IT++ 4.3.1
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Functions | |
double | itpp::cheb (int n, double x) |
Chebyshev polynomial of the first kind. | |
vec | itpp::cheb (int n, const vec &x) |
Chebyshev polynomial of the first kind. | |
mat | itpp::cheb (int n, const mat &x) |
Chebyshev polynomial of the first kind. | |
void | itpp::poly (const vec &r, vec &p) |
Create a polynomial of the given roots. | |
void | itpp::poly (const cvec &r, cvec &p) |
Create a polynomial of the given roots. | |
vec | itpp::poly (const vec &r) |
Create a polynomial of the given roots. | |
cvec | itpp::poly (const cvec &r) |
Create a polynomial of the given roots. | |
void | itpp::roots (const vec &p, cvec &r) |
Calculate the roots of the polynomial. | |
void | itpp::roots (const cvec &p, cvec &r) |
Calculate the roots of the polynomial. | |
cvec | itpp::roots (const vec &p) |
Calculate the roots of the polynomial. | |
cvec | itpp::roots (const cvec &p) |
Calculate the roots of the polynomial. | |
vec | itpp::polyval (const vec &p, const vec &x) |
Evaluate polynomial. | |
cvec | itpp::polyval (const vec &p, const cvec &x) |
Evaluate polynomial. | |
cvec | itpp::polyval (const cvec &p, const vec &x) |
Evaluate polynomial. | |
cvec | itpp::polyval (const cvec &p, const cvec &x) |
Evaluate polynomial. | |
ITPP_EXPORT void itpp::poly | ( | const vec & | r, |
vec & | p ) |
Create a polynomial of the given roots.
Create a polynomial p
with roots r
Definition at line 40 of file poly.cpp.
Referenced by poly(), poly(), poly2ac(), poly2lsf(), poly2rc(), polystab(), polystab(), itpp::CRC_Code::set_code(), and itpp::CRC_Code::set_generator().
ITPP_EXPORT void itpp::roots | ( | const vec & | p, |
cvec & | r ) |
Calculate the roots of the polynomial.
Calculate the roots r
of the polynomial p
Definition at line 66 of file poly.cpp.
References concat(), diag(), eig(), find(), ones(), and zeros_c().
Referenced by polystab(), polystab(), roots(), roots(), and itpp::Turbo_Codec::wcdma_turbo_interleaver_sequence().
ITPP_EXPORT 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
\[p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N \]
Definition at line 135 of file poly.cpp.
References elem_mult(), and it_error_if.
ITPP_EXPORT double itpp::cheb | ( | int | n, |
double | x ) |
Chebyshev polynomial of the first kind.
Chebyshev polynomials of the first kind can be defined as follows:
\[T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right. \]
n | order of the Chebyshev polynomial |
x | value at which the Chebyshev polynomial is to be evaluated |
Definition at line 195 of file poly.cpp.
ITPP_EXPORT 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:
\[T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right. \]
n | order of the Chebyshev polynomial |
x | vector of values at which the Chebyshev polynomial is to be evaluated |
x
Definition at line 209 of file poly.cpp.
References cheb(), and it_assert_debug.
ITPP_EXPORT 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:
\[T(x) = \left\{ \begin{array}{ll} \cos(n\arccos(x)),& |x| \leq 0 \\ \cosh(n\mathrm{arccosh}(x)),& x > 1 \\ (-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1 \end{array} \right. \]
n | order of the Chebyshev polynomial |
x | matrix of values at which the Chebyshev polynomial is to be evaluated |
x
.Definition at line 220 of file poly.cpp.
References cheb(), and it_assert_debug.
ITPP_EXPORT void itpp::poly | ( | const cvec & | r, |
cvec & | p ) |
ITPP_EXPORT void itpp::roots | ( | const cvec & | p, |
cvec & | r ) |
ITPP_EXPORT cvec itpp::polyval | ( | const vec & | p, |
const cvec & | x ) |
Evaluate polynomial.
Evaluate the polynomial p
(of length \(N+1\) at the points x
The output is given by
\[p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N \]
Definition at line 150 of file poly.cpp.
References elem_mult(), and it_error_if.
ITPP_EXPORT cvec itpp::polyval | ( | const cvec & | p, |
const vec & | x ) |
Evaluate polynomial.
Evaluate the polynomial p
(of length \(N+1\) at the points x
The output is given by
\[p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N \]
Definition at line 165 of file poly.cpp.
References elem_mult(), it_error_if, and to_cvec().
ITPP_EXPORT cvec itpp::polyval | ( | const cvec & | p, |
const cvec & | x ) |
Evaluate polynomial.
Evaluate the polynomial p
(of length \(N+1\) at the points x
The output is given by
\[p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N \]
Definition at line 180 of file poly.cpp.
References elem_mult(), and it_error_if.
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