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Diffstat (limited to 'src/main/java/ch/obermuhlner/math/big/BigComplexMath.java')
| -rw-r--r-- | src/main/java/ch/obermuhlner/math/big/BigComplexMath.java | 413 |
1 files changed, 0 insertions, 413 deletions
diff --git a/src/main/java/ch/obermuhlner/math/big/BigComplexMath.java b/src/main/java/ch/obermuhlner/math/big/BigComplexMath.java deleted file mode 100644 index a73d9bccdd..0000000000 --- a/src/main/java/ch/obermuhlner/math/big/BigComplexMath.java +++ /dev/null @@ -1,413 +0,0 @@ -package ch.obermuhlner.math.big; - -import java.math.BigDecimal; -import java.math.MathContext; -import java.util.List; - -import static ch.obermuhlner.math.big.BigComplex.I; - -/** - * Provides advanced functions operating on {@link BigComplex}s. - */ -public class BigComplexMath { - - private static final BigDecimal TWO = BigDecimal.valueOf(2); - - /** - * Calculates the reciprocal of the given complex number using the specified {@link MathContext}. - * - * @param x the complex number to calculate the reciprocal - * @param mathContext the {@link MathContext} used to calculate the result - * @return the calculated {@link BigComplex} result - * @see BigComplex#reciprocal(MathContext) - */ - public static BigComplex reciprocal(BigComplex x, MathContext mathContext) { - return x.reciprocal(mathContext); - } - - /** - * Calculates the conjugate of the given complex number using the specified {@link MathContext}. - * - * @param x the complex number to calculate the conjugate - * @return the calculated {@link BigComplex} result - * @see BigComplex#conjugate() - */ - public static BigComplex conjugate(BigComplex x) { - return x.conjugate(); - } - - /** - * Calculates the absolute value (also known as magnitude, length or radius) of the given complex number using the specified {@link MathContext}. - * - * @param x the complex number to calculate the absolute value - * @param mathContext the {@link MathContext} used to calculate the result - * @return the calculated {@link BigComplex} result - * @see BigComplex#abs(MathContext) - */ - public static BigDecimal abs(BigComplex x, MathContext mathContext) { - return x.abs(mathContext); - } - - /** - * Calculates the square of the absolute value (also known as magnitude, length or radius) of the given complex number using the specified {@link MathContext}. - * - * @param x the complex number to calculate the square of the absolute value - * @param mathContext the {@link MathContext} used to calculate the result - * @return the calculated {@link BigComplex} result - * @see BigComplex#absSquare(MathContext) - */ - public static BigDecimal absSquare(BigComplex x, MathContext mathContext) { - return x.absSquare(mathContext); - } - - /** - * Calculates the angle in radians of the given complex number using the specified {@link MathContext}. - * - * @param x the complex number to calculate the angle - * @param mathContext the {@link MathContext} used to calculate the result - * @return the calculated {@link BigComplex} angle in radians - * @see BigComplex#angle(MathContext) - */ - public static BigDecimal angle(BigComplex x, MathContext mathContext) { - return x.angle(mathContext); - } - - /** - * Calculates the factorial of the specified {@link BigComplex}. - * - * <p>This implementation uses - * <a href="https://en.wikipedia.org/wiki/Spouge%27s_approximation">Spouge's approximation</a> - * to calculate the factorial for non-integer values.</p> - * - * <p>This involves calculating a series of constants that depend on the desired precision. - * Since this constant calculation is quite expensive (especially for higher precisions), - * the constants for a specific precision will be cached - * and subsequent calls to this method with the same precision will be much faster.</p> - * - * <p>It is therefore recommended to do one call to this method with the standard precision of your application during the startup phase - * and to avoid calling it with many different precisions.