mirror of
https://github.com/UpsilonNumworks/Upsilon.git
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259 lines
8.8 KiB
C++
259 lines
8.8 KiB
C++
#include <poincare/solver.h>
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#include <assert.h>
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#include <float.h>
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#include <cmath>
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namespace Poincare {
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Coordinate2D<double> Solver::BrentMinimum(double ax, double bx, ValueAtAbscissa evaluation, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit, const void * context1, const void * context2, const void * context3) {
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/* Bibliography: R. P. Brent, Algorithms for finding zeros and extrema of
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* functions without calculating derivatives */
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if (ax > bx) {
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return BrentMinimum(bx, ax, evaluation, context, complexFormat, angleUnit, context1, context2, context3);
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}
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double e = 0.0;
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double a = ax;
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double b = bx;
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double x = a+k_goldenRatio*(b-a);
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double v = x;
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double w = x;
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double fx = evaluation(x, context, complexFormat, angleUnit, context1, context2, context3);
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double fw = fx;
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double fv = fw;
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double d = NAN;
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double u, fu;
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for (int i = 0; i < 100; i++) {
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double m = 0.5*(a+b);
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double tol1 = k_sqrtEps*std::fabs(x)+1E-10;
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double tol2 = 2.0*tol1;
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if (std::fabs(x-m) <= tol2-0.5*(b-a)) {
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double middleFax = evaluation((x+a)/2.0, context, complexFormat, angleUnit, context1, context2, context3);
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double middleFbx = evaluation((x+b)/2.0, context, complexFormat, angleUnit, context1, context2, context3);
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double fa = evaluation(a, context, complexFormat, angleUnit, context1, context2, context3);
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double fb = evaluation(b, context, complexFormat, angleUnit, context1, context2, context3);
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if (middleFax-fa <= k_sqrtEps && fx-middleFax <= k_sqrtEps && fx-middleFbx <= k_sqrtEps && middleFbx-fb <= k_sqrtEps) {
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return Coordinate2D<double>(x, fx);
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}
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}
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double p = 0;
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double q = 0;
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double r = 0;
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if (std::fabs(e) > tol1) {
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r = (x-w)*(fx-fv);
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q = (x-v)*(fx-fw);
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p = (x-v)*q -(x-w)*r;
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q = 2.0*(q-r);
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if (q>0.0) {
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p = -p;
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} else {
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q = -q;
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}
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r = e;
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e = d;
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}
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if (std::fabs(p) < std::fabs(0.5*q*r) && p<q*(a-x) && p<q*(b-x)) {
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d = p/q;
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u= x+d;
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if (u-a < tol2 || b-u < tol2) {
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d = x < m ? tol1 : -tol1;
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}
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} else {
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e = x<m ? b-x : a-x;
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d = k_goldenRatio*e;
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}
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u = x + (std::fabs(d) >= tol1 ? d : (d>0 ? tol1 : -tol1));
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fu = evaluation(u, context, complexFormat, angleUnit, context1, context2, context3);
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if (fu <= fx) {
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if (u<x) {
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b = x;
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} else {
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a = x;
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}
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v = w;
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fv = fw;
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w = x;
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fw = fx;
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x = u;
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fx = fu;
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} else {
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if (u<x) {
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a = u;
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} else {
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b = u;
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}
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if (fu <= fw || w == x) {
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v = w;
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fv = fw;
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w = u;
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fw = fu;
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} else if (fu <= fv || v == x || v == w) {
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v = u;
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fv = fu;
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}
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}
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}
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return Coordinate2D<double>(x, fx);
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}
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double Solver::BrentRoot(double ax, double bx, double precision, ValueAtAbscissa evaluation, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit, const void * context1, const void * context2, const void * context3) {
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if (ax > bx) {
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return BrentRoot(bx, ax, precision, evaluation, context, complexFormat, angleUnit, context1, context2, context3);
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}
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double a = ax;
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double b = bx;
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double c = bx;
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double d = b-a;
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double e = b-a;
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double fa = evaluation(a, context, complexFormat, angleUnit, context1, context2, context3);
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if (fa == 0) {
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// We are looking for a root. If a is already a root, just return it.
