mirror of
https://github.com/UpsilonNumworks/Upsilon.git
synced 2026-01-19 00:37:25 +01:00
662 lines
25 KiB
C++
662 lines
25 KiB
C++
#include <poincare/expression.h>
|
|
#include <poincare/expression_node.h>
|
|
#include <poincare/rational.h>
|
|
#include <poincare/opposite.h>
|
|
#include <poincare/undefined.h>
|
|
#include <poincare/symbol.h>
|
|
#include <poincare/variable_context.h>
|
|
#include <ion.h>
|
|
#include <cmath>
|
|
#include <float.h>
|
|
|
|
#include "expression_lexer_parser.h"
|
|
#include "expression_parser.hpp"
|
|
#include "expression_lexer.hpp"
|
|
|
|
int poincare_expression_yyparse(Poincare::Expression * expressionOutput);
|
|
|
|
namespace Poincare {
|
|
|
|
#include <stdio.h>
|
|
|
|
/* Constructor & Destructor */
|
|
|
|
Expression Expression::clone() const { TreeHandle c = TreeHandle::clone(); return static_cast<Expression&>(c); }
|
|
|
|
Expression Expression::parse(char const * string) {
|
|
if (string[0] == 0) {
|
|
return Expression();
|
|
}
|
|
|
|
static YY_BUFFER_STATE buf = nullptr;
|
|
if (buf != nullptr) {
|
|
poincare_expression_yy_delete_buffer(buf);
|
|
}
|
|
buf = poincare_expression_yy_scan_string(string);
|
|
|
|
Expression expression;
|
|
if (poincare_expression_yyparse(&expression) != 0) {
|
|
// Parsing failed because of invalid input or memory exhaustion
|
|
expression = Expression();
|
|
}
|
|
return expression;
|
|
}
|
|
|
|
/* Circuit breaker */
|
|
|
|
static Expression::CircuitBreaker sCircuitBreaker = nullptr;
|
|
static bool sSimplificationHasBeenInterrupted = false;
|
|
|
|
void Expression::setCircuitBreaker(CircuitBreaker cb) {
|
|
sCircuitBreaker = cb;
|
|
}
|
|
|
|
bool Expression::shouldStopProcessing() {
|
|
if (sCircuitBreaker == nullptr) {
|
|
return false;
|
|
}
|
|
if (sCircuitBreaker()) {
|
|
sSimplificationHasBeenInterrupted = true;
|
|
return true;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
/* Hierarchy */
|
|
|
|
Expression Expression::childAtIndex(int i) const {
|
|
TreeHandle c = TreeHandle::childAtIndex(i);
|
|
return static_cast<Expression &>(c);
|
|
}
|
|
|
|
/* Properties */
|
|
|
|
bool Expression::isRationalZero() const {
|
|
return type() == ExpressionNode::Type::Rational && convert<const Rational>().isZero();
|
|
}
|
|
|
|
bool Expression::isRationalOne() const {
|
|
return type() == ExpressionNode::Type::Rational && convert<const Rational>().isOne();
|
|
}
|
|
|
|
bool Expression::recursivelyMatches(ExpressionTest test, Context & context) const {
|
|
if (test(*this, context)) {
|
|
return true;
|
|
}
|
|
for (int i = 0; i < this->numberOfChildren(); i++) {
|
|
if (childAtIndex(i).recursivelyMatches(test, context)) {
|
|
return true;
|
|
}
|
|
}
|
|
return false;
|
|
}
|
|
|
|
bool Expression::isApproximate(Context & context) const {
|
|
return recursivelyMatches([](const Expression e, Context & context) {
|
|
return e.type() == ExpressionNode::Type::Decimal || e.type() == ExpressionNode::Type::Float || Expression::IsMatrix(e, context) || (e.type() == ExpressionNode::Type::Symbol && Symbol::isApproximate(static_cast<const Symbol&>(e).name(), context));
|
|
}, context);
|
|
}
|
|
|
|
bool Expression::IsMatrix(const Expression e, Context & context) {
|
|
