|---| | [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/normal_cdf.py#L32-L94) | Compute `Y = g(X) = NormalCDF(x)`. Inherits From: [`AutoCompositeTensorBijector`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/AutoCompositeTensorBijector), [`Bijector`](https://www.tensorflow.org/probability/api_docs/python/tfp/bijectors/Bijector), [`AutoCompositeTensor`](https://www.tensorflow.org/probability/api_docs/python/tfp/experimental/AutoCompositeTensor) tfp.bijectors.NormalCDF( validate_args=False, name='normal' ) ### Used in the notebooks | Used in the tutorials | |---| | - [A Tour of TensorFlow Probability](https://www.tensorflow.org/probability/examples/A_Tour_of_TensorFlow_Probability) | This bijector maps inputs from `[-inf, inf]` to `[0, 1]`. The inverse of the bijector applied to a uniform random variable `X ~ U(0, 1)` gives back a random variable with the [Normal distribution](https://en.wikipedia.org/wiki/Normal_distribution): Y ~ Normal(0, 1) pdf(y; 0., 1.) = 1 / sqrt(2 * pi) * exp(-y ** 2 / 2)


| ## Args || |---|---| | `validate_args` | Python `bool` indicating whether arguments should be checked for correctness. | | `name` | Python `str` name given to ops managed by this object. |



| ## Attributes || |---|---| | `dtype` |

| | `forward_min_event_ndims` | Returns the minimal number of dimensions bijector.forward operates on.
Multipart bijectors return structured `ndims`, which indicates the expected structure of their inputs. Some multipart bijectors, notably Composites, may return structures of `None`. | | `graph_parents` | Returns this `Bijector`'s graph_parents as a Python list. | | `inverse_min_event_ndims` | Returns the minimal number of dimensions bijector.inverse operates on.
Multipart bijectors return structured `event_ndims`, which indicates the expected structure of their outputs. Some multipart bijectors, notably Composites, may return structures of `None`. | | `is_constant_jacobian` | Returns true iff the Jacobian matrix is not a function of x.
> [!NOTE] > **Note:** Jacobian matrix is either constant for both forward and inverse or neither. | | `name` | Returns the string name of this `Bijector`. | | `name_scope` | Returns a [`tf.name_scope`](https://www.tensorflow.org/api_docs/python/tf/name_scope) instance for this class. | | `non_trainable_variables` | Sequence of non-trainable variables owned by this module and its submodules. > [!NOTE] > **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. | | `parameters` | Dictionary of parameters used to instantiate this `Bijector`. | | `submodules` | Sequence of all sub-modules. Submodules are modules which are properties of this module, or found as properties of modules which are properties of this module (and so on). a = tf.Module() b = tf.Module() c = tf.Module() a.b = b b.c = c list(a.submodules) == [b, c] True list(b.submodules) == [c] True list(c.submodules) == [] True
| | `trainable_variables` | Sequence of trainable variables owned by this module and its submodules.
> [!NOTE] > **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. | | `validate_args` | Returns True if Tensor arguments will be validated. | | `variables` | Sequence of variables owned by this module and its submodules. > [!NOTE] > **Note:** this method uses reflection to find variables on the current instance and submodules. For performance reasons you may wish to cache the result of calling this method if you don't expect the return value to change. | ## Methods ### `copy` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L916-L936) copy( **override_parameters_kwargs ) Creates a copy of the bijector. > [!NOTE] > **Note:** the copy bijector may continue to depend on the original initialization arguments.


| Args || |---|---| | `**override_parameters_kwargs` | String/value dictionary of initialization arguments to override with new values. |



