/usr/include/chebyshev.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _chebyshev_h
#define _chebyshev_h
#include "ap.h"
#include "ialglib.h"
/*************************************************************************
Calculation of the value of the Chebyshev polynomials of the
first and second kinds.
Parameters:
r - polynomial kind, either 1 or 2.
n - degree, n>=0
x - argument, -1 <= x <= 1
Result:
the value of the Chebyshev polynomial at x
*************************************************************************/
double chebyshevcalculate(const int& r, const int& n, const double& x);
/*************************************************************************
Summation of Chebyshev polynomials using Clenshaw�s recurrence formula.
This routine calculates
c[0]*T0(x) + c[1]*T1(x) + ... + c[N]*TN(x)
or
c[0]*U0(x) + c[1]*U1(x) + ... + c[N]*UN(x)
depending on the R.
Parameters:
r - polynomial kind, either 1 or 2.
n - degree, n>=0
x - argument
Result:
the value of the Chebyshev polynomial at x
*************************************************************************/
double chebyshevsum(const ap::real_1d_array& c,
const int& r,
const int& n,
const double& x);
/*************************************************************************
Representation of Tn as C[0] + C[1]*X + ... + C[N]*X^N
Input parameters:
N - polynomial degree, n>=0
Output parameters:
C - coefficients
*************************************************************************/
void chebyshevcoefficients(const int& n, ap::real_1d_array& c);
/*************************************************************************
Conversion of a series of Chebyshev polynomials to a power series.
Represents A[0]*T0(x) + A[1]*T1(x) + ... + A[N]*Tn(x) as
B[0] + B[1]*X + ... + B[N]*X^N.
Input parameters:
A - Chebyshev series coefficients
N - degree, N>=0
Output parameters
B - power series coefficients
*************************************************************************/
void fromchebyshev(const ap::real_1d_array& a,
const int& n,
ap::real_1d_array& b);
#endif
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