# tf.contrib.distributions.bijectors.Chain

<br />

|---|
| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/contrib/distributions/python/ops/bijectors/chain.py#L127-L324) |

Bijector which applies a sequence of bijectors.

Inherits From: [`Bijector`](https://www.tensorflow.org/versions/r1.15/api_docs/python/tf/contrib/distributions/bijectors/Bijector)

    tf.contrib.distributions.bijectors.Chain(
        bijectors=None, validate_args=False, name=None
    )

#### Example Use:

    chain = Chain([Exp(), Softplus()], name="one_plus_exp")

#### Results in:

- Forward:

     exp = Exp()
     softplus = Softplus()
     Chain([exp, softplus]).forward(x)
     = exp.forward(softplus.forward(x))
     = tf.exp(tf.math.log(1. + tf.exp(x)))
     = 1. + tf.exp(x)
     ```

    * Inverse:

     ```python
     exp = Exp()
     softplus = Softplus()
     Chain([exp, softplus]).inverse(y)
     = softplus.inverse(exp.inverse(y))
     = tf.math.log(tf.exp(tf.math.log(y)) - 1.)
     = tf.math.log(y - 1.)
     ```

    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2"><h2 class="add-link">Args</h2></th></tr>

    <tr>
    <td>
    `bijectors`
    </td>
    <td>
    Python `list` of bijector instances. An empty list makes this
    bijector equivalent to the `Identity` bijector.
    </td>
    </tr><tr>
    <td>
    `validate_args`
    </td>
    <td>
    Python `bool` indicating whether arguments should be
    checked for correctness.
    </td>
    </tr><tr>
    <td>
    `name`
    </td>
    <td>
    Python `str`, name given to ops managed by this object. Default:
    E.g., `Chain([Exp(), Softplus()]).name == "chain_of_exp_of_softplus"`.
    </td>
    </tr>
    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2"><h2 class="add-link">Raises</h2></th></tr>

    <tr>
    <td>
    `ValueError`
    </td>
    <td>
    if bijectors have different dtypes.
    </td>
    </tr>
    </table>





    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2"><h2 class="add-link">Attributes</h2></th></tr>

    <tr>
    <td>
    `bijectors`
    </td>
    <td>

    </td>
    </tr><tr>
    <td>
    `dtype`
    </td>
    <td>
    dtype of `Tensor`s transformable by this distribution.
    </td>
    </tr><tr>
    <td>
    `forward_min_event_ndims`
    </td>
    <td>
    Returns the minimal number of dimensions bijector.forward operates on.
    </td>
    </tr><tr>
    <td>
    `graph_parents`
    </td>
    <td>
    Returns this `Bijector`'s graph_parents as a Python list.
    </td>
    </tr><tr>
    <td>
    `inverse_min_event_ndims`
    </td>
    <td>
    Returns the minimal number of dimensions bijector.inverse operates on.
    </td>
    </tr><tr>
    <td>
    `is_constant_jacobian`
    </td>
    <td>
    Returns true iff the Jacobian matrix is not a function of x.

    Note: Jacobian matrix is either constant for both forward and inverse or
    neither.
    </td>
    </tr><tr>
    <td>
    `name`
    </td>
    <td>
    Returns the string name of this `Bijector`.
    </td>
    </tr><tr>
    <td>
    `validate_args`
    </td>
    <td>
    Returns True if Tensor arguments will be validated.
    </td>
    </tr>
    </table>



    ## Methods

    <h3 id="forward"><code>forward</code></h3>

    <a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L753-L768">View source</a>

    <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
    <code>forward(
        x, name='forward'
    )
    </code></pre>

    Returns the forward `Bijector` evaluation, i.e., X = g(Y).


    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Args</th></tr>

    <tr>
    <td>
    `x`
    </td>
    <td>
    `Tensor`. The input to the "forward" evaluation.
    </td>
    </tr><tr>
    <td>
    `name`
    </td>
    <td>
    The name to give this op.
    </td>
    </tr>
    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Returns</th></tr>
    <tr class="alt">
    <td colspan="2">
    `Tensor`.
    </td>
    </tr>

    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Raises</th></tr>

    <tr>
    <td>
    `TypeError`
    </td>
    <td>
    if `self.dtype` is specified and `x.dtype` is not
    `self.dtype`.
    </td>
    </tr><tr>
    <td>
    `NotImplementedError`
    </td>
    <td>
    if `_forward` is not implemented.
    </td>
    </tr>
    </table>



    <h3 id="forward_event_shape"><code>forward_event_shape</code></h3>

    <a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L677-L690">View source</a>

    <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
    <code>forward_event_shape(
        input_shape
    )
    </code></pre>

    Shape of a single sample from a single batch as a `TensorShape`.

