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//# tChebyshev: test the Chebyshev class
//# Copyright (C) 2000,2001,2002,2003
//# Associated Universities, Inc. Washington DC, USA.
//#
//# 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; 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.
//#
//# You should have received a copy of the GNU General Public License along
//# with this program; if not, write to the Free Software Foundation, Inc.,
//# 675 Massachusetts Ave, Cambridge, MA 02139, USA.
//#
//# Correspondence concerning AIPS++ should be addressed as follows:
//# Internet email: casa-feedback@nrao.edu.
//# Postal address: AIPS++ Project Office
//# National Radio Astronomy Observatory
//# 520 Edgemont Road
//# Charlottesville, VA 22903-2475 USA
#ifdef DEBUG
#define DIAGNOSTICS
#endif
#include <casacore/scimath/Functionals/Chebyshev.h>
#include <casacore/scimath/Functionals/Polynomial.h>
#include <casacore/casa/Containers/Record.h>
#include <casacore/casa/Arrays/Vector.h>
#include <casacore/casa/Arrays/ArrayMath.h>
#include <casacore/casa/BasicMath/Math.h>
#include <casacore/scimath/Mathematics/AutoDiffA.h>
#include <casacore/scimath/Mathematics/AutoDiffMath.h>
#include <casacore/scimath/Mathematics/AutoDiffIO.h>
#include <casacore/casa/Utilities/Assert.h>
#include <casacore/casa/Exceptions.h>
#include <casacore/casa/iostream.h>
#include <casacore/casa/namespace.h>
int main() {
Chebyshev<Double> cheb;
Vector<Double> coeffs(4, 0);
coeffs(3) = 2.0;
cheb.setCoefficients(coeffs);
#ifdef DIAGNOSTICS
cout << "Chebyshev " << coeffs;
#endif
cheb.chebyshevToPower(coeffs);
#ifdef DIAGNOSTICS
cout << " maps to polynomials coeffs: " << coeffs << endl;
#endif
AlwaysAssertExit(coeffs(0) == 0 && coeffs(1) == -6 &&
coeffs(2) == 0 && coeffs(3) == 8 );
#ifdef DIAGNOSTICS
cout << "And power series coeffs " << coeffs;
#endif
cheb.powerToChebyshev(coeffs);
#ifdef DIAGNOSTICS
cout << " maps to chebyshev coeffs: " << coeffs << endl;
cout << "coeffs: " << coeffs << ", " << cheb << endl;
#endif
AlwaysAssertExit(coeffs(0) == cheb.getCoefficient(0) &&
coeffs(1) == cheb.getCoefficient(1) &&
coeffs(2) == cheb.getCoefficient(2) &&
coeffs(3) == cheb.getCoefficient(3) );
coeffs = 2.0;
coeffs(0) += 1.0;
cheb.setCoefficients(coeffs);
#ifdef DIAGNOSTICS
cout << "Chebyshev " << coeffs;
#endif
cheb.chebyshevToPower(coeffs);
#ifdef DIAGNOSTICS
cout << " maps to power series coeffs: " << coeffs << endl;
#endif
AlwaysAssertExit(coeffs(0) == 1 && coeffs(1) == -4 &&
coeffs(2) == 4 && coeffs(3) == 8 );
Double xmin = 0, xmax = 4, xp;
cheb.setInterval(xmin, xmax);
AlwaysAssertExit(xmin == cheb.getIntervalMin());
AlwaysAssertExit(xmax == cheb.getIntervalMax());
Polynomial<Double> poly(3);
poly.setCoefficients(coeffs);
Chebyshev<Double> chebp = cheb.derivative();
#ifdef DIAGNOSTICS
Vector<Double> dce;
dce = chebp.getCoefficients();
chebp.chebyshevToPower(dce);
cout << "dcheb: " << dce << endl;
#endif
Polynomial<Double> polyp = poly.derivative();
polyp.setCoefficients(polyp.coefficients() * (2/(xmax-xmin)));
#ifdef DIAGNOSTICS
cout << "dpoly: " << polyp.coefficients() << endl;
#endif
for (Double x=xmin; x <= xmax; x += 0.1) {
xp = (2*x-xmin-xmax)/(xmax-xmin);
