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Create Complex Numbers Utils #5128
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add basic complex numbers methods and unit tests
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add trigs
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add exceptions for the trigonometric functions
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Merge branch 'master' of https://github.com/rozi26/java_algo_fork1
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Merge branch 'feature/improve_code_look' of https://github.com/rozi26…
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change the order or final static
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Update src/test/java/com/thealgorithms/maths/ComplexNumberUtilTest.java
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Update src/main/java/com/thealgorithms/maths/ComplexNumberUtil.java
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Update src/main/java/com/thealgorithms/maths/ComplexNumberUtil.java
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Update src/main/java/com/thealgorithms/maths/ComplexNumberUtil.java
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264 changes: 264 additions & 0 deletions
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src/main/java/com/thealgorithms/maths/ComplexNumberUtil.java
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,264 @@ | ||
| package com.thealgorithms.maths; | ||
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| public class ComplexNumberUtil { | ||
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| public static class ComplexNumber { | ||
| public final double REAL; | ||
| public final double IMAGINARY; | ||
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| public ComplexNumber(double real, double imaginary) { | ||
| REAL = real; | ||
| IMAGINARY = imaginary; | ||
| } | ||
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| @Override | ||
| public boolean equals(Object obj) { | ||
| if (obj instanceof ComplexNumber num) { | ||
| return this.REAL == num.REAL && this.IMAGINARY == num.IMAGINARY; | ||
| } | ||
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| return super.equals(obj); | ||
| } | ||
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| @Override | ||
| public String toString() { | ||
| return REAL + ((IMAGINARY < 0) ? (" - " + Math.abs(IMAGINARY)) : (" + " + IMAGINARY)) + "i"; | ||
| } | ||
| } | ||
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| public static final ComplexNumber ZERO = new ComplexNumber(0, 0); | ||
| public static final ComplexNumber ONE = new ComplexNumber(1, 0); | ||
| public static final ComplexNumber TWO = new ComplexNumber(2, 0); | ||
| public static final ComplexNumber PLUS_I = new ComplexNumber(0, 1); | ||
| public static final ComplexNumber MINUS_I = new ComplexNumber(0, -1); | ||
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| /** | ||
| * add two complex numbers | ||
| * @param num1 the first complex number | ||
| * @param num2 the second complex number | ||
| * @return the sum of num1 and num2 | ||
| */ | ||
| public static ComplexNumber add(ComplexNumber num1, ComplexNumber num2) { | ||
| return new ComplexNumber(num1.REAL + num2.REAL, num1.IMAGINARY + num2.IMAGINARY); | ||
| } | ||
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| /** | ||
| * Subtracts the second complex number from the first complex number. | ||
| * | ||
| * @param num1 the first complex number | ||
| * @param num2 the second complex number | ||
| * @return the result of subtracting num2 from num1 | ||
| */ | ||
| public static ComplexNumber subtract(ComplexNumber num1, ComplexNumber num2) { | ||
| return new ComplexNumber(num1.REAL - num2.REAL, num1.IMAGINARY - num2.IMAGINARY); | ||
| } | ||
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| /** | ||
| * Multiplies two complex numbers. | ||
| * | ||
| * @param num1 the first complex number | ||
| * @param num2 the second complex number | ||
| * @return the product of num1 and num2 | ||
| * @link <a href="https://en.wikipedia.org/wiki/Complex_number#Multiplication">...</a> | ||
| */ | ||
| public static ComplexNumber multiply(ComplexNumber num1, ComplexNumber num2) { | ||
| return new ComplexNumber(num1.REAL * num2.REAL - num1.IMAGINARY * num2.IMAGINARY, num1.REAL * num2.IMAGINARY + num1.IMAGINARY * num2.REAL); | ||
| } | ||
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| /** | ||
| * Divides the first complex number by the second complex number. | ||
| * | ||
| * @param num1 the numerator complex number | ||
| * @param num2 the denominator complex number | ||
| * @return the result of dividing num1 by num2 | ||
| * @throws RuntimeException if the divisor (num2) is zero | ||
