103 lines
2.3 KiB
Java
103 lines
2.3 KiB
Java
package org.nevec.rjm;
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import java.math.BigInteger;
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import java.util.Vector;
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import it.cavallium.warppi.util.Error;
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/**
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* Bernoulli numbers.
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*
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* @since 2006-06-25
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* @author Richard J. Mathar
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*/
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public class Bernoulli {
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/*
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* The list of all Bernoulli numbers as a vector, n=0,2,4,....
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*/
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static Vector<Rational> a = new Vector<>();
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public Bernoulli() {
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if (Bernoulli.a.size() == 0) {
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Bernoulli.a.add(Rational.ONE);
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Bernoulli.a.add(new Rational(1, 6));
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}
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}
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/**
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* Set a coefficient in the internal table.
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*
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* @param n
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* the zero-based index of the coefficient. n=0 for the constant
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* term.
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* @param value
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* the new value of the coefficient.
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*/
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protected void set(final int n, final Rational value) {
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final int nindx = n / 2;
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if (nindx < Bernoulli.a.size()) {
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Bernoulli.a.set(nindx, value);
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} else {
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while (Bernoulli.a.size() < nindx) {
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Bernoulli.a.add(Rational.ZERO);
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}
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Bernoulli.a.add(value);
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}
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}
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/**
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* The Bernoulli number at the index provided.
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*
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* @param n
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* the index, non-negative.
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* @return the B_0=1 for n=0, B_1=-1/2 for n=1, B_2=1/6 for n=2 etc
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* @throws Error
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*/
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public Rational at(final int n) throws Error {
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if (n == 1) {
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return new Rational(-1, 2);
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} else if (n % 2 != 0) {
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return Rational.ZERO;
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} else {
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final int nindx = n / 2;
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if (Bernoulli.a.size() <= nindx) {
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for (int i = 2 * Bernoulli.a.size(); i <= n; i += 2) {
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set(i, doubleSum(i));
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}
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}
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return Bernoulli.a.elementAt(nindx);
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}
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}
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/*
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* Generate a new B_n by a standard double sum.
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*
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* @param n The index of the Bernoulli number.
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*
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* @return The Bernoulli number at n.
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*/
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private Rational doubleSum(final int n) throws Error {
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Rational resul = Rational.ZERO;
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for (int k = 0; k <= n; k++) {
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Rational jsum = Rational.ZERO;
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BigInteger bin = BigInteger.ONE;
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for (int j = 0; j <= k; j++) {
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final BigInteger jpown = new BigInteger("" + j).pow(n);
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if (j % 2 == 0) {
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jsum = jsum.add(bin.multiply(jpown));
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} else {
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jsum = jsum.subtract(bin.multiply(jpown));
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}
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/*
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* update binomial(k,j) recursively
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*/
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bin = bin.multiply(new BigInteger("" + (k - j))).divide(new BigInteger("" + (j + 1)));
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}
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resul = resul.add(jsum.divide(new BigInteger("" + (k + 1))));
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}
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return resul;
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}
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} /* Bernoulli */
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