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hypercoil prototype (unreleased) documentation - Home

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  • Installation
  • Technical overview
  • Framework
  • API reference
  • Examples

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  • Installation
  • Technical overview
  • Framework
  • API reference
  • Examples

Section Navigation

  • engine: Differentiable engine
  • functional: Functions and functionals
    • activation: Activation functions
      • amplitude_tanh
      • amplitude_atanh
      • corrnorm
      • isochor: PSD normalisation
    • cmass: Centre of mass
      • cmass_coor: Centre of mass, any coordinates
      • cmass: Centre of mass, array coordinates
      • diffuse: Diffuseness around centre of mass
      • Displacement from a reference centre of mass
    • connectopy: Connectopic manifolds
      • laplacian_eigenmaps
      • diffusion_mapping
    • cov: Covariances and correlations
      • cov: Covariance
      • corr: Pearson correlation
      • partialcov: Partial covariance
      • partialcorr: Partial correlation
      • pairedcov: Paired covariance
      • pairedcorr: Paired correlation
      • conditionalcov: Conditional covariance
      • conditionalcorr: Conditional correlation
      • precision: Inverse covariance (precision)
    • fourier: Frequency-domain filter
      • product_filter
      • product_filtfilt: Zero-phase filter
      • unwrap: Unwrap phase
      • analytic_signal
      • hilbert_transform
      • envelope
      • instantaneous_phase
      • instantaneous_frequency
      • env_inst
    • graph: Graphs and networks
      • girvan_newman_null
      • modularity_matrix
      • coaffiliation: Community coaffiliation
      • relaxed_modularity
      • graph_laplacian: Graph Laplacian
    • interpolate: Interpolation and imputation
      • hybrid_interpolate: Linear + spectral interpolation
      • linear_interpolate: Linear interpolation
      • weighted_interpolate
      • spectral_interpolate
    • kernel: Parameterised kernels
      • linear_kernel
      • param_norm
      • linear_distance
      • polynomial_kernel
      • sigmoid_kernel
      • gaussian_kernel
      • rbf_kernel
      • cosine_kernel
      • cov_kernel
      • corr_kernel
    • matrix: Matrix operations
      • cholesky_invert
      • symmetric
      • spd
      • expand_outer
      • recondition_eigenspaces
      • delete_diagonal
      • diag_embed
      • fill_diagonal
      • toeplitz_2d
      • toeplitz
      • sym2vec
      • vec2sym
      • squareform
    • residualise
    • semidefinite: Positive semidefinite cone
      • tangent_project_spd
      • cone_project_spd
      • mean_euc_spd
      • mean_harm_spd
      • mean_logeuc_spd
      • mean_geom_spd
    • sparse: Sparse matrix operations
      • random_sparse
      • spdiagmm
      • dspdmm
      • spspmm_full
      • topk
      • as_topk
      • full_as_topk
      • sparse_astype
      • trace_spspmm
      • spspmm
      • spsp_pairdiff
      • select_indices
      • topkx
      • sp_block_serialise
      • splr_hadamard
      • spsp_innerpaired
      • topk_to_bcoo
      • topk_diagzero
      • topk_diagreplace
      • block_serialise
    • sphere: Spherical coordinates
      • spherical_geodesic
      • sphere_to_normals
      • sphere_to_latlong
      • spatial_conv
      • spherical_conv
      • euclidean_conv
    • sylo: Sylo function
    • symmap: Symmetric matrix maps
      • symmap
      • symexp
      • symlog
      • symsqrt
    • tsconv: Time series convolution
      • conv
      • tsconv2d
      • basischan
      • basisconv2d
      • polychan
      • polyconv2d
    • utils: Miscellaneous
      • conform_mask
      • apply_mask
      • mask_tensor
      • complex_decompose
      • complex_recompose
      • amplitude_apply
    • window: Random windowing
      • sample_windows
      • sample_nonoverlapping_windows_existing_ax
      • sample_nonoverlapping_windows_new_ax
      • sample_overlapping_windows_new_ax
      • sample_overlapping_windows_existing_ax
  • init: Initialisation schemes
    • atlas: Atlas initialisation
      • BaseAtlas
      • DirichletInitBaseAtlas
      • DiscreteVolumetricAtlas
      • MultiVolumetricAtlas
      • MultifileVolumetricAtlas
      • CortexSubcortexCIfTIAtlas
      • DirichletInitVolumetricAtlas
      • DirichletInitSurfaceAtlas