return e.type() == ExpressionNode::Type::Matrix || e.type() == ExpressionNode::Type::ConfidenceInterval || e.type() == ExpressionNode::Type::MatrixDimension || e.type() == ExpressionNode::Type::PredictionInterval || e.type() == ExpressionNode::Type::MatrixInverse || e.type() == ExpressionNode::Type::MatrixTranspose || (e.type() == ExpressionNode::Type::Symbol && Symbol::isMatrixSymbol(static_cast<const Symbol&>(e).name()));
|
|
}
|
|
|
|
bool Expression::DependsOnVariables(const Expression e, Context & context) {
|
|
return e.type() == ExpressionNode::Type::Symbol && Symbol::isVariableSymbol(static_cast<const Symbol&>(e).name());
|
|
}
|
|
|
|
bool Expression::getLinearCoefficients(char * variables, Expression coefficients[], Expression constant[], Context & context, Preferences::AngleUnit angleUnit) const {
|
|
char * x = variables;
|
|
while (*x != 0) {
|
|
int degree = polynomialDegree(*x);
|
|
if (degree > 1 || degree < 0) {
|
|
return false;
|
|
}
|
|
x++;
|
|
}
|
|
Expression equation = *this;
|
|
x = variables;
|
|
int index = 0;
|
|
Expression polynomialCoefficients[k_maxNumberOfPolynomialCoefficients];
|
|
while (*x != 0) {
|
|
int degree = equation.getPolynomialReducedCoefficients(*x, polynomialCoefficients, context, angleUnit);
|
|
if (degree == 1) {
|
|
coefficients[index] = polynomialCoefficients[1];
|
|
} else {
|
|
assert(degree == 0);
|
|
coefficients[index] = Rational(0);
|
|
}
|
|
equation = polynomialCoefficients[0];
|
|
x++;
|
|
index++;
|
|
}
|
|
constant[0] = Opposite(equation.clone()).deepReduce(context, angleUnit);
|
|
/* The expression can be linear on all coefficients taken one by one but
|
|
* non-linear (ex: xy = 2). We delete the results and return false if one of
|
|
* the coefficients contains a variable. */
|
|
bool isMultivariablePolynomial = (constant[0]).recursivelyMatches(DependsOnVariables, context);
|
|
for (int i = 0; i < index; i++) {
|
|
if (isMultivariablePolynomial) {
|
|
break;
|
|
}
|
|
isMultivariablePolynomial |= coefficients[i].recursivelyMatches(DependsOnVariables, context);
|
|
}
|
|
if (isMultivariablePolynomial) {
|
|
for (int i = 0; i < index; i++) {
|
|
coefficients[i] = Expression();
|
|
}
|
|
constant[0] = Expression();
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
// Private
|
|
|
|
Expression Expression::defaultShallowReduce(Context & context, Preferences::AngleUnit angleUnit) {
|
|
for (int i = 0; i < numberOfChildren(); i++) {
|
|
if (childAtIndex(i).type() == ExpressionNode::Type::Undefined) {
|
|
Expression result = Undefined();
|
|
replaceWithInPlace(result);
|
|
return result;
|
|
}
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
Expression Expression::parent() const {
|
|
TreeHandle p = TreeHandle::parent();
|
|
return static_cast<Expression &>(p);
|
|
}
|
|
|
|
void Expression::defaultSetChildrenInPlace(Expression other) {
|
|
assert(numberOfChildren() == other.numberOfChildren());
|
|
for (int i = 0; i < numberOfChildren(); i++) {
|
|
replaceChildAtIndexInPlace(i, other.childAtIndex(i));
|
|
}
|
|
}
|
|
|
|
template<typename U>
|
|
Evaluation<U> Expression::approximateToEvaluation(Context& context, Preferences::AngleUnit angleUnit) const {
|
|
return node()->approximate(U(), context, angleUnit);
|
|
}
|
|
|
|
Expression Expression::defaultReplaceSymbolWithExpression(char symbol, Expression expression) {
|
|
int nbChildren = numberOfChildren();
|
|
for (int i = 0; i < nbChildren; i++) {
|
|
