matlab.h

#pragma once

#include <random>
#include <iostream>
#include <fstream>
#include "../types.h"
#include <complex>
/*
 * Code translated from Matlab base functions
 * matlab translation guide : https://eigen.tuxfamily.org/dox/AsciiQuickReference.txt
 */

//-------------------------------------------------------------------------------------------------
// VARIOUS

const number pi = M_PI;

// squares a number
template<typename T> inline T squared(const T& x)
{
    return x*x;
}

//-------------------------------------------------------------------------------------------------
// ALGEBRA

// build a vector with values in the given interval
Vector make_vector(const int fromValue, const int toValue, const int by = 1)
{
    int size = 1 + (toValue - fromValue) / by;
    Vector result(size);

    int currentValue = fromValue;
    for(int i = 0; i < size; i++)
    {
        result(i) = currentValue;
        currentValue += by;
    }

    return result;
}

// repeats a column vector n times in order to build a matrix
Matrix repmat(const Vector& v, const int colNumber)
{
    Matrix result(v.size(), colNumber);

    for(int col = 0; col < colNumber; col++)
    {
        result.col(col) = v;
    }

    return result;
}

// solves m = m1 \ m2
inline ComplexMatrix mldivide(const ComplexMatrix& m1, const ComplexMatrix& m2)
{
    //return m1.colPivHouseholderQr().solve(m2);
    return m1.bdcSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(m2); // you can use JacobiSVD for improved precision
}

// returns an hermitian matrix where v is the first row and conj(v) the first column
Matrix toeplitz(const Vector& v)
{
    auto size = v.size();
    Matrix result(size, size);

    for(int row=0; row<size; row++)
    {