mathematical

Mathematical tools for Python 📐 🐍 🛠️

Includes tools for calculating mean, median and standard deviation of rows in data frames, detection of outliers, and statistical calculations

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Installation

python3 -m pip install mathematical --user

First add the required channels

conda config --add channels https://conda.anaconda.org/conda-forge
conda config --add channels https://conda.anaconda.org/domdfcoding

Then install

conda install mathematical

python3 -m pip install git+https://github.com/domdfcoding/mathematical@master --user

Contents

`mathematical.data_frames`

Mathematical operations for Data Frames.

Data:

ColumnLabelList

Type hint for the column_label_list parameter in the df_*() functions.

Functions:

`df_count`(row[, column_label_list])	Count the number of occurrences of a non-NaN value in the specified columns of a `data frame`.
`df_data_points`(row, column_label_list)	Compile the values for the specified columns in each row into a list.
`df_delta`(row, left_column, right_column)	Calculate the difference between values in the two columns for each row of a `data frame`.
`df_delta_relative`(row, left_column, right_column)	Calculate the relative difference between values in the two columns for each row of a `data frame`.
`df_log`(row, column_label_list[, base])	Calculate the logarithm of the values in each row for the specified columns of a `data frame`.
`df_log_stdev`(row[, column_label_list])	Calculate the standard deviation of the log10 values in each row for the specified columns of a `data frame`.
`df_mean`(row[, column_label_list])	Calculate the mean of each row for the specified columns of a `data frame`.
`df_median`(row[, column_label_list])	Calculate the median of each row for the specified columns of a `data frame`.
`df_outliers`(row[, column_label_list, …])	Identify outliers in each row.
`df_percentage`(row, column_label, total)	Returns the value of the specified column as a percentage of the given total.
`df_stdev`(row[, column_label_list])	Calculate the standard deviation of each row for the specified columns of a `data frame`.
`set_display_options`([desired_width, …])	Set the display options for numpy and pandas.

ColumnLabelList

Type hint for the column_label_list parameter in the df_*() functions.

Alias of Optional[Sequence[str]]

df_count(row, column_label_list=None)[source]

Count the number of occurrences of a non-NaN value in the specified columns of a data frame.

Do not call this function directly; use it with df.apply() instead:

data_frame["Count"] = data_frame.apply(
    func=df_count,
    args=[["Bob", "Alice"]],
    axis=1,
    )

Parameters

row (Series) – Row of the data frame.
column_label_list (Optional[Sequence[str]]) – List of column labels to count occurrences in. Default None.

Return type

int

Returns

Count of the occurrences of non-NaN values.

df_data_points(row, column_label_list)[source]

Compile the values for the specified columns in each row into a list.

Do not call this function directly; use it with df.apply() instead:

data_frame["Data Points"] = data_frame.apply(
        func=df_data_points,
        args=[["Bob", "Alice"]],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
column_label_list (Sequence[str]) – List of column labels to calculate standard deviation for.

Return type

List

Returns

The number of data points.

df_delta(row, left_column, right_column)[source]

Calculate the difference between values in the two columns for each row of a data frame.

Do not call this function directly; use it with df.apply() instead:

data_frame["Delta"] = data_frame.apply(
        func=df_delta,
        args=["Bob", "Alice"],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
left_column (str)
right_column (str)

Return type

float

Returns

The difference between left_column and right_column.

New in version 0.4.0.

df_delta_relative(row, left_column, right_column)[source]

Calculate the relative difference between values in the two columns for each row of a data frame:

(left - right) / right

Do not call this function directly; use it with df.apply() instead:

data_frame["Rel. Delta"] = data_frame.apply(
        func=df_delta_relative,
        args=["Bob", "Alice"],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
left_column (str)
right_column (str)

Return type

float

Returns

The relative difference between left_column and right_column.

New in version 0.4.0.

df_log(row, column_label_list, base=10)[source]

Calculate the logarithm of the values in each row for the specified columns of a data frame.

Do not call this function directly; use it with df.apply() instead:

data_frame["Bob Log10"] = data_frame.apply(
        func=df_log,
        args=[["Bob"], 10],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
column_label_list (Sequence[str]) – List of column labels to calculate log for.
base (float) – The logarithmic base. Default 10.

Return type

float

Returns

The logarithmic value.

df_log_stdev(row, column_label_list=None)[source]

Calculate the standard deviation of the log10 values in each row for the specified columns of a data frame.

Do not call this function directly; use it with df.apply() instead:

data_frame["Log Stdev"] = data_frame.apply(
        func=df_log_stdev,
        args=[["Bob", "Alice"]],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
column_label_list (Optional[Sequence[str]]) – List of column labels to calculate standard deviation for. Default None.

Return type

float

Returns

The standard deviation

df_mean(row, column_label_list=None)[source]

Calculate the mean of each row for the specified columns of a data frame.

