Maths

utils/maths

Helper module for mathematical processing.

These functions and classes are only used internally, meaning an end-user shouldn’t need to access anything here.

utils/maths.FFT

FFT class provides functionality for performing Fast Fourier Transform on arrays Code adapted from https://www.npmjs.com/package/fft.js

Kind: static class of utils/maths

new FFT(size)

Throws:

  • Error FFT size must be a power of two and bigger than 1.

Param
Type
Description

size

number

The size of the input array. Must be a power of two and bigger than 1.

ffT.createComplexArray() ⇒ <code> Float32Array </code>

Create a complex number array with size 2 * size

Kind: instance method of FFT Returns: Float32Array - A complex number array with size 2 * size

ffT.fromComplexArray(complex, [storage]) ⇒ <code> Array. < number > </code>

Converts a complex number representation stored in a Float32Array to an array of real numbers.

Kind: instance method of FFT Returns: Array.<number> - An array of real numbers representing the input complex number representation.

Param
Type
Description

complex

Float32Array

The complex number representation to be converted.

[storage]

Array.<number>

An optional array to store the result in.

ffT.toComplexArray(input, [storage]) ⇒ <code> Float32Array </code>

Convert a real-valued input array to a complex-valued output array.

Kind: instance method of FFT Returns: Float32Array - The complex-valued output array.

Param
Type
Description

input

Float32Array

The real-valued input array.

[storage]

Float32Array

Optional buffer to store the output array.

ffT.completeSpectrum(spectrum) ⇒ <code> void </code>

Completes the spectrum by adding its mirrored negative frequency components.

Kind: instance method of FFT

Param
Type
Description

spectrum

Float32Array

The input spectrum.

ffT.transform(out, data) ⇒ <code> void </code>

Performs a Fast Fourier Transform (FFT) on the given input data and stores the result in the output buffer.

Kind: instance method of FFT Throws:

  • Error Input and output buffers must be different.

Param
Type
Description

out

Float32Array

The output buffer to store the result.

data

Float32Array

The input data to transform.

ffT.realTransform(out, data)

Performs a real-valued forward FFT on the given input buffer and stores the result in the given output buffer. The input buffer must contain real values only, while the output buffer will contain complex values. The input and output buffers must be different.

Kind: instance method of FFT Throws:

  • Error If the input and output buffers are the same.

Param
Type
Description

out

Float32Array

The output buffer.

data

Float32Array

The input buffer containing real values.

ffT.inverseTransform(out, data) ⇒ <code> void </code>

Performs an inverse FFT transformation on the given data array, and stores the result in out. The out array must be a different buffer than the data array. The out array will contain the result of the transformation. The data array will not be modified.

Kind: instance method of FFT Throws:

  • Error If `out` and `data` refer to the same buffer.

Param
Type
Description

out

Float32Array

The output buffer for the transformed data.

data

Float32Array

The input data to transform.

ffT._transform4(out, data, inv) ⇒ <code> void </code>

Performs a radix-4 implementation of a discrete Fourier transform on a given set of data.

Kind: instance method of FFT

Param
Type
Description

out

Float32Array

The output buffer for the transformed data.

data

Float32Array

The input buffer of data to be transformed.

inv

number

A scaling factor to apply to the transform.

ffT._singleTransform2(data, out, outOff, off, step) ⇒ <code> void </code>

Performs a radix-2 implementation of a discrete Fourier transform on a given set of data.

Kind: instance method of FFT

Param
Type
Description

data

Float32Array

The input buffer of data to be transformed.

out

Float32Array

The output buffer for the transformed data.

outOff

number

The offset at which to write the output data.

off

number

The offset at which to begin reading the input data.

step

number

The step size for indexing the input data.

ffT._singleTransform4(data, out, outOff, off, step, inv) ⇒ <code> void </code>

Performs radix-4 transformation on input data of length 8

Kind: instance method of FFT

Param
Type
Description

data

Float32Array

Input data array of length 8

out

Float32Array

Output data array of length 8

outOff

number

Index of output array to start writing from

off

number

Index of input array to start reading from

step

number

Step size between elements in input array

inv

number

Scaling factor for inverse transform

ffT._realTransform4(out, data, inv)

Real input radix-4 implementation

Kind: instance method of FFT

Param
Type
Description

out

Float32Array

Output array for the transformed data

data

Float32Array

Input array of real data to be transformed

inv

number

The scale factor used to normalize the inverse transform

ffT._singleRealTransform2(data, out, outOff, off, step) ⇒ <code> void </code>

Performs a single real input radix-2 transformation on the provided data

Kind: instance method of FFT

Param
Type
Description

data

Float32Array

The input data array

out

Float32Array

The output data array

outOff

number

The output offset

off

number

The input offset

step

number

The step

ffT._singleRealTransform4(data, out, outOff, off, step, inv)

Computes a single real-valued transform using radix-4 algorithm. This method is only called for len=8.