</p> - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Factorial#Extension_of_factorial_to_non-integer_values_of_argument">Wikipedia: Factorial - Extension of factorial to non-integer values of argument</a></p> - * - * @param x the {@link BigComplex} - * @param mathContext the {@link MathContext} used for the result - * @return the factorial {@link BigComplex} - * @throws ArithmeticException if x is a negative integer value (-1, -2, -3, ...) - * @see BigDecimalMath#factorial(BigDecimal, MathContext) - * @see #gamma(BigComplex, MathContext) - */ - public static BigComplex factorial(BigComplex x, MathContext mathContext) { - if (x.isReal() && BigDecimalMath.isIntValue(x.re)) { - return BigComplex.valueOf(BigDecimalMath.factorial(x.re.intValueExact()).round(mathContext)); - } - - // https://en.wikipedia.org/wiki/Spouge%27s_approximation - MathContext mc = new MathContext(mathContext.getPrecision() * 2, mathContext.getRoundingMode()); - - int a = mathContext.getPrecision() * 13 / 10; - List<BigDecimal> constants = BigDecimalMath.getSpougeFactorialConstants(a); - - BigDecimal bigA = BigDecimal.valueOf(a); - - boolean negative = false; - BigComplex factor = BigComplex.valueOf(constants.get(0)); - for (int k = 1; k < a; k++) { - BigDecimal bigK = BigDecimal.valueOf(k); - factor = factor.add(BigComplex.valueOf(constants.get(k)).divide(x.add(bigK), mc), mc); - negative = !negative; - } - - BigComplex result = pow(x.add(bigA, mc), x.add(BigDecimal.valueOf(0.5), mc), mc); - result = result.multiply(exp(x.negate().subtract(bigA, mc), mc), mc); - result = result.multiply(factor, mc); - - return result.round(mathContext); - } - - /** - * Calculates the gamma function of the specified {@link BigComplex}. - * - * <p>This implementation uses {@link #factorial(BigComplex, MathContext)} internally, - * therefore the performance implications described there apply also for this method. - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Gamma_function">Wikipedia: Gamma function</a></p> - * - * @param x the {@link BigComplex} - * @param mathContext the {@link MathContext} used for the result - * @return the gamma {@link BigComplex} - * @throws ArithmeticException if x-1 is a negative integer value (-1, -2, -3, ...) - * @see BigDecimalMath#gamma(BigDecimal, MathContext) - * @see #factorial(BigComplex, MathContext) - */ - public static BigComplex gamma(BigComplex x, MathContext mathContext) { - return factorial(x.subtract(BigComplex.ONE), mathContext); - } - - - /** - * Calculates the natural exponent of {@link BigComplex} x (e<sup>x</sup>) in the complex domain. - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Exponential_function#Complex_plane">Wikipedia: Exponent (Complex plane)</a></p> - * - * @param x the {@link BigComplex} to calculate the exponent for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated exponent {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex exp(BigComplex x, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - BigDecimal expRe = BigDecimalMath.exp(x.re, mc); - return BigComplex.valueOf( - expRe.multiply(BigDecimalMath.cos(x.im, mc), mc).round(mathContext), - expRe.multiply(BigDecimalMath.sin(x.im, mc), mc)).round(mathContext); - } - - /** - * Calculates the sine (sinus) of {@link BigComplex} x in the complex domain. - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Sine#Sine_with_a_complex_argument">Wikipedia: Sine (Sine with a complex argument)</a></p> - * - * @param x the {@link BigComplex} to calculate the sine for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated sine {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex sin(BigComplex x, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return BigComplex.valueOf( - BigDecimalMath.sin(x.re, mc).multiply(BigDecimalMath.cosh(x.im, mc), mc).round(mathContext), - BigDecimalMath.cos(x.re, mc).multiply(BigDecimalMath.sinh(x.im, mc), mc).round(mathContext)); - } - - /** - * Calculates the cosine (cosinus) of {@link BigComplex} x in the complex domain. - * - * @param x the {@link BigComplex} to calculate the cosine for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated cosine {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex cos(BigComplex x, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return BigComplex.valueOf( - BigDecimalMath.cos(x.re, mc).multiply(BigDecimalMath.cosh(x.im, mc), mc).round(mathContext), - BigDecimalMath.sin(x.re, mc).multiply(BigDecimalMath.sinh(x.im, mc), mc).negate().round(mathContext)); - } - - // - // http://scipp.ucsc.edu/~haber/archives/physics116A10/arc_10.pdf - - /** - * Calculates the tangens of {@link BigComplex} x in the complex domain. - * - * @param x the {@link BigComplex} to calculate the tangens for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated