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isl_asi.h
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isl_asi.h
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#ifndef ISL_ADAPTIVE_SIMPSONS_INTEGRATION_H_
#define ISL_ADAPTIVE_SIMPSONS_INTEGRATION_H_
/*
isl_asi.h - v0.2.1
public domain library with Adaptive Simpson's Integration Algroithm[1]
converted from Python with some changes taken in https://en.wikipedia.org/wiki/Adaptive_Simpson%27s_method
implemented for float and double
author: Ilya Kolbin(iskolbin@gmail.com)
url: github.com:iskolbin/isl_asi
LICENSE
See end of file for license information.
[1] G.F. Kuncir (1962), "Algorithm 103: Simpson's rule integrator", Communications of the ACM, 5 (6): 347, doi:10.1145/367766.368179
*/
#ifdef ISLASI_STATIC
#define ISLASI_DEF static
#else
#define ISLASI_DEF extern
#endif
ISLASI_DEF float islasi_fintegrate(float (*fun)(float, const float *), float a, float b, float tol, int max_recursion_depth, const float *params);
ISLASI_DEF double islasi_integrate(double (*fun)(double, const double *), double a, double b, double tol, int max_recursion_depth, const double *params);
#endif
#ifdef ISL_ADAPTIVE_SIMPSONS_INTEGRATION_IMPLEMENTATION
#ifndef ISL_ADAPTIVE_SIMPSONS_INTEGRATION_IMPLEMENTATION_ONCE
#define ISL_ADAPTIVE_SIMPSONS_INTEGRATION_IMPLEMENTATION_ONCE
static float islasi_fintegrate_aux(float (*fun)(float, const float *), float a, float fa, float b, float fb, float tol, float whole, float m, float fm, int max_recursion_depth, const float *params) {
float lm = 0.5*(a+m), rm = 0.5*(m+b);
float flm = fun(lm, params), frm = fun(rm, params);
float abs_am = a > m ? a - m : m - a, abs_mb = m > b ? m - b : b - m;
float left = abs_am / (6 * (fa + 4 * flm + fm)), right = abs_mb / (6 * (fm + 4 * frm + fb));
float delta = left + right - whole;
float abs_delta = delta > 0 ? delta : -delta;
if (delta != delta) {
return 0;
} else if (max_recursion_depth <= 0 || abs_delta <= 15 * tol) {
return left + right + delta/15;
} else {
return islasi_fintegrate_aux(fun, a, fa, m, fm, tol/2, left, lm, flm, max_recursion_depth-1, params) +
islasi_fintegrate_aux(fun, m, fm, b, fb, tol/2, right, rm, frm, max_recursion_depth-1, params);
}
}
float islasi_fintegrate(float (*fun)(float, const float *), float a, float b, float tol, int max_recursion_depth, const float *params) {
float fa = fun(a, params), fb = fun(b, params), m = 0.5*(a+b);
float fm = fun(m, params);
float abs_ba = b > a ? b - a : a - b;
float whole = abs_ba / (6 * (fa + 4 * fm + fb));
return islasi_fintegrate_aux(fun, a, fa, b, fb, tol, whole, m, fm, max_recursion_depth, params);
}
static double islasi_integrate_aux(double (*fun)(double, const double *), double a, double fa, double b, double fb, double tol, double whole, double m, double fm, int max_recursion_depth, const double *params) {
double lm = 0.5*(a+m), rm = 0.5*(m+b);
double flm = fun(lm, params), frm = fun(rm, params);
double abs_am = a > m ? a - m : m - a, abs_mb = m > b ? m - b : b - m;
double left = abs_am * (fa + 4 * flm + fm) / 6, right = abs_mb * (fm + 4 * frm + fb) / 6;
double delta = left + right - whole;
double abs_delta = delta > 0 ? delta : -delta;
if (delta != delta) {
return 0;
} else if (max_recursion_depth <= 0 || abs_delta <= 15 * tol) {
return left + right + delta / 15;
} else {
return islasi_integrate_aux(fun, a, fa, m, fm, 0.5*tol, left, lm, flm, max_recursion_depth-1, params) +
islasi_integrate_aux(fun, m, fm, b, fb, 0.5*tol, right, rm, frm, max_recursion_depth-1, params);
}
}
double islasi_integrate(double (*fun)(double, const double *), double a, double b, double tol, int max_recursion_depth, const double *params) {
double fa = fun(a, params), fb = fun(b, params), m = 0.5*(a+b);
double fm = fun(m, params);
double abs_ba = b > a ? b - a : a - b;
double whole = abs_ba * (fa + 4 * fm + fb)/ 6;
return islasi_integrate_aux(fun, a, fa, b, fb, tol, whole, m, fm, max_recursion_depth, params);
}
/*
------------------------------------------------------------------------------
This software is available under 2 licenses -- choose whichever you prefer.
------------------------------------------------------------------------------
ALTERNATIVE A - MIT License
Copyright (c) 2019 Ilya Kolbin
Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is furnished to do
so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
------------------------------------------------------------------------------
ALTERNATIVE B - Public Domain (www.unlicense.org)
This is free and unencumbered software released into the public domain.
Anyone is free to copy, modify, publish, use, compile, sell, or distribute this
software, either in source code form or as a compiled binary, for any purpose,
commercial or non-commercial, and by any means.
In jurisdictions that recognize copyright laws, the author or authors of this
software dedicate any and all copyright interest in the software to the public
domain. We make this dedication for the benefit of the public at large and to
the detriment of our heirs and successors. We intend this dedication to be an
overt act of relinquishment in perpetuity of all present and future rights to
this software under copyright law.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
------------------------------------------------------------------------------
*/
#endif
#endif