tf_quant_finance.math.pde.grids.uniform_grid_with_extra_point

Last updated: 2023-03-16.

tf_quant_finance.math.pde.grids.uniform_grid_with_extra_point#

View source

Creates a grid spec for a uniform grid with an extra grid point.

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

A uniform grid is characterized by having a constant gap between neighboring points along each axis. An extra grid point is useful, for example, when computing sensitivities for a value through a grid pricing method

Examples#

dtype = np.float64
extra_locations = tf.constant([[1, 2], [2, 3]], dtype=dtype)
min_x, max_x, sizes = [[0, 0], [0, 0]], [[10, 5], [100, 5]], [3, 2]
# Here min_x and max_x are in the original space and *not* in the log-space.
grid = 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, 5, 10], [0, 2, 50, 100]]
print(grid.locations[1])
# [[0, 2, 5], [0, 3, 5]]

Note that the shape of all four parameters must be fully defined and equal to each other. The shape is used to determine the dimension of the grid.

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). For example, if minimums = [0.] and maximums = [1.] and sizes = [3], the grid will have three points at [0.0, 0.5, 1.0].

  • 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) 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.

Contents