/**
* Copyright (C) 2009 - present by OpenGamma Inc. and the OpenGamma group of companies
*
* Please see distribution for license.
*/
package com.opengamma.analytics.math;
import static com.opengamma.analytics.math.number.ComplexNumber.I;
import org.apache.commons.lang.Validate;
import com.opengamma.analytics.math.number.ComplexNumber;
/**
*
*/
public class TrigonometricFunctionUtils {
private static final ComplexNumber NEGATIVE_I = new ComplexNumber(0, -1);
public static double acos(final double x) {
return Math.acos(x);
}
/**
* arccos - the inverse of cos
* @param z A complex number
* @return acos(z)
*/
public static ComplexNumber acos(final ComplexNumber z) {
Validate.notNull(z, "z");
return ComplexMathUtils.multiply(NEGATIVE_I, ComplexMathUtils.log(ComplexMathUtils.add(z, ComplexMathUtils.sqrt(ComplexMathUtils.subtract(ComplexMathUtils.multiply(z, z), 1)))));
}
public static double acosh(final double x) {
final double y = x * x - 1;
Validate.isTrue(y >= 0, "|x|>=1.0 for real solution");
return Math.log(x + Math.sqrt(x * x - 1));
}
public static ComplexNumber acosh(final ComplexNumber z) {
Validate.notNull(z, "z");
return ComplexMathUtils.log(ComplexMathUtils.add(z, ComplexMathUtils.sqrt(ComplexMathUtils.subtract(ComplexMathUtils.multiply(z, z), 1))));
}
public static double asin(final double x) {
return Math.asin(x);
}
public static ComplexNumber asin(final ComplexNumber z) {
Validate.notNull(z, "z");
return ComplexMathUtils.multiply(NEGATIVE_I,
ComplexMathUtils.log(ComplexMathUtils.add(ComplexMathUtils.multiply(I, z), ComplexMathUtils.sqrt(ComplexMathUtils.subtract(1, ComplexMathUtils.multiply(z, z))))));
}
public static double asinh(final double x) {
return Math.log(x + Math.sqrt(x * x + 1));
}
public static ComplexNumber asinh(final ComplexNumber z) {
Validate.notNull(z, "z");
return ComplexMathUtils.log(ComplexMathUtils.add(z, ComplexMathUtils.sqrt(ComplexMathUtils.add(ComplexMathUtils.multiply(z, z), 1))));
}
public static double atan(final double x) {
return Math.atan(x);
}
public static ComplexNumber atan(final ComplexNumber z) {
Validate.notNull(z, "z");
final ComplexNumber iZ = ComplexMathUtils.multiply(z, I);
final ComplexNumber half = new ComplexNumber(0, 0.5);
return ComplexMathUtils.multiply(half, ComplexMathUtils.log(ComplexMathUtils.divide(ComplexMathUtils.subtract(1, iZ), ComplexMathUtils.add(1, iZ))));
}
public static double atanh(final double x) {
return 0.5 * Math.log((1 + x) / (1 - x));
}
//TODO R White 21/07/2011 not sure why this was used over the equivalent below
// public static ComplexNumber atanh(final ComplexNumber z) {
// Validate.notNull(z, "z");
// return ComplexMathUtils.log(ComplexMathUtils.divide(ComplexMathUtils.sqrt(ComplexMathUtils.subtract(1, ComplexMathUtils.multiply(z, z))), ComplexMathUtils.subtract(1, z)));
// }
public static ComplexNumber atanh(final ComplexNumber z) {
Validate.notNull(z, "z");
return ComplexMathUtils.multiply(0.5, ComplexMathUtils.log(ComplexMathUtils.divide(ComplexMathUtils.add(1, z), ComplexMathUtils.subtract(1, z))));
}
public static double cos(final double x) {
return Math.cos(x);
}
public static ComplexNumber cos(final ComplexNumber z) {
Validate.notNull(z, "z");
final double x = z.getReal();
final double y = z.getImaginary();
return new ComplexNumber(Math.cos(x) * Math.cosh(y), -Math.sin(x) * Math.sinh(y));
}
public static double cosh(final double x) {
return Math.cosh(x);
}
public static ComplexNumber cosh(final ComplexNumber z) {
Validate.notNull(z, "z");
return new ComplexNumber(Math.cosh(z.getReal()) * Math.cos(z.getImaginary()), Math.sinh(z.getReal()) * Math.sin(z.getImaginary()));
}
public static double sin(final double x) {
return Math.sin(x);
}
public static ComplexNumber sin(final ComplexNumber z) {
Validate.notNull(z, "z");
final double x = z.getReal();
final double y = z.getImaginary();
return new ComplexNumber(Math.sin(x) * Math.cosh(y), Math.cos(x) * Math.sinh(y));
}
public static double sinh(final double x) {
return Math.sinh(x);
}
public static ComplexNumber sinh(final ComplexNumber z) {
Validate.notNull(z, "z");
return new ComplexNumber(Math.sinh(z.getReal()) * Math.cos(z.getImaginary()), Math.cosh(z.getReal()) * Math.sin(z.getImaginary()));
}
public static double tan(final double x) {
return Math.tan(x);
}
public static ComplexNumber tan(final ComplexNumber z) {
final ComplexNumber b = ComplexMathUtils.exp(ComplexMathUtils.multiply(ComplexMathUtils.multiply(I, 2), z));
return ComplexMathUtils.divide(ComplexMathUtils.subtract(b, 1), ComplexMathUtils.multiply(I, ComplexMathUtils.add(b, 1)));
}
public static double tanh(final double x) {
return Math.tanh(x);
}
public static ComplexNumber tanh(final ComplexNumber z) {
final ComplexNumber z2 = ComplexMathUtils.exp(z);
final ComplexNumber z3 = ComplexMathUtils.exp(ComplexMathUtils.multiply(z, -1));
return ComplexMathUtils.divide(ComplexMathUtils.subtract(z2, z3), ComplexMathUtils.add(z2, z3));
}
}