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oj! Algorithms - ojAlgo - is Open Source Java code that has to do with mathematics, linear algebra and optimisation.
/*
* Copyright 1997-2024 Optimatika
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
package org.ojalgo.function.special;
import static org.ojalgo.function.constant.PrimitiveMath.ONE;
import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;
import org.ojalgo.function.constant.BigMath;
/**
* Math utilities missing from {@link Math}.
*
* @author apete
*/
public abstract class MissingMath {
/**
* Corresponding to binary 256 octuple precision
*/
private static final MathContext MC256 = new MathContext(71, RoundingMode.HALF_EVEN);
public static double acosh(final double arg) {
return Math.log(arg + Math.sqrt(arg * arg - 1.0));
}
public static double asinh(final double arg) {
return Math.log(arg + Math.sqrt(arg * arg + 1.0));
}
/**
*
* https://math.stackexchange.com/questions/1098487/atan2-faster-approximation/1105038
*
*
* This is about 10x faster than {@link Math#atan2(double, double)}
*
*/
public static double atan2(final double y, final double x) {
if (y == 0.0 && x == 0.0) {
return 0.0;
}
double ay = Math.abs(y);
double ax = Math.abs(x);
double a = Math.min(ay, ax) / Math.max(ay, ax);
double s = a * a;
double retVal = ((-0.0464964749 * s + 0.15931422) * s - 0.327622764) * s * a + a;
if (ay > ax) {
retVal = 1.570796326794897 - retVal;
}
if (x < 0.0) {
retVal = 3.141592653589793 - retVal;
}
if (y < 0.0) {
retVal = -retVal;
}
return retVal;
}
public static double atanh(final double arg) {
return Math.log((1.0 + arg) / (1.0 - arg)) / 2.0;
}
public static BigDecimal divide(final BigDecimal numerator, final BigDecimal denominator) {
return numerator.divide(denominator, MC256);
}
/**
* 13! does not fit in an int, and 21! does not fit in a
* long - that's why this method returns a double.
*/
public static double factorial(final int arg) {
if (arg < 0) {
throw new IllegalArgumentException();
}
if (arg < 2) {
return ONE;
}
if (arg < 13) {
return MissingMath.factorialInt(arg);
}
if (arg < 21) {
return MissingMath.factorialLong(arg);
}
return MissingMath.factorialDouble(arg);
}
/**
* Greatest Common Denominator
*/
public static int gcd(final int val1, final int val2) {
int retVal = 1;
int abs1 = Math.abs(val1);
int abs2 = Math.abs(val2);
int tmpMax = Math.max(abs1, abs2);
int tmpMin = Math.min(abs1, abs2);
while (tmpMin != 0) {
retVal = tmpMin;
tmpMin = tmpMax % tmpMin;
tmpMax = retVal;
}
return retVal;
}
public static int gcd(final int val1, final int... vals) {
int retVal = val1;
if (retVal == 1) {
return 1;
}
for (int i = 0; i < vals.length; i++) {
retVal = MissingMath.gcd(retVal, vals[i]);
if (retVal == 1) {
return 1;
}
}
return retVal;
}
public static int gcd(final int[] vals) {
return MissingMath.gcd(vals[0], vals);
}
public static long gcd(final long val1, final long... vals) {
long retVal = val1;
if (retVal == 1L) {
return 1L;
}
for (int i = 0; i < vals.length; i++) {
retVal = MissingMath.gcd(retVal, vals[i]);
if (retVal == 1L) {
return 1L;
}
}
return retVal;
}
/**
* Greatest Common Denominator
*/
public static long gcd(final long val1, final long val2) {
long retVal = 1L;
long abs1 = Math.abs(val1);
long abs2 = Math.abs(val2);
long tmpMax = Math.max(abs1, abs2);
long tmpMin = Math.min(abs1, abs2);
while (tmpMin != 0L) {
retVal = tmpMin;
tmpMin = tmpMax % tmpMin;
tmpMax = retVal;
}
return retVal;
}
public static long gcd(final long[] vals) {
return MissingMath.gcd(vals[0], vals);
}
public static BigDecimal hypot(final BigDecimal arg1, final BigDecimal arg2) {
BigDecimal prod1 = arg1.multiply(arg1);
BigDecimal prod2 = arg2.multiply(arg2);
return MissingMath.root(prod1.add(prod2), 2);
}
public static double hypot(final double arg1, final double arg2) {
if (Double.isNaN(arg1) || Double.isNaN(arg2)) {
return Double.NaN;
}
double abs1 = Math.abs(arg1);
double abs2 = Math.abs(arg2);
double retVal = 0.0;
if (abs1 > abs2) {
retVal = abs1 * MissingMath.sqrt1px2(abs2 / abs1);
} else if (abs2 > 0.0) {
retVal = abs2 * MissingMath.sqrt1px2(abs1 / abs2);
}
return retVal;
}
/**
* For very small arguments (regardless of sign) the replacement is returned instead
*/
public static double log10(final double arg, final double replacement) {
if (Math.abs(arg) < Double.MIN_NORMAL) {
return replacement;
}
return Math.log10(arg);
}
public static double logistic(final double arg) {
return 1.0 / (1.0 + Math.exp(-arg));
}
public static double logit(final double arg) {
return Math.log(1.0 / (1.0 - arg));
}
/**
* Returns a rough approximation of {@link Math#log10(double)} for {@link BigDecimal}.
