# tf.math.log_sigmoid

Computes log sigmoid of `x` element-wise.

Specifically, `y = log(1 / (1 + exp(-x)))`. For numerical stability, we use `y = -tf.nn.softplus(-x)`.

`x` A Tensor with type `float32` or `float64`.
`name` A name for the operation (optional).

A Tensor with the same type as `x`.

#### Usage Example:

If a positive number is large, then its log_sigmoid will approach to 0 since the formula will be `y = log( <large_num> / (1 + <large_num>) )` which approximates to `log (1)` which is 0.

````x = tf.constant([0.0, 1.0, 50.0, 100.0])`
`tf.math.log_sigmoid(x)`
`<tf.Tensor: shape=(4,), dtype=float32, numpy=`
`array([-6.9314718e-01, -3.1326169e-01, -1.9287499e-22, -0.0000000e+00],`
`      dtype=float32)>`
```

If a negative number is large, its log_sigmoid will approach to the number itself since the formula will be `y = log( 1 / (1 + <large_num>) )` which is `log (1) - log ( (1 + <large_num>) )` which approximates to `- <large_num>` that is the number itself.

````x = tf.constant([-100.0, -50.0, -1.0, 0.0])`
`tf.math.log_sigmoid(x)`
`<tf.Tensor: shape=(4,), dtype=float32, numpy=`
`array([-100.       ,  -50.       ,   -1.3132616,   -0.6931472],`
`      dtype=float32)>`
```
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