Misc Tools

Derivative Taker

class sumpy.derivative_taker.ExprDerivativeTaker(expr, var_list, rscale=1, sac=None)

Facilitates the efficient computation of (potentially) high-order derivatives of a given sympy expression expr while attempting to maximize the number of common subexpressions generated. This class defines the interface and realizes a baseline implementation. More specialized implementations may offer better efficiency for special cases. .. automethod:: diff

class sumpy.derivative_taker.LaplaceDerivativeTaker(expr, var_list, rscale=1, sac=None)

Specialized derivative taker for Laplace potential.

class sumpy.derivative_taker.RadialDerivativeTaker(expr, var_list, rscale=1, sac=None)

Specialized derivative taker for radial expressions.

class sumpy.derivative_taker.HelmholtzDerivativeTaker(expr, var_list, rscale=1, sac=None)

Specialized derivative taker for Helmholtz potential.

class sumpy.derivative_taker.DifferentiatedExprDerivativeTaker(taker: ExprDerivativeTaker, derivative_coeff_dict: dict[tuple[int, ...], Any])

Implements the ExprDerivativeTaker interface for an expression that is itself a linear combination of derivatives of a base expression. To take the actual derivatives, it makes use of an underlying derivative taker taker.

taker

A :class:`ExprDerivativeTaker` for the base expression.

derivative_coeff_dict

A dictionary mapping a derivative multi-index to a coefficient.

The expression represented by this derivative taker is the linear

combination of the derivatives of the expression for the

base expression.

Symbolic Tools

class sumpy.symbolic.Basic

The expression base class for the “heavy-duty” computer algebra toolkit in use. Either sympy.core.basic.Basic or symengine.Basic.

class sumpy.symbolic.SpatialConstant(name: str)

A symbolic constant to represent a symbolic variable that is spatially constant.

For example the wave-number \(k\) in the setting of a constant-coefficient Helmholtz problem. For use in sumpy.kernel.ExpressionKernel.expression. Any variable occurring there that is not a SpatialConstant is assumed to have a spatial dependency.

prefix: ClassVar[str] = '_spatial_constant_'

Prefix used in code generation for variables of this type.

as_sympy() → Symbol

Convert variable to a sympy expression.

classmethod from_sympy(expr: Symbol) → SpatialConstant

Convert sympy expression to a constant.

Tools

sumpy.tools.to_complex_dtype(dtype)

sumpy.tools.is_obj_array_like(ary)

sumpy.tools.vector_to_device(queue, vec)

sumpy.tools.vector_from_device(queue, vec)

class sumpy.tools.OrderedSet(iterable=None)

Multi-index Helpers

sumpy.tools.add_mi(mi1: Sequence[int], mi2: Sequence[int]) → tuple[int, ...]

sumpy.tools.mi_factorial(mi: Sequence[int]) → int

sumpy.tools.mi_increment_axis(mi: Sequence[int], axis: int, increment: int) → tuple[int, ...]

sumpy.tools.mi_set_axis(mi: Sequence[int], axis: int, value: int) → tuple[int, ...]

sumpy.tools.mi_power(vector: Sequence[Any], mi: Sequence[int], evaluate: bool = True) → Any

Symbolic Helpers

sumpy.tools.add_to_sac(sac, expr)

sumpy.tools.gather_arguments(kernel_likes)

sumpy.tools.gather_source_arguments(kernel_likes)

sumpy.tools.gather_loopy_arguments(kernel_likes)

sumpy.tools.gather_loopy_source_arguments(kernel_likes)

class sumpy.tools.ScalingAssignmentTag

class sumpy.tools.KernelComputation(ctx: Any, target_kernels: list[Kernel], source_kernels: list[Kernel], strength_usage: list[int] | None = None, value_dtypes: list[numpy.dtype[Any]] | None = None, name: str | None = None, device: Any | None = None)

Common input processing for kernel computations.

name

target_kernels

source_kernels

strength_usage

abstract get_kernel()

class sumpy.tools.KernelCacheMixin

sumpy.tools.reduced_row_echelon_form(m, atol=0)

Calculates a reduced row echelon form of a matrix m.

Parameters:

• m – a 2D numpy.ndarray or a list of lists or a sympy Matrix

• atol – absolute tolerance for values to be considered zero

Returns:

reduced row echelon form as a 2D numpy.ndarray and a list of pivots

sumpy.tools.nullspace(m, atol=0)

Calculates the nullspace of a matrix m.

