Baroque

Make coding with complex numbers more real

Baroque provides a single generic type, Complex, comprising of real and imaginary values of the same numeric type. This could be a Double, Int or a Quantity with units (as provided by Quantitative), or any other type which defines Symbolism typeclass instances.

Features

• provides a generic representation of complex numbers
• extends any numerical type to the complex
• provides many standard complex numerical operations on values
• allows conversion between cartesian and polar forms

Availability

Getting Started

All terms and types are defined in the baroque package, which can be imported with:

import baroque.*

Constructing complex numbers

There are several ways to construct complex numbers. The factory method of specifying real and imaginary part is the most straightforward, for example,

val complex = Complex(3.2, -1.25)

represents the complex number 3.2 - 1.25i.

This is an instance of Complex[Double], since the real and imaginary parts of the number are both Doubles. With Quantitative, we could similarly create a complex quantity, for example,

val complex2 = Complex(3.2*Metre, -1.25*Metre)

which would be a Complex[Quantity[Metres[1]]].

But it is also possible construct a complex number by adding the real part to the imaginary part, where the imaginary part is created by multiplying a real number by i, the imaginary unit value, which is called I in Baroque:

val complex3 = 0.8 + 1.8*I

I further possibility is to specify the complex number in polar form, using the Complex.polar constructor. This takes two parameter, magnitude and argument. The magnitude should have the same type a the real and imaginary parts of the number, and the argument must be a Double, in radians. For example,

val complex4 = Complex.polar(12*Kilo(Gram), 0.3845)

Operations with Complex Numbers

Standard arithmetic operations between Complex instances, using the +, -, * and / operators work intuitively. Additionally, the prefix ~ operator can be used to find the complex conjugate of a number.

The methods modulus and argument on Complex values provide, predictably, the modulus and argument. And sqrt will yield one of the two square roots of a Complex number; the other will be its negation.

These operations are defined, in general, so long as the necessary operations (such as addition, multiplication and square root) are defined on the underlying type of the real and imaginary parts.

Status

Baroque is classified as embryotic. For reference, Soundness projects are categorized into one of the following five stability levels:

• embryonic: for experimental or demonstrative purposes only, without any guarantees of longevity
• fledgling: of proven utility, seeking contributions, but liable to significant redesigns
• maturescent: major design decisions broady settled, seeking probatory adoption and refinement
• dependable: production-ready, subject to controlled ongoing maintenance and enhancement; tagged as version 1.0.0 or later
• adamantine: proven, reliable and production-ready, with no further breaking changes ever anticipated

Projects at any stability level, even embryonic projects, can still be used, as long as caution is taken to avoid a mismatch between the project's stability level and the required stability and maintainability of your own project.

Baroque is designed to be small. Its entire source code currently consists of 139 lines of code.

Building

Baroque will ultimately be built by Fury, when it is published. In the meantime, two possibilities are offered, however they are acknowledged to be fragile, inadequately tested, and unsuitable for anything more than experimentation. They are provided only for the necessity of providing some answer to the question, "how can I try Baroque?".

1. Copy the sources into your own project

   Read the fury file in the repository root to understand Baroque's build structure, dependencies and source location; the file format should be short and quite intuitive. Copy the sources into a source directory in your own project, then repeat (recursively) for each of the dependencies.

   The sources are compiled against the latest nightly release of Scala 3. There should be no problem to compile the project together with all of its dependencies in a single compilation.

2. Build with Wrath

   Wrath is a bootstrapping script for building Baroque and other projects in the absence of a fully-featured build tool. It is designed to read the fury file in the project directory, and produce a collection of JAR files which can be added to a classpath, by compiling the project and all of its dependencies, including the Scala compiler itself.

   Download the latest version of wrath, make it executable, and add it to your path, for example by copying it to /usr/local/bin/.

   Clone this repository inside an empty directory, so that the build can safely make clones of repositories it depends on as peers of baroque. Run wrath -F in the repository root. This will download and compile the latest version of Scala, as well as all of Baroque's dependencies.

   If the build was successful, the compiled JAR files can be found in the .wrath/dist directory.

Contributing

Contributors to Baroque are welcome and encouraged. New contributors may like to look for issues marked beginner.

We suggest that all contributors read the Contributing Guide to make the process of contributing to Baroque easier.

Please do not contact project maintainers privately with questions unless there is a good reason to keep them private. While it can be tempting to repsond to such questions, private answers cannot be shared with a wider audience, and it can result in duplication of effort.

Author

Baroque was designed and developed by Jon Pretty, and commercial support and training on all aspects of Scala 3 is available from Propensive OÜ.

Name

Baroque music, architecture and design is characterized by its ornate complexity which alludes to complex numbers.

In general, Soundness project names are always chosen with some rationale, however it is usually frivolous. Each name is chosen for more for its uniqueness and intrigue than its concision or catchiness, and there is no bias towards names with positive or "nice" meanings—since many of the libraries perform some quite unpleasant tasks.

Names should be English words, though many are obscure or archaic, and it should be noted how willingly English adopts foreign words. Names are generally of Greek or Latin origin, and have often arrived in English via a romance language.

Logo

The logo shows an alto clef, used predominantly in music for viola (which features in Baroque music), and also resembles a capital B, the first letter of "Baroque".

License

Baroque is copyright © 2024 Jon Pretty & Propensive OÜ, and is made available under the Apache 2.0 License.