693 lines
21 KiB
Markdown
693 lines
21 KiB
Markdown
# Inventory
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- [Inventory](#inventory)
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- [General Arithmetic Operations](#general-arithmetic-operations)
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- [Addition](#addition)
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- [Subtraction](#subtraction)
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- [Multiplication](#multiplication)
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- [Element-wise multiplication](#element-wise-multiplication)
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- [Division)](#division)
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- [Element-wise Division)](#element-wise-division)
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- [Modulo](#modulo)
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- [Remainder](#remainder)
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- [Square Root](#square-root)
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- [Summation](#summation)
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- [Dot Product](#dot-product)
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- [Distance](#distance)
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- [Squared Distance](#squared-distance)
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- [Power)](#power)
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- [Exponential](#exponential)
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- [Trigonometric Operations](#trigonometric-operations)
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- [Sine/Cosine/Tangent](#sinecosinetangent)
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- [Arc Sine/Cosine/Tangent](#arc-sinecosinetangent)
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- [Hyperbolic Sine/Cosine/Tangent](#hyperbolic-sinecosinetangent)
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- [Inverse Hyperbolic Sine/Cosine/Tangent](#inverse-hyperbolic-sinecosinetangent)
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- [Radians ↔︎ Degrees](#radians-%e2%86%94%ef%b8%8e-degrees)
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- [Exponential Function](#exponential-function)
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- [Logarithm](#logarithm)
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- [Statistical Operations](#statistical-operations)
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- [Summation](#summation-1)
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- [Minimum/Maximum](#minimummaximum)
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- [Mean](#mean)
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- [Auxiliary Functions](#auxiliary-functions)
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- [Rounding Functions](#rounding-functions)
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- [Absolute value](#absolute-value)
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- [Signum function](#signum-function)
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- [Multiplicative inverse](#multiplicative-inverse)
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- [Matrix-specific Operations](#matrix-specific-operations)
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- [Matrix Inversion](#matrix-inversion)
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- [Matrix Transposition](#matrix-transposition)
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- [Matrix Determinant](#matrix-determinant)
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- [Eigen Decomposition](#eigen-decomposition)
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- [DSP-specific Operations](#dsp-specific-operations)
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- [Fast Fourier Transform](#fast-fourier-transform)
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- [Convolution](#convolution)
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- [Cross-Correlation](#cross-correlation)
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## General Arithmetic Operations
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### [Addition](https://en.wikipedia.org/wiki/Addition)
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<details open>
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<summary>
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Addition functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|------------|--------------|-------------------|
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| `(Array, Array)` | `add` | `.+` (infix) | `.+=` (infix) |
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| `(Array, Scalar)` | `add` | `+` (infix) | `+=` (infix) |
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| `(Matrix, Matrix)` | `add` | `+` (infix) | n/a |
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| `(Matrix, Scalar)` | n/a | `+` (infix) | n/a |
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| `(Vector, Vector)` | `func add` | `+` (infix) | `+=` (infix) |
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| `(Vector, Scalar)` | `func add` | `+` (infix) | `+=` (infix) |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| `addInPlace` |
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| `addInPlace` |
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| n/a |
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| n/a |
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| `addInPlace` |
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| `addInPlace` |
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-->
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<!-- FIXME: `add` for `(Array, Array)` should be called `eladd`/`.+`, no? -->
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<!-- FIXME: Missing `add` function for `(Matrix, Scalar)`. -->
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<!-- FIXME: Missing `add` functions/operators for `(Matrix, Vector)`. -->
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<!-- FIXME: Missing `addInPlace` function for `(Matrix, Scalar)` & `(Matrix, Matrix)`. -->
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</details>
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### [Subtraction](https://en.wikipedia.org/wiki/Subtraction)
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<details open>
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<summary>