Do not call this function directly; use it with df.apply() instead:

data_frame["Mean"] = data_frame.apply(
        func=df_mean,
        args=[["Bob", "Alice"]],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
column_label_list (Optional[Sequence[str]]) – List of column labels to calculate the mean for. Default None.

Return type

float

Returns

The mean

df_median(row, column_label_list=None)[source]

Calculate the median of each row for the specified columns of a data frame.

Do not call this function directly; use it with df.apply() instead:

data_frame["Median"] = data_frame.apply(
        func=df_median,
        args=[["Bob", "Alice"]],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
column_label_list (Optional[Sequence[str]]) – List of column labels to calculate median for. Default None.

Return type

float

Returns

The median

df_outliers(row, column_label_list=None, outlier_mode=1)[source]

Identify outliers in each row.

This function only returns the list of outliers (if any). If you want the list of values without the outliers see the functions in mathematical.outliers.

Do not call this function directly; use it with df.apply() instead:

data_frame["Outliers"] = data_frame.apply(
        func=df_outliers,
        args=[["Bob", "Alice"]],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
column_label_list (Optional[Sequence[str]]) – List of column labels to determine outliers for. Default None.
outlier_mode (int) – outlier detection method to use. Default 1.

The supported outlier modes are:

1 or :py:data`mathematical.data_frames.MAD` – Use the Median Absolute Deviation

2 or :py:data`mathematical.data_frames.QUARTILES` – Treat values more than 3× the inter-quartile range away from the upper or lower quartile as outliers.

3 or :py:data`mathematical.data_frames.STDEV2` – Treat values more than rng × stdev away from mean as outliers

Return type: List
Returns: The outliers.

df_percentage(row, column_label, total)[source]

Returns the value of the specified column as a percentage of the given total.

The total is usually the sum of the specified column.

Do not call this function directly; use it with df.apply() instead:

data_frame["Bob Percentage"] = data_frame.apply(
        func=df_percentage,
        args=[13, "Bob"],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
column_label (str) – The column to calculate percentage for.
total (float) – The total value.

Return type

float

Returns

Percentage * 100

df_stdev(row, column_label_list=None)[source]

Calculate the standard deviation of each row for the specified columns of a data frame.

Do not call this function directly; use it with df.apply() instead:

data_frame["Stdev"] = data_frame.apply(
        func=df_stdev,
        args=[["Bob", "Alice"]],
        axis=1,
        )

Parameters

row (Series) – Row of the data frame.
column_label_list (Optional[Sequence[str]]) – List of column labels to calculate standard deviation for. Default None.

Return type

float

Returns

The standard deviation

set_display_options(desired_width=300, max_columns=15, max_rows=20)[source]

Set the display options for numpy and pandas.

Parameters

desired_width (int) – The desired maximum output width, in characters. Default 300.
max_columns (int) – The maximum number of columns to display in a pandas.DataFrame. Default 15.
max_rows (int) – The maximum number of rows to display in a pandas.DataFrame. Default 20.

New in version 0.3.0.

`mathematical.linear_regression`

Functions for performing linear regression.

Data:

ArrayLike_Float

Type hint for arguments that take either a sequence of floats or a numpy array.

Functions:

`linear_regression_perpendicular`(x[, y])	Calculate coefficients of a linear regression y = a * x + b.
`linear_regression_vertical`(x[, y, a, b])	Calculate coefficients of a linear regression y = a * x + b.

ArrayLike_Float

Type hint for arguments that take either a sequence of floats or a numpy array.

Alias of Union[Sequence[float], ndarray]

linear_regression_perpendicular(x, y=None)[source]

Calculate coefficients of a linear regression y = a * x + b. The fit minimizes perpendicular distances between the points and the line.

Parameters

x (Union[Sequence[float], ndarray]) – 1-D array of floats.
y (Union[Sequence[float], ndarray, None]) – 1-D array of floats. Default None.

If y is omitted, x must be a 2-D array of shape (N, 2).

Return type: Tuple[float, float, float, float]
Returns: (a, b, r, stderr), where a – slope coefficient, b – free term, r – Peason correlation coefficient, stderr – standard deviation.

linear_regression_vertical(x, y=None, a=None, b=None)[source]

Calculate coefficients of a linear regression y = a * x + b. The fit minimizes vertical distances between the points and the line.

Parameters

x (Union[Sequence[float], ndarray]) – 1-D array of floats
y (Union[Sequence[float], ndarray, None]) – 1-D array of floats. Default None.
a (Optional[float]) – If specified then the slope coefficient is fixed as this value. Default None.
b (Optional[float]) – If specified then the free term is fixed as this value. Default None.

If y is omitted, x must be a 2-D array of shape (N, 2).