Parameters:

• m – a 2D numpy.ndarray or a list of lists or a sympy Matrix

• atol – absolute tolerance for values to be considered zero

Returns:

nullspace of m as a 2D numpy.ndarray

FFT

sumpy.tools.fft(seq, inverse=False, sac=None)

Return the discrete fourier transform of the sequence seq. seq should be a python iterable with tuples of length 2 corresponding to the real part and imaginary part.

sumpy.tools.fft_toeplitz_upper_triangular(first_row, x, sac=None)

Returns the matvec of the Toeplitz matrix given by the first row and the vector x using a Fourier transform

sumpy.tools.matvec_toeplitz_upper_triangular(first_row, vector)

class sumpy.tools.FFTBackend(value, names=<not given>, *values, module=None, qualname=None, type=None, start=1, boundary=None)

loopy = 2

FFT backend based on loopy used as a fallback.

pyvkfft = 1

FFT backend based on the vkFFT library.

sumpy.tools.loopy_fft(shape, inverse, complex_dtype, index_dtype=None, name=None)

sumpy.tools.get_opencl_fft_app(queue: pyopencl.CommandQueue, shape: tuple[int, ...], dtype: numpy.dtype[Any], inverse: bool) → Any

Setup an object for out-of-place FFT on with given shape and dtype on given queue.

sumpy.tools.run_opencl_fft(fft_app: tuple[Any, FFTBackend], queue: pyopencl.CommandQueue, input_vec: Any, inverse: bool = False, wait_for: list[pyopencl.Event] | None = None) → tuple[pyopencl.Event, Any]

Runs an FFT on input_vec and returns a MarkerBasedProfilingEvent that indicate the end and start of the operations carried out and the output vector. Only supports in-order queues.

Profiling

sumpy.tools.get_native_event(evt)

class sumpy.tools.ProfileGetter(start: 'int', end: 'int')

class sumpy.tools.AggregateProfilingEvent(events)

An object to hold a list of events and provides compatibility with some of the functionality of pyopencl.Event. Assumes that the last event waits on all of the previous events.

class sumpy.tools.MarkerBasedProfilingEvent(*, end_event, start_event)

An object to hold two marker events and provides compatibility with some of the functionality of pyopencl.Event.

Array Context

class sumpy.array_context.PyOpenCLArrayContext(queue: pyopencl.CommandQueue, allocator: pyopencl.tools.AllocatorBase | None = None, wait_event_queue_length: int | None = None, force_device_scalars: bool | None = None)

Installation

This command should install sumpy:

pip install sumpy

You may need to run this with sudo. If you don’t already have pip, run this beforehand:

curl -O https://raw.github.com/pypa/pip/master/contrib/get-pip.py
python get-pip.py

For a more manual installation, download the source, unpack it, and say:

python setup.py install

In addition, you need to have numpy installed.

Usage

Environment variables

Name	Purpose
SUMPY_FORCE_SYMBOLIC_BACKEND	Symbolic backend control, see Symbolic backends
SUMPY_NO_CACHE	If set, disables the on-disk cache
SUMPY_NO_OPT	If set, disables performance-oriented loopy transformations

Symbolic backends

sumpy supports two symbolic backends: sympy and SymEngine. To use the SymEngine backend, ensure that the SymEngine library and the SymEngine Python bindings are installed.

By default, sumpy prefers using SymEngine but falls back to sympy if it detects that SymEngine is not installed. To force the use of a particular backend, set the environment variable SUMPY_FORCE_SYMBOLIC_BACKEND to symengine or sympy.

User-visible Changes

Version 2016.1

Note

This version is currently under development. You can get snapshots from sumpy’s git repository

• Initial release.

License

sumpy is licensed to you under the MIT/X Consortium license:

Copyright (c) 2012-16 Andreas Klöckner

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Frequently Asked Questions

The FAQ is maintained collaboratively on the Wiki FAQ page.

Acknowledgments

Work on meshmode was supported in part by

• the US National Science Foundation under grant numbers DMS-1418961, DMS-1654756, SHF-1911019, and OAC-1931577.

AK also gratefully acknowledges a hardware gift from Nvidia Corporation.

The views and opinions expressed herein do not necessarily reflect those of the funding agencies.