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https://github.com/UpsilonNumworks/Upsilon.git
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226 lines
8.2 KiB
C++
226 lines
8.2 KiB
C++
#include <poincare/integral.h>
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#include <poincare/symbol.h>
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#include <poincare/context.h>
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#include <poincare/undefined.h>
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#include <cmath>
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extern "C" {
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#include <assert.h>
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#include <float.h>
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#include <stdlib.h>
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}
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#include "layout/integral_layout.h"
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#include "layout/horizontal_layout.h"
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namespace Poincare {
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Expression::Type Integral::type() const {
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return Type::Integral;
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}
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Expression * Integral::clone() const {
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Integral * a = new Integral(m_operands, true);
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return a;
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}
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int Integral::polynomialDegree(char symbolName) const {
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if (symbolName == 'x') {
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int da = operand(1)->polynomialDegree(symbolName);
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int db = operand(2)->polynomialDegree(symbolName);
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if (da != 0 || db != 0) {
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return -1;
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}
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return 0;
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}
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return Expression::polynomialDegree(symbolName);
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}
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Expression * Integral::shallowReduce(Context& context, AngleUnit angleUnit) {
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Expression * e = Expression::shallowReduce(context, angleUnit);
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if (e != this) {
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return e;
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}
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#if MATRIX_EXACT_REDUCING
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if (operand(0)->type() == Type::Matrix || operand(1)->type() == Type::Matrix || operand(2)->type() == Type::Matrix) {
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return replaceWith(new Undefined(), true);
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}
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#endif
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return this;
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}
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template<typename T>
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Complex<T> * Integral::templatedApproximate(Context & context, AngleUnit angleUnit) const {
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Expression * aInput = operand(1)->approximate<T>(context, angleUnit);
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T a = aInput->type() == Type::Complex ? static_cast<Complex<T> *>(aInput)->toScalar() : NAN;
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delete aInput;
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Expression * bInput = operand(2)->approximate<T>(context, angleUnit);
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T b = bInput->type() == Type::Complex ? static_cast<Complex<T> *>(bInput)->toScalar() : NAN;
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delete bInput;
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if (std::isnan(a) || std::isnan(b)) {
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return new Complex<T>(Complex<T>::Float(NAN));
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}
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#ifdef LAGRANGE_METHOD
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T result = lagrangeGaussQuadrature<T>(a, b, context, angleUnit);
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#else
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T result = adaptiveQuadrature<T>(a, b, 0.1, k_maxNumberOfIterations, context, angleUnit);
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#endif
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return new Complex<T>(Complex<T>::Float(result));
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}
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ExpressionLayout * Integral::privateCreateLayout(PrintFloat::Mode floatDisplayMode, ComplexFormat complexFormat) const {
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assert(floatDisplayMode != PrintFloat::Mode::Default);
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assert(complexFormat != ComplexFormat::Default);
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return new IntegralLayout(
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operand(0)->createLayout(floatDisplayMode, complexFormat),
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operand(1)->createLayout(floatDisplayMode, complexFormat),
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operand(2)->createLayout(floatDisplayMode, complexFormat),
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false);
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}
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template<typename T>
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T Integral::functionValueAtAbscissa(T x, Context & context, AngleUnit angleUnit) const {
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return operand(0)->approximateWithValueForSymbol('x', x, context);
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}
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#ifdef LAGRANGE_METHOD
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template<typename T>
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T Integral::lagrangeGaussQuadrature(T a, T b, Context & context, AngleUnit angleUnit) const {
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/* We here use Gauss-Legendre quadrature with n = 5
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* Gauss-Legendre abscissae and weights can be found in
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* C/C++ library source code. */
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const static T x[10]={0.0765265211334973337546404, 0.2277858511416450780804962, 0.3737060887154195606725482, 0.5108670019508270980043641,
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0.6360536807265150254528367, 0.7463319064601507926143051, 0.8391169718222188233945291, 0.9122344282513259058677524,
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0.9639719272779137912676661, 0.9931285991850949247861224};
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const static T w[10]={0.1527533871307258506980843, 0.1491729864726037467878287, 0.1420961093183820513292983, 0.1316886384491766268984945, 0.1181945319615184173123774,
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0.1019301198172404350367501, 0.0832767415767047487247581, 0.0626720483341090635695065, 0.0406014298003869413310400, 0.0176140071391521183118620};
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T xm = 0.5*(a+b);
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T xr = 0.5*(b-a);
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T result = 0;
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for (int j = 0; j < 10; j++) {
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T dx = xr * x[j];
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T evaluationAfterx = functionValueAtAbscissa(xm+dx, context, angleUnit);
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if (std::isnan(evaluationAfterx)) {
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return NAN;
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}
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T evaluationBeforex = functionValueAtAbscissa(xm-dx, context, angleUnit);
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if (std::isnan(evaluationBeforex)) {
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return NAN;
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}
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result += w[j]*(evaluationAfterx + fevaluationBeforex);
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}
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result *= xr;
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return result;
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}
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#else
