edu.princeton.cs.algs4.StdStats Maven / Gradle / Ivy
/******************************************************************************
* Compilation: javac StdStats.java
* Execution: java StdStats < input.txt
* Dependencies: StdOut.java
*
* Library of statistical functions.
*
* The test client reads an array of real numbers from standard
* input, and computes the minimum, mean, maximum, and
* standard deviation.
*
* The functions all throw a java.lang.IllegalArgumentException
* if the array passed in as an argument is null.
*
* The floating-point functions all return NaN if any input is NaN.
*
* Unlike Math.min() and Math.max(), the min() and max() functions
* do not differentiate between -0.0 and 0.0.
*
* % more tiny.txt
* 5
* 3.0 1.0 2.0 5.0 4.0
*
* % java StdStats < tiny.txt
* min 1.000
* mean 3.000
* max 5.000
* std dev 1.581
*
* Should these funtions use varargs instead of array arguments?
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code StdStats} class provides static methods for computing
* statistics such as min, max, mean, sample standard deviation, and
* sample variance.
*
* For additional documentation, see
* Section 2.2 of
* Computer Science: An Interdisciplinary Approach
* by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public final class StdStats {
private StdStats() { }
/**
* Returns the maximum value in the specified array.
*
* @param a the array
* @return the maximum value in the array {@code a[]};
* {@code Double.NEGATIVE_INFINITY} if no such value
*/
public static double max(double[] a) {
validateNotNull(a);
double max = Double.NEGATIVE_INFINITY;
for (int i = 0; i < a.length; i++) {
if (Double.isNaN(a[i])) return Double.NaN;
if (a[i] > max) max = a[i];
}
return max;
}
/**
* Returns the maximum value in the specified subarray.
*
* @param a the array
* @param lo the left endpoint of the subarray (inclusive)
* @param hi the right endpoint of the subarray (exclusive)
* @return the maximum value in the subarray {@code a[lo..hi)};
* {@code Double.NEGATIVE_INFINITY} if no such value
* @throws IllegalArgumentException if {@code a} is {@code null}
* @throws IllegalArgumentException unless {@code (0 <= lo) && (lo < hi) && (hi <= a.length)}
*/
public static double max(double[] a, int lo, int hi) {
validateNotNull(a);
validateSubarrayIndices(lo, hi, a.length);
double max = Double.NEGATIVE_INFINITY;
for (int i = lo; i < hi; i++) {
if (Double.isNaN(a[i])) return Double.NaN;
if (a[i] > max) max = a[i];
}
return max;
}
/**
* Returns the maximum value in the specified array.
*
* @param a the array
* @return the maximum value in the array {@code a[]};
* {@code Integer.MIN_VALUE} if no such value
*/
public static int max(int[] a) {
validateNotNull(a);
int max = Integer.MIN_VALUE;
for (int i = 0; i < a.length; i++) {
if (a[i] > max) max = a[i];
}
return max;
}
/**
* Returns the minimum value in the specified array.
*
* @param a the array
* @return the minimum value in the array {@code a[]};
* {@code Double.POSITIVE_INFINITY} if no such value
*/
public static double min(double[] a) {
validateNotNull(a);
double min = Double.POSITIVE_INFINITY;
for (int i = 0; i < a.length; i++) {
if (Double.isNaN(a[i])) return Double.NaN;
if (a[i] < min) min = a[i];
}
return min;
}
/**
* Returns the minimum value in the specified subarray.
*
* @param a the array
* @param lo the left endpoint of the subarray (inclusive)
* @param hi the right endpoint of the subarray (exclusive)
* @return the maximum value in the subarray {@code a[lo..hi)};
* {@code Double.POSITIVE_INFINITY} if no such value
* @throws IllegalArgumentException if {@code a} is {@code null}
* @throws IllegalArgumentException unless {@code (0 <= lo) && (lo < hi) && (hi <= a.length)}
*/
public static double min(double[] a, int lo, int hi) {
validateNotNull(a);
validateSubarrayIndices(lo, hi, a.length);
double min = Double.POSITIVE_INFINITY;
for (int i = lo; i < hi; i++) {
if (Double.isNaN(a[i])) return Double.NaN;
if (a[i] < min) min = a[i];
}
return min;
}
/**
* Returns the minimum value in the specified array.
*
* @param a the array
* @return the minimum value in the array {@code a[]};
* {@code Integer.MAX_VALUE} if no such value
*/
public static int min(int[] a) {
validateNotNull(a);
int min = Integer.MAX_VALUE;
for (int i = 0; i < a.length; i++) {
if (a[i] < min) min = a[i];
}
return min;
}
/**
* Returns the average value in the specified array.
*
* @param a the array
* @return the average value in the array {@code a[]};
* {@code Double.NaN} if no such value
*/
public static double mean(double[] a) {
validateNotNull(a);
if (a.length == 0) return Double.NaN;
double sum = sum(a);
return sum / a.length;
}
/**
* Returns the average value in the specified subarray.