| Returns || |---|---| | `bijector` | A new instance of `type(self)` initialized from the union of self.parameters and override_parameters_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`. |
### `experimental_batch_shape` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1132-L1182) experimental_batch_shape( x_event_ndims=None, y_event_ndims=None ) Returns the batch shape of this bijector for inputs of the given rank. The batch shape of a bijector decribes the set of distinct transformations it represents on events of a given size. For example: the bijector `tfb.Scale([1., 2.])` has batch shape `[2]` for scalar events (`event_ndims = 0`), because applying it to a scalar event produces two scalar outputs, the result of two different scaling transformations. The same bijector has batch shape `[]` for vector events, because applying it to a vector produces (via elementwise multiplication) a single vector output. Bijectors that operate independently on multiple state parts, such as `tfb.JointMap`, must broadcast to a coherent batch shape. Some events may not be valid: for example, the bijector `tfd.JointMap([tfb.Scale([1., 2.]), tfb.Scale([1., 2., 3.])])` does not produce a valid batch shape when `event_ndims = [0, 0]`, since the batch shapes of the two parts are inconsistent. The same bijector does define valid batch shapes of `[]`, `[2]`, and `[3]` if `event_ndims` is `[1, 1]`, `[0, 1]`, or `[1, 0]`, respectively. Since transforming a single event produces a scalar log-det-Jacobian, the batch shape of a bijector with non-constant Jacobian is expected to equal the shape of `forward_log_det_jacobian(x, event_ndims=x_event_ndims)` or `inverse_log_det_jacobian(y, event_ndims=y_event_ndims)`, for `x` or `y` of the specified `ndims`.


| Args || |---|---| | `x_event_ndims` | Optional Python `int` (structure) number of dimensions in a probabilistic event passed to `forward`; this must be greater than or equal to `self.forward_min_event_ndims`. If `None`, defaults to `self.forward_min_event_ndims`. Mutually exclusive with `y_event_ndims`. Default value: `None`. | | `y_event_ndims` | Optional Python `int` (structure) number of dimensions in a probabilistic event passed to `inverse`; this must be greater than or equal to `self.inverse_min_event_ndims`. Mutually exclusive with `x_event_ndims`. Default value: `None`. |



| Returns || |---|---| | `batch_shape` | `TensorShape` batch shape of this bijector for a value with the given event rank. May be unknown or partially defined. |
### `experimental_batch_shape_tensor` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1198-L1248) experimental_batch_shape_tensor( x_event_ndims=None, y_event_ndims=None ) Returns the batch shape of this bijector for inputs of the given rank. The batch shape of a bijector decribes the set of distinct transformations it represents on events of a given size. For example: the bijector `tfb.Scale([1., 2.])` has batch shape `[2]` for scalar events (`event_ndims = 0`), because applying it to a scalar event produces two scalar outputs, the result of two different scaling transformations. The same bijector has batch shape `[]` for vector events, because applying it to a vector produces (via elementwise multiplication) a single vector output. Bijectors that operate independently on multiple state parts, such as `tfb.JointMap`, must broadcast to a coherent batch shape. Some events may not be valid: for example, the bijector `tfd.JointMap([tfb.Scale([1., 2.]), tfb.Scale([1., 2., 3.])])` does not produce a valid batch shape when `event_ndims = [0, 0]`, since the batch shapes of the two parts are inconsistent. The same bijector does define valid batch shapes of `[]`, `[2]`, and `[3]` if `event_ndims` is `[1, 1]`, `[0, 1]`, or `[1, 0]`, respectively. Since transforming a single event produces a scalar log-det-Jacobian, the batch shape of a bijector with non-constant Jacobian is expected to equal the shape of `forward_log_det_jacobian(x, event_ndims=x_event_ndims)` or `inverse_log_det_jacobian(y, event_ndims=y_event_ndims)`, for `x` or `y` of the specified `ndims`.


| Args || |---|---| | `x_event_ndims` | Optional Python `int` (structure) number of dimensions in a probabilistic event passed to `forward`; this must be greater than or equal to `self.forward_min_event_ndims`. If `None`, defaults to `self.forward_min_event_ndims`. Mutually exclusive with `y_event_ndims`. Default value: `None`. | | `y_event_ndims` | Optional Python `int` (structure) number of dimensions in a probabilistic event passed to `inverse`; this must be greater than or equal to `self.inverse_min_event_ndims`. Mutually exclusive with `x_event_ndims`. Default value: `None`. |



| Returns || |---|---| | `batch_shape_tensor` | integer `Tensor` batch shape of this bijector for a value with the given event rank. |
### `experimental_compute_density_correction` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1643-L1674) experimental_compute_density_correction( x, tangent_space, backward_compat=False, **kwargs ) Density correction for this transformation wrt the tangent space, at x. Subclasses of Bijector may call the most specific applicable method of `TangentSpace`, based on whether the transformation is dimension-preserving, coordinate-wise, a projection, or something more general. The backward-compatible assumption is that the transformation is dimension-preserving (goes from R\^n to R\^n).


