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 itpp::poly(), itpp::poly(), itpp::polystab(), itpp::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 itpp::concat(), itpp::diag(), itpp::eig(), itpp::find(), itpp::ones(), and itpp::zeros_c().
Referenced by itpp::polystab(), itpp::polystab(), itpp::roots(), itpp::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 
x The output is given by
![\[
p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N
\]](form_270.png)
Definition at line 135 of file poly.cpp.
References itpp::elem_mult(), and it_error_if.
Referenced by itpp::freqz(), and itpp::freqz().
| 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:
![\[
T(x) = \left\{
\begin{array}{ll}
\cos(n\arccos(x)),& |x| \leq 0 \\
\cosh(n\mathrm{arccosh}(x)),& x > 1 \\
(-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1
\end{array}
\right.
\]](form_271.png)
| 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.
References itpp::acosh(), itpp::is_even(), and it_assert.
Referenced by itpp::cheb(), itpp::cheb(), and itpp::chebwin().
| 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:
![\[
T(x) = \left\{
\begin{array}{ll}
\cos(n\arccos(x)),& |x| \leq 0 \\
\cosh(n\mathrm{arccosh}(x)),& x > 1 \\
(-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1
\end{array}
\right.
\]](form_271.png)
| 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 itpp::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:
![\[
T(x) = \left\{
\begin{array}{ll}
\cos(n\arccos(x)),& |x| \leq 0 \\
\cosh(n\mathrm{arccosh}(x)),& x > 1 \\
(-1)^n \cosh(n\mathrm{arccosh}(-x)),& x < -1
\end{array}
\right.
\]](form_271.png)
| 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 itpp::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 ) |
Calculate the roots of the polynomial.
Calculate the roots r of the polynomial p
Definition at line 99 of file poly.cpp.
References itpp::concat(), itpp::diag(), itpp::eig(), itpp::ones_c(), and itpp::zeros_c().
| ITPP_EXPORT cvec itpp::polyval | ( | const vec & | p, |
| const cvec & | x ) |
Evaluate polynomial.
Evaluate the polynomial p (of length 
x The output is given by
![\[
p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N
\]](form_270.png)
Definition at line 150 of file poly.cpp.
References itpp::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 
x The output is given by
![\[
p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N
\]](form_270.png)
Definition at line 165 of file poly.cpp.
References itpp::elem_mult(), it_error_if, and itpp::to_cvec().
| ITPP_EXPORT cvec itpp::polyval | ( | const cvec & | p, |
| const cvec & | x ) |
Evaluate polynomial.
Evaluate the polynomial p (of length 
x The output is given by
![\[
p_0 x^N + p_1 x^{N-1} + \ldots + p_{N-1} x + p_N
\]](form_270.png)
Definition at line 180 of file poly.cpp.
References itpp::elem_mult(), and it_error_if.
|
inline |
Create a polynomial of the given roots.
Create a polynomial p with roots r
Definition at line 47 of file poly.h.
References itpp::poly().
|
inline |
Create a polynomial of the given roots.
Create a polynomial p with roots r
Definition at line 49 of file poly.h.
References itpp::poly().
|
inline |
Calculate the roots of the polynomial.
Calculate the roots r of the polynomial p
Definition at line 62 of file poly.h.
References itpp::roots().
|
inline |
Calculate the roots of the polynomial.
Calculate the roots r of the polynomial p
Definition at line 64 of file poly.h.
References itpp::roots().
Generated on Tue Dec 10 2024 04:49:37 for IT++ by Doxygen 1.12.0