WVFourierStorageLayout

Describe how horizontal Fourier storage maps to the WaveVortex grid.

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Overview

WVFourierStorageLayout is developer infrastructure shared by horizontal transform backends. It describes indexing only: the class does not execute an FFT, normalize coefficients, own a backend buffer, or select a transform backend. Model code continues to expose coefficients on the canonical WV grid with shape [Nbatch,Nkl].

Four representations appear in this contract:

• Spatial arrays have shape [Nx,Ny,Nbatch].
• Fourier storage has its natural backend shape. Full-complex storage is [Nx,Ny,Nbatch], half-x storage is [floor(Nx/2)+1,Ny,Nbatch], and half-y storage is [Nx,floor(Ny/2)+1,Nbatch].
• A Fourier row view reshapes the first two storage dimensions to [nFourierStorageRows,Nbatch]. No data is reordered by this reshape.
• The WV grid has shape [Nbatch,Nkl] and uses the ordering defined by WVGeometryDoublyPeriodic.

For real spatial fields, Fourier coefficients obey

\[\hat u(-k,-l)=\overline{\hat u(k,l)}.\]

A full-complex layout stores both sides of this relation. A hermitian-half layout stores one side and recovers WV modes with a negative compressed-direction mode by conjugating the stored positive mode. On zero and even-grid Nyquist boundaries, the other horizontal mode may still require explicit Hermitian completion. Modes that are their own conjugates are made exactly real during insertion.

Mapping indices are one-based uint64 column vectors. They never contain Nbatch- or Nz-replicated offsets. A performance-sensitive backend may consume these properties directly, instead of calling the convenience mapping methods, when doing so preserves a measured MATLAB indexing and assignment expression.

This visible, sealed class is intended for WaveVortex backend developers. It is not an end-user modeling API and is not a supported subclassing point.

Topics

Developer Topics

These items document internal implementation details and are not part of the primary public API.

• Describe Fourier storage
  • Nkl Number of horizontal coefficients in the canonical WV grid.
  • WVFourierStorageLayout Create a Fourier-storage mapping for a doubly periodic geometry.
  • compressedDimension Compressed horizontal dimension for Hermitian-half storage.
  • fourierStorageSize Natural two-dimensional Fourier storage shape.
  • fourierStorageType Fourier storage representation, “full-complex” or “hermitian-half”.
  • horizontalGridSize Physical horizontal grid shape [Nx,Ny].
  • mappingMethod Measured MATLAB mapping implementation used by the layout.
  • nFourierStorageRows Number of rows in the two-dimensional Fourier row view.
• Manage Fourier storage
  • allocateFourierStorage Allocate a zeroed complex Fourier row view.
  • reshapeFourierRowsToStorage Reshape a row view to natural Fourier-storage dimensions.
  • reshapeFourierStorageToRows Reshape natural Fourier storage to its two-dimensional row view.
• Map Fourier storage and WV grid
  • conjugatedWVIndices WV-grid indices recovered by conjugating stored Fourier rows.
  • directWVIndices WV-grid indices supplied directly by stored Fourier rows.
  • fourierRowsForConjugatedWVIndices Fourier rows conjugated while recovering the corresponding WV modes.
  • fourierRowsForDirectWVIndices Fourier rows copied directly to the corresponding WV indices.
  • hermitianCompletionRows Destination rows filled from Hermitian partners before an inverse FFT.
  • hermitianSourceRows Stored rows whose conjugates fill hermitianCompletionRows.
  • hermitianSourceWVIndices WV-grid indices corresponding to hermitianSourceRows.
  • selfConjugateFourierRows Fourier rows representing modes equal to their own Hermitian partner.
  • transformFromFourierStorageToWVGrid Map a Fourier row view to canonical WV-grid ordering.
  • transformFromWVGridToFourierStorage Insert WV-grid coefficients into caller-owned Fourier storage.
• Legacy compatibility
  • expandedLegacyMappings Materialize the vertically expanded legacy full-storage mappings.
• Inspect Fourier storage
  • mappingMemoryBytes Exact bytes occupied by all one-based uint64 mapping arrays.
  • mappingMemoryUsage Return exact memory usage for each mapping array.

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