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Subtraction functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|----------|--------------|-------------------|
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| `(Array, Array)` | `sub` | `.-` (infix) | `.-=` (infix) |
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| `(Array, Scalar)` | `sub` | `-` (infix) | `-=` (infix) |
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| `(Matrix, Matrix)` | `sub` | `-` (infix) | n/a |
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| `(Matrix, Scalar)` | n/a | n/a | n/a |
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| `(Vector, Vector)` | `sub` | `-` (infix) | `-=` (infix) |
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| `(Vector, Scalar)` | `sub` | `-` (infix) | `-=` (infix) |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| `subInPlace` |
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| `subInPlace` |
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| n/a |
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| n/a |
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| `subInPlace` |
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| `subInPlace` |
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-->
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<!-- FIXME: `sub` for `(Array, Array)` should be called `elsub`/`.-`, no? -->
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<!-- FIXME: Missing `sub` function/operator for `(Matrix, Scalar)`. -->
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<!-- FIXME: Missing `sub` functions/operators for `(Matrix, Vector)`. -->
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<!-- FIXME: Missing `subInPlace` function for `(Matrix, Scalar)` & `(Matrix, Matrix)`. -->
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</details>
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### [Multiplication](https://en.wikipedia.org/wiki/Multiplication)
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<details open>
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<summary>
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Multiplication functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|----------|--------------|-------------------|
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| `(Array, Array)` | `mul` | `.*` (infix) | `.*=` (infix) |
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| `(Array, Scalar)` | `mul` | `*` (infix) | `*=` (infix) |
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| `(Matrix, Matrix)` | `mul` | `*` (infix) | n/a |
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| `(Matrix, Vector)` | `mul` | `*` (infix) | n/a |
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| `(Matrix, Scalar)` | `mul` | `*` (infix) | n/a |
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| `(Vector, Matrix)` | `mul` | `*` (infix) | n/a |
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| `(Vector, Scalar)` | `mul` | `*` (infix) | `*=` (infix) |
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| `(Scalar, Array)` | `mul` | `*` (infix) | n/a |
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| `(Scalar, Matrix)` | `mul` | `*` (infix) | n/a |
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| `(Scalar, Vector)` | `mul` | `*` (infix) | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| `mulInPlace` |
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| `mulInPlace` |
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| n/a |
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| n/a |
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| n/a |
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| `mulInPlace` |
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| n/a |
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-->
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</details>
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### [Element-wise multiplication](https://en.wikipedia.org/wiki/Multiplication)
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<details open>
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<summary>
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Element-wise multiplication functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|----------|--------------|-------------------|
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| `(Matrix, Matrix)` | `elmul` | n/a | n/a |
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| `(Vector, Vector)` | `elmul` | `.*` (infix) | `.*=` (infix) |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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| `elmulInPlace` |
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-->
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<!-- FIXME: The does not seem to be a `.*` implemented for `(Matrix, Matrix)`. -->
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</details>
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### [Division](https://en.wikipedia.org/wiki/Division_(mathematics))
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<details open>
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<summary>
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Division functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|----------|--------------|-------------------|
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| `(Array, Array)` | `div` | `./` (infix) | `./=` (infix) |
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| `(Array, Scalar)` | `div` | `/` (infix) | `/=` (infix) |
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| `(Matrix, Matrix)` | `div` | `/` (infix) | n/a |
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| `(Matrix, Scalar)` | n/a | `/` (infix) | n/a |
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| `(Vector, Scalar)` | `div` | `/` (infix) | `/=` (infix) |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| `divInPlace` |
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| `divInPlace` |
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| n/a |
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| n/a |
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| `divInPlace` |
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-->
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<!-- FIXME: Func `div` of `(Array, Array)` should be called `eldiv`, no? -->
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<!-- FIXME: Missing `div` function for `(Matrix, Scalar)`. -->
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</details>
