/usr/include/gq.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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Copyright (c) 2005-2007, Sergey Bochkanov (ALGLIB project).
>>> 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 _gq_h
#define _gq_h
#include "ap.h"
#include "ialglib.h"
#include "hblas.h"
#include "reflections.h"
#include "creflections.h"
#include "sblas.h"
#include "ablasf.h"
#include "ablas.h"
#include "ortfac.h"
#include "blas.h"
#include "rotations.h"
#include "hsschur.h"
#include "evd.h"
#include "gammafunc.h"
/*************************************************************************
Computation of nodes and weights for a Gauss quadrature formula
The algorithm generates the N-point Gauss quadrature formula with weight
function given by coefficients alpha and beta of a recurrence relation
which generates a system of orthogonal polynomials:
P-1(x) = 0
P0(x) = 1
Pn+1(x) = (x-alpha(n))*Pn(x) - beta(n)*Pn-1(x)
and zeroth moment Mu0
Mu0 = integral(W(x)dx,a,b)
INPUT PARAMETERS:
Alpha � array[0..N-1], alpha coefficients
Beta � array[0..N-1], beta coefficients
Zero-indexed element is not used and may be arbitrary.
Beta[I]>0.
Mu0 � zeroth moment of the weight function.
N � number of nodes of the quadrature formula, N>=1
OUTPUT PARAMETERS:
Info - error code:
* -3 internal eigenproblem solver hasn't converged
* -2 Beta[i]<=0
* -1 incorrect N was passed
* 1 OK
X - array[0..N-1] - array of quadrature nodes,
in ascending order.
W - array[0..N-1] - array of quadrature weights.
-- ALGLIB --
Copyright 2005-2009 by Bochkanov Sergey
*************************************************************************/
void gqgeneraterec(const ap::real_1d_array& alpha,
const ap::real_1d_array& beta,
double mu0,
int n,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& w);
/*************************************************************************
Computation of nodes and weights for a Gauss-Lobatto quadrature formula
The algorithm generates the N-point Gauss-Lobatto quadrature formula with
weight function given by coefficients alpha and beta of a recurrence which
generates a system of orthogonal polynomials.
P-1(x) = 0
P0(x) = 1
Pn+1(x) = (x-alpha(n))*Pn(x) - beta(n)*Pn-1(x)
and zeroth moment Mu0
Mu0 = integral(W(x)dx,a,b)
INPUT PARAMETERS:
Alpha � array[0..N-2], alpha coefficients
Beta � array[0..N-2], beta coefficients.
Zero-indexed element is not used, may be arbitrary.
Beta[I]>0
Mu0 � zeroth moment of the weighting function.
A � left boundary of the integration interval.
B � right boundary of the integration interval.
N � number of nodes of the quadrature formula, N>=3
(including the left and right boundary nodes).
OUTPUT PARAMETERS:
Info - error code:
* -3 internal eigenproblem solver hasn't converged
* -2 Beta[i]<=0
* -1 incorrect N was passed
* 1 OK
X - array[0..N-1] - array of quadrature nodes,
in ascending order.
W - array[0..N-1] - array of quadrature weights.
-- ALGLIB --
Copyright 2005-2009 by Bochkanov Sergey
*************************************************************************/
void gqgenerategausslobattorec(ap::real_1d_array alpha,
ap::real_1d_array beta,
double mu0,
double a,
double b,
int n,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& w);
/*************************************************************************
Computation of nodes and weights for a Gauss-Radau quadrature formula
The algorithm generates the N-point Gauss-Radau quadrature formula with
weight function given by the coefficients alpha and beta of a recurrence
which generates a system of orthogonal polynomials.
P-1(x) = 0
P0(x) = 1
Pn+1(x) = (x-alpha(n))*Pn(x) - beta(n)*Pn-1(x)
and zeroth moment Mu0
Mu0 = integral(W(x)dx,a,b)
INPUT PARAMETERS:
Alpha � array[0..N-2], alpha coefficients.
Beta � array[0..N-1], beta coefficients
Zero-indexed element is not used.
Beta[I]>0
Mu0 � zeroth moment of the weighting function.
A � left boundary of the integration interval.