| * @link <a href="https://en.wikipedia.org/wiki/Complex_number#Complex_conjugate,_absolute_value_and_argument">...</a> | ||
| */ | ||
| public static ComplexNumber divide(ComplexNumber num1, ComplexNumber num2) { | ||
| final double divisor = num2.REAL * num2.REAL + num2.IMAGINARY * num2.IMAGINARY; | ||
| if (divisor == 0) { | ||
| throw new RuntimeException("Cannot divide by zero"); | ||
| } | ||
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| return new ComplexNumber((num1.REAL * num2.REAL + num1.IMAGINARY * num2.IMAGINARY) / divisor, (num1.IMAGINARY * num2.REAL - num1.REAL * num2.IMAGINARY) / divisor); | ||
| } | ||
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| /** | ||
| * Computes the absolute value (magnitude) of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the absolute value of num | ||
| * @link <a href="https://en.wikipedia.org/wiki/Complex_number#Complex_conjugate,_absolute_value_and_argument">...</a> | ||
| */ | ||
| public static double abs(ComplexNumber num) { | ||
| return Math.sqrt(num.REAL * num.REAL + num.IMAGINARY * num.IMAGINARY); | ||
| } | ||
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| /** | ||
| * Computes the exponential function of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return e raised to the power of num | ||
| * @link <a href="https://en.wikipedia.org/wiki/Exponential_function#Continued_fractions_for_ex">...</a> | ||
| */ | ||
| public static ComplexNumber exp(ComplexNumber num) { | ||
| final double coefficient = Math.exp(num.REAL); | ||
| return new ComplexNumber(coefficient * Math.cos(num.IMAGINARY), coefficient * Math.sin(num.IMAGINARY)); | ||
| } | ||
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| /** | ||
| * Computes the principal value of natural logarithm of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the natural logarithm of num | ||
| * @throws RuntimeException if num is zero | ||
| * @link <a href="https://en.wikipedia.org/wiki/Complex_logarithm#Calculating_the_principal_value">...</a> | ||
| */ | ||
| public static ComplexNumber log(ComplexNumber num) { | ||
| if (num.equals(ZERO)) { | ||
| throw new RuntimeException("Cannot take the logarithm of zero"); | ||
| } | ||
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| return new ComplexNumber(Math.log(abs(num)), Math.atan2(num.IMAGINARY, num.REAL)); | ||
| } | ||
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| /** | ||
| * Computes the power of a complex number raised to another complex number. | ||
| * | ||
| * @param num1 the base complex number | ||
| * @param num2 the exponent complex number | ||
| * @return num1 raised to the power of num2 | ||
| * link <a href="https://en.wikipedia.org/wiki/Exponentiation#Complex_exponents_with_a_positive_real_base">...</a> | ||
| */ | ||
| public static ComplexNumber pow(ComplexNumber num1, ComplexNumber num2) { | ||
| if (num1.equals(ZERO)) { | ||
| return num2.equals(ZERO) ? ONE : ZERO; | ||
| } | ||
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| return exp(multiply(ln(num1), num2)); | ||
| } | ||
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| /** | ||
| * Computes the principal square root of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the square root of num | ||
| */ | ||
| public static ComplexNumber sqrt(ComplexNumber num) { | ||
| return pow(num, new ComplexNumber(0.5, 0)); | ||
| } | ||
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| /** | ||
| * Computes the sine of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the sine of num | ||
| * @link <a href="https://en.wikipedia.org/wiki/Trigonometric_functions#Relationship_to_exponential_function_">...</a>(Euler's_formula) | ||
| */ | ||
| public static ComplexNumber sin(ComplexNumber num) { | ||
| ComplexNumber exp1 = exp(multiply(num, PLUS_I)); | ||
| ComplexNumber exp2 = exp(multiply(num, MINUS_I)); | ||
| return divide(subtract(exp1, exp2), multiply(new ComplexNumber(2, 0), PLUS_I)); | ||
| } | ||
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| /** | ||
| * Computes the cosine of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the cosine of num | ||
| * @link <a href="https://en.wikipedia.org/wiki/Trigonometric_functions#Relationship_to_exponential_function_">...</a>(Euler's_formula) | ||
| */ | ||
| public static ComplexNumber cos(ComplexNumber num) { | ||
| ComplexNumber exp1 = exp(multiply(num, PLUS_I)); | ||
| ComplexNumber exp2 = exp(multiply(num, MINUS_I)); | ||
| return divide(add(exp1, exp2), TWO); | ||
| } | ||
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| /** | ||
| * Computes the tangent of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the tangent of num | ||
| * @throws RuntimeException if <code>num.real = pi*(n+0.5)</code> | ||
