# Math

Miscellaneous mathematical operators.

## ecdf(s)

Return cumulative distribution of values in a series.

Null values must be dropped from the series, otherwise a ValueError is raised.

Also, if the dtype of the series is not numeric, a TypeError is raised.

Examples:

>>> import pandas as pd
>>> import janitor
>>> s = pd.Series([0, 4, 0, 1, 2, 1, 1, 3])
>>> x, y = s.ecdf()
>>> x
array([0, 0, 1, 1, 1, 2, 3, 4])
>>> y
array([0.125, 0.25 , 0.375, 0.5  , 0.625, 0.75 , 0.875, 1.   ])


You can then plot the ECDF values, for example:

>>> from matplotlib import pyplot as plt
>>> plt.scatter(x, y)


Parameters:

Name Type Description Default
s Series

A pandas series. dtype should be numeric.

required

Raises:

Type Description
TypeError

If series is not numeric.

ValueError

If series contains nulls.

Returns:

Name Type Description
x ndarray

Sorted array of values.

y ndarray

Cumulative fraction of data points with value x or lower.

Source code in janitor/math.py
 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 @pf.register_series_method def ecdf(s: "Series") -> Tuple["ndarray", "ndarray"]: """Return cumulative distribution of values in a series. Null values must be dropped from the series, otherwise a ValueError is raised. Also, if the dtype of the series is not numeric, a TypeError is raised. Examples: >>> import pandas as pd >>> import janitor >>> s = pd.Series([0, 4, 0, 1, 2, 1, 1, 3]) >>> x, y = s.ecdf() >>> x # doctest: +SKIP array([0, 0, 1, 1, 1, 2, 3, 4]) >>> y # doctest: +SKIP array([0.125, 0.25 , 0.375, 0.5 , 0.625, 0.75 , 0.875, 1. ]) You can then plot the ECDF values, for example: >>> from matplotlib import pyplot as plt >>> plt.scatter(x, y) # doctest: +SKIP Args: s: A pandas series. dtype should be numeric. Raises: TypeError: If series is not numeric. ValueError: If series contains nulls. Returns: x: Sorted array of values. y: Cumulative fraction of data points with value x or lower. """ import numpy as np import pandas.api.types as pdtypes if not pdtypes.is_numeric_dtype(s): raise TypeError(f"series {s.name} must be numeric!") if not s.isna().sum() == 0: raise ValueError(f"series {s.name} contains nulls. Please drop them.") n = len(s) x = np.sort(s) y = np.arange(1, n + 1) / n return x, y 

## exp(s)

Take the exponential transform of the series.

Examples:

>>> import pandas as pd
>>> import janitor
>>> s = pd.Series([0, 1, 3], name="numbers")
>>> s.exp()
0     1.000000
1     2.718282
2    20.085537
Name: numbers, dtype: float64


Parameters:

Name Type Description Default
s Series

Input Series.

required

Returns:

Type Description
Series

Transformed Series.

Source code in janitor/math.py
 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 @pf.register_series_method def exp(s: "Series") -> "Series": """Take the exponential transform of the series. Examples: >>> import pandas as pd >>> import janitor >>> s = pd.Series([0, 1, 3], name="numbers") >>> s.exp() 0 1.000000 1 2.718282 2 20.085537 Name: numbers, dtype: float64 Args: s: Input Series. Returns: Transformed Series. """ import numpy as np return np.exp(s) 

## log(s, error='warn')

Take natural logarithm of the Series.

Each value in the series should be positive. Use error to control the behavior if there are nonpositive entries in the series.

Examples:

>>> import pandas as pd
>>> import janitor
>>> s = pd.Series([0, 1, 3], name="numbers")
>>> s.log(error="ignore")
0         NaN
1    0.000000
2    1.098612
Name: numbers, dtype: float64


Parameters:

Name Type Description Default
s Series

Input Series.

required
error str

Determines behavior when taking the log of nonpositive entries. If 'warn' then a RuntimeWarning is thrown. If 'raise', then a RuntimeError is thrown. Otherwise, nothing is thrown and log of nonpositive values is np.nan.

'warn'

Raises:

Type Description
RuntimeError

Raised when there are nonpositive values in the Series and error='raise'.

Returns:

Type Description
Series

Transformed Series.

Source code in janitor/math.py
 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 @pf.register_series_method def log(s: "Series", error: str = "warn") -> "Series": """ Take natural logarithm of the Series. Each value in the series should be positive. Use error to control the behavior if there are nonpositive entries in the series. Examples: >>> import pandas as pd >>> import janitor >>> s = pd.Series([0, 1, 3], name="numbers") >>> s.log(error="ignore") 0 NaN 1 0.000000 2 1.098612 Name: numbers, dtype: float64 Args: s: Input Series. error: Determines behavior when taking the log of nonpositive entries. If 'warn' then a RuntimeWarning is thrown. If 'raise', then a RuntimeError is thrown. Otherwise, nothing is thrown and log of nonpositive values is np.nan. Raises: RuntimeError: Raised when there are nonpositive values in the Series and error='raise'. Returns: Transformed Series. """ import numpy as np s = s.copy() nonpositive = s <= 0 if (nonpositive).any(): msg = f"Log taken on {nonpositive.sum()} nonpositive value(s)" if error.lower() == "warn": warnings.warn(msg, RuntimeWarning) if error.lower() == "raise": raise RuntimeError(msg) else: pass s[nonpositive] = np.nan return np.log(s) 

## logit(s, error='warn')

Take logit transform of the Series.

