tf_quant_finance.math.pde.boundary_conditions.dirichlet

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Last updated: 2023-03-16.

tf_quant_finance.math.pde.boundary_conditions.dirichlet#

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Wrapper for Dirichlet boundary conditions to be used in PDE solvers.

tf_quant_finance.math.pde.boundary_conditions.dirichlet(
    boundary_values_fn
)

Example: the boundary value is 1 on both boundaries.

def lower_boundary_fn(t, location_grid):
  return 1

def upper_boundary_fn(t, location_grid):
  return 0

solver = fd_solvers.solve_forward(...,
    boundary_conditions = [(dirichlet(lower_boundary_fn),
                            dirichlet(upper_boundary_fn))],
    ...)

Also can be used as a decorator:

@dirichlet
def lower_boundary_fn(t, location_grid):
  return 1

@dirichlet
def upper_boundary_fn(t, location_grid):
  return 0

solver = fd_solvers.solve_forward(...,
    boundary_conditions = [(lower_boundary_fn, upper_boundary_fn)],
    ...)

Args:#

  • boundary_values_fn: Callable returning the boundary values at given time. Accepts two arguments - the moment of time and the current coordinate grid. Returns a number, a zero-rank Tensor or a Tensor of shape batch_shape + grid_shape', where grid_shape' is grid_shape excluding the axis orthogonal to the boundary. For example, in 3D the value grid shape is batch_shape + (z_size, y_size, x_size), and the boundary tensors on the planes y = y_min and y = y_max should be either scalars or have shape batch_shape + (z_size, x_size). In 1D case this reduces to just batch_shape.

Returns:#

Callable suitable for PDE solvers.

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