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/*******************************************************************************
* Copyright (c) 2015-2018 Skymind, Inc.
*
* This program and the accompanying materials are made available under the
* terms of the Apache License, Version 2.0 which is available at
* https://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.
*
* SPDX-License-Identifier: Apache-2.0
******************************************************************************/
package org.nd4j.common.util;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.util.FastMath;
import org.nd4j.common.primitives.Counter;
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
import java.util.Set;
/**
* This is a math jcuda.utils class.
*
* @author Adam Gibson
*/
public class MathUtils {
/**
* The natural logarithm of 2.
*/
public static final double log2 = Math.log(2);
/**
* The small deviation allowed in double comparisons.
*/
public static final double SMALL = 1e-6;
public static double pow(double base, double exponent) {
double result = 1;
if (exponent == 0) {
return result;
}
if (exponent < 0) {
return 1 / pow(base, exponent * -1);
}
return FastMath.pow(base, exponent);
}
/**
* Normalize a value
* (val - min) / (max - min)
*
* @param val value to normalize
* @param max max value
* @param min min value
* @return the normalized value
*/
public static double normalize(double val, double min, double max) {
if (max < min)
throw new IllegalArgumentException("Max must be greather than min");
return (val - min) / (max - min);
}
/**
* Clamps the value to a discrete value
*
* @param value the value to clamp
* @param min min for the probability distribution
* @param max max for the probability distribution
* @return the discrete value
*/
public static int clamp(int value, int min, int max) {
if (value < min)
value = min;
if (value > max)
value = max;
return value;
}
/**
* Discretize the given value
*
* @param value the value to discretize
* @param min the min of the distribution
* @param max the max of the distribution
* @param binCount the number of bins
* @return the discretized value
*/
public static int discretize(double value, double min, double max, int binCount) {
int discreteValue = (int) (binCount * normalize(value, min, max));
return clamp(discreteValue, 0, binCount - 1);
}
/**
* See: https://stackoverflow.com/questions/466204/rounding-off-to-nearest-power-of-2
*
* @param v the number to getFromOrigin the next power of 2 for
* @return the next power of 2 for the passed in value
*/
public static long nextPowOf2(long v) {
v--;
v |= v >> 1;
v |= v >> 2;
v |= v >> 4;
v |= v >> 8;
v |= v >> 16;
v++;
return v;
}
/**
* Generates a binomial distributed number using
* the given rng
*
* @param rng
* @param n
* @param p
* @return
*/
public static int binomial(RandomGenerator rng, int n, double p) {
if ((p < 0) || (p > 1)) {
return 0;
}
int c = 0;
for (int i = 0; i < n; i++) {
if (rng.nextDouble() < p) {
c++;
}
}
return c;
}
/**
* Generate a uniform random number from the given rng
*
* @param rng the rng to use
* @param min the min num
* @param max the max num
* @return a number uniformly distributed between min and max
*/
public static double uniform(Random rng, double min, double max) {
return rng.nextDouble() * (max - min) + min;
}
/**
* Returns the correlation coefficient of two double vectors.
*
* @param residuals residuals
* @param targetAttribute target attribute vector
* @return the correlation coefficient or r
*/
public static double correlation(double[] residuals, double targetAttribute[]) {
double[] predictedValues = new double[residuals.length];
for (int i = 0; i < predictedValues.length; i++) {
predictedValues[i] = targetAttribute[i] - residuals[i];
}
double ssErr = ssError(predictedValues, targetAttribute);
double total = ssTotal(residuals, targetAttribute);
return 1 - (ssErr / total);
}//end correlation
/**
* 1 / 1 + exp(-x)
*
* @param x
* @return
*/
public static double sigmoid(double x) {
return 1.0 / (1.0 + Math.pow(Math.E, -x));
}
/**
* How much of the variance is explained by the regression
*
* @param residuals error
* @param targetAttribute data for target attribute
* @return the sum squares of regression
*/
public static double ssReg(double[] residuals, double[] targetAttribute) {
double mean = sum(targetAttribute) / targetAttribute.length;
double ret = 0;
for (int i = 0; i < residuals.length; i++) {
ret += Math.pow(residuals[i] - mean, 2);
}
return ret;
}
/**
* How much of the variance is NOT explained by the regression
*
* @param predictedValues predicted values
* @param targetAttribute data for target attribute
