# 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.

Notes

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

New in version 0.10.0.

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()
```