# tf.where

Return the elements where `condition` is `True` (multiplexing `x` and `y`).

### Used in the notebooks

This operator has two modes: in one mode both `x` and `y` are provided, in another mode neither are provided. `condition` is always expected to be a `tf.Tensor` of type `bool`.

#### Retrieving indices of `True` elements

If `x` and `y` are not provided (both are None):

`tf.where` will return the indices of `condition` that are `True`, in the form of a 2-D tensor with shape (n, d). (Where n is the number of matching indices in `condition`, and d is the number of dimensions in `condition`).

Indices are output in row-major order.

````tf.where([True, False, False, True])`
`<tf.Tensor: shape=(2, 1), dtype=int64, numpy=`
`array([[0],`
`       [3]])>`
```
````tf.where([[True, False], [False, True]])`
`<tf.Tensor: shape=(2, 2), dtype=int64, numpy=`
`array([[0, 0],`
`       [1, 1]])>`
```
````tf.where([[[True, False], [False, True], [True, True]]])`
`<tf.Tensor: shape=(4, 3), dtype=int64, numpy=`
`array([[0, 0, 0],`
`       [0, 1, 1],`
`       [0, 2, 0],`
`       [0, 2, 1]])>`
```

#### Multiplexing between `x` and `y`

If `x` and `y` are provided (both have non-None values):

`tf.where` will choose an output shape from the shapes of `condition`, `x`, and `y` that all three shapes are broadcastable to.

The `condition` tensor acts as a mask that chooses whether the corresponding element / row in the output should be taken from `x` (if the element in `condition` is True) or `y` (if it is false).

````tf.where([True, False, False, True], [1,2,3,4], [100,200,300,400])`
`<tf.Tensor: shape=(4,), dtype=int32, numpy=array([  1, 200, 300,   4],`
`dtype=int32)>`
`tf.where([True, False, False, True], [1,2,3,4], [100])`
`<tf.Tensor: shape=(4,), dtype=int32, numpy=array([  1, 100, 100,   4],`
`dtype=int32)>`
`tf.where([True, False, False, True], [1,2,3,4], 100)`
`<tf.Tensor: shape=(4,), dtype=int32, numpy=array([  1, 100, 100,   4],`
`dtype=int32)>`
`tf.where([True, False, False, True], 1, 100)`
`<tf.Tensor: shape=(4,), dtype=int32, numpy=array([  1, 100, 100,   1],`
`dtype=int32)>`
```
````tf.where(True, [1,2,3,4], 100)`
`<tf.Tensor: shape=(4,), dtype=int32, numpy=array([1, 2, 3, 4],`
`dtype=int32)>`
`tf.where(False, [1,2,3,4], 100)`
`<tf.Tensor: shape=(4,), dtype=int32, numpy=array([100, 100, 100, 100],`
`dtype=int32)>`
```

Note that if the gradient of either branch of the tf.where generates a NaN, then the gradient of the entire tf.where will be NaN. This is because the gradient calculation for tf.where combines the two branches, for performance reasons.

A workaround is to use an inner tf.where to ensure the function has no asymptote, and to avoid computing a value whose gradient is NaN by replacing dangerous inputs with safe inputs.

````x = tf.constant(0., dtype=tf.float32)`
`with tf.GradientTape() as tape:`
`  tape.watch(x)`
`  y = tf.where(x < 1., 0., 1. / x)`
`print(tape.gradient(y, x))`
`tf.Tensor(nan, shape=(), dtype=float32)`
```

Although, the `1. / x` values are never used, its gradient is a NaN when x =

1. Instead, we should guard that with another `tf.where`
````x = tf.constant(0., dtype=tf.float32)`
`with tf.GradientTape() as tape:`
`  tape.watch(x)`
`  safe_x = tf.where(tf.equal(x, 0.), 1., x)`
`  y = tf.where(x < 1., 0., 1. / safe_x)`
`print(tape.gradient(y, x))`
`tf.Tensor(0.0, shape=(), dtype=float32)`
```

`condition` A `tf.Tensor` of type `bool`
`x` If provided, a Tensor which is of the same type as `y`, and has a shape broadcastable with `condition` and `y`.
`y` If provided,