* @return the sum squares of regression
*/
public static double ssError(double[] predictedValues, double[] targetAttribute) {
double ret = 0;
for (int i = 0; i < predictedValues.length; i++) {
ret += Math.pow(targetAttribute[i] - predictedValues[i], 2);
}
return ret;
}
/**
* Calculate string similarity with tfidf weights relative to each character
* frequency and how many times a character appears in a given string
* @param strings the strings to calculate similarity for
* @return the cosine similarity between the strings
*/
public static double stringSimilarity(String... strings) {
if (strings == null)
return 0;
Counter counter = new Counter<>();
Counter counter2 = new Counter<>();
for (int i = 0; i < strings[0].length(); i++)
counter.incrementCount(String.valueOf(strings[0].charAt(i)), 1.0f);
for (int i = 0; i < strings[1].length(); i++)
counter2.incrementCount(String.valueOf(strings[1].charAt(i)), 1.0f);
Set v1 = counter.keySet();
Set v2 = counter2.keySet();
Set both = SetUtils.intersection(v1, v2);
double sclar = 0, norm1 = 0, norm2 = 0;
for (String k : both)
sclar += counter.getCount(k) * counter2.getCount(k);
for (String k : v1)
norm1 += counter.getCount(k) * counter.getCount(k);
for (String k : v2)
norm2 += counter2.getCount(k) * counter2.getCount(k);
return sclar / Math.sqrt(norm1 * norm2);
}
/**
* Returns the vector length (sqrt(sum(x_i))
*
* @param vector the vector to return the vector length for
* @return the vector length of the passed in array
*/
public static double vectorLength(double[] vector) {
double ret = 0;
if (vector == null)
return ret;
else {
for (int i = 0; i < vector.length; i++) {
ret += Math.pow(vector[i], 2);
}
}
return ret;
}
/**
* Inverse document frequency: the total docs divided by the number of times the word
* appeared in a document
*
* @param totalDocs the total documents for the data applyTransformToDestination
* @param numTimesWordAppearedInADocument the number of times the word occurred in a document
* @return log(10) (totalDocs/numTImesWordAppearedInADocument)
*/
public static double idf(double totalDocs, double numTimesWordAppearedInADocument) {
return totalDocs > 0 ? Math.log10(totalDocs / numTimesWordAppearedInADocument) : 0;
}
/**
* Term frequency: 1+ log10(count)
*
* @param count the count of a word or character in a given string or document
* @return 1+ log(10) count
*/
public static double tf(int count) {
return count > 0 ? 1 + Math.log10(count) : 0;
}
/**
* Return td * idf
*
* @param td the term frequency (assumed calculated)
* @param idf inverse document frequency (assumed calculated)
* @return td * idf
*/
public static double tfidf(double td, double idf) {
return td * idf;
}
private static int charForLetter(char c) {
char[] chars = {'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's',
't', 'u', 'v', 'w', 'x', 'y', 'z'};
for (int i = 0; i < chars.length; i++)
if (chars[i] == c)
return i;
return -1;
}
/**
* Total variance in target attribute
*
* @param residuals error
* @param targetAttribute data for target attribute
* @return Total variance in target attribute
*/
public static double ssTotal(double[] residuals, double[] targetAttribute) {
return ssReg(residuals, targetAttribute) + ssError(residuals, targetAttribute);
}
/**
* This returns the sum of the given array.
*
* @param nums the array of numbers to sum
* @return the sum of the given array
*/
public static double sum(double[] nums) {
double ret = 0;
for (double d : nums)
ret += d;
return ret;
}//end sum
/**
* This will merge the coordinates of the given coordinate system.
*
* @param x the x coordinates
* @param y the y coordinates
* @return a vector such that each (x,y) pair is at ret[i],ret[i+1]
*/
public static double[] mergeCoords(double[] x, double[] y) {
if (x.length != y.length)
throw new IllegalArgumentException(
"Sample sizes must be the same for each data applyTransformToDestination.");
double[] ret = new double[x.length + y.length];
for (int i = 0; i < x.length; i++) {
ret[i] = x[i];
ret[i + 1] = y[i];
}
return ret;
}//end mergeCoords
/**
* This will merge the coordinates of the given coordinate system.
*
* @param x the x coordinates
* @param y the y coordinates
* @return a vector such that each (x,y) pair is at ret[i],ret[i+1]
*/
public static List mergeCoords(List x, List y) {
if (x.size() != y.size())
throw new IllegalArgumentException(
"Sample sizes must be the same for each data applyTransformToDestination.");
List ret = new ArrayList();
for (int i = 0; i < x.size(); i++) {
ret.add(x.get(i));
ret.add(y.get(i));
}
return ret;
}//end mergeCoords
/**
* This returns the minimized loss values for a given vector.
