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Commit de48f601 authored by Davis King's avatar Davis King
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minor cleanup and formatting

parent ad427072
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dlib/integrate_function_adapt_simpson.h deleted 100644 → 0
View file @ ad427072
// Copyright (C) 2013 Steve Taylor (steve98654@gmail.com)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_HEADER
#define DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_HEADER
#include "matrix.h"
#include "numerical_integration/integrate_function_adapt_simpson.h"
#endif // DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_HEADER
dlib/numerical_integration.h
View file @ de48f601
......@@ -3,7 +3,6 @@
#ifndef DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_HEADER
#define DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_HEADER
#include "matrix.h"
#include "numerical_integration/integrate_function_adapt_simpson.h"
#endif // DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_HEADER
dlib/numerical_integration/integrate_function_adapt_simpson.h
View file @ de48f601
// Copyright (C) 2013 Steve Taylor (steve98654@gmail.com)
// License: Boost Software License See LICENSE.txt for full license
#ifndef DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON__
#define DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON__
#include "integrate_function_adapt_simpson_abstract.h"
// ----------------------------------------------------------------------------------------
template <typename T, typename funct>
T impl_adapt_simp_stop(const funct& f, T a, T b, T fa, T fm, T fb, T is, int cnt)
{
int MAXINT = 1000;
const int MAXINT = 500;
T m = (a + b)/2.0;
T h = (b - a)/4.0;
......@@ -18,14 +21,15 @@ T impl_adapt_simp_stop(const funct& f, T a, T b, T fa, T fm, T fb, T is, int cnt
i1 = (16.0*i2 - i1)/15.0;
T Q = 0;
if((std::abs(i1-i2) <= std::abs(is)) || (m <= a) || (b <= m))
if ((std::abs(i1-i2) <= std::abs(is)) || (m <= a) || (b <= m))
{
Q = i1;
}
else
{
if(cnt < MAXINT)
{cnt = cnt + 1;
{
cnt = cnt + 1;
Q = impl_adapt_simp_stop(f,a,m,fa,fml,fm,is,cnt)
+ impl_adapt_simp_stop(f,m,b,fm,fmr,fb,is,cnt);
......@@ -35,11 +39,17 @@ T impl_adapt_simp_stop(const funct& f, T a, T b, T fa, T fm, T fb, T is, int cnt
return Q;
}
// ----------------------------------------------------------------------------------------
template <typename T, typename funct>
T integrate_function_adapt_simp(const funct& f, T a, T b, T tol)
T integrate_function_adapt_simp(
const funct& f,
T a,
T b,
T tol = 1e-10
)
{
T eps = std::numeric_limits<double>::epsilon();
T eps = std::numeric_limits<T>::epsilon();
if(tol < eps)
{
tol = eps;
......@@ -50,7 +60,7 @@ T integrate_function_adapt_simp(const funct& f, T a, T b, T tol)
const T fb = f(b);
const T fm = f((a+b)/2);
T is =ba/8*(fa+fb+fm+ f(a + 0.9501*ba) + f(a + 0.2311*ba) + f(a + 0.6068*ba)
T is = ba/8*(fa+fb+fm+ f(a + 0.9501*ba) + f(a + 0.2311*ba) + f(a + 0.6068*ba)
+ f(a + 0.4860*ba) + f(a + 0.8913*ba));
if(is == 0)
......@@ -62,11 +72,10 @@ T integrate_function_adapt_simp(const funct& f, T a, T b, T tol)
int cnt = 0;
T tstvl = impl_adapt_simp_stop(f, a, b, fa, fm, fb, is, cnt);
return tstvl;
return impl_adapt_simp_stop(f, a, b, fa, fm, fb, is, cnt);
}
// ----------------------------------------------------------------------------------------
#endif //DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON.h__
dlib/numerical_integration/integrate_function_adapt_simpson_abstract.h
View file @ de48f601
// Copyright (C) 2013 Steve Taylor (steve98654@gmail.com)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_ABSTRACT__
#define DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_ABSTRACT__
#undef DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_ABSTRACT__
#ifdef DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON_ABSTRACT__
template <typename T, typename funct>
T integrate_function_adapt_simp(const funct& f, T a, T b, T tol);
T integrate_function_adapt_simp(
const funct& f,
T a,
T b,
T tol = 1e-10
);
/*!
requires
- b > a
- tol > 0
- f to be real valued single variable function
- T should be either float, double, or long double
- The expression f(a) should be a valid expression that evaluates to a T.
I.e. f() should be a real valued function of a single variable.
ensures
- returns an approximation of the integral of f over the domain [a,b]
using the adaptive Simpson method outlined in
Gander, W. and W. Gautshi, "Adaptive Quadrature -- Revisited"
BIT, Vol. 40, (2000), pp.84-101
- tol is a tolerance parameter that typically determines
the overall accuracy of approximated integral. We suggest
a default value of 1e-10 for tol.