AlwaysAssertExit(nearAbs(cheb(x), poly(xp), 1.0e-14));
AlwaysAssertExit(nearAbs(chebp(x), polyp(xp), 1.0e-14));
}
// Test auto differentiation wrt x
Chebyshev<AutoDiffA<Double> > chebad(cheb.nparameters());
chebad.setInterval(cheb.getIntervalMin(), cheb.getIntervalMax());
/// for (uInt i=0; i<4; ++i) chebad[i] = AutoDiffA<Double>(cheb[i]);
for (uInt i=0; i<4; ++i) chebad[i] = cheb[i];
for (AutoDiffA<Double> x(xmin, 1, 0); x <= xmax; x += 0.1) {
AlwaysAssertExit(nearAbs(chebp(x.value()), chebad(x).deriv(0), 1.0e-14));
}
// test out-of-interval modes
AlwaysAssertExit(0 == cheb.getDefault());
cheb.setDefault(5);
AlwaysAssertExit(5 == cheb.getDefault());
AlwaysAssertExit(cheb(xmin-1) == cheb.getDefault());
cheb.setOutOfIntervalMode(ChebyshevEnums::EXTRAPOLATE);
AlwaysAssertExit(cheb(xmin-0.2) != cheb.getDefault());
xp = (2*(xmin-0.2)-xmin-xmax)/(xmax-xmin);
#ifdef DIAGNOSTICS
cout << xmin-0.2 << ": cheb-poly=" << cheb(xmin-0.2)-poly(xp) << endl;
#endif
AlwaysAssertExit(nearAbs(cheb(xmin-0.2), poly(xp), 1.0e-14));
cheb.setOutOfIntervalMode(ChebyshevEnums::CYCLIC);
#ifdef DIAGNOSTICS
cout << xmin-1.3 << ": cheb(-1.3)-cheb(2.7)="
<< cheb(xmin-1.3)-cheb(xmin-1.3+(xmax-xmin)) << endl;
#endif
AlwaysAssertExit(nearAbs(cheb(xmin-1.3),
cheb(xmin-1.3+(xmax-xmin)), 1.0e-15));
#ifdef DIAGNOSTICS
cout << xmax+1.3 << ": cheb(5.3)-cheb(1.3)="
<< cheb(xmin+1.3)-cheb(xmin+1.3-(xmax-xmin)) << endl;
#endif
AlwaysAssertExit(nearAbs(cheb(xmax+1.3),
cheb(xmax+1.3-(xmax-xmin)), 1.0e-15));
cheb.setOutOfIntervalMode(ChebyshevEnums::ZEROTH);
cheb.setCoefficient(0, 1);
AlwaysAssertExit(cheb(xmax+1) == cheb.getCoefficient(0));
// Test setMode()
AlwaysAssertExit(cheb.hasMode());
Record rec;
Vector<Double> intv(2);
intv(0) = -10.0; intv(1) = 10.0;
rec.define(RecordFieldId("intervalMode"), "cyclic");
rec.define(RecordFieldId("interval"), intv);
rec.define(RecordFieldId("default"), 80.0);
cheb.setMode(rec);
#ifdef DIAGNOSTICS
cout << "Results from setMode():" << endl
<< " Interval Mode: " << cheb.getOutOfIntervalMode() << endl
<< " Range: " << cheb.getIntervalMin() << ", "
<< cheb.getIntervalMax() << endl
<< " Default: " << cheb.getDefault() << endl;
#endif
AlwaysAssertExit(cheb.getOutOfIntervalMode() ==
ChebyshevEnums::CYCLIC &&
cheb.getIntervalMin() == -10.0 &&
cheb.getIntervalMax() == 10.0 &&
cheb.getDefault() == 80.0);
// test setMode() via constructor
Chebyshev<Double> cheb2(2, rec);
AlwaysAssertExit(cheb2.getOutOfIntervalMode() ==
ChebyshevEnums::CYCLIC &&
cheb2.getIntervalMin() == -10.0 &&
cheb2.getIntervalMax() == 10.0 &&
cheb2.getDefault() == 80.0);
// test getMode()
Record rec2;
cheb.setInterval(-15.0, 15.0);
cheb.setDefault(70.0);
cheb.setOutOfIntervalMode(ChebyshevEnums::ZEROTH);
cheb.getMode(rec2);
try {
Vector<Double> tmp(2);
rec2.get(RecordFieldId("interval"), tmp);
Double def;
rec2.get(RecordFieldId("default"), def);
String mode;
rec2.get(RecordFieldId("intervalMode"), mode);
AlwaysAssertExit(mode == String("zeroth") &&
tmp(0) == -15.0 && tmp(1) == 15.0 &&
def == 70.0);
}
catch (std::exception& ex) {
cerr << "Exception: " << ex.what() << endl;
exit(1);
}
cout << "OK" << endl;
return 0;
}
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