Return type: Tuple[float, float, float, float]
Returns: (a, b, r, stderr), where a – slope coefficient, b – free term, r – Pearson correlation coefficient, stderr – standard deviation.

`mathematical.outliers`

Outlier detection functions.

Functions:

`mad_outliers`(dataset[, strip_zero, threshold])	Identifies outlier values using the Median Absolute Deviation.
`quartile_outliers`(dataset[, strip_zero])	Identifies outlier values that are more than `3×` the inter-quartile range from the upper or lower quartile.
`spss_outliers`(dataset[, strip_zero, mode])	Identifies outlier values using the IBM SPSS method.
`stdev_outlier`(dataset[, strip_zero, rng])	Identifies outlier values that are greater than `rng × stdev` from mean.
`two_stdev`(dataset[, strip_zero])	Identifies outlier values that are greater than `2×` stdev from the mean.

mad_outliers(dataset, strip_zero=True, threshold=3)[source]

Identifies outlier values using the Median Absolute Deviation.

Parameters

dataset (Sequence)
strip_zero (bool) – Default True.
threshold (int) –
The multiple of MAD above which values are considered to be outliers. Default 3.

Leys et al. (2013) make the following recommendations:
1. In univariate statistics, the Median Absolute Deviation is the most robust dispersion/scale measure in presence of outliers, and hence we strongly recommend the median plus or minus 2.5 times the MAD method for outlier detection.
2. The threshold should be justified and the justification should clearly state that other concerns than cherry-picking degrees of freedom guided the selection. By default, we suggest a threshold of 2.5 as a reasonable choice.
3. We encourage researchers to report information about outliers, namely: the number of outliers removed and their value (or at least the distance between outliers and the selected threshold)
See also

https://dipot.ulb.ac.be/dspace/bitstream/2013/139499/1/Leys_MAD_final-libre.pdf

Return type

Tuple[List[float], List[float]]

Returns

A list of the outlier values, and the remaining data points.

quartile_outliers(dataset, strip_zero=True)[source]

Identifies outlier values that are more than 3× the inter-quartile range from the upper or lower quartile.

Parameters

dataset (Sequence)
strip_zero (bool) – Default True.

Return type

Tuple[List[float], List[float]]

Returns

A list of the outlier values, and the remaining data points.

spss_outliers(dataset, strip_zero=True, mode='all')[source]

Identifies outlier values using the IBM SPSS method.

Outlier values are more than 1.5 × IQR from Q1 or Q3.

“Extreme values” are more than 3 × IQR from Q1 or Q3.

Parameters

dataset (Sequence)
mode (str) – str. Default 'all'.

Return type

Tuple[List[float], List[float], List[float]]

Returns

A list of extreme outliers, a list of other outliers, and the remaining data points.

stdev_outlier(dataset, strip_zero=True, rng=2)[source]

Identifies outlier values that are greater than rng × stdev from mean.

Parameters

dataset (Sequence)
strip_zero (bool) – Default True.
rng (int) – Default 2.

Return type

Tuple[List[float], List[float]]

Returns

A list of the outlier values, and the remaining data points.

two_stdev(dataset, strip_zero=True)[source]

Identifies outlier values that are greater than 2× stdev from the mean.

Parameters

dataset (Sequence)
strip_zero (bool) – Default True.

Return type

Tuple[List[float], List[float]]

Returns

A list of the outlier values, and the remaining data points.

`mathematical.stats`

Functions for calculating statistics.

Functions:

`absolute_deviation`(x[, axis, center, nan_policy])	Compute the absolute deviations from the median of the data along the given axis.
`absolute_deviation_from_median`(x[, axis, …])	Compute the absolute deviation from the median of each point in the data along the given axis, given in terms of the MAD.
`d_cohen`(sample1, sample2[, which, tail, pooled])	Calculates and returns Cohen’s effect size index d.
`g_durlak_bias`(g, n)	Application of Durlak’s bias correction to the Hedge’s g statistic.
`g_hedge`(sample1, sample2)	Calculates and returns Hedge’s g-Statistic.
`interpret_d`(d_or_g)	Interpret Cohen’s d or Hedge’s g values using Table 1 from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3444174/
`iqr_none`(dataset)	Calculate the interquartile range, excluding NaN, strings, boolean values, and zeros.
`mean_none`(dataset)	Calculate the mean, excluding NaN, strings, boolean values, and zeros.
`median_absolute_deviation`(x[, axis, center, …])	Compute the median absolute deviation of the data along the given axis.
`median_none`(dataset)	Calculate the median, excluding NaN, strings, boolean values, and zeros.
`percentile_none`(dataset, percentage)	Calculate the given percentile, excluding NaN, strings, boolean values, and zeros.
`pooled_sd`(sample1, sample2[, weighted])	Returns the pooled standard deviation.
`std_none`(dataset[, ddof])	Calculate the standard deviation, excluding NaN, strings, boolean values, and zeros.
`within1min`(value1, value2)	Returns whether `value2` is within one minute of `value1`.

absolute_deviation(x, axis=0, center=<function median>, nan_policy='propagate')[source]

Compute the absolute deviations from the median of the data along the given axis.

