numojo.routines.statistics.averages

Averages and dispersion routines for NuMojo (numojo.routines.statistics.averages).

Implements mean, median, mode, variance, and standard deviation helpers for NDArrays and Matrices.

Functions

mean_1d

mean_1d[dtype: DType, //, returned_dtype: DType = DType.float64](a: NDArray[dtype]) -> Scalar[returned_dtype]

Calculate the arithmetic average of all items in an array. Regardless of the shape of input, it is treated as a 1-d array. It is the backend function for mean, with or without axis.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• a (NDArray): A 1-d array.

Returns:

• Scalar

Raises

mean

Overload 1

mean[dtype: DType, //, returned_dtype: DType = DType.float64](a: NDArray[dtype]) -> Scalar[returned_dtype]

Calculate the arithmetic average of all items in the array.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• a (NDArray): NDArray.

Returns:

• Scalar

Raises

Overload 2

mean[dtype: DType, //, returned_dtype: DType = DType.float64](a: NDArray[dtype], axis: Int) -> NDArray[returned_dtype]

Mean of array elements over a given axis.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• a (NDArray): NDArray.
• axis (Int): The axis along which the mean is performed.

Returns:

• NDArray

Raises

Overload 3

mean[dtype: DType, //, returned_dtype: DType = DType.float64](a: Matrix[dtype]) -> Scalar[returned_dtype]

Calculate the arithmetic average of all items in the Matrix.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• a (Matrix): A matrix.

Returns:

• Scalar

Overload 4

mean[dtype: DType, //, returned_dtype: DType = DType.float64](a: Matrix[dtype], axis: Int) -> Matrix[returned_dtype]

Calculate the arithmetic average of a Matrix along the axis.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• a (Matrix): A matrix.
• axis (Int): The axis along which the mean is performed.

Returns:

• Matrix

Raises

median_1d

median_1d[dtype: DType, //, returned_dtype: DType = DType.float64](a: NDArray[dtype]) -> Scalar[returned_dtype]

Median value of all items an array. Regardless of the shape of input, it is treated as a 1-d array.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• a (NDArray): A 1-d array.

Returns:

• Scalar

Raises

median

Overload 1

median[dtype: DType, //, returned_dtype: DType = DType.float64](a: NDArray[dtype]) -> Scalar[returned_dtype]

Median value of all items of an array.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• a (NDArray): A 1-d array.

Returns:

• Scalar

Raises

Overload 2

median[dtype: DType, //, returned_dtype: DType = DType.float64](a: NDArray[dtype], axis: Int) -> NDArray[returned_dtype]

Returns median of the array elements along the given axis.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• a (NDArray): An array.
• axis (Int): The axis along which the median is performed.

Returns:

• NDArray

Raises

mode_1d

mode_1d[dtype: DType](a: NDArray[dtype]) -> Scalar[dtype]

Returns mode of all items of an array. Regardless of the shape of input, it is treated as a 1-d array.

Parameters:

• dtype (DType): The element type.

Args:

• a (NDArray): An NDArray.

Returns:

• Scalar

Raises

mode

Overload 1

mode[dtype: DType](array: NDArray[dtype]) -> Scalar[dtype]

Mode of all items of an array.

Parameters:

• dtype (DType): The element type.

Args:

• array (NDArray): An NDArray.

Returns:

• Scalar

Raises

Overload 2

mode[dtype: DType](a: NDArray[dtype], axis: Int) -> NDArray[dtype]

Returns mode of the array elements along the given axis.

Parameters:

• dtype (DType): The element type.

Args:

• a (NDArray): An NDArray.
• axis (Int): The axis along which the mode is performed.

Returns:

• NDArray

Raises

std

Overload 1

std[dtype: DType, //, returned_dtype: DType = DType.float64](A: NDArray[dtype], ddof: Int = 0) -> Scalar[returned_dtype]

Compute the standard deviation.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• A (NDArray): An array.
• ddof (Int): Delta degree of freedom.

Returns:

• Scalar

Raises

Overload 2

std[dtype: DType, //, returned_dtype: DType = DType.float64](A: NDArray[dtype], axis: Int, ddof: Int = 0) -> NDArray[returned_dtype]

Computes the standard deviation along the axis.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• A (NDArray): An array.
• axis (Int): The axis along which the mean is performed.
• ddof (Int): Delta degree of freedom.

Returns:

• NDArray

Raises

Error: If the axis is out of bounds.

Error: If ddof is not smaller than the size of the axis.

Overload 3

std[dtype: DType, //, returned_dtype: DType = DType.float64](A: Matrix[dtype], ddof: Int = 0) -> Scalar[returned_dtype]

Compute the standard deviation.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• A (Matrix): Matrix.
• ddof (Int): Delta degree of freedom.

Returns:

• Scalar

Raises

Overload 4

std[dtype: DType, //, returned_dtype: DType = DType.float64](A: Matrix[dtype], axis: Int, ddof: Int = 0) -> Matrix[returned_dtype]

Compute the standard deviation along axis.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• A (Matrix): Matrix.
• axis (Int): 0 or 1.
• ddof (Int): Delta degree of freedom.

Returns:

• Matrix

Raises

variance

Overload 1

variance[dtype: DType, //, returned_dtype: DType = DType.float64](A: NDArray[dtype], ddof: Int = 0) -> Scalar[returned_dtype]

Compute the variance.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• A (NDArray): An array.
• ddof (Int): Delta degree of freedom.

Returns:

• Scalar

Raises

Overload 2

variance[dtype: DType, //, returned_dtype: DType = DType.float64](A: NDArray[dtype], axis: Int, ddof: Int = 0) -> NDArray[returned_dtype]

Computes the variance along the axis.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• A (NDArray): An array.
• axis (Int): The axis along which the mean is performed.
• ddof (Int): Delta degree of freedom.

Returns:

• NDArray

Raises

Error: If the axis is out of bounds.

Error: If ddof is not smaller than the size of the axis.

Overload 3

variance[dtype: DType, //, returned_dtype: DType = DType.float64](A: Matrix[dtype], ddof: Int = 0) -> Scalar[returned_dtype]

Compute the variance.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• A (Matrix): Matrix.
• ddof (Int): Delta degree of freedom.

Returns:

• Scalar

Raises

Overload 4

variance[dtype: DType, //, returned_dtype: DType = DType.float64](A: Matrix[dtype], axis: Int, ddof: Int = 0) -> Matrix[returned_dtype]

Compute the variance along axis.

Parameters:

• dtype (DType): The element type.
• returned_dtype (DType): The returned data type, defaulting to float64.

Args:

• A (Matrix): Matrix.
• axis (Int): 0 or 1.
• ddof (Int): Delta degree of freedom.

Returns:

• Matrix

Raises