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

  • static

    • .FFT

      • new FFT(size)

      • .createComplexArray() ⇒ Float32Array

      • .fromComplexArray(complex, [storage]) ⇒ Array.<number>

      • .toComplexArray(input, [storage]) ⇒ Float32Array

      • .completeSpectrum(spectrum) ⇒ void

      • .transform(out, data) ⇒ void

      • .realTransform(out, data)

      • .inverseTransform(out, data) ⇒ void

      • ._transform4(out, data, inv) ⇒ void

      • ._singleTransform2(data, out, outOff, off, step) ⇒ void

      • ._singleTransform4(data, out, outOff, off, step, inv) ⇒ void

      • ._realTransform4(out, data, inv)

      • ._singleRealTransform2(data, out, outOff, off, step) ⇒ void

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

    • .interpolate_data(input)

    • .transpose_data(array, dims, axes) ⇒ *

    • .softmax(arr) ⇒ Array.<number>

    • .log_softmax(arr) ⇒ any

    • .dot(arr1, arr2) ⇒ number

    • .getTopItems(items, [top_k]) ⇒ Array

    • .cos_sim(arr1, arr2) ⇒ number

    • .magnitude(arr) ⇒ number

    • .min(arr) ⇒ Array.<number>

    • .max(arr) ⇒ Array.<number>

    • .rfftfreq(n, [d]) ⇒ Array.<number>

    • .medianFilter(data, windowSize)

    • .round(num, decimals) ⇒ number

  • inner

    • ~AnyTypedArray : Int8Array | Uint8Array | Uint8ClampedArray | Int16Array | Uint16Array | Int32Array | Uint32Array | Float32Array | Float64Array

---

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

• .FFT

  • new FFT(size)
  • .createComplexArray() ⇒ Float32Array
  • .fromComplexArray(complex, [storage]) ⇒ Array.<number>
  • .toComplexArray(input, [storage]) ⇒ Float32Array
  • .completeSpectrum(spectrum) ⇒ void
  • .transform(out, data) ⇒ void
  • .realTransform(out, data)
  • .inverseTransform(out, data) ⇒ void
  • ._transform4(out, data, inv) ⇒ void
  • ._singleTransform2(data, out, outOff, off, step) ⇒ void
  • ._singleTransform4(data, out, outOff, off, step, inv) ⇒ void
  • ._realTransform4(out, data, inv)
  • ._singleRealTransform2(data, out, outOff, off, step) ⇒ void
  • ._singleRealTransform4(data, out, outOff, off, step, inv)

---

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