Kind: instance method of FFT

Param
Type
Description

data

Float32Array

The input data array.

out

Float32Array

The output data array.

outOff

number

The offset into the output array.

off

number

The offset into the input array.

step

number

The step size for the input array.

inv

number

The value of inverse.

utils/maths.interpolate_data(input)

Kind: static method of utils/maths

Param
Type

input

TypedArray

utils/maths.transpose_data(array, dims, axes) ⇒ <code> * </code>

Helper method to transpose a AnyTypedArray directly

Kind: static method of utils/maths Returns: * - The transposed array and the new shape.

Param
Type

array

T

dims

Array.<number>

axes

Array.<number>

utils/maths.softmax(arr) ⇒ <code> Array. < number > </code>

Compute the softmax of an array of numbers.

Kind: static method of utils/maths Returns: Array.<number> - The softmax array.

Param
Type
Description

arr

Array.<number>

The array of numbers to compute the softmax of.

utils/maths.log_softmax(arr) ⇒ <code> any </code>

Calculates the logarithm of the softmax function for the input array.

Kind: static method of utils/maths Returns: any - The resulting log_softmax array.

Param
Type
Description

arr

Array.<number>

The input array to calculate the log_softmax function for.

utils/maths.dot(arr1, arr2) ⇒ <code> number </code>

Calculates the dot product of two arrays.

Kind: static method of utils/maths Returns: number - The dot product of arr1 and arr2.

Param
Type
Description

arr1

Array.<number>

The first array.

arr2

Array.<number>

The second array.

utils/maths.getTopItems(items, [top_k]) ⇒ <code> Array </code>

Get the top k items from an iterable, sorted by descending order

Kind: static method of utils/maths Returns: Array - The top k items, sorted by descending order

Param
Type
Default
Description

items

Array

The items to be sorted

[top_k]

number

0

The number of top items to return (default: 0 = return all)

utils/maths.cos_sim(arr1, arr2) ⇒ <code> number </code>

Computes the cosine similarity between two arrays.

Kind: static method of utils/maths Returns: number - The cosine similarity between the two arrays.

Param
Type
Description

arr1

Array.<number>

The first array.

arr2

Array.<number>

The second array.

utils/maths.magnitude(arr) ⇒ <code> number </code>

Calculates the magnitude of a given array.

Kind: static method of utils/maths Returns: number - The magnitude of the array.

Param
Type
Description

arr

Array.<number>

The array to calculate the magnitude of.

utils/maths.min(arr) ⇒ <code> Array. < number > </code>

Returns the value and index of the minimum element in an array.

Kind: static method of utils/maths Returns: Array.<number> - the value and index of the minimum element, of the form: [valueOfMin, indexOfMin] Throws:

  • Error If array is empty.

Param
Type
Description

arr

Array.<number>

array of numbers.

utils/maths.max(arr) ⇒ <code> Array. < number > </code>

Returns the value and index of the maximum element in an array.

Kind: static method of utils/maths Returns: Array.<number> - the value and index of the maximum element, of the form: [valueOfMax, indexOfMax] Throws:

  • Error If array is empty.

Param
Type
Description

arr

Array.<number>

array of numbers.

utils/maths.rfftfreq(n, [d]) ⇒ <code> Array. < number > </code>

Return the Discrete Fourier Transform sample frequencies.

Code adapted from https://github.com/numpy/numpy/blob/25908cacd19915bf3ddd659c28be28a41bd97a54/numpy/fft/helper.py#L173-L221 Original Python doc: https://numpy.org/doc/stable/reference/generated/numpy.fft.rfftfreq.html

Kind: static method of utils/maths Returns: Array.<number> - Array of length Math.floor(n / 2) + 1; containing the sample frequencies. Throws:

  • TypeError If n is not an integer.

Param
Type
Default
Description

n

number

Window length

[d]

number

1.0

Sample spacing (inverse of the sampling rate). Defaults to 1.

Example

Copied

rfftfreq(400, 1 / 16000) // (201) [0, 40, 80, 120, 160, 200, ..., 8000]

utils/maths.medianFilter(data, windowSize)

Performs median filter on the provided data. Padding is done by mirroring the data.

Kind: static method of utils/maths

Param
Type
Description

data

AnyTypedArray

The input array

windowSize

number

The window size

utils/maths.round(num, decimals) ⇒ <code> number </code>

Helper function to round a number to a given number of decimals

Kind: static method of utils/maths Returns: number - The rounded number

Param
Type
Description

num

number

The number to round

decimals

number

The number of decimals

utils/maths~AnyTypedArray : <code> Int8Array </code> | <code> Uint8Array </code> | <code> Uint8ClampedArray </code> | <code> Int16Array </code> | <code> Uint16Array </code> | <code> Int32Array </code> | <code> Uint32Array </code> | <code> Float32Array </code> | <code> Float64Array </code>

Kind: inner typedef of utils/maths

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