Parameters

x (array_like) – Input array or object that can be converted to an array.
axis (Optional[int]) – Axis along which the range is computed. If None, compute the MAD over the entire array. Default 0.
center (Callable) – A function that will return the central value. The default is to use numpy.median. Any user defined function used will need to have the function signature func(arr, axis). Default <function median at 0x7f234bd32a70>.
nan_policy (Literal['propagate', 'raise', 'omit']) – Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default 'propagate'.

Returns

If axis=None, a scalar is returned. If the input contains integers or floats of smaller precision than numpy.float64, then the output data-type is numpy.float64. Otherwise, the output data-type is the same as that of the input.

Return type

scalar or ndarray

Overloads

absolute_deviation(x, axis: None, center = …, nan_policy = … ) -> float
absolute_deviation(x, axis: int = …, center = …, nan_policy = … ) -> ndarray

Note

The center argument only affects the calculation of the central value around which the MAD is calculated. That is, passing in center=numpy.mean will calculate the MAD around the mean - it will not calculate the mean absolute deviation.

absolute_deviation_from_median(x, axis=0, center=<function median>, nan_policy='propagate')[source]

Compute the absolute deviation from the median of each point in the data along the given axis, given in terms of the MAD.

Parameters

x (array_like) – Input array or object that can be converted to an array.
axis (Optional[int]) – Axis along which the range is computed. If None, compute the MAD over the entire array. Default 0.
center (Callable) – A function that will return the central value. The default is to use numpy.median. Any user defined function used will need to have the function signature func(arr, axis). Default <function median at 0x7f234bd32a70>.
nan_policy (Literal['propagate', 'raise', 'omit']) – Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default 'propagate'.

Returns

If axis=None, a scalar is returned. If the input contains integers or floats of smaller precision than numpy.float64, then the output data-type is numpy.float64. Otherwise, the output data-type is the same as that of the input.

Return type

scalar or ndarray

Overloads

absolute_deviation_from_median(x, axis: None, center = …, nan_policy = … ) -> float
absolute_deviation_from_median(x, axis: int = …, center = …, nan_policy = … ) -> ndarray

Note

The center argument only affects the calculation of the central value around which the MAD is calculated. That is, passing in center=numpy.mean will calculate the MAD around the mean - it will not calculate the mean absolute deviation.

d_cohen(sample1, sample2, which=1, tail=1, pooled=False)[source]

Calculates and returns Cohen’s effect size index d.

See also

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd Edition). Hillsdale, NJ: Lawrence Erlbaum Associates

Parameters

sample1 (Sequence[float]) – datapoints for first sample
sample2 (Sequence[float]) – datapoints for second sample
which (Literal[1, 2]) – Use the standard deviation of the first sample (1) or the second sample (2). Default 1.
tail (Literal[1, 2]) – The number of tails to consider. Default 1.
pooled (bool) – Whether to use the pooled standard deviation. Default False.

Return type

float

g_durlak_bias(g, n)[source]

Application of Durlak’s bias correction to the Hedge’s g statistic.

n = n1+n2

Parameters

g (float) – Hedge’s g-Statistic, calculated using g_hedge().
n (float) – The total number of samples in both datasets.

Return type: float

g_hedge(sample1, sample2)[source]

Calculates and returns Hedge’s g-Statistic.

Formula from https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/hedgeg.htm

Parameters

sample1 (Sequence[float]) – datapoints for first sample
sample2 (Sequence[float]) – datapoints for second sample

Return type

float

interpret_d(d_or_g)[source]

Interpret Cohen’s d or Hedge’s g values using Table 1 from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3444174/

Parameters: d_or_g (float)
Return type: str

iqr_none(dataset)[source]

Calculate the interquartile range, excluding NaN, strings, boolean values, and zeros.

Parameters: dataset (Sequence[Union[float, bool, None]]) – A list to calculate iqr from.
Return type: float
Returns: The interquartile range.

mean_none(dataset)[source]

Calculate the mean, excluding NaN, strings, boolean values, and zeros.

Parameters: dataset (Sequence[Union[float, bool, None]]) – list to calculate mean from
Return type: float
Returns: mean

median_absolute_deviation(x, axis=0, center=<function median>, scale=1.4826, nan_policy='propagate')[source]

Compute the median absolute deviation of the data along the given axis. The median absolute deviation (MAD, 1) computes the median over the absolute deviations from the median. It is a measure of dispersion similar to the standard deviation, but is more robust to outliers 2. The MAD of an empty array is numpy.nan.