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### [Element-wise Division](https://en.wikipedia.org/wiki/Division_(mathematics))
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<details open>
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<summary>
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Element-wise multiplication functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|----------|--------------|-------------------|
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| `(Vector, Vector)` | `eldiv` | `./` (infix) | `./=` (infix) |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| `eldivInPlace` |
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-->
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</details>
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### [Modulo](https://en.wikipedia.org/wiki/Modulo_operation)
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<details open>
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<summary>
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Modulo functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|-------------------|----------|--------------|-------------------|
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| `(Array, Array)` | `mod` | `.%` (infix) | n/a |
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| `(Array, Scalar)` | `mod` | `%` (infix) | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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-->
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<!-- FIXME: Do we need `mod` functions/operators for `Matrix`? -->
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<!-- FIXME: Do we need `mod` functions/operators for `Vector`? -->
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</details>
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### [Remainder](https://en.wikipedia.org/wiki/Remainder)
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<details open>
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<summary>
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Remainder functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|-------------------|-------------|----------|-------------------|
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| `(Array, Array)` | `remainder` | n/a | n/a |
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| `(Array, Scalar)` | `remainder` | n/a | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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| n/a |
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-->
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<!-- FIXME: Do we need `remainder` functions /operators for `Matrix`? -->
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<!-- FIXME: Do we need `remainder` functions /operators for `Vector`? -->
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</details>
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### [Square Root](https://en.wikipedia.org/wiki/Square_root)
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<details open>
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<summary>
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Square root functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|-----------|----------|----------|-------------------|
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| `(Array)` | `sqrt` | n/a | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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-->
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<!-- FIXME: The seems to be a variant `func sqrt<MI, MO>(_ x: MI, into results: inout MO)` that could be made into a `sqrtInPlace`-->
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<!-- FIXME: Do we need `sqrt` functions/operators for `Matrix`? -->
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<!-- FIXME: Do we need `sqrt` functions/operators for `Vector`? -->
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</details>
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### [Summation](https://en.wikipedia.org/wiki/Summation)
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<details open>
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<summary>
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Sum functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|------------|----------|----------|-------------------|
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| `(Array)` | `sum` | n/a | n/a |
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| `(Matrix)` | `sum` | n/a | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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-->
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<!-- FIXME: Do we need `sum` functions/operators for `Vector`? -->
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</details>
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### [Dot Product](https://en.wikipedia.org/wiki/Dot_product)
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<details open>
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<summary>
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Dot product functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|----------|-------------|-------------------|
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| `(Array, Array)` | `dot` | `•` (infix) | n/a |
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| `(Vector, Vector)` | `dot` | `•` (infix) | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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-->
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<!-- FIXME: Do we need `dot` functions/operators for `Matrix`? -->
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</details>
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### [Distance](https://en.wikipedia.org/wiki/Euclidean_distance)
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<details open>
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<summary>
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Distance functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|----------|----------|-------------------|
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| `(Array, Array)` | `dist` | n/a | n/a |
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| `(Vector, Vector)` | `dist` | n/a | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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-->
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### [Squared Distance](https://en.wikipedia.org/wiki/Euclidean_distance#Squared_Euclidean_distance)