| Args || |---|---| | `x` | `Tensor` (structure). The point at which to calculate the density. | | `tangent_space` | `TangentSpace` or one of its subclasses. The tangent to the support manifold at `x`. | | `backward_compat` | `bool` specifying whether to assume that the Bijector is dimension-preserving. | | `**kwargs` | Optional keyword arguments forwarded to tangent space methods. |



| Returns || |---|---| | `density_correction` | `Tensor` representing the density correction---in log space---under the transformation that this Bijector denotes. |



| Raises || |---|---| | TypeError if `backward_compat` is False but no method of `TangentSpace` has been called explicitly. ||
### `forward` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1311-L1327) forward( x, name='forward', **kwargs ) Returns the forward `Bijector` evaluation, i.e., X = g(Y).


| Args || |---|---| | `x` | `Tensor` (structure). The input to the 'forward' evaluation. | | `name` | The name to give this op. | | `**kwargs` | Named arguments forwarded to subclass implementation. |



| Returns || |---|---| | `Tensor` (structure). ||



| Raises || |---|---| | `TypeError` | if `self.dtype` is specified and `x.dtype` is not `self.dtype`. | | `NotImplementedError` | if `_forward` is not implemented. |
### `forward_dtype` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1695-L1722) forward_dtype( dtype=UNSPECIFIED, name='forward_dtype', **kwargs ) Returns the dtype returned by `forward` for the provided input. ### `forward_event_ndims` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1753-L1780) forward_event_ndims( event_ndims, **kwargs ) Returns the number of event dimensions produced by `forward`.


| Args || |---|---| | `event_ndims` | Structure of Python and/or Tensor `int`s, and/or `None` values. The structure should match that of `self.forward_min_event_ndims`, and all non-`None` values must be greater than or equal to the corresponding value in `self.forward_min_event_ndims`. | | `**kwargs` | Optional keyword arguments forwarded to nested bijectors. |



| Returns || |---|---| | `forward_event_ndims` | Structure of integers and/or `None` values matching `self.inverse_min_event_ndims`. These are computed using 'prefer static' semantics: if any inputs are `None`, some or all of the outputs may be `None`, indicating that the output dimension could not be inferred (conversely, if all inputs are non-`None`, all outputs will be non-`None`). If all input `event_ndims` are Python `int`s, all of the (non-`None`) outputs will be Python `int`s; otherwise, some or all of the outputs may be `Tensor` `int`s. |
### `forward_event_shape` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L983-L1003) forward_event_shape( input_shape ) Shape of a single sample from a single batch as a `TensorShape`. Same meaning as `forward_event_shape_tensor`. May be only partially defined.


| Args || |---|---| | `input_shape` | `TensorShape` (structure) indicating event-portion shape passed into `forward` function. |



| Returns || |---|---| | `forward_event_shape_tensor` | `TensorShape` (structure) indicating event-portion shape after applying `forward`. Possibly unknown. |
### `forward_event_shape_tensor` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L943-L976) forward_event_shape_tensor( input_shape, name='forward_event_shape_tensor' ) Shape of a single sample from a single batch as an `int32` 1D `Tensor`.


| Args || |---|---| | `input_shape` | `Tensor`, `int32` vector (structure) indicating event-portion shape passed into `forward` function. | | `name` | name to give to the op |



| Returns || |---|---| | `forward_event_shape_tensor` | `Tensor`, `int32` vector (structure) indicating event-portion shape after applying `forward`. |
### `forward_log_det_jacobian` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1604-L1641) forward_log_det_jacobian( x, event_ndims=None, name='forward_log_det_jacobian', **kwargs ) Returns both the forward_log_det_jacobian.


| Args || |---|---| | `x` | `Tensor` (structure). The input to the 'forward' Jacobian determinant evaluation. | | `event_ndims` | Optional number of dimensions in the probabilistic events being transformed; this must be greater than or equal to `self.forward_min_event_ndims`. If `event_ndims` is specified, the log Jacobian determinant is summed to produce a scalar log-determinant for each event. Otherwise (if `event_ndims` is `None`), no reduction is performed. Multipart bijectors require *structured* event_ndims, such that the batch rank `rank(y[i]) - event_ndims[i]` is the same for all elements `i` of the structured input. In most cases (with the exception of `tfb.JointMap`) they further require that `event_ndims[i] - self.inverse_min_event_ndims[i]` is the same for all elements `i` of the structured input. Default value: `None` (equivalent to `self.forward_min_event_ndims`). | | `name` | The name to give this op. | | `**kwargs` | Named arguments forwarded to subclass implementation. |