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return a;
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}
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double fb = evaluation(b, context, complexFormat, angleUnit, context1, context2, context3);
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double fc = fb;
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for (int i = 0; i < 100; i++) {
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if ((fb > 0.0 && fc > 0.0) || (fb < 0.0 && fc < 0.0)) {
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c = a;
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fc = fa;
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e = b-a;
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d = b-a;
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}
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if (std::fabs(fc) < std::fabs(fb)) {
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a = b;
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b = c;
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c = a;
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fa = fb;
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fb = fc;
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fc = fa;
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}
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double tol1 = 2.0*DBL_EPSILON*std::fabs(b)+0.5*precision;
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double xm = 0.5*(c-b);
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if (std::fabs(xm) <= tol1 || fb == 0.0) {
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double fbcMiddle = evaluation(0.5*(b+c), context, complexFormat, angleUnit, context1, context2, context3);
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double isContinuous = (fb <= fbcMiddle && fbcMiddle <= fc) || (fc <= fbcMiddle && fbcMiddle <= fb);
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if (isContinuous) {
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return b;
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}
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}
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if (std::fabs(e) >= tol1 && std::fabs(fa) > std::fabs(b)) {
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double s = fb/fa;
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double p = 2.0*xm*s;
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double q = 1.0-s;
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if (a != c) {
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q = fa/fc;
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double r = fb/fc;
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p = s*(2.0*xm*q*(q-r)-(b-a)*(r-1.0));
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q = (q-1.0)*(r-1.0)*(s-1.0);
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}
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q = p > 0.0 ? -q : q;
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p = std::fabs(p);
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double min1 = 3.0*xm*q-std::fabs(tol1*q);
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double min2 = std::fabs(e*q);
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if (2.0*p < (min1 < min2 ? min1 : min2)) {
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e = d;
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d = p/q;
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} else {
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d = xm;
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e =d;
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}
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} else {
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d = xm;
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e = d;
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}
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a = b;
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fa = fb;
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if (std::fabs(d) > tol1) {
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b += d;
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} else {
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b += xm > 0.0 ? tol1 : tol1;
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}
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fb = evaluation(b, context, complexFormat, angleUnit, context1, context2, context3);
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}
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return NAN;
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}
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Coordinate2D<double> Solver::IncreasingFunctionRoot(double ax, double bx, double resultPrecision, double valuePrecision, ValueAtAbscissa evaluation, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit, const void * context1, const void * context2, const void * context3, double * resultEvaluation) {
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assert(ax < bx);
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double min = ax;
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double max = bx;
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double currentAbscissa = min;
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double eval = evaluation(currentAbscissa, context, complexFormat, angleUnit, context1, context2, context3);
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if (eval >= 0) {
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if (resultEvaluation != nullptr) {
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*resultEvaluation = eval;
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}
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// The minimal value is already bigger than 0, return NAN.
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return Coordinate2D<double>(currentAbscissa, eval);
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}
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while (max - min > resultPrecision) {
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currentAbscissa = (min + max) / 2.0;
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eval = evaluation(currentAbscissa, context, complexFormat, angleUnit, context1, context2, context3);
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if (eval > DBL_EPSILON) {
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max = currentAbscissa;
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} else if (eval < -DBL_EPSILON) {
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min = currentAbscissa;
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} else {
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break;
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}
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}
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if (resultEvaluation != nullptr) {
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*resultEvaluation = eval;
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}
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return Coordinate2D<double>(currentAbscissa, eval);
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}
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template<typename T>
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T Solver::CumulativeDistributiveInverseForNDefinedFunction(T * probability, ValueAtAbscissa evaluation, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit, const void * context1, const void * context2, const void * context3) {
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T precision = sizeof(T) == sizeof(double) ? DBL_EPSILON : FLT_EPSILON;
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assert(*probability <= (((T)1.0) - precision) && *probability >= precision);
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(void) precision;
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T p = 0.0;
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int k = 0;
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T delta = 0.0;
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do {
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delta = std::fabs(*probability-p);
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p += evaluation(k++, context, complexFormat, angleUnit, context1, context2, context3);
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if (p >= k_maxProbability && std::fabs(*probability-1.0) <= delta) {
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*probability = (T)1.0;
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return (T)(k-1);
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}
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} while (std::fabs(*probability-p) <= delta && k < k_maxNumberOfOperations && p < 1.0);
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p -= evaluation(--k, context, complexFormat, angleUnit, context1, context2, context3);
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if (k == k_maxNumberOfOperations) {
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*probability = (T)1.0;
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return INFINITY;
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}
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*probability = p;
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if (std::isnan(p)) {
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return NAN;
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}
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return k-1;
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}
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template<typename T>
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T Solver::CumulativeDistributiveFunctionForNDefinedFunction(T x, ValueAtAbscissa evaluation, Context * context, Preferences::ComplexFormat complexFormat, Preferences::AngleUnit angleUnit, const void * context1, const void * context2, const void * context3) {
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int end = std::round(x);
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double result = 0.0;
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for (int k = 0; k <=end; k++) {
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result += evaluation(k, context, complexFormat, angleUnit, context1, context2, context3);
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/* Avoid too long loop */
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if (k > k_maxNumberOfOperations) {
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break;
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}
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if (result >= k_maxProbability) {
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result = 1.0;
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break;
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}
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}
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return result;
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}
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template float Solver::CumulativeDistributiveInverseForNDefinedFunction(float *, ValueAtAbscissa, Context *, Preferences::ComplexFormat, Preferences::AngleUnit, const void *, const void *, const void *);
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template double Solver::CumulativeDistributiveInverseForNDefinedFunction(double *, ValueAtAbscissa, Context *, Preferences::ComplexFormat, Preferences::AngleUnit, const void *, const void *, const void *);
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template float Solver::CumulativeDistributiveFunctionForNDefinedFunction(float, ValueAtAbscissa, Context *, Preferences::ComplexFormat, Preferences::AngleUnit, const void *, const void *, const void *);
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template double Solver::CumulativeDistributiveFunctionForNDefinedFunction(double, ValueAtAbscissa, Context *, Preferences::ComplexFormat, Preferences::AngleUnit, const void *, const void *, const void *);
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}
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