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0db42306ec
* initial implementation of multidimensional std and var * consolidated std function into var, cleaned up the interface for var, fixed bias correction * added documentation of variable axis for std and var * updated documentation for std and var * changed the order of normalization and dimension for a three parameter input in the functions * updated documentation for var and std * add transform expressions for std and var with variable axis * added test coverage for std and var with a variable axis * update to documentation * change n dim std to use apply function * fixed tests, removed unnecessary code, updated docs * fixed typo in docs * update docs to remove a type * changed location of apply function * updated tests to use deepStrictEqual to pass linter * adding test coverage for var.transform and std.transform
71 lines
2.2 KiB
Markdown
71 lines
2.2 KiB
Markdown
<!-- Note: This file is automatically generated from source code comments. Changes made in this file will be overridden. -->
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# Function std
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Compute the standard deviation of a matrix or a list with values.
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The standard deviations is defined as the square root of the variance:
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`std(A) = sqrt(var(A))`.
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In case of a (multi dimensional) array or matrix, the standard deviation
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over all elements will be calculated by default, unless an axis is specified
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in which case the standard deviation will be computed along that axis.
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Additionally, it is possible to compute the standard deviation along the rows
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or columns of a matrix by specifying the dimension as the second argument.
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Optionally, the type of normalization can be specified as the final
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parameter. The parameter `normalization` can be one of the following values:
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- 'unbiased' (default) The sum of squared errors is divided by (n - 1)
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- 'uncorrected' The sum of squared errors is divided by n
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- 'biased' The sum of squared errors is divided by (n + 1)
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## Syntax
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```js
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math.std(a, b, c, ...)
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math.std(A)
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math.std(A, normalization)
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math.std(A, dimension)
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math.std(A, dimension, normalization)
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```
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### Parameters
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Parameter | Type | Description
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--------- | ---- | -----------
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`array` | Array | Matrix | A single matrix or or multiple scalar values
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`normalization` | string | Determines how to normalize the variance. Choose 'unbiased' (default), 'uncorrected', or 'biased'. Default value: 'unbiased'.
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### Returns
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Type | Description
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---- | -----------
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* | The standard deviation
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## Examples
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```js
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math.std(2, 4, 6) // returns 2
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math.std([2, 4, 6, 8]) // returns 2.581988897471611
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math.std([2, 4, 6, 8], 'uncorrected') // returns 2.23606797749979
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math.std([2, 4, 6, 8], 'biased') // returns 2
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math.std([[1, 2, 3], [4, 5, 6]]) // returns 1.8708286933869707
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math.std([[1, 2, 3], [4, 6, 8]], 0) // returns [2.1213203435596424, 2.8284271247461903, 3.5355339059327378]
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math.std([[1, 2, 3], [4, 6, 8]], 1) // returns [1, 2]
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math.std([[1, 2, 3], [4, 6, 8]], 1, 'biased') // returns [0.7071067811865476, 1.4142135623730951]
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```
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## See also
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[mean](mean.md),
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[median](median.md),
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[max](max.md),
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[min](min.md),
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[prod](prod.md),
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[sum](sum.md),
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[var](var.md)
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