From fd7e2b4728aeb777259d20bf6f4e4bc7e8f036ce Mon Sep 17 00:00:00 2001 From: thibaut-germain Date: Mon, 9 Feb 2026 14:29:44 +0100 Subject: [PATCH 01/14] Sienna & Thibaut works --- RELEASES.md | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/RELEASES.md b/RELEASES.md index 1660913cd..33cc56992 100644 --- a/RELEASES.md +++ b/RELEASES.md @@ -1,5 +1,13 @@ # Releases + +## Upcomming 0.9.7.post1 + +#### New features +The next release will add cost functions between linear operators following [A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems](https://arxiv.org/pdf/2509.24920). + + + ## 0.9.7.dev0 This new release adds support for sparse cost matrices and a new lazy EMD solver that computes distances on-the-fly from coordinates, reducing memory usage from O(n×m) to O(n+m). Both implementations are backend-agnostic and preserve gradient computation for automatic differentiation. From 9b49c768b1a0415ff6a020cbb9eeaf338056e536 Mon Sep 17 00:00:00 2001 From: thibaut-germain Date: Mon, 9 Feb 2026 15:05:52 +0100 Subject: [PATCH 02/14] add sgot file --- ot/sgot.py | 8 ++++++++ 1 file changed, 8 insertions(+) create mode 100644 ot/sgot.py diff --git a/ot/sgot.py b/ot/sgot.py new file mode 100644 index 000000000..5811827da --- /dev/null +++ b/ot/sgot.py @@ -0,0 +1,8 @@ +# -*- coding: utf-8 -*- +""" +Optimal transport for linear operators. +""" + +# Author: Sienna O'Shea +# Thibaut Germain +# License: MIT License From ba3303287f4efc3def0395b5399e45c14928c070 Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Sun, 15 Feb 2026 21:52:31 +0100 Subject: [PATCH 03/14] first draft of sgot.py --- ot/sgot.py | 911 ++++++++++++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 910 insertions(+), 1 deletion(-) diff --git a/ot/sgot.py b/ot/sgot.py index 5811827da..929078f7e 100644 --- a/ot/sgot.py +++ b/ot/sgot.py @@ -1,8 +1,917 @@ # -*- coding: utf-8 -*- """ -Optimal transport for linear operators. +Spectral-Grassmann optimal transport for linear operators. + +This module implements the Spectral-Grassmann Wasserstein framework for +comparing dynamical systems via their learned operator representations. + +It provides tools to extract spectral "atoms" (eigenvalues and associated +eigenspaces) from linear operators and to compute an optimal transport metric +that combines a spectral term on eigenvalues with a Grassmannian term on +eigenspaces. """ # Author: Sienna O'Shea # Thibaut Germain # License: MIT License + +import numpy as np +import ot +from sklearn.utils.extmath import randomized_svd +from ot.backend import get_backend + +### +# Settings : (Ds,Rs,Ls) if primal, (Ds,Xs,prs,pls) if dual +### + +##################################################################################################################################### +##################################################################################################################################### +### PRINCIPAL ANGLE METRICS ### +##################################################################################################################################### +##################################################################################################################################### + + +def hs_metric(Ds, Rs, Ls, Dt, Rt, Lt, sampfreqs: int = 1, sampfreqt: int = 1): + """Compute the Hilbert-Schmidt (Frobenius) distance between two operators. + + Parameters + ---------- + Ds: array-like, shape (n_s,) + Source eigenvalues. + Rs: array-like, shape (L, n_s) + Source right eigenvectors. + Ls: array-like, shape (L, n_s) + Source left eigenvectors. + Dt: array-like, shape (n_t,) + Target eigenvalues. + Rt: array-like, shape (L, n_t) + Target right eigenvectors. + Lt: array-like, shape (L, n_t) + Target left eigenvectors. + sampfreqs: int, optional, sampling frequency for the source operator with default 1 + sampfreqt: int, optional, sampling frequency for the target operator with default 1 + + Returns + ---------- + dist: float, Frobenius norm + """ + Ts = Rs @ (np.exp(Ds / sampfreqs).reshape(-1, 1) * Ls.conj().T) + Tt = Rt @ (np.exp(Dt / sampfreqt).reshape(-1, 1) * Lt.conj().T) + C = Ts - Tt + return np.linalg.norm(C, "fro") + + +def operator_metric( + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, + sampfreqs: int = 1, + sampfreqt: int = 1, + exact: bool = False, + n_iter: int = 5, + random_state: int = None, +): + """Compute the spectral norm distance between two reconstructed operators. + + Parameters + ---------- + Ds: array-like, shape (n_s,) + Source eigenvalues. + Rs: array-like, shape (L, n_s) + Source right eigenvectors. + Ls: array-like, shape (L, n_s) + Source left eigenvectors. + Dt: array-like, shape (n_t,) + Target eigenvalues. + Rt: array-like, shape (L, n_t) + Target right eigenvectors. + Lt: array-like, shape (L, n_t) + Target left eigenvectors. + sampfreqs: int, optional + Sampling frequency for the source operator with default 1 + sampfreqt: int, optional + Sampling frequency for the target operator with default 1 + exact: bool, optional + n_iter: int, optional + random_state: int or None, optional + + Returns + ---------- + dist: float + """ + Ts = Rs @ (np.exp(Ds / sampfreqs).reshape(-1, 1) * Ls.conj().T) + Tt = Rt @ (np.exp(Dt / sampfreqt).reshape(-1, 1) * Lt.conj().T) + C = Ts - Tt + if exact: + return np.linalg.norm(C, 2) + else: + _, S, _ = randomized_svd( + C.real, n_components=1, n_iter=n_iter, random_state=random_state + ) + return S[0] + + +def principal_angles_via_svd(A, B): + """Compute principal angles between two subspaces using SVD of QA^T QB. + + Parameters + A: array-like, shape (d, p) whose columns span the first subspace + B: array-like, shape (d, q) whose columns span the second subspace + + Returns + angle: sorted principal angles (in radians), shape (min(p, q),) + """ + QA, _ = np.linalg.qr(A, mode="reduced") + QB, _ = np.linalg.qr(B, mode="reduced") + C = QA.T @ QB + # SVD of small matrix C + _, S, _ = np.linalg.svd(C, full_matrices=False) + S = np.clip(S, -1.0, 1.0) + angles = np.arccos(S) + return np.sort(angles) + + +def principal_angles_distance( + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, +): + """Compute a principal angles distance between two spectral decompositions. + + Parameters + ---------- + Ds: array-like, shape (n_s,) + Source eigenvalues. + Rs: array-like, shape (L, n_s) + Source right eigenvectors. + Ls: array-like, shape (L, n_s) + Source left eigenvectors. + Dt: array-like, shape (n_t,) + Target eigenvalues. + Rt: array-like, shape (L, n_t) + Target right eigenvectors. + Lt: array-like, shape (L, n_t) + Target left eigenvectors. + + Returns + ------- + dist: float + Principal-angles distance between the two decompositions. + """ + ns = Rs.shape[1] + nt = Rt.shape[1] + Ms = np.vstack( + [(ls[:, None] * rs.conj()[None, :]).flatten() for ls, rs in zip(Ls.T, Rs.T)] + ).T + Mt = np.vstack( + [(lt[:, None] * rt.conj()[None, :]).flatten() for lt, rt in zip(Lt.T, Rt.T)] + ).T + angles = principal_angles_via_svd(Ms, Mt) + if angles.shape[0] != max(ns, nt): + angles = np.hstack([angles, np.pi / 2 * np.ones(max(ns, nt) - angles.shape[0])]) + return np.sqrt(np.sum(angles**2)) + + +##################################################################################################################################### +##################################################################################################################################### +### OT METRIC ### +##################################################################################################################################### +##################################################################################################################################### + + +def principal_grassman_matrix(Ps, Pt, eps: float = 1e-12): + """Compute the unitary Grassmann matrix for source and target domains. + + Parameters + ---------- + Ps : array-like, shape (l, n_ds) + Source domain data, with columns spanning the source subspace. + Pt : array-like, shape (l, n_dt) + Target domain data, with columns spanning the target subspace. + eps : float, optional + Minimum column norm used to avoid division by zero. Default is 1e-12. + + Returns + ------- + C : np.ndarray, shape (n_ds, n_dt) + Grassmann matrix between source and target subspaces. + """ + ns = np.linalg.norm(Ps, axis=0, keepdims=True) + nt = np.linalg.norm(Pt, axis=0, keepdims=True) + ns = np.maximum(ns, eps) + nt = np.maximum(nt, eps) + + Psn = Ps / ns + Ptn = Pt / nt + + C = Psn.conj().T @ Ptn + return C + + +def eigenvector_chordal_cost_matrix(Rs, Ls, Rt, Lt): + """Compute pairwise Grassmann matrices for source and target domains. + + Parameters + ---------- + Rs: array-like, shape (L, n_s) + Source right eigenvectors. + Ls: array-like, shape (L, n_s) + Source left eigenvectors. + Rt: array-like, shape (L, n_t) + Target right eigenvectors. + Lt: array-like, shape (L, n_t) + Target left eigenvectors. + + Returns + ---------- + C: np.ndarray, shape (n_s, n_t) + Eigenvector chordal cost matrix. + """ + Cr = principal_grassman_matrix(Rs, Rt) + Cl = principal_grassman_matrix(Ls, Lt) + C = np.sqrt(1 - np.clip((Cr * Cl).real, a_min=0, a_max=1)) + return C + + +def eigenvalue_cost_matrix(Ds, Dt, real_scale: float = 1.0, imag_scale: float = 1.0): + """Compute pairwise eigenvalue distances for source and target domains. + + Parameters + ---------- + Ds: array-like, shape (n_s,) + Source eigenvalues. + Dt: array-like, shape (n_t,) + Target eigenvalues. + real_scale: float, optional + Scale factor for real parts, default 1.0. + imag_scale: float, optional + Scale factor for imaginary parts, default 1.0. + + Returns + ---------- + C: np.ndarray, shape (n_s, n_t) + Eigenvalue cost matrix. + """ + Dsn = Ds.real * real_scale + 1j * Ds.imag * imag_scale + Dtn = Dt.real * real_scale + 1j * Dt.imag * imag_scale + C = np.abs(Dsn[:, None] - Dtn[None, :]) + return C + + +def ChordalCostFunction( + real_scale: float = 1.0, imag_scale: float = 1.0, alpha: float = 0.5, p: int = 2 +): + """Generate the chordal cost function. + + Parameters + ---------- + real_scale: float, optional + Scale factor for real parts, default 1.0. + imag_scale: float, optional + Scale factor for imaginary parts, default 1.0. + alpha: float, optional + Weighting factor for the eigenvalue cost, default 0.5. + p: int, optional + Power for the chordal distance, default 2. + + Returns + ---------- + cost_function: Chordal cost function. + """ + + def cost_function(Ds, Rs, Ls, Dt, Rt, Lt) -> np.ndarray: + """Compute the chordal cost matrix between source and target spectral decompositions. + + Parameters + ---------- + Ds: array-like, shape (n_s,) + Source eigenvalues. + Rs: array-like, shape (L, n_s) + Source right eigenvectors. + Ls: array-like, shape (L, n_s) + Source left eigenvectors. + Dt: array-like, shape (n_t,) + Target eigenvalues. + Rt: array-like, shape (L, n_t) + Target right eigenvectors. + Lt: array-like, shape (L, n_t) + Target left eigenvectors. + + Returns + ---------- + C: np.ndarray, shape (n_s, n_t) + Chordal cost matrix. + """ + CD = eigenvalue_cost_matrix( + Ds, Dt, real_scale=real_scale, imag_scale=imag_scale + ) + CC = eigenvector_chordal_cost_matrix(Rs, Ls, Rt, Lt) + C = alpha * CD + (1 - alpha) * CC + return C**p + + return cost_function + + +def ot_plan(C, Ws=None, Wt=None): + """Compute the optimal transport plan for a given cost matrix and marginals. + + Parameters + ---------- + C: array-like, shape (n, m) + Cost matrix. + Ws: array-like, shape (n,), optional + Source distribution. If None, uses a uniform distribution. + Wt: array-like, shape (m,), optional + Target distribution. If None, uses a uniform distribution. + + Returns + ---------- + P: np.ndarray, shape (n, m) + Optimal transport plan. + """ + if Ws is None: + Ws = np.ones(C.shape[0]) / C.shape[0] + if Wt is None: + Wt = np.ones(C.shape[1]) / C.shape[1] + return ot.emd(Ws, Wt, C) + + +def ot_score(C, P, p: int = 2) -> float: + """Compute the OT score (distance) given a cost matrix and a transport plan. + + Parameters + ---------- + C: array-like, shape (n, m) + Cost matrix. + P: array-like, shape (n, m) + Transport plan. + p: int, optional + Power for the OT score, default 2. + + Returns + ---------- + dist: float + OT score (distance). + """ + return np.sum(C * P) ** (1 / p) + + +def chordal_metric( + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, + real_scale: float = 1.0, + imag_scale: float = 1.0, + alpha: float = 0.5, + p: int = 2, +): + """Compute the chordal OT metric between two spectral decompositions. + + Parameters + ---------- + Ds: array-like, shape (n_s,) + Source eigenvalues. + Rs: array-like, shape (L, n_s) + Source right eigenvectors. + Ls: array-like, shape (L, n_s) + Source left eigenvectors. + Dt: array-like, shape (n_t,) + Target eigenvalues. + Rt: array-like, shape (L, n_t) + Target right eigenvectors. + Lt: array-like, shape (L, n_t) + Target left eigenvectors. + real_scale: float, optional + Scale factor for real parts, default 1.0. + imag_scale: float, optional + Scale factor for imaginary parts, default 1.0. + alpha: float, optional + Weighting factor for the eigenvalue cost, default 0.5. + p: int, optional + Power for the chordal distance, default 2. + + Returns + ---------- + dist: float + Chordal OT metric value. + """ + cost_fn = ChordalCostFunction(real_scale, imag_scale, alpha, p) + C = cost_fn(Ds, Rs, Ls, Dt, Rt, Lt) + P = ot_plan(C) + return ot_score(C, P, p) + + +##################################################################################################################################### +##################################################################################################################################### +### NORMALISATION AND OPERATOR ATOMS ### +##################################################################################################################################### +##################################################################################################################################### + + +def _normalize_columns(A, nx, eps=1e-12): + """Normalize the columns of an array with a backend-aware norm. + + Parameters + ---------- + A: array-like, shape (d, n) + Input array whose columns are normalized. + nx: module + Backend (NumPy-compatible) used for math operations. + eps: float, optional + Minimum norm value to avoid division by zero, default 1e-12. + + Returns + ---------- + A_norm: array-like, shape (d, n) + Column-normalized array. + """ + nrm = nx.sqrt(nx.sum(A * nx.conj(A), axis=0, keepdims=True)) + nrm = nx.maximum(nrm, eps) + return A / nrm + + +def _delta_matrix_1d_hs(Rs, Ls, Rt, Lt, nx=None, eps=1e-12): + """Compute the normalized inner-product delta matrix for eigenspaces. + + Parameters + ---------- + Rs: array-like, shape (L, n_s) + Source right eigenvectors. + Ls: array-like, shape (L, n_s) + Source left eigenvectors. + Rt: array-like, shape (L, n_t) + Target right eigenvectors. + Lt: array-like, shape (L, n_t) + Target left eigenvectors. + nx: module, optional + Backend (NumPy-compatible). If None, inferred from inputs. + eps: float, optional + Minimum norm value used in normalization, default 1e-12. + + Returns + ---------- + delta: array-like, shape (n_s, n_t) + Delta matrix with entries in [0, 1]. + """ + if nx is None: + nx = get_backend(Rs, Ls, Rt, Lt) + + Rs = nx.asarray(Rs) + Ls = nx.asarray(Ls) + Rt = nx.asarray(Rt) + Lt = nx.asarray(Lt) + + Rsn = _normalize_columns(Rs, nx=nx, eps=eps) + Lsn = _normalize_columns(Ls, nx=nx, eps=eps) + Rtn = _normalize_columns(Rt, nx=nx, eps=eps) + Ltn = _normalize_columns(Lt, nx=nx, eps=eps) + + Cr = nx.dot(nx.conj(Rsn).T, Rtn) + Cl = nx.dot(nx.conj(Lsn).T, Ltn) + + delta = nx.abs(Cr * Cl) + delta = nx.minimum(nx.maximum(delta, 0.0), 1.0) + return delta + + +def _atoms_from_operator(T, r=None, sort_mode="closest_to_1"): + """Extract dua; eigen-atoms from a square operator. + + Parameters + ---------- + T: array-like, shape (d, d) + Input linear operator. + r: int, optional + Number of modes to keep. If None, keep all modes. + sort_mode: str, optional + Eigenvalue sorting mode: "closest_to_1", "closest_to_0", or "largest_mag". + + Returns + ---------- + D: np.ndarray, shape (r,) + Selected eigenvalues. + R: np.ndarray, shape (d, r) + Corresponding right eigenvectors. + L: np.ndarray, shape (d, r) + Dual left eigenvectors. + """ + T = np.asarray(T) + if T.ndim != 2 or T.shape[0] != T.shape[1]: + raise ValueError(f"T must be a square 2D array; got shape {T.shape}") + + d = T.shape[0] + if r is None: + r = d + r = int(r) + if not (1 <= r <= d): + raise ValueError(f"r must be an integer in [1, {d}], got r={r}") + + evals, evecs = np.linalg.eig(T) + + if sort_mode == "closest_to_1": + order = np.argsort(np.abs(evals - 1.0)) + elif sort_mode == "closest_to_0": + order = np.argsort(np.abs(evals)) + elif sort_mode == "largest_mag": + order = np.argsort(-np.abs(evals)) + else: + raise ValueError( + "sort_mode must be one of 'closest_to_1', 'closest_to_0', or 'largest_mag'" + ) + + idx = order[:r] + D = evals[idx] + R = evecs[:, idx] + + evalsL, evecsL = np.linalg.eig(T.conj().T) + + L = np.zeros((d, r), dtype=complex) + used = set() + + for i, lam in enumerate(D): + targets = np.abs(evalsL - np.conj(lam)) + for j in np.argsort(targets): + if j not in used: + used.add(j) + L[:, i] = evecsL[:, j] + break + + G = L.conj().T @ R + if np.linalg.matrix_rank(G) < r: + raise ValueError("Dual normalization failed: L^* R is singular.") + + L = L @ np.linalg.inv(G).conj().T + + return D, R, L + + +##################################################################################################################################### +##################################################################################################################################### +### GRASSMANNIAN METRIC ### +##################################################################################################################################### +##################################################################################################################################### + + +def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1e-300): + """Compute squared Grassmannian distances from delta similarities. + + Parameters + ---------- + delta: array-like + Similarity values in [0, 1]. + grassman_metric: str, optional + Metric type: "geodesic", "chordal", "procrustes", or "martin". + nx: module, optional + Backend (NumPy-compatible). If None, inferred from inputs. + eps: float, optional + Minimum value used for numerical stability, default 1e-300. + + Returns + ---------- + dist2: array-like + Squared Grassmannian distance(s). + """ + if nx is None: + nx = get_backend(delta) + + delta = nx.asarray(delta) + delta = nx.minimum(nx.maximum(delta, 0.0), 1.0) + + if grassman_metric == "geodesic": + return nx.arccos(delta) ** 2 + if grassman_metric == "chordal": + return 1.0 - delta**2 + if grassman_metric == "procrustes": + return 2.0 * (1.0 - delta) + if grassman_metric == "martin": + return -nx.log(nx.maximum(delta**2, eps)) + raise ValueError(f"Unknown grassman_metric: {grassman_metric}") + + +##################################################################################################################################### +##################################################################################################################################### +### SPECTRAL-GRASSMANNIAN WASSERSTEIN METRIC ### +##################################################################################################################################### +##################################################################################################################################### +def cost( + D1, + R1, + L1, + D2, + R2, + L2, + eta=0.5, + p=2, + grassman_metric="chordal", + real_scale=1.0, + imag_scale=1.0, +): + """Compute the SGOT cost matrix between two spectral decompositions. + + Parameters + ---------- + D1: array-like, shape (n_1,) or (n_1, n_1) + Eigenvalues of operator T1 (or diagonal matrix). + R1: array-like, shape (L, n_1) + Right eigenvectors of operator T1. + L1: array-like, shape (L, n_1) + Left eigenvectors of operator T1. + D2: array-like, shape (n_2,) or (n_2, n_2) + Eigenvalues of operator T2 (or diagonal matrix). + R2: array-like, shape (L, n_2) + Right eigenvectors of operator T2. + L2: array-like, shape (L, n_2) + Left eigenvectors of operator T2. + eta: float, optional + Weighting between spectral and Grassmann terms, default 0.5. + p: int, optional + Power for the OT cost, default 2. + grassman_metric: str, optional + Metric type: "geodesic", "chordal", "procrustes", or "martin". + real_scale: float, optional + Scale factor for real parts, default 1.0. + imag_scale: float, optional + Scale factor for imaginary parts, default 1.0. + + Returns + ---------- + C: array-like, shape (n_1, n_2) + SGOT cost matrix. + """ + nx = get_backend(D1, R1, L1, D2, R2, L2) + + D1 = nx.asarray(D1) + D2 = nx.asarray(D2) + if len(D1.shape) == 2: + lam1 = nx.diag(D1) + else: + lam1 = D1.reshape((-1,)) + if len(D2.shape) == 2: + lam2 = nx.diag(D2) + else: + lam2 = D2.reshape((-1,)) + + lam1 = lam1.astype(complex) + lam2 = lam2.astype(complex) + + lam1s = nx.real(lam1) * real_scale + 1j * nx.imag(lam1) * imag_scale + lam2s = nx.real(lam2) * real_scale + 1j * nx.imag(lam2) * imag_scale + C_lambda = nx.abs(lam1s[:, None] - lam2s[None, :]) ** 