scipy.special.logit#

scipy.special.logit(x, out=None) = <ufunc 'logit'>#

Logit ufunc for ndarrays.

The logit function is defined as logit(p) = log(p/(1-p)). Note that logit(0) = -inf, logit(1) = inf, and logit(p) for p<0 or p>1 yields nan.

Parameters:

xndarray: The ndarray to apply logit to element-wise.
outndarray, optional: Optional output array for the function results

Returns:

scalar or ndarray: An ndarray of the same shape as x. Its entries are logit of the corresponding entry of x.

See also

expit

Notes

As a ufunc logit takes a number of optional keyword arguments. For more information see ufuncs

Added in version 0.10.0.

Array API Standard Support

logit has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	✅
JAX	✅	✅
Dask	✅	n/a

For the NumPy backend, this function supports all NumPy ufunc keyword arguments. Other backends may support out, but none of the other ufunc kwargs. out is typically supported for CuPy and PyTorch, but not currently in cases where SciPy relies on a generic Array API implementation or, for PyTorch on CPU, falls back to the NumPy backend. out is never supported for JAX because JAX arrays are immutable.

See Support for the array API standard for more information.

Examples

>>> import numpy as np
>>> from scipy.special import logit, expit

>>> logit([0, 0.25, 0.5, 0.75, 1])
array([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])

expit is the inverse of logit:

>>> expit(logit([0.1, 0.75, 0.999]))
array([ 0.1  ,  0.75 ,  0.999])

Plot logit(x) for x in [0, 1]:

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(0, 1, 501)
>>> y = logit(x)
>>> plt.plot(x, y)
>>> plt.grid()
>>> plt.ylim(-6, 6)
>>> plt.xlabel('x')
>>> plt.title('logit(x)')
>>> plt.show()