CmplxLib

A Scala library for complex numbers, complex vectors, and complex matrices.

Project goals

CmplxLib is an extension of VecMatLib adding complex numbers, complex vectors, and complex matrices.

Vectors and matrices structures are written in Scala to make the best use possible of Scala's operator overloading. All methods with symbolic names have an alias for better interoperability with java.

All operations in CmplxLib are designed to not modify the object on which the operation is invoked to respect the principles of purity and immutability of functional programming.

Complex numbers

The Complex class is the cartesian representation of a complex number in cartesian coordinates in the form a + ib, where a is the real part and b is the imaginary part.

Complex numbers use two double-precision floating point numbers.

Scala example:

val z = Complex(2.0, 1.0) // 2 + i
val w = Complex.I // The imaginary unit

val sum = z + w // Result: 2 + 2i

val product = z * (1.0, 1.0) // (2 + i) * (1 + i) = 1 + 3i

Java example:

Complex z = new Complex(2.0, 1.0); // 2 + i
Complex w = Complex.I; // The imaginary unit

Complex sum = z.plus(w); // Result: 2 + 2i

Complex product = z.multiply(1.0, 1.0); // (2 + i) * (1 + i) = 1 + 3i

In Scala, complex numbers can also be expressed in their cartesian form using the constant I.

import io.github.scalamath.cmplxlib.Complex.I

val z = 3.0 + 2.0 * I // Equivalent to Complex(3.0, 2.0)
val w = z + 3.0 // Results in 6 + 2i

Vectors and matrices

The vector and matrix packages offer 2-dimensional, 3-dimensional, and 4-dimensional complex vectors, as well as 2x2, 3x3, and 4x4 complex matrices.

They offer the same operations as real vectors and matrices, with the additional operations involving complex numbers.

Scala example:

import io.github.scalamath.cmplxlib.Complex.I

val vector = Vec2c(1.0 + 2.0 * I, 2.0 + 1.0 * I)
val conjugate = vector.conjugate // (1 - 2i, 2 - i)

val matrix = Mat2c(
  1.0 + 2.0 * I, 1.5 + 1.0 * I,
  0.5 + 1.5 * I, 3.0 + 2.0 * I
)

val product = matrix * vector

Java example:

Vec2c vector = new Vec2c(new Complex(1.0, 2.0), new Complex(2.0, 1.0)); // [1 + 2i, 2 + i]
Vec2c conjugate = vector.conjugate(); // [1 - 2i, 2 - i]

Mat2c matrix = new Mat2c(
  new Complex(1.0, 2.0), new Complex(1.5, 1.0),
  new Complex(0.5, 1.5), new Complex(3.0, 2.0)
);

Vec2c product = matrix.multiply(vector);

Multithreading

Due to VecMatLib not using any internal or temporal objects during any computations, neither modifying objects on which operations are called, it can be used safely in a multithreaded application.

Add CmplxLib to your project

sbt

libraryDependencies += "io.github.scalamath" % "cmplxlib" % "2.0"

Maven

<dependency>
    <groupId>io.github.scalamath</groupId>
    <artifactId>cmplxlib</artifactId>
    <version>2.0</version>
</dependency>

Gradle

implementation 'io.github.scalamath:cmplxlib:2.0'

Questions and answers

Q: Why does CmplxLib not use scala 3?

A: One of the design goals of CmplxLib is to be usable both in Scala and Java. Support for Scala 3 in IDEs is still actively being developed, therefore a Scala 3 library may not be suitable to work with.

Q: Why are complex vectors and matrices not included in VecMatLib?

A: There may be applications where complex numbers are not necessary, therefore in that case one can depend on VecMatLib without having to include an unnecessary dependency for complex numbers.

Contributing

CmplxLib was developed by a single person as an extension of VecMatLib.

Your contributions are always welcome! Please submit a pull request or open an issue if you want to contribute with bug fixes, code improvements, documentation, and better unit test coverage.

Support

Support the project with a donation:

• PayPal
• Ko-fi