2 + + delta = _delta_matrix_1d_hs(R1, L1, R2, L2, nx=nx) + C_grass = _grassmann_distance_squared(delta, grassman_metric=grassman_metric, nx=nx) + + C2 = eta * C_lambda + (1.0 - eta) * C_grass + C = C2 ** (p / 2.0) + + return C + + +def metric( + D1, + R1, + L1, + D2, + R2, + L2, + eta=0.5, + p=2, + q=1, + grassman_metric="chordal", + real_scale=1.0, + imag_scale=1.0, + Ws=None, + Wt=None, +): + """Compute the SGOT metric between two spectral decompositions. + + Parameters + ---------- + D1: array-like, shape (n_1,) or (n_1, n_1) + Eigenvalues of operator T1 (or diagonal matrix). + R1: array-like, shape (L, n_1) + Right eigenvectors of operator T1. + L1: array-like, shape (L, n_1) + Left eigenvectors of operator T1. + D2: array-like, shape (n_2,) or (n_2, n_2) + Eigenvalues of operator T2 (or diagonal matrix). + R2: array-like, shape (L, n_2) + Right eigenvectors of operator T2. + L2: array-like, shape (L, n_2) + Left eigenvectors of operator T2. + eta: float, optional + Weighting between spectral and Grassmann terms, default 0.5. + p: int, optional + Power for the OT cost, default 2. + q: int, optional + Outer root applied to the OT objective, default 1. + grassman_metric: str, optional + Metric type: "geodesic", "chordal", "procrustes", or "martin". + real_scale: float, optional + Scale factor for real parts, default 1.0. + imag_scale: float, optional + Scale factor for imaginary parts, default 1.0. + Ws: array-like, shape (n_1,), optional + Source distribution. If None, uses a uniform distribution. + Wt: array-like, shape (n_2,), optional + Target distribution. If None, uses a uniform distribution. + + Returns + ---------- + dist: float + SGOT metric value. + """ + C = cost( + D1, + R1, + L1, + D2, + R2, + L2, + eta=eta, + p=p, + grassman_metric=grassman_metric, + real_scale=real_scale, + imag_scale=imag_scale, + ) + + nx = get_backend(C) + n, m = C.shape + + if Ws is None: + Ws = nx.ones((n,), dtype=C.dtype) / float(n) + else: + Ws = nx.asarray(Ws) + + if Wt is None: + Wt = nx.ones((m,), dtype=C.dtype) / float(m) + else: + Wt = nx.asarray(Wt) + + Ws = Ws / nx.sum(Ws) + Wt = Wt / nx.sum(Wt) + + C_np = ot.backend.to_numpy(C) + Ws_np = ot.backend.to_numpy(Ws) + Wt_np = ot.backend.to_numpy(Wt) + + P = ot_plan(C_np, Ws=Ws_np, Wt=Wt_np) + obj = ot_score(C_np, P, p=p) + + return float(obj) ** (1.0 / float(q)) + + +def metric_from_operator( + T1, + T2, + r=None, + eta=0.5, + p=2, + q=1, + grassman_metric="chordal", + real_scale=1.0, + imag_scale=1.0, + Ws=None, + Wt=None, +): + """Compute the SGOT metric directly from two operators. + + Parameters + ---------- + T1: array-like, shape (d, d) + First operator. + T2: array-like, shape (d, d) + Second operator. + r: int, optional + Number of modes to keep. If None, keep all modes. + eta: float, optional + Weighting between spectral and Grassmann terms, default 0.5. + p: int, optional + Power for the OT cost, default 2. + q: int, optional + Outer root applied to the OT objective, default 1. + grassman_metric: str, optional + Metric type: "geodesic", "chordal", "procrustes", or "martin". + real_scale: float, optional + Scale factor for real parts, default 1.0. + imag_scale: float, optional + Scale factor for imaginary parts, default 1.0. + Ws: array-like, shape (n_1,), optional + Source distribution. If None, uses a uniform distribution. + Wt: array-like, shape (n_2,), optional + Target distribution. If None, uses a uniform distribution. + + Returns + ---------- + dist: float + SGOT metric value. + """ + D1, R1, L1 = _atoms_from_operator(T1, r=r, sort_mode="closest_to_1") + D2, R2, L2 = _atoms_from_operator(T2, r=r, sort_mode="closest_to_1") + + return metric( + D1, + R1, + L1, + D2, + R2, + L2, + eta=eta, + p=p, + q=q, + grassman_metric=grassman_metric, + real_scale=real_scale, + imag_scale=imag_scale, + Ws=Ws, + Wt=Wt, + ) + + +def operator_estimator( + X, + Y=None, + r=None, + ref=1e-8, + force_complex=False, +): + """Estimate a linear operator from data. + + Parameters + ---------- + X: array-like, shape (n_samples, d) or (d, n_samples) + Input snapshot matrix. + Y: array-like, shape like X, optional + Output snapshot matrix. If None, uses a one-step shift of X. + r: int, optional + Rank for optional truncated SVD of the estimated operator. + ref: float, optional + Tikhonov regularization strength, default 1e-8. + force_complex: bool, optional + If True, cast inputs to complex dtype. + + Returns + ---------- + T_hat: np.ndarray, shape (d, d) + Estimated linear operator. + """ + X = np.asarray(X) + + if Y is None: + if X.ndim != 2 or X.shape[0] < 2: + raise ValueError("If Y is None, X must be 2D with at least 2 samples/rows.") + X0 = X[:-1] + Y0 = X[1:] + else: + Y = np.asarray(Y) + if X.shape != Y.shape: + raise ValueError( + f"X and Y must have the same shape; got {X.shape} vs {Y.shape}" + ) + X0, Y0 = X, Y + + if X0.shape[0] >= 1 and X0.shape[0] != X0.shape[1]: + if X0.shape[0] >= X0.shape[1]: + Xc = X0.T + Yc = Y0.T + else: + Xc = X0 + Yc = Y0 + else: + Xc = X0 + Yc = Y0 + + if Xc.ndim != 2 or Yc.ndim != 2: + raise ValueError("X and Y must be 2D arrays after processing.") + + d, n = Xc.shape + if Yc.shape != (d, n): + raise ValueError( + f"After formatting, expected Y to have shape {(d, n)}, got {Yc.shape}" + ) + + if force_complex: + Xc = Xc.astype(complex) + Yc = Yc.astype(complex) + + XXH = Xc @ Xc.conj().T + YXH = Yc @ Xc.conj().T + A = XXH + ref * np.eye(d, dtype=XXH.dtype) + + T_hat = np.linalg.solve(A.T.conj(), YXH.T.conj()).T.conj() + + if r is not None: + if not (1 <= r <= d): + raise ValueError(f"r must be in [1, {d}], got r={r}") + U, S, Vh = np.linalg.svd(T_hat, full_matrices=False) + T_hat = (U[:, :r] * S[:r]) @ Vh[:r, :] + + return T_hat From 3f1011104c107d51ccdbbf900319514a02aea51d Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Fri, 20 Feb 2026 14:29:54 +0100 Subject: [PATCH 04/14] rewrite backend and refactor OT metric --- ot/sgot.py | 568 ++++++++++++++++++++++++----------------------------- 1 file changed, 255 insertions(+), 313 deletions(-) diff --git a/ot/sgot.py b/ot/sgot.py index 929078f7e..86d3a6036 100644 --- a/ot/sgot.py +++ b/ot/sgot.py @@ -17,167 +17,12 @@ import numpy as np import ot -from sklearn.utils.extmath import randomized_svd from ot.backend import get_backend ### # Settings : (Ds,Rs,Ls) if primal, (Ds,Xs,prs,pls) if dual ### -##################################################################################################################################### -##################################################################################################################################### -### PRINCIPAL ANGLE METRICS ### -##################################################################################################################################### -##################################################################################################################################### - - -def hs_metric(Ds, Rs, Ls, Dt, Rt, Lt, sampfreqs: int = 1, sampfreqt: int = 1): - """Compute the Hilbert-Schmidt (Frobenius) distance between two operators. - - Parameters - ---------- - Ds: array-like, shape (n_s,) - Source eigenvalues. - Rs: array-like, shape (L, n_s) - Source right eigenvectors. - Ls: array-like, shape (L, n_s) - Source left eigenvectors. - Dt: array-like, shape (n_t,) - Target eigenvalues. - Rt: array-like, shape (L, n_t) - Target right eigenvectors. - Lt: array-like, shape (L, n_t) - Target left eigenvectors. - sampfreqs: int, optional, sampling frequency for the source operator with default 1 - sampfreqt: int, optional, sampling frequency for the target operator with default 1 - - Returns - ---------- - dist: float, Frobenius norm - """ - Ts = Rs @ (np.exp(Ds / sampfreqs).reshape(-1, 1) * Ls.conj().T) - Tt = Rt @ (np.exp(Dt / sampfreqt).reshape(-1, 1) * Lt.conj().T) - C = Ts - Tt - return np.linalg.norm(C, "fro") - - -def operator_metric( - Ds, - Rs, - Ls, - Dt, - Rt, - Lt, - sampfreqs: int = 1, - sampfreqt: int = 1, - exact: bool = False, - n_iter: int = 5, - random_state: int = None, -): - """Compute the spectral norm distance between two reconstructed operators. - - Parameters - ---------- - Ds: array-like, shape (n_s,) - Source eigenvalues. - Rs: array-like, shape (L, n_s) - Source right eigenvectors. - Ls: array-like, shape (L, n_s) - Source left eigenvectors. - Dt: array-like, shape (n_t,) - Target eigenvalues. - Rt: array-like, shape (L, n_t) - Target right eigenvectors. - Lt: array-like, shape (L, n_t) - Target left eigenvectors. - sampfreqs: int, optional - Sampling frequency for the source operator with default 1 - sampfreqt: int, optional - Sampling frequency for the target operator with default 1 - exact: bool, optional - n_iter: int, optional - random_state: int or None, optional - - Returns - ---------- - dist: float - """ - Ts = Rs @ (np.exp(Ds / sampfreqs).reshape(-1, 1) * Ls.conj().T) - Tt = Rt @ (np.exp(Dt / sampfreqt).reshape(-1, 1) * Lt.conj().T) - C = Ts - Tt - if exact: - return np.linalg.norm(C, 2) - else: - _, S, _ = randomized_svd( - C.real, n_components=1, n_iter=n_iter, random_state=random_state - ) - return S[0] - - -def principal_angles_via_svd(A, B): - """Compute principal angles between two subspaces using SVD of QA^T QB. - - Parameters - A: array-like, shape (d, p) whose columns span the first subspace - B: array-like, shape (d, q) whose columns span the second subspace - - Returns - angle: sorted principal angles (in radians), shape (min(p, q),) - """ - QA, _ = np.linalg.qr(A, mode="reduced") - QB, _ = np.linalg.qr(B, mode="reduced") - C = QA.T @ QB - # SVD of small matrix C - _, S, _ = np.linalg.svd(C, full_matrices=False) - S = np.clip(S, -1.0, 1.0) - angles = np.arccos(S) - return np.sort(angles) - - -def principal_angles_distance( - Ds, - Rs, - Ls, - Dt, - Rt, - Lt, -): - """Compute a principal angles distance between two spectral decompositions. - - Parameters - ---------- - Ds: array-like, shape (n_s,) - Source eigenvalues. - Rs: array-like, shape (L, n_s) - Source right eigenvectors. - Ls: array-like, shape (L, n_s) - Source left eigenvectors. - Dt: array-like, shape (n_t,) - Target eigenvalues. - Rt: array-like, shape (L, n_t) - Target right eigenvectors. - Lt: array-like, shape (L, n_t) - Target left eigenvectors. - - Returns - ------- - dist: float - Principal-angles distance between the two decompositions. - """ - ns = Rs.shape[1] - nt = Rt.shape[1] - Ms = np.vstack( - [(ls[:, None] * rs.conj()[None, :]).flatten() for ls, rs in zip(Ls.T, Rs.T)] - ).T - Mt = np.vstack( - [(lt[:, None] * rt.conj()[None, :]).flatten() for lt, rt in zip(Lt.T, Rt.T)] - ).T - angles = principal_angles_via_svd(Ms, Mt) - if angles.shape[0] != max(ns, nt): - angles = np.hstack([angles, np.pi / 2 * np.ones(max(ns, nt) - angles.shape[0])]) - return np.sqrt(np.sum(angles**2)) - - ##################################################################################################################################### ##################################################################################################################################### ### OT METRIC ### @@ -185,7 +30,7 @@ def principal_angles_distance( ##################################################################################################################################### -def principal_grassman_matrix(Ps, Pt, eps: float = 1e-12): +def principal_grassman_matrix(Ps, Pt, eps: float = 1e-12, nx=None): """Compute the unitary Grassmann matrix for source and target domains. Parameters @@ -202,19 +47,25 @@ def principal_grassman_matrix(Ps, Pt, eps: float = 1e-12): C : np.ndarray, shape (n_ds, n_dt) Grassmann matrix between source and target subspaces. """ - ns = np.linalg.norm(Ps, axis=0, keepdims=True) - nt = np.linalg.norm(Pt, axis=0, keepdims=True) - ns = np.maximum(ns, eps) - nt = np.maximum(nt, eps) + if nx is None: + nx = get_backend(Ps, Pt) + + Ps = nx.asarray(Ps) + Pt = nx.asarray(Pt) + + ns = nx.sqrt(nx.sum(Ps * nx.conj(Ps), axis=0, keepdims=True)) + nt = nx.sqrt(nx.sum(Pt * nx.conj(Pt), axis=0, keepdims=True)) + + ns = nx.clip(ns, eps, 1e300) + nt = nx.clip(nt, eps, 1e300) Psn = Ps / ns Ptn = Pt / nt - C = Psn.conj().T @ Ptn - return C + return nx.dot(nx.conj(Psn).T, Ptn) -def eigenvector_chordal_cost_matrix(Rs, Ls, Rt, Lt): +def eigenvector_chordal_cost_matrix(Rs, Ls, Rt, Lt, nx=None): """Compute pairwise Grassmann matrices for source and target domains. Parameters @@ -233,13 +84,20 @@ def eigenvector_chordal_cost_matrix(Rs, Ls, Rt, Lt): C: np.ndarray, shape (n_s, n_t) Eigenvector chordal cost matrix. """ - Cr = principal_grassman_matrix(Rs, Rt) - Cl = principal_grassman_matrix(Ls, Lt) - C = np.sqrt(1 - np.clip((Cr * Cl).real, a_min=0, a_max=1)) - return C + if nx is None: + nx = get_backend(Rs, Ls, Rt, Lt) + + Cr = principal_grassman_matrix(Rs, Rt, nx=nx) + Cl = principal_grassman_matrix(Ls, Lt, nx=nx) + prod = nx.real(Cr * Cl) + prod = nx.clip(prod, 0.0, 1.0) + return nx.sqrt(1.0 - prod) -def eigenvalue_cost_matrix(Ds, Dt, real_scale: float = 1.0, imag_scale: float = 1.0): + +def eigenvalue_cost_matrix( + Ds, Dt, real_scale: float = 1.0, imag_scale: float = 1.0, nx=None +): """Compute pairwise eigenvalue distances for source and target domains. Parameters @@ -258,19 +116,35 @@ def eigenvalue_cost_matrix(Ds, Dt, real_scale: float = 1.0, imag_scale: float = C: np.ndarray, shape (n_s, n_t) Eigenvalue cost matrix. """ - Dsn = Ds.real * real_scale + 1j * Ds.imag * imag_scale - Dtn = Dt.real * real_scale + 1j * Dt.imag * imag_scale - C = np.abs(Dsn[:, None] - Dtn[None, :]) - return C + if nx is None: + nx = get_backend(Ds, Dt) + + Ds = nx.asarray(Ds) + Dt = nx.asarray(Dt) + Dsn = nx.real(Ds) * real_scale + 1j * nx.imag(Ds) * imag_scale + Dtn = nx.real(Dt) * real_scale + 1j * nx.imag(Dt) * imag_scale + return nx.abs(Dsn[:, None] - Dtn[None, :]) -def ChordalCostFunction( - real_scale: float = 1.0, imag_scale: float = 1.0, alpha: float = 0.5, p: int = 2 +def chordal_cost_matrix( + Ds, Rs, Ls, Dt, Rt, Lt, real_scale=1.0, imag_scale=1.0, alpha=0.5, p=2, nx=None ): - """Generate the chordal cost function. + """Compute the chordal cost matrix between source and target spectral decompositions. Parameters ---------- + Ds: array-like, shape (n_s,) + Source eigenvalues. + Rs: array-like, shape (L, n_s) + Source right eigenvectors. + Ls: array-like, shape (L, n_s) + Source left eigenvectors. + Dt: array-like, shape (n_t,) + Target eigenvalues. + Rt: array-like, shape (L, n_t) + Target right eigenvectors. + Lt: array-like, shape (L, n_t) + Target left eigenvectors. real_scale: float, optional Scale factor for real parts, default 1.0. imag_scale: float, optional @@ -282,43 +156,20 @@ def ChordalCostFunction( Returns ---------- - cost_function: Chordal cost function. + C: np.ndarray, shape (n_s, n_t) + Chordal cost matrix. """ - - def cost_function(Ds, Rs, Ls, Dt, Rt, Lt) -> np.ndarray: - """Compute the chordal cost matrix between source and target spectral decompositions. - - Parameters - ---------- - Ds: array-like, shape (n_s,) - Source eigenvalues. - Rs: array-like, shape (L, n_s) - Source right eigenvectors. - Ls: array-like, shape (L, n_s) - Source left eigenvectors. - Dt: array-like, shape (n_t,) - Target eigenvalues. - Rt: array-like, shape (L, n_t) - Target right eigenvectors. - Lt: array-like, shape (L, n_t) - Target left eigenvectors. - - Returns - ---------- - C: np.ndarray, shape (n_s, n_t) - Chordal cost matrix. - """ - CD = eigenvalue_cost_matrix( - Ds, Dt, real_scale=real_scale, imag_scale=imag_scale - ) - CC = eigenvector_chordal_cost_matrix(Rs, Ls, Rt, Lt) - C = alpha * CD + (1 - alpha) * CC - return C**p - - return cost_function + if nx is None: + nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) + CD = eigenvalue_cost_matrix( + Ds, Dt, real_scale=real_scale, imag_scale=imag_scale, nx=nx + ) + CC = eigenvector_chordal_cost_matrix(Rs, Ls, Rt, Lt, nx=nx) + C = alpha * CD + (1.0 - alpha) * CC + return C**p -def ot_plan(C, Ws=None, Wt=None): +def ot_plan(C, Ws=None, Wt=None, nx=None): """Compute the optimal transport plan for a given cost matrix and marginals. Parameters @@ -335,14 +186,35 @@ def ot_plan(C, Ws=None, Wt=None): P: np.ndarray, shape (n, m) Optimal transport plan. """ + if nx is None: + nx = get_backend(C) + + C = nx.asarray(C) + n, m = C.shape + if Ws is None: - Ws = np.ones(C.shape[0]) / C.shape[0] + Ws = nx.ones((n,), dtype=C.dtype) / float(n) + else: + Ws = nx.asarray(Ws) + if Wt is None: - Wt = np.ones(C.shape[1]) / C.shape[1] - return ot.emd(Ws, Wt, C) + Wt = nx.ones((m,), dtype=C.dtype) / float(m) + else: + Wt = nx.asarray(Wt) + + Ws = Ws / nx.sum(Ws) + Wt = Wt / nx.sum(Wt) + + C_real = nx.real(C) + + C_np = ot.backend.to_numpy(C_real) + Ws_np = ot.backend.to_numpy(Ws) + Wt_np = ot.backend.to_numpy(Wt) + + return ot.emd(Ws_np, Wt_np, C_np) -def ot_score(C, P, p: int = 2) -> float: +def ot_score(C, P, p: int = 2, nx=None): """Compute the OT score (distance) given a cost matrix and a transport plan. Parameters @@ -359,7 +231,11 @@ def ot_score(C, P, p: int = 2) -> float: dist: float OT score (distance). """ - return np.sum(C * P) ** (1 / p) + if nx is None: + nx = get_backend(C) + C = nx.asarray(C) + P = nx.asarray(P) + return float(nx.sum(C * P) ** (1.0 / p)) def chordal_metric( @@ -373,6 +249,7 @@ def chordal_metric( imag_scale: float = 1.0, alpha: float = 0.5, p: int = 2, + nx=None, ): """Compute the chordal OT metric between two spectral decompositions. @@ -404,10 +281,24 @@ def chordal_metric( dist: float Chordal OT metric value. """ - cost_fn = ChordalCostFunction(real_scale, imag_scale, alpha, p) - C = cost_fn(Ds, Rs, Ls, Dt, Rt, Lt) - P = ot_plan(C) - return ot_score(C, P, p) + if nx is None: + nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) + + C = chordal_cost_matrix( + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, + real_scale=real_scale, + imag_scale=imag_scale, + alpha=alpha, + p=p, + nx=nx, + ) + P = ot_plan(C, nx=nx) + return ot_score(C, P, p=p, nx=nx) ##################################################################################################################################### @@ -435,7 +326,7 @@ def _normalize_columns(A, nx, eps=1e-12): Column-normalized array. """ nrm = nx.sqrt(nx.sum(A * nx.conj(A), axis=0, keepdims=True)) - nrm = nx.maximum(nrm, eps) + nrm = nx.clip(nrm, eps, 1e300) return A / nrm @@ -479,7 +370,7 @@ def _delta_matrix_1d_hs(Rs, Ls, Rt, Lt, nx=None, eps=1e-12): Cl = nx.dot(nx.conj(Lsn).T, Ltn) delta = nx.abs(Cr * Cl) - delta = nx.minimum(nx.maximum(delta, 0.0), 1.0) + delta = nx.clip(delta, 0.0, 1.0) return delta @@ -504,52 +395,72 @@ def _atoms_from_operator(T, r=None, sort_mode="closest_to_1"): L: np.ndarray, shape (d, r) Dual left eigenvectors. """ - T = np.asarray(T) + nx = get_backend(T) + T = nx.asarray(T) + if T.ndim != 2 or T.shape[0] != T.shape[1]: raise ValueError(f"T must be a square 2D array; got shape {T.shape}") - d = T.shape[0] + d = int(T.shape[0]) if r is None: r = d r = int(r) if not (1 <= r <= d): raise ValueError(f"r must be an integer in [1, {d}], got r={r}") - evals, evecs = np.linalg.eig(T) + T_np = ot.backend.to_numpy(T) + evals_np, evecs_np = np.linalg.eig(T_np) if sort_mode == "closest_to_1": - order = np.argsort(np.abs(evals - 1.0)) + order = np.argsort(np.abs(evals_np - 1.0)) elif sort_mode == "closest_to_0": - order = np.argsort(np.abs(evals)) + order = np.argsort(np.abs(evals_np)) elif sort_mode == "largest_mag": - order = np.argsort(-np.abs(evals)) + order = np.argsort(-np.abs(evals_np)) else: raise ValueError( "sort_mode must be one of 'closest_to_1', 'closest_to_0', or 'largest_mag'" ) idx = order[:r] - D = evals[idx] - R = evecs[:, idx] + D_np = evals_np[idx] + R_np = evecs_np[:, idx] - evalsL, evecsL = np.linalg.eig(T.conj().T) + evalsL_np, evecsL_np = np.linalg.eig(T_np.conj().T) - L = np.zeros((d, r), dtype=complex) + L_np = np.zeros((d, r), dtype=np.complex128) used = set() - for i, lam in enumerate(D): - targets = np.abs(evalsL - np.conj(lam)) + for i, lam in enumerate(D_np): + targets = np.abs(evalsL_np - np.conj(lam)) for j in np.argsort(targets): if j not in used: used.add(j) - L[:, i] = evecsL[:, j] + L_np[:, i] = evecsL_np[:, j] break - G = L.conj().T @ R - if np.linalg.matrix_rank(G) < r: + if hasattr(nx, "from_numpy"): + D = nx.from_numpy(D_np, type_as=T) + R = nx.from_numpy(R_np, type_as=T) + L = nx.from_numpy(L_np, type_as=T) + else: + D = nx.asarray(D_np) + R = nx.asarray(R_np) + L = nx.asarray(L_np) + + G = nx.dot(nx.conj(L).T, R) + + G_np = ot.backend.to_numpy(G) + if np.linalg.matrix_rank(G_np) < r: raise ValueError("Dual normalization failed: L^* R is singular.") - L = L @ np.linalg.inv(G).conj().T + invG_H_np = np.linalg.inv(G_np).conj().T + if hasattr(nx, "from_numpy"): + invG_H = nx.from_numpy(invG_H_np, type_as=T) + else: + invG_H = nx.asarray(invG_H_np) + + L = nx.dot(L, invG_H) return D, R, L @@ -584,7 +495,7 @@ def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1 nx = get_backend(delta) delta = nx.asarray(delta) - delta = nx.minimum(nx.maximum(delta, 0.0), 1.0) + delta = nx.clip(delta, 0.0, 1.0) if grassman_metric == "geodesic": return nx.arccos(delta) ** 2 @@ -593,7 +504,7 @@ def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1 if grassman_metric == "procrustes": return 2.0 * (1.0 - delta) if grassman_metric == "martin": - return -nx.log(nx.maximum(delta**2, eps)) + return -nx.log(nx.clip(delta**2, eps, 1e300)) raise ValueError(f"Unknown