* It is assumed that the x, y pairs are at
* vector[i], vector[i+1]
*
* @param vector the vector of numbers to getFromOrigin the weights for
* @return a double array with w_0 and w_1 are the associated indices.
*/
public static double[] weightsFor(List vector) {
/* split coordinate system */
List coords = coordSplit(vector);
/* x vals */
double[] x = coords.get(0);
/* y vals */
double[] y = coords.get(1);
double meanX = sum(x) / x.length;
double meanY = sum(y) / y.length;
double sumOfMeanDifferences = sumOfMeanDifferences(x, y);
double xDifferenceOfMean = sumOfMeanDifferencesOnePoint(x);
double w_1 = sumOfMeanDifferences / xDifferenceOfMean;
double w_0 = meanY - (w_1) * meanX;
//double w_1=(n*sumOfProducts(x,y) - sum(x) * sum(y))/(n*sumOfSquares(x) - Math.pow(sum(x),2));
// double w_0=(sum(y) - (w_1 * sum(x)))/n;
double[] ret = new double[vector.size()];
ret[0] = w_0;
ret[1] = w_1;
return ret;
}//end weightsFor
/**
* This will return the squared loss of the given
* points
*
* @param x the x coordinates to use
* @param y the y coordinates to use
* @param w_0 the first weight
* @param w_1 the second weight
* @return the squared loss of the given points
*/
public static double squaredLoss(double[] x, double[] y, double w_0, double w_1) {
double sum = 0;
for (int j = 0; j < x.length; j++) {
sum += Math.pow((y[j] - (w_1 * x[j] + w_0)), 2);
}
return sum;
}//end squaredLoss
public static double w_1(double[] x, double[] y, int n) {
return (n * sumOfProducts(x, y) - sum(x) * sum(y)) / (n * sumOfSquares(x) - Math.pow(sum(x), 2));
}
public static double w_0(double[] x, double[] y, int n) {
double weight1 = w_1(x, y, n);
return (sum(y) - (weight1 * sum(x))) / n;
}
/**
* This returns the minimized loss values for a given vector.
* It is assumed that the x, y pairs are at
* vector[i], vector[i+1]
*
* @param vector the vector of numbers to getFromOrigin the weights for
* @return a double array with w_0 and w_1 are the associated indices.
*/
public static double[] weightsFor(double[] vector) {
/* split coordinate system */
List coords = coordSplit(vector);
/* x vals */
double[] x = coords.get(0);
/* y vals */
double[] y = coords.get(1);
double meanX = sum(x) / x.length;
double meanY = sum(y) / y.length;
double sumOfMeanDifferences = sumOfMeanDifferences(x, y);
double xDifferenceOfMean = sumOfMeanDifferencesOnePoint(x);
double w_1 = sumOfMeanDifferences / xDifferenceOfMean;
double w_0 = meanY - (w_1) * meanX;
double[] ret = new double[vector.length];
ret[0] = w_0;
ret[1] = w_1;
return ret;
}//end weightsFor
public static double errorFor(double actual, double prediction) {
return actual - prediction;
}
/**
* Used for calculating top part of simple regression for
* beta 1
*
* @param vector the x coordinates
* @param vector2 the y coordinates
* @return the sum of mean differences for the input vectors
*/
public static double sumOfMeanDifferences(double[] vector, double[] vector2) {
double mean = sum(vector) / vector.length;
double mean2 = sum(vector2) / vector2.length;
double ret = 0;
for (int i = 0; i < vector.length; i++) {
double vec1Diff = vector[i] - mean;
double vec2Diff = vector2[i] - mean2;
ret += vec1Diff * vec2Diff;
}
return ret;
}//end sumOfMeanDifferences
/**
* Used for calculating top part of simple regression for
* beta 1
*
* @param vector the x coordinates
* @return the sum of mean differences for the input vectors
*/
public static double sumOfMeanDifferencesOnePoint(double[] vector) {
double mean = sum(vector) / vector.length;
double ret = 0;
for (int i = 0; i < vector.length; i++) {
double vec1Diff = Math.pow(vector[i] - mean, 2);
ret += vec1Diff;
}
return ret;
}//end sumOfMeanDifferences
/**
* This returns the product of all numbers in the given array.
