polar

A = UP, U unitary and P positive semidefinite.

{
  "variable": "measurement_matrix",
  "domain": "Industrial sensor calibration",
  "feature_names": [
    "temperature_c",
    "vibration_mm_s"
  ],
  "matrix": [
    [
      2.0,
      1.0
    ],
    [
      0.0,
      3.0
    ]
  ]
}

# DataLens.ai example
# Factorise the named two- or three-sensor calibration matrix.
from scipy.linalg import polar
U, P = polar(A)
assert np.allclose(U @ P, A) and np.allclose(U.T @ U, np.eye(2))
print("Expected output verified")

BernoulliNB CategoricalNB ComplementNB DecisionTreeClassifier ExtraTreeClassifier GaussianNB GaussianProcessClassifier KNeighborsClassifier LinearDiscriminantAnalysis LinearSVC Logistic Regression MLPClassifier MultinomialNB NuSVC PassiveAggressiveClassifier QuadraticDiscriminantAnalysis RadiusNeighborsClassifier RidgeClassifier RidgeClassifierCV SGDClassifier SVC ARDRegression BayesianRidge BernoulliRBM DecisionTreeRegressor ElasticNet ElasticNetCV ExtraTreeRegressor GammaRegressor GaussianProcessRegressor HuberRegressor KernelDensity KNeighborsRegressor KNeighborsTransformer Lars LarsCV Lasso LassoCV LassoLars LassoLarsCV LassoLarsIC Linear Regression LinearSVR LogisticRegressionCV MLPRegressor MultiTaskElasticNet MultiTaskElasticNetCV MultiTaskLasso MultiTaskLassoCV NearestCentroid NearestNeighbors NeighborhoodComponentsAnalysis NuSVR OneClassSVM OrthogonalMatchingPursuit OrthogonalMatchingPursuitCV PassiveAggressiveRegressor Perceptron PoissonRegressor QuantileRegressor 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median_abs_deviation mode percentileofscore pmean rankdata sem skew trim_mean variation anderson ansari bartlett binomtest bootstrap brunnermunzel chi2_contingency chisquare cramervonmises epps_singleton_2samp f_oneway fisher_exact fligner friedmanchisquare jarque_bera kendalltau kruskal ks_2samp kstest levene mannwhitneyu median_test mood normaltest page_trend_test pearsonr permutation_test ranksums shapiro sobol_indices spearmanr ttest_1samp ttest_ind ttest_rel wilcoxon bessel butter cheby1 cheby2 chirp coherence convolve correlate correlate2d csd deconvolve detrend ellip fftconvolve filtfilt find_peaks firls firwin firwin2 freqs freqz hilbert istft lfilter lombscargle max_len_seq peak_prominences peak_widths periodogram remez resample resample_poly savgol_filter sosfilt sosfiltfilt spectrogram stft welch wiener all_shortest_paths astar_path astar_path_length average_shortest_path_length bellman_ford_path bellman_ford_path_length bidirectional_dijkstra cycle_basis dag_longest_path dag_longest_path_length dijkstra_path dijkstra_path_length find_cycle floyd_warshall floyd_warshall_numpy goldberg_radzik johnson lexicographical_topological_sort maximum_spanning_edges maximum_spanning_tree minimum_cycle_basis minimum_spanning_edges minimum_spanning_tree multi_source_dijkstra negative_edge_cycle random_spanning_tree shortest_path shortest_path_length simple_cycles single_source_dijkstra topological_sort transitive_closure transitive_reduction adamic_adar_index attribute_assortativity_coefficient betweenness_centrality closeness_centrality cn_soundarajan_hopcroft communicability_betweenness_centrality current_flow_betweenness_centrality degree_assortativity_coefficient degree_centrality edge_betweenness_centrality eigenvector_centrality group_betweenness_centrality harmonic_centrality in_degree_centrality information_centrality jaccard_coefficient katz_centrality load_centrality numeric_assortativity_coefficient out_degree_centrality preferential_attachment ra_index_soundarajan_hopcroft resource_allocation_index second_order_centrality subgraph_centrality trophic_levels within_inter_cluster asyn_fluidc asyn_lpa_communities average_clustering clustering edge_betweenness_partition girvan_newman greedy_modularity_communities kernighan_lin_bisection label_propagation_communities louvain_communities modularity partition_quality square_clustering transitivity triangles all_node_cuts average_node_connectivity boykov_kolmogorov capacity_scaling dinitz edge_connectivity edge_disjoint_paths edmonds_karp k_edge_components k_edge_subgraphs local_edge_connectivity local_node_connectivity max_flow_min_cost maximum_flow min_cost_flow minimum_cut minimum_edge_cut minimum_node_cut network_simplex node_connectivity node_disjoint_paths preflow_push shortest_augmenting_path max_clique max_weight_matching maximal_matching maximum_independent_set min_maximal_matching min_weight_matching min_weighted_vertex_cover braycurtis canberra cdist chebyshev cityblock correlation cosine cosine_similarity dice directed_hausdorff euclidean euclidean_distances hamming jaccard jensenshannon mahalanobis manhattan_distances minkowski pairwise_distances pdist rogerstanimoto russellrao seuclidean sokalsneath sqeuclidean yule cumulative_simpson cumulative_trapezoid dblquad nquad odeint polygamma quad romb simpson solve_bvp solve_ivp tplquad trapezoid Akima1DInterpolator BarycentricInterpolator CubicSpline griddata interp1d interpn InterpolatedUnivariateSpline KroghInterpolator lagrange LSQUnivariateSpline PchipInterpolator RBFInterpolator RegularGridInterpolator UnivariateSpline affine_transform binary_closing binary_dilation binary_erosion binary_fill_holes binary_opening black_tophat center_of_mass distance_transform_cdt distance_transform_edt gaussian_filter gaussian_filter1d gaussian_laplace grey_closing grey_dilation grey_erosion grey_opening label laplace map_coordinates maximum_filter median_filter minimum_filter prewitt rotate shift sobel uniform_filter watershed_ift white_tophat zoom cKDTree ConvexHull Delaunay distance_matrix geometric_slerp HalfspaceIntersection KDTree procrustes SphericalVoronoi Voronoi cholesky eig eigh eigvals eigvalsh expm fractional_matrix_power hessenberg logm lu ordqz polar qr qz schur sqrtm svd Shannon entropy