grassman_metric: {grassman_metric}") @@ -603,33 +514,34 @@ def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1 ##################################################################################################################################### ##################################################################################################################################### def cost( - D1, - R1, - L1, - D2, - R2, - L2, + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, eta=0.5, p=2, grassman_metric="chordal", real_scale=1.0, imag_scale=1.0, + nx=None, ): """Compute the SGOT cost matrix between two spectral decompositions. Parameters ---------- - D1: array-like, shape (n_1,) or (n_1, n_1) + Ds: array-like, shape (n_s,) or (n_s, n_s) Eigenvalues of operator T1 (or diagonal matrix). - R1: array-like, shape (L, n_1) + Rs: array-like, shape (L, n_s) Right eigenvectors of operator T1. - L1: array-like, shape (L, n_1) + Ls: array-like, shape (L, n_s) Left eigenvectors of operator T1. - D2: array-like, shape (n_2,) or (n_2, n_2) + Dt: array-like, shape (n_t,) or (n_t, n_t) Eigenvalues of operator T2 (or diagonal matrix). - R2: array-like, shape (L, n_2) + Rt: array-like, shape (L, n_t) Right eigenvectors of operator T2. - L2: array-like, shape (L, n_2) + Lt: array-like, shape (L, n_t) Left eigenvectors of operator T2. eta: float, optional Weighting between spectral and Grassmann terms, default 0.5. @@ -644,21 +556,22 @@ def cost( Returns ---------- - C: array-like, shape (n_1, n_2) + C: array-like, shape (n_s, n_t) SGOT cost matrix. """ - nx = get_backend(D1, R1, L1, D2, R2, L2) + if nx is None: + nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) - D1 = nx.asarray(D1) - D2 = nx.asarray(D2) - if len(D1.shape) == 2: - lam1 = nx.diag(D1) + Ds = nx.asarray(Ds) + Dt = nx.asarray(Dt) + if len(Ds.shape) == 2: + lam1 = nx.diag(Ds) else: - lam1 = D1.reshape((-1,)) - if len(D2.shape) == 2: - lam2 = nx.diag(D2) + lam1 = Ds.reshape((-1,)) + if len(Dt.shape) == 2: + lam2 = nx.diag(Dt) else: - lam2 = D2.reshape((-1,)) + lam2 = Dt.reshape((-1,)) lam1 = lam1.astype(complex) lam2 = lam2.astype(complex) @@ -667,7 +580,7 @@ def cost( lam2s = nx.real(lam2) * real_scale + 1j * nx.imag(lam2) * imag_scale C_lambda = nx.abs(lam1s[:, None] - lam2s[None, :]) ** 2 - delta = _delta_matrix_1d_hs(R1, L1, R2, L2, nx=nx) + delta = _delta_matrix_1d_hs(Rs, Ls, Rt, Lt, nx=nx) C_grass = _grassmann_distance_squared(delta, grassman_metric=grassman_metric, nx=nx) C2 = eta * C_lambda + (1.0 - eta) * C_grass @@ -677,12 +590,12 @@ def cost( def metric( - D1, - R1, - L1, - D2, - R2, - L2, + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, eta=0.5, p=2, q=1, @@ -691,22 +604,23 @@ def metric( imag_scale=1.0, Ws=None, Wt=None, + nx=None, ): """Compute the SGOT metric between two spectral decompositions. Parameters ---------- - D1: array-like, shape (n_1,) or (n_1, n_1) + Ds: array-like, shape (n_s,) or (n_s, n_s) Eigenvalues of operator T1 (or diagonal matrix). - R1: array-like, shape (L, n_1) + Rs: array-like, shape (L, n_s) Right eigenvectors of operator T1. - L1: array-like, shape (L, n_1) + Ls: array-like, shape (L, n_s) Left eigenvectors of operator T1. - D2: array-like, shape (n_2,) or (n_2, n_2) + Dt: array-like, shape (n_t,) or (n_t, n_t) Eigenvalues of operator T2 (or diagonal matrix). - R2: array-like, shape (L, n_2) + Rt: array-like, shape (L, n_t) Right eigenvectors of operator T2. - L2: array-like, shape (L, n_2) + Lt: array-like, shape (L, n_t) Left eigenvectors of operator T2. eta: float, optional Weighting between spectral and Grassmann terms, default 0.5. @@ -720,9 +634,9 @@ def metric( Scale factor for real parts, default 1.0. imag_scale: float, optional Scale factor for imaginary parts, default 1.0. - Ws: array-like, shape (n_1,), optional + Ws: array-like, shape (n_s,), optional Source distribution. If None, uses a uniform distribution. - Wt: array-like, shape (n_2,), optional + Wt: array-like, shape (n_t,), optional Target distribution. If None, uses a uniform distribution. Returns @@ -730,21 +644,24 @@ def metric( dist: float SGOT metric value. """ + if nx is None: + nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) + C = cost( - D1, - R1, - L1, - D2, - R2, - L2, + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, eta=eta, p=p, grassman_metric=grassman_metric, real_scale=real_scale, imag_scale=imag_scale, + nx=nx, ) - nx = get_backend(C) n, m = C.shape if Ws is None: @@ -760,13 +677,8 @@ def metric( Ws = Ws / nx.sum(Ws) Wt = Wt / nx.sum(Wt) - C_np = ot.backend.to_numpy(C) - Ws_np = ot.backend.to_numpy(Ws) - Wt_np = ot.backend.to_numpy(Wt) - - P = ot_plan(C_np, Ws=Ws_np, Wt=Wt_np) - obj = ot_score(C_np, P, p=p) - + P = ot_plan(C, Ws=Ws, Wt=Wt, nx=nx) + obj = ot_score(C, P, p=p, nx=nx) return float(obj) ** (1.0 / float(q)) @@ -805,9 +717,9 @@ def metric_from_operator( Scale factor for real parts, default 1.0. imag_scale: float, optional Scale factor for imaginary parts, default 1.0. - Ws: array-like, shape (n_1,), optional + Ws: array-like, shape (n_s,), optional Source distribution. If None, uses a uniform distribution. - Wt: array-like, shape (n_2,), optional + Wt: array-like, shape (n_t,), optional Target distribution. If None, uses a uniform distribution. Returns @@ -815,16 +727,16 @@ def metric_from_operator( dist: float SGOT metric value. """ - D1, R1, L1 = _atoms_from_operator(T1, r=r, sort_mode="closest_to_1") - D2, R2, L2 = _atoms_from_operator(T2, r=r, sort_mode="closest_to_1") + Ds, Rs, Ls = _atoms_from_operator(T1, r=r, sort_mode="closest_to_1") + Dt, Rt, Lt = _atoms_from_operator(T2, r=r, sort_mode="closest_to_1") return metric( - D1, - R1, - L1, - D2, - R2, - L2, + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, eta=eta, p=p, q=q, @@ -863,16 +775,18 @@ def operator_estimator( T_hat: np.ndarray, shape (d, d) Estimated linear operator. """ - X = np.asarray(X) + nx = get_backend(X, Y) if Y is not None else get_backend(X) + + X = nx.asarray(X) if Y is None: - if X.ndim != 2 or X.shape[0] < 2: + if X.ndim != 2 or int(X.shape[0]) < 2: raise ValueError("If Y is None, X must be 2D with at least 2 samples/rows.") X0 = X[:-1] Y0 = X[1:] else: - Y = np.asarray(Y) - if X.shape != Y.shape: + Y = nx.asarray(Y) + if tuple(X.shape) != tuple(Y.shape): raise ValueError( f"X and Y must have the same shape; got {X.shape} vs {Y.shape}" ) @@ -892,26 +806,54 @@ def operator_estimator( if Xc.ndim != 2 or Yc.ndim != 2: raise ValueError("X and Y must be 2D arrays after processing.") - d, n = Xc.shape - if Yc.shape != (d, n): + d, n = int(Xc.shape[0]), int(Xc.shape[1]) + if tuple(Yc.shape) != (d, n): raise ValueError( f"After formatting, expected Y to have shape {(d, n)}, got {Yc.shape}" ) if force_complex: - Xc = Xc.astype(complex) - Yc = Yc.astype(complex) + Xc_np = ot.backend.to_numpy(Xc) # explicit backend->NumPy copy + Yc_np = ot.backend.to_numpy(Yc) + Xc_np = Xc_np.astype(np.complex128, copy=False) + Yc_np = Yc_np.astype(np.complex128, copy=False) + if hasattr(nx, "from_numpy"): + Xc = nx.from_numpy(Xc_np, type_as=Xc) + Yc = nx.from_numpy(Yc_np, type_as=Yc) + else: + Xc = nx.asarray(Xc_np) + Yc = nx.asarray(Yc_np) + + XXH = nx.dot(Xc, nx.conj(Xc).T) + YXH = nx.dot(Yc, nx.conj(Xc).T) + A = XXH + ref * nx.eye(d, type_as=XXH) - XXH = Xc @ Xc.conj().T - YXH = Yc @ Xc.conj().T - A = XXH + ref * np.eye(d, dtype=XXH.dtype) + AH = nx.conj(A).T + BH = nx.conj(YXH).T - T_hat = np.linalg.solve(A.T.conj(), YXH.T.conj()).T.conj() + AH_np = ot.backend.to_numpy(AH) # explicit backend->NumPy copy + BH_np = ot.backend.to_numpy(BH) + Xsol_np = np.linalg.solve(AH_np, BH_np) + + if hasattr(nx, "from_numpy"): + Xsol = nx.from_numpy(Xsol_np, type_as=YXH) + else: + Xsol = nx.asarray(Xsol_np) + + T_hat = nx.conj(Xsol).T if r is not None: + r = int(r) if not (1 <= r <= d): raise ValueError(f"r must be in [1, {d}], got r={r}") - U, S, Vh = np.linalg.svd(T_hat, full_matrices=False) - T_hat = (U[:, :r] * S[:r]) @ Vh[:r, :] + + T_np = ot.backend.to_numpy(T_hat) # explicit backend->NumPy copy + U, S, Vh = np.linalg.svd(T_np, full_matrices=False) + T_np = (U[:, :r] * S[:r]) @ Vh[:r, :] + + if hasattr(nx, "from_numpy"): + T_hat = nx.from_numpy(T_np, type_as=T_hat) + else: + T_hat = nx.asarray(T_np) return T_hat From d5fef5b6ab5a366b5bb029e13fa8c2fc868ffdd4 Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Sun, 22 Feb 2026 22:37:14 +0100 Subject: [PATCH 05/14] refactor sgot, and implement tests for sgot and backend --- ot/backend.py | 134 +++++++++ ot/sgot.py | 626 +++++-------------------------------------- test/test_backend.py | 24 ++ test/test_sgot.py | 333 +++++++++++++++++++++++ 4 files changed, 564 insertions(+), 553 deletions(-) create mode 100644 test/test_sgot.py diff --git a/ot/backend.py b/ot/backend.py index 3f158d166..b2dfc4024 100644 --- a/ot/backend.py +++ b/ot/backend.py @@ -603,6 +603,55 @@ def clip(self, a, a_min, a_max): """ raise NotImplementedError() + def real(self, a): + """ + Return the real part of the tensor element-wise. + + This function follows the api from :any:`numpy.real` + + See: https://numpy.org/doc/stable/reference/generated/numpy.real.html + """ + raise NotImplementedError() + + def imag(self, a): + """ + Return the imaginary part of the tensor element-wise. + + This function follows the api from :any:`numpy.imag` + + See: https://numpy.org/doc/stable/reference/generated/numpy.imag.html + """ + raise NotImplementedError() + + def conj(self, a): + """ + Return the complex conjugate, element-wise. + + This function follows the api from :any:`numpy.conj` + + See: https://numpy.org/doc/stable/reference/generated/numpy.conj.html + """ + raise NotImplementedError() + + def arccos(self, a): + """ + Trigonometric inverse cosine, element-wise. + + This function follows the api from :any:`numpy.arccos` + + See: https://numpy.org/doc/stable/reference/generated/numpy.arccos.html + """ + raise NotImplementedError() + + def astype(self, a, dtype): + """ + Cast tensor to a given dtype. + + dtype can be a string (e.g. "complex128", "float64") or backend-specific + dtype. Backend converts to the corresponding type. + """ + raise NotImplementedError() + def repeat(self, a, repeats, axis=None): r""" Repeats elements of a tensor. @@ -1294,6 +1343,23 @@ def outer(self, a, b): def clip(self, a, a_min, a_max): return np.clip(a, a_min, a_max) + def real(self, a): + return np.real(a) + + def imag(self, a): + return np.imag(a) + + def conj(self, a): + return np.conj(a) + + def arccos(self, a): + return np.arccos(a) + + def astype(self, a, dtype): + if isinstance(dtype, str): + dtype = getattr(np, dtype, None) or np.dtype(dtype) + return np.asarray(a, dtype=dtype) + def repeat(self, a, repeats, axis=None): return np.repeat(a, repeats, axis) @@ -1711,6 +1777,23 @@ def outer(self, a, b): def clip(self, a, a_min, a_max): return jnp.clip(a, a_min, a_max) + def real(self, a): + return jnp.real(a) + + def imag(self, a): + return jnp.imag(a) + + def conj(self, a): + return jnp.conj(a) + + def arccos(self, a): + return jnp.arccos(a) + + def astype(self, a, dtype): + if isinstance(dtype, str): + dtype = getattr(jnp, dtype, None) or jnp.dtype(dtype) + return jnp.asarray(a, dtype=dtype) + def repeat(self, a, repeats, axis=None): return jnp.repeat(a, repeats, axis) @@ -2208,6 +2291,23 @@ def outer(self, a, b): def clip(self, a, a_min, a_max): return torch.clamp(a, a_min, a_max) + def real(self, a): + return torch.real(a) + + def imag(self, a): + return torch.imag(a) + + def conj(self, a): + return torch.conj(a) + + def arccos(self, a): + return torch.acos(a) + + def astype(self, a, dtype): + if isinstance(dtype, str): + dtype = getattr(torch, dtype, None) + return a.to(dtype=dtype) + def repeat(self, a, repeats, axis=None): return torch.repeat_interleave(a, repeats, dim=axis) @@ -2709,6 +2809,23 @@ def outer(self, a, b): def clip(self, a, a_min, a_max): return cp.clip(a, a_min, a_max) + def real(self, a): + return cp.real(a) + + def imag(self, a): + return cp.imag(a) + + def conj(self, a): + return cp.conj(a) + + def arccos(self, a): + return cp.arccos(a) + + def astype(self, a, dtype): + if isinstance(dtype, str): + dtype = getattr(cp, dtype, None) or cp.dtype(dtype) + return cp.asarray(a, dtype=dtype) + def repeat(self, a, repeats, axis=None): return cp.repeat(a, repeats, axis) @@ -3143,6 +3260,23 @@ def outer(self, a, b): def clip(self, a, a_min, a_max): return tnp.clip(a, a_min, a_max) + def real(self, a): + return tnp.real(a) + + def imag(self, a): + return tnp.imag(a) + + def conj(self, a): + return tnp.conj(a) + + def arccos(self, a): + return tnp.arccos(a) + + def astype(self, a, dtype): + if isinstance(dtype, str): + dtype = getattr(tnp, dtype, None) or tnp.dtype(dtype) + return tnp.array(a, dtype=dtype) + def repeat(self, a, repeats, axis=None): return tnp.repeat(a, repeats, axis) diff --git a/ot/sgot.py b/ot/sgot.py index 86d3a6036..08620b0d2 100644 --- a/ot/sgot.py +++ b/ot/sgot.py @@ -15,88 +15,18 @@ # Thibaut Germain # License: MIT License -import numpy as np import ot from ot.backend import get_backend -### -# Settings : (Ds,Rs,Ls) if primal, (Ds,Xs,prs,pls) if dual -### - ##################################################################################################################################### ##################################################################################################################################### -### OT METRIC ### +### NORMALISATION AND OPERATOR ATOMS ### ##################################################################################################################################### ##################################################################################################################################### -def principal_grassman_matrix(Ps, Pt, eps: float = 1e-12, nx=None): - """Compute the unitary Grassmann matrix for source and target domains. - - Parameters - ---------- - Ps : array-like, shape (l, n_ds) - Source domain data, with columns spanning the source subspace. - Pt : array-like, shape (l, n_dt) - Target domain data, with columns spanning the target subspace. - eps : float, optional - Minimum column norm used to avoid division by zero. Default is 1e-12. - - Returns - ------- - C : np.ndarray, shape (n_ds, n_dt) - Grassmann matrix between source and target subspaces. - """ - if nx is None: - nx = get_backend(Ps, Pt) - - Ps = nx.asarray(Ps) - Pt = nx.asarray(Pt) - - ns = nx.sqrt(nx.sum(Ps * nx.conj(Ps), axis=0, keepdims=True)) - nt = nx.sqrt(nx.sum(Pt * nx.conj(Pt), axis=0, keepdims=True)) - - ns = nx.clip(ns, eps, 1e300) - nt = nx.clip(nt, eps, 1e300) - - Psn = Ps / ns - Ptn = Pt / nt - - return nx.dot(nx.conj(Psn).T, Ptn) - - -def eigenvector_chordal_cost_matrix(Rs, Ls, Rt, Lt, nx=None): - """Compute pairwise Grassmann matrices for source and target domains. - - Parameters - ---------- - Rs: array-like, shape (L, n_s) - Source right eigenvectors. - Ls: array-like, shape (L, n_s) - Source left eigenvectors. - Rt: array-like, shape (L, n_t) - Target right eigenvectors. - Lt: array-like, shape (L, n_t) - Target left eigenvectors. - - Returns - ---------- - C: np.ndarray, shape (n_s, n_t) - Eigenvector chordal cost matrix. - """ - if nx is None: - nx = get_backend(Rs, Ls, Rt, Lt) - - Cr = principal_grassman_matrix(Rs, Rt, nx=nx) - Cl = principal_grassman_matrix(Ls, Lt, nx=nx) - - prod = nx.real(Cr * Cl) - prod = nx.clip(prod, 0.0, 1.0) - return nx.sqrt(1.0 - prod) - - def eigenvalue_cost_matrix( - Ds, Dt, real_scale: float = 1.0, imag_scale: float = 1.0, nx=None + Ds, Dt, q=1, real_scale: float = 1.0, imag_scale: float = 1.0, nx=None ): """Compute pairwise eigenvalue distances for source and target domains. @@ -119,54 +49,11 @@ def eigenvalue_cost_matrix( if nx is None: nx = get_backend(Ds, Dt) - Ds = nx.asarray(Ds) - Dt = nx.asarray(Dt) Dsn = nx.real(Ds) * real_scale + 1j * nx.imag(Ds) * imag_scale Dtn = nx.real(Dt) * real_scale + 1j * nx.imag(Dt) * imag_scale - return nx.abs(Dsn[:, None] - Dtn[None, :]) - - -def chordal_cost_matrix( - Ds, Rs, Ls, Dt, Rt, Lt, real_scale=1.0, imag_scale=1.0, alpha=0.5, p=2, nx=None -): - """Compute the chordal cost matrix between source and target spectral decompositions. - - Parameters - ---------- - Ds: array-like, shape (n_s,) - Source eigenvalues. - Rs: array-like, shape (L, n_s) - Source right eigenvectors. - Ls: array-like, shape (L, n_s) - Source left eigenvectors. - Dt: array-like, shape (n_t,) - Target eigenvalues. - Rt: array-like, shape (L, n_t) - Target right eigenvectors. - Lt: array-like, shape (L, n_t) - Target left eigenvectors. - real_scale: float, optional - Scale factor for real parts, default 1.0. - imag_scale: float, optional - Scale factor for imaginary parts, default 1.0. - alpha: float, optional - Weighting factor for the eigenvalue cost, default 0.5. - p: int, optional - Power for the chordal distance, default 2. - - Returns - ---------- - C: np.ndarray, shape (n_s, n_t) - Chordal cost matrix. - """ - if nx is None: - nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) - CD = eigenvalue_cost_matrix( - Ds, Dt, real_scale=real_scale, imag_scale=imag_scale, nx=nx - ) - CC = eigenvector_chordal_cost_matrix(Rs, Ls, Rt, Lt, nx=nx) - C = alpha * CD + (1.0 - alpha) * CC - return C**p + prod = Dsn[:, None] - Dtn[None, :] + prod = nx.real(prod * nx.conj(prod)) + return prod ** (q / 2) def ot_plan(C, Ws=None, Wt=None, nx=None): @@ -189,123 +76,20 @@ def ot_plan(C, Ws=None, Wt=None, nx=None): if nx is None: nx = get_backend(C) - C = nx.asarray(C) n, m = C.shape if Ws is None: - Ws = nx.ones((n,), dtype=C.dtype) / float(n) - else: - Ws = nx.asarray(Ws) + Ws = nx.ones((n,), type_as=C) / float(n) if Wt is None: - Wt = nx.ones((m,), dtype=C.dtype) / float(m) - else: - Wt = nx.asarray(Wt) + Wt = nx.ones((m,), type_as=C) / float(m) Ws = Ws / nx.sum(Ws) Wt = Wt / nx.sum(Wt) C_real = nx.real(C) - C_np = ot.backend.to_numpy(C_real) - Ws_np = ot.backend.to_numpy(Ws) - Wt_np = ot.backend.to_numpy(Wt) - - return ot.emd(Ws_np, Wt_np, C_np) - - -def ot_score(C, P, p: int = 2, nx=None): - """Compute the OT score (distance) given a cost matrix and a transport plan. - - Parameters - ---------- - C: array-like, shape (n, m) - Cost matrix. - P: array-like, shape (n, m) - Transport plan. - p: int, optional - Power for the OT score, default 2. - - Returns - ---------- - dist: float - OT score (distance). - """ - if nx is None: - nx = get_backend(C) - C = nx.asarray(C) - P = nx.asarray(P) - return float(nx.sum(C * P) ** (1.0 / p)) - - -def chordal_metric( - Ds, - Rs, - Ls, - Dt, - Rt, - Lt, - real_scale: float = 1.0, - imag_scale: float = 1.0, - alpha: float = 0.5, - p: int = 2, - nx=None, -): - """Compute the chordal OT metric between two spectral decompositions. - - Parameters - ---------- - Ds: array-like, shape (n_s,) - Source eigenvalues. - Rs: array-like, shape (L, n_s) - Source right eigenvectors. - Ls: array-like, shape (L, n_s) - Source left eigenvectors. - Dt: array-like, shape (n_t,) - Target eigenvalues. - Rt: array-like, shape (L, n_t) - Target right eigenvectors. - Lt: array-like, shape (L, n_t) - Target left eigenvectors. - real_scale: float, optional - Scale factor for real parts, default 1.0. - imag_scale: float, optional - Scale factor for imaginary parts, default 1.0. - alpha: float, optional - Weighting factor for the eigenvalue cost, default 0.5. - p: int, optional - Power for the chordal distance, default 2. - - Returns - ---------- - dist: float - Chordal OT metric value. - """ - if nx is None: - nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) - - C = chordal_cost_matrix( - Ds, - Rs, - Ls, - Dt, - Rt, - Lt, - real_scale=real_scale, - imag_scale=imag_scale, - alpha=alpha, - p=p, - nx=nx, - ) - P = ot_plan(C, nx=nx) - return ot_score(C, P, p=p, nx=nx) - - -##################################################################################################################################### -##################################################################################################################################### -### NORMALISATION AND OPERATOR ATOMS ### -##################################################################################################################################### -##################################################################################################################################### + return ot.emd(Ws, Wt, C_real) def _normalize_columns(A, nx, eps=1e-12): @@ -326,11 +110,12 @@ def _normalize_columns(A, nx, eps=1e-12): Column-normalized array. """ nrm = nx.sqrt(nx.sum(A * nx.conj(A), axis=0, keepdims=True)) - nrm = nx.clip(nrm, eps, 1e300) + nrm = nx.real(nrm) # norm is real; avoid complex dtype for maximum (e.g. torch) + nrm = nx.maximum(nrm, eps) return A / nrm -def _delta_matrix_1d_hs(Rs, Ls, Rt, Lt, nx=None, eps=1e-12): +def _delta_matrix_1d(Rs, Ls, Rt, Lt, nx=None, eps=1e-12): """Compute the normalized inner-product delta matrix for eigenspaces. Parameters @@ -356,11 +141,6 @@ def _delta_matrix_1d_hs(Rs, Ls, Rt, Lt, nx=None, eps=1e-12): if nx is None: nx = get_backend(Rs, Ls, Rt, Lt) - Rs = nx.asarray(Rs) - Ls = nx.asarray(Ls) - Rt = nx.asarray(Rt) - Lt = nx.asarray(Lt) - Rsn = _normalize_columns(Rs, nx=nx, eps=eps) Lsn = _normalize_columns(Ls, nx=nx, eps=eps) Rtn = _normalize_columns(Rt, nx=nx, eps=eps) @@ -374,104 +154,6 @@ def _delta_matrix_1d_hs(Rs, Ls, Rt, Lt, nx=None, eps=1e-12): return delta -def _atoms_from_operator(T, r=None, sort_mode="closest_to_1"): - """Extract