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polys.cpp
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polys.cpp
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#include "polys.h"
#include <ctype.h>
#include <math.h>
using namespace std;
Polys::Polys(string input)
{
parse(input,p);
}
Polys::~Polys()
{
}
// 彈出數字
void Polys::pop(string& s, int& i, double &n,int mode){
bool valid = false;
if(mode == 0)
valid = true;
// 忽略次方符號
if (s[i] == '^'){
++i;
if(mode == 1)
valid = true;
}
// 忽略乘法符號
if (s[i] == '*') ++i;
// 忽略括弧
if (s[i] == '(') ++i;
if (s[i] == ')') ++i;
// 忽略空白
if (s[i] == ' ') ++i;
// 數值
if(valid == true){
n = 0;
int m = 1;
bool digit = false;
unsigned int start,end;
if(s[i]=='-'){
m = -1;
i++;
}
if(isdigit(s[i])){
digit = true;
start = i;
for (; (isdigit(s[i])||s[i]=='.')&&i<(s.size()-1); ++i){}
end = i-1;
if(i==(s.size()-1))
end = i;
n = stod(s.substr(start,end-start+1));
n = n * m;
}
if (n == 0 && !digit) n = 1;
}else
n = 1;
}
void Polys::parse(string &s, vector<poly> &p){
int n = 0;
for (int i=0; i<s.size()-1; ++n)
{
poly tmp;
// 正負號
int m = 1;
if (s[i] == '+') m = +1, ++i;
if (s[i] == '-') m = -1, ++i;
// 係數
pop(s, i, tmp.c,0);
tmp.c *= m;
if (s[i] == '*') ++i;
// 元與次方
if (s[i] == 'x') pop(s, ++i, tmp.x,1);
if (s[i] == '*') ++i;
if (s[i] == 'y') pop(s, ++i, tmp.y,1);
if (s[i] == '*') ++i;
if (s[i] == 'z') pop(s, ++i, tmp.z,1);
p.push_back(tmp);
}
}
//求值
double Polys::eval(double x,double y,double z){
double result = 0;
for(int i=0;i<p.size();i++){
double term = 1;
term *= pow(x,p[i].x);
term *= pow(y,p[i].y);
term *= pow(z,p[i].z);
term *= p[i].c;
result += term;
}
return result;
}
void Polys::createSuber(double xc,double xa,double yc,double ya){
subx.c = xc;
subx.x = xa;
suby.c = yc;
suby.x = ya;
}
double Polys::evalSuber(double a){
return eval(subx.c+subx.x*a,suby.c+suby.x*a,0);
}
void Polys::deleteSuber(){
subx.c = 0;
subx.x = 0;
suby.c = 0;
suby.x = 0;
}
array<double,2> Polys::gradient(double x,double y){
double h = 0.000001;
array<double,2> result;
result[0] = (eval(x+h,y,0)-eval(x-h,y,0))/(2*h);
result[1] = (eval(x,y+h,0)-eval(x,y-h,0))/(2*h);
return result;
}
double Polys::dx (double x,double y){
double h = 0.000001;
return (eval(x+h,y,0)-eval(x-h,y,0))/(2*h);
}
double Polys::dy (double x,double y){
double h = 0.000001;
return (eval(x,y+h,0)-eval(x,y-h,0))/(2*h);
}
double Polys::dxx (double x,double y){
double h = 0.000001;
return (dx(x+h,y)-dx(x-h,y))/(2*h);
}
double Polys::dyy (double x,double y){
double h = 0.000001;
return (dy(x,y+h)-dy(x,y-h))/(2*h);
}
double Polys::dxy (double x,double y){
double h = 0.000001;
return (dx(x,y+h)-dx(x,y-h))/(2*h);
}
double Polys::dyx (double x,double y){
double h = 0.000001;
return (dy(x+h,y)-dy(x-h,y))/(2*h);
}
array<array<double,2>,2> Polys::hessian(double x,double y){
double h = 0.001;
array<array<double,2>,2> result;
result[0][0] = dxx(x,y);
result[0][1] = dxy(x,y);
result[1][0] = dyx(x,y);
result[1][1] = dyy(x,y);
return result;
}