The logit transform is defined:

logit(p) = log(p/(1-p))


Each value in the series should be between 0 and 1. Use error to control the behavior if any series entries are outside of (0, 1).

Examples:

>>> import pandas as pd
>>> import janitor
>>> s = pd.Series([0.1, 0.5, 0.9], name="numbers")
>>> s.logit()
0   -2.197225
1    0.000000
2    2.197225
Name: numbers, dtype: float64


Parameters:

Name Type Description Default
s Series

Input Series.

required
error str

Determines behavior when s is outside of (0, 1). If 'warn' then a RuntimeWarning is thrown. If 'raise', then a RuntimeError is thrown. Otherwise, nothing is thrown and np.nan is returned for the problematic entries; defaults to 'warn'.

'warn'

Raises:

Type Description
RuntimeError

If error is set to 'raise'.

Returns:

Type Description
Series

Transformed Series.

Source code in janitor/math.py
 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 @pf.register_series_method def logit(s: "Series", error: str = "warn") -> "Series": """Take logit transform of the Series. The logit transform is defined: python logit(p) = log(p/(1-p))  Each value in the series should be between 0 and 1. Use error to control the behavior if any series entries are outside of (0, 1). Examples: >>> import pandas as pd >>> import janitor >>> s = pd.Series([0.1, 0.5, 0.9], name="numbers") >>> s.logit() 0 -2.197225 1 0.000000 2 2.197225 Name: numbers, dtype: float64 Args: s: Input Series. error: Determines behavior when s is outside of (0, 1). If 'warn' then a RuntimeWarning is thrown. If 'raise', then a RuntimeError is thrown. Otherwise, nothing is thrown and np.nan is returned for the problematic entries; defaults to 'warn'. Raises: RuntimeError: If error is set to 'raise'. Returns: Transformed Series. """ import numpy as np import scipy s = s.copy() outside_support = (s <= 0) | (s >= 1) if (outside_support).any(): msg = f"{outside_support.sum()} value(s) are outside of (0, 1)" if error.lower() == "warn": warnings.warn(msg, RuntimeWarning) if error.lower() == "raise": raise RuntimeError(msg) else: pass s[outside_support] = np.nan return scipy.special.logit(s) 

## normal_cdf(s)

Transforms the Series via the CDF of the Normal distribution.

Examples:

>>> import pandas as pd
>>> import janitor
>>> s = pd.Series([-1, 0, 3], name="numbers")
>>> s.normal_cdf()
0    0.158655
1    0.500000
2    0.998650
dtype: float64


Parameters:

Name Type Description Default
s Series

Input Series.

required

Returns:

Type Description
Series

Transformed Series.

Source code in janitor/math.py
 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 @pf.register_series_method def normal_cdf(s: "Series") -> "Series": """Transforms the Series via the CDF of the Normal distribution. Examples: >>> import pandas as pd >>> import janitor >>> s = pd.Series([-1, 0, 3], name="numbers") >>> s.normal_cdf() 0 0.158655 1 0.500000 2 0.998650 dtype: float64 Args: s: Input Series. Returns: Transformed Series. """ import pandas as pd import scipy return pd.Series(scipy.stats.norm.cdf(s), index=s.index) 

## probit(s, error='warn')

Transforms the Series via the inverse CDF of the Normal distribution.

Each value in the series should be between 0 and 1. Use error to control the behavior if any series entries are outside of (0, 1).

Examples:

>>> import pandas as pd
>>> import janitor
>>> s = pd.Series([0.1, 0.5, 0.8], name="numbers")
>>> s.probit()
0   -1.281552
1    0.000000
2    0.841621
dtype: float64


Parameters:

Name Type Description Default
s Series

Input Series.

required
error str

Determines behavior when s is outside of (0, 1). If 'warn' then a RuntimeWarning is thrown. If 'raise', then a RuntimeError is thrown. Otherwise, nothing is thrown and np.nan is returned for the problematic entries.

'warn'

Raises:

Type Description
RuntimeError

When there are problematic values in the Series and error='raise'.