dua; eigen-atoms from a square operator. - - Parameters - ---------- - T: array-like, shape (d, d) - Input linear operator. - r: int, optional - Number of modes to keep. If None, keep all modes. - sort_mode: str, optional - Eigenvalue sorting mode: "closest_to_1", "closest_to_0", or "largest_mag". - - Returns - ---------- - D: np.ndarray, shape (r,) - Selected eigenvalues. - R: np.ndarray, shape (d, r) - Corresponding right eigenvectors. - L: np.ndarray, shape (d, r) - Dual left eigenvectors. - """ - nx = get_backend(T) - T = nx.asarray(T) - - if T.ndim != 2 or T.shape[0] != T.shape[1]: - raise ValueError(f"T must be a square 2D array; got shape {T.shape}") - - d = int(T.shape[0]) - if r is None: - r = d - r = int(r) - if not (1 <= r <= d): - raise ValueError(f"r must be an integer in [1, {d}], got r={r}") - - T_np = ot.backend.to_numpy(T) - evals_np, evecs_np = np.linalg.eig(T_np) - - if sort_mode == "closest_to_1": - order = np.argsort(np.abs(evals_np - 1.0)) - elif sort_mode == "closest_to_0": - order = np.argsort(np.abs(evals_np)) - elif sort_mode == "largest_mag": - order = np.argsort(-np.abs(evals_np)) - else: - raise ValueError( - "sort_mode must be one of 'closest_to_1', 'closest_to_0', or 'largest_mag'" - ) - - idx = order[:r] - D_np = evals_np[idx] - R_np = evecs_np[:, idx] - - evalsL_np, evecsL_np = np.linalg.eig(T_np.conj().T) - - L_np = np.zeros((d, r), dtype=np.complex128) - used = set() - - for i, lam in enumerate(D_np): - targets = np.abs(evalsL_np - np.conj(lam)) - for j in np.argsort(targets): - if j not in used: - used.add(j) - L_np[:, i] = evecsL_np[:, j] - break - - if hasattr(nx, "from_numpy"): - D = nx.from_numpy(D_np, type_as=T) - R = nx.from_numpy(R_np, type_as=T) - L = nx.from_numpy(L_np, type_as=T) - else: - D = nx.asarray(D_np) - R = nx.asarray(R_np) - L = nx.asarray(L_np) - - G = nx.dot(nx.conj(L).T, R) - - G_np = ot.backend.to_numpy(G) - if np.linalg.matrix_rank(G_np) < r: - raise ValueError("Dual normalization failed: L^* R is singular.") - - invG_H_np = np.linalg.inv(G_np).conj().T - if hasattr(nx, "from_numpy"): - invG_H = nx.from_numpy(invG_H_np, type_as=T) - else: - invG_H = nx.asarray(invG_H_np) - - L = nx.dot(L, invG_H) - - return D, R, L - - -##################################################################################################################################### -##################################################################################################################################### -### GRASSMANNIAN METRIC ### -##################################################################################################################################### -##################################################################################################################################### - - def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1e-300): """Compute squared Grassmannian distances from delta similarities. @@ -494,7 +176,6 @@ def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1 if nx is None: nx = get_backend(delta) - delta = nx.asarray(delta) delta = nx.clip(delta, 0.0, 1.0) if grassman_metric == "geodesic": @@ -522,6 +203,7 @@ def cost( Lt, eta=0.5, p=2, + q=1, grassman_metric="chordal", real_scale=1.0, imag_scale=1.0, @@ -531,14 +213,14 @@ def cost( Parameters ---------- - Ds: array-like, shape (n_s,) or (n_s, n_s) - Eigenvalues of operator T1 (or diagonal matrix). + Ds: array-like, shape (n_s,) + Eigenvalues of operator T1. Rs: array-like, shape (L, n_s) Right eigenvectors of operator T1. Ls: array-like, shape (L, n_s) Left eigenvectors of operator T1. - Dt: array-like, shape (n_t,) or (n_t, n_t) - Eigenvalues of operator T2 (or diagonal matrix). + Dt: array-like, shape (n_t,) + Eigenvalues of operator T2. Rt: array-like, shape (L, n_t) Right eigenvectors of operator T2. Lt: array-like, shape (L, n_t) @@ -562,25 +244,44 @@ def cost( if nx is None: nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) - Ds = nx.asarray(Ds) - Dt = nx.asarray(Dt) - if len(Ds.shape) == 2: - lam1 = nx.diag(Ds) - else: - lam1 = Ds.reshape((-1,)) - if len(Dt.shape) == 2: - lam2 = nx.diag(Dt) - else: - lam2 = Dt.reshape((-1,)) - - lam1 = lam1.astype(complex) - lam2 = lam2.astype(complex) - - lam1s = nx.real(lam1) * real_scale + 1j * nx.imag(lam1) * imag_scale - lam2s = nx.real(lam2) * real_scale + 1j * nx.imag(lam2) * imag_scale - C_lambda = nx.abs(lam1s[:, None] - lam2s[None, :]) ** 2 - - delta = _delta_matrix_1d_hs(Rs, Ls, Rt, Lt, nx=nx) + if Ds.ndim != 1: + raise ValueError(f"cost() expects Ds to be 1D (n,), got shape {Ds.shape}") + lam1 = Ds + + if Dt.ndim != 1: + raise ValueError(f"cost() expects Dt to be 1D (n,), got shape {Dt.shape}") + lam2 = Dt + + lam1 = nx.astype(lam1, "complex128") + lam2 = nx.astype(lam2, "complex128") + + if Rs.shape != Ls.shape: + raise ValueError( + f"Rs and Ls must have the same shape, got {Rs.shape} and {Ls.shape}" + ) + + if Rt.shape != Lt.shape: + raise ValueError( + f"Rt and Lt must have the same shape, got {Rt.shape} and {Lt.shape}" + ) + + if Rs.shape[1] != lam1.shape[0]: + raise ValueError( + f"Number of source eigenvectors ({Rs.shape[1]}) must match " + f"number of source eigenvalues ({lam1.shape[0]})" + ) + + if Rt.shape[1] != lam2.shape[0]: + raise ValueError( + f"Number of target eigenvectors ({Rt.shape[1]}) must match " + f"number of target eigenvalues ({lam2.shape[0]})" + ) + + C_lambda = eigenvalue_cost_matrix( + lam1, lam2, q=q, real_scale=real_scale, imag_scale=imag_scale, nx=nx + ) + + delta = _delta_matrix_1d(Rs, Ls, Rt, Lt, nx=nx) C_grass = _grassmann_distance_squared(delta, grassman_metric=grassman_metric, nx=nx) C2 = eta * C_lambda + (1.0 - eta) * C_grass @@ -599,6 +300,7 @@ def metric( eta=0.5, p=2, q=1, + r=2, grassman_metric="chordal", real_scale=1.0, imag_scale=1.0, @@ -610,14 +312,14 @@ def metric( Parameters ---------- - Ds: array-like, shape (n_s,) or (n_s, n_s) - Eigenvalues of operator T1 (or diagonal matrix). + Ds: array-like, shape (n_s,) + Eigenvalues of operator T1. Rs: array-like, shape (L, n_s) Right eigenvectors of operator T1. Ls: array-like, shape (L, n_s) Left eigenvectors of operator T1. - Dt: array-like, shape (n_t,) or (n_t, n_t) - Eigenvalues of operator T2 (or diagonal matrix). + Dt: array-like, shape (n_t,) + Eigenvalues of operator T2. Rt: array-like, shape (L, n_t) Right eigenvectors of operator T2. Lt: array-like, shape (L, n_t) @@ -625,9 +327,13 @@ def metric( eta: float, optional Weighting between spectral and Grassmann terms, default 0.5. p: int, optional - Power for the OT cost, default 2. + Exponent defining the OT ground cost and Wasserstein order. The cost matrix is raised to the power p/2 and the OT objective + is raised to the power 1/p. Default is 2. q: int, optional - Outer root applied to the OT objective, default 1. + Exponent applied to the eigenvalue distance in the spectral term. Controls the geometry of the eigenvalue cost matrix. + Default is 1. + r: int, optional + Outer root applied to the Wasserstein objective. Default is 2. grassman_metric: str, optional Metric type: "geodesic", "chordal", "procrustes", or "martin". real_scale: float, optional @@ -647,6 +353,11 @@ def metric( if nx is None: nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) + if Ds.ndim != 1: + raise ValueError(f"metric() expects Ds to be 1D (n,), got shape {Ds.shape}") + if Dt.ndim != 1: + raise ValueError(f"metric() expects Dt to be 1D (n,), got shape {Dt.shape}") + C = cost( Ds, Rs, @@ -656,204 +367,13 @@ def metric( Lt, eta=eta, p=p, + q=q, grassman_metric=grassman_metric, real_scale=real_scale, imag_scale=imag_scale, nx=nx, ) - n, m = C.shape - - if Ws is None: - Ws = nx.ones((n,), dtype=C.dtype) / float(n) - else: - Ws = nx.asarray(Ws) - - if Wt is None: - Wt = nx.ones((m,), dtype=C.dtype) / float(m) - else: - Wt = nx.asarray(Wt) - - Ws = Ws / nx.sum(Ws) - Wt = Wt / nx.sum(Wt) - P = ot_plan(C, Ws=Ws, Wt=Wt, nx=nx) - obj = ot_score(C, P, p=p, nx=nx) - return float(obj) ** (1.0 / float(q)) - - -def metric_from_operator( - T1, - T2, - r=None, - eta=0.5, - p=2, - q=1, - grassman_metric="chordal", - real_scale=1.0, - imag_scale=1.0, - Ws=None, - Wt=None, -): - """Compute the SGOT metric directly from two operators. - - Parameters - ---------- - T1: array-like, shape (d, d) - First operator. - T2: array-like, shape (d, d) - Second operator. - r: int, optional - Number of modes to keep. If None, keep all modes. - eta: float, optional - Weighting between spectral and Grassmann terms, default 0.5. - p: int, optional - Power for the OT cost, default 2. - q: int, optional - Outer root applied to the OT objective, default 1. - grassman_metric: str, optional - Metric type: "geodesic", "chordal", "procrustes", or "martin". - real_scale: float, optional - Scale factor for real parts, default 1.0. - imag_scale: float, optional - Scale factor for imaginary parts, default 1.0. - Ws: array-like, shape (n_s,), optional - Source distribution. If None, uses a uniform distribution. - Wt: array-like, shape (n_t,), optional - Target distribution. If None, uses a uniform distribution. - - Returns - ---------- - dist: float - SGOT metric value. - """ - Ds, Rs, Ls = _atoms_from_operator(T1, r=r, sort_mode="closest_to_1") - Dt, Rt, Lt = _atoms_from_operator(T2, r=r, sort_mode="closest_to_1") - - return metric( - Ds, - Rs, - Ls, - Dt, - Rt, - Lt, - eta=eta, - p=p, - q=q, - grassman_metric=grassman_metric, - real_scale=real_scale, - imag_scale=imag_scale, - Ws=Ws, - Wt=Wt, - ) - - -def operator_estimator( - X, - Y=None, - r=None, - ref=1e-8, - force_complex=False, -): - """Estimate a linear operator from data. - - Parameters - ---------- - X: array-like, shape (n_samples, d) or (d, n_samples) - Input snapshot matrix. - Y: array-like, shape like X, optional - Output snapshot matrix. If None, uses a one-step shift of X. - r: int, optional - Rank for optional truncated SVD of the estimated operator. - ref: float, optional - Tikhonov regularization strength, default 1e-8. - force_complex: bool, optional - If True, cast inputs to complex dtype. - - Returns - ---------- - T_hat: np.ndarray, shape (d, d) - Estimated linear operator. - """ - nx = get_backend(X, Y) if Y is not None else get_backend(X) - - X = nx.asarray(X) - - if Y is None: - if X.ndim != 2 or int(X.shape[0]) < 2: - raise ValueError("If Y is None, X must be 2D with at least 2 samples/rows.") - X0 = X[:-1] - Y0 = X[1:] - else: - Y = nx.asarray(Y) - if tuple(X.shape) != tuple(Y.shape): - raise ValueError( - f"X and Y must have the same shape; got {X.shape} vs {Y.shape}" - ) - X0, Y0 = X, Y - - if X0.shape[0] >= 1 and X0.shape[0] != X0.shape[1]: - if X0.shape[0] >= X0.shape[1]: - Xc = X0.T - Yc = Y0.T - else: - Xc = X0 - Yc = Y0 - else: - Xc = X0 - Yc = Y0 - - if Xc.ndim != 2 or Yc.ndim != 2: - raise ValueError("X and Y must be 2D arrays after processing.") - - d, n = int(Xc.shape[0]), int(Xc.shape[1]) - if tuple(Yc.shape) != (d, n): - raise ValueError( - f"After formatting, expected Y to have shape {(d, n)}, got {Yc.shape}" - ) - - if force_complex: - Xc_np = ot.backend.to_numpy(Xc) # explicit backend->NumPy copy - Yc_np = ot.backend.to_numpy(Yc) - Xc_np = Xc_np.astype(np.complex128, copy=False) - Yc_np = Yc_np.astype(np.complex128, copy=False) - if hasattr(nx, "from_numpy"): - Xc = nx.from_numpy(Xc_np, type_as=Xc) - Yc = nx.from_numpy(Yc_np, type_as=Yc) - else: - Xc = nx.asarray(Xc_np) - Yc = nx.asarray(Yc_np) - - XXH = nx.dot(Xc, nx.conj(Xc).T) - YXH = nx.dot(Yc, nx.conj(Xc).T) - A = XXH + ref * nx.eye(d, type_as=XXH) - - AH = nx.conj(A).T - BH = nx.conj(YXH).T - - AH_np = ot.backend.to_numpy(AH) # explicit backend->NumPy copy - BH_np = ot.backend.to_numpy(BH) - Xsol_np = np.linalg.solve(AH_np, BH_np) - - if hasattr(nx, "from_numpy"): - Xsol = nx.from_numpy(Xsol_np, type_as=YXH) - else: - Xsol = nx.asarray(Xsol_np) - - T_hat = nx.conj(Xsol).T - - if r is not None: - r = int(r) - if not (1 <= r <= d): - raise ValueError(f"r must be in [1, {d}], got r={r}") - - T_np = ot.backend.to_numpy(T_hat) # explicit backend->NumPy copy - U, S, Vh = np.linalg.svd(T_np, full_matrices=False) - T_np = (U[:, :r] * S[:r]) @ Vh[:r, :] - - if hasattr(nx, "from_numpy"): - T_hat = nx.from_numpy(T_np, type_as=T_hat) - else: - T_hat = nx.asarray(T_np) - - return T_hat + obj = float(nx.sum(C * P) ** (1.0 / p)) + return float(obj) ** (1.0 / float(r)) diff --git a/test/test_backend.py b/test/test_backend.py index efd696ef0..e322e5d35 100644 --- a/test/test_backend.py +++ b/test/test_backend.py @@ -338,6 +338,9 @@ def test_func_backends(nx): sp_col = np.array([0, 3, 1, 2, 2]) sp_data = np.array([4, 5, 7, 9, 0], dtype=np.float64) + M_complex = M + 1j * rnd.randn(10, 3) + v_acos = np.clip(v, -0.99, 0.99) + lst_tot = [] for nx in [ot.backend.NumpyBackend(), nx]: @@ -722,6 +725,27 @@ def test_func_backends(nx): lst_b.append(nx.to_numpy(A)) lst_name.append("atan2") + M_complex_b = nx.from_numpy(M_complex) + A = nx.real(M_complex_b) + lst_b.append(nx.to_numpy(A)) + lst_name.append("real") + A = nx.imag(M_complex_b) + lst_b.append(nx.to_numpy(A)) + lst_name.append("imag") + A = nx.conj(M_complex_b) + lst_b.append(nx.to_numpy(A)) + lst_name.append("conj") + v_acos_b = nx.from_numpy(v_acos) + A = nx.arccos(v_acos_b) + lst_b.append(nx.to_numpy(A)) + lst_name.append("arccos") + A = nx.astype(Mb, "float64") + lst_b.append(nx.to_numpy(A)) + lst_name.append("astype float64") + A = nx.astype(vb, "complex128") + lst_b.append(nx.to_numpy(A)) + lst_name.append("astype complex128") + A = nx.transpose(Mb) lst_b.append(nx.to_numpy(A)) lst_name.append("transpose") diff --git a/test/test_sgot.py b/test/test_sgot.py new file mode 100644 index 000000000..c1330696b --- /dev/null +++ b/test/test_sgot.py @@ -0,0 +1,333 @@ +"""Tests for ot.sgot module""" + +# Author: Sienna O'Shea +# Thibaut Germain +# License: MIT License + +import numpy as np +import pytest + +from ot.backend import get_backend + +try: + import torch +except ImportError: + torch = None + +try: + import jax + import jax.numpy as jnp +except ImportError: + jax = None + +from ot.sgot import ( + eigenvalue_cost_matrix, + _delta_matrix_1d, + _grassmann_distance_squared, + cost, + metric, +) + +rng = np.random.RandomState(0) + + +def rand_complex(shape): + real = rng.randn(*shape) + imag = rng.randn(*shape) + return real + 1j * imag + + +def random_atoms(d=8, r=4): + Ds = rand_complex((r,)) + Rs = rand_complex((d, r)) + Ls = rand_complex((d, r)) + Dt = rand_complex((r,)) + Rt = rand_complex((d, r)) + Lt = rand_complex((d, r)) + return Ds, Rs, Ls, Dt, Rt, Lt + + +# --------------------------------------------------------------------- +# DATA / SAMPLING TESTS +# --------------------------------------------------------------------- + + +def test_atoms_are_complex(): + """Confirm sampled atoms are complex (Gaussian real + 1j*imag).""" + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + for name, arr in [ + ("Ds", Ds), + ("Rs", Rs), + ("Ls", Ls), + ("Dt", Dt), + ("Rt", Rt), + ("Lt", Lt), + ]: + assert np.iscomplexobj(arr), f"{name} should be complex" + assert np.any(np.imag(arr) != 0), f"{name} should have non-zero imaginary part" + + +def test_random_d_r(): + """Sample d and r uniformly and run cost (and metric when available) with those shapes.""" + d_min, d_max = 4, 12 + r_min, r_max = 2, 6 + for _ in range(5): + d = int(rng.randint(d_min, d_max + 1)) + r = int(rng.randint(r_min, r_max + 1)) + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms(d=d, r=r) + C = cost(Ds, Rs, Ls, Dt, Rt, Lt) + np.testing.assert_allclose(C.shape, (r, r)) + assert np.all(np.isfinite(C)) and np.all(C >= 0) + try: + dist = metric(Ds, Rs, Ls, Dt, Rt, Lt) + assert np.isfinite(dist) and dist >= 0 + except TypeError: + pytest.skip("metric() unavailable (emd_c signature mismatch)") + + +# --------------------------------------------------------------------- +# BACKEND CONSISTENCY TESTS +# --------------------------------------------------------------------- + + +def test_backend_return(): + """Confirm get_backend returns the correct backend for numpy/torch/jax arrays.""" + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) + assert nx is not None + assert nx.__name__ == "numpy" + + if torch is not None: + Ds_t = torch.from_numpy(Ds) + nx_t = get_backend(Ds_t) + assert nx_t is not None + assert nx_t.__name__ == "torch" + + if jax is not None: + Ds_j = jnp.array(Ds) + nx_j = get_backend(Ds_j) + assert nx_j is not None + assert nx_j.__name__ == "jax" + + +@pytest.mark.parametrize("backend_name", ["numpy", "torch", "jax"]) +def test_cost_backend_consistency(backend_name): + if backend_name == "torch" and torch is None: + pytest.skip("Torch not available") + if backend_name == "jax" and jax is None: + pytest.skip("JAX not available") + + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + + C_np = cost(Ds, Rs, Ls, Dt, Rt, Lt) + + if backend_name == "numpy": + C_backend = C_np + + elif backend_name == "torch": + Ds_b = torch.from_numpy(Ds) + Rs_b = torch.from_numpy(Rs) + Ls_b = torch.from_numpy(Ls) + Dt_b = torch.from_numpy(Dt) + Rt_b = torch.from_numpy(Rt) + Lt_b = torch.from_numpy(Lt) + C_backend = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) + C_backend = C_backend.detach().cpu().numpy() + + elif backend_name == "jax": + Ds_b = jnp.array(Ds) + Rs_b = jnp.array(Rs) + Ls_b = jnp.array(Ls) + Dt_b = jnp.array(Dt) + Rt_b = jnp.array(Rt) + Lt_b = jnp.array(Lt) + C_backend = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) + C_backend = np.array(C_backend) + + np.testing.assert_allclose(C_backend, C_np, atol=1e-6) + + +# --------------------------------------------------------------------- +# DELTA MATRIX TESTS +# --------------------------------------------------------------------- + + +def test_delta_identity(): + r = 4 + I = np.eye(r, dtype=complex) + delta = _delta_matrix_1d(I, I, I, I) + np.testing.assert_allclose(delta, np.eye(r), atol=1e-12) + + +def test_delta_swap_invariance(): + d, r = 6, 3 + R = rand_complex((d, r)) + L = R.copy() + delta1 = _delta_matrix_1d(R, L, R, L) + delta2 = _delta_matrix_1d(L, R, L, R) + np.testing.assert_allclose(delta1, delta2, atol=1e-12) + + +# --------------------------------------------------------------------- +# GRASSMANN DISTANCE TESTS +# --------------------------------------------------------------------- + + +@pytest.mark.parametrize("metric_name", ["geodesic", "chordal", "procrustes", "martin"]) +def test_grassmann_zero_distance(metric_name): + delta = np.ones((3, 3)) + dist2 = _grassmann_distance_squared(delta, grassman_metric=metric_name) + np.testing.assert_allclose(dist2, 0.0, atol=1e-12) + + +def test_grassmann_invalid_name(): + delta = np.ones((2, 2)) + with pytest.raises(ValueError): + _grassmann_distance_squared(delta, grassman_metric="cordal") + + +# --------------------------------------------------------------------- +# COST TESTS +# --------------------------------------------------------------------- + + +def test_cost_self_zero(nx): + """(D_S R_S L_S D_S): diagonal of cost matrix (same atom to same atom) should be near zero.""" + Ds, Rs, Ls, _, _, _ = random_atoms() + Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2 = nx.from_numpy(Ds, Rs, Ls, Ds, Rs, Ls) + C = cost(Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2) + C_np = nx.to_numpy(C) + np.testing.assert_allclose(np.diag(C_np), np.zeros(C_np.shape[0]), atol=1e-10) + np.testing.assert_allclose(C_np, C_np.T, atol=1e-10) + + +def test_cost_reference(nx): + """Cost with same inputs and HPs should be deterministic (np.testing.assert_allclose).""" + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) + eta, p, q = 0.5, 2, 1 + C1 = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, eta=eta, p=p, q=q) + C2 = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, eta=eta, p=p, q=q) + np.testing.assert_allclose(nx.to_numpy(C1), nx.to_numpy(C2), atol=1e-12) + + +@pytest.mark.parametrize( + "grassman_metric", ["geodesic", "chordal", "procrustes", "martin"] +) +def test_cost_basic(grassman_metric, nx): + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) + C = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, grassman_metric=grassman_metric) + C_np = nx.to_numpy(C) + assert C_np.shape == (Ds.shape[0], Dt.shape[0]) + assert np.all(np.isfinite(C_np)) + assert np.all(C_np >= 0) + + +def test_cost_validation(): + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + + with pytest.raises(ValueError): + cost(Ds.reshape(-1, 1), Rs, Ls, Dt, Rt, Lt) + + with pytest.raises(ValueError): + cost(Ds, Rs[:, :-1], Ls, Dt, Rt, Lt) + + +# --------------------------------------------------------------------- +# METRIC TESTS +# --------------------------------------------------------------------- + + +def test_metric_self_zero(): + Ds, Rs, Ls, _, _, _ = random_atoms() + dist = metric(Ds, Rs, Ls, Ds, Rs, Ls) + assert np.isfinite(dist) + assert abs(dist) < 2e-4 + + +def test_metric_symmetry(): + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + d1 = metric(Ds, Rs, Ls, Dt, Rt, Lt) + d2 = metric(Dt, Rt, Lt, Ds, Rs, Ls) + np.testing.assert_allclose(d1, d2, atol=1e-8) + + +def test_metric_with_weights(): + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + r = Ds.shape[0] + + logits_s = rng.randn(r) + logits_t = rng.randn(r) + + Ws = np.exp(logits_s) + Ws = Ws / np.sum(Ws) + + Wt = np.exp(logits_t) + Wt = Wt / np.sum(Wt) + + dist = metric(Ds, Rs, Ls, Dt, Rt, Lt, Ws=Ws, Wt=Wt) + assert