replaceChildAtIndexInPlace(i, childAtIndex(i).replaceSymbolWithExpression(symbol, expression));
|
|
}
|
|
return *this;
|
|
}
|
|
|
|
int Expression::defaultGetPolynomialCoefficients(char symbol, Expression coefficients[]) const {
|
|
int deg = polynomialDegree(symbol);
|
|
if (deg == 0) {
|
|
coefficients[0] = clone();
|
|
return 0;
|
|
}
|
|
return -1;
|
|
}
|
|
|
|
int Expression::getPolynomialReducedCoefficients(char symbolName, Expression coefficients[], Context & context, Preferences::AngleUnit angleUnit) const {
|
|
int degree = getPolynomialCoefficients(symbolName, coefficients);
|
|
for (int i = 0; i <= degree; i++) {
|
|
coefficients[i] = coefficients[i].deepReduce(context, angleUnit);
|
|
}
|
|
return degree;
|
|
}
|
|
|
|
/* Comparison */
|
|
|
|
bool Expression::isIdenticalTo(const Expression e) const {
|
|
/* We use the simplification order only because it is a already-coded total
|
|
* order on expresssions. */
|
|
return ExpressionNode::SimplificationOrder(node(), e.node(), true) == 0;
|
|
}
|
|
|
|
bool Expression::isEqualToItsApproximationLayout(Expression approximation, int bufferSize, Preferences::AngleUnit angleUnit, Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits, Context & context) {
|
|
char buffer[bufferSize];
|
|
approximation.serialize(buffer, bufferSize, floatDisplayMode, numberOfSignificantDigits);
|
|
/* Warning: we cannot use directly the the approximate expression but we have
|
|
* to re-serialize it because the number of stored significative
|
|
* numbers and the number of displayed significative numbers might not be
|
|
* identical. (For example, 0.000025 might be displayed "0.00003" and stored
|
|
* as Decimal(0.000025) and isEqualToItsApproximationLayout should return
|
|
* false) */
|
|
Expression approximateOutput = Expression::ParseAndSimplify(buffer, context, angleUnit);
|
|
bool equal = isIdenticalTo(approximateOutput);
|
|
return equal;
|
|
}
|
|
|
|
/* Layout Helper */
|
|
|
|
LayoutReference Expression::createLayout(Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const {
|
|
return isUninitialized() ? LayoutReference() : node()->createLayout(floatDisplayMode, numberOfSignificantDigits);
|
|
}
|
|
|
|
int Expression::serialize(char * buffer, int bufferSize, Preferences::PrintFloatMode floatDisplayMode, int numberOfSignificantDigits) const { return isUninitialized() ? 0 : node()->serialize(buffer, bufferSize, floatDisplayMode, numberOfSignificantDigits); }
|
|
|
|
/* Simplification */
|
|
|
|
Expression Expression::ParseAndSimplify(const char * text, Context & context, Preferences::AngleUnit angleUnit) {
|
|
Expression exp = parse(text);
|
|
if (exp.isUninitialized()) {
|
|
return Undefined();
|
|
}
|
|
exp = exp.simplify(context, angleUnit);
|
|
/* simplify might have been interrupted, in which case the resulting
|
|
* expression is uninitialized, so we need to check that. */
|
|
if (exp.isUninitialized()) {
|
|
return parse(text);
|
|
}
|
|
return exp;
|
|
}
|
|
|
|
Expression Expression::simplify(Context & context, Preferences::AngleUnit angleUnit) {
|
|
sSimplificationHasBeenInterrupted = false;
|
|
#if MATRIX_EXACT_REDUCING
|
|
#else
|
|
if (recursivelyMatches(IsMatrix, context)) {
|
|
return *this;
|
|
}
|
|
#endif
|
|
Expression e = deepReduce(context, angleUnit);
|
|
e = e.deepBeautify(context, angleUnit);
|
|
