teilab.utils.math_utils module

teilab.utils.math_utils.assign_rank(arr: nptyping.types._ndarray.NDArray[Any, nptyping.types._object.Object], method: str = 'average') → nptyping.types._ndarray.NDArray[Any, nptyping.types._number.Float]

Assign rank to data, dealing with ties appropriately.

Parameters

• arr (NDArray[Any,Number]) – The array of values to be ranked

• method (str, optional) – The method used to assign ranks to tied elements. Defaults to "average".

The following ``method``s are available.

method	description
"average"	The average of the ranks that would have been assigned to all the tied values is assigned to each value.
"min"	The minimum of the ranks that would have been assigned to all the tied values is assigned to each value.
"max"	The maximum of the ranks that would have been assigned to all the tied values is assigned to each value.
"dense"	Like "min", but the rank of the next highest element is assigned the rank immediately after those assigned to the tied elements.
"ordinal"	All values are given a distinct rank, corresponding to the order that the values occur in arr

Returns

An array of size equal to the size of arr, containing rank scores.

Return type

NDArray[Any,float]

Examples

>>> import numpy as np
>>> from teilab.utils import assign_rank
>>> arr = np.asarray([0,2,3,2])
>>> assign_rank(arr, method="average")
array([1. , 2.5, 4. , 2.5])
>>> assign_rank(arr, method="min")
array([1, 2, 4, 2])
>>> assign_rank(arr, method="max")
array([1, 3, 4, 3])
>>> assign_rank(arr, method="dense")
array([1, 2, 3, 2])
>>> assign_rank(arr, method="ordinal")
array([1, 2, 4, 3])

See also

• Ranking

• scipy.stats.rankdata(a, method=’average’)

teilab.utils.math_utils.tiecorrect(ranks: nptyping.types._ndarray.NDArray[Any, nptyping.types._object.Object]) → float

Tie correction factor for Mann-Whitney U and Kruskal-Wallis H tests.

Parameters

ranks (NDArray[Any,Number]) – A 1-D sequence of ranks. Typically this will be the array returned by assign_rank .

Returns

Correction factor for U or H .

Return type

float

Examples

>>> import numpy as np
>>> from teilab.utils import tiecorrect, assign_rank
>>> tiecorrect(np.asarray([0,2,3,2]))
0.9
>>> ranks = assign_rank(np.asarray([1,3,2,4,5,7,2,8,4]), method="average")
>>> ranks
array([1. , 4. , 2.5, 5.5, 7. , 8. , 2.5, 9. , 5.5])
>>> tiecorrect(ranks)
0.9833333333333333

See also

• Nonparametric Statistics for the Behavioral Sciences.

• scipy.stats.tiecorrect(rankvals)

teilab.utils.math_utils.optimize_linear(X: nptyping.types._ndarray.NDArray[Any, nptyping.types._object.Object], Y: nptyping.types._ndarray.NDArray[Any, nptyping.types._object.Object]) → Tuple[float, float, callable]

Optimize linear function using least-squares method.

\[\begin{split}\begin{cases} a&=\frac{\displaystyle n\sum x_iy_i-\sum x_i\sum y_i}{\displaystyle n\sum x^2_i-\left( \sum x_i \right)^2}\\ b&=\frac{\displaystyle \sum x^2_i\sum y_i-\sum x_iy_i\sum x_i}{\displaystyle n\sum x^2_i-\left( \sum x_i \right)^2} \end{cases}\end{split}\]

Parameters

• X (NDArray[Any,Number]) – explanatory variables.

• Y (NDArray[Any,Number]) – objective variables.

Returns

Optimal linear functions and their components.

Return type

Tuple[float,float,callable]