np.isfinite(dist) + + +# --------------------------------------------------------------------- +# HYPERPARAMETER SWEEP TEST +# --------------------------------------------------------------------- + + +def test_hyperparameter_sweep_cost(nx): + """Create test_cost for each trial: sweep over HPs and run cost().""" + grassmann_types = ["geodesic", "chordal", "procrustes", "martin"] + n_trials = 10 + for _ in range(n_trials): + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) + eta = rng.uniform(0.0, 1.0) + p = rng.choice([1, 2]) + q = rng.choice([1, 2]) + gm = rng.choice(grassmann_types) + C = cost( + Ds_b, + Rs_b, + Ls_b, + Dt_b, + Rt_b, + Lt_b, + eta=eta, + p=p, + q=q, + grassman_metric=gm, + ) + C_np = nx.to_numpy(C) + assert C_np.shape == (Ds.shape[0], Dt.shape[0]) + assert np.all(np.isfinite(C_np)) + assert np.all(C_np >= 0) + + +def test_hyperparameter_sweep(): + grassmann_types = ["geodesic", "chordal", "procrustes", "martin"] + + for _ in range(10): + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + eta = rng.uniform(0.0, 1.0) + p = rng.choice([1, 2]) + q = rng.choice([1, 2]) + r = rng.choice([1, 2]) + gm = rng.choice(grassmann_types) + + dist = metric( + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, + eta=eta, + p=p, + q=q, + r=r, + grassman_metric=gm, + ) + + assert np.isfinite(dist) + assert dist >= 0 From 630e359c59b8aedebeeac95bd13e327e18245ce3 Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Mon, 23 Feb 2026 12:41:58 +0100 Subject: [PATCH 06/14] fix astype in backend --- ot/backend.py | 20 +++++++++++++++++++- 1 file changed, 19 insertions(+), 1 deletion(-) diff --git a/ot/backend.py b/ot/backend.py index b2dfc4024..1def519a9 100644 --- a/ot/backend.py +++ b/ot/backend.py @@ -2305,7 +2305,25 @@ def arccos(self, a): def astype(self, a, dtype): if isinstance(dtype, str): - dtype = getattr(torch, dtype, None) + # Map common numpy-style string dtypes to torch dtypes explicitly. + # This makes backend.astype robust across torch versions and aliases. + mapping = { + "float32": torch.float32, + "float64": torch.float64, + "float": torch.float32, + "double": torch.float64, + "complex64": getattr(torch, "complex64", None), + "complex128": getattr(torch, "complex128", None), + } + torch_dtype = mapping.get(dtype) + if torch_dtype is None: + # Fallback: try direct attribute lookup (e.g. torch.float16) + torch_dtype = getattr(torch, dtype, None) + if torch_dtype is None: + raise ValueError( + f"Unsupported dtype for TorchBackend.astype: {dtype!r}" + ) + dtype = torch_dtype return a.to(dtype=dtype) def repeat(self, a, repeats, axis=None): From 57c7a0ca6d0f6841d9b9eeb2d0234712ca7579ab Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Wed, 25 Feb 2026 17:09:32 +0100 Subject: [PATCH 07/14] edits as per PR #792 --- RELEASES.md | 12 +- ot/backend.py | 62 +---------- ot/sgot.py | 250 +++++++++++++++++++++++++----------------- test/test_backend.py | 9 +- test/test_sgot.py | 255 +++++++++++++++---------------------------- 5 files changed, 247 insertions(+), 341 deletions(-) diff --git a/RELEASES.md b/RELEASES.md index e2e16f145..c734202c0 100644 --- a/RELEASES.md +++ b/RELEASES.md @@ -1,13 +1,6 @@ # Releases -## Upcomming 0.9.7.post1 - -#### New features -The next release will add cost functions between linear operators following [A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems](https://arxiv.org/pdf/2509.24920). - - - ## 0.9.7.dev0 This new release adds support for sparse cost matrices and a new lazy EMD solver that computes distances on-the-fly from coordinates, reducing memory usage from O(n×m) to O(n+m). Both implementations are backend-agnostic and preserve gradient computation for automatic differentiation. @@ -20,8 +13,13 @@ This new release adds support for sparse cost matrices and a new lazy EMD solver - Migrate backend from deprecated `scipy.sparse.coo_matrix` to modern `scipy.sparse.coo_array` (PR #782) - Geomloss function now handles both scalar and slice indices for i and j (PR #785) - Add support for sparse cost matrices in EMD solver (PR #778, Issue #397) +<<<<<<< HEAD - Added UOT1D with Frank-Wolfe in `ot.unbalanced.uot_1d` (PR #765) - Add Sliced UOT and Unbalanced Sliced OT in `ot/unbalanced/_sliced.py` (PR #765) +======= +- Add cost functions between linear operators following + [A Spectral-Grassmann Wasserstein metric for operator representations of dynamical systems](https://arxiv.org/pdf/2509.24920) (PR #792) +>>>>>>> 8d13c55 (edits as per PR #792) #### Closed issues diff --git a/ot/backend.py b/ot/backend.py index 59fbb3082..0568f2e2f 100644 --- a/ot/backend.py +++ b/ot/backend.py @@ -662,15 +662,6 @@ def arccos(self, a): """ raise NotImplementedError() - def astype(self, a, dtype): - """ - Cast tensor to a given dtype. - - dtype can be a string (e.g. "complex128", "float64") or backend-specific - dtype. Backend converts to the corresponding type. - """ - raise NotImplementedError() - def repeat(self, a, repeats, axis=None): r""" Repeats elements of a tensor. @@ -1242,7 +1233,7 @@ def _from_numpy(self, a, type_as=None): elif isinstance(a, float): return a else: - return a.astype(type_as.dtype) + return np.asarray(a, dtype=type_as.dtype) def set_gradients(self, val, inputs, grads): # No gradients for numpy @@ -1374,11 +1365,6 @@ def conj(self, a): def arccos(self, a): return np.arccos(a) - def astype(self, a, dtype): - if isinstance(dtype, str): - dtype = getattr(np, dtype, None) or np.dtype(dtype) - return np.asarray(a, dtype=dtype) - def repeat(self, a, repeats, axis=None): return np.repeat(a, repeats, axis) @@ -1670,7 +1656,7 @@ def _from_numpy(self, a, type_as=None): if type_as is None: return jnp.array(a) else: - return self._change_device(jnp.array(a).astype(type_as.dtype), type_as) + return self._change_device(jnp.asarray(a, dtype=type_as.dtype), type_as) def set_gradients(self, val, inputs, grads): from jax.flatten_util import ravel_pytree @@ -1808,11 +1794,6 @@ def conj(self, a): def arccos(self, a): return jnp.arccos(a) - def astype(self, a, dtype): - if isinstance(dtype, str): - dtype = getattr(jnp, dtype, None) or jnp.dtype(dtype) - return jnp.asarray(a, dtype=dtype) - def repeat(self, a, repeats, axis=None): return jnp.repeat(a, repeats, axis) @@ -1886,7 +1867,9 @@ def randperm(self, size, type_as=None): if not isinstance(size, int): raise ValueError("size must be an integer") if type_as is not None: - return jax.random.permutation(subkey, size).astype(type_as.dtype) + return jnp.asarray( + jax.random.permutation(subkey, size), dtype=type_as.dtype + ) else: return jax.random.permutation(subkey, size) @@ -2322,29 +2305,6 @@ def conj(self, a): def arccos(self, a): return torch.acos(a) - def astype(self, a, dtype): - if isinstance(dtype, str): - # Map common numpy-style string dtypes to torch dtypes explicitly. - # This makes backend.astype robust across torch versions and aliases. - mapping = { - "float32": torch.float32, - "float64": torch.float64, - "float": torch.float32, - "double": torch.float64, - "complex64": getattr(torch, "complex64", None), - "complex128": getattr(torch, "complex128", None), - } - torch_dtype = mapping.get(dtype) - if torch_dtype is None: - # Fallback: try direct attribute lookup (e.g. torch.float16) - torch_dtype = getattr(torch, dtype, None) - if torch_dtype is None: - raise ValueError( - f"Unsupported dtype for TorchBackend.astype: {dtype!r}" - ) - dtype = torch_dtype - return a.to(dtype=dtype) - def repeat(self, a, repeats, axis=None): return torch.repeat_interleave(a, repeats, dim=axis) @@ -2858,11 +2818,6 @@ def conj(self, a): def arccos(self, a): return cp.arccos(a) - def astype(self, a, dtype): - if isinstance(dtype, str): - dtype = getattr(cp, dtype, None) or cp.dtype(dtype) - return cp.asarray(a, dtype=dtype) - def repeat(self, a, repeats, axis=None): return cp.repeat(a, repeats, axis) @@ -2954,7 +2909,7 @@ def randperm(self, size, type_as=None): return self.rng_.permutation(size) else: with cp.cuda.Device(type_as.device): - return self.rng_.permutation(size).astype(type_as.dtype) + return cp.asarray(self.rng_.permutation(size), dtype=type_as.dtype) def coo_matrix(self, data, rows, cols, shape=None, type_as=None): data = self.from_numpy(data) @@ -3309,11 +3264,6 @@ def conj(self, a): def arccos(self, a): return tnp.arccos(a) - def astype(self, a, dtype): - if isinstance(dtype, str): - dtype = getattr(tnp, dtype, None) or tnp.dtype(dtype) - return tnp.array(a, dtype=dtype) - def repeat(self, a, repeats, axis=None): return tnp.repeat(a, repeats, axis) diff --git a/ot/sgot.py b/ot/sgot.py index 08620b0d2..d443c3490 100644 --- a/ot/sgot.py +++ b/ot/sgot.py @@ -25,9 +25,7 @@ ##################################################################################################################################### -def eigenvalue_cost_matrix( - Ds, Dt, q=1, real_scale: float = 1.0, imag_scale: float = 1.0, nx=None -): +def eigenvalue_cost_matrix(Ds, Dt, q=1, eigen_scaling=None, nx=None): """Compute pairwise eigenvalue distances for source and target domains. Parameters @@ -36,10 +34,10 @@ def eigenvalue_cost_matrix( Source eigenvalues. Dt: array-like, shape (n_t,) Target eigenvalues. - real_scale: float, optional - Scale factor for real parts, default 1.0. - imag_scale: float, optional - Scale factor for imaginary parts, default 1.0. + eigen_scaling: None or array-like of length 2, optional + Scaling (real_scale, imag_scale) applied to eigenvalues before computing + distances. If None, defaults to (1.0, 1.0). Accepts tuple/list or + array/tensor with two entries. Returns ---------- @@ -49,6 +47,14 @@ def eigenvalue_cost_matrix( if nx is None: nx = get_backend(Ds, Dt) + if eigen_scaling is None: + real_scale, imag_scale = 1.0, 1.0 + else: + if isinstance(eigen_scaling, (tuple, list)): + real_scale, imag_scale = eigen_scaling + else: + real_scale, imag_scale = eigen_scaling[0], eigen_scaling[1] + Dsn = nx.real(Ds) * real_scale + 1j * nx.imag(Ds) * imag_scale Dtn = nx.real(Dt) * real_scale + 1j * nx.imag(Dt) * imag_scale prod = Dsn[:, None] - Dtn[None, :] @@ -56,42 +62,6 @@ def eigenvalue_cost_matrix( return prod ** (q / 2) -def ot_plan(C, Ws=None, Wt=None, nx=None): - """Compute the optimal transport plan for a given cost matrix and marginals. - - Parameters - ---------- - C: array-like, shape (n, m) - Cost matrix. - Ws: array-like, shape (n,), optional - Source distribution. If None, uses a uniform distribution. - Wt: array-like, shape (m,), optional - Target distribution. If None, uses a uniform distribution. - - Returns - ---------- - P: np.ndarray, shape (n, m) - Optimal transport plan. - """ - if nx is None: - nx = get_backend(C) - - n, m = C.shape - - if Ws is None: - Ws = nx.ones((n,), type_as=C) / float(n) - - if Wt is None: - Wt = nx.ones((m,), type_as=C) / float(m) - - Ws = Ws / nx.sum(Ws) - Wt = Wt / nx.sum(Wt) - - C_real = nx.real(C) - - return ot.emd(Ws, Wt, C_real) - - def _normalize_columns(A, nx, eps=1e-12): """Normalize the columns of an array with a backend-aware norm. @@ -185,7 +155,11 @@ def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1 if grassman_metric == "procrustes": return 2.0 * (1.0 - delta) if grassman_metric == "martin": - return -nx.log(nx.clip(delta**2, eps, 1e300)) + # Martin-type Grassmann metric: -log(delta^2) with lower clamp at eps. + # We deliberately avoid any upper threshold to stay close to the + # information-geometric interpretation in Germain et al. (2025). + delta2 = nx.maximum(delta**2, eps) + return -nx.log(delta2) raise ValueError(f"Unknown grassman_metric: {grassman_metric}") @@ -194,7 +168,7 @@ def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1 ### SPECTRAL-GRASSMANNIAN WASSERSTEIN METRIC ### ##################################################################################################################################### ##################################################################################################################################### -def cost( +def sgot_cost_matrix( Ds, Rs, Ls, @@ -205,11 +179,50 @@ def cost( p=2, q=1, grassman_metric="chordal", - real_scale=1.0, - imag_scale=1.0, + eigen_scaling=None, nx=None, ): - """Compute the SGOT cost matrix between two spectral decompositions. + r"""Compute the SGOT cost matrix between two spectral decompositions. + + This returns the discrete ground cost matrix used in the SGOT optimal transport + objective. Each spectral atom is :math:`z_i=(\lambda_i, V_i)` where + :math:`\lambda_i \in \mathbb{C}` is an eigenvalue and :math:`V_i` is the + associated (bi-orthogonal) eigenspace point. + + .. math:: + C_2(i,j) \;=\; \eta\,C_\lambda(i,j) \;+\; (1-\eta)\,C_G(i,j), + + with spectral term + + .. math:: + C_\lambda(i,j) \;=\; \big|\lambda_i - \lambda'_j\big|^{q}, + + and Grassmann term computed from a similarity score :math:`\delta_{ij}\in[0,1]` + built from left/right eigenvectors + + .. math:: + \delta_{ij} \;=\; \left|\langle r_i, r'_j\rangle\,\langle \ell_i, \ell'_j\rangle\right|. + + Depending on ``grassman_metric``, the Grassmann contribution is: + + - ``"chordal"``: + .. math:: + C_G(i,j) \;=\; 1 - \delta_{ij}^2 + - ``"geodesic"``: + .. math:: + C_G(i,j) \;=\; \arccos(\delta_{ij})^2 + - ``"procrustes"``: + .. math:: + C_G(i,j) \;=\; 2(1-\delta_{ij}) + - ``"martin"``: + .. math:: + C_G(i,j) \;=\; -\log\!\left(\max(\delta_{ij}^2,\varepsilon)\right) + + Finally, we return a matrix suited for a :math:`p`-Wasserstein objective by + treating :math:`C_2 \approx d^2` and outputting + + .. math:: + C(i,j) \;=\; \big(\operatorname{Re}(C_2(i,j))\big)^{p/2}. Parameters ---------- @@ -228,69 +241,75 @@ def cost( eta: float, optional Weighting between spectral and Grassmann terms, default 0.5. p: int, optional - Power for the OT cost, default 2. + Exponent defining the OT ground cost. The returned cost is :math:`d^p` with + :math:`d^2 \approx C_2`. Default is 2. + q: int, optional + Exponent applied to the eigenvalue distance in the spectral term. + Default is 1. grassman_metric: str, optional Metric type: "geodesic", "chordal", "procrustes", or "martin". - real_scale: float, optional - Scale factor for real parts, default 1.0. - imag_scale: float, optional - Scale factor for imaginary parts, default 1.0. + eigen_scaling: None or array-like of length 2, optional + Scaling ``(real_scale, imag_scale)`` applied to eigenvalues before computing + :math:`C_\lambda`. If provided, eigenvalues are transformed as + :math:`\lambda \mapsto \alpha\operatorname{Re}(\lambda) + i\,\beta\operatorname{Im}(\lambda)`. + If None, defaults to ``(1.0, 1.0)``. Accepts tuple/list or array/tensor with + two entries. + nx: module, optional + Backend (NumPy-compatible). If None, inferred from inputs. Returns ---------- C: array-like, shape (n_s, n_t) - SGOT cost matrix. + SGOT cost matrix :math:`C = d^p`. + + References + ---------- + Germain et al., *Spectral-Grassmann Optimal Transport* (SGOT). """ if nx is None: nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) - if Ds.ndim != 1: - raise ValueError(f"cost() expects Ds to be 1D (n,), got shape {Ds.shape}") - lam1 = Ds - - if Dt.ndim != 1: - raise ValueError(f"cost() expects Dt to be 1D (n,), got shape {Dt.shape}") - lam2 = Dt - - lam1 = nx.astype(lam1, "complex128") - lam2 = nx.astype(lam2, "complex128") - - if Rs.shape != Ls.shape: + if Ds.ndim != 1 or Dt.ndim != 1: raise ValueError( - f"Rs and Ls must have the same shape, got {Rs.shape} and {Ls.shape}" + f"sgot_cost_matrix() expects Ds, Dt 1D; got Ds {getattr(Ds,'shape',None)}, Dt {getattr(Dt,'shape',None)}" ) - if Rt.shape != Lt.shape: + if Rs.shape != Ls.shape or Rt.shape != Lt.shape: raise ValueError( - f"Rt and Lt must have the same shape, got {Rt.shape} and {Lt.shape}" + f"Right/left eigenvector shapes must match; got (Rs,Ls)=({Rs.shape},{Ls.shape}), (Rt,Lt)=({Rt.shape},{Lt.shape})" ) - if Rs.shape[1] != lam1.shape[0]: + if Rs.shape[1] != Ds.shape[0] or Rt.shape[1] != Dt.shape[0]: raise ValueError( - f"Number of source eigenvectors ({Rs.shape[1]}) must match " - f"number of source eigenvalues ({lam1.shape[0]})" + f"Eigenvectors columns must match eigenvalues: Rs {Rs.shape[1]} vs Ds {Ds.shape[0]}, " + f"Rt {Rt.shape[1]} vs Dt {Dt.shape[0]}" ) - if Rt.shape[1] != lam2.shape[0]: - raise ValueError( - f"Number of target eigenvectors ({Rt.shape[1]}) must match " - f"number of target eigenvalues ({lam2.shape[0]})" - ) - - C_lambda = eigenvalue_cost_matrix( - lam1, lam2, q=q, real_scale=real_scale, imag_scale=imag_scale, nx=nx - ) + C_lambda = eigenvalue_cost_matrix(Ds, Dt, q=q, eigen_scaling=eigen_scaling, nx=nx) delta = _delta_matrix_1d(Rs, Ls, Rt, Lt, nx=nx) C_grass = _grassmann_distance_squared(delta, grassman_metric=grassman_metric, nx=nx) C2 = eta * C_lambda + (1.0 - eta) * C_grass - C = C2 ** (p / 2.0) + C = nx.real(C2) ** (p / 2.0) return C -def metric( +def _validate_sgot_metric_inputs(Ds, Dt): + """Validate that eigenvalue inputs for SGOT metric are 1D.""" + Ds_shape = getattr(Ds, "shape", None) + Dt_shape = getattr(Dt, "shape", None) + Ds_ndim = getattr(Ds, "ndim", None) + Dt_ndim = getattr(Dt, "ndim", None) + if Ds_ndim != 1 or Dt_ndim != 1: + raise ValueError( + "sgot_metric() expects Ds and Dt to be 1D (n,), " + f"got Ds shape {Ds_shape} and Dt shape {Dt_shape}" + ) + + +def sgot_metric( Ds, Rs, Ls, @@ -302,13 +321,30 @@ def metric( q=1, r=2, grassman_metric="chordal", - real_scale=1.0, - imag_scale=1.0, + eigen_scaling=None, Ws=None, Wt=None, nx=None, ): - """Compute the SGOT metric between two spectral decompositions. + r"""Compute the SGOT metric between two spectral decompositions. + + This function computes a discrete optimal transport problem between two measures + over spectral atoms :math:`z_i=(\lambda_i, V_i)` and :math:`z'_j=(\lambda'_j, V'_j)`. + Using the ground cost matrix :math:`C=d^p` returned by :func:`sgot_cost_matrix`, + we solve: + + .. math:: + P^\star \in \arg\min_{P\in\Pi(W_s, W_t)} \langle C, P\rangle, + + and compute the associated :math:`p`-Wasserstein objective: + + .. math:: + \mathrm{obj} \;=\; \left(\sum_{i,j} C(i,j)\,P^\star_{ij}\right)^{1/p}. + + This implementation returns an additional outer root: + + .. math:: + \mathrm{SGOT} \;=\; \mathrm{obj}^{1/r}. Parameters ---------- @@ -327,38 +363,41 @@ def metric( eta: float, optional Weighting between spectral and Grassmann terms, default 0.5. p: int, optional - Exponent defining the OT ground cost and Wasserstein order. The cost matrix is raised to the power p/2 and the OT objective - is raised to the power 1/p. Default is 2. + Exponent defining the OT ground cost and Wasserstein order. The cost matrix + is :math:`d^p` and the OT objective is raised to the power :math:`1/p`. + Default is 2. q: int, optional - Exponent applied to the eigenvalue distance in the spectral term. Controls the geometry of the eigenvalue cost matrix. + Exponent applied to the eigenvalue distance in the spectral term. Default is 1. r: int, optional Outer root applied to the Wasserstein objective. Default is 2. grassman_metric: str, optional Metric type: "geodesic", "chordal", "procrustes", or "martin". - real_scale: float, optional - Scale factor for real parts, default 1.0. - imag_scale: float, optional - Scale factor for imaginary parts, default 1.0. + eigen_scaling: None or array-like of length 2, optional + Scaling ``(real_scale, imag_scale)`` applied to eigenvalues before computing + the spectral part of the cost. If None, defaults to ``(1.0, 1.0)``. Ws: array-like, shape (n_s,), optional Source distribution. If None, uses a uniform distribution. Wt: array-like, shape (n_t,), optional Target distribution. If None, uses a uniform distribution. + nx: module, optional + Backend (NumPy-compatible). If None, inferred from inputs. Returns ---------- dist: float SGOT metric value. + + References + ---------- + Germain et al., *Spectral-Grassmann Optimal Transport* (SGOT). """ if nx is None: nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) - if Ds.ndim != 1: - raise ValueError(f"metric() expects Ds to be 1D (n,), got shape {Ds.shape}") - if Dt.ndim != 1: - raise ValueError(f"metric() expects Dt to be 1D (n,), got shape {Dt.shape}") + _validate_sgot_metric_inputs(Ds, Dt) - C = cost( + C = sgot_cost_matrix( Ds, Rs, Ls, @@ -369,11 +408,18 @@ def metric( p=p, q=q, grassman_metric=grassman_metric, - real_scale=real_scale, - imag_scale=imag_scale, + eigen_scaling=eigen_scaling, nx=nx, ) - P = ot_plan(C, Ws=Ws, Wt=Wt, nx=nx) + if Ws is None: + Ws = nx.ones((C.shape[0],), type_as=C) / float(C.shape[0]) + if Wt is None: + Wt = nx.ones((C.shape[1],), type_as=C) / float(C.shape[1]) + + Ws = Ws / nx.sum(Ws) + Wt = Wt / nx.sum(Wt) + + P = ot.emd2(Ws, Wt, nx.real(C)) obj = float(nx.sum(C * P) ** (1.0 / p)) - return float(obj) ** (1.0 / float(r)) + return obj ** (1.0 / float(r)) diff --git a/test/test_backend.py b/test/test_backend.py index e25297bfa..fe6af9c67 100644 --- a/test/test_backend.py +++ b/test/test_backend.py @@ -730,22 +730,19 @@ def test_func_backends(nx): A = nx.real(M_complex_b) lst_b.append(nx.to_numpy(A)) lst_name.append("real") + A = nx.imag(M_complex_b) lst_b.append(nx.to_numpy(A)) lst_name.append("imag") + A = nx.conj(M_complex_b) lst_b.append(nx.to_numpy(A)) lst_name.append("conj") + v_acos_b = nx.from_numpy(v_acos) A = nx.arccos(v_acos_b) lst_b.append(nx.to_numpy(A)) lst_name.append("arccos") - A = nx.astype(Mb, "float64") - lst_b.append(nx.to_numpy(A)) - lst_name.append("astype float64") - A = nx.astype(vb, "complex128") - lst_b.append(nx.to_numpy(A)) - lst_name.append("astype