fmm package

Subpackages

• fmm.backend package
  • Subpackages
    • fmm.backend.test package
      • Module contents
  • Submodules
  • fmm.backend.api module
  • fmm.backend.numba module
  • Module contents
• fmm.test package
  • Submodules
  • fmm.test.test_fmm module
  • fmm.test.test_kernel module
  • fmm.test.test_linalg module
  • fmm.test.test_surface module
  • Module contents

Submodules

fmm.dtype module

Supported datatypes.

fmm.fmm module

The Fmm object acts as the API for interacting the PyExaFMM.

class fmm.fmm.Fmm(config_filename=None)

Bases: object

FMM class. Configure with pre-computed operators and octree.

>>> e = Fmm('config') # Initialise experiment
>>> e.run() # Run upward & downward passes together
>>> e.clear() # Clear containers, to re-run experiment

clear()

Clear containers

downward_pass()

Pre-order traversal of tree. Compute local expansions for all nodes,

and evaluate these at target points.

run()

Run full algorithm

upward_pass()

Post-order traversal of tree, compute multipole expansions for all

nodes.

fmm.kernel module

Kernels

fmm.kernel.laplace_grad_cpu(x, y, c, m_inv_4pi, zero)

Numba Laplace kernel gradient.

x : np.array(shape=(3), dtype=float) y : np.array(shape=(3), dtype=float) c : int

Component to consider, c ∈ {0, 1, 2}.

float

fmm.kernel.laplace_gradient(sources, targets, source_densities)

Numba P2P operator for gradient of Laplace kernel.

sources : np.array(shape=(n, 3), dtype=float) targets : np.array(shape=(m, 3), dtype=float) source_densities : np.array(shape=(m), dtype=float)

np.array(shape=(m, 3), dtype=float)

Target potential gradients.

fmm.kernel.laplace_gram_matrix_parallel(sources, targets)

Dense Numba P2P operator for Laplace kernel.

sources : np.array(shape=(n, 3), dtype=float) targets : np.array(shape=(m, 3), dtype=float)

np.array(shape=(m, n), dtype=float)

The Gram matrix.

fmm.kernel.laplace_gram_matrix_serial(sources, targets)

Dense Numba P2P operator for Laplace kernel.

sources : np.array(shape=(n, 3), dtype=float) targets : np.array(shape=(m, 3), dtype=float)

np.array(shape=(m, n), dtype=float)

The Gram matrix.

fmm.kernel.laplace_kernel_cpu(x, y, m_inv_4pi, zero)

Numba Laplace CPU kernel.

xnp.array(shape=(3), dtype=float)

Source coordinate.

ynp.array(shape=(3), dtype=float)

Target coordinate.

float

fmm.kernel.laplace_p2p_parallel(sources, targets, source_densities, source_index_pointer, target_index_pointer)

Parallelised P2P function, which relies on source/target data being described

by index pointers such that they are arranged by interaction. i.e. targets and all sources required for P2P evaluation have the same pointer. This is needed to maximise cache re-use, and reduce accesses to memory during the parallel evaluation. This function calculates potentials and gradients.

sources: np.array((nsources, 3), dtype=float) targets : np.array((ntargets, 3), dtype=float) source_densities : np.array((nsources, 3), dtype=float) source_index_pointer: np.array(nnodes+1, dtype=int)

Created using the backend.prepare_u_list_data function.

target_index_pointer: np.array(nnodes+1, dtype=int)

Created using the backend.prepare_u_list_data function.

fmm.kernel.laplace_p2p_serial(sources, targets, source_densities)

Numba P2P operator for Laplace kernel.

sources : np.array(shape=(n, 3), dtype=float) targets : np.array(shape=(m, 3), dtype=float) source_densities : np.array(shape=(m,), dtype=float)

np.array(shape=(m), dtype=float)

Target potential densities.

fmm.kernel.laplace_scale(level)

Level scale for the Laplace kernel.

level : int

float

fmm.linalg module

Linear algebra utilities

fmm.linalg.pinv(a)

Moore-Penrose Pseudo-Inverse calculation via SVD.

a : np.array(shape=(m, n), dtype=float)

fmm.linalg.pinv2(a)

Moore-Penrose Pseudo-Inverse calculation via SVD. Return SVD result in two

components, as in Malhotra et. al. (2015).

a : np.array(shape=(m, n), dtype=float)

fmm.surface module

Surface creation utilities

fmm.surface.compute_surface(order, dtype)

Compute surface to a specified order.

orderint

Order, n_coefficients = 6(order-1)^2 + 2

dtypetype

np.float32, np.float64

fmm.surface.scale_surface(surf, radius, level, center, alpha)

Shift and scale a given surface to a new center, and radius relative to the

original surface.

surfnp.array(shape=(n, 3), dtype=float)

Discretized surface.

radiusfloat

Half side length of the octree root node.

levelint

Tree level of the scaled node.

centernp.array(shape=(1, 3), dtype=float)

Centre of the shifted node.

alphafloat

Relative size of surface.

np.array(shape=(n_coeffs, 3), dtype=float)

Scaled and shifted surface.

Module contents