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Functions
Polynomial Functions
Signal Processing (SP) Module

Functions

double itpp::cheb (int n, double x)
 Chebyshev polynomial of the first kindChebyshev 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 kindChebyshev 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 kindChebyshev 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 rootsCreate a polynomial p with roots r.
void itpp::poly (const cvec &r, cvec &p)
 Create a polynomial of the given rootsCreate a polynomial p with roots r.
vec itpp::poly (const vec &r)
 Create a polynomial of the given rootsCreate a polynomial p with roots r.
cvec itpp::poly (const cvec &r)
 Create a polynomial of the given rootsCreate a polynomial p with roots r.
void itpp::roots (const vec &p, cvec &r)
 Calculate the roots of the polynomialCalculate the roots r of the polynomial p.
void itpp::roots (const cvec &p, cvec &r)
 Calculate the roots of the polynomialCalculate the roots r of the polynomial p.
cvec itpp::roots (const vec &p)
 Calculate the roots of the polynomialCalculate the roots r of the polynomial p.
cvec itpp::roots (const cvec &p)
 Calculate the roots of the polynomialCalculate the roots r of the polynomial p.
vec itpp::polyval (const vec &p, const vec &x)
 Evaluate polynomialEvaluate 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)
 Evaluate polynomialEvaluate 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 cvec &p, const vec &x)
 Evaluate polynomialEvaluate 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 cvec &p, const cvec &x)
 Evaluate polynomialEvaluate the polynomial p (of length $N+1$ at the points x The output is given by

\[ p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N \]

.


Function Documentation

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

Chebyshev polynomial of the first kindChebyshev polynomials of the first kind can be defined as follows:

\[ T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right. \]

.

Parameters:
norder of the Chebyshev polynomial
xvalue at which the Chebyshev polynomial is to be evaluated
Author:
Kumar Appaiah, Adam Piatyszek (code review)

Definition at line 195 of file poly.cpp.

References itpp::acos(), itpp::acosh(), itpp::cos(), itpp::cosh(), itpp::is_even(), and it_assert.

Referenced by itpp::cheb(), and itpp::chebwin().

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

Chebyshev polynomial of the first kindChebyshev polynomials of the first kind can be defined as follows:

\[ T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right. \]

.

Parameters:
norder of the Chebyshev polynomial
xvector of values at which the Chebyshev polynomial is to be evaluated
Returns:
values of the Chebyshev polynomial evaluated for each element of x
Author:
Kumar Appaiah, Adam Piatyszek (code review)

Definition at line 209 of file poly.cpp.

References itpp::cheb(), and it_assert_debug.

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

Chebyshev polynomial of the first kindChebyshev polynomials of the first kind can be defined as follows:

\[ T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right. \]

.

Parameters:
norder of the Chebyshev polynomial
xmatrix of values at which the Chebyshev polynomial is to be evaluated
Returns:
values of the Chebyshev polynomial evaluated for each element in x.
Author:
Kumar Appaiah, Adam Piatyszek (code review)

Definition at line 220 of file poly.cpp.

References itpp::cheb(), and it_assert_debug.

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