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Moved improved ‘Inventory’ back into README

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Vincent Esche 2019-08-30 00:47:06 +02:00
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@ -74,10 +74,6 @@ Then run `carthage update` and use the framework in `Carthage/Build/<platform>`.
---
## Inventory
For a (near-)complete inventory of functions see [INVENTORY.md](./INVENTORY.md).
## Usage
### Computing Sum of `[Double]`
@ -100,6 +96,694 @@ let b = [2.0, 4.0, 6.0, 8.0]
let product = Surge.mul(a, b) // [2.0, 12.0, 30.0, 56.0]
```
---
# Inventory
- [General Arithmetic Operations](#general-arithmetic-operations)
- [Addition](#addition)
- [Subtraction](#subtraction)
- [Multiplication](#multiplication)
- [Element-wise multiplication](#element-wise-multiplication)
- [Division)](#division)
- [Element-wise Division)](#element-wise-division)
- [Modulo](#modulo)
- [Remainder](#remainder)
- [Square Root](#square-root)
- [Summation](#summation)
- [Dot Product](#dot-product)
- [Distance](#distance)
- [Squared Distance](#squared-distance)
- [Power)](#power)
- [Exponential](#exponential)
- [Trigonometric Operations](#trigonometric-operations)
- [Sine/Cosine/Tangent](#sinecosinetangent)
- [Arc Sine/Cosine/Tangent](#arc-sinecosinetangent)
- [Hyperbolic Sine/Cosine/Tangent](#hyperbolic-sinecosinetangent)
- [Inverse Hyperbolic Sine/Cosine/Tangent](#inverse-hyperbolic-sinecosinetangent)
- [Radians ↔︎ Degrees](#radians-%e2%86%94%ef%b8%8e-degrees)
- [Exponential Function](#exponential-function)
- [Logarithm](#logarithm)
- [Statistical Operations](#statistical-operations)
- [Summation](#summation-1)
- [Minimum/Maximum](#minimummaximum)
- [Mean](#mean)
- [Auxiliary Functions](#auxiliary-functions)
- [Rounding Functions](#rounding-functions)
- [Absolute value](#absolute-value)
- [Signum function](#signum-function)
- [Multiplicative inverse](#multiplicative-inverse)
- [Matrix-specific Operations](#matrix-specific-operations)
- [Matrix Inversion](#matrix-inversion)
- [Matrix Transposition](#matrix-transposition)
- [Matrix Determinant](#matrix-determinant)
- [Eigen Decomposition](#eigen-decomposition)
- [DSP-specific Operations](#dsp-specific-operations)
- [Fast Fourier Transform](#fast-fourier-transform)
- [Convolution](#convolution)
- [Cross-Correlation](#cross-correlation)
## General Arithmetic Operations
### [Addition](https://en.wikipedia.org/wiki/Addition)
<details open>
<summary>
Addition functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|------------|--------------|-------------------|
| `(Array, Array)` | `add` | `.+` (infix) | `.+=` (infix) |
| `(Array, Scalar)` | `add` | `+` (infix) | `+=` (infix) |
| `(Matrix, Matrix)` | `add` | `+` (infix) | n/a |
| `(Matrix, Scalar)` | n/a | `+` (infix) | n/a |
| `(Vector, Vector)` | `func add` | `+` (infix) | `+=` (infix) |
| `(Vector, Scalar)` | `func add` | `+` (infix) | `+=` (infix) |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| `addInPlace` |
| `addInPlace` |
| n/a |
| n/a |
| `addInPlace` |
| `addInPlace` |
-->
<!-- FIXME: `add` for `(Array, Array)` should be called `eladd`/`.+`, no? -->
<!-- FIXME: Missing `add` function for `(Matrix, Scalar)`. -->
<!-- FIXME: Missing `add` functions/operators for `(Matrix, Vector)`. -->
<!-- FIXME: Missing `addInPlace` function for `(Matrix, Scalar)` & `(Matrix, Matrix)`. -->
</details>
### [Subtraction](https://en.wikipedia.org/wiki/Subtraction)
<details open>
<summary>
Subtraction functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|----------|--------------|-------------------|
| `(Array, Array)` | `sub` | `.-` (infix) | `.-=` (infix) |
| `(Array, Scalar)` | `sub` | `-` (infix) | `-=` (infix) |
| `(Matrix, Matrix)` | `sub` | `-` (infix) | n/a |
| `(Matrix, Scalar)` | n/a | n/a | n/a |
| `(Vector, Vector)` | `sub` | `-` (infix) | `-=` (infix) |
| `(Vector, Scalar)` | `sub` | `-` (infix) | `-=` (infix) |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| `subInPlace` |
| `subInPlace` |
| n/a |
| n/a |
| `subInPlace` |
| `subInPlace` |
-->
<!-- FIXME: `sub` for `(Array, Array)` should be called `elsub`/`.-`, no? -->
<!-- FIXME: Missing `sub` function/operator for `(Matrix, Scalar)`. -->
<!-- FIXME: Missing `sub` functions/operators for `(Matrix, Vector)`. -->
