public static void derivative(Polynomial poly, Polynomial deriv) {
deriv.size = poly.size - 1;
for (int i = 1; i < poly.size; i++) {
deriv.c[i - 1] = poly.c[i] * i;
}
}
/**
* Polynomial division. Computes both the quotient and the remainder.<br>
* <br>
* quotient = numerator/denominator<br>
* remainder = numerator % denominator
*
* @param numerator Numerator in the division. Not modified.
* @param denominator Denominator in the division. Not modified.
* @param quotient Output quotient, Modified.
* @param remainder Output remainder. Modified.
*/
public static void divide(
Polynomial numerator, Polynomial denominator, Polynomial quotient, Polynomial remainder) {
int nn = numerator.size - 1;
int nd = denominator.size - 1;
while (nd >= 0 && denominator.c[nd] == 0) nd -= 1;
quotient.size = nn - nd + 1;
remainder.setTo(numerator);
for (int k = nn - nd; k >= 0; k--) {
double c = quotient.c[k] = remainder.c[nd + k] / denominator.c[nd];
for (int j = k + nd; j >= k; j--) {
remainder.c[j] -= c * denominator.c[j - k];
}
}
// The remainder can't be larger than the denominator
remainder.size = nd;
}
/**
* Multiplies the two polynomials together.
*
* @param a Polynomial
* @param b Polynomial
* @param result Optional storage parameter for the results. Must be have enough coefficients to
* store the results. If null a new instance is declared.
* @return Results of the multiplication
*/
public static Polynomial multiply(Polynomial a, Polynomial b, Polynomial result) {
int N = Math.max(0, a.size() + b.size() - 1);
if (result == null) {
result = new Polynomial(N);
} else {
if (result.size < N) throw new IllegalArgumentException("Unexpected length of 'result'");
result.zero();
}
for (int i = 0; i < a.size; i++) {
double coef = a.c[i];
int index = i;
for (int j = 0; j < b.size; j++) {
result.c[index++] += coef * b.c[j];
}
}
return result;
}
// TODO try using a linear search alg here
public static double refineRoot(Polynomial poly, double root, int maxIterations) {
// for( int i = 0; i < maxIterations; i++ ) {
//
// double v = poly.c[poly.size-1];
// double d = v*(poly.size-1);
//
// for( int j = poly.size-1; j > 0; j-- ) {
// v = poly.c[j] + v*root;
// d = poly.c[j]*j + d*root;
// }
// v = poly.c[0] + v*root;
//
// if( d == 0 )
// return root;
//
// root -= v/d;
// }
//
// return root;
Polynomial deriv = new Polynomial(poly.size());
derivative(poly, deriv);
for (int i = 0; i < maxIterations; i++) {
double v = poly.evaluate(root);
double d = deriv.evaluate(root);
if (d == 0) return root;
root -= v / d;
}
return root;
}