if (sSimplificationHasBeenInterrupted) {
|
|
e = Expression();
|
|
}
|
|
return e;
|
|
}
|
|
|
|
Expression Expression::deepReduce(Context & context, Preferences::AngleUnit angleUnit) {
|
|
for (int i = 0; i < numberOfChildren(); i++) {
|
|
childAtIndex(i).deepReduce(context, angleUnit);
|
|
}
|
|
return shallowReduce(context, angleUnit);
|
|
}
|
|
|
|
Expression Expression::deepBeautify(Context & context, Preferences::AngleUnit angleUnit) {
|
|
Expression e = shallowBeautify(context, angleUnit);
|
|
int nbChildren = e.numberOfChildren();
|
|
for (int i = 0; i < nbChildren; i++) {
|
|
e.childAtIndex(i).deepBeautify(context, angleUnit);
|
|
}
|
|
return e;
|
|
}
|
|
|
|
Expression Expression::setSign(ExpressionNode::Sign s, Context & context, Preferences::AngleUnit angleUnit) {
|
|
return node()->setSign(s, context, angleUnit);
|
|
}
|
|
|
|
/* Evaluation */
|
|
|
|
template<typename U>
|
|
Expression Expression::approximate(Context& context, Preferences::AngleUnit angleUnit, Preferences::ComplexFormat complexFormat) const {
|
|
return isUninitialized() ? Undefined() : approximateToEvaluation<U>(context, angleUnit).complexToExpression(complexFormat);
|
|
}
|
|
|
|
|
|
template<typename U>
|
|
U Expression::approximateToScalar(Context& context, Preferences::AngleUnit angleUnit) const {
|
|
return approximateToEvaluation<U>(context, angleUnit).toScalar();
|
|
}
|
|
|
|
template<typename U>
|
|
U Expression::approximateToScalar(const char * text, Context& context, Preferences::AngleUnit angleUnit) {
|
|
Expression exp = ParseAndSimplify(text, context, angleUnit);
|
|
return exp.approximateToScalar<U>(context, angleUnit);
|
|
}
|
|
|
|
template<typename U>
|
|
U Expression::approximateWithValueForSymbol(char symbol, U x, Context & context, Preferences::AngleUnit angleUnit) const {
|
|
VariableContext<U> variableContext = VariableContext<U>(symbol, &context);
|
|
variableContext.setApproximationForVariable(x);
|
|
return approximateToScalar<U>(variableContext, angleUnit);
|
|
}
|
|
|
|
template<typename U>
|
|
U Expression::epsilon() {
|
|
static U epsilon = sizeof(U) == sizeof(double) ? 1E-15 : 1E-7f;
|
|
return epsilon;
|
|
}
|
|
|
|
/* Expression roots/extrema solver*/
|
|
|
|
typename Expression::Coordinate2D Expression::nextMinimum(char symbol, double start, double step, double max, Context & context, Preferences::AngleUnit angleUnit) const {
|
|
return nextMinimumOfExpression(symbol, start, step, max, [](char symbol, double x, Context & context, Preferences::AngleUnit angleUnit, const Expression expression0, const Expression expression1 = Expression()) {
|
|
return expression0.approximateWithValueForSymbol(symbol, x, context, angleUnit);
|
|
}, context, angleUnit);
|
|
}
|
|
|
|
typename Expression::Coordinate2D Expression::nextMaximum(char symbol, double start, double step, double max, Context & context, Preferences::AngleUnit angleUnit) const {
|
|
Coordinate2D minimumOfOpposite = nextMinimumOfExpression(symbol, start, step, max, [](char symbol, double x, Context & context, Preferences::AngleUnit angleUnit, const Expression expression0, const Expression expression1 = Expression()) {
|
|
return -expression0.approximateWithValueForSymbol(symbol, x, context, angleUnit);
|
|
}, context, angleUnit);
|
|
return {.abscissa = minimumOfOpposite.abscissa, .value = -minimumOfOpposite.value};
