statutils.java

Apache的common math数学软件包

    public static double variance(final double[] values) {
        return variance.evaluate(values);
    }

    /**
     * Returns the variance of the entries in the specified portion of
     * the input array, or <code>Double.NaN</code> if the designated subarray
     * is empty.
     * <p>
     * See {@link org.apache.commons.math.stat.descriptive.moment.Variance} for
     * details on the computing algorithm.</p>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>IllegalArgumentException</code> if the array is null or the
     * array index parameters are not valid.</p>
     * 
     * @param values the input array
     * @param begin index of the first array element to include
     * @param length the number of elements to include
     * @return the variance of the values or Double.NaN if length = 0
     * @throws IllegalArgumentException if the array is null or the array index
     *  parameters are not valid
     */
    public static double variance(final double[] values, final int begin,
            final int length) {
        return variance.evaluate(values, begin, length);
    }
    
    /**
     * Returns the variance of the entries in the specified portion of
     * the input array, using the precomputed mean value.  Returns 
     * <code>Double.NaN</code> if the designated subarray is empty.
     * <p>
     * See {@link org.apache.commons.math.stat.descriptive.moment.Variance} for
     * details on the computing algorithm.</p>
     * <p>
     * The formula used assumes that the supplied mean value is the arithmetic
     * mean of the sample data, not a known population parameter.  This method
     * is supplied only to save computation when the mean has already been
     * computed.</p>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>IllegalArgumentException</code> if the array is null or the
     * array index parameters are not valid.</p>
     * 
     * @param values the input array
     * @param mean the precomputed mean value
     * @param begin index of the first array element to include
     * @param length the number of elements to include
     * @return the variance of the values or Double.NaN if length = 0
     * @throws IllegalArgumentException if the array is null or the array index
     *  parameters are not valid
     */
    public static double variance(final double[] values, final double mean, 
            final int begin, final int length) {
        return variance.evaluate(values, mean, begin, length);    
    }
    
    /**
     * Returns the variance of the entries in the input array, using the
     * precomputed mean value.  Returns <code>Double.NaN</code> if the array
     * is empty.  
     * <p>
     * See {@link org.apache.commons.math.stat.descriptive.moment.Variance} for
     * details on the computing algorithm.</p>  
     * <p>
     * The formula used assumes that the supplied mean value is the arithmetic
     * mean of the sample data, not a known population parameter.  This method
     * is supplied only to save computation when the mean has already been
     * computed.</p>
     * <p>
     * Returns 0 for a single-value (i.e. length = 1) sample.</p>
     * <p>
     * Throws <code>IllegalArgumentException</code> if the array is null.</p>
     * 
     * @param values the input array
     * @param mean the precomputed mean value
     * @return the variance of the values or Double.NaN if the array is empty
     * @throws IllegalArgumentException if the array is null
     */
    public static double variance(final double[] values, final double mean) {
        return variance.evaluate(values, mean);    
    }

    /**
     * Returns the maximum of the entries in the input array, or 
     * <code>Double.NaN</code> if the array is empty.
     * <p>
     * Throws <code>IllegalArgumentException</code> if the array is null.</p>
     * <p>
     * <ul>
     * <li>The result is <code>NaN</code> iff all values are <code>NaN</code> 
     * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
     * <li>If any of the values equals <code>Double.POSITIVE_INFINITY</code>, 
     * the result is <code>Double.POSITIVE_INFINITY.</code></li>
     * </ul></p>
     * 
     * @param values the input array
     * @return the maximum of the values or Double.NaN if the array is empty
     * @throws IllegalArgumentException if the array is null
     */
    public static double max(final double[] values) {
        return max.evaluate(values);
    }

    /**
     * Returns the maximum of the entries in the specified portion of
     * the input array, or <code>Double.NaN</code> if the designated subarray
     * is empty.
     * <p>
     * Throws <code>IllegalArgumentException</code> if the array is null or
     * the array index parameters are not valid.</p>
     * <p>
     * <ul>
     * <li>The result is <code>NaN</code> iff all values are <code>NaN</code> 
     * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
     * <li>If any of the values equals <code>Double.POSITIVE_INFINITY</code>, 
     * the result is <code>Double.POSITIVE_INFINITY.</code></li>
     * </ul></p>
     * 
     * @param values the input array
     * @param begin index of the first array element to include
     * @param length the number of elements to include
     * @return the maximum of the values or Double.NaN if length = 0
     * @throws IllegalArgumentException if the array is null or the array index
     * parameters are not valid
     */
    public static double max(final double[] values, final int begin,
            final int length) {
        return max.evaluate(values, begin, length);
    }

     /**
     * Returns the minimum of the entries in the input array, or 
     * <code>Double.NaN</code> if the array is empty.
     * <p>
     * Throws <code>IllegalArgumentException</code> if the array is null.</p>
     * <p>
     * <ul>
     * <li>The result is <code>NaN</code> iff all values are <code>NaN</code> 
     * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
     * <li>If any of the values equals <code>Double.NEGATIVE_INFINITY</code>, 
     * the result is <code>Double.NEGATIVE_INFINITY.</code></li>
     * </ul> </p>
     * 
     * @param values the input array
     * @return the minimum of the values or Double.NaN if the array is empty
     * @throws IllegalArgumentException if the array is null
     */
    public static double min(final double[] values) {
        return min.evaluate(values);
    }