    Same meaning as `forward_event_shape_tensor`. May be only partially defined.

    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Args</th></tr>

    <tr>
    <td>
    `input_shape`
    </td>
    <td>
    `TensorShape` indicating event-portion shape passed into
    `forward` function.
    </td>
    </tr>
    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Returns</th></tr>

    <tr>
    <td>
    `forward_event_shape_tensor`
    </td>
    <td>
    `TensorShape` indicating event-portion shape
    after applying `forward`. Possibly unknown.
    </td>
    </tr>
    </table>



    <h3 id="forward_event_shape_tensor"><code>forward_event_shape_tensor</code></h3>

    <a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L653-L670">View source</a>

    <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
    <code>forward_event_shape_tensor(
        input_shape, name='forward_event_shape_tensor'
    )
    </code></pre>

    Shape of a single sample from a single batch as an `int32` 1D `Tensor`.


    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Args</th></tr>

    <tr>
    <td>
    `input_shape`
    </td>
    <td>
    `Tensor`, `int32` vector indicating event-portion shape
    passed into `forward` function.
    </td>
    </tr><tr>
    <td>
    `name`
    </td>
    <td>
    name to give to the op
    </td>
    </tr>
    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Returns</th></tr>

    <tr>
    <td>
    `forward_event_shape_tensor`
    </td>
    <td>
    `Tensor`, `int32` vector indicating
    event-portion shape after applying `forward`.
    </td>
    </tr>
    </table>



    <h3 id="forward_log_det_jacobian"><code>forward_log_det_jacobian</code></h3>

    <a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L973-L997">View source</a>

    <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
    <code>forward_log_det_jacobian(
        x, event_ndims, name='forward_log_det_jacobian'
    )
    </code></pre>

    Returns both the forward_log_det_jacobian.


    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Args</th></tr>

    <tr>
    <td>
    `x`
    </td>
    <td>
    `Tensor`. The input to the "forward" Jacobian determinant evaluation.
    </td>
    </tr><tr>
    <td>
    `event_ndims`
    </td>
    <td>
    Number of dimensions in the probabilistic events being
    transformed. Must be greater than or equal to
    `self.forward_min_event_ndims`. The result is summed over the final
    dimensions to produce a scalar Jacobian determinant for each event,
    i.e. it has shape `x.shape.ndims - event_ndims` dimensions.
    </td>
    </tr><tr>
    <td>
    `name`
    </td>
    <td>
    The name to give this op.
    </td>
    </tr>
    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Returns</th></tr>
    <tr class="alt">
    <td colspan="2">
    `Tensor`, if this bijector is injective.
    If not injective this is not implemented.
    </td>
    </tr>

    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Raises</th></tr>

    <tr>
    <td>
    `TypeError`
    </td>
    <td>
    if `self.dtype` is specified and `y.dtype` is not
    `self.dtype`.
    </td>
    </tr><tr>
    <td>
    `NotImplementedError`
    </td>
    <td>
    if neither `_forward_log_det_jacobian`
    nor {`_inverse`, `_inverse_log_det_jacobian`} are implemented, or
    this is a non-injective bijector.
    </td>
    </tr>
    </table>



    <h3 id="inverse"><code>inverse</code></h3>

    <a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L787-L804">View source</a>

    <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
    <code>inverse(
        y, name='inverse'
    )
    </code></pre>

    Returns the inverse `Bijector` evaluation, i.e., X = g^{-1}(Y).