- returns an approximation of the integral of f over the domain [a,b] using the
adaptive Simpson method outlined in Gander, W. and W. Gautshi, "Adaptive
Quadrature -- Revisited" BIT, Vol. 40, (2000), pp.84-101
- tol is a tolerance parameter that determines the overall accuracy of approximated
integral. We suggest a default value of 1e-10 for tol.
!*/
#endif // DLIB_INTEGRATE_FUNCTION_ADAPT_SIMPSON__
......
examples/adapt_simp.cpp deleted 100644 → 0
View file @ ad427072
// Numerical Integration method based on the adaptive Simpson method in
// Gander, W. and W. Gautschi, "Adaptive Quadrature – Revisited,"
// BIT, Vol. 40, 2000, pp. 84-101
// Test functions taken from Pedro Gonnet's dissertation at ETH:
// Adaptive Quadrature Re-Revisited
// http://e-collection.library.ethz.ch/eserv/eth:65/eth-65-02.pdf
#include <iostream>
#include <iomanip>
#include <stdint.h>
#include <dlib/matrix.h>
using namespace std;
using namespace dlib;
//***************************************************************//
//*Begin definitions of test functions //
//Initial Test Function
double f(double x)
{
return pow(x,0.5);
}
// The Lyness - Kaganove test functions from page 167 of Gonnet's thesis.
// lambda in [0,1], alpha in [-0.5,0], x in [0,1]
double LK1(double x, double lambda, double alpha)
{
return pow(abs(x-lambda),alpha);
}
// lambda in [0,1], alpha in [0,1], x in [0,1]
double LK2(double x, double lambda, double alpha)
{
if(x > lambda)
{
return 0;
}
else
{
return pow(e, alpha*x);
}
}
// lambda in [0,1], alpha in [0,4], x in [0,1]
double LK3(double x, double lambda, double alpha)
{
return pow(e,-alpha*abs(x-lambda));
}
// lambda in [1,2], alpha in [-6,-3], x in [1,2]
double LK4(double x, double lambda, double alpha)
{
return pow(10,alpha)/((x-lambda)*(x-lambda)+pow(10,alpha));
}
// lambda_i in [1,2], alpha in [-5,-3], x in [1,2]
double LK5(double x, double lambda1, double lambda2, double lambda3, double lambda4, double alpha)
{
return pow(10,alpha)/((x-lambda1)*(x-lambda1)+pow(10,alpha))
+ pow(10,alpha)/((x-lambda2)*(x-lambda2)+pow(10,alpha))
+ pow(10,alpha)/((x-lambda3)*(x-lambda3)+pow(10,alpha))
+ pow(10,alpha)/((x-lambda4)*(x-lambda4)+pow(10,alpha));
}
// lambda in [0,1], alpha in [1.8,2], x in [0,1]
double LK6(double x, double lambda, double alpha)
{
double beta = pow(10,alpha)/max(lambda*lambda,(1-lambda)*(1-lambda));
return 2*beta*cos(beta*(x-lambda)*(x-lambda));
}
// Test Battery from reference [33] and p. 168 of Gonnet's thesis.
// x in [0,1]
double GG1(double x)
{
return pow(e,x);
}
// x in [0,1]
double GG2(double x)
{
if(x > 0.3)
{
return 1.0;
}
else
{
return 0;
}
}
// x in [0,1]
double GG3(double x)
{
return pow(x,0.5);
}
// x in [0,1]
double GG4(double x)
{
return 22/25*cosh(x)-cos(x);
}
// x in [-1,1]
double GG5(double x)
{
return 1/(pow(x,4) + pow(x,2) + 0.9);
}
// x in [0,1]
double GG6(double x)
{
return pow(x,1.5);
}
// x in [0,1]
double GG7(double x)
{
return pow(x,-0.5);
}
// x in [0,1]
double GG8(double x)
{
return 1/(1 + pow(x,4));
}
// x in [0,1]
double GG9(double x)
{
return 2/(2 + sin(10*pi*x));
}
// x in [0,1]
double GG10(double x)
{
return 1/(1+x);
}
// x in [0,1]
double GG11(double x)
{
1/(1 + pow(e,x));
}
// x in [0,1]
double GG12(double x)
{
return x/(pow(e,x)-1);
}
// x in [0.1, 1]
double GG13(double x)
{
return sin(100.0*pi*x)/(pi*x);
}
// x in [0, 10]
double GG14(double x)
{
return sqrt(50)*pow(e,-50.0*pi*x*x);
}
// x in [0, 10]
double GG15(double x)
{