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<details open>
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<summary>
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Squared distance functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|----------|----------|-------------------|
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| `(Array, Array)` | `distSq` | n/a | n/a |
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| `(Vector, Vector)` | `distSq` | n/a | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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| n/a |
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-->
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</details>
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### [Power](https://en.wikipedia.org/wiki/Power_(mathematics))
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<details open>
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<summary>
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Power functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|--------------------|----------|--------------|-------------------|
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| `(Array, Array)` | `pow` | `**` (infix) | n/a |
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| `(Array, Scalar)` | `pow` | `**` (infix) | n/a |
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| `(Matrix, Scalar)` | `pow` | `**` (infix) | n/a |
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| `(Vector, Vector)` | `pow` | n/a | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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| n/a |
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| n/a |
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| n/a |
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-->
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<!-- FIXME: Shouldn't the `pow`/`**` function/operator of `(Array, Array)` be `elpow`/`.**`? -->
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<!-- FIXME: Shouldn't the `pow`/`**` function/operator of `(Vector, Vector)` be `elpow`/`.**`? -->
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<!-- FIXME: The does not seem to be a corresponding `.**` operator implemented. -->
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<!-- FIXME: Do we need `pow` functions/operators for `(Vector, Scalar)`? -->
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### [Exponential](https://en.wikipedia.org/wiki/Exponential_function)
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<details open>
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<summary>
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Exponential functions & operators
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</summary>
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| Arguments | Function | Operator | In-Place Operator |
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|------------|----------|----------|-------------------|
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| `(Array)` | `exp` | n/a | n/a |
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| `(Matrix)` | `exp` | n/a | n/a |
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| `(Vector)` | `exp` | n/a | n/a |
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<!--
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Internal use only:
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| In-Place Function |
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|-------------------|
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| n/a |
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| n/a |
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| n/a |
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-->
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</details>
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## Trigonometric Operations
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<details open>
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<summary>
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Trigonometric functions & operators
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</summary>
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### [Sine/Cosine/Tangent](https://en.wikipedia.org/wiki/Trigonometric_functions)
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| Arguments | Function | Operation |
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|-----------|----------|---------------|
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| `(Array)` | `sin` | Sine |
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| `(Array)` | `cos` | Cosine |
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| `(Array)` | `tan` | Tangent |
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| `(Array)` | `sincos` | Sine & Cosine |
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### [Arc Sine/Cosine/Tangent](https://en.wikipedia.org/wiki/Trigonometric_functions)
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| Arguments | Function | Operation |
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|-----------|----------|-------------|
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| `(Array)` | `asin` | Arc Sine |
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| `(Array)` | `acos` | Arc Cosine |
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| `(Array)` | `atan` | Arc Tangent |
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### [Hyperbolic Sine/Cosine/Tangent](https://en.wikipedia.org/wiki/Hyperbolic_function)
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| Arguments | Function | Operation |
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|-----------|----------|--------------------|
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| `(Array)` | `sinh` | Hyperbolic Sine |
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| `(Array)` | `cosh` | Hyperbolic Cosine |
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| `(Array)` | `tanh` | Hyperbolic Tangent |
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### [Inverse Hyperbolic Sine/Cosine/Tangent](https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions)
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| Arguments | Function | Operation |
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|-----------|----------|----------------------------|
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| `(Array)` | `asinh` | Inverse Hyperbolic Sine |