tangens {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex tan(BigComplex x, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return sin(x, mc).divide(cos(x, mc), mc).round(mathContext); - } - - /** - * Calculates the arc tangens (inverted tangens) of {@link BigComplex} x in the complex domain. - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_complex_plane">Wikipedia: Inverse trigonometric functions (Extension to complex plane)</a></p> - * - * @param x the {@link BigComplex} to calculate the arc tangens for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated arc tangens {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex atan(BigComplex x, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return log(I.subtract(x, mc).divide(I.add(x, mc), mc), mc).divide(I, mc).divide(TWO, mc).round(mathContext); - } - - /** - * Calculates the arc cotangens (inverted cotangens) of {@link BigComplex} x in the complex domain. - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_complex_plane">Wikipedia: Inverse trigonometric functions (Extension to complex plane)</a></p> - * - * @param x the {@link BigComplex} to calculate the arc cotangens for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated arc cotangens {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex acot(BigComplex x, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return log(x.add(I, mc).divide(x.subtract(I, mc), mc), mc).divide(I, mc).divide(TWO, mc).round(mathContext); - } - - /** - * Calculates the arc sine (inverted sine) of {@link BigComplex} x in the complex domain. - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_complex_plane">Wikipedia: Inverse trigonometric functions (Extension to complex plane)</a></p> - * - * @param x the {@link BigComplex} to calculate the arc sine for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated arc sine {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex asin(BigComplex x, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return I.negate().multiply(log(I.multiply(x, mc).add(sqrt(BigComplex.ONE.subtract(x.multiply(x, mc), mc), mc), mc), mc), mc).round(mathContext); - } - - /** - * Calculates the arc cosine (inverted cosine) of {@link BigComplex} x in the complex domain. - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_complex_plane">Wikipedia: Inverse trigonometric functions (Extension to complex plane)</a></p> - * - * @param x the {@link BigComplex} to calculate the arc cosine for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated arc cosine {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex acos(BigComplex x, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return I.negate().multiply(log(x.add(sqrt(x.multiply(x, mc).subtract(BigComplex.ONE, mc), mc), mc), mc), mc).round(mathContext); - } - - /** - * Calculates the square root of {@link BigComplex} x in the complex domain (sqrt x). - * - * <p>See <a href="https://en.wikipedia.org/wiki/Square_root#Square_root_of_an_imaginary_number">Wikipedia: Square root (Square root of an imaginary number)</a></p> - * - * @param x the {@link BigComplex} to calculate the square root for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated square root {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex sqrt(BigComplex x, MathContext mathContext) { - // https://math.stackexchange.com/questions/44406/how-do-i-get-the-square-root-of-a-complex-number - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - BigDecimal magnitude = x.abs(mc); - - BigComplex a = x.add(magnitude, mc); - return a.divide(a.abs(mc), mc).multiply(BigDecimalMath.sqrt(magnitude, mc), mc).round(mathContext); - } - - /** - * Calculates the natural logarithm of {@link BigComplex} x in the complex domain. - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Complex_logarithm">Wikipedia: Complex logarithm</a></p> - * - * @param x the {@link BigComplex} to calculate the natural logarithm for - * @param mathContext the {@link MathContext} used for the result - * @return the calculated natural logarithm {@link BigComplex} with the precision specified in the <code>mathContext</code> - */ - public static BigComplex log(BigComplex x, MathContext mathContext) { - // https://en.wikipedia.org/wiki/Complex_logarithm - MathContext mc1 = new MathContext(mathContext.getPrecision() + 20, mathContext.getRoundingMode()); - MathContext mc2 = new MathContext(mathContext.getPrecision() + 5, mathContext.getRoundingMode()); - - return BigComplex.valueOf( - BigDecimalMath.log(x.abs(mc1), mc1).round(mathContext), - x.angle(mc2)).round(mathContext); - } - - /** - * Calculates {@link BigComplex} x to the power of <code>long</code> y (x<sup>y</sup>). - * - * <p>The implementation tries to minimize the number of multiplications of {@link BigComplex x} (using squares whenever possible).