     /**
     * Returns the minimum of the entries in the specified portion of
     * the input array, or <code>Double.NaN</code> if the designated subarray
     * is empty.
     * <p>
     * Throws <code>IllegalArgumentException</code> if the array is null or
     * the array index parameters are not valid.</p>
     * <p>
     * <ul>
     * <li>The result is <code>NaN</code> iff all values are <code>NaN</code> 
     * (i.e. <code>NaN</code> values have no impact on the value of the statistic).</li>
     * <li>If any of the values equals <code>Double.NEGATIVE_INFINITY</code>, 
     * the result is <code>Double.NEGATIVE_INFINITY.</code></li>
     * </ul></p>
     * 
     * @param values the input array
     * @param begin index of the first array element to include
     * @param length the number of elements to include
     * @return the minimum of the values or Double.NaN if length = 0
     * @throws IllegalArgumentException if the array is null or the array index
     * parameters are not valid
     */
    public static double min(final double[] values, final int begin,
            final int length) {
        return min.evaluate(values, begin, length);
    }
    
    /**
     * Returns an estimate of the <code>p</code>th percentile of the values
     * in the <code>values</code> array.
     * <p>
     * <ul>
     * <li>Returns <code>Double.NaN</code> if <code>values</code> has length 
     * <code>0</code></li></p>
     * <li>Returns (for any value of <code>p</code>) <code>values[0]</code>
     *  if <code>values</code> has length <code>1</code></li>
     * <li>Throws <code>IllegalArgumentException</code> if <code>values</code>
     * is null  or p is not a valid quantile value (p must be greater than 0
     * and less than or equal to 100)</li>
     * </ul></p>
     * <p>
     * See {@link org.apache.commons.math.stat.descriptive.rank.Percentile} for
     * a description of the percentile estimation algorithm used.</p>
     * 
     * @param values input array of values
     * @param p the percentile value to compute
     * @return the percentile value or Double.NaN if the array is empty
     * @throws IllegalArgumentException if <code>values</code> is null 
     * or p is invalid
     */
    public static double percentile(final double[] values, final double p) {
            return percentile.evaluate(values,p);
    }

     /**
     * Returns an estimate of the <code>p</code>th percentile of the values
     * in the <code>values</code> array, starting with the element in (0-based)
     * position <code>begin</code> in the array and including <code>length</code>
     * values.
     * <p>
     * <ul>
     * <li>Returns <code>Double.NaN</code> if <code>length = 0</code></li>
     * <li>Returns (for any value of <code>p</code>) <code>values[begin]</code>
     *  if <code>length = 1 </code></li>
     * <li>Throws <code>IllegalArgumentException</code> if <code>values</code>
     *  is null , <code>begin</code> or <code>length</code> is invalid, or 
     * <code>p</code> is not a valid quantile value (p must be greater than 0
     * and less than or equal to 100)</li>
     * </ul></p>
     * <p>
      * See {@link org.apache.commons.math.stat.descriptive.rank.Percentile} for
      * a description of the percentile estimation algorithm used.</p>
     * 
     * @param values array of input values
     * @param p  the percentile to compute
     * @param begin  the first (0-based) element to include in the computation
     * @param length  the number of array elements to include
     * @return  the percentile value
     * @throws IllegalArgumentException if the parameters are not valid or the
     * input array is null
     */
    public static double percentile(final double[] values, final int begin, 
            final int length, final double p) {
        return percentile.evaluate(values, begin, length, p);
    }   
    
    /**
     * Returns the sum of the (signed) differences between corresponding elements of the
     * input arrays -- i.e., sum(sample1[i] - sample2[i]).
     * 
     * @param sample1  the first array
     * @param sample2  the second array
     * @return sum of paired differences
     * @throws IllegalArgumentException if the arrays do not have the same
     * (positive) length
     */
    public static double sumDifference(final double[] sample1, final double[] sample2)
        throws IllegalArgumentException {
        int n = sample1.length;
        if (n  != sample2.length || n < 1) {
            throw new IllegalArgumentException 
                ("Input arrays must have the same (positive) length.");
        }
        double result = 0;
        for (int i = 0; i < n; i++) {
            result += sample1[i] - sample2[i];
        }
        return result;
    }
    
    /**
     * Returns the mean of the (signed) differences between corresponding elements of the
     * input arrays -- i.e., sum(sample1[i] - sample2[i]) / sample1.length.
     * 
     * @param sample1  the first array
     * @param sample2  the second array
     * @return mean of paired differences
     * @throws IllegalArgumentException if the arrays do not have the same
     * (positive) length
     */
    public static double meanDifference(final double[] sample1, final double[] sample2)
    throws IllegalArgumentException {
        return sumDifference(sample1, sample2) / (double) sample1.length;
    }
    
    /**
     * Returns the variance of the (signed) differences between corresponding elements of the
     * input arrays -- i.e., var(sample1[i] - sample2[i]).
     * 
     * @param sample1  the first array
     * @param sample2  the second array
     * @param meanDifference   the mean difference between corresponding entries 
     * @see #meanDifference(double[],double[])
     * @return variance of paired differences
     * @throws IllegalArgumentException if the arrays do not have the same
     * length or their common length is less than 2.
     */
    public static double varianceDifference(final double[] sample1, final double[] sample2, 
            double meanDifference)  throws IllegalArgumentException {
        double sum1 = 0d;
        double sum2 = 0d;
        double diff = 0d;
        int n = sample1.length;
        if (n < 2 || n != sample2.length) {
            throw new IllegalArgumentException("Input array lengths must be equal and at least 2.");
        }
        for (int i = 0; i < n; i++) {
            diff = sample1[i] - sample2[i];
            sum1 += (diff - meanDifference) *(diff - meanDifference);
            sum2 += diff - meanDifference;
        }
        return (sum1 - (sum2 * sum2 / (double) n)) / (double) (n - 1);
    }      
    
}