code: def fast_walsh_hadamard_transform(x):
      """Applies the fast Walsh-Hadamard transform to a set of vectors.
  
      This method uses a composition of existing TensorFlow operations to implement
      the transform.
  
      Args:
        x: A `Tensor`. Must be of shape `[a, b]`, where `a` can be anything (not
          necessarily known), and `b` must be a power of two, not required to be
          statically known.
  
      Returns:
        A `Tensor` of shape `[a, b]`, where `[i, :]` is the product `x[i, :]*H`,
          where `H` is the Hadamard matrix.
  
      Raises:
        ValueError: If the input is not rank 2 `Tensor`, and if the second dimension
          is statically known and is not a power of two.
        OpError: If the second dimension is not statically known and is not a power
          of two. Note that in graph execution, this error is not raised during the
          execution of the Python function, but during execution of the resulting
          computation.
      """
      with tf.compat.v1.name_scope(
          None, "fast_walsh_hadamard_transform"
      ):
          # Validate input.
          x = tf.convert_to_tensor(x)
          if x.shape.ndims != 2:
              raise ValueError(
                  "Number of dimensions of x must be 2. Shape of x: %s"
                  % x.shape
              )
  
          original_x_shape = x.shape.as_list()
          dim = x.shape.as_list()[-1]
  
          if dim is None:  # dim is not statically known.
              dim = tf.shape(x)[-1]
              log2 = tf.cast(
                  tf.math.round(
                      tf.math.log(tf.cast(dim, tf.float32))
                      / tf.math.log(2.0)
                  ),
                  tf.int32,
              )
              with tf.control_dependencies(
                  [
                      tf.compat.v1.assert_equal(
                          dim,
                          tf.math.pow(2, log2),
                          message="The dimension of x must be a power of two."
                          "Provided dimension is: %s" % dim,
                      )
                  ]
              ):
                  x = tf.identity(x)
          else:  # dim is statically known.
              if not (dim and ((dim & (dim - 1)) == 0)):
                  raise ValueError(
                      "The dimension of x must be a power of two. "
                      "Provided dimension is: %s" % dim
                  )
              log2 = int(np.ceil(np.log2(dim)))
              if dim == 1:  # Equivalent to identity.
                  return tf.identity(x)
  
          h_core = tf.constant(
              [[1.0, 1.0], [1.0, -1.0]],
              dtype=x.dtype,
              name="hadamard_weights_2x2",
          )
          permutation = tf.constant(
              [0, 2, 1], name="hadamard_permutation"
          )
  
          # A step of the fast Walsh-Hadamard algorithm.
          def _hadamard_step(x, dim):
              """A single step in the fast Walsh-Hadamard transform."""
              x_shape = x.shape.as_list()
              x = tf.reshape(
                  x, [-1, 2]
              )  # Reshape so that we have a matrix.
              x = tf.matmul(x, h_core)  # Multiply.
              x = tf.reshape(x, [-1, dim // 2, 2])  # Reshape to rank-3.
              x = tf.transpose(
                  x, perm=permutation
              )  # Swap last two dimensions.
              x.set_shape(
                  x_shape
              )  # Failed shape inference in tf.while_loop.
              return x
  
          def _fwht(x, dim, log2):
              x = tf.reshape(x, [-1, 2, dim // 2])
              # The fast Walsh-Hadamard transform.
  
              i = tf.constant(0)
              c = lambda i, x: tf.less(i, log2)
              b = lambda i, x: [i + 1, _hadamard_step(x, dim)]
              i, x = tf.while_loop(c, b, [i, x])
              return x
  
          x = tf.cond(
              tf.equal(dim, 1),
              lambda: tf.identity(x),
              lambda: _fwht(x, dim, log2),
          )
  
          x = tf.reshape(x, [-1, dim])
          x /= tf.sqrt(tf.cast(dim, x.dtype))  # Normalize.
          x.set_shape(
              original_x_shape
          )  # Failed shape inference after tf.while_loop.
          return x
  
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  import logging
  import math
  import numpy
  import tensorflow
label_desc: Use image node_id 1 for calling a global function with example usage: fast_walsh_hadamard_transform(x) and returns: x, x, x, tf