|
|
}
|
|
|
|
double Expression::nextRoot(char symbol, double start, double step, double max, Context & context, Preferences::AngleUnit angleUnit) const {
|
|
return nextIntersectionWithExpression(symbol, start, step, max, [](char symbol, double x, Context & context, Preferences::AngleUnit angleUnit, const Expression expression0, const Expression expression1 = Expression()) {
|
|
return expression0.approximateWithValueForSymbol(symbol, x, context, angleUnit);
|
|
}, context, angleUnit, nullptr);
|
|
}
|
|
|
|
typename Expression::Coordinate2D Expression::nextIntersection(char symbol, double start, double step, double max, Poincare::Context & context, Preferences::AngleUnit angleUnit, const Expression expression) const {
|
|
double resultAbscissa = nextIntersectionWithExpression(symbol, start, step, max, [](char symbol, double x, Context & context, Preferences::AngleUnit angleUnit, const Expression expression0, const Expression expression1) {
|
|
return expression0.approximateWithValueForSymbol(symbol, x, context, angleUnit)-expression1.approximateWithValueForSymbol(symbol, x, context, angleUnit);
|
|
}, context, angleUnit, expression);
|
|
typename Expression::Coordinate2D result = {.abscissa = resultAbscissa, .value = approximateWithValueForSymbol(symbol, resultAbscissa, context, angleUnit)};
|
|
if (std::fabs(result.value) < step*k_solverPrecision) {
|
|
result.value = 0.0;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
typename Expression::Coordinate2D Expression::nextMinimumOfExpression(char symbol, double start, double step, double max, EvaluationAtAbscissa evaluate, Context & context, Preferences::AngleUnit angleUnit, const Expression expression, bool lookForRootMinimum) const {
|
|
Coordinate2D result = {.abscissa = NAN, .value = NAN};
|
|
if (start == max || step == 0.0) {
|
|
return result;
|
|
}
|
|
double bracket[3];
|
|
double x = start;
|
|
bool endCondition = false;
|
|
do {
|
|
bracketMinimum(symbol, x, step, max, bracket, evaluate, context, angleUnit, expression);
|
|
result = brentMinimum(symbol, bracket[0], bracket[2], evaluate, context, angleUnit, expression);
|
|
x = bracket[1];
|
|
// Because of float approximation, exact zero is never reached
|
|
if (std::fabs(result.abscissa) < std::fabs(step)*k_solverPrecision) {
|
|
result.abscissa = 0;
|
|
result.value = evaluate(symbol, 0, context, angleUnit, *this, expression);
|
|
}
|
|
/* Ignore extremum whose value is undefined or too big because they are
|
|
* really unlikely to be local extremum. */
|
|
if (std::isnan(result.value) || std::fabs(result.value) > k_maxFloat) {
|
|
result.abscissa = NAN;
|
|
}
|
|
// Idem, exact 0 never reached
|
|
if (std::fabs(result.value) < std::fabs(step)*k_solverPrecision) {
|
|
result.value = 0;
|
|
}
|
|
endCondition = std::isnan(result.abscissa) && (step > 0.0 ? x <= max : x >= max);
|
|
if (lookForRootMinimum) {
|
|
endCondition |= std::fabs(result.value) > 0 && (step > 0.0 ? x <= max : x >= max);
|
|
}
|
|
} while (endCondition);
|
|
if (lookForRootMinimum) {
|
|
result.abscissa = std::fabs(result.value) > 0 ? NAN : result.abscissa;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
void Expression::bracketMinimum(char symbol, double start, double step, double max, double result[3], EvaluationAtAbscissa evaluate, Context & context, Preferences::AngleUnit angleUnit, const Expression expression) const {
