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Adds complex class and fast fourier transform #22

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2ee06a3
Adds complex class and fast fourier transform
kokil87 Oct 1, 2018
e282154
Minor bug fixes
kokil87 Oct 1, 2018
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178 changes: 152 additions & 26 deletions mathx/algebra.h
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Original file line number Diff line number Diff line change
Expand Up @@ -8,62 +8,155 @@

namespace mathx {

double const PI = acos(-1);

class Complex
{
double imaginary, real;
public:
//Constructor
Complex(double a = 0, double b = 0) : real(a), imaginary(b) { }
//Operators
Complex operator +(const Complex &o) const {
return Complex(this->real + o.real, this->imaginary + o.imaginary);
}
Complex operator -(const Complex &o) const {
return Complex(this->real - o.real, this->imaginary - o.imaginary);
}
Complex operator *(const Complex &o) const {
return Complex(this->real * o.real - this->imaginary * o.imaginary, this->real * o.imaginary + this->imaginary * o.real);
}
Complex operator *(const double &o) const {
return Complex(this->real * o, this->imaginary * o);
}
Complex operator /(const double &o) const {
return Complex(this->real / o, this->imaginary / o);
}
Complex operator /=(const double &o) {
this->real /= o; this->imaginary /= o;
return *this;
}
Complex &operator *=(const Complex &o) {
double r = this->real;
this->real = this->real * o.real - this->imaginary * o.imaginary;
this->imaginary = r * o.imaginary + this->imaginary * o.real ;
return (*this);
}
friend ostream &operator<<(ostream &output, const Complex &o ) {
output << "(" << o.real << ", " << o.imaginary << ")" ;
return output;
}
//Accessors
double Real() const {
return this->real;
}
double Imag() const {
return this->imaginary;
}

};

class Polynomial {
private:
std::string var; //variable For eg. "x","y"
float coefficients[100];
int max_coefficient;
std::vector<double> coefficients;

void fft(std::vector<Complex>& a, bool invert) //sub part which must be abstracted and must not be public
{
unsigned n = a.size();
for (unsigned i = 0, j = 0; i < n; i++) {

if (i > j)
swap(a[i], a[j]);

for (unsigned l = n >> 1; (j ^= l) < l; l >>= 1);

}
for (unsigned len = 2; len <= n; len <<= 1) {

double ang = (double)(invert ? -2 : 2) * PI / (double)(len);
Complex wlen((double)cos(ang), (double)sin(ang));

for (unsigned i = 0; i < n; i += len) {

Complex w(1);

for (unsigned j = 0; j < (len >> 1); j++) {

Complex u = a[i + j], v = a[i + j + (len >> 1)] * w;

a[i + j] = u + v;
a[i + j + (len >> 1)] = u - v;
w *= wlen;
}
}
}

if (invert)
for (int i = 0; i < n; ++i)
a[i] /= (double)(n);
}
public:
Polynomial () {
var = "x";
for(int i = 0 ; i < 100; i++)
coefficients[i] = 0;
coefficients.resize(1);
coefficients[0] = 0;
max_coefficient = 0;
}

Polynomial (std::string x) {
var = "x";
for(int i = 0 ; i < 100; i++)
coefficients[i] = 0;
coefficients.resize(1);
max_coefficient = 0;
coefficients[0] = 0;
parse(x);
}

void parse (std::string exp) { // Kanav: Needs a lot of revision.
trim(exp);
bool flag = false;
int temp_power, start = 0;
float temp_co;
for(int i = 0; i < exp.length(); )
double temp_co;
for (int i = 0; i < exp.length(); )
{
start = i;
if(exp[i] == '-' || exp[i] == '+')
if (exp[i] == '-' || exp[i] == '+')
i++;
while(exp[i] >= 48 && exp[i] <= 57 )
while (exp[i] >= 48 && exp[i] <= 57 )
i++;
if ( exp.substr(start,i-start) == "+" || exp.substr(start,i-start) == "-") {
temp_co = std::stof(exp.substr(start,i-start) + "1");
if ( exp.substr(start, i - start) == "+" || exp.substr(start, i - start) == "-") {
temp_co = std::stod(exp.substr(start, i - start) + "1");
}
else
temp_co = std::stof(exp.substr(start,i-start));
while(!(exp[i] >= 48 && exp[i] <= 57))
temp_co = std::stod(exp.substr(start, i - start));
while (!(exp[i] >= 48 && exp[i] <= 57))
i++;
start = i;
while(exp[i] >= 48 && exp[i] <= 57 )
while (exp[i] >= 48 && exp[i] <= 57 )
i++;
temp_power = std::stof(exp.substr(start,i-start));
temp_power = std::stod(exp.substr(start, i - start));
if (temp_power > max_coefficient)
{
max_coefficient = temp_power;
coefficients.resize(temp_power + 1);
}
coefficients[temp_power] = temp_co;
}
}

float evaluate (float const x) {
float sum = 0;
for(int i = 0; i<100; i++) {
double evaluate (double const x) {
double sum = 0;
for (int i = 0; i <= max_coefficient; i++) {
if (coefficients[i] != 0)
sum += std::pow(x,i)*coefficients[i];
sum += std::pow(x, i) * coefficients[i];
}
return sum;
}

float const getCoeff (int i) {
double const getCoeff (int i) {
if (i > max_coefficient)
return static_cast<double>(0);
return coefficients[i];
}

Expand All @@ -73,17 +166,22 @@ namespace mathx {

Polynomial derivative () {
Polynomial der;
for(int i = 0; i < 99; i++) {
der.coefficients[i] = (i+1)*coefficients[i+1];
}
der.coefficients.resize(max_coefficient);
for (int i = 0; i < max_coefficient; i++)
der.coefficients[i] = (i + 1) * coefficients[i + 1];
return der;
}

std::string const display () {
std::string exp = "";
for (int i = 99; i >= 0; i--) {
if(coefficients[i] != 0) {
exp += "+(";
bool first = true;
for (int i = max_coefficient; i >= 0; i--) {
if (coefficients[i] != 0) {
if (!first)
exp += "+";
else
first = false;
exp += "(";
exp += std::to_string(coefficients[i]);
exp += ")x^(";
exp += std::to_string(i);
Expand All @@ -92,6 +190,34 @@ namespace mathx {
}
return exp;
}

Polynomial operator *(const Polynomial &b) const
{
unsigned n = 1;

while (n < this->max_coefficient + b.max_coefficient + 1)
n <<= 1;

std::vector<Complex> fa(this->coefficients.begin(), this->coefficients.end()), fb(b.coefficients.begin(), b.coefficients.end());
fa.resize(n);
fb.resize(n);

fft(fa, false);
fft(fb, false);

for (unsigned i = 0; i < n; ++i)
fa[i] *= fb[i];

fft(fa, true);

Polynomial res;
res.max_coefficient = this->max_coefficient + b.max_coefficient;

for (unsigned i = 0; i <= res.max_coefficient; ++i)
res.coefficients[i] = round(fa[i].Real());

return res;
}
};
}

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