*
* @param a the array
* @param lo the left endpoint of the subarray (inclusive)
* @param hi the right endpoint of the subarray (exclusive)
* @return the average value in the subarray {@code a[lo..hi)};
* {@code Double.NaN} if no such value
* @throws IllegalArgumentException if {@code a} is {@code null}
* @throws IllegalArgumentException unless {@code (0 <= lo) && (lo < hi) && (hi <= a.length)}
*/
public static double mean(double[] a, int lo, int hi) {
validateNotNull(a);
validateSubarrayIndices(lo, hi, a.length);
int length = hi - lo;
if (length == 0) return Double.NaN;
double sum = sum(a, lo, hi);
return sum / length;
}
/**
* Returns the average value in the specified array.
*
* @param a the array
* @return the average value in the array {@code a[]};
* {@code Double.NaN} if no such value
*/
public static double mean(int[] a) {
validateNotNull(a);
if (a.length == 0) return Double.NaN;
int sum = sum(a);
return 1.0 * sum / a.length;
}
/**
* Returns the sample variance in the specified array.
*
* @param a the array
* @return the sample variance in the array {@code a[]};
* {@code Double.NaN} if no such value
*/
public static double var(double[] a) {
validateNotNull(a);
if (a.length == 0) return Double.NaN;
double avg = mean(a);
double sum = 0.0;
for (int i = 0; i < a.length; i++) {
sum += (a[i] - avg) * (a[i] - avg);
}
return sum / (a.length - 1);
}
/**
* Returns the sample variance in the specified subarray.
*
* @param a the array
* @param lo the left endpoint of the subarray (inclusive)
* @param hi the right endpoint of the subarray (exclusive)
* @return the sample variance in the subarray {@code a[lo..hi)};
* {@code Double.NaN} if no such value
* @throws IllegalArgumentException if {@code a} is {@code null}
* @throws IllegalArgumentException unless {@code (0 <= lo) && (lo < hi) && (hi <= a.length)}
*/
public static double var(double[] a, int lo, int hi) {
validateNotNull(a);
validateSubarrayIndices(lo, hi, a.length);
int length = hi - lo;
if (length == 0) return Double.NaN;
double avg = mean(a, lo, hi);
double sum = 0.0;
for (int i = lo; i < hi; i++) {
sum += (a[i] - avg) * (a[i] - avg);
}
return sum / (length - 1);
}
/**
* Returns the sample variance in the specified array.
*
* @param a the array
* @return the sample variance in the array {@code a[]};
* {@code Double.NaN} if no such value
*/
public static double var(int[] a) {
validateNotNull(a);
if (a.length == 0) return Double.NaN;
double avg = mean(a);
double sum = 0.0;
for (int i = 0; i < a.length; i++) {
sum += (a[i] - avg) * (a[i] - avg);
}
return sum / (a.length - 1);
}
/**
* Returns the population variance in the specified array.
*
* @param a the array
* @return the population variance in the array {@code a[]};
* {@code Double.NaN} if no such value
*/
public static double varp(double[] a) {
validateNotNull(a);
if (a.length == 0) return Double.NaN;
double avg = mean(a);
double sum = 0.0;
for (int i = 0; i < a.length; i++) {
sum += (a[i] - avg) * (a[i] - avg);
}
return sum / a.length;
}
/**
* Returns the population variance in the specified subarray.
*
* @param a the array
* @param lo the left endpoint of the subarray (inclusive)
* @param hi the right endpoint of the subarray (exclusive)
* @return the population variance in the subarray {@code a[lo..hi)};
* {@code Double.NaN} if no such value
* @throws IllegalArgumentException if {@code a} is {@code null}
* @throws IllegalArgumentException unless {@code (0 <= lo) && (lo < hi) && (hi <= a.length)}
*/
public static double varp(double[] a, int lo, int hi) {
validateNotNull(a);
validateSubarrayIndices(lo, hi, a.length);
int length = hi - lo;
if (length == 0) return Double.NaN;
double avg = mean(a, lo, hi);
double sum = 0.0;
for (int i = lo; i < hi; i++) {
sum += (a[i] - avg) * (a[i] - avg);
}
return sum / length;
}
/**
* Returns the sample standard deviation in the specified array.
*
* @param a the array
* @return the sample standard deviation in the array {@code a[]};
* {@code Double.NaN} if no such value
*/
public static double stddev(double[] a) {
validateNotNull(a);
return Math.sqrt(var(a));
}
/**
* Returns the sample standard deviation in the specified array.
*
* @param a the array
* @return the sample standard deviation in the array {@code a[]};
* {@code Double.NaN} if no such value
*/
public static double stddev(int[] a) {
validateNotNull(a);
return Math.sqrt(var(a));
}
/**
* Returns the sample standard deviation in the specified subarray.
*
* @param a the array
* @param lo the left endpoint of the subarray (inclusive)
* @param hi the right endpoint of the subarray (exclusive)
* @return the sample standard deviation in the subarray {@code a[lo..hi)};
* {@code Double.NaN} if no such value
* @throws IllegalArgumentException if {@code a} is {@code null}
* @throws IllegalArgumentException unless {@code (0 <= lo) && (lo < hi) && (hi <= a.length)}
*/
public static double stddev(double[] a, int lo, int hi) {
validateNotNull(a);
validateSubarrayIndices(lo, hi, a.length);
return Math.sqrt(var(a, lo, hi));
}
/**
* Returns the population standard deviation in the specified array.