| Returns || |---|---| | `Tensor` (structure), if this bijector is injective. If not injective this is not implemented. ||



| Raises || |---|---| | `TypeError` | if `y`'s dtype is incompatible with the expected output dtype. | | `NotImplementedError` | if neither `_forward_log_det_jacobian` nor {`_inverse`, `_inverse_log_det_jacobian`} are implemented, or this is a non-injective bijector. | | `ValueError` | if the value of `event_ndims` is not valid for this bijector. |
### `inverse` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1372-L1390) inverse( y, name='inverse', **kwargs ) Returns the inverse `Bijector` evaluation, i.e., X = g\^{-1}(Y).


| Args || |---|---| | `y` | `Tensor` (structure). The input to the 'inverse' evaluation. | | `name` | The name to give this op. | | `**kwargs` | Named arguments forwarded to subclass implementation. |



| Returns || |---|---| | `Tensor` (structure), if this bijector is injective. If not injective, returns the k-tuple containing the unique `k` points `(x1, ..., xk)` such that `g(xi) = y`. ||



| Raises || |---|---| | `TypeError` | if `y`'s structured dtype is incompatible with the expected output dtype. | | `NotImplementedError` | if `_inverse` is not implemented. |
### `inverse_dtype` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1724-L1751) inverse_dtype( dtype=UNSPECIFIED, name='inverse_dtype', **kwargs ) Returns the dtype returned by `inverse` for the provided input. ### `inverse_event_ndims` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1782-L1809) inverse_event_ndims( event_ndims, **kwargs ) Returns the number of event dimensions produced by `inverse`.


| Args || |---|---| | `event_ndims` | Structure of Python and/or Tensor `int`s, and/or `None` values. The structure should match that of `self.inverse_min_event_ndims`, and all non-`None` values must be greater than or equal to the corresponding value in `self.inverse_min_event_ndims`. | | `**kwargs` | Optional keyword arguments forwarded to nested bijectors. |



| Returns || |---|---| | `inverse_event_ndims` | Structure of integers and/or `None` values matching `self.forward_min_event_ndims`. These are computed using 'prefer static' semantics: if any inputs are `None`, some or all of the outputs may be `None`, indicating that the output dimension could not be inferred (conversely, if all inputs are non-`None`, all outputs will be non-`None`). If all input `event_ndims` are Python `int`s, all of the (non-`None`) outputs will be Python `int`s; otherwise, some or all of the outputs may be `Tensor` `int`s. |
### `inverse_event_shape` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1048-L1068) inverse_event_shape( output_shape ) Shape of a single sample from a single batch as a `TensorShape`. Same meaning as `inverse_event_shape_tensor`. May be only partially defined.


| Args || |---|---| | `output_shape` | `TensorShape` (structure) indicating event-portion shape passed into `inverse` function. |



| Returns || |---|---| | `inverse_event_shape_tensor` | `TensorShape` (structure) indicating event-portion shape after applying `inverse`. Possibly unknown. |
### `inverse_event_shape_tensor` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1010-L1041) inverse_event_shape_tensor( output_shape, name='inverse_event_shape_tensor' ) Shape of a single sample from a single batch as an `int32` 1D `Tensor`.


| Args || |---|---| | `output_shape` | `Tensor`, `int32` vector (structure) indicating event-portion shape passed into `inverse` function. | | `name` | name to give to the op |



| Returns || |---|---| | `inverse_event_shape_tensor` | `Tensor`, `int32` vector (structure) indicating event-portion shape after applying `inverse`. |
### `inverse_log_det_jacobian` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1478-L1520) inverse_log_det_jacobian( y, event_ndims=None, name='inverse_log_det_jacobian', **kwargs ) 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)`.