complex128") A = nx.transpose(Mb) lst_b.append(nx.to_numpy(A)) diff --git a/test/test_sgot.py b/test/test_sgot.py index c1330696b..4ecfd2e40 100644 --- a/test/test_sgot.py +++ b/test/test_sgot.py @@ -7,19 +7,6 @@ import numpy as np import pytest -from ot.backend import get_backend - -try: - import torch -except ImportError: - torch = None - -try: - import jax - import jax.numpy as jnp -except ImportError: - jax = None - from ot.sgot import ( eigenvalue_cost_matrix, _delta_matrix_1d, @@ -28,22 +15,23 @@ metric, ) -rng = np.random.RandomState(0) +def random_atoms(d=8, r=4, seed=42): + """Deterministic complex atoms for given d, r.""" -def rand_complex(shape): - real = rng.randn(*shape) - imag = rng.randn(*shape) - return real + 1j * imag + def _rand_complex(shape, seed_): + rng = np.random.RandomState(seed_) + real = rng.randn(*shape) + imag = rng.randn(*shape) + return real + 1j * imag + Ds = _rand_complex((r,), seed + 0) + Rs = _rand_complex((d, r), seed + 1) + Ls = _rand_complex((d, r), seed + 2) + Dt = _rand_complex((r,), seed + 3) + Rt = _rand_complex((d, r), seed + 4) + Lt = _rand_complex((d, r), seed + 5) -def random_atoms(d=8, r=4): - Ds = rand_complex((r,)) - Rs = rand_complex((d, r)) - Ls = rand_complex((d, r)) - Dt = rand_complex((r,)) - Rt = rand_complex((d, r)) - Lt = rand_complex((d, r)) return Ds, Rs, Ls, Dt, Rt, Lt @@ -52,101 +40,28 @@ def random_atoms(d=8, r=4): # --------------------------------------------------------------------- -def test_atoms_are_complex(): - """Confirm sampled atoms are complex (Gaussian real + 1j*imag).""" - Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() - for name, arr in [ - ("Ds", Ds), - ("Rs", Rs), - ("Ls", Ls), - ("Dt", Dt), - ("Rt", Rt), - ("Lt", Lt), - ]: - assert np.iscomplexobj(arr), f"{name} should be complex" - assert np.any(np.imag(arr) != 0), f"{name} should have non-zero imaginary part" - - -def test_random_d_r(): +def test_random_d_r(nx): """Sample d and r uniformly and run cost (and metric when available) with those shapes.""" + rng = np.random.RandomState(0) d_min, d_max = 4, 12 r_min, r_max = 2, 6 for _ in range(5): d = int(rng.randint(d_min, d_max + 1)) r = int(rng.randint(r_min, r_max + 1)) Ds, Rs, Ls, Dt, Rt, Lt = random_atoms(d=d, r=r) - C = cost(Ds, Rs, Ls, Dt, Rt, Lt) - np.testing.assert_allclose(C.shape, (r, r)) - assert np.all(np.isfinite(C)) and np.all(C >= 0) + Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) + C = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) + C_np = nx.to_numpy(C) + np.testing.assert_allclose(C_np.shape, (r, r)) + assert np.all(np.isfinite(C_np)) and np.all(C_np >= 0) try: - dist = metric(Ds, Rs, Ls, Dt, Rt, Lt) - assert np.isfinite(dist) and dist >= 0 + dist = metric(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) + dist_np = nx.to_numpy(dist) + assert np.isfinite(dist_np) and dist_np >= 0 except TypeError: pytest.skip("metric() unavailable (emd_c signature mismatch)") -# --------------------------------------------------------------------- -# BACKEND CONSISTENCY TESTS -# --------------------------------------------------------------------- - - -def test_backend_return(): - """Confirm get_backend returns the correct backend for numpy/torch/jax arrays.""" - Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() - nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) - assert nx is not None - assert nx.__name__ == "numpy" - - if torch is not None: - Ds_t = torch.from_numpy(Ds) - nx_t = get_backend(Ds_t) - assert nx_t is not None - assert nx_t.__name__ == "torch" - - if jax is not None: - Ds_j = jnp.array(Ds) - nx_j = get_backend(Ds_j) - assert nx_j is not None - assert nx_j.__name__ == "jax" - - -@pytest.mark.parametrize("backend_name", ["numpy", "torch", "jax"]) -def test_cost_backend_consistency(backend_name): - if backend_name == "torch" and torch is None: - pytest.skip("Torch not available") - if backend_name == "jax" and jax is None: - pytest.skip("JAX not available") - - Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() - - C_np = cost(Ds, Rs, Ls, Dt, Rt, Lt) - - if backend_name == "numpy": - C_backend = C_np - - elif backend_name == "torch": - Ds_b = torch.from_numpy(Ds) - Rs_b = torch.from_numpy(Rs) - Ls_b = torch.from_numpy(Ls) - Dt_b = torch.from_numpy(Dt) - Rt_b = torch.from_numpy(Rt) - Lt_b = torch.from_numpy(Lt) - C_backend = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) - C_backend = C_backend.detach().cpu().numpy() - - elif backend_name == "jax": - Ds_b = jnp.array(Ds) - Rs_b = jnp.array(Rs) - Ls_b = jnp.array(Ls) - Dt_b = jnp.array(Dt) - Rt_b = jnp.array(Rt) - Lt_b = jnp.array(Lt) - C_backend = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) - C_backend = np.array(C_backend) - - np.testing.assert_allclose(C_backend, C_np, atol=1e-6) - - # --------------------------------------------------------------------- # DELTA MATRIX TESTS # --------------------------------------------------------------------- @@ -161,7 +76,7 @@ def test_delta_identity(): def test_delta_swap_invariance(): d, r = 6, 3 - R = rand_complex((d, r)) + _, R, _, _, _, _ = random_atoms(d=d, r=r) L = R.copy() delta1 = _delta_matrix_1d(R, L, R, L) delta2 = _delta_matrix_1d(L, R, L, R) @@ -173,11 +88,14 @@ def test_delta_swap_invariance(): # --------------------------------------------------------------------- -@pytest.mark.parametrize("metric_name", ["geodesic", "chordal", "procrustes", "martin"]) -def test_grassmann_zero_distance(metric_name): - delta = np.ones((3, 3)) - dist2 = _grassmann_distance_squared(delta, grassman_metric=metric_name) - np.testing.assert_allclose(dist2, 0.0, atol=1e-12) +@pytest.mark.parametrize( + "grassman_metric", ["geodesic", "chordal", "procrustes", "martin"] +) +def test_grassmann_zero_distance(grassman_metric, nx): + delta = nx.from_numpy(np.ones((3, 3))) + dist2 = _grassmann_distance_squared(delta, grassman_metric=grassman_metric, nx=nx) + dist2_np = nx.to_numpy(dist2) + np.testing.assert_allclose(dist2_np, 0.0, atol=1e-12) def test_grassmann_invalid_name(): @@ -257,13 +175,11 @@ def test_metric_with_weights(): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() r = Ds.shape[0] - logits_s = rng.randn(r) - logits_t = rng.randn(r) - - Ws = np.exp(logits_s) + rng = np.random.RandomState(1) + Ws = rng.rand(r) Ws = Ws / np.sum(Ws) - Wt = np.exp(logits_t) + Wt = rng.rand(r) Wt = Wt / np.sum(Wt) dist = metric(Ds, Rs, Ls, Dt, Rt, Lt, Ws=Ws, Wt=Wt) @@ -276,58 +192,57 @@ def test_metric_with_weights(): def test_hyperparameter_sweep_cost(nx): - """Create test_cost for each trial: sweep over HPs and run cost().""" + """Sweep over a random set of HPs and run cost().""" grassmann_types = ["geodesic", "chordal", "procrustes", "martin"] - n_trials = 10 - for _ in range(n_trials): - Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() - Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) - eta = rng.uniform(0.0, 1.0) - p = rng.choice([1, 2]) - q = rng.choice([1, 2]) - gm = rng.choice(grassmann_types) - C = cost( - Ds_b, - Rs_b, - Ls_b, - Dt_b, - Rt_b, - Lt_b, - eta=eta, - p=p, - q=q, - grassman_metric=gm, - ) - C_np = nx.to_numpy(C) - assert C_np.shape == (Ds.shape[0], Dt.shape[0]) - assert np.all(np.isfinite(C_np)) - assert np.all(C_np >= 0) + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) + rng = np.random.RandomState(2) + eta = rng.uniform(0.0, 1.0) + p = rng.choice([1, 2]) + q = rng.choice([1, 2]) + gm = rng.choice(grassmann_types) + C = cost( + Ds_b, + Rs_b, + Ls_b, + Dt_b, + Rt_b, + Lt_b, + eta=eta, + p=p, + q=q, + grassman_metric=gm, + ) + C_np = nx.to_numpy(C) + assert C_np.shape == (Ds.shape[0], Dt.shape[0]) + assert np.all(np.isfinite(C_np)) + assert np.all(C_np >= 0) -def test_hyperparameter_sweep(): - grassmann_types = ["geodesic", "chordal", "procrustes", "martin"] +@pytest.mark.parametrize( + "grassman_metric", ["geodesic", "chordal", "procrustes", "martin"] +) +def test_hyperparameter_sweep(grassman_metric): + Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() + rng = np.random.RandomState(3) + eta = rng.uniform(0.0, 1.0) + p = rng.choice([1, 2]) + q = rng.choice([1, 2]) + r = rng.choice([1, 2]) + + dist = metric( + Ds, + Rs, + Ls, + Dt, + Rt, + Lt, + eta=eta, + p=p, + q=q, + r=r, + grassman_metric=grassman_metric, + ) - for _ in range(10): - Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() - eta = rng.uniform(0.0, 1.0) - p = rng.choice([1, 2]) - q = rng.choice([1, 2]) - r = rng.choice([1, 2]) - gm = rng.choice(grassmann_types) - - dist = metric( - Ds, - Rs, - Ls, - Dt, - Rt, - Lt, - eta=eta, - p=p, - q=q, - r=r, - grassman_metric=gm, - ) - - assert np.isfinite(dist) - assert dist >= 0 + assert np.isfinite(dist) + assert dist >= 0 From a0e74beca4ae9979334742063534c3dfee1dd14d Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Fri, 27 Feb 2026 14:03:31 +0100 Subject: [PATCH 08/14] cost & metric fixed in test_sgot --- test/test_sgot.py | 38 ++++++++++++++++++++------------------ 1 file changed, 20 insertions(+), 18 deletions(-) diff --git a/test/test_sgot.py b/test/test_sgot.py index 4ecfd2e40..10c9cb70e 100644 --- a/test/test_sgot.py +++ b/test/test_sgot.py @@ -11,8 +11,8 @@ eigenvalue_cost_matrix, _delta_matrix_1d, _grassmann_distance_squared, - cost, - metric, + sgot_cost_matrix, + sgot_metric, ) @@ -50,16 +50,16 @@ def test_random_d_r(nx): r = int(rng.randint(r_min, r_max + 1)) Ds, Rs, Ls, Dt, Rt, Lt = random_atoms(d=d, r=r) Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) - C = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) + C = sgot_cost_matrix(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) C_np = nx.to_numpy(C) np.testing.assert_allclose(C_np.shape, (r, r)) assert np.all(np.isfinite(C_np)) and np.all(C_np >= 0) try: - dist = metric(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) + dist = sgot_metric(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b) dist_np = nx.to_numpy(dist) assert np.isfinite(dist_np) and dist_np >= 0 except TypeError: - pytest.skip("metric() unavailable (emd_c signature mismatch)") + pytest.skip("sgot_metric() unavailable (emd_c signature mismatch)") # --------------------------------------------------------------------- @@ -113,7 +113,7 @@ def test_cost_self_zero(nx): """(D_S R_S L_S D_S): diagonal of cost matrix (same atom to same atom) should be near zero.""" Ds, Rs, Ls, _, _, _ = random_atoms() Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2 = nx.from_numpy(Ds, Rs, Ls, Ds, Rs, Ls) - C = cost(Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2) + C = sgot_cost_matrix(Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2) C_np = nx.to_numpy(C) np.testing.assert_allclose(np.diag(C_np), np.zeros(C_np.shape[0]), atol=1e-10) np.testing.assert_allclose(C_np, C_np.T, atol=1e-10) @@ -124,8 +124,8 @@ def test_cost_reference(nx): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) eta, p, q = 0.5, 2, 1 - C1 = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, eta=eta, p=p, q=q) - C2 = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, eta=eta, p=p, q=q) + C1 = sgot_cost_matrix(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, eta=eta, p=p, q=q) + C2 = sgot_cost_matrix(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, eta=eta, p=p, q=q) np.testing.assert_allclose(nx.to_numpy(C1), nx.to_numpy(C2), atol=1e-12) @@ -135,7 +135,9 @@ def test_cost_reference(nx): def test_cost_basic(grassman_metric, nx): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) - C = cost(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, grassman_metric=grassman_metric) + C = sgot_cost_matrix( + Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, grassman_metric=grassman_metric + ) C_np = nx.to_numpy(C) assert C_np.shape == (Ds.shape[0], Dt.shape[0]) assert np.all(np.isfinite(C_np)) @@ -146,10 +148,10 @@ def test_cost_validation(): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() with pytest.raises(ValueError): - cost(Ds.reshape(-1, 1), Rs, Ls, Dt, Rt, Lt) + sgot_cost_matrix(Ds.reshape(-1, 1), Rs, Ls, Dt, Rt, Lt) with pytest.raises(ValueError): - cost(Ds, Rs[:, :-1], Ls, Dt, Rt, Lt) + sgot_cost_matrix(Ds, Rs[:, :-1], Ls, Dt, Rt, Lt) # --------------------------------------------------------------------- @@ -159,15 +161,15 @@ def test_cost_validation(): def test_metric_self_zero(): Ds, Rs, Ls, _, _, _ = random_atoms() - dist = metric(Ds, Rs, Ls, Ds, Rs, Ls) + dist = sgot_metric(Ds, Rs, Ls, Ds, Rs, Ls) assert np.isfinite(dist) - assert abs(dist) < 2e-4 + assert abs(dist) < 5e-4 def test_metric_symmetry(): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() - d1 = metric(Ds, Rs, Ls, Dt, Rt, Lt) - d2 = metric(Dt, Rt, Lt, Ds, Rs, Ls) + d1 = sgot_metric(Ds, Rs, Ls, Dt, Rt, Lt) + d2 = sgot_metric(Dt, Rt, Lt, Ds, Rs, Ls) np.testing.assert_allclose(d1, d2, atol=1e-8) @@ -182,7 +184,7 @@ def test_metric_with_weights(): Wt = rng.rand(r) Wt = Wt / np.sum(Wt) - dist = metric(Ds, Rs, Ls, Dt, Rt, Lt, Ws=Ws, Wt=Wt) + dist = sgot_metric(Ds, Rs, Ls, Dt, Rt, Lt, Ws=Ws, Wt=Wt) assert np.isfinite(dist) @@ -201,7 +203,7 @@ def test_hyperparameter_sweep_cost(nx): p = rng.choice([1, 2]) q = rng.choice([1, 2]) gm = rng.choice(grassmann_types) - C = cost( + C = sgot_cost_matrix( Ds_b, Rs_b, Ls_b, @@ -230,7 +232,7 @@ def test_hyperparameter_sweep(grassman_metric): q = rng.choice([1, 2]) r = rng.choice([1, 2]) - dist = metric( + dist = sgot_metric( Ds, Rs, Ls, From e994303f7f0a08e4b6b04cd72d5b51d453512056 Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Fri, 27 Feb 2026 14:21:09 +0100 Subject: [PATCH 09/14] correct issues on test_sgot --- test/test_sgot.py | 52 +++++++++++++++++++++++++++++------------------ 1 file changed, 32 insertions(+), 20 deletions(-) diff --git a/test/test_sgot.py b/test/test_sgot.py index 10c9cb70e..267d43a1c 100644 --- a/test/test_sgot.py +++ b/test/test_sgot.py @@ -41,7 +41,7 @@ def _rand_complex(shape, seed_): def test_random_d_r(nx): - """Sample d and r uniformly and run cost (and metric when available) with those shapes.""" + """Sample d and r uniformly and run sgot_cost_matrix (and sgot_metric when available) with those shapes.""" rng = np.random.RandomState(0) d_min, d_max = 4, 12 r_min, r_max = 2, 6 @@ -67,14 +67,22 @@ def test_random_d_r(nx): # --------------------------------------------------------------------- -def test_delta_identity(): +def test_eigenvalue_cost_matrix_simple(): + Ds = np.array([0.0, 1.0]) + Dt = np.array([0.0, 2.0]) + C = eigenvalue_cost_matrix(Ds, Dt, q=2) + expected = np.array([[0.0, 4.0], [1.0, 1.0]]) + np.testing.assert_allclose(C, expected) + + +def test_delta_matrix_1d_identity(): r = 4 I = np.eye(r, dtype=complex) delta = _delta_matrix_1d(I, I, I, I) np.testing.assert_allclose(delta, np.eye(r), atol=1e-12) -def test_delta_swap_invariance(): +def test_delta_matrix_1d_swap_invariance(): d, r = 6, 3 _, R, _, _, _, _ = random_atoms(d=d, r=r) L = R.copy() @@ -98,7 +106,7 @@ def test_grassmann_zero_distance(grassman_metric, nx): np.testing.assert_allclose(dist2_np, 0.0, atol=1e-12) -def test_grassmann_invalid_name(): +def test_grassmann_distance_invalid_name(): delta = np.ones((2, 2)) with pytest.raises(ValueError): _grassmann_distance_squared(delta, grassman_metric="cordal") @@ -110,7 +118,7 @@ def test_grassmann_invalid_name(): def test_cost_self_zero(nx): - """(D_S R_S L_S D_S): diagonal of cost matrix (same atom to same atom) should be near zero.""" + """(D_S R_S L_S D_S): diagonal of sgot_cost_matrix matrix (same atom to same atom) should be near zero.""" Ds, Rs, Ls, _, _, _ = random_atoms() Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2 = nx.from_numpy(Ds, Rs, Ls, Ds, Rs, Ls) C = sgot_cost_matrix(Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2) @@ -119,7 +127,7 @@ def test_cost_self_zero(nx): np.testing.assert_allclose(C_np, C_np.T, atol=1e-10) -def test_cost_reference(nx): +def test_grassmann_cost_reference(nx): """Cost with same inputs and HPs should be deterministic (np.testing.assert_allclose).""" Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) @@ -132,7 +140,7 @@ def test_cost_reference(nx): @pytest.mark.parametrize( "grassman_metric", ["geodesic", "chordal", "procrustes", "martin"] ) -def test_cost_basic(grassman_metric, nx): +def test_grassmann_cost_basic_properties(grassman_metric, nx): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) C = sgot_cost_matrix( @@ -144,7 +152,7 @@ def test_cost_basic(grassman_metric, nx): assert np.all(C_np >= 0) -def test_cost_validation(): +def test_sgot_cost_input_validation(): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() with pytest.raises(ValueError): @@ -159,21 +167,21 @@ def test_cost_validation(): # --------------------------------------------------------------------- -def test_metric_self_zero(): +def test_sgot_metric_self_zero(): Ds, Rs, Ls, _, _, _ = random_atoms() dist = sgot_metric(Ds, Rs, Ls, Ds, Rs, Ls) assert np.isfinite(dist) assert abs(dist) < 5e-4 -def test_metric_symmetry(): +def test_sgot_metric_symmetry(): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() d1 = sgot_metric(Ds, Rs, Ls, Dt, Rt, Lt) d2 = sgot_metric(Dt, Rt, Lt, Ds, Rs, Ls) np.testing.assert_allclose(d1, d2, atol=1e-8) -def test_metric_with_weights(): +def test_sgot_metric_with_weights(): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() r = Ds.shape[0] @@ -193,16 +201,20 @@ def test_metric_with_weights(): # --------------------------------------------------------------------- -def test_hyperparameter_sweep_cost(nx): - """Sweep over a random set of HPs and run cost().""" - grassmann_types = ["geodesic", "chordal", "procrustes", "martin"] +@pytest.mark.parametrize( + "eta, p, q, grassman_metric", + [ + (0.5, 1, 1, "geodesic"), + (0.5, 2, 1, "chordal"), + (0.3, 2, 2, "procrustes"), + (0.7, 1, 2, "martin"), + ], +) +def test_hyperparameter_sweep_cost(nx, eta, p, q, grassman_metric): + """Sweep over a set of fixed HPs and run cost().""" Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b = nx.from_numpy(Ds, Rs, Ls, Dt, Rt, Lt) - rng = np.random.RandomState(2) - eta = rng.uniform(0.0, 1.0) - p = rng.choice([1, 2]) - q = rng.choice([1, 2]) - gm = rng.choice(grassmann_types) + C = sgot_cost_matrix( Ds_b, Rs_b, @@ -213,7 +225,7 @@ def test_hyperparameter_sweep_cost(nx): eta=eta, p=p, q=q, - grassman_metric=gm, + grassman_metric=grassman_metric, ) C_np = nx.to_numpy(C) assert C_np.shape == (Ds.shape[0], Dt.shape[0]) From e9f8be7abcf06fb3ff1f367bb944387fe3012c7a Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Fri, 27 Feb 2026 14:50:29 +0100 Subject: [PATCH 10/14] fixing test failures --- ot/sgot.py | 13 ++++++++----- test/test_sgot.py | 10 ++++++---- 2 files changed, 14 insertions(+), 9 deletions(-) diff --git a/ot/sgot.py b/ot/sgot.py index d443c3490..c8ee5b91c 100644 --- a/ot/sgot.py +++ b/ot/sgot.py @@ -271,17 +271,20 @@ def sgot_cost_matrix( if Ds.ndim != 1 or Dt.ndim != 1: raise ValueError( - f"sgot_cost_matrix() expects Ds, Dt 1D; got Ds {getattr(Ds,'shape',None)}, Dt {getattr(Dt,'shape',None)}" + f"sgot_cost_matrix() expects Ds, Dt 1D; " + f"got Ds {getattr(Ds, 'shape', None)}, Dt {getattr(Dt, 'shape', None)}" ) if Rs.shape != Ls.shape or Rt.shape != Lt.shape: raise ValueError( - f"Right/left eigenvector shapes must match; got (Rs,Ls)=({Rs.shape},{Ls.shape}), (Rt,Lt)=({Rt.shape},{Lt.shape})" + "Right/left eigenvector shapes must match; got " + f"(Rs,Ls)=({Rs.shape},{Ls.shape}), (Rt,Lt)=({Rt.shape},{Lt.shape})" ) if Rs.shape[1] != Ds.shape[0] or Rt.shape[1] != Dt.shape[0]: raise ValueError( - f"Eigenvectors columns must match eigenvalues: Rs {Rs.shape[1]} vs Ds {Ds.shape[0]}, " + "Eigenvector columns must match eigenvalues: " + f"Rs {Rs.shape[1]} vs Ds {Ds.shape[0]}, " f"Rt {Rt.shape[1]} vs Dt {Dt.shape[0]}" ) @@ -420,6 +423,6 @@ def sgot_metric( Ws = Ws / nx.sum(Ws) Wt = Wt / nx.sum(Wt) - P = ot.emd2(Ws, Wt, nx.real(C)) - obj = float(nx.sum(C * P) ** (1.0 / p)) + obj = ot.emd2(Ws, Wt, nx.real(C)) + obj = obj ** (1.0 / p) return obj ** (1.0 / float(r)) diff --git a/test/test_sgot.py b/test/test_sgot.py index 267d43a1c..af64e20fb 100644 --- a/test/test_sgot.py +++ b/test/test_sgot.py @@ -167,11 +167,13 @@ def test_sgot_cost_input_validation(): # --------------------------------------------------------------------- -def test_sgot_metric_self_zero(): +def test_sgot_metric_self_zero(nx): Ds, Rs, Ls, _, _, _ = random_atoms() - dist = sgot_metric(Ds, Rs, Ls, Ds, Rs, Ls) - assert np.isfinite(dist) - assert abs(dist) < 5e-4 + Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2 = nx.from_numpy(Ds, Rs, Ls, Ds, Rs, Ls) + dist = sgot_metric(Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2, nx=nx) + dist_np = nx.to_numpy(dist) + assert np.isfinite(dist_np) + assert abs(float(dist_np)) < 5e-4 def test_sgot_metric_symmetry(): From 37aa7219d3da4bd76bb1b46781ea3a22619ed231 Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Sat, 14 Mar 2026 14:15:55 +0100 Subject: [PATCH 11/14] sgot documentation --- docs/source/all.