    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Args</th></tr>

    <tr>
    <td>
    `y`
    </td>
    <td>
    `Tensor`. The input to the "inverse" evaluation.
    </td>
    </tr><tr>
    <td>
    `name`
    </td>
    <td>
    The name to give this op.
    </td>
    </tr>
    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Returns</th></tr>
    <tr class="alt">
    <td colspan="2">
    `Tensor`, if this bijector is injective.
    If not injective, returns the k-tuple containing the unique
    `k` points `(x1, ..., xk)` such that `g(xi) = y`.
    </td>
    </tr>

    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Raises</th></tr>

    <tr>
    <td>
    `TypeError`
    </td>
    <td>
    if `self.dtype` is specified and `y.dtype` is not
    `self.dtype`.
    </td>
    </tr><tr>
    <td>
    `NotImplementedError`
    </td>
    <td>
    if `_inverse` is not implemented.
    </td>
    </tr>
    </table>



    <h3 id="inverse_event_shape"><code>inverse_event_shape</code></h3>

    <a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L721-L734">View source</a>

    <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
    <code>inverse_event_shape(
        output_shape
    )
    </code></pre>

    Shape of a single sample from a single batch as a `TensorShape`.

    Same meaning as `inverse_event_shape_tensor`. May be only partially defined.

    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Args</th></tr>

    <tr>
    <td>
    `output_shape`
    </td>
    <td>
    `TensorShape` indicating event-portion shape passed into
    `inverse` function.
    </td>
    </tr>
    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Returns</th></tr>

    <tr>
    <td>
    `inverse_event_shape_tensor`
    </td>
    <td>
    `TensorShape` indicating event-portion shape
    after applying `inverse`. Possibly unknown.
    </td>
    </tr>
    </table>



    <h3 id="inverse_event_shape_tensor"><code>inverse_event_shape_tensor</code></h3>

    <a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L697-L714">View source</a>

    <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
    <code>inverse_event_shape_tensor(
        output_shape, name='inverse_event_shape_tensor'
    )
    </code></pre>

    Shape of a single sample from a single batch as an `int32` 1D `Tensor`.


    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Args</th></tr>

    <tr>
    <td>
    `output_shape`
    </td>
    <td>
    `Tensor`, `int32` vector indicating event-portion shape
    passed into `inverse` function.
    </td>
    </tr><tr>
    <td>
    `name`
    </td>
    <td>
    name to give to the op
    </td>
    </tr>
    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Returns</th></tr>

    <tr>
    <td>
    `inverse_event_shape_tensor`
    </td>
    <td>
    `Tensor`, `int32` vector indicating
    event-portion shape after applying `inverse`.
    </td>
    </tr>
    </table>



    <h3 id="inverse_log_det_jacobian"><code>inverse_log_det_jacobian</code></h3>

    <a target="_blank" href="https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L871-L900">View source</a>

    <pre class="devsite-click-to-copy prettyprint lang-py tfo-signature-link">
    <code>inverse_log_det_jacobian(
        y, event_ndims, name='inverse_log_det_jacobian'
    )
    </code></pre>

    Returns the (log o det o Jacobian o inverse)(y).

    Mathematically, returns: `log(det(dX/dY))(Y)`. (Recall that: `X=g^{-1}(Y)`.)

    Note that `forward_log_det_jacobian` is the negative of this function,
    evaluated at `g^{-1}(y)`.

    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Args</th></tr>

    <tr>
    <td>
    `y`
    </td>
    <td>
    `Tensor`. The input to the "inverse" Jacobian determinant evaluation.
    </td>
    </tr><tr>
    <td>
    `event_ndims`
    </td>
    <td>
    Number of dimensions in the probabilistic events being
    transformed. Must be greater than or equal to
    `self.inverse_min_event_ndims`. The result is summed over the final
    dimensions to produce a scalar Jacobian determinant for each event,
    i.e. it has shape `y.shape.ndims - event_ndims` dimensions.
    </td>
    </tr><tr>
    <td>
    `name`
    </td>
    <td>
    The name to give this op.
    </td>
    </tr>
    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Returns</th></tr>
    <tr class="alt">
    <td colspan="2">
    `Tensor`, if this bijector is injective.
    If not injective, returns the tuple of local log det
    Jacobians, `log(det(Dg_i^{-1}(y)))`, where `g_i` is the restriction
    of `g` to the `ith` partition `Di`.
    </td>
    </tr>

    </table>



    <!-- Tabular view -->
     <table class="responsive fixed orange">
    <colgroup><col width="214px"><col></colgroup>
    <tr><th colspan="2">Raises</th></tr>

    <tr>
    <td>
    `TypeError`
    </td>
    <td>
    if `self.dtype` is specified and `y.dtype` is not
    `self.dtype`.
    </td>
    </tr><tr>
    <td>
    `NotImplementedError`
    </td>
    <td>
    if `_inverse_log_det_jacobian` is not implemented.
    </td>
    </tr>
    </table>