Returns:

Type Description
Series

Transformed Series

Source code in janitor/math.py
 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 @pf.register_series_method def probit(s: "Series", error: str = "warn") -> "Series": """Transforms the Series via the inverse CDF of the Normal distribution. Each value in the series should be between 0 and 1. Use error to control the behavior if any series entries are outside of (0, 1). Examples: >>> import pandas as pd >>> import janitor >>> s = pd.Series([0.1, 0.5, 0.8], name="numbers") >>> s.probit() 0 -1.281552 1 0.000000 2 0.841621 dtype: float64 Args: s: Input Series. error: Determines behavior when s is outside of (0, 1). If 'warn' then a RuntimeWarning is thrown. If 'raise', then a RuntimeError is thrown. Otherwise, nothing is thrown and np.nan is returned for the problematic entries. Raises: RuntimeError: When there are problematic values in the Series and error='raise'. Returns: Transformed Series """ import numpy as np import pandas as pd import scipy s = s.copy() outside_support = (s <= 0) | (s >= 1) if (outside_support).any(): msg = f"{outside_support.sum()} value(s) are outside of (0, 1)" if error.lower() == "warn": warnings.warn(msg, RuntimeWarning) if error.lower() == "raise": raise RuntimeError(msg) else: pass s[outside_support] = np.nan with np.errstate(all="ignore"): out = pd.Series(scipy.stats.norm.ppf(s), index=s.index) return out 

## sigmoid(s)

Take the sigmoid transform of the series.

The sigmoid function is defined:

sigmoid(x) = 1 / (1 + exp(-x))


Examples:

>>> import pandas as pd
>>> import janitor
>>> s = pd.Series([-1, 0, 4], name="numbers")
>>> s.sigmoid()
0    0.268941
1    0.500000
2    0.982014
Name: numbers, dtype: float64


Parameters:

Name Type Description Default
s Series

Input Series.

required

Returns:

Type Description
Series

Transformed Series.

Source code in janitor/math.py
  86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 @pf.register_series_method def sigmoid(s: "Series") -> "Series": """Take the sigmoid transform of the series. The sigmoid function is defined: python sigmoid(x) = 1 / (1 + exp(-x))  Examples: >>> import pandas as pd >>> import janitor >>> s = pd.Series([-1, 0, 4], name="numbers") >>> s.sigmoid() 0 0.268941 1 0.500000 2 0.982014 Name: numbers, dtype: float64 Args: s: Input Series. Returns: Transformed Series. """ import scipy return scipy.special.expit(s) 

## softmax(s)

Take the softmax transform of the series.

The softmax function transforms each element of a collection by computing the exponential of each element divided by the sum of the exponentials of all the elements.

That is, if x is a one-dimensional numpy array or pandas Series:

softmax(x) = exp(x)/sum(exp(x))


Examples:

>>> import pandas as pd
>>> import janitor
>>> s = pd.Series([0, 1, 3], name="numbers")
>>> s.softmax()
0    0.042010
1    0.114195
2    0.843795
Name: numbers, dtype: float64


Parameters:

Name Type Description Default
s Series

Input Series.

required

Returns:

Type Description
Series

Transformed Series.

Source code in janitor/math.py
 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 @pf.register_series_method def softmax(s: "Series") -> "Series": """Take the softmax transform of the series. The softmax function transforms each element of a collection by computing the exponential of each element divided by the sum of the exponentials of all the elements. That is, if x is a one-dimensional numpy array or pandas Series: python softmax(x) = exp(x)/sum(exp(x))  Examples: >>> import pandas as pd >>> import janitor >>> s = pd.Series([0, 1, 3], name="numbers") >>> s.softmax() 0 0.042010 1 0.114195 2 0.843795 Name: numbers, dtype: float64 Args: s: Input Series. Returns: Transformed Series. """ import pandas as pd import scipy return pd.Series(scipy.special.softmax(s), index=s.index, name=s.name) 

## z_score(s, moments_dict=None, keys=('mean', 'std'))

Transforms the Series into z-scores.

The z-score is defined:

z = (s - s.mean()) / s.std()


Examples:

>>> import pandas as pd
>>> import janitor
>>> s = pd.Series([0, 1, 3], name="numbers")
>>> s.z_score()
0   -0.872872
1   -0.218218
2    1.091089
Name: numbers, dtype: float64


Parameters:

Name Type Description Default
s Series

Input Series.

required
moments_dict dict

If not None, then the mean and standard deviation used to compute the z-score transformation is saved as entries in moments_dict with keys determined by the keys argument; defaults to None.

None
keys Tuple[str, str]

Determines the keys saved in moments_dict if moments are saved; defaults to ('mean', 'std').

('mean', 'std')

Returns:

Type Description
Series

Transformed Series.

Source code in janitor/math.py
 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 @pf.register_series_method def z_score( s: "Series", moments_dict: dict = None, keys: Tuple[str, str] = ("mean", "std"), ) -> "Series": """Transforms the Series into z-scores. The z-score is defined: python z = (s - s.mean()) / s.std()  Examples: >>> import pandas as pd >>> import janitor >>> s = pd.Series([0, 1, 3], name="numbers") >>> s.z_score() 0 -0.872872 1 -0.218218 2 1.091089 Name: numbers, dtype: float64 Args: s: Input Series. moments_dict: If not None, then the mean and standard deviation used to compute the z-score transformation is saved as entries in moments_dict with keys determined by the keys argument; defaults to None. keys: Determines the keys saved in moments_dict if moments are saved; defaults to ('mean', 'std'). Returns: Transformed Series. """ mean = s.mean() std = s.std() if std == 0: return 0 if moments_dict is not None: moments_dict[keys[0]] = mean moments_dict[keys[1]] = std return (s - mean) / std