*
* @param nums the numbers to multiply over
* @return the product of all numbers in the array, or 0
* if the length is or or nums i null
*/
public static double times(double[] nums) {
if (nums == null || nums.length == 0)
return 0;
double ret = 1;
for (int i = 0; i < nums.length; i++)
ret *= nums[i];
return ret;
}//end times
/**
* This returns the sum of products for the given
* numbers.
*
* @param nums the sum of products for the give numbers
* @return the sum of products for the given numbers
*/
public static double sumOfProducts(double[]... nums) {
if (nums == null || nums.length < 1)
return 0;
double sum = 0;
for (int i = 0; i < nums.length; i++) {
/* The ith column for all of the rows */
double[] column = column(i, nums);
sum += times(column);
}
return sum;
}//end sumOfProducts
/**
* This returns the given column over an n arrays
*
* @param column the column to getFromOrigin values for
* @param nums the arrays to extract values from
* @return a double array containing all of the numbers in that column
* for all of the arrays.
* @throws IllegalArgumentException if the index is < 0
*/
private static double[] column(int column, double[]... nums) throws IllegalArgumentException {
double[] ret = new double[nums.length];
for (int i = 0; i < nums.length; i++) {
double[] curr = nums[i];
ret[i] = curr[column];
}
return ret;
}//end column
/**
* This returns the coordinate split in a list of coordinates
* such that the values for ret[0] are the x values
* and ret[1] are the y values
*
* @param vector the vector to split with x and y values/
* @return a coordinate split for the given vector of values.
* if null, is passed in null is returned
*/
public static List coordSplit(double[] vector) {
if (vector == null)
return null;
List ret = new ArrayList();
/* x coordinates */
double[] xVals = new double[vector.length / 2];
/* y coordinates */
double[] yVals = new double[vector.length / 2];
/* current points */
int xTracker = 0;
int yTracker = 0;
for (int i = 0; i < vector.length; i++) {
//even value, x coordinate
if (i % 2 == 0)
xVals[xTracker++] = vector[i];
//y coordinate
else
yVals[yTracker++] = vector[i];
}
ret.add(xVals);
ret.add(yVals);
return ret;
}//end coordSplit
/**
* This will partition the given whole variable data applyTransformToDestination in to the specified chunk number.
*
* @param arr the data applyTransformToDestination to pass in
* @param chunk the number to separate by
* @return a partition data applyTransformToDestination relative to the passed in chunk number
*/
public static List> partitionVariable(List arr, int chunk) {
int count = 0;
List> ret = new ArrayList>();
while (count < arr.size()) {
List sublist = arr.subList(count, count + chunk);
count += chunk;
ret.add(sublist);
}
//All data sets must be same size
for (List lists : ret) {
if (lists.size() < chunk)
ret.remove(lists);
}
return ret;
}//end partitionVariable
/**
* This returns the coordinate split in a list of coordinates
* such that the values for ret[0] are the x values
* and ret[1] are the y values
*
* @param vector the vector to split with x and y values
* Note that the list will be more stable due to the size operator.
* The array version will have extraneous values if not monitored
* properly.
* @return a coordinate split for the given vector of values.
* if null, is passed in null is returned
*/
public static List coordSplit(List vector) {
if (vector == null)
return null;
List ret = new ArrayList();
/* x coordinates */
double[] xVals = new double[vector.size() / 2];
/* y coordinates */
double[] yVals = new double[vector.size() / 2];
/* current points */
int xTracker = 0;
int yTracker = 0;
for (int i = 0; i < vector.size(); i++) {
//even value, x coordinate
if (i % 2 == 0)
xVals[xTracker++] = vector.get(i);
//y coordinate
else
yVals[yTracker++] = vector.get(i);
}
ret.add(xVals);
ret.add(yVals);
return ret;
}//end coordSplit
/**
* This returns the x values of the given vector.
* These are assumed to be the even values of the vector.
*
* @param vector the vector to getFromOrigin the values for
* @return the x values of the given vector
*/
public static double[] xVals(double[] vector) {
if (vector == null)
return null;
double[] x = new double[vector.length / 2];
int count = 0;
for (int i = 0; i < vector.length; i++) {
if (i % 2 != 0)
x[count++] = vector[i];
}
return x;
}//end xVals
/**
* This returns the odd indexed values for the given vector
*
* @param vector the odd indexed values of rht egiven vector
* @return the y values of the given vector
*/
public static double[] yVals(double[] vector) {
double[] y = new double[vector.length / 2];
int count = 0;
for (int i = 0; i < vector.length; i++) {
if (i % 2 == 0)
y[count++] = vector[i];
}
return y;
}//end yVals
/**
* This returns the sum of squares for the given vector.