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/source/all.rst b/docs/source/all.rst index 0f7025ec1..2452dafca 100644 --- a/docs/source/all.rst +++ b/docs/source/all.rst @@ -34,6 +34,7 @@ API and modules plot regpath sliced + sgot smooth stochastic unbalanced From 7641f7fe9d6fc2158528505d40c0cd698f0d6faa Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Tue, 31 Mar 2026 10:13:07 +0200 Subject: [PATCH 12/14] fix backend error and example notebook --- examples/plot_sgot.ipynb | 791 +++++++++++++++++++++++++++++++++++++++ ot/backend.py | 2 +- ot/sgot.py | 186 ++++----- 3 files changed, 885 insertions(+), 94 deletions(-) create mode 100644 examples/plot_sgot.ipynb diff --git a/examples/plot_sgot.ipynb b/examples/plot_sgot.ipynb new file mode 100644 index 000000000..4ab84b4d1 --- /dev/null +++ b/examples/plot_sgot.ipynb @@ -0,0 +1,791 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 19, + "id": "03c2cded", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'\\n=========================================\\nSGOT example for a rotated linear system\\n=========================================\\n\\nThis notebook presents a synthetic example of Spectral Grassmannian-Wasserstein\\nOptimal Transport (SGOT) on linear dynamical systems.\\n\\nWe consider a signal formed by the sum of two damped oscillatory modes evolving\\nalong a rotated direction in the plane. The signal is then associated with an\\nunderlying continuous linear dynamical system, and we study how its spectral\\nrepresentation varies under rotation. The SGOT cost and metric are used to\\ncompare the reference and rotated systems.\\n\\n[1] T. Germain; R. Flamary; V. R. Kostic; K. Lounici, A Spectral-Grassmann Wasserstein Metric for Operator Representations of Dynamical Systems, arXiv preprint arXiv:2509.24920, 2025.\\n\\n'" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "=========================================\n", + "SGOT example for a rotated linear system\n", + "=========================================\n", + "\n", + "This notebook presents a synthetic example of Spectral Grassmannian-Wasserstein\n", + "Optimal Transport (SGOT) on linear dynamical systems.\n", + "\n", + "We consider a signal formed by the sum of two damped oscillatory modes evolving\n", + "along a rotated direction in the plane. The signal is then associated with an\n", + "underlying continuous linear dynamical system, and we study how its spectral\n", + "representation varies under rotation. The SGOT cost and metric are used to\n", + "compare the reference and rotated systems.\n", + "\n", + "[1] T. Germain; R. Flamary; V. R. Kostic; K. Lounici, A Spectral-Grassmann Wasserstein Metric for Operator Representations of Dynamical Systems, arXiv preprint arXiv:2509.24920, 2025.\n", + "\n", + "\"\"\"" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "bdcd6755", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from ot.sgot import sgot_metric, sgot_cost_matrix\n", + "\n", + "from scipy.linalg import eig" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "3c0a2a11", + "metadata": {}, + "outputs": [], + "source": [ + "# sampling parameters and time grid\n", + "fs = 50\n", + "max_t = 5\n", + "time = np.linspace(0, max_t, fs * max_t)\n", + "dt = 1 / fs" + ] + }, + { + "cell_type": "markdown", + "id": "abe935cd", + "metadata": {}, + "source": [ + "# Example: rotating a linear dynamical system in 3D" + ] + }, + { + "cell_type": "markdown", + "id": "17b22e68", + "metadata": {}, + "source": [ + "## 1. Build a simple observed signal \n", + "\n", + "We begin by assuming that the observed signal is made of two oscillatory components:\n", + "$$\n", + "x(t)=e^{-\\tau_1 t}\\cos(2\\pi\\omega_1 t)\\,\\vec e(\\theta)\n", + "\\;+\\;\n", + "e^{-\\tau_2 t}\\cos(2\\pi\\omega_2 t)\\,\\vec e(\\theta),\n", + "$$\n", + "where $\\vec e(\\theta)\\in\\mathbb{R}^2$ is a fixed real vector. Thus, $x(t)$ evolves along the one-dimensional subspace spanned by $\\vec e(\\theta)$, while its time dependence exhibits oscillatory and dissipative behaviour.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "9cea207f", + "metadata": {}, + "outputs": [], + "source": [ + "tau_0 = np.array([0.08, 0.18])\n", + "freq_0 = np.array([1., 2.])\n", + "theta_0 = np.pi / 4\n", + "\n", + "def generate_data(time,tau,freq,theta):\n", + " t_ = np.sin(2 * np.pi * freq[None,:] * time[:,None]) * np.exp(-tau[None,:] * time[:,None])\n", + " t_ = t_.sum(axis=1)\n", + " traj_0 = np.zeros((t_.shape[0],2))\n", + " traj_0[:,0] = t_\n", + " rotation_matrix = np.array([[np.cos(theta), -np.sin(theta)],\n", + " [np.sin(theta), np.cos(theta)]])\n", + " traj_0 = traj_0 @ rotation_matrix.T\n", + " return traj_0\n", + "traj_0 = generate_data(time,tau_0,freq_0,theta_0)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "320650e0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plot the observed signal components and their sum\n", + "plt.figure(figsize=(10, 4))\n", + "plt.plot(time, traj_0, label=\"base trajectory\", linewidth=2)\n", + "plt.xlabel(\"time\")\n", + "plt.ylabel(\"amplitude\")\n", + "plt.legend()\n", + "plt.title(r\"Observed scalar signal along $\\vec{e}(\\theta)$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "1216ab22", + "metadata": {}, + "source": [ + "## 2. Interpret the signal as coming from a continuous linear dynamical system\n", + "We assume that $x(t)$ is generated by an underlying continuous linear dynamical system. Since the observed signal is a superposition of two sinusoidal modes, the corresponding linear dynamics are naturally described by a fourth-order model. We therefore introduce the state vector\n", + "$$\n", + "z(t)=\n", + "\\begin{pmatrix}\n", + "x_1(t)\\\\\n", + "x_2(t)\\\\\n", + "\\vdots\\\\\n", + "x_1^{(3)}(t)\\\\\n", + "x_2^{(3)}(t)\n", + "\\end{pmatrix}\n", + "\\in\\mathbb{R}^8.\n", + "$$\n", + "This allows us to rewrite the dynamics as a first-order linear system:\n", + "$$\n", + "\\dot{z}(t)=Az(t),\n", + "$$\n", + "where $A\\in\\mathbb{R}^{8\\times 8}$. Its solution is then given by\n", + "$$\n", + "z(t)=e^{tA}z_0.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "679bd14e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(9, 6))\n", + "ax = fig.add_subplot(projection=\"3d\")\n", + "\n", + "ax.plot(time, traj_0[:, 0], traj_0[:, 1])\n", + "ax.set_xlabel(\"time\")\n", + "ax.set_ylabel(\"x₁(t)\")\n", + "ax.set_title(\"Observed trajectory in time\")\n", + "\n", + "ax.text2D(1.08, 0.5, \"x₂(t)\", transform=ax.transAxes, rotation=90, va=\"center\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "3435803e", + "metadata": {}, + "source": [ + "## 3. Sampling and preprocessing discrete trajectories of dynamical system\n", + "We now have a bridge between the continuous system and the operator we later aim to infer from sampled data. Since in practice we do not observe the full continuous trajectory, we work instead with discrete samples of the signal. We take snapshots at uniform time intervals $\\Delta t$, and write the sampled signal as\n", + "\n", + "$$\n", + "S=\n", + "\\begin{pmatrix}\n", + "x_1(0) & x_2(0)\\\\\n", + "x_1(\\Delta t) & x_2(\\Delta t)\\\\\n", + "\\vdots\\\\\n", + "x_1(N\\Delta t) & x_2(N\\Delta t)\\\\\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "The goal is now to use these observations to recover the operator governing the evolution. \n", + "To do this, we augment the signal $s$ using a sliding window of length $w$. For each $k$, define\n", + "$$z_k =\n", + "\\begin{pmatrix}\n", + "s_k\\\\\n", + "s_{k+1}\\\\\n", + "\\vdots\\\\\n", + "s_{k+w-1}\n", + "\\end{pmatrix}\n", + "$$\n", + "We then form the data matrices\n", + "$$\n", + "X=\n", + "\\begin{pmatrix}\n", + "z_1\\\\\n", + "z_2\\\\\n", + "\\vdots\\\\\n", + "z_{N-w}\n", + "\\end{pmatrix},\n", + "\\qquad\n", + "Y=\n", + "\\begin{pmatrix}\n", + "z_2\\\\\n", + "z_3\\\\\n", + "\\vdots\\\\\n", + "z_{N-w+1}\n", + "\\end{pmatrix},\n", + "$$\n", + "so that $X$ contains the present windowed states and $Y$ the corresponding shifted future states." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "f84a0f1e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "X shape: (246, 4)\n", + "Y shape: (246, 4)\n" + ] + } + ], + "source": [ + "# build a 4-dimensional state using delay embedding\n", + "def augment(traj, window_length = 2):\n", + " Z = np.lib.stride_tricks.sliding_window_view(traj,(window_length,1))\n", + " Z = Z.reshape(Z.shape[0], -1)\n", + " return Z\n", + "\n", + "# create the embedded state matrix Z\n", + "Z = augment(traj_0[:, [0]], 4)\n", + "Z.shape\n", + "\n", + "# inspect one embedded state vector\n", + "Z[0]\n", + "\n", + "# create X and Y for the SGOT metric\n", + "X = Z[:-1]\n", + "Y = Z[1:]\n", + "\n", + "# inspect shapes of X and Y\n", + "print(\"X shape:\", X.shape)\n", + "print(\"Y shape:\", Y.shape)" + ] + }, + { + "cell_type": "markdown", + "id": "0c8749bb", + "metadata": {}, + "source": [ + "## 4. Estimate the discrete-time operator\n", + "Now, we look to identify the operator that maps $X$ to $Y$. From\n", + "$$\n", + "\\dot{z}=Az,\n", + "$$\n", + "we have\n", + "$$\n", + "z(t+\\Delta t)=e^{\\Delta tA}z(t).\n", + "$$\n", + "Setting\n", + "$$\n", + "B=e^{\\Delta tA},\n", + "$$\n", + "the corresponding discrete-time evolution is governed by $B$, and we seek the best linear map satisfying\n", + "$$\n", + "Y\\approx X B^T.\n", + "$$\n", + "Equivalently, we solve the optimisation problem\n", + "$$\n", + "\\min_B \\|Y-XB\\|^2.\n", + "$$\n", + "\n", + "We want to recover the best rank-$r$ operator, whose estimator is defined as follows\n", + "$$\n", + "B = C_{xx}^{-\\frac{1}{2}}[C_{xx}^{-\\frac{1}{2}}C_{xy}]_r \\quad \\text{s.t} \\quad C_{xx} = X^T X \\quad \\text{and} \\quad C_{xy} = X^TY.\n", + "$$\n", + "where $[ ]_r$ is the best rank-$r$ estimator through SVD decomposition. [2]\n", + "\n", + "[2] Kostic, V., Novelli, P., Maurer, A., Ciliberto, C., Rosasco, L. and Pontil, M., 2022. Learning dynamical systems via Koopman operator regression in reproducing kernel Hilbert spaces. Advances in Neural Information Processing Systems, 35, pp.4017-4031." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "49a6b573", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def estimator(X,Y,rank=4):\n", + " # X: (n_samples, n_features)\n", + " # Y: (n_samples, n_features)\n", + "\n", + " # estimate operator\n", + " cxx = X.T @ X\n", + " U, S, Vt = np.linalg.svd(cxx)\n", + " S_inv = np.divide(1, S, out=np.zeros_like(S), where=S!=0)\n", + " cxx_inv_half = Vt.T @ np.diag(np.sqrt(S_inv)) @ U.T\n", + " cxy = X.T @ Y\n", + " T = cxx_inv_half @ cxy\n", + " U,S,Vt = np.linalg.svd(T)\n", + " S[rank:] = 0\n", + " T_rank = U @ np.diag(S) @ Vt\n", + " T = cxx_inv_half @ T_rank\n", + "\n", + " # estimate spectral decomposition\n", + " val, vl, vr = eig(T, left=True, right=True)\n", + " sort_idx = np.argsort(np.abs(val))[::-1]\n", + " val = val[sort_idx][:rank]\n", + " vl = vl[:, sort_idx][:,:rank]\n", + " vr = vr[:, sort_idx][:,:rank]\n", + " \n", + " return T, {\"eig_val\": val, \"eig_vec_left\": vl, \"eig_vec_right\": vr}\n", + "\n", + "B_0, B_0_spec = estimator(X, Y, rank=4)\n", + "Y_pred = X @ B_0\n", + "\n", + "plt.figure(figsize=(10, 4))\n", + "plt.plot(Y[:, 0], label=\"true\")\n", + "plt.plot(Y_pred[:, 0], \"--\", label=\"predicted\")\n", + "plt.xlabel(\"sample index\")\n", + "plt.ylabel(\"first state coordinate\")\n", + "plt.title(\"True Signal vs Predicted Signal\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "a1c01574", + "metadata": {}, + "source": [ + "The predicted signal is nearly indistinguishable from the true signal, indicating that the estimated operator accurately captures the observed dynamics." + ] + }, + { + "cell_type": "markdown", + "id": "c202a029", + "metadata": {}, + "source": [ + "## 6. Recover continuous-time spectral information from the discrete operator\n", + "To recover the continuous generator $A$, we study the spectral structure of $B$. We diagonalise $B$ as\n", + "$$\n", + "B=PDP^{-1},\n", + "$$\n", + "where\n", + "$$\n", + "D=\\operatorname{diag}(\\mu_1,\\dots,\\mu_n).\n", + "$$\n", + "The continuous-time eigenvalues are of the form\n", + "$$\n", + "\\lambda_k=-\\tau_k+2\\pi i\\,\\omega_k,\n", + "\\qquad k\\in\\{1,2\\},\n", + "$$\n", + "and the corresponding eigenvalues of $B$ are\n", + "$$\n", + "\\mu_k=e^{\\Delta t\\lambda_k}\n", + " =e^{\\Delta t(-\\tau_k+2\\pi i\\omega_k)}.\n", + "$$\n", + "\n", + "Since $B=e^{\\Delta tA}$, we recover $A$ by taking the logarithm:\n", + "$$\n", + "A=P\\,\\frac{\\log(D)}{\\Delta t}\\,P^{-1}.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "5844072d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "First mode: frequency: 1.00 Hz -- decay: 0.08\n", + "Second mode: frequency: 2.01 Hz -- decay: 0.18\n" + ] + } + ], + "source": [ + "D_0 = np.log(B_0_spec[\"eig_val\"]) * fs\n", + "L_0 = B_0_spec[\"eig_vec_left\"]\n", + "R_0 = B_0_spec[\"eig_vec_right\"]\n", + "\n", + "freq = D_0.imag / (2 * np.pi)\n", + "mask = freq > 0\n", + "freq = freq[mask]\n", + "decay = -D_0.real[mask]\n", + "print(f\"First mode: frequency: {freq[0]:.2f} Hz -- decay: {decay[0]:.2f}\")\n", + "print(f\"Second mode: frequency: {freq[1]:.2f} Hz -- decay: {decay[1]:.2f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "fbe56661", + "metadata": {}, + "source": [ + "## Applying a rotation in the notebook\n", + "\n", + "The rotation is introduced through the parameter `theta`. In the data-generation step, the trajectory is rotated in the observation plane by the 2D rotation matrix\n", + "\n", + "$$\n", + "R(\\theta)=\n", + "\\begin{pmatrix}\n", + "\\cos\\theta & -\\sin\\theta \\\\\n", + "\\sin\\theta & \\cos\\theta\n", + "\\end{pmatrix},\n", + "$$\n", + "\n", + "via `traj_0 = traj_0 @ R(theta).T`.\n", + "\n", + "At the operator level, the same transformation is represented by conjugation of the reference operator,\n", + "\n", + "$$\n", + "A_{\\mathrm{rot}} = P(\\theta),A_{\\mathrm{ref}},P(\\theta)^\\top,\n", + "$$\n", + "\n", + "where $P(\\theta)$ is the block rotation acting on both state coordinates and their derivatives.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "id": "2ebe8f8b", + "metadata": {}, + "outputs": [], + "source": [ + "# [X_1,X_2,X_1_,X_2_]\n", + "A_ref= np.array([[0,0,1,0],[0,0,0,0],[-1,0,0,0],[0,0,0,0]])\n", + "\n", + "b = 0.1\n", + "c = 1\n", + "A_shift= np.array([[0,0,1,0],[0,0,0,0],[-c,0,-b,0],[0,0,0,0]])\n", + "\n", + "def rotation_matrix(theta):\n", + " c, s = np.cos(theta), np.sin(theta)\n", + " return np.array([[c, -s, 0, 0], [s, c, 0, 0], [0, 0, c, -s], [0, 0, s, c]])\n", + "\n", + "P = rotation_matrix(np.pi/4)\n", + "A_rot = P @ A_ref @ P.T\n", + "\n", + "A_ref_decomp = np.linalg.eig(A_ref)\n", + "A_rot_decomp = np.linalg.eig(A_rot)" + ] + }, + { + "cell_type": "markdown", + "id": "06cb87fd", + "metadata": {}, + "source": [ + "# Introduction to SGOT for linear operators\n", + "\n", + "To compare two linear operators through their spectral structure, we use the SGOT framework introduced in Theorem 1 of [1]. For a non-defective finite-rank operator $T \\in S_r(\\mathcal H)$, the theorem associates a discrete spectral measure\n", + "\n", + "$$\n", + "\\mu(T) \\triangleq \\sum_{j\\in[\\ell]} \\frac{m_j}{m_{\\mathrm{tot}}},\\delta_{(\\lambda_j,\\mathcal V_j)},\n", + "$$\n", + "\n", + "where $\\lambda_j$ are the eigenvalues of $T$, $m_j$ their algebraic multiplicities, and $\\mathcal V_j$ the corresponding eigenspaces. Thus, each spectral component of the operator is represented by an atom of the form\n", + "\n", + "$$\n", + "(\\lambda_j,\\mathcal V_j),\n", + "$$\n", + "\n", + "combining one eigenvalue with its associated invariant subspace.\n", + "\n", + "Theorem 1 then defines a ground cost between two such atoms by combining a spectral discrepancy and a geometric discrepancy:\n", + "\n", + "$$\n", + "d_\\eta\\big((\\lambda,\\mathcal V),(\\lambda',\\mathcal V')\\big)\n", + "\\triangleq\n", + "\\eta,|\\lambda-\\lambda'| + (1-\\eta), d_{\\mathcal G}(\\mathcal V,\\mathcal V'),\n", + "$$\n", + "\n", + "where $d_{\\mathcal G}$ denotes the Grassmann distance between eigenspaces and $\\eta\\in(0,1)$ balances the contribution of eigenvalues and eigenspaces.\n", + "\n", + "The SGOT distance between two operators $T$ and $T'$ is then the Wasserstein distance between their associated spectral measures:\n", + "\n", + "$$\n", + "d_S(T,T') = W_{d_\\eta,p}\\big(\\mu(T),\\mu(T')\\big).\n", + "$$\n", + "\n", + "In this way, SGOT compares linear operators by optimally matching their spectral atoms, taking into account both the location of eigenvalues and the relative geometry of their eigenspaces.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "id": "77cea0bf", + "metadata": {}, + "outputs": [], + "source": [ + "thetas = np.linspace(0, np.pi, 10)\n", + "lst = []\n", + "for i, theta in enumerate(thetas):\n", + " traj = generate_data(time, tau_0, freq_0, theta)\n", + " Z = augment(traj[:, [0]], 4)\n", + " X = Z[:-1]\n", + " Y = Z[1:]\n", + " B, B_spec = estimator(X, Y, rank=4)\n", + " D, R, L = B_spec[\"eig_val\"], B_spec[\"eig_vec_right\"], B_spec[\"eig_vec_left\"]\n", + " D = np.log(D) * fs \n", + " lst.append(sgot_metric(D_0, R_0, L_0, D, R, L, eta=0.01))\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "1b1f7126", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", 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NAO+oDrd0HLuwcGBnJjzS+COFiIw4pkZM0Z42bRomT54sp12LRHlr1qypGgwsgpOkpKSq/Tt37ox58+bJIEZMwRanjZYtW4aWLVtW7bN8+XK0bt1aBj3CsGHD5PXKKd8iad+2bdtkANO4cWNZBzc3N5kDx8+vdhlMybwsfOkuRG+4KLcPdvXBsC9uvtfFpkmELD2Tax53Rbcm/sBWeBRAng6M6Tv8lo4V0vF2WYo1pMTsNiIio+SpMVfMU2N+/vvGMLRYdFBG3mLpg/u+216rwaj7tyyF41OvykR8wdt+h6d3oEHra2l++3wCGn+5GqleQI+dx295VtvhtjFwKgayPpqAznc9obd6EpF5M1ieGiJjWfL+aDRfrAQ0R6Kdax3QCK263IlcZ8C2HNj927cGq6ulunLykCyzvOs26+ladvYOcgaVcGnv77d8PCIyvhWzXkZ+Xg7UxKCGTM7yT8eh8S87ZP6TY80dMOSnHXWaLiwek+qvzKrJPPCHAWpq2ewvK+Ocrvp76uV4eb6Osiw/f1YvxyMi49m54luEfbECcX06IvXSGaiFQQ2ZlNVfv4aQb9bBrgyIb2yLO37aKn/F11V+feUL1+7CX+O8SD880pVBvXaNmujleOUN6svSJYUJE4nMzeVvP5cBRaaPLfyC/n3pIkNhUEMmY+MvH8F/5hI4lAKnQ63R55ctcHK5tfxCjs1aydI7pVhPtSRBDOb1zVDaomHHfnppFK+ojrL0SVNmVBGRedi/6X+IOKF8xro++IiqdWFQQyZh25JZcP/4ezlQ9FwDa3T9aR1cPeq26vO1ovo/LEuxPhFT8OvPgU2LYF8GXLUDorvdrZdjtun/kJxJJWZUiZlVRGQeTs9+Tw4XONPQ+h/r8BkbgxpS3a41P8Lu3ZlwvQokBFihzXfL4OV7a8ncKoVHdUaGu/Ifff/K7/RyTPprMK8Y3Hsrpwev5RMYhnQvZTt+8//YzERm4PieDYg4Uii3rYbcpXZ1GNSQug5s+xWlb0yVv84v+wLN5sxHQIh+xmhUSvO3k2XeEabg15fSisG8uT7K4F59yfRV3quC+MN6PS4RGcahT1+VYyAv1LfCgCfeUb2Z2VNDqjmx73fkvjwR9fKAlHpAyMxv5OKG+lYU7CNLp4vKbB26dc4pebIsC1KSburL1QClq8Y+qWLADhGZrLPHdiPikPJZUDSwV50XtdUnBjWk2h9D0vNj4JsNeXrIZ8YMNInuYpDncqtI4e+bUmqQ41si74wyWbpHttbrcZ2aNJOlVxoHdhOZut0fvwCHEuCiHzBo3GcwBQxqyOjEgN0zT49EQAaQ7Qo4TX0bLSvS5BtC7MDH5ABU0SMUv3+zwZ7HUiSeOYJ6FSsZtLxtqF6P3aT7PVUDu7MzOA2fyJQ/x5vEZcrt3L7tTaKXRmBQQ0aVnnQOh0ffhwapQJ4TgDdfQuxt9xv0OcUYnVRvZfvYuvkGfS5LcPT3hbLMdIPeTxdGxvaW/y/ETIq4tb/o9dhEpD/bPngWzkVAcj3grv/7a4FqtTGoIaMRv7x3jRyEhpd1yHcACiY+hU6DRhvluTMDlBk6RSeOGOX5tCz7mDLgOsNHydasT+LXXpqv8rGUfnC73o9PRLcuMyURYXtS5HZar5Z6mwGpDwxqyCjEeiBbHumLRgnlMrdJ5gsPoufQ8UZr/ZKQimy1SdlGe06tsrmULMsCPzeDHP+Kr4uykZBokOMT0a1Z9+5ouBcA6R7Ana+a1rp6DGrI4IoKC7Du4W5oerYMxbbApacHod+jbxi15X3b9pRlQHI5yko5YPhWuKddlaVNaBgMwaphiCzdUgsMcnwiqrvcrFSE7FR+cFzuGn7LWd/1jUENGVRJcRF+e6QLIuNLUGoNnBvZA4PGfGz0Vu8w6HGU2EAm+DuwZanRn19L76dvhk5uB8X2MshzBLRRAlC/dB0DUCITs/q9x+F1RZnkcfvrppfQlEENGYzoEVn6aFe0OHIV5VZA/LB2GPLybFVaXCy5kOxjJbfPbmVQU1eHti2XS1mIADG61wMwhDZ9H5QBsBiEeGj7bwZ5DiKq25pv9bedktsXOjaAu5cfTA2DGjKYRU/0QFScsuLy0SHNcd/kH1Vt7exAMd0KKD99WtV6mLMLu9bIMrUe4OLmYbAAtHK22rkdKw3yHERUeyumPgGfHGXmap/XTGfG07UY1JBBzH+6F6J3KjkMDt4ehgemmsBaPmGhsnBPVgItqr3isydlmeNr2NkO2RXHLz4db9DnIaKbP/Xss+mQ3D7Tzleu1WaKGNSQ3i0YfztiNiszZA72CsSwT1aZRCsHd7lDloGpOtmNSrXnmKLMHisJrOhKMZCS+r7Vno+I1PXbtGdlwtQCe6Dr/31psm8HgxrSq4UT70H0mvNy+2Cnehj2H2U1Z1PQtt/DKLSHTOu9d+1PalfHLHmlKzPHXJpGGfR5XJvFyNI7jTPViExhfKTb2p1y+1QbTwSHt4SpYlBDerP47RFo+etxuX041hX3z9liUq0rEkQl+yn/5ZN2bVC7OmaZcMsnS9lu2kNZzsBQWvUZLktx/j7pwgmDPhcR3djKmS+iQYoORbZAuxenw5QxqCG9WPbx04hYsAfWOuBoS0fcO3enyawFcq28+q6ytDp3Qe2qmJ24db/ID4xcZyAiprtBnyskog2yKnL7HVzH5RKI1GT323pZnmzlivCozib9ZjCooVu2YuZLCPthC2zLgeMRdrjzp+0mGdAIto0jZOmZXKh2VcxOxuE/ZZnuY5yPjfSKZRiyj+41yvMR0T+tmfMGQi/pZJqF5s+/DVPHoIZuydrv3kbQVythXwacDLdB/5+3wcHJ2WRbNbzXvbIMSOcq0LVllXhRlld8jfP+FgQomUptLyqDzonI+Er+t0SW8S0c0bLj7Sb/FjCooTrbtGAGfD6bD8cS4EyINXr8uN5guUv0JarTQHn6RPQq7f7tG7WrY1Zc0yp6t4KDjfJ8tmGNZemeVmSU5yOi6n6fNw2Nz5fL5KmhT/8fzAGDGqqTnSu+hcuHc2TW1wtBVug4dwU8vQNNvjXFabEUf+W0RsZ+rgJdm9kPPhnlcts3uguMIaRjP1n6Z3AKPpEacufNlWV8hD3a3jbMLN4EBjVUa/s2LgLenAa3QuCivxWivllssomYalIQ5CVLh4QktatiNk7u3yzfb/GLrU2/B43ynK173i9XdLcvBQ5sWmSU5yQixY7lcxBxWkmp4DdqDMwFgxqqlSN/rkbhpMnwvAIkewNNZv+IoLDmZtWKTs1aybJeSrHaVTEbJ7f+KstULxitR05MwU+tWK/r4p6NRnlOIlIkfz9TlvGNbdF18JMwFwxq6KadOrgd6RMmwDsXSPMEAj+fhdBmbc2uBaNuHylL/0zg0rljalfHLBSePirLbF87oz5vrp+jLMvPnTXq8xJZem980xPKjz73B5XPS3PBoIZuSkJ8HBLGPi4DgUw3wP3jDxAZ29ssW69R8/ZIrxjPvH/Ft2pXxyzYJ2XI8qq/curOWMqClF4h59Q8oz4vkSU7O3sqbHTAmYbW6P3gSzAnDGroXyUnnMKJpx5G/TQgxxmwe+81xHQbbNYtl+6v9DjkHd2ndlXMgme68qvNMTzSqM9br1VHWfqkKYOUiciwju5ah4hjykxHm3uHmF1zM6ihf02NH/fYYAQn63DFESh543m07/ew2bdaUQNlwUSni0oPBF3flZxM+CoLriOss7IoqLG06f8wRDjjma+c/iQiwzr6+WuwKwPOB1nh9iffM7vmZlBDN/wy2z5yAMIu6uRCkLkvj0K3u5/RRIu5t+ogS78ULpj4b+LWz5N5fcTqvCLPjzGJWXXpFWe8TmzmDCgiQzpzeAeaHrwit0sG9THLxq5TUDNr1iyEhobC0dERHTp0wO7du2+4/6JFixAZGSn3j4qKwqpVq6rdv2TJEvTr1w/e3t6wsrLCgQMHqt2fmZmJ5557DhEREXByckJISAief/555OTk1KX6dBMK83Ox4aEeMvGSWMQsZew9uO2hVzTTdm3vHC2nJ3vlASf2mc5K4qYo5cA2Wab5Wqmy/EWmj3KqMD/+sNGfm8iS7JnxEhxKlVQdA5+bAYsIahYuXIgJEyZgypQpiIuLQ3R0NPr374/U1NQa99+xYweGDx+O0aNHY//+/RgyZIi8HDlypGqf/Px8dO3aFR9++GGNx7h8+bK8TJs2TT7uhx9+wJo1a+QxSf9Kiouw6uFuMkdBiQ2Q8Hg/s+yGvBG/oHCkeCvbx9cvULs6Jq084bws83ycVHn+q4GesrS/nK7K8xNZgkvnjqFJXJbczu3X0WTX7/s3VjqdTlebB4iemXbt2mHmTGUOe3l5OYKDg2VPysSJE/+x/9ChQ2XQsmLFiqrbOnbsiJiYGMyePbvavufPn0dYWJgMfsT9/9b78/DDD8tj295E4+fm5sLDw0P27ri7K2vKUM2ZY5c81B4tDxaizAo4OaIL7pmkzeUEFt8bgxZHi3CwUz0M+57jNa7ntwEtZI/doYHhGDr9r79jY1n60dOI/G4LknyA3n8cN/rzE1mC+U/2QMzWVJl/rOumAzJPlKmozfd3rXpqiouLsW/fPvTp89e5Nmtra3l9586dNT5G3H7t/oLo2bne/jer8sVdL6ApKiqSDXHthf49oFk