| * @link <a href="https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions">...</a> | ||
| */ | ||
| public static ComplexNumber tan(ComplexNumber num) { | ||
| if (num.REAL % Math.PI == Math.PI / 2) { | ||
| throw new RuntimeException("Cannot take the tan of a number where the real part can be expressed as pi*(n+0.5)"); | ||
| } | ||
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| return divide(sin(num), cos(num)); | ||
| } | ||
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| /** | ||
| * Computes the cotangent of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the cotangent of num | ||
| * @throws RuntimeException if <code>num.real = pi*n</code> | ||
| * @link <a href="https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions">...</a> | ||
| */ | ||
| public static ComplexNumber cot(ComplexNumber num) { | ||
| if (num.REAL % Math.PI == 0) { | ||
| throw new RuntimeException("Cannot take the cot of number with real part dividable by pi"); | ||
| } | ||
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| return divide(cos(num), sin(num)); | ||
| } | ||
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| /** | ||
| * Computes the arcsine of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the arcsine of num | ||
| * @link <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_the_complex_plane">...</a> | ||
| */ | ||
| public static ComplexNumber arcsin(ComplexNumber num) { | ||
| ComplexNumber temp = sqrt(subtract(ONE, multiply(num, num))); | ||
| return multiply(MINUS_I, ln(add(multiply(PLUS_I, num), temp))); | ||
| } | ||
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| /** | ||
| * Computes the arccosine of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the arccosine of num | ||
| * @link <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_the_complex_plane">...</a> | ||
| */ | ||
| public static ComplexNumber arccos(ComplexNumber num) { | ||
| ComplexNumber temp = sqrt(subtract(ONE, multiply(num, num))); | ||
| return multiply(MINUS_I, ln(add(num, multiply(temp, PLUS_I)))); | ||
| } | ||
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| /** | ||
| * Computes the arctangent of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the arctangent of num | ||
| * @throws RuntimeException if <code>num=i</code> or <code>num=-i</code> | ||
| * @link <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_the_complex_plane">...</a> | ||
| */ | ||
| public static ComplexNumber arctan(ComplexNumber num) { | ||
| if (num.equals(PLUS_I) || num.equals(MINUS_I)) { | ||
| throw new RuntimeException("Cannot take the arctan of " + num); | ||
| } | ||
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| return multiply(divide(MINUS_I, TWO), ln(divide(subtract(PLUS_I, num), add(PLUS_I, num)))); | ||
| } | ||
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| /** | ||
| * Computes the arccotangent of a complex number. | ||
| * | ||
| * @param num the complex number | ||
| * @return the arccotangent of num | ||
| * @throws RuntimeException if <code>num=i</code> or <code>num=-i</code> | ||
| * @link <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_the_complex_plane">...</a> | ||
| */ | ||
| public static ComplexNumber arccot(ComplexNumber num) { | ||
| if (num.equals(PLUS_I) || num.equals(MINUS_I)) { | ||
| throw new RuntimeException("Cannot take the arccot of " + num); | ||
| } | ||
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| return multiply(divide(MINUS_I, TWO), ln(divide(add(num, PLUS_I), subtract(num, PLUS_I)))); | ||
| } | ||
| } | ||
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Why did you decide to make it a
staticmethod? In the standard implementation ofComplexaddis an object method.There was a problem hiding this comment.
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I decided to make it a static method for a few reasons:
Uniformity in Code: The file MatrixUtil.java, which is similar to this, uses static methods for the operations.
Ease of Expansion: Creating independent static methods makes it easier to add more advanced operations for complex numbers than integrating additional code into the ComplexNumber class itself.
Clarity: I find it easier to conceptualize operations as direct interactions between two entities, A and B (i.e., how do you add them), rather than how one adds B to A.
These are my reasons, but if you believe it should be an instance method, I would be happy to make that change.
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Making them
staticyou loose all of the object oriented magic. The whole thing could be then simpler, because theComplexNumberUtilwould not be needed. Furthermore, you have marked both of the fieldsREALandIMAGINARYasfinal, so it is pretty clear that theaddmethod will not change them.