Alexandria
2.16
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MathUtils
src
lib
numericalDifferentiation
FiniteDifference.cpp
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/*
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* Copyright (C) 2012-2020 Euclid Science Ground Segment
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*
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* This library is free software; you can redistribute it and/or modify it under
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* the terms of the GNU Lesser General Public License as published by the Free
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* Software Foundation; either version 3.0 of the License, or (at your option)
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* any later version.
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*
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* This library is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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* FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
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* details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this library; if not, write to the Free Software Foundation, Inc.,
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* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
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*/
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#include "
MathUtils/numericalDifferentiation/FiniteDifference.h
"
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#include <cmath>
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#include <limits>
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namespace
Euclid
{
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namespace
MathUtils {
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static
double
guess_h
(
double
initial_h,
double
x) {
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volatile
double
xh = x + initial_h;
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volatile
double
h = xh - x;
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if
(h == 0) {
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h =
std::nextafter
(x,
std::numeric_limits<double>::max
()) - x;
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}
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return
h;
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}
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double
derivative
(
const
Function
& f,
const
double
x) {
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double
h =
std::sqrt
(
std::numeric_limits<double>::epsilon
()) * 2;
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h =
guess_h
(h, x);
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double
yh = f(x + h);
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double
y0 = f(x);
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return
(yh - y0) / h;
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}
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double
derivative2nd
(
const
Function
& f,
const
double
x) {
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double
h =
std::sqrt
(
std::sqrt
(
std::numeric_limits<double>::epsilon
())) * 2;
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h =
guess_h
(h, x);
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double
ymh = f(x - h);
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double
y = f(x);
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double
yph = f(x + h);
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return
(yph - 2 * y + ymh) / (h * h);
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}
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}
// end namespace MathUtils
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}
// end namespace Euclid
Euclid::MathUtils::derivative
double derivative(const Function &f, const double x)
Definition:
FiniteDifference.cpp:41
Euclid::MathUtils::derivative2nd
double derivative2nd(const Function &f, const double x)
Definition:
FiniteDifference.cpp:50
Euclid::MathUtils::Function
Interface class representing a function.
Definition:
Function.h:46
std::sqrt
T sqrt(T... args)
FiniteDifference.h
std::nextafter
T nextafter(T... args)
Euclid::MathUtils::guess_h
static double guess_h(double initial_h, double x)
Definition:
FiniteDifference.cpp:32
Euclid
Definition:
InstOrRefHolder.h:29
std::numeric_limits
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