Parameters

x (array_like) – Input array or object that can be converted to an array.
axis (Optional[int]) – Axis along which the range is computed. If None, compute the MAD over the entire array. Default 0.
center (Callable) – A function that will return the central value. The default is to use numpy.median. Any user defined function used will need to have the function signature func(arr, axis). Default <function median at 0x7f234bd32a70>.
scale (float) – The scaling factor applied to the MAD. The default scale (1.4826) ensures consistency with the standard deviation for normally distributed data. Default 1.4826.
nan_policy (Literal['propagate', 'raise', 'omit']) – Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default 'propagate'.

Returns

If axis=None, a scalar is returned. If the input contains integers or floats of smaller precision than numpy.float64, then the output data-type is numpy.float64. Otherwise, the output data-type is the same as that of the input.

Return type

scalar or ndarray

Overloads

median_absolute_deviation(x, axis: None, center = …, scale = …, nan_policy = … ) -> float
median_absolute_deviation(x, axis: int = …, center = …, scale = …, nan_policy = … ) -> ndarray

Note

The center argument only affects the calculation of the central value around which the MAD is calculated. That is, passing in center=numpy.mean will calculate the MAD around the mean - it will not calculate the mean absolute deviation.

References

1: “Median absolute deviation” https://en.wikipedia.org/wiki/Median_absolute_deviation
2: “Robust measures of scale” https://en.wikipedia.org/wiki/Robust_measures_of_scale

Examples

When comparing the behavior of median_absolute_deviation with numpy.std, the latter is affected when we change a single value of an array to have an outlier value while the MAD hardly changes:

>>> import scipy.stats
>>> import mathematical.stats
>>> x = scipy.stats.norm.rvs(size=100, scale=1, random_state=123456)
>>> x.std()
0.9973906394005013
>>> mathematical.stats.median_absolute_deviation(x)
1.2280762773108278
>>> x[0] = 345.6
>>> x.std()
34.42304872314415
>>> mathematical.stats.median_absolute_deviation(x)
1.2340335571164334
Axis handling example:
>>> x = numpy.array([[10, 7, 4], [3, 2, 1]])
>>> x
array([[10,  7,  4], [ 3,  2,  1],])
>>> mathematical.stats.median_absolute_deviation(x)
array([5.1891, 3.7065, 2.2239])
>>> mathematical.stats.median_absolute_deviation(x, axis=None)
2.9652

median_none(dataset)[source]

Calculate the median, excluding NaN, strings, boolean values, and zeros.

Parameters: dataset (Sequence[Union[float, bool, None]]) – list to calculate median from
Return type: float
Returns: standard deviation

percentile_none(dataset, percentage)[source]

Calculate the given percentile, excluding NaN, strings, boolean values, and zeros.

Parameters

dataset (Sequence[Union[float, bool, None]]) – Sequence to calculate the percentile from.
percentage (float)

Raises

ValueError if dataset contains fewer than two values

Return type

float

Returns

The interquartile range.

pooled_sd(sample1, sample2, weighted=False)[source]

Returns the pooled standard deviation.

Parameters

sample1 (Sequence[float]) – datapoints for first sample
sample2 (Sequence[float]) – datapoints for second sample
weighted (bool) – True for weighted pooled SD. Default False.

Return type: float

std_none(dataset, ddof=1)[source]

Calculate the standard deviation, excluding NaN, strings, boolean values, and zeros.

Parameters

dataset (Sequence[Union[float, bool, None]]) – list to calculate mean from.
ddof (int) – Means Delta Degrees of Freedom. The divisor used in calculations is N - ddof, where N represents the number of elements. Default 1.

Return type

float

Returns

standard deviation

within1min(value1, value2)[source]

Returns whether value2 is within one minute of value1.

Parameters

value1 (float) – A time in minutes.
value2 (float) – Another time in minutes.

Return type

bool

`mathematical.utils`

Utilities for mathematical operations.

Classes:

FRange()

Returns a range of floating-point numbers.

Functions:

