#include <iostream>
#include <cmath>

#include "ivp.h"
#include "vec.h"

// The critical frequency
double const fc{ 0.5 };

// Function declarations
int main();
double v( double t );

#include "lowpass.h"

// Input signal
double v( double t ) {
    return std::sin(t) + std::sin(10*t);
}

int main() {
    std::cout.precision( 6 );
    std::clog.precision( 16 );

    ivp<vec<1>> y{ f, 0.0, 0.0, 0.05, std::make_pair( 1e-5, 0.1 ), 1e-5, vec<1>::norm };

    double t_max{ 20.0 };
    double step{ 0.1 };

    // Calculate this once, so that it finds an approximation
    // for all values on the interval [0, t_max]
    y( t_max );

    std::cout << "L := [" << std::endl;

    for ( double t{0.0}; t < t_max + 0.5*step; t += step ) {
       std::cout << "[" << t << ", " << y( t )[0] << "]," << std::endl;
    }

    std::cout << "NULL]:" << std::endl;

    std::cout << "phase := " << phase( 1.0/(2.0*M_PI) ) << ":" << std::endl;

    return 0;
}