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

New in version 0.10.0.

Examples

>>> 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()