N � number of nodes of the quadrature formula, N>=2
(including the left boundary node).
OUTPUT PARAMETERS:
Info - error code:
* -3 internal eigenproblem solver hasn't converged
* -2 Beta[i]<=0
* -1 incorrect N was passed
* 1 OK
X - array[0..N-1] - array of quadrature nodes,
in ascending order.
W - array[0..N-1] - array of quadrature weights.
-- ALGLIB --
Copyright 2005-2009 by Bochkanov Sergey
*************************************************************************/
void gqgenerategaussradaurec(ap::real_1d_array alpha,
ap::real_1d_array beta,
double mu0,
double a,
int n,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& w);
/*************************************************************************
Returns nodes/weights for Gauss-Legendre quadrature on [-1,1] with N
nodes.
INPUT PARAMETERS:
N - number of nodes, >=1
OUTPUT PARAMETERS:
Info - error code:
* -4 an error was detected when calculating
weights/nodes. N is too large to obtain
weights/nodes with high enough accuracy.
Try to use multiple precision version.
* -3 internal eigenproblem solver hasn't converged
* -1 incorrect N was passed
* +1 OK
X - array[0..N-1] - array of quadrature nodes,
in ascending order.
W - array[0..N-1] - array of quadrature weights.
-- ALGLIB --
Copyright 12.05.2009 by Bochkanov Sergey
*************************************************************************/
void gqgenerategausslegendre(int n,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& w);
/*************************************************************************
Returns nodes/weights for Gauss-Jacobi quadrature on [-1,1] with weight
function W(x)=Power(1-x,Alpha)*Power(1+x,Beta).
INPUT PARAMETERS:
N - number of nodes, >=1
Alpha - power-law coefficient, Alpha>-1
Beta - power-law coefficient, Beta>-1
OUTPUT PARAMETERS:
Info - error code:
* -4 an error was detected when calculating
weights/nodes. Alpha or Beta are too close
to -1 to obtain weights/nodes with high enough
accuracy, or, may be, N is too large. Try to
use multiple precision version.
* -3 internal eigenproblem solver hasn't converged
* -1 incorrect N/Alpha/Beta was passed
* +1 OK
X - array[0..N-1] - array of quadrature nodes,
in ascending order.
W - array[0..N-1] - array of quadrature weights.
-- ALGLIB --
Copyright 12.05.2009 by Bochkanov Sergey
*************************************************************************/
void gqgenerategaussjacobi(int n,
double alpha,
double beta,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& w);
/*************************************************************************
Returns nodes/weights for Gauss-Laguerre quadrature on [0,+inf) with
weight function W(x)=Power(x,Alpha)*Exp(-x)
INPUT PARAMETERS:
N - number of nodes, >=1
Alpha - power-law coefficient, Alpha>-1
OUTPUT PARAMETERS:
Info - error code:
* -4 an error was detected when calculating
weights/nodes. Alpha is too close to -1 to
obtain weights/nodes with high enough accuracy
or, may be, N is too large. Try to use
multiple precision version.
* -3 internal eigenproblem solver hasn't converged
* -1 incorrect N/Alpha was passed
* +1 OK
X - array[0..N-1] - array of quadrature nodes,
in ascending order.
W - array[0..N-1] - array of quadrature weights.
-- ALGLIB --
Copyright 12.05.2009 by Bochkanov Sergey
*************************************************************************/
void gqgenerategausslaguerre(int n,
double alpha,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& w);
/*************************************************************************
Returns nodes/weights for Gauss-Hermite quadrature on (-inf,+inf) with
weight function W(x)=Exp(-x*x)
INPUT PARAMETERS:
N - number of nodes, >=1
OUTPUT PARAMETERS:
Info - error code:
* -4 an error was detected when calculating
weights/nodes. May be, N is too large. Try to
use multiple precision version.
* -3 internal eigenproblem solver hasn't converged
* -1 incorrect N/Alpha was passed
* +1 OK
X - array[0..N-1] - array of quadrature nodes,
in ascending order.
W - array[0..N-1] - array of quadrature weights.
-- ALGLIB --
Copyright 12.05.2009 by Bochkanov Sergey
*************************************************************************/
void gqgenerategausshermite(int n,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& w);
#endif
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