`concatenate_csv`(*files[, outfile])	Concatenate multiple CSV files together and return a `pandas.DataFrame` representing the output.
`gcd`(a, b)	Returns the GCD (HCF) of `a` and `b` using Euclid’s Algorithm.
`gcd2`(numbers)	Returns the GCD (HCF) of a list of numbers using Euclid’s Algorithm.
`gcd_array`(array)	Returns the GCD for an array of numbers using Euclid’s Algorithm.
`hcf`(a, b)	Returns the GCD (HCF) of `a` and `b` using Euclid’s Algorithm.
`hcf2`(numbers)	Returns the GCD (HCF) of a list of numbers using Euclid’s Algorithm.
`intdiv`(p, q)	Integer divsions which rounds toward zero.
`isint`(num)	Checks whether a float is an integer value.
`lcm`(numbers)	Returns the LCM of a list of numbers using Euclid’s Algorithm.
`log_factorial`(x)	Returns the natural logarithm of `x` factorial (`ln(x!`).
`magnitude`(x)	Returns the magnitude of the given value.
`mod_inverse`(a, m)	Returns the modular inverse of `a % m`, which is the number `x` such that `a × x % m = 1`.
`nanmean`(ls[, dtype])	Returns the mean of the given sequence, ignoring `None` and `numpy.nan` values etc.
`nanrsd`(ls[, dtype])	Returns the relative standard deviation of the given sequence, ignoring `None` and `numpy.nan` values etc.
`nanstd`(ls[, dtype])	Returns the standard deviation of the given sequence, ignoring `None` and `numpy.nan` values etc.
`remove_zero`(inputlist)	Remove zero values from the given list.
`represents_int`(s)	Checks whether a value can be converted to an `int`.
`roman`(num)	Retuns the Roman numeral represtation of the given value.
`rounders`(val_to_round, round_format)	Round a value to the specified number format, e.g.
`strip_booleans`(ls)	Remove booleans from a list.
`strip_none_bool_string`(ls)	Remove `None`, boolean and string values from a list.
`strip_nonetype`(ls)	Remove `None` from a list.
`strip_strings`(ls)	Remove strings from a list.

class FRange(stop: float)[source]

class FRange(start: float, stop: float, step: float = '...')

Bases: Sequence[float]

Returns a range of floating-point numbers.

The arguments to the range constructor may be integers or floats.

Parameters

start – Default None.
stop – Default None.
step – Default 1.0.

Raises

ValueError – If step is zero, or if any value is larger than 1×10 ¹⁴.

New in version 0.2.0.

Methods:

`__contains__`(o)	Returns whether `o` is in the range.
`__delattr__`(key)	Implement `delattr(self, name)`.
`__eq__`(other)	Return `self == other`.
`__getitem__`(item)	Returns the value in the range at index `item`.
`__iter__`()	Iterates over values in the range.
`__len__`()	Returns the number of values in the range.
`__repr__`()	Return a string representation of the `FRange`.
`__reversed__`()	Returns `reversed(self)`.
`__setattr__`(key, value)	Implement `setattr(self, name)`.
`count`(value)	Returns `1` if the value is within the range, `0` otherwise.
`index`(value)	Returns the index of `value` in the range.

Attributes:

`start`	The value of the `start` parameter (or `0.0` if the parameter was not supplied)
`step`	The value of the `step` parameter (or `1.0` if the parameter was not supplied)
`stop`	The value of the `stop` parameter

__contains__(o)[source]

Returns whether o is in the range.

Parameters: o (object)
Return type: bool

__delattr__(key)[source]: Implement delattr(self, name).

__eq__(other)[source]

Return self == other.

Return type: bool

__getitem__(item)[source]

Returns the value in the range at index item.

Parameters

item

Overloads

__getitem__(i: int) -> int
__getitem__(s: slice) -> FRange

__iter__()[source]

Iterates over values in the range.

Return type: Iterator[float]

__len__()[source]

Returns the number of values in the range.

Return type: int

__repr__()[source]

Return a string representation of the FRange.

Return type: str

__reversed__()[source]

Returns reversed(self).

Return type: Iterator[float]

__setattr__(key, value)[source]: Implement setattr(self, name).

count(value)[source]

Returns 1 if the value is within the range, 0 otherwise.

Parameters: value (float)
Return type: int

index(value)[source]

Returns the index of value in the range.

Parameters: value (float)
Raises: ValueError – if the value is not in the range.
Return type: int

start

Type: float

The value of the start parameter (or 0.0 if the parameter was not supplied)

step

Type: float

The value of the step parameter (or 1.0 if the parameter was not supplied)

stop

Type: float

The value of the stop parameter

concatenate_csv(*files, outfile=None)[source]

Concatenate multiple CSV files together and return a pandas.DataFrame representing the output.

Parameters

*files (Union[str, Path, PathLike]) – The files to concatenate.
outfile (Union[str, Path, PathLike, None]) – The file to save the output as. If None no file will be saved. Default None.

Return type

DataFrame

Returns

A pandas.DataFrame containing the concatenated CSV data.

New in version 0.3.0.

gcd(a, b)[source]

Returns the GCD (HCF) of a and b using Euclid’s Algorithm.

Parameters

a (int)
b (int)

Return type

int

gcd2(numbers)[source]

Returns the GCD (HCF) of a list of numbers using Euclid’s Algorithm.

Parameters: numbers (Sequence[int])
Return type: int

gcd_array(array)[source]

Returns the GCD for an array of numbers using Euclid’s Algorithm.

Based on https://www.geeksforgeeks.org/python-program-for-gcd-of-more-than-two-or-array-numbers/

Parameters: array
Return type: float

hcf(a, b)

Returns the GCD (HCF) of a and b using Euclid’s Algorithm.