*
* - For numbers like 10^n it returns the exact correct number, n.
*
- The magnitude of 0.0 is 0.
*
- The error is [0.0,1.0) and the returned value is never more than the actual/correct value. For
* 999.0 the correct value is close to 3, but this method returns 2, as the implementation simply counts
* the digits.
*
- Works for negative numbers as the sign is disregarded.
*
- Works for fractional numbers 0.1, 0.0456, 1.2 or whatever.
*
*/
public static int magnitude(final BigDecimal arg) {
return arg.signum() == 0 ? 0 : arg.precision() - arg.scale() - 1;
}
public static double max(final double... values) {
double retVal = values[0];
for (int i = values.length; i-- != 1;) {
retVal = values[i] > retVal ? values[i] : retVal;
}
return retVal;
}
public static double max(final double a, final double b) {
return Math.max(a, b);
}
public static double max(final double a, final double b, final double c) {
return Math.max(Math.max(a, b), c);
}
public static double max(final double a, final double b, final double c, final double d) {
return Math.max(Math.max(a, b), Math.max(c, d));
}
public static int max(final int... values) {
int retVal = values[0];
for (int i = values.length; i-- != 1;) {
retVal = values[i] > retVal ? values[i] : retVal;
}
return retVal;
}
public static int max(final int a, final int b) {
return Math.max(a, b);
}
public static int max(final int a, final int b, final int c) {
return Math.max(Math.max(a, b), c);
}
public static int max(final int a, final int b, final int c, final int d) {
return Math.max(Math.max(a, b), Math.max(c, d));
}
public static long max(final long... values) {
long retVal = values[0];
for (int i = values.length; i-- != 1;) {
retVal = values[i] > retVal ? values[i] : retVal;
}
return retVal;
}
public static long max(final long a, final long b) {
return Math.max(a, b);
}
public static long max(final long a, final long b, final long c) {
return Math.max(Math.max(a, b), c);
}
public static long max(final long a, final long b, final long c, final long d) {
return Math.max(Math.max(a, b), Math.max(c, d));
}
public static double min(final double... values) {
double retVal = values[0];
for (int i = values.length; i-- != 1;) {
retVal = values[i] < retVal ? values[i] : retVal;
}
return retVal;
}
public static double min(final double a, final double b) {
return Math.min(a, b);
}
public static double min(final double a, final double b, final double c) {
return Math.min(Math.min(a, b), c);
}
public static double min(final double a, final double b, final double c, final double d) {
return Math.min(Math.min(a, b), Math.min(c, d));
}
public static int min(final int... values) {
int retVal = values[0];
for (int i = values.length; i-- != 1;) {
retVal = values[i] < retVal ? values[i] : retVal;
}
return retVal;
}
public static int min(final int a, final int b) {
return Math.min(a, b);
}
public static int min(final int a, final int b, final int c) {
return Math.min(Math.min(a, b), c);
}
public static int min(final int a, final int b, final int c, final int d) {
return Math.min(Math.min(a, b), Math.min(c, d));
}
public static long min(final long... values) {
long retVal = values[0];
for (int i = values.length; i-- != 1;) {
retVal = values[i] < retVal ? values[i] : retVal;
}
return retVal;
}
public static long min(final long a, final long b) {
return Math.min(a, b);
}
public static long min(final long a, final long b, final long c) {
return Math.min(Math.min(a, b), c);
}
public static long min(final long a, final long b, final long c, final long d) {
return Math.min(Math.min(a, b), Math.min(c, d));
}
public static double norm(final double... values) {
double retVal = Math.abs(values[0]);
for (int i = values.length; i-- != 1;) {
retVal = values[i] > retVal ? Math.abs(values[i]) : retVal;
}
return retVal;
}
public static double norm(final double a, final double b) {
return Math.max(Math.abs(a), Math.abs(b));
}
public static double norm(final double a, final double b, final double c) {
return Math.max(Math.max(Math.abs(a), Math.abs(b)), Math.abs(c));
}
public static double norm(final double a, final double b, final double c, final double d) {