*
* @param vector the vector to obtain the sum of squares for
* @return the sum of squares for this vector
*/
public static double sumOfSquares(double[] vector) {
double ret = 0;
for (double d : vector)
ret += Math.pow(d, 2);
return ret;
}
/**
* This returns the determination coefficient of two vectors given a length
*
* @param y1 the first vector
* @param y2 the second vector
* @param n the length of both vectors
* @return the determination coefficient or r^2
*/
public static double determinationCoefficient(double[] y1, double[] y2, int n) {
return Math.pow(correlation(y1, y2), 2);
}
/**
* Returns the logarithm of a for base 2.
*
* @param a a double
* @return the logarithm for base 2
*/
public static double log2(double a) {
if (a == 0)
return 0.0;
return Math.log(a) / log2;
}
/**
* This returns the root mean squared error of two data sets
*
* @param real the realComponent values
* @param predicted the predicted values
* @return the root means squared error for two data sets
*/
public static double rootMeansSquaredError(double[] real, double[] predicted) {
double ret = 1 / real.length;
for (int i = 0; i < real.length; i++) {
ret += Math.pow((real[i] - predicted[i]), 2);
}
return Math.sqrt(ret);
}//end rootMeansSquaredError
/**
* This returns the entropy (information gain, or uncertainty of a random variable): -sum(x*log(x))
*
* @param vector the vector of values to getFromOrigin the entropy for
* @return the entropy of the given vector
*/
public static double entropy(double[] vector) {
if (vector == null || vector.length == 0)
return 0;
else {
double ret = 0;
for (double d : vector)
ret += d * Math.log(d);
return -ret;
}
}//end entropy
/**
* This returns the kronecker delta of two doubles.
*
* @param i the first number to compare
* @param j the second number to compare
* @return 1 if they are equal, 0 otherwise
*/
public static int kroneckerDelta(double i, double j) {
return (i == j) ? 1 : 0;
}
/**
* This calculates the adjusted r^2 including degrees of freedom.
* Also known as calculating "strength" of a regression
*
* @param rSquared the r squared value to calculate
* @param numRegressors number of variables
* @param numDataPoints size of the data applyTransformToDestination
* @return an adjusted r^2 for degrees of freedom
*/
public static double adjustedrSquared(double rSquared, int numRegressors, int numDataPoints) {
double divide = (numDataPoints - 1) / (numDataPoints - numRegressors - 1);
double rSquaredDiff = 1 - rSquared;
return 1 - (rSquaredDiff * divide);
}
public static double[] normalizeToOne(double[] doubles) {
normalize(doubles, sum(doubles));
return doubles;
}
public static double min(double[] doubles) {
double ret = doubles[0];
for (double d : doubles)
if (d < ret)
ret = d;
return ret;
}
public static double max(double[] doubles) {
double ret = doubles[0];
for (double d : doubles)
if (d > ret)
ret = d;
return ret;
}
/**
* Normalizes the doubles in the array using the given value.
*
* @param doubles the array of double
* @param sum the value by which the doubles are to be normalized
* @throws IllegalArgumentException if sum is zero or NaN
*/
public static void normalize(double[] doubles, double sum) {
if (Double.isNaN(sum)) {
throw new IllegalArgumentException("Can't normalize array. Sum is NaN.");
}
if (sum == 0) {
// Maybe this should just be a return.
throw new IllegalArgumentException("Can't normalize array. Sum is zero.");
}
for (int i = 0; i < doubles.length; i++) {
doubles[i] /= sum;
}
}//end normalize
/**
* Converts an array containing the natural logarithms of
* probabilities stored in a vector back into probabilities.
* The probabilities are assumed to sum to one.
*
* @param a an array holding the natural logarithms of the probabilities
* @return the converted array
*/
public static double[] logs2probs(double[] a) {
double max = a[maxIndex(a)];
double sum = 0.0;
double[] result = new double[a.length];
for (int i = 0; i < a.length; i++) {
result[i] = Math.exp(a[i] - max);
sum += result[i];
}
normalize(result, sum);
return result;
}//end logs2probs
/**
* This returns the entropy for a given vector of probabilities.
*
* @param probabilities the probabilities to getFromOrigin the entropy for
* @return the entropy of the given probabilities.
*/
public static double information(double[] probabilities) {
double total = 0.0;
for (double d : probabilities) {
total += (-1.0 * log2(d) * d);
}
return total;
}//end information
/**
* Returns index of maximum element in a given
* array of doubles. First maximum is returned.