|
|
Coordinate2D p[3];
|
|
p[0] = {.abscissa = start, .value = evaluate(symbol, start, context, angleUnit, *this, expression)};
|
|
p[1] = {.abscissa = start+step, .value = evaluate(symbol, start+step, context, angleUnit, *this, expression)};
|
|
double x = start+2.0*step;
|
|
while (step > 0.0 ? x <= max : x >= max) {
|
|
p[2] = {.abscissa = x, .value = evaluate(symbol, x, context, angleUnit, *this, expression)};
|
|
if ((p[0].value > p[1].value || std::isnan(p[0].value)) && (p[2].value > p[1].value || std::isnan(p[2].value)) && (!std::isnan(p[0].value) || !std::isnan(p[2].value))) {
|
|
result[0] = p[0].abscissa;
|
|
result[1] = p[1].abscissa;
|
|
result[2] = p[2].abscissa;
|
|
return;
|
|
}
|
|
if (p[0].value > p[1].value && p[1].value == p[2].value) {
|
|
} else {
|
|
p[0] = p[1];
|
|
p[1] = p[2];
|
|
}
|
|
x += step;
|
|
}
|
|
result[0] = NAN;
|
|
result[1] = NAN;
|
|
result[2] = NAN;
|
|
}
|
|
|
|
typename Expression::Coordinate2D Expression::brentMinimum(char symbol, double ax, double bx, EvaluationAtAbscissa evaluate, Context & context, Preferences::AngleUnit angleUnit, const Expression expression) const {
|
|
/* Bibliography: R. P. Brent, Algorithms for finding zeros and extrema of
|
|
* functions without calculating derivatives */
|
|
if (ax > bx) {
|
|
return brentMinimum(symbol, bx, ax, evaluate, context, angleUnit, expression);
|
|
}
|
|
double e = 0.0;
|
|
double a = ax;
|
|
double b = bx;
|
|
double x = a+k_goldenRatio*(b-a);
|
|
double v = x;
|
|
double w = x;
|
|
double fx = evaluate(symbol, x, context, angleUnit, *this, expression);
|
|
double fw = fx;
|
|
double fv = fw;
|
|
|
|
double d = NAN;
|
|
double u, fu;
|
|
|
|
for (int i = 0; i < 100; i++) {
|
|
double m = 0.5*(a+b);
|
|
double tol1 = k_sqrtEps*std::fabs(x)+1E-10;
|
|
double tol2 = 2.0*tol1;
|
|
if (std::fabs(x-m) <= tol2-0.5*(b-a)) {
|
|
double middleFax = evaluate(symbol, (x+a)/2.0, context, angleUnit, *this, expression);
|
|
double middleFbx = evaluate(symbol, (x+b)/2.0, context, angleUnit, *this, expression);
|
|
double fa = evaluate(symbol, a, context, angleUnit, *this, expression);
|
|
double fb = evaluate(symbol, b, context, angleUnit, *this, expression);
|
|
if (middleFax-fa <= k_sqrtEps && fx-middleFax <= k_sqrtEps && fx-middleFbx <= k_sqrtEps && middleFbx-fb <= k_sqrtEps) {
|
|
Coordinate2D result = {.abscissa = x, .value = fx};
|
|
return result;
|
|
}
|
|
}
|
|
double p = 0;
|
|
double q = 0;
|
|
double r = 0;
|
|
if (std::fabs(e) > tol1) {
|
|
r = (x-w)*(fx-fv);
|
|
q = (x-v)*(fx-fw);
|
|
p = (x-v)*q -(x-w)*r;
|
|
q = 2.0*(q-r);
|
|
if (q>0.0) {
|
|
p = -p;
|
|
} else {
|
|
q = -q;
|
|
}
|
|
r = e;
|
|
e = d;
|
|
}
|
|
if (std::fabs(p) < std::fabs(0.5*q*r) && p<q*(a-x) && p<q*(b-x)) {
|
|
d = p/q;
|
|
u= x+d;
|
|
if (u-a < tol2 || b-u < tol2) {
|
|
d = x < m ? tol1 : -tol1;
|
|
}
|
|
} else {
|
|
e = x<m ? b-x : a-x;
|
|
d = k_goldenRatio*e;
|
|
}
|
|
u = x + (std::fabs(d) >= tol1 ? d : (d>0 ? tol1 : -tol1));
|
|
fu = evaluate(symbol, u, context, angleUnit, *this, expression);
|
|
if (fu <= fx) {
|
|
if (u<x) {
|
|
b = x;
|
|
} else {
|
|
a = x;
|
|
}
|
|
v = w;
|
|
fv = fw;
|
|
w = x;
|
|
fw = fx;
|
|
x = u;
|
|
fx = fu;
|
|
} else {
|
|
if (u<x) {
|
|
a = u;
|
|
} else {
|
|
b = u;
|
|
}
|
|
if (fu <= fw || w == x) {
|
|