</p> - * - * <p>See: <a href="https://en.wikipedia.org/wiki/Exponentiation#Efficient_computation_with_integer_exponents">Wikipedia: Exponentiation - efficient computation</a></p> - * - * @param x the {@link BigComplex} value to take to the power - * @param y the <code>long</code> value to serve as exponent - * @param mathContext the {@link MathContext} used for the result - * @return the calculated x to the power of y with the precision specified in the <code>mathContext</code> - */ - public static BigComplex pow(BigComplex x, long y, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 10, mathContext.getRoundingMode()); - - if (y < 0) { - return BigComplex.ONE.divide(pow(x, -y, mc), mc).round(mathContext); - } - - BigComplex result = BigComplex.ONE; - while (y > 0) { - if ((y & 1) == 1) { - // odd exponent -> multiply result with x - result = result.multiply(x, mc); - y -= 1; - } - - if (y > 0) { - // even exponent -> square x - x = x.multiply(x, mc); - } - - y >>= 1; - } - - return result.round(mathContext); - } - - /** - * Calculates {@link BigComplex} x to the power of {@link BigDecimal} y (x<sup>y</sup>). - * - * @param x the {@link BigComplex} value to take to the power - * @param y the {@link BigDecimal} value to serve as exponent - * @param mathContext the {@link MathContext} used for the result - * @return the calculated x to the power of y with the precision specified in the <code>mathContext</code> - */ - public static BigComplex pow(BigComplex x, BigDecimal y, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - BigDecimal angleTimesN = x.angle(mc).multiply(y, mc); - return BigComplex.valueOf( - BigDecimalMath.cos(angleTimesN, mc), - BigDecimalMath.sin(angleTimesN, mc)).multiply(BigDecimalMath.pow(x.abs(mc), y, mc), mc).round(mathContext); - } - - /** - * Calculates {@link BigComplex} x to the power of {@link BigComplex} y (x<sup>y</sup>). - * - * @param x the {@link BigComplex} value to take to the power - * @param y the {@link BigComplex} value to serve as exponent - * @param mathContext the {@link MathContext} used for the result - * @return the calculated x to the power of y with the precision specified in the <code>mathContext</code> - */ - public static BigComplex pow(BigComplex x, BigComplex y, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return exp(y.multiply(log(x, mc), mc), mc).round(mathContext); - } - - /** - * Calculates the {@link BigDecimal} n'th root of {@link BigComplex} x (<sup>n</sup>sqrt x). - * - * <p>See <a href="http://en.wikipedia.org/wiki/Square_root">Wikipedia: Square root</a></p> - * @param x the {@link BigComplex} value to calculate the n'th root - * @param n the {@link BigDecimal} defining the root - * @param mathContext the {@link MathContext} used for the result - * - * @return the calculated n'th root of x with the precision specified in the <code>mathContext</code> - */ - public static BigComplex root(BigComplex x, BigDecimal n, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return pow(x, BigDecimal.ONE.divide(n, mc), mc).round(mathContext); - } - - /** - * Calculates the {@link BigComplex} n'th root of {@link BigComplex} x (<sup>n</sup>sqrt x). - * - * <p>See <a href="http://en.wikipedia.org/wiki/Square_root">Wikipedia: Square root</a></p> - * @param x the {@link BigComplex} value to calculate the n'th root - * @param n the {@link BigComplex} defining the root - * @param mathContext the {@link MathContext} used for the result - * - * @return the calculated n'th root of x with the precision specified in the <code>mathContext</code> - */ - public static BigComplex root(BigComplex x, BigComplex n, MathContext mathContext) { - MathContext mc = new MathContext(mathContext.getPrecision() + 4, mathContext.getRoundingMode()); - - return pow(x, BigComplex.ONE.divide(n, mc), mc).round(mathContext); - } - - // TODO add root() for the k'th root - https://math.stackexchange.com/questions/322481/principal-nth-root-of-a-complex-number -} |