solprop.backends.numpy_ref.tdse#

Assemble independently projected TDSE polarisation and current sources.

The native closure’s gated, edge-free source (SEP 26) multiplies the remainder current S by its gate g before the transform and subtracts the edge term DFT[g' S] / (i omega) on the active bins, so that the current is held after the window instead of switched off.

Module Attributes

FFT_ERROR_CONSTANT

Constant c_F of the forward FFT's normwise relative bound c_F eps log2 N.

Functions

`atomic_edge_source`(result, problem, bundle)	Form a gated source's edge array `g' S`, scaled exactly as its current.
`atomic_sources`(fields, result, problem, bundle)	Subtract discrete shadows and apply the declared density and scales once.
`project_atomic_sources`(polarisation, ...[, edge])	Project both sources and reuse atomic rows for an embedded radial indicator.

solprop.backends.numpy_ref.tdse.FFT_ERROR_CONSTANT = 8.0#

Constant c_F of the forward FFT’s normwise relative bound c_F eps log2 N.

Higham (2002), Theorem 24.2: a radix-2 Cooley-Tukey transform with twiddles accurate to mu has ||y - fl(y)|| / ||y|| <= log2(N) eta / (1 - log2(N) eta), eta = mu + gamma_4 (sqrt 2 + mu), about 3.4 eps per level with correctly rounded twiddles. A radix-3 or radix-5 butterfly does more operations per level, but spans log2 3 or log2 5 levels of log2 N; 8 covers the 2-, 3- and 5-smooth sizes solprop’s lattices use (SEP 26 section 4.5). The SEP 26 T3 test measures the constant at a power-of-two and at a 2^a 3^b 5^c size; any other size is flagged in the diagnostic as unqualified. doi:10.1137/1.9780898718027

solprop.backends.numpy_ref.tdse.atomic_edge_source(result, problem, bundle)[source]#

Form a gated source’s edge array g' S, scaled exactly as its current.

S = J - j_1 is the same unscaled remainder atomic_sources() gates (the gated filter admits tdse_native only), g' the analytic derivative of the same gate (SEP 26 section 4.2), and density and remainder_scale enter once, as for the current. Nothing here is differentiated numerically.

Parameters:

resultTDSEResult: Owning microscopic SI histories, already matched to this configuration.
problemKernelProblem: Compiled optical and atomic scientific specification.
bundleStageScalars: Density and other scalars at this evaluation’s absolute position.

Returns:

numpy.ndarray or None: rho s g'(t) S(t) in A/(m² s), shape (n_nodes, 1, n_to), for a gated (native) source; None for a cubic replacement, which has no gate.

Raises:

BackendError: If the descriptor is absent, the result is not this configuration’s, or the array is not finite.

solprop.backends.numpy_ref.tdse.atomic_sources(fields, result, problem, bundle)[source]#

Subtract discrete shadows and apply the declared density and scales once.

Parameters:

fieldsnumpy.ndarray: Chronological real physical fields in V/m, shape (n_nodes, n_to).
resultTDSEResult: Owning microscopic SI histories for these exact inputs.
problemKernelProblem: Compiled optical and atomic scientific specification.
bundleStageScalars: Density and other scalars at this evaluation’s absolute position.

Returns:

tuple of numpy.ndarray: Polarisation in C/m² and current in A/m², each with a scalar component axis. These new arrays never alias or mutate the provider’s histories.

Raises:

BackendError: If an identity, shape or required observable does not match the model.

solprop.backends.numpy_ref.tdse.project_atomic_sources(polarisation, current, result, problem, bundle, prefactor, *, edge=None)[source]#

Project both sources and reuse atomic rows for an embedded radial indicator.

For a gated (native) source the current’s spectrum is the edge-free X - E / (i omega) on the active bins (SEP 26 section 4.4), X and E the raw transforms of the projected gated current and edge array, before the current factor; 1/(i omega) is never formed at the zero or inactive bins, where the current factor is zero anyway.

Parameters:

polarisationnumpy.ndarray: Already calibrated macroscopic polarisation in C/m², shape (n_nodes, 1, n_to).
currentnumpy.ndarray: Already scaled macroscopic remainder current in A/m², same shape.
resultTDSEResult: Unscaled microscopic operands used to derive an absolute cancellation floor.
problemKernelProblem: Resolved modal maps, crop, spectral collar and independent current numerator.
bundleStageScalars: Stage position in m, density in m⁻³ and modal taper scale.
prefactornumpy.ndarray: Stage polarisation factor, including the crop scale and effective index, shape (n_modes, 1, n_omega).
edgenumpy.ndarray or None, optional: atomic_edge_source()’s g' S, same shape as current. Required for a gated (native) source and refused for an ungated one.

Returns:

sourcenumpy.ndarray: Complete spectral derivative before the spectral collar and interaction propagator, shape (n_modes, 1, n_omega). The caller applies these once.
diagnosticsdict: JSON-compatible complete-source and remainder-source norms after the spectral collar, in the same raw FFT modal derivative units. Each reports the embedded discrepancy, an absolute floating-point floor, and no relative score when the fine source is floor dominated. available=False means there is no distinct embedded map. This same-row indicator is not the independent 17-versus-33-node qualification screen. A gated source adds the edge entry of SEP 26 section 5, on the fine projection.

Raises:

BackendError: If a required descriptor, map or source shape is absent or nonfinite.