| Args || |---|---| | `y` | `Tensor` (structure). The input to the 'inverse' Jacobian determinant evaluation. | | `event_ndims` | Optional number of dimensions in the probabilistic events being transformed; this must be greater than or equal to `self.inverse_min_event_ndims`. If `event_ndims` is specified, the log Jacobian determinant is summed to produce a scalar log-determinant for each event. Otherwise (if `event_ndims` is `None`), no reduction is performed. Multipart bijectors require *structured* event_ndims, such that the batch rank `rank(y[i]) - event_ndims[i]` is the same for all elements `i` of the structured input. In most cases (with the exception of `tfb.JointMap`) they further require that `event_ndims[i] - self.inverse_min_event_ndims[i]` is the same for all elements `i` of the structured input. Default value: `None` (equivalent to `self.inverse_min_event_ndims`). | | `name` | The name to give this op. | | `**kwargs` | Named arguments forwarded to subclass implementation. |



| Returns || |---|---| | `ildj` | `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`. |



| Raises || |---|---| | `TypeError` | if `x`'s dtype is incompatible with the expected inverse-dtype. | | `NotImplementedError` | if `_inverse_log_det_jacobian` is not implemented. | | `ValueError` | if the value of `event_ndims` is not valid for this bijector. |
### `parameter_properties` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1255-L1274) @classmethod parameter_properties( dtype=tf.float32 ) Returns a dict mapping constructor arg names to property annotations. This dict should include an entry for each of the bijector's `Tensor`-valued constructor arguments.


| Args || |---|---| | `dtype` | Optional float `dtype` to assume for continuous-valued parameters. Some constraining bijectors require advance knowledge of the dtype because certain constants (e.g., `tfb.Softplus.low`) must be instantiated with the same dtype as the values to be transformed. |



| Returns || |---|---| | `parameter_properties` | A `str ->`tfp.python.internal.parameter_properties.ParameterProperties`dict mapping constructor argument names to`ParameterProperties\` instances. |
### `with_name_scope` @classmethod with_name_scope( method ) Decorator to automatically enter the module name scope. class MyModule(tf.Module): @tf.Module.with_name_scope def __call__(self, x): if not hasattr(self, 'w'): self.w = tf.Variable(tf.random.normal([x.shape[1], 3])) return tf.matmul(x, self.w) Using the above module would produce [`tf.Variable`](https://www.tensorflow.org/api_docs/python/tf/Variable)s and [`tf.Tensor`](https://www.tensorflow.org/api_docs/python/tf/Tensor)s whose names included the module name: mod = MyModule() mod(tf.ones([1, 2])) mod.w


| Args || |---|---| | `method` | The method to wrap. |



| Returns || |---|---| | The original method wrapped such that it enters the module's name scope. ||
### `__call__` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L829-L914) __call__( value, name=None, **kwargs ) Applies or composes the `Bijector`, depending on input type. This is a convenience function which applies the `Bijector` instance in three different ways, depending on the input: 1. If the input is a `tfd.Distribution` instance, return `tfd.TransformedDistribution(distribution=input, bijector=self)`. 2. If the input is a `tfb.Bijector` instance, return `tfb.Chain([self, input])`. 3. Otherwise, return `self.forward(input)`


| Args || |---|---| | `value` | A `tfd.Distribution`, `tfb.Bijector`, or a (structure of) `Tensor`. | | `name` | Python `str` name given to ops created by this function. | | `**kwargs` | Additional keyword arguments passed into the created `tfd.TransformedDistribution`, `tfb.Bijector`, or `self.forward`. |



| Returns || |---|---| | `composition` | A `tfd.TransformedDistribution` if the input was a `tfd.Distribution`, a `tfb.Chain` if the input was a `tfb.Bijector`, or a (structure of) `Tensor` computed by `self.forward`. |
#### Examples sigmoid = tfb.Reciprocal()( tfb.Shift(shift=1.)( tfb.Exp()( tfb.Scale(scale=-1.)))) # ==> `tfb.Chain([ # tfb.Reciprocal(), # tfb.Shift(shift=1.), # tfb.Exp(), # tfb.Scale(scale=-1.), # ])` # ie, `tfb.Sigmoid()` log_normal = tfb.Exp()(tfd.Normal(0, 1)) # ==> `tfd.TransformedDistribution(tfd.Normal(0, 1), tfb.Exp())` tfb.Exp()([-1., 0., 1.]) # ==> tf.exp([-1., 0., 1.]) ### `__eq__` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L784-L819) __eq__( other ) Return self==value. ### `__getitem__` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1081-L1092) __getitem__( slices ) ### `__iter__` [View source](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/bijectors/bijector.py#L1094-L1095) __iter__()