Java Variance varianceTwo(final double[] values)

Description

variance Two

License

Open Source License

Declaration

static public final double varianceTwo(final double[] values) 

Method Source Code

//package com.java2s;
/*/*from  www  .ja  va2 s . co m*/
 * ====================================================
 * Copyright (C) 2013 by Idylwood Technologies, LLC. All rights reserved.
 *
 * Developed at Idylwood Technologies, LLC.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * The License should have been distributed to you with the source tree.
 * If not, it can be found at
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
 * Author: Charles Cooper
 * Date: 2013
 * ====================================================
 */

public class Main {
    static public final double varianceTwo(final double[] values) {
        final long n = values.length;
        final long n1 = values.length - 1;
        final double sumOfSquares = sum(pow(values, 2)) / n1;
        final double squareOfSum = Math.pow(sum(values), 2) / (n * n1);
        return sumOfSquares - squareOfSum;
    }

    /**
     * Implementation of sum which is both more numerically
     * stable _and faster_ than the naive implementation
     * which is used in all standard numerical libraries I know of:
     * Colt, OpenGamma, Apache Commons Math, EJML.
     *
     * Implementation uses variant of Kahan's algorithm keeping a running error
     * along with the accumulator to try to cancel out the error at the end.
     * This is much faster than Schewchuk's algorithm but not
     * guaranteed to be perfectly precise
     * In most cases, however, it is just as precise.
     * Due to optimization it is about 30% faster
     * even than the naive implementation on my machine.
     * @param values
     * @return
     * Side Effects: none
     */
    public static final double sum(final double... values) {
        double sum = 0;
        double err = 0;
        final int unroll = 6; // empirically it doesn't get much better than this
        final int len = values.length - values.length % unroll;

        // unroll the loop. due to IEEE 754 restrictions
        // the JIT shouldn't be allowed to unroll it dynamically, so it's
        // up to us to do it by hand ;)
        int i = 0;
        for (; i < len; i += unroll) {
            final double val = values[i] + values[i + 1] + values[i + 2] + values[i + 3] + values[i + 4]
                    + values[i + 5];
            final double partial = val - err;
            final double hi = sum + val;
            err = (hi - sum) - partial;
            sum = hi;
        }
        for (; i < values.length; i++) {
            final double val = values[i];
            final double partial = val - err;
            final double hi = sum + val;
            err = (hi - sum) - partial;
            sum = hi;
        }
        return sum;
    }

    /**
     * Performs termwise Math.pow(double,double) on the elements.
     * @param values
     * @param exp
     * @return Newly allocated array whose elements are
     * termwise exponentiations of the input.
     * Side Effects: Allocation of new array
     */
    public static final double[] pow(final double[] values, final double exp) {
        final double[] ret = new double[values.length];
        for (int i = values.length; i-- != 0;)
            ret[i] = Math.pow(values[i], exp);
        return ret;
    }
}

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