solprop.backends.numba_cpu.spatial#

Execute separable spatial coefficients and bounded Cartesian column transfers.

Functions

`absorber_columns`(samples, rates, first, ...)	Apply spatial and temporal rates without a broadcast-sized allocation.
`accumulate_stage`(stage, weights, solution, error)	Accumulate a complete Cartesian stage into solution and embedded error.
`crop_columns`(fine, crop, target)	Return one transformed physical chunk to its coarse spectral scratch.
`far_field_sum`(partials, totals)	Stage two of the far-field pass: sum the bands serially, in ascending order.
`finish_material`(data, spectrum, window, ...)	Apply the separable prefactor and interaction factor directly to a stage.
`flux_measure`(plane, grid, weights, field, *, ...)	Return a spectrum's axial-flux energy and, when asked, its closure (SEP 34).
`make_far_field`(*, parallel)	Compile stage one of the far-field pass: every band's partial sums.
`make_flux_columns`(*, parallel)	Compile the per-column pass of the plane measure: energy and the closure.
`make_kernels`(*, parallel[, parallel_transfers])	Compile spatial passes with independent stage and copy scheduling.
`pack_columns`(source, crop, fine, scale, analytic)	Pad one physical-space chunk for an unnormalised temporal inverse.
`rotate_noise`(noise, phase, output)	Rotate a fixed noise realization into a persistent stage buffer.
`write_exponent`(data, distance, exponent)	Evaluate the exponent `D distance` that `write_propagator()` takes.
`write_phase`(data, z, phase)	Evaluate the unitary noise phase without a coefficient volume.
`write_propagator`(data, distance, forward, ...)	Evaluate both propagation signs without constructing a coefficient table.

Classes

`FarFieldPass`(problem, *, parallel)	Form the far-field statistics and the on-axis amplitude in one banded pass.
`SpatialKernels`(write_propagator, ...)	Group the independently specialised Cartesian stage operations.

class solprop.backends.numba_cpu.spatial.FarFieldPass(problem, *, parallel)[source]#

Bases: object

Form the far-field statistics and the on-axis amplitude in one banded pass.

SEP 23 section 6 on numba_cpu: stage one (make_far_field()) writes one row of partials per band of columns, in a prange when parallel; stage two (far_field_sum()) adds the bands in ascending order; a finishing step on the host applies epsilon_0 c/2, the spectral-density factor, the energy weights of absorbed_power and the pairing Re(A conj(G)) of each on-axis amplitude with its magnetic closure (SEP 34). The partials are sized from the problem’s own request at construction (solprop.backends.spatial.far_field_partials()) and reused by every call, the periodic channel’s included; a call that needs more slots than were sized for (a spec handed to the run loop with other tables) uses buffers of its own.

Parameters:

problemsolprop.translate.problem.KernelProblem: A Cartesian or line problem, whose separable operator and columns the pass reads.
parallelbool: Whether stage one runs its bands in a prange.

Raises:

BackendError: If the problem is not a Cartesian or line problem with a separable operator that is its own plane measure.

property nbytes: int[source]#

Return the bytes of the partials and their band sum held for the run.

Returns:

int: The statistics_partials row of the memory ledger.

class solprop.backends.numba_cpu.spatial.SpatialKernels(write_propagator, write_exponent, finish_material, accumulate_stage, pack_columns, crop_columns)[source]#

Bases: NamedTuple

Group the independently specialised Cartesian stage operations.

Attributes:

write_propagator, write_exponent, finish_material, accumulate_stagecallable: Wide stage traversals, serial or parallel across independent columns.
pack_columns, crop_columnscallable: Temporal-buffer transfers, with their own parallelism choice.

accumulate_stage: Any#: Alias for field number 3

crop_columns: Any#: Alias for field number 5

finish_material: Any#: Alias for field number 2

pack_columns: Any#: Alias for field number 4

write_exponent: Any#: Alias for field number 1

write_propagator: Any#: Alias for field number 0

solprop.backends.numba_cpu.spatial.absorber_columns(samples, rates, first, n_pol, output)[source]#

Apply spatial and temporal rates without a broadcast-sized allocation.

Parameters:

samplesnumpy.ndarray: Physical time samples, real for a field grid.
ratestuple of numpy.ndarray: Spatial and temporal power rates in m^-1.
firstint: First physical node of this chunk.
n_polint: State polarisation count.
outputnumpy.ndarray: Planned forward-FFT input, overwritten for the active chunk.

solprop.backends.numba_cpu.spatial.accumulate_stage(stage, weights, solution, error)#

Accumulate a complete Cartesian stage into solution and embedded error.

Parameters:

stagenumpy.ndarray: Complete interaction-picture derivative.
weightstuple of float: Solution and embedded-error tableau weights.
solution, errornumpy.ndarray: Persistent accumulators, updated in the existing stage order.

solprop.backends.numba_cpu.spatial.crop_columns(fine, crop, target)#

Return one transformed physical chunk to its coarse spectral scratch.

Parameters:

finenumpy.ndarray: Planned temporal forward output, complex128.
cropnumpy.ndarray: Coarse-to-fine frequency indices.
targetnumpy.ndarray: Coarse scratch rows, overwritten in place.

solprop.backends.numba_cpu.spatial.far_field_sum(partials, totals)[source]#

Stage two of the far-field pass: sum the bands serially, in ascending order.

