tf_quant_finance.math.pde.grids.log_uniform_grid_with_extra_point

Last updated: 2023-03-16.

tf_quant_finance.math.pde.grids.log_uniform_grid_with_extra_point#

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Creates a grid for a uniform grid in a log-space with an extra grid point.

tf_quant_finance.math.pde.grids.log_uniform_grid_with_extra_point(
    minimums, maximums, sizes, extra_grid_point, dtype=None, validate_args=False,
    name=None
)

A log-uniform grid is characterized by having a constant gap between neighboring points along each axis in the log-space, i.e., the logarithm of output grid is the uniform grid. An extra grid point is useful, for example, when computing sensitivities for a value through a grid pricing method.

Note that the shape of all three parameters must be fully defined and equal to each other. The shape is used to determine the dimension of the grid. Note that all the parameters are supplied and returned for the original space and not the log-space.

Examples#

dtype = np.float64
extra_locations = tf.constant([[0.5, 2], [2, 3]], dtype=dtype)
min_x, max_x, sizes = [[0.1, 0.1], [0.01, 0.1]], [[10, 5], [100, 5]], [3, 2]
# Here min_x and max_x are in the original space and *not* in the log-space.
grid = log_uniform_grid_with_extra_point(
    min_x, max_x, sizes,
    extra_grid_point=extra_locations, dtype=dtype)
with tf.Session() as sess:
  grid = sess.run(grid)
# Note that the minimum and maximum grid locations are the same as min_x and
# max_x.
print(grid.locations[0])
# [[0.1, 0.5, 1.0, 10.0], [0.01, 1.0, 2.0, 100.0]]
print(grid.locations[1])
# [[0.1, 2, 5], [0.1, 3, 5]]

Args:#

  • minimums: Real Tensor of rank 1 or 2 containing the lower end points of the grid. Must have the same shape as those of maximums. When rank is 2 the first dimension is the batch dimension.

  • maximums: Tensor of the same dtype and shape as minimums. The upper endpoints of the grid.

  • sizes: Integer rank 1 Tensor of the same shape as minimums. The size of the grid in each axis. Each entry must be greater than or equal to 2 (i.e. the sizes include the end points).

  • extra_grid_point: A Tensor of the same dtype as minimums and of shape [batch_size, n], where batch_shape is a positive integer and n is the number of points along a dimension. These are the extra points added to the grid, so that the output grid locations have shape [batch_shape, n+1].

  • dtype: Optional tf.dtype. The default dtype to use for the grid.

  • validate_args: Python boolean indicating whether to validate the supplied arguments. The validation checks performed are (a) maximums > minimums (b) minimums > 0.0 (c) sizes >= 2.

  • name: Python str. The name prefixed to the ops created by this function. If not supplied, the default name ‘uniform_grid_spec’ is used.

Returns:#

The grid locations as projected along each axis. One Tensor of shape [..., n], where n is the number of points along that axis. The first dimensions are the batch shape. The grid itself can be seen as a cartesian product of the locations array.

Raises:#

ValueError if the shape of maximums, minimums and sizes are not fully defined or they are not identical to each other or they are not rank 1.

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