<!-- FIXME: Missing `subInPlace` function for `(Matrix, Scalar)` & `(Matrix, Matrix)`. -->
</details>
### [Multiplication](https://en.wikipedia.org/wiki/Multiplication)
<details open>
<summary>
Multiplication functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|----------|--------------|-------------------|
| `(Array, Array)` | `mul` | `.*` (infix) | `.*=` (infix) |
| `(Array, Scalar)` | `mul` | `*` (infix) | `*=` (infix) |
| `(Matrix, Matrix)` | `mul` | `*` (infix) | n/a |
| `(Matrix, Vector)` | `mul` | `*` (infix) | n/a |
| `(Matrix, Scalar)` | `mul` | `*` (infix) | n/a |
| `(Vector, Matrix)` | `mul` | `*` (infix) | n/a |
| `(Vector, Scalar)` | `mul` | `*` (infix) | `*=` (infix) |
| `(Scalar, Array)` | `mul` | `*` (infix) | n/a |
| `(Scalar, Matrix)` | `mul` | `*` (infix) | n/a |
| `(Scalar, Vector)` | `mul` | `*` (infix) | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| `mulInPlace` |
| `mulInPlace` |
| n/a |
| n/a |
| n/a |
| n/a |
| `mulInPlace` |
| n/a |
| n/a |
| n/a |
-->
</details>
### [Element-wise multiplication](https://en.wikipedia.org/wiki/Multiplication)
<details open>
<summary>
Element-wise multiplication functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|----------|--------------|-------------------|
| `(Matrix, Matrix)` | `elmul` | n/a | n/a |
| `(Vector, Vector)` | `elmul` | `.*` (infix) | `.*=` (infix) |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
| `elmulInPlace` |
-->
<!-- FIXME: The does not seem to be a `.*` implemented for `(Matrix, Matrix)`. -->
</details>
### [Division](https://en.wikipedia.org/wiki/Division_(mathematics))
<details open>
<summary>
Division functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|----------|--------------|-------------------|
| `(Array, Array)` | `div` | `./` (infix) | `./=` (infix) |
| `(Array, Scalar)` | `div` | `/` (infix) | `/=` (infix) |
| `(Matrix, Matrix)` | `div` | `/` (infix) | n/a |
| `(Matrix, Scalar)` | n/a | `/` (infix) | n/a |
| `(Vector, Scalar)` | `div` | `/` (infix) | `/=` (infix) |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| `divInPlace` |
| `divInPlace` |
| n/a |
| n/a |
| `divInPlace` |
-->
<!-- FIXME: Func `div` of `(Array, Array)` should be called `eldiv`, no? -->
<!-- FIXME: Missing `div` function for `(Matrix, Scalar)`. -->
</details>
### [Element-wise Division](https://en.wikipedia.org/wiki/Division_(mathematics))
<details open>
<summary>
Element-wise multiplication functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|----------|--------------|-------------------|
| `(Vector, Vector)` | `eldiv` | `./` (infix) | `./=` (infix) |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| `eldivInPlace` |
-->
</details>
### [Modulo](https://en.wikipedia.org/wiki/Modulo_operation)
<details open>
<summary>
Modulo functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|-------------------|----------|--------------|-------------------|
| `(Array, Array)` | `mod` | `.%` (infix) | n/a |
| `(Array, Scalar)` | `mod` | `%` (infix) | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
| n/a |
-->
<!-- FIXME: Do we need `mod` functions/operators for `Matrix`? -->
<!-- FIXME: Do we need `mod` functions/operators for `Vector`? -->
</details>
### [Remainder](https://en.wikipedia.org/wiki/Remainder)
<details open>
<summary>
Remainder functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|-------------------|-------------|----------|-------------------|
| `(Array, Array)` | `remainder` | n/a | n/a |
| `(Array, Scalar)` | `remainder` | n/a | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
| n/a |
-->
<!-- FIXME: Do we need `remainder` functions /operators for `Matrix`? -->
<!-- FIXME: Do we need `remainder` functions /operators for `Vector`? -->
</details>
### [Square Root](https://en.wikipedia.org/wiki/Square_root)
<details open>
<summary>
Square root functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|-----------|----------|----------|-------------------|
| `(Array)` | `sqrt` | n/a | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
-->
<!-- FIXME: The seems to be a variant `func sqrt<MI, MO>(_ x: MI, into results: inout MO)` that could be made into a `sqrtInPlace`-->
<!-- FIXME: Do we need `sqrt` functions/operators for `Matrix`? -->
<!-- FIXME: Do we need `sqrt` functions/operators for `Vector`? -->