*
* @param doubles the array of doubles
* @return the index of the maximum element
*/
public static /*@pure@*/ int maxIndex(double[] doubles) {
double maximum = 0;
int maxIndex = 0;
for (int i = 0; i < doubles.length; i++) {
if ((i == 0) || (doubles[i] > maximum)) {
maxIndex = i;
maximum = doubles[i];
}
}
return maxIndex;
}//end maxIndex
/**
* This will return the factorial of the given number n.
*
* @param n the number to getFromOrigin the factorial for
* @return the factorial for this number
*/
public static double factorial(double n) {
if (n == 1 || n == 0)
return 1;
for (double i = n; i > 0; i--, n *= (i > 0 ? i : 1)) {
}
return n;
}//end factorial
/**
* Returns the log-odds for a given probability.
*
* @param prob the probability
* @return the log-odds after the probability has been mapped to
* [Utils.SMALL, 1-Utils.SMALL]
*/
public static /*@pure@*/ double probToLogOdds(double prob) {
if (gr(prob, 1) || (sm(prob, 0))) {
throw new IllegalArgumentException("probToLogOdds: probability must " + "be in [0,1] " + prob);
}
double p = SMALL + (1.0 - 2 * SMALL) * prob;
return Math.log(p / (1 - p));
}
/**
* Rounds a double to the next nearest integer value. The JDK version
* of it doesn't work properly.
*
* @param value the double value
* @return the resulting integer value
*/
public static /*@pure@*/ int round(double value) {
int roundedValue = value > 0 ? (int) (value + 0.5) : -(int) (Math.abs(value) + 0.5);
return roundedValue;
}//end round
/**
* This returns the permutation of n choose r.
*
* @param n the n to choose
* @param r the number of elements to choose
* @return the permutation of these numbers
*/
public static double permutation(double n, double r) {
double nFac = MathUtils.factorial(n);
double nMinusRFac = MathUtils.factorial((n - r));
return nFac / nMinusRFac;
}//end permutation
/**
* This returns the combination of n choose r
*
* @param n the number of elements overall
* @param r the number of elements to choose
* @return the amount of possible combinations for this applyTransformToDestination of elements
*/
public static double combination(double n, double r) {
double nFac = MathUtils.factorial(n);
double rFac = MathUtils.factorial(r);
double nMinusRFac = MathUtils.factorial((n - r));
return nFac / (rFac * nMinusRFac);
}//end combination
/**
* sqrt(a^2 + b^2) without under/overflow.
*/
public static double hypotenuse(double a, double b) {
double r;
if (Math.abs(a) > Math.abs(b)) {
r = b / a;
r = Math.abs(a) * Math.sqrt(1 + r * r);
} else if (b != 0) {
r = a / b;
r = Math.abs(b) * Math.sqrt(1 + r * r);
} else {
r = 0.0;
}
return r;
}//end hypotenuse
/**
* Rounds a double to the next nearest integer value in a probabilistic
* fashion (e.g. 0.8 has a 20% chance of being rounded down to 0 and a
* 80% chance of being rounded up to 1). In the limit, the average of
* the rounded numbers generated by this procedure should converge to
* the original double.
*
* @param value the double value
* @param rand the random number generator
* @return the resulting integer value
*/
public static int probRound(double value, Random rand) {
if (value >= 0) {
double lower = Math.floor(value);
double prob = value - lower;
if (rand.nextDouble() < prob) {
return (int) lower + 1;
} else {
return (int) lower;
}
} else {
double lower = Math.floor(Math.abs(value));
double prob = Math.abs(value) - lower;
if (rand.nextDouble() < prob) {
return -((int) lower + 1);
} else {
return -(int) lower;
}
}
}//end probRound
/**
* Rounds a double to the given number of decimal places.
*
* @param value the double value
* @param afterDecimalPoint the number of digits after the decimal point
* @return the double rounded to the given precision
*/
public static /*@pure@*/ double roundDouble(double value, int afterDecimalPoint) {
double mask = Math.pow(10.0, (double) afterDecimalPoint);
return (double) (Math.round(value * mask)) / mask;
}//end roundDouble
/**
* Rounds a double to the given number of decimal places.
*
* @param value the double value
* @param afterDecimalPoint the number of digits after the decimal point
* @return the double rounded to the given precision
*/
public static /*@pure@*/ float roundFloat(float value, int afterDecimalPoint) {
float mask = (float) Math.pow(10, (float) afterDecimalPoint);
return (float) (Math.round(value * mask)) / mask;
}//end roundDouble
/**
* This will return the bernoulli trial for the given event.