return Math.max(Math.max(Math.abs(a), Math.abs(b)), Math.max(Math.abs(c), Math.abs(d)));
}
public static BigDecimal pow(final BigDecimal arg1, final BigDecimal arg2) {
if (arg2.signum() == 0) {
return BigDecimal.ONE;
}
if (arg1.signum() == 0) {
return BigDecimal.ZERO;
}
if (arg2.compareTo(BigDecimal.ONE) == 0) {
return arg1;
}
return BigDecimal.valueOf(Math.pow(arg1.doubleValue(), arg2.doubleValue()));
}
public static BigDecimal power(final BigDecimal arg, final int param) {
switch (param) {
case 0:
return BigDecimal.ONE;
case 1:
return arg;
case 2:
return arg.multiply(arg, MC256);
case 3:
return arg.multiply(arg).multiply(arg, MC256);
case 4:
BigDecimal arg2 = arg.multiply(arg);
return arg2.multiply(arg2, MC256);
default:
return arg.pow(param, MC256);
}
}
public static double power(final double arg, int param) {
if (param < 0) {
return 1.0 / MissingMath.power(arg, -param);
}
double retVal = 1.0;
while (param > 0) {
retVal = retVal * arg;
param--;
}
return retVal;
}
public static long power(final long arg, final int param) {
if (param == 0) {
return 1L;
}
if (param == 1) {
return arg;
}
if (param == 2) {
return arg * arg;
}
if (param < 0) {
return Math.round(Math.pow(arg, param));
}
long retVal = arg;
for (int p = 1; p < param; p++) {
retVal *= arg;
}
return retVal;
}
public static BigDecimal root(final BigDecimal arg, final int param) {
if (param <= 0) {
throw new IllegalArgumentException();
}
if (param == 1) {
return arg;
}
BigDecimal bigArg = arg.round(MC256);
BigDecimal bigParam = BigDecimal.valueOf(param);
BigDecimal retVal = BigDecimal.ZERO;
double primArg = bigArg.doubleValue();
if (!Double.isInfinite(primArg) && !Double.isNaN(primArg)) {
retVal = BigDecimal.valueOf(Math.pow(primArg, 1.0 / param)); // Intial guess
}
BigDecimal shouldBeZero;
while ((shouldBeZero = MissingMath.power(retVal, param).subtract(bigArg)).signum() != 0) {
retVal = retVal.subtract(shouldBeZero.divide(bigParam.multiply(retVal.pow(param - 1)), MC256));
}
return retVal;
}
public static double root(final double arg, final int param) {
if (param != 0) {
return Math.pow(arg, 1.0 / param);
}
throw new IllegalArgumentException();
}
public static int roundToInt(final double value) {
return Math.toIntExact(Math.round(value));
}
public static double scale(final double arg, int param) {
if (param == 0) {
return 1.0;
}
if (param < 0) {
int factor = 1;
while (param < 0) {
factor *= 10;
param++;
}
return Math.rint(factor / arg) * factor;
}
int factor = 1;
while (param > 0) {
factor *= 10;
param--;
}
return Math.rint(factor * arg) / factor;
}
public static BigDecimal signum(final BigDecimal arg) {
switch (arg.signum()) {
case 1:
return BigDecimal.ONE;
case -1:
return BigDecimal.ONE.negate();
default:
return BigDecimal.ZERO;
}
}
public static double sqrt1px2(final double arg) {
return Math.sqrt(1.0 + arg * arg);
}
public static BigDecimal tanh(final BigDecimal arg) {
BigDecimal retVal;
BigDecimal plus = BigMath.EXP.invoke(arg);
BigDecimal minus = BigMath.EXP.invoke(arg.negate());
BigDecimal dividend = plus.subtract(minus);
BigDecimal divisor = plus.add(minus);
if (dividend.equals(divisor)) {
retVal = BigDecimal.ONE;
} else if (dividend.equals(divisor.negate())) {
retVal = BigDecimal.ONE.negate();
} else {
retVal = BigMath.DIVIDE.apply(dividend, divisor);
}
return retVal;
}
public static int toMinIntExact(final long... values) {
return Math.toIntExact(MissingMath.min(values));
}
public static int toMinIntExact(final long a, final long b) {
return Math.toIntExact(Math.min(a, b));
}
public static int toMinIntExact(final long a, final long b, final long c) {
return Math.toIntExact(MissingMath.min(a, b, c));
}
public static int toMinIntExact(final long a, final long b, final long c, final long d) {
return Math.toIntExact(MissingMath.min(a, b, c, d));
}
static double factorialDouble(final int arg) {
double retVal = ONE;
for (int i = 2; i <= arg; i++) {
retVal *= i;
}
return retVal;
}
static int factorialInt(final int arg) {
int retVal = 1;
for (int i = 2; i <= arg; i++) {
retVal *= i;
}
return retVal;
}
static long factorialLong(final int arg) {
long retVal = 1L;
for (int i = 2; i <= arg; i++) {
retVal *= i;
}
return retVal;
}
}