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| `(Array)` | `acosh` | Inverse Hyperbolic Cosine |
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| `(Array)` | `atanh` | Inverse Hyperbolic Tangent |
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### [Radians ↔︎ Degrees](https://en.wikipedia.org/wiki/Angle#Types_of_angles)
|
||
|
||
| Arguments | Function | Operation |
|
||
|-----------|-----------|------------------------------------------------------------------------------------------------------------|
|
||
| `(Array)` | `rad2deg` | [Radians](https://en.wikipedia.org/wiki/Radian) to [Degrees](https://en.wikipedia.org/wiki/Degree_(angle)) |
|
||
| `(Array)` | `deg2rad` | [Degrees](https://en.wikipedia.org/wiki/Degree_(angle)) to [Radians](https://en.wikipedia.org/wiki/Radian) |
|
||
|
||
</details>
|
||
|
||
## [Exponential Function](https://en.wikipedia.org/wiki/Exponential_function)
|
||
|
||
<details open>
|
||
|
||
<summary>
|
||
Exponential functions & operators
|
||
</summary>
|
||
|
||
| Arguments | Function | Operation |
|
||
|-----------|----------|-----------------------------|
|
||
| `(Array)` | `exp` | Base-e Exponential Function |
|
||
| `(Array)` | `exp2` | Base-2 Exponential Function |
|
||
|
||
</details>
|
||
|
||
## [Logarithm](https://en.wikipedia.org/wiki/Logarithm)
|
||
|
||
<details open>
|
||
|
||
<summary>
|
||
Exponential functions & operators
|
||
</summary>
|
||
|
||
| Arguments | Function | Operation |
|
||
|-----------|----------|-------------------|
|
||
| `(Array)` | `log` | Base-e Logarithm |
|
||
| `(Array)` | `log2` | Base-2 Logarithm |
|
||
| `(Array)` | `log10` | Base-10 Logarithm |
|
||
| `(Array)` | `logb` | Base-b Logarithm |
|
||
|
||
</details>
|
||
|
||
## Statistical Operations
|
||
|
||
<details open>
|
||
|
||
<summary>
|
||
Statistical functions & operators
|
||
</summary>
|
||
|
||
### [Summation](https://en.wikipedia.org/wiki/Summation)
|
||
|
||
| Arguments | Function | Operation |
|
||
|-----------|----------|--------------------|
|
||
| `(Array)` | `sum` | Summation |
|
||
| `(Array)` | `asum` | Absolute Summation |
|
||
|
||
### [Minimum/Maximum](https://en.wikipedia.org/wiki/Maximal_and_minimal_elements)
|
||
|
||
| Arguments | Function | Operation |
|
||
|-----------|----------|-----------|
|
||
| `(Array)` | `min` | Minimum |
|
||
| `(Array)` | `max` | Maximum |
|
||
|
||
### [Mean](https://en.wikipedia.org/wiki/Mean)
|
||
|
||
| Arguments | Function | Operation |
|
||
|-----------|----------|--------------------------------------------------------------|
|
||
| `(Array)` | `mean` | [Mean](https://en.wikipedia.org/wiki/Mean) |
|
||
| `(Array)` | `meamg` | Mean of Magnitudes |
|
||
| `(Array)` | `measq` | [Mean of squares](https://en.wikipedia.org/wiki/Mean_square) |
|
||
|
||
</details>
|
||
|
||
## Auxiliary Functions
|
||
|
||
<details open>
|
||
|
||
<summary>
|
||
Auxiliary functions & operators
|
||
</summary>
|
||
|
||
### [Rounding Functions](https://en.wikipedia.org/wiki/Rounding)
|
||
|
||
| Arguments | Function | Operation |
|
||
|-----------|----------|-----------------------------------------------------------------------|
|
||
| `(Array)` | `ceil` | [Ceiling](https://en.wikipedia.org/wiki/Floor_and_ceiling_functions) |
|
||
| `(Array)` | `floor` | [Flooring](https://en.wikipedia.org/wiki/Floor_and_ceiling_functions) |
|
||
| `(Array)` | `round` | [Rounding](https://en.wikipedia.org/wiki/Rounding) |
|
||
| `(Array)` | `trunc` | [Integer truncation](https://en.wikipedia.org/wiki/Truncation) |
|
||
|
||
### [Absolute value](https://en.wikipedia.org/wiki/Absolute_value)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|-----------|----------|-------------------|----------|-------------------|
|
||
| `(Array)` | `abs` | n/a | n/a | n/a |
|
||
|
||
### [Signum function](https://en.wikipedia.org/wiki/Sign_function)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|-----------|------------|-------------------|----------|-------------------|
|
||
| `(Array)` | `copysign` | n/a | n/a | n/a |
|
||
|
||
### [Multiplicative inverse](https://en.wikipedia.org/wiki/Multiplicative_inverse)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|-----------|----------|-------------------|----------|-------------------|
|
||
| `(Array)` | `rec` | n/a | n/a | n/a |
|
||
|
||
</details>
|
||
|
||
## Matrix-specific Operations
|
||
|
||
<details open>
|
||
|
||
<summary>
|
||
Matrix-specific functions & operators
|
||
</summary>
|
||
|
||
### [Matrix Inversion](https://en.wikipedia.org/wiki/Invertible_matrix)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|------------|----------|-------------------|----------|-------------------|
|
||
| `(Matrix)` | `inv` | n/a | n/a | n/a |
|
||
|
||
### [Matrix Transposition](https://en.wikipedia.org/wiki/Matrix_transpose)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|------------|-------------|-------------------|---------------|-------------------|
|
||
| `(Matrix)` | `transpose` | n/a | `′` (postfix) | n/a |
|
||
|
||
### [Matrix Determinant](https://en.wikipedia.org/wiki/Matrix_determinant)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|------------|----------|-------------------|----------|-------------------|
|
||
| `(Matrix)` | `det` | n/a | n/a | n/a |
|
||
|
||
### [Eigen Decomposition](https://en.wikipedia.org/wiki/Eigen_decomposition)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|------------|------------------|-------------------|----------|-------------------|
|
||
| `(Matrix)` | `eigenDecompose` | n/a | n/a | n/a |
|
||
|
||
</details>
|
||
|
||
## DSP-specific Operations
|
||
|
||
<details open>
|
||
|
||
<summary>
|
||
Fast fourier transform functions & operators
|
||
</summary>
|
||
|
||
### [Fast Fourier Transform](https://en.wikipedia.org/wiki/Convolution)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|-----------|----------|-------------------|----------|-------------------|
|
||
| `(Array)` | `fft` | n/a | n/a | n/a |
|
||
|
||
### [Convolution](https://en.wikipedia.org/wiki/Convolution)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|------------------|----------|-------------------|----------|-------------------|
|
||
| `(Array, Array)` | `conv` | n/a | n/a | n/a |
|
||
|
||
### [Cross-Correlation](https://en.wikipedia.org/wiki/Cross-correlation)
|
||
|
||
| Arguments | Function | In-Place Function | Operator | In-Place Operator |
|
||
|------------------|----------|-------------------|----------|-------------------|
|
||
| `(Array, Array)` | `xcorr` | n/a | n/a | n/a |
|
||
| `(Array)` | `xcorr` | n/a | n/a | n/a |
|
||
|
||
</details>
|