return 25.0*pow(e,-25.0*x);
}
// x in [0, 10]
double GG16(double x)
{
return 50.0/(pi*(2500.0*x*x+1));
}
// x in [0.01, 1]
double GG17(double x)
{
return 50.0*pow((sin(50.0*pi*x)/(50.0*pi*x)),2);
}
// x in [0, pi]
double GG18(double x)
{
return cos(cos(x)+3*sin(x)+2*cos(2*x)+3*cos(3*x));
}
// x in [0,1]
double GG19(double x)
{
return log10(x);
}
// x in [-1,1]
double GG20(double x)
{
return 1/(1.005+x*x);
}
// x in [0,1]
double GG21(double x)
{
return 1/cosh(20.0*(x-1/5)) + 1/cosh(400.0*(x-2/5)) + 1/cosh(8000.0*(x-3/5));
}
// x in [0,1]
double GG22(double x)
{
return 4*pi*pi*x*sin(20.0*pi*x)*cos(2*pi*x);
}
// x in [0,1]
double GG23(double x)
{
return 1/(1+(230*x-30)*(230*x-30));
}
// x in [0,3]
double GG24(double x)
{
return floor(pow(e,x));
}
// x in [0,5]
double GG25(double x)
{
if(x < 1)
{
return (x + 1);
}
else if(x >= 1 && x <= 3)
{
return 3 - x;
}
else
{
return 2;
}
}
// Returns double machine precision
// Taken from Wikipedia en.wikipedia.org/wiki/Machine_epsilon
template<typename float_t, typename int_t>
float_t machine_eps()
{
union
{
float_t f;
int_t i;
} one, one_plus, little, last_little;
one.f = 1.0;
little.f = 1.0;
last_little.f = little.f;
while(true)
{
one_plus.f = one.f;
one_plus.f += little.f;
if( one.i != one_plus.i )
{
last_little.f = little.f;
little.f /= 2.0;
}
else
{
return last_little.f;
}
}
}
// Main Integration Function.
// Supporting Integration Function
template <typename T, typename funct>
T AdaptSimpstp(const funct& f, T a, T b, T fa, T fm, T fb, T is)
{
T m = (a + b)/2;
T h = (b - a)/4;
T fml = f(a + h);
T fmr = f(b - h);
T i1 = h/1.5*(fa+4*fm+fb);
T i2 = h/3.0*(fa+4*(fml+fmr)+2*fm+fb);
i1 = (16.0*i2 - i1)/15.0;
T Q = 0;
if((is+(i1-i2) == is) || (m <= a) || (b <= m))
{
if((m <= a) || (b <= m))
{
cout << "INT ERR" << endl;
}
Q = i1;
}
else
{
Q = AdaptSimpstp(f, a, m, fa, fml, fm, is) + AdaptSimpstp(f,m,b,fm,fmr,fb,is);
}
return Q;
}
// Main integration function.
// f -- function to integrate,
// a -- left end point
// b -- right end point
// tol -- error tolerance
template <typename T, typename funct>
T AdaptSimp(const funct& f, T a, T b, T tol)
{
T eps = machine_eps<T, uint64_t>();
if(tol < eps)
{
tol = eps;
}
const T ba = b-a;
const T fa = f(a);
const T fb = f(b);
const T fm = f((a+b)/2);
T is =ba/8*(fa+fb+fm+ f(a + 0.9501*ba) + f(a + 0.2311*ba) + f(a + 0.6068*ba)
+ f(a + 0.4860*ba) + f(a + 0.8913*ba));
if(is == 0)
{
is = b-a;
}
is = is*tol/eps;
T tstvl = AdaptSimpstp(f, a, b, fa, fm, fb, is);
return tstvl;
}
// Examples
int main()
{
typedef double T;
T tol = 1e-10;
T a = 0;
T b = 5;
T tstvl2 = AdaptSimp(&f, a, b, tol);
cout << "Integral Value is: " << std::setprecision(18) << tstvl2 << endl;
return 0;
}
examples/integrate_function_adapt_simp_ex.cpp
View file @ de48f601
......@@ -68,8 +68,6 @@ int main()
double tol = 1e-10;
// Here we instantiate a class which contains the numerical quadrature method.
// adapt_simp ad;
// Here we compute the integrals of the five functions defined above using the same
// tolerance level for each.
......@@ -88,7 +86,7 @@ int main()
cout << "The integral of 1/(x^2 + cos(x)^2) for in [0,pi] is " << std::setprecision(10) << m3 << endl;
cout << "The integral of sin(x) for in [-pi,pi] is " << std::setprecision(10) << m4 << endl;
cout << "The integral of 1/(1+x^2) for in [0,2] is " << std::setprecision(10) << m5 << endl;
cout << "" << endl;
cout << endl;
return 0;
}
......
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