IT++ Logo
Functions
Polynomial Functions

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.
 

Detailed Description

Function Documentation

◆ poly() [1/4]

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.

References itpp::Array< T >::set_size(), and itpp::Array< T >::size().

Referenced by itpp::poly(), itpp::poly(), itpp::polystab(), itpp::polystab(), itpp::CRC_Code::set_code(), and itpp::CRC_Code::set_generator().

◆ roots() [1/4]

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(), itpp::Array< T >::size(), and itpp::zeros_c().

Referenced by itpp::polystab(), itpp::polystab(), itpp::roots(), itpp::roots(), and itpp::Turbo_Codec::wcdma_turbo_interleaver_sequence().

◆ polyval() [1/4]

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 itpp::elem_mult(), it_error_if, and itpp::Array< T >::size().

Referenced by itpp::freqz(), and itpp::freqz().

◆ cheb() [1/3]

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:

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

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::acosh(), itpp::is_even(), and it_assert.

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

◆ cheb() [2/3]

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:

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

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(), it_assert_debug, and itpp::Array< T >::size().

◆ cheb() [3/3]

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:

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

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.

◆ poly() [2/4]

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

Create a polynomial of the given roots.

Create a polynomial p with roots r

Definition at line 52 of file poly.cpp.

References itpp::Array< T >::set_size(), and itpp::Array< T >::size().

◆ roots() [2/4]

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(), itpp::Array< T >::size(), and itpp::zeros_c().

◆ polyval() [2/4]

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 itpp::elem_mult(), it_error_if, and itpp::Array< T >::size().

◆ polyval() [3/4]

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 itpp::elem_mult(), it_error_if, itpp::Array< T >::size(), and itpp::to_cvec().

◆ polyval() [4/4]

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 itpp::elem_mult(), it_error_if, and itpp::Array< T >::size().

◆ poly() [3/4]

vec itpp::poly ( const vec &  r)
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().

◆ poly() [4/4]

cvec itpp::poly ( const cvec &  r)
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().

◆ roots() [3/4]

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

◆ roots() [4/4]

cvec itpp::roots ( const cvec &  p)
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().

SourceForge Logo

Generated on Mon Jun 10 2024 11:49:31 for IT++ by Doxygen 1.9.8