</details>
### [Summation](https://en.wikipedia.org/wiki/Summation)
<details open>
<summary>
Sum functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|------------|----------|----------|-------------------|
| `(Array)` | `sum` | n/a | n/a |
| `(Matrix)` | `sum` | n/a | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
| n/a |
-->
<!-- FIXME: Do we need `sum` functions/operators for `Vector`? -->
</details>
### [Dot Product](https://en.wikipedia.org/wiki/Dot_product)
<details open>
<summary>
Dot product functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|----------|-------------|-------------------|
| `(Array, Array)` | `dot` | `•` (infix) | n/a |
| `(Vector, Vector)` | `dot` | `•` (infix) | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
| n/a |
-->
<!-- FIXME: Do we need `dot` functions/operators for `Matrix`? -->
</details>
### [Distance](https://en.wikipedia.org/wiki/Euclidean_distance)
<details open>
<summary>
Distance functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|----------|----------|-------------------|
| `(Array, Array)` | `dist` | n/a | n/a |
| `(Vector, Vector)` | `dist` | n/a | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
| n/a |
-->
### [Squared Distance](https://en.wikipedia.org/wiki/Euclidean_distance#Squared_Euclidean_distance)
<details open>
<summary>
Squared distance functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|----------|----------|-------------------|
| `(Array, Array)` | `distSq` | n/a | n/a |
| `(Vector, Vector)` | `distSq` | n/a | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
| n/a |
-->
</details>
### [Power](https://en.wikipedia.org/wiki/Power_(mathematics))
<details open>
<summary>
Power functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|--------------------|----------|--------------|-------------------|
| `(Array, Array)` | `pow` | `**` (infix) | n/a |
| `(Array, Scalar)` | `pow` | `**` (infix) | n/a |
| `(Matrix, Scalar)` | `pow` | `**` (infix) | n/a |
| `(Vector, Vector)` | `pow` | n/a | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
| n/a |
| n/a |
| n/a |
-->
<!-- FIXME: Shouldn't the `pow`/`**` function/operator of `(Array, Array)` be `elpow`/`.**`? -->
<!-- FIXME: Shouldn't the `pow`/`**` function/operator of `(Vector, Vector)` be `elpow`/`.**`? -->
<!-- FIXME: The does not seem to be a corresponding `.**` operator implemented. -->
<!-- FIXME: Do we need `pow` functions/operators for `(Vector, Scalar)`? -->
### [Exponential](https://en.wikipedia.org/wiki/Exponential_function)
<details open>
<summary>
Exponential functions & operators
</summary>
| Arguments | Function | Operator | In-Place Operator |
|------------|----------|----------|-------------------|
| `(Array)` | `exp` | n/a | n/a |
| `(Matrix)` | `exp` | n/a | n/a |
| `(Vector)` | `exp` | n/a | n/a |
<!--
Internal use only:
| In-Place Function |
|-------------------|
| n/a |
| n/a |
| n/a |
-->
</details>
## Trigonometric Operations
<details open>
<summary>
Trigonometric functions & operators
</summary>
### [Sine/Cosine/Tangent](https://en.wikipedia.org/wiki/Trigonometric_functions)
| Arguments | Function | Operation |
|-----------|----------|---------------|
| `(Array)` | `sin` | Sine |
| `(Array)` | `cos` | Cosine |
| `(Array)` | `tan` | Tangent |
| `(Array)` | `sincos` | Sine & Cosine |
### [Arc Sine/Cosine/Tangent](https://en.wikipedia.org/wiki/Trigonometric_functions)
| Arguments | Function | Operation |
|-----------|----------|-------------|
| `(Array)` | `asin` | Arc Sine |
| `(Array)` | `acos` | Arc Cosine |
| `(Array)` | `atan` | Arc Tangent |
### [Hyperbolic Sine/Cosine/Tangent](https://en.wikipedia.org/wiki/Hyperbolic_function)
| Arguments | Function | Operation |
|-----------|----------|--------------------|
| `(Array)` | `sinh` | Hyperbolic Sine |
| `(Array)` | `cosh` | Hyperbolic Cosine |
| `(Array)` | `tanh` | Hyperbolic Tangent |
### [Inverse Hyperbolic Sine/Cosine/Tangent](https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions)
| Arguments | Function | Operation |
|-----------|----------|----------------------------|
| `(Array)` | `asinh` | Inverse Hyperbolic Sine |
| `(Array)` | `acosh` | Inverse Hyperbolic Cosine |
| `(Array)` | `atanh` | Inverse Hyperbolic Tangent |
### [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>