/usr/include/gkq.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) 2005-2009, 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 _gkq_h
#define _gkq_h
#include "ap.h"
#include "ialglib.h"
#include "tsort.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"
#include "gq.h"
/*************************************************************************
Computation of nodes and weights of a Gauss-Kronrod quadrature formula
The algorithm generates the N-point Gauss-Kronrod 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 zero moment Mu0
Mu0 = integral(W(x)dx,a,b)
INPUT PARAMETERS:
Alpha � alpha coefficients, array[0..floor(3*K/2)].
Beta � beta coefficients, array[0..ceil(3*K/2)].
Beta[0] is not used and may be arbitrary.
Beta[I]>0.
Mu0 � zeroth moment of the weight function.
N � number of nodes of the Gauss-Kronrod quadrature formula,
N >= 3,
N = 2*K+1.
OUTPUT PARAMETERS:
Info - error code:
* -5 no real and positive Gauss-Kronrod formula can
be created for such a weight function with a
given number of nodes.
* -4 N is too large, task may be ill conditioned -
x[i]=x[i+1] found.
* -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.
WKronrod - array[0..N-1] - Kronrod weights
WGauss - array[0..N-1] - Gauss weights (interleaved with zeros
corresponding to extended Kronrod nodes).
-- ALGLIB --
Copyright 08.05.2009 by Bochkanov Sergey
*************************************************************************/
void gkqgeneraterec(ap::real_1d_array alpha,
ap::real_1d_array beta,
double mu0,
int n,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& wkronrod,
ap::real_1d_array& wgauss);
/*************************************************************************
Returns Gauss and Gauss-Kronrod nodes/weights for Gauss-Legendre
quadrature with N points.
GKQLegendreCalc (calculation) or GKQLegendreTbl (precomputed table) is
used depending on machine precision and number of nodes.
INPUT PARAMETERS:
N - number of Kronrod nodes, must be odd number, >=3.
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, ordered in
ascending order.
WKronrod - array[0..N-1] - Kronrod weights
WGauss - array[0..N-1] - Gauss weights (interleaved with zeros
corresponding to extended Kronrod nodes).
-- ALGLIB --
Copyright 12.05.2009 by Bochkanov Sergey
*************************************************************************/
void gkqgenerategausslegendre(int n,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& wkronrod,
ap::real_1d_array& wgauss);
/*************************************************************************
Returns Gauss and Gauss-Kronrod 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 Kronrod nodes, must be odd number, >=3.
Alpha - power-law coefficient, Alpha>-1
Beta - power-law coefficient, Beta>-1
OUTPUT PARAMETERS:
Info - error code:
* -5 no real and positive Gauss-Kronrod formula can
be created for such a weight function with a
given number of nodes.
* -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 was passed
* +1 OK
* +2 OK, but quadrature rule have exterior nodes,
x[0]<-1 or x[n-1]>+1
X - array[0..N-1] - array of quadrature nodes, ordered in
ascending order.
WKronrod - array[0..N-1] - Kronrod weights
WGauss - array[0..N-1] - Gauss weights (interleaved with zeros
corresponding to extended Kronrod nodes).
-- ALGLIB --
Copyright 12.05.2009 by Bochkanov Sergey
*************************************************************************/
void gkqgenerategaussjacobi(int n,
double alpha,
double beta,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& wkronrod,
ap::real_1d_array& wgauss);
/*************************************************************************
Returns Gauss and Gauss-Kronrod nodes for quadrature with N points.
Reduction to tridiagonal eigenproblem is used.
INPUT PARAMETERS:
N - number of Kronrod nodes, must be odd number, >=3.
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, ordered in
ascending order.
WKronrod - array[0..N-1] - Kronrod weights
WGauss - array[0..N-1] - Gauss weights (interleaved with zeros
corresponding to extended Kronrod nodes).
-- ALGLIB --
Copyright 12.05.2009 by Bochkanov Sergey
*************************************************************************/
void gkqlegendrecalc(int n,
int& info,
ap::real_1d_array& x,
ap::real_1d_array& wkronrod,
ap::real_1d_array& wgauss);
/*************************************************************************
Returns Gauss and Gauss-Kronrod nodes for quadrature with N points using
pre-calculated table. Nodes/weights were computed with accuracy up to
1.0E-32 (if MPFR version of ALGLIB is used). In standard double precision
accuracy reduces to something about 2.0E-16 (depending on your compiler's
handling of long floating point constants).
INPUT PARAMETERS:
N - number of Kronrod nodes.
N can be 15, 21, 31, 41, 51, 61.
OUTPUT PARAMETERS:
X - array[0..N-1] - array of quadrature nodes, ordered in
ascending order.
WKronrod - array[0..N-1] - Kronrod weights
WGauss - array[0..N-1] - Gauss weights (interleaved with zeros
corresponding to extended Kronrod nodes).
-- ALGLIB --
Copyright 12.05.2009 by Bochkanov Sergey
*************************************************************************/
void gkqlegendretbl(int n,
ap::real_1d_array& x,
ap::real_1d_array& wkronrod,
ap::real_1d_array& wgauss,
double& eps);
#endif
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