      • AtlasInitialiser
    • atlasmixins: Atlas mixins
    • base: Base initialisations
      • from_distr_init
      • constant_init
      • identity_init
      • MappedInitialiser
      • DistributionInitialiser
      • IdentityInitialiser
    • deltaplus
    • dirichlet
    • freqfilter: Frequency band init
      • FreqFilterSpec
    • iirfilter: IIR filter init
    • laplace
    • mapparam: Mapped parameters and parameter maps
      • MappedParameter
      • DomainMappedParameter
      • IdentityMappedParameter
      • AffineMappedParameter
      • TanhMappedParameter
      • AmplitudeTanhMappedParameter
      • MappedLogits
      • NormSphereParameter
      • ProbabilitySimplexParameter
      • AmplitudeProbabilitySimplexParameter
      • OrthogonalParameter
      • IsochoricParameter
      • Clip
      • Renormalise
      • ForcePositiveDefinite
      • PhaseAmplitudeMixin
    • mpbl
    • semidefinite
      • TangencyInitialiser
      • SemidefiniteMean
    • sylo
    • toeplitz
  • loss: Loss and regularisation
    • Loss: Base class for scalar-valued losses
    • ParameterisedLoss: Extensible class for custom parameterised losses
    • MSELoss: Mean squared error
    • NormedLoss: Normed parameter regularisation
    • identity: Identity function
    • zero: Zero function
    • difference: Elementwise difference
    • constraint_violation: Soft constraints
    • unilateral_loss: Unilateral penalties
    • hinge_loss: SVM hinge loss
    • smoothness: Backwards differences
    • bimodal_symmetric: Minimal distance from 2 modes
    • det_gram: Gramian determinant
    • log_det_gram: Gram log-determinant loss
    • entropy: Categorical entropy
    • kl_divergence: Kullback-Leibler divergence
    • js_divergence: Jensen-Shannon divergence
    • bregman_divergence: Bregman divergences
    • equilibrium: Equilibrium loss
    • second_moment: Second moments
    • auto_tol: Significance tolerance
    • batch_corr: Batch-axis correlation
    • qcfc: QC-FC measures and loss
    • reference_tether: Spatial tether to reference points
    • interhemispheric_tether: Inter-hemispheric tethering loss
    • compactness: Compactness
    • dispersion: Vector dispersion
    • multivariate_kurtosis: Time series stationarity
    • connectopy: Generalised connectopy
    • modularity: Relaxed modularity
    • sum_scalarise: Sum scalarisation
    • mean_scalarise: Mean scalarisation
    • meansq_scalarise: Squared mean scalarisation
    • max_scalarise: Maximum-value scalarisation
    • norm_scalarise: Norm scalarisation
    • vnorm_scalarise: Vector norm scalarisation
    • wmean_scalarise: Weighted mean scalarisation
    • selfwmean_scalarise: Self-weighted mean scalarisation
    • LossApply: Selectively apply loss to parameters
    • LossScheme: Scheme for multiple losses
  • neuro: Neuroscience data utilities
    • synth: Data synthesis
      • match_spectra
      • match_covariance
      • match_reference
      • match_cov_and_spectrum
      • synthesise_matched
      • synthesise_from_cov_and_spectrum
  • nn: Neural network modules
    • activation: Activation functions as modules
      • CorrelationNorm: Correlation normalisation
      • Isochor: Isochoric normalisation
    • atlas: Atlas layers
      • AtlasLinear: Linear atlas layer
    • cov: Covariance modules
      • BaseCovariance: Covariance base class
      • UnaryCovariance
      • UnaryCovarianceTW
      • UnaryCovarianceUW
      • BinaryCovariance
      • BinaryCovarianceTW
      • BinaryCovarianceUW
    • freqfilter: Frequency-domain filter layer
    • iirfilter: IIR filter layer
    • interpolate: Interpolation layers
      • SpectralInterpolate
      • LinearInterpolate
      • HybridInterpolate
    • recombinator
      • Recombinator
    • Residualise
    • semidefinite
      • TangentProject
      • BatchTangentProject
    • SPDNoise
    • SVM
    • sylo
      • Sylo
      • SyloResNet
    • vertcom: Vertex compression
      • VerticalCompression
    • WindowAmplifier
  • API reference
  • init: Initialisation schemes

semidefinite#

Initialise and compute means and mean blocks in the positive semidefinite cone.

  • TangencyInitialiser
    • tangency_init
    • TangencyInitialiser
  • SemidefiniteMean
    • SPDEuclideanMean
    • SPDHarmonicMean
    • SPDLogEuclideanMean
    • SPDGeometricMean
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