v = w;
|
|
fv = fw;
|
|
w = u;
|
|
fw = fu;
|
|
} else if (fu <= fv || v == x || v == w) {
|
|
v = u;
|
|
fv = fu;
|
|
}
|
|
}
|
|
}
|
|
Coordinate2D result = {.abscissa = x, .value = fx};
|
|
return result;
|
|
}
|
|
|
|
double Expression::nextIntersectionWithExpression(char symbol, double start, double step, double max, EvaluationAtAbscissa evaluation, Context & context, Preferences::AngleUnit angleUnit, const Expression expression) const {
|
|
if (start == max || step == 0.0) {
|
|
return NAN;
|
|
}
|
|
double bracket[2];
|
|
double result = NAN;
|
|
static double precisionByGradUnit = 1E6;
|
|
double x = start+step;
|
|
do {
|
|
bracketRoot(symbol, x, step, max, bracket, evaluation, context, angleUnit, expression);
|
|
result = brentRoot(symbol, bracket[0], bracket[1], std::fabs(step/precisionByGradUnit), evaluation, context, angleUnit, expression);
|
|
x = bracket[1];
|
|
} while (std::isnan(result) && (step > 0.0 ? x <= max : x >= max));
|
|
|
|
double extremumMax = std::isnan(result) ? max : result;
|
|
Coordinate2D resultExtremum[2] = {
|
|
nextMinimumOfExpression(symbol, start, step, extremumMax, [](char symbol, double x, Context & context, Preferences::AngleUnit angleUnit, const Expression expression0, const Expression expression1) {
|
|
if (expression1.isUninitialized()) {
|
|
return expression0.approximateWithValueForSymbol(symbol, x, context, angleUnit);
|
|
} else {
|
|
return expression0.approximateWithValueForSymbol(symbol, x, context, angleUnit)-expression1.approximateWithValueForSymbol(symbol, x, context, angleUnit);
|
|
}
|
|
}, context, angleUnit, expression, true),
|
|
nextMinimumOfExpression(symbol, start, step, extremumMax, [](char symbol, double x, Context & context, Preferences::AngleUnit angleUnit, const Expression expression0, const Expression expression1) {
|
|
if (expression1.isUninitialized()) {
|
|
return -expression0.approximateWithValueForSymbol(symbol, x, context, angleUnit);
|
|
} else {
|
|
return expression1.approximateWithValueForSymbol(symbol, x, context, angleUnit)-expression0.approximateWithValueForSymbol(symbol, x, context, angleUnit);
|
|
}
|
|
}, context, angleUnit, expression, true)};
|
|
for (int i = 0; i < 2; i++) {
|
|
if (!std::isnan(resultExtremum[i].abscissa) && (std::isnan(result) || std::fabs(result - start) > std::fabs(resultExtremum[i].abscissa - start))) {
|
|
result = resultExtremum[i].abscissa;
|
|
}
|
|
}
|
|
if (std::fabs(result) < std::fabs(step)*k_solverPrecision) {
|
|
result = 0;
|
|
}
|
|
return result;
|
|
}
|
|
|
|
void Expression::bracketRoot(char symbol, double start, double step, double max, double result[2], EvaluationAtAbscissa evaluation, Context & context, Preferences::AngleUnit angleUnit, const Expression expression) const {
|
|
double a = start;
|
|
double b = start+step;
|
|
while (step > 0.0 ? b <= max : b >= max) {
|
|
double fa = evaluation(symbol, a, context, angleUnit, *this, expression);
|
|
double fb = evaluation(symbol, b, context, angleUnit,* this, expression);
|
|
if (fa*fb <= 0) {
|
|
result[0] = a;
|
|
result[1] = b;
|
|
return;
|
|
}
|
|
a = b;
|
|
b = b+step;
|
|
}
|
|
result[0] = NAN;
|
|
result[1] = NAN;
|
|
}
|
|
|
|
double Expression::brentRoot(char symbol, double ax, double bx, double precision, EvaluationAtAbscissa evaluation, Context & context, Preferences::AngleUnit angleUnit, const Expression expression) const {