*
* @param a the array
* @return the population standard deviation in the array;
* {@code Double.NaN} if no such value
*/
public static double stddevp(double[] a) {
validateNotNull(a);
return Math.sqrt(varp(a));
}
/**
* Returns the population standard deviation in the specified subarray.
*
* @param a the array
* @param lo the left endpoint of the subarray (inclusive)
* @param hi the right endpoint of the subarray (exclusive)
* @return the population standard deviation in the subarray {@code a[lo..hi)};
* {@code Double.NaN} if no such value
* @throws IllegalArgumentException if {@code a} is {@code null}
* @throws IllegalArgumentException unless {@code (0 <= lo) && (lo < hi) && (hi <= a.length)}
*/
public static double stddevp(double[] a, int lo, int hi) {
validateNotNull(a);
validateSubarrayIndices(lo, hi, a.length);
return Math.sqrt(varp(a, lo, hi));
}
/**
* Returns the sum of all values in the specified array.
*
* @param a the array
* @return the sum of all values in the array {@code a[]};
* {@code 0.0} if no such value
*/
private static double sum(double[] a) {
validateNotNull(a);
double sum = 0.0;
for (int i = 0; i < a.length; i++) {
sum += a[i];
}
return sum;
}
/**
* Returns the sum of all values in the specified subarray.
*
* @param a the array
* @param lo the left endpoint of the subarray (inclusive)
* @param hi the right endpoint of the subarray (exclusive)
* @return the sum of all values in the subarray {@code a[lo..hi)};
* {@code 0.0} if no such value
* @throws IllegalArgumentException if {@code a} is {@code null}
* @throws IllegalArgumentException unless {@code (0 <= lo) && (lo < hi) && (hi <= a.length)}
*/
private static double sum(double[] a, int lo, int hi) {
validateNotNull(a);
validateSubarrayIndices(lo, hi, a.length);
double sum = 0.0;
for (int i = lo; i < hi; i++) {
sum += a[i];
}
return sum;
}
/**
* Returns the sum of all values in the specified array.
*
* @param a the array
* @return the sum of all values in the array {@code a[]};
* {@code 0.0} if no such value
*/
private static int sum(int[] a) {
validateNotNull(a);
int sum = 0;
for (int i = 0; i < a.length; i++) {
sum += a[i];
}
return sum;
}
/**
* Plots the points (0, a0), (1, a1), ...,
* (n-1, an-1) to standard draw.
*
* @param a the array of values
*/
public static void plotPoints(double[] a) {
validateNotNull(a);
int n = a.length;
StdDraw.setXscale(-1, n);
StdDraw.setPenRadius(1.0 / (3.0 * n));
for (int i = 0; i < n; i++) {
StdDraw.point(i, a[i]);
}
}
/**
* Plots the line segments connecting
* (i, ai) to
* (i+1, ai+1) for
* each i to standard draw.
*
* @param a the array of values
*/
public static void plotLines(double[] a) {
validateNotNull(a);
int n = a.length;
StdDraw.setXscale(-1, n);
StdDraw.setPenRadius();
for (int i = 1; i < n; i++) {
StdDraw.line(i-1, a[i-1], i, a[i]);
}
}
/**
* Plots bars from (0, ai) to
* (ai) for each i
* to standard draw.
*
* @param a the array of values
*/
public static void plotBars(double[] a) {
validateNotNull(a);
int n = a.length;
StdDraw.setXscale(-1, n);
for (int i = 0; i < n; i++) {
StdDraw.filledRectangle(i, a[i]/2, 0.25, a[i]/2);
}
}
// throw an IllegalArgumentException if x is null
// (x is either of type double[] or int[])
private static void validateNotNull(Object x) {
if (x == null)
throw new IllegalArgumentException("argument is null");
}
// throw an exception unless 0 <= lo <= hi <= length
private static void validateSubarrayIndices(int lo, int hi, int length) {
if (lo < 0 || hi > length || lo > hi)
throw new IllegalArgumentException("subarray indices out of bounds: [" + lo + ", " + hi + ")");
}
/**
* Unit tests {@code StdStats}.
* Convert command-line arguments to array of doubles and call various methods.
*
* @param args the command-line arguments
*/
public static void main(String[] args) {
double[] a = StdArrayIO.readDouble1D();
StdOut.printf(" min %10.3f\n", min(a));
StdOut.printf(" mean %10.3f\n", mean(a));
StdOut.printf(" max %10.3f\n", max(a));
StdOut.printf(" stddev %10.3f\n", stddev(a));
StdOut.printf(" var %10.3f\n", var(a));
StdOut.printf(" stddevp %10.3f\n", stddevp(a));
StdOut.printf(" varp %10.3f\n", varp(a));
}
}
/******************************************************************************
* Copyright 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with algs4.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/