* A bernoulli trial is a mechanism for detecting the probability
* of a given event occurring k times in n independent trials
*
* @param n the number of trials
* @param k the number of times the target event occurs
* @param successProb the probability of the event happening
* @return the probability of the given event occurring k times.
*/
public static double bernoullis(double n, double k, double successProb) {
double combo = MathUtils.combination(n, k);
double p = successProb;
double q = 1 - successProb;
return combo * Math.pow(p, k) * Math.pow(q, n - k);
}//end bernoullis
/**
* Tests if a is smaller than b.
*
* @param a a double
* @param b a double
*/
public static /*@pure@*/ boolean sm(double a, double b) {
return (b - a > SMALL);
}
/**
* Tests if a is greater than b.
*
* @param a a double
* @param b a double
*/
public static /*@pure@*/ boolean gr(double a, double b) {
return (a - b > SMALL);
}
/**
* This will take a given string and separator and convert it to an equivalent
* double array.
*
* @param data the data to separate
* @param separator the separator to use
* @return the new double array based on the given data
*/
public static double[] fromString(String data, String separator) {
String[] split = data.split(separator);
double[] ret = new double[split.length];
for (int i = 0; i < split.length; i++) {
ret[i] = Double.parseDouble(split[i]);
}
return ret;
}//end fromString
/**
* Computes the mean for an array of doubles.
*
* @param vector the array
* @return the mean
*/
public static /*@pure@*/ double mean(double[] vector) {
double sum = 0;
if (vector.length == 0) {
return 0;
}
for (int i = 0; i < vector.length; i++) {
sum += vector[i];
}
return sum / (double) vector.length;
}//end mean
/**
* This will convert the given binary string to a decimal based
* integer
*
* @param binary the binary string to convert
* @return an equivalent base 10 number
*/
public static int toDecimal(String binary) {
long num = Long.parseLong(binary);
long rem;
/* Use the remainder method to ensure validity */
while (num > 0) {
rem = num % 10;
num = num / 10;
if (rem != 0 && rem != 1) {
System.out.println("This is not a binary number.");
System.out.println("Please try once again.");
return -1;
}
}
int i = Integer.parseInt(binary, 2);
return i;
}//end toDecimal
/**
* This will translate a vector in to an equivalent integer
*
* @param vector the vector to translate
* @return a z value such that the value is the interleaved lsd to msd for each
* double in the vector
*/
public static int distanceFinderZValue(double[] vector) {
StringBuilder binaryBuffer = new StringBuilder();
List binaryReps = new ArrayList(vector.length);
for (int i = 0; i < vector.length; i++) {
double d = vector[i];
int j = (int) d;
String binary = Integer.toBinaryString(j);
binaryReps.add(binary);
}
//append from left to right, the least to the most significant bit
//till all strings are empty
while (!binaryReps.isEmpty()) {
for (int j = 0; j < binaryReps.size(); j++) {
String curr = binaryReps.get(j);
if (!curr.isEmpty()) {
char first = curr.charAt(0);
binaryBuffer.append(first);
curr = curr.substring(1);
binaryReps.set(j, curr);
} else
binaryReps.remove(j);
}
}
return Integer.parseInt(binaryBuffer.toString(), 2);
}//end distanceFinderZValue
/**
* This returns the euclidean distance of two vectors
* sum(i=1,n) (q_i - p_i)^2
*
* @param p the first vector
* @param q the second vector
* @return the euclidean distance between two vectors
*/
public static double euclideanDistance(double[] p, double[] q) {
double ret = 0;
for (int i = 0; i < p.length; i++) {
double diff = (q[i] - p[i]);
double sq = Math.pow(diff, 2);
ret += sq;
}
return ret;
}//end euclideanDistance
/**
* This returns the euclidean distance of two vectors
* sum(i=1,n) (q_i - p_i)^2
*
* @param p the first vector
* @param q the second vector
* @return the euclidean distance between two vectors
*/
public static double euclideanDistance(float[] p, float[] q) {
double ret = 0;
for (int i = 0; i < p.length; i++) {
double diff = (q[i] - p[i]);
double sq = Math.pow(diff, 2);
ret += sq;
}
return ret;
}//end euclideanDistance
/**
* This will generate a series of uniformally distributed
* numbers between l times
*
* @param l the number of numbers to generate
* @return l uniformally generated numbers
*/
public static double[] generateUniform(int l) {
double[] ret = new double[l];
Random rgen = new Random();
for (int i = 0; i < l; i++) {
ret[i] = rgen.nextDouble();
}
return ret;
}//end generateUniform
/**
* This will calculate the Manhattan distance between two sets of points.