|
|
if (ax > bx) {
|
|
return brentRoot(symbol, bx, ax, precision, evaluation, context, angleUnit, expression);
|
|
}
|
|
double a = ax;
|
|
double b = bx;
|
|
double c = bx;
|
|
double d = b-a;
|
|
double e = b-a;
|
|
double fa = evaluation(symbol, a, context, angleUnit, *this, expression);
|
|
double fb = evaluation(symbol, b, context, angleUnit, *this, expression);
|
|
double fc = fb;
|
|
for (int i = 0; i < 100; i++) {
|
|
if ((fb > 0.0 && fc > 0.0) || (fb < 0.0 && fc < 0.0)) {
|
|
c = a;
|
|
fc = fa;
|
|
e = b-a;
|
|
d = b-a;
|
|
}
|
|
if (std::fabs(fc) < std::fabs(fb)) {
|
|
a = b;
|
|
b = c;
|
|
c = a;
|
|
fa = fb;
|
|
fb = fc;
|
|
fc = fa;
|
|
}
|
|
double tol1 = 2.0*DBL_EPSILON*std::fabs(b)+0.5*precision;
|
|
double xm = 0.5*(c-b);
|
|
if (std::fabs(xm) <= tol1 || fb == 0.0) {
|
|
double fbcMiddle = evaluation(symbol, 0.5*(b+c), context, angleUnit, *this, expression);
|
|
double isContinuous = (fb <= fbcMiddle && fbcMiddle <= fc) || (fc <= fbcMiddle && fbcMiddle <= fb);
|
|
if (isContinuous) {
|
|
return b;
|
|
}
|
|
}
|
|
if (std::fabs(e) >= tol1 && std::fabs(fa) > std::fabs(b)) {
|
|
double s = fb/fa;
|
|
double p = 2.0*xm*s;
|
|
double q = 1.0-s;
|
|
if (a != c) {
|
|
q = fa/fc;
|
|
double r = fb/fc;
|
|
p = s*(2.0*xm*q*(q-r)-(b-a)*(r-1.0));
|
|
q = (q-1.0)*(r-1.0)*(s-1.0);
|
|
}
|
|
q = p > 0.0 ? -q : q;
|
|
p = std::fabs(p);
|
|
double min1 = 3.0*xm*q-std::fabs(tol1*q);
|
|
double min2 = std::fabs(e*q);
|
|
if (2.0*p < (min1 < min2 ? min1 : min2)) {
|
|
e = d;
|
|
d = p/q;
|
|
} else {
|
|
d = xm;
|
|
e =d;
|
|
}
|
|
} else {
|
|
d = xm;
|
|
e = d;
|
|
}
|
|
a = b;
|
|
fa = fb;
|
|
if (std::fabs(d) > tol1) {
|
|
b += d;
|
|
} else {
|
|
b += xm > 0.0 ? tol1 : tol1;
|
|
}
|
|
fb = evaluation(symbol, b, context, angleUnit, *this, expression);
|
|
}
|
|
return NAN;
|
|
}
|
|
|
|
template float Expression::epsilon<float>();
|
|
template double Expression::epsilon<double>();
|
|
|
|
template Expression Expression::approximate<float>(Context& context, Preferences::AngleUnit angleUnit, Preferences::ComplexFormat complexFormat) const;
|
|
template Expression Expression::approximate<double>(Context& context, Preferences::AngleUnit angleUnit, Preferences::ComplexFormat complexFormat) const;
|
|
|
|
template float Expression::approximateToScalar(Context& context, Preferences::AngleUnit angleUnit) const;
|
|
template double Expression::approximateToScalar(Context& context, Preferences::AngleUnit angleUnit) const;
|
|
|
|
template float Expression::approximateToScalar<float>(const char * text, Context& context, Preferences::AngleUnit angleUnit);
|
|
template double Expression::approximateToScalar<double>(const char * text, Context& context, Preferences::AngleUnit angleUnit);
|
|
|
|
template Evaluation<float> Expression::approximateToEvaluation(Context& context, Preferences::AngleUnit angleUnit) const;
|
|
template Evaluation<double> Expression::approximateToEvaluation(Context& context, Preferences::AngleUnit angleUnit) const;
|
|
|
|
template float Expression::approximateWithValueForSymbol(char symbol, float x, Context & context, Preferences::AngleUnit angleUnit) const;
|
|
template double Expression::approximateWithValueForSymbol(char symbol, double x, Context & context, Preferences::AngleUnit angleUnit) const;
|
|
|
|
}
|