Java Array Covariance covariance(final double[][] data)

Description

covariance

License

Open Source License

Declaration

public static final double[][] covariance(final double[][] data) 

Method Source Code

//package com.java2s;
/*/*from   www  .  jav a2  s  .  c  o  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 {
    public static final double[][] covariance(final double[][] data) {
        final int len = data.length;
        final double[] means = new double[len]; // precalculate the means
        final double[][] ret = new double[len][len];
        for (int i = 0; i < len; i++) {
            means[i] = mean(data[i]);
            for (int j = 0; j <= i; j++) {
                final double d = sum(multiply(shift(data[i], -means[i]), shift(data[j], -means[j]))) / (len);
                ret[i][j] = d;
                ret[j][i] = d;
            }
        }
        return ret;
    }

    public final static double mean(final double[] values) {
        return sum(values) / values.length;
    }

    /**
     * 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;
    }

    /**
     * Returns newly allocated array which is the result
     * of termwise multiplication of the input arrays
     * @param first
     * @param second
     * @throws ArrayIndexOutOfBoundsException if the arrays are of unequal length
     * @return
     * Side Effects: Allocation of the returned array
     */
    final public static double[] multiply(final double[] x, final double[] y) {
        final int len = x.length;
        if (len != y.length)
            throw new ArrayIndexOutOfBoundsException("Tried to multiply two vectors of unequal length!");
        final double ret[] = new double[len];
        for (int i = 0; i < len; i++)
            ret[i] = x[i] * y[i];
        return ret;
    }

    /**
     * Shifts all the elements of <code>values</code> by <code>constant</code>.
     * @param values
     * @param constant
     * @return Newly allocated array whose values are values[i]+constant
     * Side Effects: Allocation of new array
     */
    public static final double[] shift(final double[] values, final double constant) {
        final double ret[] = new double[values.length];
        for (int i = values.length; i-- != 0;)
            ret[i] = values[i] + constant;
        return ret;
    }
}

Related

1. covariance(double[] a, double amean, double[] b, double bmean)
2. covariance(double[] a, double[] b)
3. covariance(double[] x, double[] y)
4. covariance(double[] x, double[] y, int delay)
5. covariance(final double[] xArray, final double[] yArray)
6. covariance(int[] v1, int[] v2)
7. covariance(Number[] x, Number[] y)
8. covarianceOfDoubleArrays(double[] x, double[] y)
9. covarianceTwoColumns(double[][] data, int col1, int col2)