base/matfunc.h>
namespace itpp {
void poly(const vec &r, vec &p)
{
int n = r.size();
p.set_size(n+1, false);
p.zeros();
p(0) = 1.0;
for (int i=0; i<n; i++)
p.set_subvector(1, i+1, p(1,i+1) - r(i)*p(0,i));
}
void poly(const cvec &r, cvec &p)
{
int n = r.size();
p.set_size(n+1, false);
p.zeros();
p(0) = 1.0;
for (int i=0; i<n; i++)
p.set_subvector(1, i+1, p(1,i+1) - r(i)*p(0,i));
}
void roots(const vec &p, cvec &r)
{
int n = p.size(), m, l;
ivec f = find(p != 0.0);
m = f.size();
vec v = p;
mat A;
if (m > 0 && n > 1) {
v = v(f(0),f(m-1));
l = v.size();
if (l>1) {
A = diag(ones(l-2), -1);
A.set_row(0, -v(1,l-1)/v(0));
r = eig(A);
cvec d;
cmat V;
eig(A, d ,V);
if (f(m-1) < n)
r = concat(r, zeros_c(n-f(m-1)-1));
} else {
r.set_size(n-f(m-1)-1, false);
r.zeros();
}
} else
r.set_size(0, false);
}
void roots(const cvec &p, cvec &r)
{
int n = p.size(), m, l;
ivec f;
// find all non-zero elements
for (int i=0; i<n; i++)
if( p(i) != 0.0 )
f = concat(f, i);
m = f.size();
cvec v = p;
cmat A;
if (m > 0 && n > 1) {
v = v(f(0),f(m-1));
l = v.size();
if (l>1) {
A = diag(ones_c(l-2), -1);
A.set_row(0, -v(1,l-1)/v(0));
r = eig(A);
if (f(m-1) < n)
r = concat(r, zeros_c(n-f(m-1)-1));
} else {
r.set_size(n-f(m-1)-1, false);
r.zeros();
}
} else
r.set_size(0, false);
}
vec polyval(const vec &p, const vec &x)
{
it_error_if(p.size() == 0, "polyval: size of polynomial is zero");
it_error_if(x.size() == 0, "polyval: size of input value vector is zero");
vec out(x.size());
out = p(0);
for (int i=1; i<p.size(); i++)
out = p(i) + elem_mult(x, out);
return out;
}
cvec polyval(const vec &p, const cvec &x)
{
it_error_if(p.size() == 0, "polyval: size of polynomial is zero");
it_error_if(x.size() == 0, "polyval: size of input value vector is zero");
cvec out(x.size());
out = p(0);
for (int i=1; i<p.size(); i++)
out = std::complex<double>(p(i)) + elem_mult(x, out);
return out;
}
cvec polyval(const cvec &p, const vec &x)
{
it_error_if(p.size() == 0, "polyval: size of polynomial is zero");
it_error_if(x.size() == 0, "polyval: size of input value vector is zero");
cvec out(x.size());
out = p(0);
for (int i=1; i<p.size(); i++)
out = std::complex<double>(p(i)) + elem_mult(to_cvec(x), out);
return out;
}
cvec polyval(const cvec &p, const cvec &x)
{
it_error_if(p.size() == 0, "polyval: size of polynomial is zero");
it_error_if(x.size() == 0, "polyval: size of input value vector is zero");
cvec out(x.size());
out = p(0);
for (int i=1; i<p.size(); i++)
out = p(i) + elem_mult(x, out);
return out;
}
} // namespace itpp
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