* The Manhattan distance is equivalent to:
* 1_sum_n |p_i - q_i|
*
* @param p the first point vector
* @param q the second point vector
* @return the Manhattan distance between two object
*/
public static double manhattanDistance(double[] p, double[] q) {
double ret = 0;
for (int i = 0; i < p.length; i++) {
double difference = p[i] - q[i];
ret += Math.abs(difference);
}
return ret;
}//end manhattanDistance
public static double[] sampleDoublesInInterval(double[][] doubles, int l) {
double[] sample = new double[l];
for (int i = 0; i < l; i++) {
int rand1 = randomNumberBetween(0, doubles.length - 1);
int rand2 = randomNumberBetween(0, doubles[i].length);
sample[i] = doubles[rand1][rand2];
}
return sample;
}
/**
* Generates a random integer between the specified numbers
*
* @param begin the begin of the interval
* @param end the end of the interval
* @param anchor the base number (assuming to be generated from an external rng)
* @return an int between begin and end
*/
public static int randomNumberBetween(double begin, double end,double anchor) {
if (begin > end)
throw new IllegalArgumentException("Begin must not be less than end");
return (int) begin + (int) (anchor * ((end - begin) + 1));
}
/**
* Generates a random integer between the specified numbers
*
* @param begin the begin of the interval
* @param end the end of the interval
* @return an int between begin and end
*/
public static int randomNumberBetween(double begin, double end) {
if (begin > end)
throw new IllegalArgumentException("Begin must not be less than end");
return (int) begin + (int) (Math.random() * ((end - begin) + 1));
}
/**
* Generates a random integer between the specified numbers
*
* @param begin the begin of the interval
* @param end the end of the interval
* @return an int between begin and end
*/
public static int randomNumberBetween(double begin, double end, RandomGenerator rng) {
if (begin > end)
throw new IllegalArgumentException("Begin must not be less than end");
return (int) begin + (int) (rng.nextDouble() * ((end - begin) + 1));
}
public static float randomFloatBetween(float begin, float end) {
float rand = (float) Math.random();
return begin + (rand * (end - begin));
}
public static double randomDoubleBetween(double begin, double end) {
return begin + (Math.random() * (end - begin));
}
/**
* This returns the slope of the given points.
*
* @param x1 the first x to use
* @param x2 the end x to use
* @param y1 the begin y to use
* @param y2 the end y to use
* @return the slope of the given points
*/
public double slope(double x1, double x2, double y1, double y2) {
return (y2 - y1) / (x2 - x1);
}//end slope
/**
* Shuffle the array elements using the specified RNG seed.
* Uses Fisher Yates shuffle internally:
* https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle#The_modern_algorithm
*
* @param array Array to shuffle
* @param rngSeed RNG seed to use for shuffling
*/
public static void shuffleArray(int[] array, long rngSeed) {
shuffleArray(array, new Random(rngSeed));
}
/**
* Shuffle the array elements using the specified Random instance
* Uses Fisher Yates shuffle internally:
* https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle#The_modern_algorithm
*
* @param array Array to shuffle
* @param rng Random instance to use for shuffling
*/
public static void shuffleArray(int[] array, Random rng) {
shuffleArraySubset(array, array.length, rng);
}
/**
* Shuffle the first N elements of the array using the specified Random instance.
* If shuffleFirst < array.length, only the elements 0 to shuffleFirst-1 are modified; values at indices shuffleFirst to
* array.length-1 are not changed.
* Uses Fisher Yates shuffle internally:
* https://en.wikipedia.org/wiki/Fisher%E2%80%93Yates_shuffle#The_modern_algorithm
*
* @param array Array to shuffle first N elements of
*
* @param rng Random instance to use for shuffling
*/
public static void shuffleArraySubset(int[] array, int shuffleFirst, Random rng) {
for (int i = shuffleFirst-1; i > 0; i--) {
int j = rng.nextInt(i + 1);
int temp = array[j];
array[j] = array[i];
array[i] = temp;
}
}
/**
* hashCode method, taken from Java 1.8 Double.hashCode(double) method
*
* @param value Double value to hash
* @return Hash code for the double value
*/
public static int hashCode(double value) {
long bits = Double.doubleToLongBits(value);
return (int) (bits ^ (bits >>> 32));
}
}