Parameters

a (int)
b (int)

Return type

int

hcf2(numbers)

Returns the GCD (HCF) of a list of numbers using Euclid’s Algorithm.

Parameters: numbers (Sequence[int])
Return type: int

intdiv(p, q)[source]

Integer divsions which rounds toward zero.

Examples >>> intdiv(3, 2) 1 >>> intdiv(-3, 2) -1 >>> -3 // 2 -2

Return type: int

isint(num)[source]

Checks whether a float is an integer value.

Note

This function only works with floating-point numbers

Parameters: num (float) – value to check
Return type: bool

lcm(numbers)[source]

Returns the LCM of a list of numbers using Euclid’s Algorithm.

Parameters: numbers (Sequence[int])
Return type: float

log_factorial(x)[source]

Returns the natural logarithm of x factorial (ln(x!).

Parameters: x (float)
Return type: float

magnitude(x)[source]

Returns the magnitude of the given value.

Parameters: x (float) – Numerical value to find the magnitude of.

Changed in version 0.2.0: Now returns the absolute magnitude of negative numbers.

Return type: int

mod_inverse(a, m)[source]

Returns the modular inverse of a % m, which is the number x such that a × x % m = 1.

Parameters

a (int)
m (int)

Return type

Optional[float]

nanmean(ls, dtype=<class 'float'>)[source]

Returns the mean of the given sequence, ignoring None and numpy.nan values etc.

Similar to numpy.nanmean except it handles None.

Parameters

ls (Sequence[Any])
dtype – Default float.

Return type

float

nanrsd(ls, dtype=<class 'float'>)[source]

Returns the relative standard deviation of the given sequence, ignoring None and numpy.nan values etc.

Parameters

ls (Sequence[Any])
dtype – Default float.

Return type

float

nanstd(ls, dtype=<class 'float'>)[source]

Returns the standard deviation of the given sequence, ignoring None and numpy.nan values etc.

Similar to numpy.nanstd except it handles None.

Parameters

ls (Sequence[Any])
dtype – Default float.

Return type

float

remove_zero(inputlist)[source]

Remove zero values from the given list.

Also removes False and None.

Parameters: inputlist (Sequence[Union[float, bool, None]]) – list to remove zero values from
Return type: List[float]

represents_int(s)[source]

Checks whether a value can be converted to an int.

Parameters: s (Any) – value to check
Return type: bool

roman(num)[source]

Retuns the Roman numeral represtation of the given value.

Examples:

>>> roman(4)
'IV'
>>> roman(17)
'XVII'

Return type: str

rounders(val_to_round, round_format)[source]

Round a value to the specified number format, e.g. "0.000" for three decimal places.

Parameters

val_to_round (Union[str, float, Decimal]) – The value to round
round_format (str) – The rounding format

Return type

Decimal

strip_booleans(ls)[source]

Remove booleans from a list.

Parameters: ls (Sequence[Any]) – the list to remove booleans from.
Return type: List
Returns: The list without boolean values.

strip_none_bool_string(ls)[source]

Remove None, boolean and string values from a list.

Parameters: ls (Sequence) – The list to remove values from.
Return type: List

strip_nonetype(ls)[source]

Remove None from a list.

Parameters: ls (Sequence[Any]) – the list to remove None from.
Return type: List
Returns: The list without None values.

strip_strings(ls)[source]

Remove strings from a list.

Parameters: ls (Sequence[Any]) – the list to remove strings from.
Return type: List
Returns: The list without strings.

Contributing

mathematical uses tox to automate testing and packaging, and pre-commit to maintain code quality.

Install pre-commit with pip and install the git hook:

python -m pip install pre-commit
pre-commit install

Coding style

formate is used for code formatting.

It can be run manually via pre-commit:

pre-commit run formate -a

Or, to run the complete autoformatting suite:

pre-commit run -a

Automated tests

Tests are run with tox and pytest. To run tests for a specific Python version, such as Python 3.6:

tox -e py36

To run tests for all Python versions, simply run:

tox

Type Annotations

Type annotations are checked using mypy. Run mypy using tox:

tox -e mypy

Build documentation locally

The documentation is powered by Sphinx. A local copy of the documentation can be built with tox:

tox -e docs

Downloading source code

The mathematical source code is available on GitHub, and can be accessed from the following URL: https://github.com/domdfcoding/mathematical

If you have git installed, you can clone the repository with the following command:

git clone https://github.com/domdfcoding/mathematical

Cloning into 'mathematical'...
remote: Enumerating objects: 47, done.
remote: Counting objects: 100% (47/47), done.
remote: Compressing objects: 100% (41/41), done.
remote: Total 173 (delta 16), reused 17 (delta 6), pack-reused 126
Receiving objects: 100% (173/173), 126.56 KiB | 678.00 KiB/s, done.
Resolving deltas: 100% (66/66), done.