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template<typename T>
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Integral::DetailedResult<T> Integral::kronrodGaussQuadrature(T a, T b, Context & context, AngleUnit angleUnit) const {
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static T epsilon = sizeof(T) == sizeof(double) ? DBL_EPSILON : FLT_EPSILON;
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static T max = sizeof(T) == sizeof(double) ? DBL_MAX : FLT_MAX;
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/* We here use Kronrod-Legendre quadrature with n = 21
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* The abscissa and weights are taken from QUADPACK library. */
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const static T wg[5]= {0.066671344308688137593568809893332, 0.149451349150580593145776339657697,
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0.219086362515982043995534934228163, 0.269266719309996355091226921569469, 0.295524224714752870173892994651338};
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const static T xgk[11]= {0.995657163025808080735527280689003, 0.973906528517171720077964012084452,
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0.930157491355708226001207180059508, 0.865063366688984510732096688423493, 0.780817726586416897063717578345042,
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0.679409568299024406234327365114874, 0.562757134668604683339000099272694, 0.433395394129247190799265943165784,
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0.294392862701460198131126603103866, 0.148874338981631210884826001129720, 0.000000000000000000000000000000000};
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const static T wgk[11]= {0.011694638867371874278064396062192, 0.032558162307964727478818972459390,
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0.054755896574351996031381300244580, 0.075039674810919952767043140916190, 0.093125454583697605535065465083366,
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0.109387158802297641899210590325805, 0.123491976262065851077958109831074, 0.134709217311473325928054001771707,
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0.142775938577060080797094273138717, 0.147739104901338491374841515972068, 0.149445554002916905664936468389821};
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T fv1[10];
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T fv2[10];
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T centr = 0.5*(a+b);
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T hlgth = 0.5*(b-a);
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T dhlgth = std::fabs(hlgth);
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DetailedResult<T> errorResult;
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errorResult.integral = NAN;
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errorResult.absoluteError = 0;
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T resg = 0;
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T fc = functionValueAtAbscissa(centr, context, angleUnit);
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if (std::isnan(fc)) {
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return errorResult;
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}
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T resk = wgk[10]*fc;
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T resabs = std::fabs(resk);
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for (int j = 0; j < 5; j++) {
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int jtw = 2*j+1;
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T absc = hlgth*xgk[jtw];
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T fval1 = functionValueAtAbscissa(centr-absc, context, angleUnit);
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if (std::isnan(fval1)) {
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return errorResult;
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}
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T fval2 = functionValueAtAbscissa(centr+absc, context, angleUnit);
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if (std::isnan(fval2)) {
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return errorResult;
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}
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fv1[jtw] = fval1;
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fv2[jtw] = fval2;
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T fsum = fval1+fval2;
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resg += wg[j]*fsum;
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resk += wgk[jtw]*fsum;
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resabs += wgk[jtw]*(std::fabs(fval1)+std::fabs(fval2));
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}
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for (int j = 0; j < 5; j++) {
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int jtwm1 = 2*j;
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T absc = hlgth*xgk[jtwm1];
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T fval1 = functionValueAtAbscissa(centr-absc, context, angleUnit);
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if (std::isnan(fval1)) {
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return errorResult;
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}
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T fval2 = functionValueAtAbscissa(centr+absc, context, angleUnit);
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if (std::isnan(fval2)) {
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return errorResult;
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}
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fv1[jtwm1] = fval1;
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fv2[jtwm1] = fval2;
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T fsum = fval1+fval2;
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resk += wgk[jtwm1]*fsum;
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resabs += wgk[jtwm1]*(std::fabs(fval1)+std::fabs(fval2));
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}
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T reskh = resk*0.5;
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T resasc = wgk[10]*std::fabs(fc-reskh);
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for (int j = 0; j < 10; j++) {
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resasc += wgk[j]*(std::fabs(fv1[j]-reskh)+std::fabs(fv2[j]-reskh));
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}
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T integral = resk*hlgth;
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resabs = resabs*dhlgth;
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resasc = resasc*dhlgth;
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T abserr = std::fabs((resk-resg)*hlgth);
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if (resasc != 0 && abserr != 0) {
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abserr = 1 > std::pow((T)(200*abserr/resasc), (T)1.5)? resasc*std::pow((T)(200*abserr/resasc), (T)1.5) : resasc;
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}
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if (resabs > max/(50.0*epsilon)) {
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abserr = abserr > epsilon*50*resabs ? abserr : epsilon*50*resabs;
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}
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DetailedResult<T> result;
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result.integral = integral;
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result.absoluteError = abserr;
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return result;
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}
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template<typename T>
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T Integral::adaptiveQuadrature(T a, T b, T eps, int numberOfIterations, Context & context, AngleUnit angleUnit) const {
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if (shouldStopProcessing()) {
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return NAN;
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}
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DetailedResult<T> quadKG = kronrodGaussQuadrature(a, b, context, angleUnit);
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T result = quadKG.integral;
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if (quadKG.absoluteError <= eps) {
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return result;
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} else if (--numberOfIterations > 0) {
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T m = (a+b)/2;
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return adaptiveQuadrature<T>(a, m, eps/2, numberOfIterations, context, angleUnit) + adaptiveQuadrature<T>(m, b, eps/2, numberOfIterations, context, angleUnit);
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} else {
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return NAN;
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}
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}
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#endif
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}
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