Parameters:

partialsnumpy.ndarray: Stage one’s partials, shape (n_bands, n_slots, n_omega).
totalsnumpy.ndarray: Overwritten with their sum over bands, shape (n_slots, n_omega).

solprop.backends.numba_cpu.spatial.finish_material(data, spectrum, window, inverse, stage)#

Apply the separable prefactor and interaction factor directly to a stage.

Parameters:

datatuple: Shared schema-5 arrays, evanescent rate, polarisation count and the schema-31 transverse rate per column.
spectrumnumpy.ndarray: Transverse and temporal transform of the nonlinear polarisation.
windownumpy.ndarray: Spectral taper, dimensionless.
inversenumpy.ndarray: Inverse interaction factor.
stagenumpy.ndarray: Stage derivative overwritten in place.

solprop.backends.numba_cpu.spatial.flux_measure(plane, grid, weights, field, *, closure, parallel)[source]#

Return a spectrum’s axial-flux energy and, when asked, its closure (SEP 34).

The compiled form of collect_spatial’s energy and closure.

Parameters:

planesolprop.translate.spatial.SeparableOperator: The plane’s coefficients (FluxPlan.at).
gridsolprop.grid.TimeGrid: The temporal grid.
weightsnumpy.ndarray: The geometry’s spectral weights.
fieldnumpy.ndarray: One internal spectrum.
closurebool: Whether to form the closure conj(eta) E.
parallelbool: Whether the columns run in a prange.

Returns:

tuple: The energy in J and the closure, or None.

solprop.backends.numba_cpu.spatial.make_far_field(*, parallel)[source]#

Compile stage one of the far-field pass: every band’s partial sums.

Parameters:

parallelbool: Whether the bands run in a prange. The bands, and the order of every sum inside one, are fixed by the shapes (far_field_bands()), so the partials do not depend on the thread count.

Returns:

callable: far_field_bands(field, edges, columns, apertures, regions, operator, layout, partials), documented on the compiled function.

solprop.backends.numba_cpu.spatial.make_flux_columns(*, parallel)[source]#

Compile the per-column pass of the plane measure: energy and the closure.

Parameters:

parallelbool: Whether the columns run in a prange; each column’s sum is formed by one thread in ascending frequency order, so the partials do not depend on the thread count.

Returns:

callable: flux_columns(field, squares, kappa, active, omega, weights, energy, closure, partials), documented on the compiled function.

solprop.backends.numba_cpu.spatial.make_kernels(*, parallel, parallel_transfers=False)[source]#

Compile spatial passes with independent stage and copy scheduling.

Parameters:

parallelbool: Whether wide stage operations run across independent columns.
parallel_transfersbool, optional: Whether temporal-buffer copies run across independent columns. Efficient contiguous field copies remain serial; large strided envelope copies benefit.

Returns:

SpatialKernels: Compiled operations with unchanged within-column arithmetic.

solprop.backends.numba_cpu.spatial.pack_columns(source, crop, fine, scale, analytic)#

Pad one physical-space chunk for an unnormalised temporal inverse.

Parameters:

sourcenumpy.ndarray: Coarse physical spectra, complex128.
cropnumpy.ndarray: Coarse-to-fine frequency indices.
finenumpy.ndarray: Planned temporal inverse input, overwritten including unused rows.
scalefloat: Explicit temporal inverse scaling.
analyticbool: Whether to double the bins strictly between the zero frequency and the fine grid’s Nyquist bin, the analytic-signal rule of scipy.signal.hilbert() on the fine grid and of the modal path’s _double_positive_bins.

solprop.backends.numba_cpu.spatial.rotate_noise(noise, phase, output)[source]#

Rotate a fixed noise realization into a persistent stage buffer.

Parameters:

noisenumpy.ndarray: Unadvanced complex noise spectrum.
phasenumpy.ndarray: Unitary phase in radians.
outputnumpy.ndarray: Advanced spectrum, overwritten in place; may own the phase view.

solprop.backends.numba_cpu.spatial.write_exponent(data, distance, exponent)#

Evaluate the exponent D distance that write_propagator() takes.

Parameters:

datatuple: As for write_propagator().
distancefloat: Propagation increment in m.
exponentnumpy.ndarray: Preallocated exponent, complex128, (n_columns, n_omega); overwritten.

solprop.backends.numba_cpu.spatial.write_phase(data, z, phase)[source]#

Evaluate the unitary noise phase without a coefficient volume.

Parameters:

datatuple: Shared spatial coefficients, evanescent rate, polarisation count and the schema-31 transverse rate per column.
zfloat: Absolute propagation position in m.
phasenumpy.ndarray: Real phase buffer, overwritten in radians.

solprop.backends.numba_cpu.spatial.write_propagator(data, distance, forward, inverse)#

Evaluate both propagation signs without constructing a coefficient table.

Parameters:

datatuple: Shared schema-5 arrays, evanescent rate, polarisation count and the schema-31 transverse rate per column.
distancefloat: Propagation increment in m.
forward, inversenumpy.ndarray: Preallocated propagation-factor arrays, complex128.