arma::vec polynomial(
const arma::vec& parameter,
const arma::uword highestDegree) {
if (parameter.n_elem == 0 || highestDegree == 0) {
// By definition, the constant term is 1.
return {1.0};
}
arma::vec polynomial(polynomialSize(parameter.n_elem, highestDegree));
arma::uword n = 0;
// Generates all terms for degree > 1
for (arma::uword degree = highestDegree; degree >= 2; --degree) {
for (const auto& multicombination : multicombinations(parameter.n_elem, degree)) {
const arma::vec& partialParameter = parameter.elem(multicombination);
polynomial(n++) = arma::prod(partialParameter);
}
}
// Linear term
polynomial.subvec(n, n + parameter.n_elem - 1) = parameter;
// By definition, the constant term is 1.
polynomial(polynomial.n_elem - 1) = 1;
return polynomial;
}
arma::Col<double> polynomial(
const arma::Col<double>& parameter,
const arma::uword polynomialOrder) {
arma::Col<double> polynomial(polynomialSize(parameter.n_elem, polynomialOrder));
// For any polynomial, all constant terms are 1.
switch (polynomialOrder) {
case 0: { // Constant polynomials
// Constant term
polynomial(0) = 1.0;
}
break;
case 1: { // Linear polynomials
// Linear term
polynomial.head(parameter.n_elem) = parameter;
// Constant term
polynomial(parameter.n_elem) = 1;
}
break;
case 2: { // Quadratic polynomials
// Quadratic term
arma::uword n = 0;
for (arma::uword k = 0; k < parameter.n_elem; ++k) {
for (arma::uword l = k; l < parameter.n_elem; ++l) {
polynomial(n++) = parameter(k) * parameter(l);
}
}
// Linear term
polynomial.subvec(n, n + parameter.n_elem - 1) = parameter;
// Constant term
polynomial(polynomial.n_elem - 1) = 1;
}
break;
case 3: { // Cubic polynomials
// Cubic term
arma::uword n = 0;
for (arma::uword k = 0; k < parameter.n_elem; ++k) {
for (arma::uword l = k; l < parameter.n_elem; ++l) {
for (arma::uword m = l; m < parameter.n_elem; ++m) {
polynomial(n++) = parameter(k) * parameter(l) * parameter(m);
}
}
}
// Quadratic term
for (arma::uword k = 0; k < parameter.n_elem; ++k) {
for (arma::uword l = k; l < parameter.n_elem; ++l) {
polynomial(n++) = parameter(k) * parameter(l);
}
}
// Linear term
polynomial.subvec(n, n + parameter.n_elem - 1) = parameter;
// Constant term
polynomial(polynomial.n_elem - 1) = 1;
}
break;
default: { // Polynomials of degree >= 4
// All terms, expect the linear and constant one.
arma::uword n = 0;
// Generates the term for all degrees > 1
for (arma::uword d = 2; d <= polynomialOrder; ++d) {
for (const auto& multicombination : multicombinations(parameter.n_elem, d)) {
polynomial(n++) = arma::prod(parameter.elem(multicombination));
}
}
// Linear term
polynomial.subvec(n, n + parameter.n_elem - 1) = parameter;
// Constant term
polynomial(polynomial.n_elem - 1) = 1;
}
break;
}
return polynomial;
}
