Polynomial Functions
[Signal Processing (SP) Module]

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: .
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: .
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: .
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)
vec	itpp::poly (const vec &r)
cvec	itpp::poly (const cvec &r)
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)
cvec	itpp::roots (const vec &p)
cvec	itpp::roots (const cvec &p)
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 .
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)

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Function Documentation

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:

.

Parameters:

	n	order of the Chebyshev polynomial
	x	matrix 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)

References it_assert_debug.

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

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:

.

Parameters:

	n	order of the Chebyshev polynomial
	x	vector 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)

References itpp::cheb(), and it_assert_debug.

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

Chebyshev polynomial of the first kind

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

.

Parameters:

	n	order of the Chebyshev polynomial
	x	value at which the Chebyshev polynomial is to be evaluated

Author:

Kumar Appaiah, Adam Piatyszek (code review)

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