Alternatively, the code can be downloaded in a ‘zip’ file by clicking:

Clone or download –> Download Zip

Downloading a ‘zip’ file of the source code

Building from source

The recommended way to build mathematical is to use tox:

tox -e build

The source and wheel distributions will be in the directory dist.

If you wish, you may also use pep517.build or another PEP 517-compatible build tool.

License

mathematical is licensed under the GNU Lesser General Public License v3.0

Permissions of this copyleft license are conditioned on making available complete source code of licensed works and modifications under the same license or the GNU GPLv3. Copyright and license notices must be preserved. Contributors provide an express grant of patent rights. However, a larger work using the licensed work through interfaces provided by the licensed work may be distributed under different terms and without source code for the larger work.

Permissions	Conditions	Limitations
Commercial use Modification Distribution Patent use Private use	License and copyright notice Disclose source State changes Same license (library)	Liability Warranty

See more information on choosealicense.com ➩

                   GNU LESSER GENERAL PUBLIC LICENSE
                       Version 3, 29 June 2007

 Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
 Everyone is permitted to copy and distribute verbatim copies
 of this license document, but changing it is not allowed.


  This version of the GNU Lesser General Public License incorporates
the terms and conditions of version 3 of the GNU General Public
License, supplemented by the additional permissions listed below.

  0. Additional Definitions.

  As used herein, "this License" refers to version 3 of the GNU Lesser
General Public License, and the "GNU GPL" refers to version 3 of the GNU
General Public License.

  "The Library" refers to a covered work governed by this License,
other than an Application or a Combined Work as defined below.

  An "Application" is any work that makes use of an interface provided
by the Library, but which is not otherwise based on the Library.
Defining a subclass of a class defined by the Library is deemed a mode
of using an interface provided by the Library.

  A "Combined Work" is a work produced by combining or linking an
Application with the Library.  The particular version of the Library
with which the Combined Work was made is also called the "Linked
Version".

  The "Minimal Corresponding Source" for a Combined Work means the
Corresponding Source for the Combined Work, excluding any source code
for portions of the Combined Work that, considered in isolation, are
based on the Application, and not on the Linked Version.

  The "Corresponding Application Code" for a Combined Work means the
object code and/or source code for the Application, including any data
and utility programs needed for reproducing the Combined Work from the
Application, but excluding the System Libraries of the Combined Work.

  1. Exception to Section 3 of the GNU GPL.

  You may convey a covered work under sections 3 and 4 of this License
without being bound by section 3 of the GNU GPL.

  2. Conveying Modified Versions.

  If you modify a copy of the Library, and, in your modifications, a
facility refers to a function or data to be supplied by an Application
that uses the facility (other than as an argument passed when the
facility is invoked), then you may convey a copy of the modified
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   a) under this License, provided that you make a good faith effort to
   ensure that, in the event an Application does not supply the
   function or data, the facility still operates, and performs
   whatever part of its purpose remains meaningful, or

   b) under the GNU GPL, with none of the additional permissions of
   this License applicable to that copy.

  3. Object Code Incorporating Material from Library Header Files.

  The object code form of an Application may incorporate material from
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material is not limited to numerical parameters, data structure
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(ten or fewer lines in length), you do both of the following:

   a) Give prominent notice with each copy of the object code that the
   Library is used in it and that the Library and its use are
   covered by this License.

   b) Accompany the object code with a copy of the GNU GPL and this license
   document.

  4. Combined Works.

  You may convey a Combined Work under terms of your choice that,
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the following:

   a) Give prominent notice with each copy of the Combined Work that
   the Library is used in it and that the Library and its use are
   covered by this License.

   b) Accompany the Combined Work with a copy of the GNU GPL and this license
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   c) For a Combined Work that displays copyright notices during
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   these notices, as well as a reference directing the user to the
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   d) Do one of the following:

       0) Convey the Minimal Corresponding Source under the terms of this
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       1) Use a suitable shared library mechanism for linking with the
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   Information in the manner specified by section 6 of the GNU GPL
   for conveying Corresponding Source.)

  5. Combined Libraries.

  You may place library facilities that are a work based on the
Library side by side in a single library together with other library
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  Each version is given a distinguishing version number. If the
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View the Function Index or browse the Source Code.

Browse the GitHub Repository

mathematical

Installation

Contents

mathematical.data_frames

mathematical.linear_regression

mathematical.outliers

mathematical.stats

mathematical.utils

Contributing

Coding style

Automated tests

Type Annotations

Build documentation locally

Downloading source code

Building from source

License

`mathematical.data_frames`

`mathematical.linear_regression`

`mathematical.outliers`

`mathematical.stats`

`mathematical.utils`