poly.cpp File Reference

Polynomial functions. More...

#include <itpp/base/itcompat.h>
#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>

Functions

double itpp::cheb (int n, double x)

Chebyshev polynomial of the first kind
Chebyshev polynomials of the first kind can be defined as follows:
$T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right.$
.

vec itpp::cheb (int n, const vec &x)

Chebyshev polynomial of the first kind
Chebyshev polynomials of the first kind can be defined as follows:
$T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right.$
.

mat itpp::cheb (int n, const mat &x)

Chebyshev polynomial of the first kind
Chebyshev polynomials of the first kind can be defined as follows:
$T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right.$
.

void itpp::poly (const vec &r, vec &p)

Create a polynomial of the given roots
Create a polynomial p with roots r.

void itpp::poly (const cvec &r, cvec &p)

void itpp::roots (const vec &p, cvec &r)

Calculate the roots of the polynomial
Calculate the roots r of the polynomial p.

void itpp::roots (const cvec &p, cvec &r)

vec itpp::polyval (const vec &p, const vec &x)

Evaluate polynomial
Evaluate the polynomial p (of length $N+1$ at the points x The output is given by
$p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N$
.

cvec itpp::polyval (const vec &p, const cvec &x)

cvec itpp::polyval (const cvec &p, const vec &x)

cvec itpp::polyval (const cvec &p, const cvec &x)

Detailed Description

Polynomial functions.

Author:: Tony Ottosson, Kumar Appaiah and Adam Piatyszek

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This file is part of IT++ - a C++ library of mathematical, signal processing, speech processing, and communications classes and functions.

IT++ 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.

IT++ 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 IT++. If not, see <http://www.gnu.org/licenses/>.

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Functions
double	itpp::cheb (int n, double x)
	Chebyshev polynomial of the first kind Chebyshev polynomials of the first kind can be defined as follows: $T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& \|x\| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right.$ .
vec	itpp::cheb (int n, const vec &x)
	Chebyshev polynomial of the first kind Chebyshev polynomials of the first kind can be defined as follows: $T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& \|x\| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right.$ .
mat	itpp::cheb (int n, const mat &x)
	Chebyshev polynomial of the first kind Chebyshev polynomials of the first kind can be defined as follows: $T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& \|x\| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right.$ .

void	itpp::poly (const vec &r, vec &p)
	Create a polynomial of the given roots Create a polynomial `p` with roots `r`.
void	itpp::poly (const cvec &r, cvec &p)

void	itpp::roots (const vec &p, cvec &r)
	Calculate the roots of the polynomial Calculate the roots `r` of the polynomial `p`.
void	itpp::roots (const cvec &p, cvec &r)

vec	itpp::polyval (const vec &p, const vec &x)
	Evaluate polynomial Evaluate the polynomial `p` (of length at the points `x` The output is given by $p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N$ .
cvec	itpp::polyval (const vec &p, const cvec &x)
cvec	itpp::polyval (const cvec &p, const vec &x)
cvec	itpp::polyval (const cvec &p, const cvec &x)