InternalModesProjection

Project arbitrary vertical observations onto resolvable modes.

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Declaration

classdef InternalModesProjection < CAAnnotatedClass

Overview

InternalModesProjection stores the weighted least-squares operator for an observation matrix \(B=H\Phi\). Unlike model transforms, an observation grid may identify a non-contiguous subset of modes. The resolution matrix

\[R = A B\]

describes how true candidate-mode coefficients appear in the recovered retained coefficients.

projection = basis.observationProjection(zObs,component="G");
etaHat = projection.project(etaObs);

Topics

• Inspect projection properties
  • aliasingMatrix Alias matrix formed from rejected-mode columns of the resolution matrix.
  • candidateModes Candidate mode numbers considered by the projection.
  • component label, either "F" or "G".
  • componentRole Component role label.
  • conditionNumber Condition number of gramMatrix.
  • diagnosticFinalRelativePivot Final retained relative QR pivot.
  • diagnosticRankTolerance QR rank tolerance used for mode selection.
  • gramMatrix Retained Gram matrix used in the weighted least-squares solve.
  • isCanonicalComponent True when this projection has a canonical modal spectrum.
  • observationMatrix Explicit observation matrix, when supplied by the caller.
  • observationZ Observation depths for point-sampled projections.
  • projectionMatrix Forward projection matrix from observations to retained coefficients.
  • reconstructionMatrix Reconstruction matrix from retained coefficients to native samples.
  • rejectedModes Rejected candidate mode numbers.
  • resolutionMatrix Resolution matrix from true candidate coefficients to recovered rows.
  • retainedModes Retained mode numbers selected as resolvable.
  • transformStatus Transform construction status.
• Apply observation projections
  • project observations onto retained modal coefficients.
  • reconstruct sampled values from retained coefficients.
• Analyze observation spectra
  • crossSpectrum Compute a retained-mode observation cross-spectrum.
  • expectedRecoveredSpectrum Apply the spectral window to a true candidate-mode spectrum.
  • spectralWeights Candidate-mode spectral weights.
  • spectralWindow Squared resolution matrix used as an expected spectral window.
  • spectrum Compute a retained-mode observation spectrum.
• Persist observation projections
  • InternalModesProjection Create an observation projection from canonical persisted state.
• Other
  • classRequiredPropertyNames

Developer Topics

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

• Developer topics
  • candidateModeIndex Candidate-mode coordinate used by annotated persistence.
  • observationIndex Observation index coordinate used by annotated persistence.
  • retainedModeIndex Retained-mode coordinate used by annotated persistence.
  • selectResolvableModes Select observation-resolvable columns with pivoted QR.
  • weightedProjection Build a weighted projection for selected observation columns.

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