RecursionRelation.cpp

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/*
 *  Copyright (c) 2018, Martin Duy Tat
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#include <cmath>
#include <iostream>
#include <vector>
#include "RecursionRelation.h"
#include "DifferentialOperator.h"
 
namespace polynomial {
 
RecursionRelation::RecursionRelation(): power_m(0), highestXorder_m(10) {
    std::vector<int> poly(1, 1);
    operator_m.setPolynomial(poly, 0, 0);
}
 
RecursionRelation::RecursionRelation(const std::size_t &power,
                                     const std::size_t &highestXorder):
    power_m(power), highestXorder_m(highestXorder) {
    std::vector<int> poly(1, 1);
    operator_m.setPolynomial(poly, 0, 0);
    for (std::size_t i = 0; i < power_m; i++) {
        applyOperator();
    }
}
 
RecursionRelation::RecursionRelation(const RecursionRelation &doperator):
    operator_m(DifferentialOperator(doperator.operator_m)),
    power_m(doperator.power_m), highestXorder_m(doperator.highestXorder_m) {
}
 
RecursionRelation::~RecursionRelation() {
}
 
RecursionRelation& RecursionRelation::operator= (
                   const RecursionRelation &recursion) {
     operator_m = recursion.operator_m;
     power_m = recursion.power_m;
     highestXorder_m = recursion.highestXorder_m;
     return *this;
}
 
void RecursionRelation::truncate(std::size_t highestXorder) {
    highestXorder_m = highestXorder;
    operator_m.truncate(highestXorder);
}
 
/*  This function increases n by 1 in the differential operator used to find \n
 *  the magnetic scalar potential
 */
void RecursionRelation::applyOperator() {
/*  Differential operator has 3 terms, make three copies of current operator */
    DifferentialOperator firstTerm(operator_m);
    DifferentialOperator secondTerm(operator_m);
    DifferentialOperator thirdTerm(operator_m);
/*  Initialise polynomials
 *  p(x) = 1 - x + x^2 - ...
 *  q(x) = 1 - 2x + 3x^2 - ...
 */
    std::vector<int> p, q;
    for (std::size_t i = 0; i <= highestXorder_m; i++) {
        p.push_back(pow(-1, i));
        q.push_back(pow(-1, i) * (i + 1));
    }
/*  Differentiate first term by x, then multiply by p(x) */
    firstTerm.differentiateX();
    firstTerm.multiplyPolynomial(Polynomial(p));
/*  Differentiate second term twice by x */
    secondTerm.differentiateX();
    secondTerm.differentiateX();
/*  Differentiate third term by s twice, then multiply by q(x) */
    thirdTerm.doubleDifferentiateS();
    thirdTerm.multiplyPolynomial(Polynomial(q));
/*  Add operators to obtain final operator */
    operator_m = DifferentialOperator(firstTerm);
    operator_m.addOperator(secondTerm);
    operator_m.addOperator(thirdTerm);
}
 
}