8qosMaMTgzGP3RWs2oBFKGwbJ0vVyttpVMWk+6crMI88W7VV5/ibdlZl2fhlchJTIENKTziF8j3K2Ja1nlEkFNLVVq6AmPT0dZWVl8Pf3r3a7uJ6cXPNKuuL22ux/s/V455138OST189yOHXqVBnZVV5EbxLd2KJneqPVHiX4OzKoCR54R9unZfza9pKlf0q5DOjon84e2y2zRwvRfYar0kTN2vaVM+9E3oy4dfNUqQORlm14/ym5DIrI33Xnq+b9Q9bsZj+JHpeBAweiefPmePPNN6+736RJk2RvTuUlMTHRqPU0N5sXfYHobWly+2DfYAydthxa137gY3LMkOtVYP+WxWpXxyQdq1hzSXzYBYQ0UaUO4tx+mq/yUZV28A9V6kCkVblZqWi4U/l+vNStMZxc3C0nqPHx8YGNjQ1SUlKq3S6uBwQE1PgYcXtt9r+RvLw8DBgwAG5ubli6dCns7K6fst3BwUGenrr2QteX8/1XsjzR1A7DvlhnEU3l6lEPSb7K2kLntihrG1F1V04clGWmj7KyuVry/JxlaXWBP06I9GnVe6Nlb2yWK3DHa+afYb1WQY29vT1iY2OxceNfi8uJgcLieqdOnWp8jLj92v2F9evXX3f/G/XQiGnfog7Lly+X08NJPzb89AGani2TU5z9n3rBopo1J0D5siw/c1rtqpgk2ySl967Qr2JdCZVYhYTI0jWtQNV6EGktdUfQNuWzL6FTMNy9/GDuaj1nS0znHjlyJNq2bYv27dvj008/lTOQRo0aJe8fMWIEgoKC5JgWYdy4cejRowemT58uTxstWLAAe/fuxddff10tD01CQoKcti3Ex8fLUvTmiEtlQFNQUICff/652sBfX19f2XtEdVf4y0+yPNHMAfcOVN5Hi9EoFDhwFB7J+WrXxCS5pxXJ0i4sXNV6+LXpCSw9Br80nRz/ZK7TTYlMyW/vP46oHCDPCejzqtJbb+5qPaZGTNEW+WImT54sp12LRHkiZ0zlYGARnCQlJVXt37lzZ8ybN08GMSKnzeLFi7Fs2TK0bNmyah/R89K6dWsZ9AjDhg2T1yunfIt8OLt27cLhw4fRuHFjBAYGVl04VubWrP1mipyuW2oNNBzzzyn5Wtegi/J/LiBFJ3+10F+KCgvgl6FkfGjQXt3som37PST/j7oUAYd3rlS1LkRayUfmu1lJaHmmnZ/M3q0Ftc5TY66Yp6Zmq/q2QFhiOY5GOeK+RfthiX/Yh9rGwLkYSHt3DLrfN1btKpmMXWt+hPv4qTKjdLM9++DgpJyqU8vGbs3koqonHu2Guyf+1dNLRLX3v/ceRfOfdqHAAQhY9j8EhTU32WY0WJ4a0pYVM1+SAY2YAdR0/NuwRCIfQ4q/8meQtGu92tUxKRd3b5BlqreV6gGNkO2r5M4oOs0EfES3oqy0FO5rd8ntU228TDqgqS0GNRb8n9p2ibIG14koF7TqcicsVV6gmyytz3NmzbVKzp2RZa6PPUxBcX0fWTomM1ki0a1Y8dkLaJAKFNkB7V/+VFONyaDGgv9TN7ysQ7Et0Orlj2DJbJtEyNIrpVDtqpgUp1RlwdjS+qYxI8ItIlqW9dKZKJHoVjisUmYkx7dyRaPm6mQKNxQGNRbaS+O8XPlPfSLaDZGxvWHJmtz2gCwD0oCstEtqV8dk1Esvk6VrpBJMqK35bUNl6ZsNJF04oXZ1iMzSqtmvouElnRx20Gq8MktZSxjUWKBfP34aDVJ0uGoHtHnlE1i6Fu37I8dZScO/+zfzTz6lD8kJp+CjdNSgea/7YQrEL0qRIEw4tH6+2tUhMkvlS5VEo/EtnNCsnbqzGg2BQY0FzvbxWKWsSB3fxhNNorvA0omcJ6n+Sq6jrANcrVs4uEEJGrJdlWDCVKT7VrxPR/eoXRUis7Pxl48QfqEcZVZA42degxYxqLEwv74/Wk6LLbAHOr86S+3qmIyCIC9Z2ifUfaFVLck+uluW6T6m9RFR4K8M6ra9+FcuLCK6OXnzlUSr8ZH2aN3rXk02m2l9YpHBk6l5r9snt0+180FIRBu2eAWnZjGy9E4pZpuID4aKoKHAr+J8j4mwDQ2vlumYiG7OH79+jYjTpSgHUH/085ptNgY1FuTXdx9FQCaQ7wh0e10bKbH1Jer2R2TplwUknjkCS+eWrswEswpuCFMS3LGfLP3SdTJIJ6Kbk/q90jN/qrEtOg0ardlmY1BjIfLzchCwUUmJfaqjv6aSLemDGDeSXrFm44GV38HSZ8f5pimJxgNad4cpielxn8yt4VAK7Pt9odrVITILezcuQES80gvt/uBIaBmDGgux4p2RcipsrjNw2xuc4VOT9AA7WeYfjYMlE2sriWUjxFpLbfo+CFMiMhuneFvJ7ct7lIzHRHRj52d/CGsdcDrUGr0ffEnTzcWgxgLkZqWiwWZl5fOznYPgF6Tuisum6mqwkmTO6WIGLNm5natlmVYPcPWoB1OT6+coy9JzZ9WuCpHJO/LnakQcvSq37e69B1rHoMYCrHr7UdTLBbJdgAFT5qpdHZPl2aqDLH1TLDtj7dWKtZWyTWR5hL8raxAoS5cUrqpO9G+OfT4ZtuXA+SArDHjiHc03GIMajRMZchtuOye3L3QLhZdvkNpVMlnt7nwc5VaA1xXguAWf2nBMyZJlcaA3TJFXi3ay9EkX8ziI6HpOHdyOpoeuyO2SO/taREMxqNG4tW89Cs8rQKY7cAd7aW7IJzAMKRXf48c3LICl8kwrkaVT4xYwRdF9H5LTUsX/6zOHd6hdHSKTtW/GS3JQ/UV/KwwcOx2WgEGNhqUnnUPYjoty+2KPpnD3Mo2FCU1Zpr+DLItPHoMlys5IktPahcZdTXPl9oCQJsjwVLaPbVqsdnWITFLimSNosl9Z0T6vfyeZOd0SMKjRsPVvPQb3AsipyoMm/6h2dcxCWWgDWbpeqlj4yMLErZsnZ0lccYRJL3Sa6at8QOfHH1S7KkQmafsHz8pZjMnewJ0vfQlLwaBGo8Qqxo3/VFL+J/VpCRe3iiQsdEO+bXvJMiC1XOZrsTRpB5W1r9J8rE36l93VgIplLS6nq10VIpOTeukMGu1Nk9tpvaNhZ6/0QFsCBjUateWdJ+B6FUipBwx+nTOeblaHQY+j2AZwuQrE/b4IFidROV15xdcJpsyhcTNZeqZxWQuiv9s49Sm4FQJpnsCdE7+2qAZiUKNBCfFxaLJb+QWb3q+NTFhGN0f0aCX7Kcndzm371eKazTUtX5a6YOU0nKkK73aXLH0zlTxMRKQQfw+hOy/J7aRuTeHk4m5RTcOgRoN2TB0jz6Um+QCDX7XslP91kRNQEQSePQNLUzlN2juqI0xZi/b95RpmIv/GvrU/q10dIpOx+t3H4JkPZLkBA1//HpaGQY3GiCmuEfuUEe/Zd3S2qHOpetMoTBbuSUqvhaWIP7BVDiwXYU2bfg/BlInxPqk+ysdX6oE/1K4OkUkozM9F/T+UH2MJnUJMMiO4oTGo0Zi9H46HY4mSl2DwK1yJuy5Cug6SZUCqTn5IWIqTW5bIMt0LqOcfDFN3xV/pUbNKTFS7KkQm4bf3R8MnR1njr99r38ASMajRkBP7fkfkgTy5XXBXL5OevWLKYm8bhgJ7ZSXoXassZ5B1/kllFfcsb/P4f6MLVgIv15QCtatCpLqS4iL4bjoit8+18zeLHyaGwKBGQw5NewX2pUBCoBUGjftM7eqYLXHKLjlA+dNI2bUelsIuSVnI82pARWY7E+cX01Up0y1z+j3RtZZ/+CQCMoECB6DbRMvJS/N3DGo04tD23xB5SBkDUnLvHeyluUV5gcqMAZsLlnNqwyOtSJb2jZrCHMT2fxil1sr0+6O716pdHSLViKDeY/1uuX2qTT0EhTW32HeDQY1GxH86BXZlwLkG1hg0dpra1TF7dk0jZOmZfBWWQIwd8stUtht2GABzIJb9SKsYB3lm23K1q0OkmhWfjUNQKlBkB7R/+ROLficY1GjAvo2LEHm0UG5bD71H7epoQsRtQ2UZkA5kpmi/t2b/xoUyKC60B1pV5IAxB1m+9rIsOn1c7aoQqdZL47Byk9yOb+WGRs3bW/Q7waBGA87Pek/m6zjT0BoDnnhH7epoQrO2fZHjAtjogD0rvoXWXdqnfCimeVuZVRqAkvo+snRMqliFk8jCrJnzBhpe1qHEBmg1/n1YOgY1Zu7P1XMReVwZC+H4kGnnFjEnMg+Kv43czjqwA1pXdv6cLHN9HWFOXCKiZVkvnQOFyTLpliqnXuNbOqFZuz6wdAxqzNzl2dPlqsonG9mgz4hX1a6OphQEKQM27BNToHXOqUoqgLL6/jAnzXvdJ0vvbCA54ZTa1SEyqg0/fYDwhHKUWQGNn36Nrc+gxrxtW/ofRMSXyG2PUU+pXR3NcW4eI0vvFO0vmuidXiZLj+ZtYE7Cozoj21X5dXZw/S9qV4fIqPIXKEuExDdzQOte97L1GdSYt4xvv5Qf5vFNbNHz/ufUro7mxNzxqCz9soCEUwehVeK11VM6atDytuEwN+kVyyVkHd2jdlWIjGbbklloeqZMLmsSOHocW/5WTj/NmjULoaGhcHR0RIcOHbB7tzI//noWLVqEyMhIuX9UVBRWrVpV7f4lS5agX79+8Pb2hpWVFQ4cOPCPY3z99dfo2bMn3N3d5T7Z2cr6Rpbq9/nTEXG6VP6H9nviebWro0khEW2QVpGH7uAq7S4Md3TTf2WZ6Q4Eh7eEucn3r8gpdDFJ7aoQGU3aXGUZnFNNbNF54Ci2fF2DmoULF2LChAmYMmUK4uLiEB0djf79+yM1NbXG/Xfs2IHhw4dj9OjR2L9/P4YMGSIvR44o6ZyF/Px8dO3aFR9++OF1n7egoAADBgzAq69y3Ihw5UflSzY+0h6d73qitm8j3aQMfzulvY/GabbNco4pry3DWxkYbW5swxrJ0j3VMnIKEe1ZNx8RJyuGHjzEgOaWgpoZM2bgiSeewKhRo9C8eXPMnj0bzs7O+O6772rc/7PPPpPByMsvv4xmzZrhnXfeQZs2bTBz5syqfR555BFMnjwZffpcf+T2+PHjMXHiRHTs2BGWbt0P76DJuTI5OKzBsy+rXR1NKwpWBs46X6rITKdBNpeUgdAF/m4wR/UrZnz4Z+hQVMh1oEj7Lnz9kZwgcjrMBr2GTVC7OuYb1BQXF2Pfvn3Vgg9ra2t5fefOnTU+Rtz+92BF9Oxcb399KSoqQm5ubrWLVpTMWyDLE80d0L7fw2pXR9M8o5Ug2i9FGUirRe7pSg+HbajS42FuYnsPRZEt4FACHNiyWO3qEBnUoR0rEXFM+Zu1v0+Z/Ud1DGrS09NRVlYGf//q0z7F9eTk5BofI26vzf76MnXqVHh4eFRdgitW9DV3q2a/ikYJ5XLNm/Dnp6hdHc1rO+gx2SPmeQU4umsdtLiyr1+6Tm4Hte0Nc+Tg5IxUHyu5nfin9t4jomud+GKKTLYqlsTpP/pNNo6l5KmZNGkScnJyqi6JiYmaSIdttWiZ3D4R5YTWPe5Wu0qa5xMYhhQlaS3iNy6E1hzcthSOJUCxDRDT636Yq5yKpIGl58+oXRUigzl1cDuaHlYWLi67qz9b+laDGh8fH9jY2CAlpXoyMnE9ICCgxseI22uzv744ODjImVLXXszdqlkvIfSSTn4BNZ/wgdrVsRhZ/soXZvHJY9CaCxU9G2negJOL+f6NlDVQPk9cUirmphNp0L4ZL8GhFEj0t8Idz36kdnXMP6ixt7dHbGwsNm7cWHVbeXm5vN6pU6caHyNuv3Z/Yf369dfdn67fS2O/VPkCio92RYsO/dhURlIa2kCWbpe1My6rUslZJQtvjo/5rPdUE68W7WTpnabdsU9k2UQ+qab7lVQmVwZ0lku5kB5OP4np3HPmzMHcuXNx/PhxPPPMM3JKtpgNJYwYMUKe+qk0btw4rFmzBtOnT8eJEyfw5ptvYu/evRg7dmzVPpmZmTI3zbFjyi/h+Ph4ef3acTdiW9x2+vRpef3w4cPyunisJfjtk7EISdbJpeWjX/5Y7epYFP+2vZQypVyOQdESxxTlQ7K4YmFIcxVdMWDe6wpw9tiN82YRmaMdH46FUzGQ5APc+eIstaujnaBm6NChmDZtmpyCHRMTIwMLEbRUDgZOSEhAUtJfSbA6d+6MefPmyeR5IqfN4sWLsWzZMrRs+VeSr+XLl6N169YYOHCgvD5s2DB5XUwXryS2xW1iOrnQvXt3eV081hJ6aVx/2yK341u7I6J1T7WrZFHaDxyNYlvApQiI+11b42q8MpSFIF2btoI5CwhpUpUo8ZgGxz6RZUu9dAbhe9PldkbvGNjZm3fPqiFZ6XQ6ZeqDxokp3WIWlBg0bG7ja/733qNo/tMuFNoDngvmolHz9mpXyeKs7dUcIUk6HLmvFe5/VxtfmulJ55DS6w75y8Z24TdoEt0F5mzZoCiZZftAnyAMn7lB7eoQ6c2CMbcheuNlGbh32LRPzvizJLm1+P7W7OwnrRDJxOqt2iW3T8bWY0CjkpwA5UNEd/YstOLA+vnyAyDHGWYf0AhXA5SuGvvLyi9aIi3IzkhC6J+X5XZS9wiLC2hqi0GNiVs+dTQCMoB8B6DL68paH2R8VuHhsvRIUqZTakHGYSVYzqhYENLcOTRuJkvPNG2NeyLLtua9x+GRD2S6AQNfqzlzP/1FG59mGlWYnwu/9crinqc6+JrlYoNaEdJVGe8VkKZDfl4OtMDq4iVZXvF1gRaEd7tTln4ZwJUcy5hAQNomPmsa/KH0Did0bghXj3pqV8nkMagxYcvfeRR+WUCeE9Dr9W/Vro5Fa9N7KAocAPtSYI9GVux2TVPWSbIK0Ua27RYdbpc9miLb6t51v6hdHaJbtvL9x+CdC+Q6AwP4HXBTGNSYcIRef9NxuX22U6Cc3UHqEbMNkv2VP5fkPdXzLpnrjDrfiuURfDUwnkYQeTtSfZXlElLjNqtdHaJbHk/pt0VJc3K2fQC8fIPYojeBQY2J+u2th+GTowzi7DdlrtrVIQB5gcqoe9vzF82+PU7s+x2uVyHXtWrddzi04oqfcipNl5CgdlWIbsmKj5+Gf6YynrLnpP+wNW8SgxoTHe0eskVJMni+awjq+Wvj9IC5s2uqDET1SlFWyDVnp//4VZZp9QBP70BohS6kIvtzqnJqjchce1I9NuyR26dj6yGwYaTaVTIbDGpM0Oq3R8ErD8hyAwZM+UHt6lCFyD7DZOmfDmSmmPcCqQWnlG7tbB87aIlvdFelTCuXXwxE5ui3T59HUCpw1Q7o+PJnalfHrDCoMTHiyzLsjwtyO7F7uKZ+RZs7sd5WtgtgowP2/PYNzJlDsjI76Kq/F7SkTb8HUWoNeWrt+N71aleHqNZEMO64ShkTdjLaHaHN2rIVa4FBjYlZ99ajMidBhjswcPKPaleH/iY1wEaWWQd2mHXbeKYXy9KxIreLVogfAeKUmnBqq3KKjcicrPn6NTS8rEOxDRD9wlS1q2N2GNSYkOSEU2i0U8kceal3JHMSmKCCIOUb0z4xBeYqNysVvhVpXMK7KPl3tCTbx16WV08rp9iIzMqyFbI42dIJkbG91a6N2WFQY0I2vTsaboVAqhdw1xuc8WSKXJq3lqVPSgnMVdyGhTKXi8i7I3K7aE3liuOOScoK5ETmYsOP76NRQrmcldj42TfUro5ZYlBjIhLPHEGTXWlyO6VPNJxczGvRTUsRc/tIWfpmAwnxcTBHqQe2KaWPlcztojUuEVGyrJduvoEnWab8BfNkGd/MAa173K12dcwSgxoTsf29p+BSBCR7A4Nf5foepiokoo1cKVc4sNo8e9N0CcpA9DxfJ2hRZM/7ZemTpaxETmQOti2ZhaZny1AOIOiJF9SujtliUGMCzh/fi6Z7lUEOmQPacxVWE5ceoIzZKDi6H+bIJfWKLMsb1IcWiRXHxSw18eEWt/ZntatDdFPS5yoLFp9sYoeOFT3CVHsMakzArqlj4VQMXPIF7vq/r9WuDv2L4mB/WTpdMs9FE73TxW9BoF7L9tCqdF/loy3z0J9qV4XoX+1e9zOanlROl3o9/Bhb7BYwqFFZ/IGtiNivrPqcd2cPucYQmTav6E6y9E8pM7sEb2cO74BnvrLdqreSTFCL8v2VMWk2l5LUrgrRv0r4ahqsdcCpMBv0HDqeLXYLGNSo7ODHL8KhBEgIsMJdE2aqXR26Ce3ufFzOThD5hMwtwdvxLUtkme4BTS+SahMaJkv3VPNf0oK07dCOlYg4XiS3He5/QO3qmD0GNSo6umsdIg4o4xuKhvTV5EwULRJrcaUos4YRv3ERzMmV+EOyzPTR9v+1Bu1uk6Vfug4lxcoXBpEpOvbVuzLFwrkG1uj/2GS1q2P2GNSo6NiMSbAvA84HWWHg2OlqVoVqKcvfUZYlJ4+bVdvZXk6VZWHF6RmtanPbcBTZAo4lwP7N5hV4kmUtXtzokJJP6WrvjmpXRxMY1KjkwLZfEXlYWUm4/L7B7KUxM2Whysrpbkm5MCceFcsj2IU1hpY5ODkj1dtKbif8uU7t6hDVaN2McTLhqli8+PZxn7CV9IBBjUpOf/am7HI8G2KNgc9wfQ9z499OSV8ekFJuNqc3igoL4Jehk9vBHfpC63J9lUH3pedOq10Vohp57Dgiy4QYXyZc1RMGNSrYs24+Io8qAxjtHtTuDBQta3fHKHl6w7kI2LdxAcyBOA1jXwoU2QHR3e6B1pU2CJClc7J59aaRZdi0YAZCknRyVfnWz76tdnU0g0GNChL/8wFsdMDpMBv0e5Tre5gjFzcPJPtVnN74YyXMwcU9G2WZWs/KIhI8erZoK0uf9DK1q0L0DxmLf5Ll6SZ2iGjdky2kJwxqjGzH8jmIOK6Ma3B55FFjPz3pUW6Ai7Jx9qxZtGvpuTPVTstoXXS/h2TplWe+63SRdtf6a3xC6a13HHin2tXRFAY1RpYy5wvZ6PGNbdH7wZeM/fSkT+HhsvBIVgZ8mzqnFCXJY2l9P1iCwIaRMh+PcGjDfLWrQ1Rl+6cT4FAKJPkA/R57iy2jRwxqjGjzoi8QeapELljm/djTxnxqMoDQboNkGZCqQ36eEjCYMu+K0zBukTGwFBm+Sj6eK8cPqF0VIklMLAjcmyi3U9s34sxXPWNQY0Q5P1QsWBZhh273jDHmU5MBxPYehnwHyFxDu1Z8Y9JtnHThBLwrxsu26KWsYm0JrgYoS6rbXU5TuypE0prZk+CXBRTaAz3Hf8pW0TMGNUay4acP0PRMGcqtgMCnXzTW05IBiQzQyf7Kn1Da3k0m3daHNigztLJcgdBmygBaS2AfHiFLzzTzmHZP2le2Tlla5XRzZ00vVaIWBjVGUviLMtL9RDMHLiuvIVfqVyyceOESTFnW0T2yzPCxrD/5sM4DZemXAVzJMc9V1Ulb6zw1OaMsgtvgQQ5BMATL+oRTydpvpqDx+XKZjyB0zGtqV4f0yD6ihSzrJZv2womVq1UX+LnBkrTqcicKHCATXcatn6d2dcjCHZvzvlyNW6zz1PmuJ9SujiYxqDGCsoWLZRnfwhGxt1nOeAZL0KyPkjzRPwNITzoHU+WWpgRd1iENYWmnCFN9lHxCyXGb1a4OWTDRUxh6UOktLOgeq3Z1NItBjYGtmPkSwhLLUWIDNB3PrJFa06xdH2S7Qv762rviO5iistJSuVq1ENCmOyxNnp+SaFB3IUHtqpAFW/PJc/AoALJdgNtf+ELt6mhWnYKaWbNmITQ0FI6OjujQoQN27959w/0XLVqEyMhIuX9UVBRWrVpV7f4lS5agX79+8Pb2hpWVFQ4c+Of0y6tXr2LMmDFyH1dXV9x7771ISUmBKRNfJrZLlNd6IspFdoWT9qT6K9OGsw7uhCk6tP03OBVDScd+23BYnBBl8VHXtHy1a0IWzGXbflleiPGWGcnJRIKahQsXYsKECZgyZQri4uIQHR2N/v37IzU1tcb9d+zYgeHDh2P06NHYv38/hgwZIi9HjigLeQn5+fno2rUrPvzww+s+7wsvvIDffvtNBkhbtmzB5cuXcc89pr1+zYrPXkDDyzoU2wKtXv5I7eqQgRQE1ZOlY2LNfwNqO//nGlmmegOuHkpdLYlPdBdZ+qaVyx8aRMa2bckshF7SocwKiHpyMt8AUwpqZsyYgSeeeAKjRo1C8+bNMXv2bDg7O+O772ruev/ss88wYMAAvPzyy2jWrBneeecdtGnTBjNnzqza55FHHsHkyZPRp0+fGo+Rk5ODb7/9Vj537969ERsbi++//14GTH/++SdMkfjwdF6urLVzIsYNkbHKqs6kPa4tlfPjPsklMEVXzxyXZY6PPSxRm/4PyS8Tt0LgxL7f1a4OWaDkhd/K8nRjW7To0E/t6mharYKa4uJi7Nu3r1rwYW1tLa/v3Flz17u4/e/BiujZud7+NRHPWVJSUu044nRWSEjIdY9TVFSE3Nzcahdj+vXjp9EgRYerdkDb/2OCJS2LGfiYLH1ygPPH98LUOCZny7I40BuWyNM7EGkVHVSnti1TuzpkYUTiy/DjhXLbdsAAtaujebUKatLT01FWVgZ/f/9qt4vrycnJNT5G3F6b/a93DHt7e3h6et70caZOnQoPD4+qS3Cwcl7dWGmwPVZtl9vxsZ4Ij+pstOcm4wsOb4lUL2X70JofTe4t8EpXepCcm7SEpcryVXqpCk8eVbsqZGG2fPKCHNOWXA+4/ampaldH8zQ7+2nSpEnytFXlJTFRWWvDGH794AnUTwMK7IHOk2YZ7XlJPRn+ypdmwVFlMKCpyEq7BN8sZbtJ17tgqYrrK71UjskVjUFkpGEI/nvOy+2U9g25zpOpBTU+Pj6wsbH5x6wjcT0gIKDGx4jba7P/9Y4hTn1lZ2ff9HEcHBzg7u5e7WIMRYUF8F6jZG891c4HIRFtjPK8pK7iYKU30vmyaX1p7l8/X043z3MCmrbuCUvl3DRKlvXSTHPcE2nTmq9fQ0AG5DCEbuNmqF0di1CroEacAhKDdDduVAbACuXl5fJ6p06danyMuP3a/YX169dfd/+aiOe0s7Ordpz4+HgkJCTU6jjG8Ou7jyIgE7jiCHR7XVnAkrTPK0Y5xeiXXGZSM2zSDimnQdN9rC36V2JEz3tl6ZNl2kkSSVuKV6+W5elmTggKa652dSxCrU8/iencc+bMwdy5c3H8+HE888wzckq2mA0ljBgxQp76qTRu3DisWbMG06dPx4kTJ/Dmm29i7969GDt2bNU+mZmZMjfNsWPHqgIWcb1yvIwYEyOmhIvn3rRpkxw4LJ5PBDQdO3aEqcjPy0HAxsNy+3RHf/4ntiDt73pCzrARybWO7l4LU2GVeFGWV3yVBHSWKiKmO3JclA+8uLW/qF0dsgDH92xA4zNKz6D/A8pkAjLBoGbo0KGYNm2anIIdExMjgw8RtFQOBha9J0lJyjozQufOnTFv3jx8/fXXMqfN4sWLsWzZMrRs+degxeXLl6N169YYOFBZfG7YsGHyupguXumTTz7BoEGDZNK97t27y9NOImmfKVnxzkj4ZgO5zsBtbyhT+MgyePkGIdlH2T61aRFMhUtagbIR3ACWTvRWCVmHTTMNBGnLwa/ekmuOXQiyQvf7/voRT4ZVp/5o0ctybU/LtTZv/uf6Kvfff7+8XM+jjz4qLzcishGLTMbiYopys1LRYHO83D7XuQE6BIWrXSUysqwAJwSlFaI0/oRJtL04DSYSzgnerUzrNK0a8v3dgAs5sL54We2qkMaJXvuGB9Lldl6XaLWrY1E0O/vJ2Fa9/Sjq5UKuA9R/yg9qV4dUUB5akY4/Kc8k2v/04T9kwrlyK6B1HwtcHuFvrEPDqi3uSWQoaz59Hp5XlF77/i98xoY2IgY1epo223CbMvjwQrcweSqCLI9/eyU5ZEBKucxVpLb4LUtlme4J1PM3Xp4mUxXUVsnq7Z+mM4n3h7TLcauShPNctBfcvfzUro5FYVCjB2vfHiWj8kx34I7J7KWxVB3uGIkiW8C5GNizfp7a1UHBSWV9tSwfy531dK3Wtw2V67A5lgAHNpvWeDzSjp0rvkWjxHLZQ9r88b8mzZBxMKi5RWJ6aNh2JbHfxR5NGZVbMCcXdyT7Wcntizuqr0SvBrsk5Zz+Vf/qmbgt+f1J9Vben4RdyiKfRPqW+Mt/ZHm6kQ1adbmTDWxkDGpu0Y4Fn8D5KpDmCQyabHop8sm4cgNdlI0z6udC8UwvlqV9eITaVTEZOb4Osiw5e1rtqpAGpV46g/Cj+XLbul/NCzSTYTGouUV3vfA5ir94G4WPPwAXNw/9vCtktqzCG8vSI7liKrWKsy98M5XtsI63q1oXU1LaoCLzc0qO2lUhDdo0Y5w8/SzWghvwzIdqV8ciMajRg9jb7kf/x9/Sx6HIzIVWrK8UkKbDlZyKqEIF+39fCLsyoNAeaNllkGr1MDUezWNl6Z1WpnZVSGNECgWf3WfkdlJsA9jZK72CZFwMaoj0qE3v+5HvCNiXAbtXfqda2ybt2yTLVB8rfrheo1Xfh2RZLw9IiI9T580hTdrwwztyIWMxWaDzuGlqV8diMagh0iOxvlKyv/JnlbpXCSzUUHZBWRk4z9dRtTqYIrH+TnrFWeLDGxeqXR3SkPwVy2R5OtIRIU2YcE8tDGqI9OxKfeVb0/bCJdXa1iVVSQBYVr/mVewtWWbFFPe84/vVrgppRPyBrWhyUhmYX+/eh9WujkVjUEOkZw4Ryrpm9VLUS/Dmna6MGfGsGENCfykMUKa4211OZbOQXsR9+YZc5ykhwAq9h7/IVlURgxoiPWvWd5gs/TOUKZ7GlnDqILwqVmqI4vII/2Af3lSWHmnMKky3rqiwACH7lQA5p0sLNqnKGNQQ6VlkbG9kuQHWOmDvb8Zfrf1IxViRDHdlDAlVF9bpDln6ZShT34luxcpPn5cDz/OcgH4TPmdjqoxBDZEBpPor4zZyD+8yevvmnlBm9WT62Bj9uc1Bq26DUWAPOeU9bv3PaleHzJz95p2yPBflDk/vQLWrY/EY1BAZwNUgb1k6XEwzevvaXkqRZYG/u9Gf21xmqKX6KsslJO3bonZ1yIztXvczwi+UoxxA01GvqF0dYk8NkWG4tlQG6Poklxi9id0qxorYNmxk9Oc2F3m+zrLUVUx9J6qLc3M/k+WZMBu07nUvG9EEsKeGyACi7xglS58c4Oyx3UZr45LiIvhn6OR2UNteRntec6MLaSBL11RlnR6i2spMSUT4kStyu/y27mxAE8GghsgAgsNbyvVfhMOr5xqtjQ9sXgKHEqDYBojpdb/Rntfc+ER3lqVvWrlMb09UWxtmPA+XIshkjgOf/4QNaCIY1BAZSEaAvSwLjx8yWhsn7Fkry1RvwMmFY2qup02/h1BuBbgVAif3bzba+0PaIAJhr50n5Pal2EAuRWJCGNQQGUhxsJLN1/lSltHauOTsaVnm+nIxvRvx8g1Caj1l++TWpcZ4a0hDNv78ARqkKj2i7cd+oHZ16BoMaogMpF6brrL0Tykz2ikOxxQl70pJoK9Rns+cZfnYybLw5FG1q0JmJm/5YlmejnBAo+bt1a4OXYNBDZGBtL/zcZRaA+4FwNFdq43SzvXSleDJNaKVUZ7PnBXX95GlQ3Km2lUhMyIG/jeOV2YYegx5QO3q0N8wqCEyEJGIK0X53sSp35VfdoYklmTwzla2m/Xk9NJ/49xUWaPLK8340+7JfO3+YiLsy4CL/lbo9SBz05gaBjVEBpQV4CTL0lPKoEJDOrB+vvyDznEBwqOU2T10fRE975Glb5YyPZfoZtZ5CopLkttZHSNkIkcyLQxqiAyoPDRElm5JSj4LQ8o6ouTDSffmn/XNiGjdEznOyhpdcWt/MvC7Q1qwetZLMvdUviPQh+s8mSR++hEZUGD7PrIMSCmXifEMyeriZVnm+7kY9Hm0JN1X+QjMOPSn2lUhM2Czcassz7RwQz3/YLWrQzVgUENkQO1uH4EiO8CpGNi7zrCLJ7qlFcjSKkTpHaJ/l+/nKkvrxEtsLrqhfRsXodG5MrkdNvJ5tpaJYlBDZEAiAV6yn7J4YuIOw82AElPGfSuWR/CLVqaS07+zCg2TpVtaIZuLbuj03GnyC/NMQ2u07/cwW8tEMaghMrCcAKU3AGfPGew5ju9dD5erQJmVyJb7oMGeR2vqt+0tS790ncFPD5L5ys5IQtjhXLld0quL2tWhG2BQQ2Rg1o0by9Iz2XC9Aaf/+E2WafUAdy8/gz2P1sT2GSazworTgwe3MbMw1Wzd9OfkkhqZ7sAd4z5lM5kwBjVEBhbW/S5ZBqTpcCXHMIneCk8fq5Yll27+9GCqj3J68MKfa9hsVCOPHcrfV0KMHxycnNlKJoxBDZGBte5xH644AnZlwK4V3xjkORySlGCpOKBiQSO6aTk+ysKjJadPsdXoH36fNw0hyTqZHbztmPfZQiaOQQ2RgYkEXSn+yp9a2r4tBnkOr3QlK65j40iDHF/LShooC486VaybRXStzP8psxZPNbVHk2iOp9FkUDNr1iyEhobC0dERHTp0wO7dStKv61m0aBEiIyPl/lFRUVi1alW1+3U6HSZPnozAwEA4OTmhT58+OHWq+q+muLg49O3bF56envD29saTTz6JK1cMn9CMSB+u1PeUpd0F/U8dzs1KhW/FWa1GXe7U+/G1zqNZG1l6pyvTdYkqJZw6iCYV6zy5DBrChtFiULNw4UJMmDABU6ZMkYFGdHQ0+vfvj9TU1Br337FjB4YPH47Ro0dj//79GDJkiLwcOXKkap+PPvoIn3/+OWbPno1du3bBxcVFHvPq1avy/suXL8tAp3HjxvL+NWvW4OjRo3j00Udv5bUTGY1DpLLOUL1k/c+wiVs3DzY6IN8BaNG+v96Pr3VRfZXZYt65ypcYUaUdn70E+1Lgsi/Q59E32DDmQFdL7du3140ZM6bqellZma5+/fq6qVOn1rj/Aw88oBs4cGC12zp06KB76qmn5HZ5ebkuICBA9/HHH1fdn52drXNwcNDNnz9fXv/qq690fn5+8rkqHTp0SCTl0J06deqm6p2TkyP3FyWRsZ2I26Q7FhGpOxIRqUu6cFKvx1746n3y2Kt6N9PrcS3JtnaRsg1XfDlR7aqQiSguuqrb0kH5fzH/xUFqV8ei5dTi+7tWPTXFxcXYt2+f7DWpZG1tLa/v3LmzxseI26/dXxC9MJX7nzt3DsnJydX28fDwkKe1KvcpKiqCvb29fK5K4jSV8Mcff9T4vOIxubm51S5Eaq4zlOmmdI3uW/mdXo+tu5AgyzxfzsqoqwxfG6UNj8fp7X0h87b6y1fgmw0U2AO9X+A0bnNRq6AmPT0dZWVl8Pf3r3a7uC4Ck5qI22+0f2V5o3169+4ttz/++GMZWGVlZWHixInyvqQkZcXUv5s6daoMjiovwcFcp4PUleavrOibd/jGY9BqyyVNGVuma1Bfr8e1JIX+HrK0vZSidlXIROjWb5TlmRYu8AsKV7s6pKXZTy1atMDcuXMxffp0ODs7IyAgAGFhYTLwubb35lqTJk1CTk5O1SUxMdHo9Sa6VmEDb1k6XEzTa8P4pJfL0qtlOzZ4HdmFR8jSI41ZhQk4tP03ND6rDBxv8PAYNolWgxofHx/Y2NggJaX6rxlxXQQaNRG332j/yvLfjvnggw/K3ppLly4hIyMDb775JtLS0tCoUaMan9fBwQHu7u7VLkRqcmvZVpa+ycr0a304dXA7PPKV7ZiKAa9Ue6Edb5elfwaQn8ep3Zbu2Jz3Ya0DzgZbo/PAUWpXhwwV1IhxLbGxsdi4UemWE8rLy+X1Tp061fgYcfu1+wvr16+v2l/0uIjg5dp9xPgXMcuppmOK3hlXV1c5C0tMERfTvInMQeuBj1XNsjlzeIdejhm/dYks0zzBLvJb0KrbXXLshEiQGLdhnl7eGzJPIkVC2KFsuX21J3s/NX/6SUznnjNnjjwddPz4cTzzzDPIz8/HqFFKNDtixAh56qfSuHHj5BRsceroxIkTsodl7969GDt2rLzfysoK48ePx7vvvovly5fj8OHD8hj169eXU78rzZw5U04hP3nypMyTIx4vxs2IvDVE5iAorDlSKhL+Hl6rJPS6VVfiD8ky00cZr0N1Y2fvgDRfZbmE5H2b2YwWbO0n4+BeAGS7AneM/1zt6lAt1fqTcOjQofK0j0iWJ04HxcTEyKClcqBvQkJCtXEunTt3xrx58/D666/j1VdfRZMmTbBs2TK0bKnk7RBeeeUVGRiJhHrZ2dno2rWrPKboiakkEvyJ3Dgi4Z5I5PfVV1/hkUceqW31iVSV4W8P/8xiXD1+WC/Hs01SxudcrRjoSnWX6+sEXCpA+fnzbEYL5vaHkqvoQowPOrlw2IK5sRLzumEBxCktMQtKDBrm+BpSy/xxAxCz9gJOhdngrtV/JaCsq/U9mqNBig7HHumAe1/7QS91tFQLXx6MVr+dxJkQawxad1Tt6pAKNi/6Av5vfCnXebL7aRYiY3vzfTCz72+zmP1EpBXerbvK0j+lDGWlpbd0rML8XPhlKL9JQtoxk/AtvzetlDF8vunlt/zekHlKW/S9LE83tmNAY6YY1BAZUfs7R8tfgeKc/eGdK2/pWPs3/0+mcC+yA2J63qO3Olqq2AGPoNxKeW9OHdyqdnXIyC6dO4bGxwvltv3tA9n+ZopBDZEReXoHItlH2T696X+3dKzLe5QZg6neVnKgK90aL98gpHop2/Gbl7I5LczWTyfAsQRI9gYGPPGO2tWhOmJQQ2Rk2YHKEh9lp+Jv6TilF87KMteHAY2+ZPvaybLg1K2PdyLzIU43Bu65ILdT2ofBxpazCc0VgxoiI9OFNpSlW5KyvEFdOaco65mVBFVfYoTq7mqgMufeMSmDzWhBVs+eCP9MoNAe6DF+htrVoVvAoIbIyAI79pNlQGo5igoL6nyceulKGnf3yNZ6q5ulc24SJUvPNP1lfSbTV7pmrSzPNHNCYMNItatDt4BBDZGRtR8wElftAKdiYN/6X+o8qFFkJhaiet+v3wpasIied8vSLwvISrukdnXICI7uWofGZ5TZbgHDnmCbmzkGNURG5uDkjGQ/JXvtxZ1r6nSMIxsXyjLLDQiJaKPX+lmyJtHdkesMue7PvjU/qV0dMoLDX78NGx1wPsgK3e5+hm1u5hjUEKkgN9BVllZn65a9NuvYXllm+NjotV6WTgwQTfNRPhYzDu1UuzpkYGLx0oYHlPFT+d14GlcLGNQQqcCmcRNZeiQX1u3xl5JkWeCrBEekP/l+FQFn4kU2q8at/uQ5eOYDOc7AgBe+ULs6pAcMaohUEN5DSZYXmKaTqwLXllvaVVlaNQzVe90snXWo0qbuaXULOMl8OG/dJ8vz0fXg6lGx2iyZNQY1RCpo1W0w8pwA23Jg94rvavXYkuIi+KUryyMEtulhoBparoDYnrL0S9PJtiZt+uPXrxF2sRxlVkDLp15XuzqkJwxqiFQau5Hir/z5pcfVLiX/ke0r5MwpsdxCmz4PGqiGlku0aYmNMjvt0LblaleHDOTy/K9keTrcFi073s521ggGNUQqya/vKUu7C5dr9bjzu5ScGqnegIubh0HqZslEm6Z4K9vn/1ytdnXIAJITTqHxMSVHlG1/JW8UaQODGiKVOEQqid7qpdTuFEfRmROyzPaxN0i9CMjxVZaeKDl7ks2hQZs/HS974lLqAbc/86Ha1SE9YlBDpJLm/ZRTR34Zyi/Hm+WQnC3LksCKlTFJ70orlp5wqmhr0tY6T367lXXTkmODuc6TxjCoIVJJREx3ZLorf4T7Vnxz04/zylBS+Ds3bWnA2lk2t2ZKQkPvNGUpCtKOdd9NQWA6UGQHdOE6T5rDoIZIRWl+ymrAeUf23NT+mSmJ8M1Stpt2G2zIqlm0qD7DZCmWokg8wxW7teTqyt9keTrSEcHh/GGgNQxqiFR0NdhXlo6JaTe1//4N82UKfzEdXKT0J8MIaRKNDHdl+/D6eWxmjYjfvxmNTyk9nT73jVS7OmQADGqIVOTaMlaWPinKgnr/pjJ1v0jlL6aFk+FULkGRczyOzawR+7+cLHNDXahvhZ5Dx6tdHTIABjVEKoodNBrlFac5Th3c/u8PqEjdn+/nbPjKWbhCf2W6vN3FZLWrQnpQmJ+LkANKj2heZ2XmIWkPgxoiFQU2jERqRXb2o+v+fVVolzQlt4YuuIGhq2bx7CrX50ovtvi20IJVn46HV55y6rb/i1znSasY1BCpLDNAyYly9cSRf52K6psu+nUA31ZdjFI3S9aw4wBZiiUpxK98Mm+OW3bJ8mwrT7h7+aldHTIQBjVEKisJCZCly6WKaU3XcergVrgVAuVWQOu+w41UO8sV3e1uFNoD9mXAvg0L1K4O3YI/V89Fo4Ryeao38vGJbEsNY1BDpDKfNsosJv+Uctkbcz0nty6TZZoX4OUbZLT6WSo7ewek+ljJ7ct7f1e7OnQLEn6aKcszjWwQw1QImsaghkhl7e98XC5OKXphDm1XcmjUpOCUcnoqy9vOiLWzbHm+TrLUXTindlWojtKTziH86BW5rbutF9tR4xjUEKlMnN9P9lV6BM5s+t9197NPypBlUYCyECYZXnmw0iPmkqJ8KZL52ThjPJyLgDRP4I7npqldHTIwBjVEJiA7wFGWZaevvwZU5Swch/BIo9XL0nm36ihLnzRlgDaZF3E61/tPZVHSy7H15SlF0jYGNUQmoDysoSzdkvNqvD8/L0cufCmEdrrdmFWzaG36PyIHZnsUKNloybxs+PF9BKUBxbZA5+c/Vrs6ZAQMaohMQFBFoBKYokNRoZKL5lpxG+bJTKhiNk6rLneqUEPLVM8/WA7MFuI3L1G7OlRL+b8pp3NPRTggJEJZpJS0jUENkQlo1+9hXLUDHEuAPet+/sf9SXFbZClm43B5BOPK8lUGZhec5MKW5uTM4R1ofFI5Zet1z4NqV4eMhEENkQlwcHJGkr8yWPjSztX/uF934bws83yVsTdkPEUBSspn+8vpbHYzsnvWq7ArAxL9rXDbQ6+oXR0yEgY1RCYiL8BNltbnLvzjPudUZaxNWVCg0etl6ZyatpClV7qyujOZPnEKNzguRW5ndeLAektSp6Bm1qxZCA0NhaOjIzp06IDdu3ffcP9FixYhMjJS7h8VFYVVq1ZVu1+n02Hy5MkIDAyEk5MT+vTpg1Onqs8COXnyJAYPHgwfHx+4u7uja9eu2LRpU12qT2SSbCrWGvJMvvqP+7wrlkfwat7W6PWydE273y1L30wgK+2S2tWhm7DqiwlykdgrjkA/rvNkUWod1CxcuBATJkzAlClTEBcXh+joaPTv3x+pqak17r9jxw4MHz4co0ePxv79+zFkyBB5OXLkr/PTH330ET7//HPMnj0bu3btgouLizzm1at/fbgPGjQIpaWl+P3337Fv3z75vOK25GSuoEvaEN7rXlkGpOmQm/XX39P543vhVZEmpeVtQ9WqnsVq2rqnXATRRgfErftF7erQTbD9fZssz7Z0Z/ZtS6Orpfbt2+vGjBlTdb2srExXv3593dSpU2vc/4EHHtANHDiw2m0dOnTQPfXUU3K7vLxcFxAQoPv444+r7s/OztY5ODjo5s+fL6+npaXpRFW3bt1atU9ubq68bf369TdV75ycHLm/KIlMUWlJiW5XTKTuWESkbv3c96puXzHrFXnbtnaRqtbPkq3o21y+BwteHqx2Vehf7NkwX75XRyIi5TaZv9p8f9eqp6a4uFj2kojTQ5Wsra3l9Z07d9b4GHH7tfsLohemcv9z587J3pZr9/Hw8JCntSr38fb2RkREBH788Ufk5+fLHpuvvvoKfn5+iI2NrfF5i4qKkJubW+1CZMrErKYUf+VPMj1O+aUp5MYflGWGj41qdbN0V/xcZGmVeFHtqtC/OPP9J7I8G2qNtrcNY3tZmFoFNenp6SgrK4O/v3+128X1650GErffaP/K8kb7WFlZYcOGDfL0lZubmxybM2PGDKxZswZeXhVJJP5m6tSpMjiqvAQHB9fmpRKpIj9I+f9sl5BUdZvdJWXAY6G/B98VlVg1DJWlW+o/cwiR6RBjnhodUX7AlvbupnZ1SAVmMftJDCQeM2aM7JnZtm2bHJgsxuXceeedSEr668P/WpMmTUJOTk7VJTEx0ej1Jqotx8iWsqyXXFR1m3u6sm0bFs4GVUlgbA9Z+qXpbriSOqlr3fTn4HoVyHAX6zzN4NthgWoV1IiZRzY2NkhJUX45VhLXAwICanyMuP1G+1eWN9pHDA5esWIFFixYgC5duqBNmzb48ssv5UypuXPn1vi8Dg4OcpbUtRciU9ei3yOy9MsEki6ckFNT/TLE6WSgfixXGFZLm74Po8QGcC4GDm37VbV60I157Twhy8Q2ATL3E1meWgU19vb2cgzLxo0bq24rLy+X1zt16lTjY8Tt1+4vrF+/vmr/sLAwGbxcu48Y/yJmQVXuU1BQUDV+p1rlra3l8xNpRZPoLvJXpvifvm/Ftzi4bQkcSpS1a1r3VGZHkfG5uHkg1VvZPrvjN74FJmjDTx8gOEUng8/2Y95TuzpkLqefxHTuOXPmyB6S48eP45lnnpGDd0eNGiXvHzFihDz1U2ncuHFy7Mv06dNx4sQJvPnmm9i7dy/Gjh1bNV5m/PjxePfdd7F8+XIcPnxYHqN+/fryFJMgghsxdmbkyJE4ePCgzFnz8ssvy0HGAwcO1F9rEJmAdH9bWV45sg+Ju9bL7VRvKzi5sLdRTVmByi9/75W7kHrpjKp1oX/KWbZAlqeb2iM8qjObyELVOqgZOnQopk2bJpPlxcTE4MCBAzJoqRzom5CQUG2cS+fOnTFv3jx8/fXXMrfM4sWLsWzZMrRsqYwdEF555RU899xzePLJJ9GuXTtcuXJFHlMMCK487SWui9t79+6Ntm3b4o8//sCvv/4qj0mkJVeDfWXpmJiGknOn5XaOj73KtaKYVz9Hlivgnwlsf/Zujq0xISKXU+N4ZeyZ6+D71K4OqchKzOuGBRCntMQsKDFomONryJSt/PL/0Ojz5ch0B9L8bBFxuhQH+wZj2Bfr1K6axVv7zRTUn/FfuWL6wQENMezTNRbfJqZgwZjbEL3xMi75Ab1+P8xFXy34+9ssZj8RWZLYQY9DjBSrlwsEXVRm2rhGtFK7WiRybD3+Fo72biDbosW6C1j3wztsF5WVFBeh/r7LcjujQ1MGNBaOQQ2RiQkIaVI1KFVMTxWa9bhH1TrRX+7/dDXim9jK3hqXWfNw9tiN174jw1r1xUvwzQYKHIDbJnzK5rZwDGqITFCmv0PVdo4LOPDRxDI/d5i5CKleQL084NgLo+TUe1KH1UZlYeMzLV3hExjGt8HCMaghMkElDetXbaf78M/U1AQ2jIT1y2NRZAuEXyjH0rH91a6SRdq/ZSnCz5bJ7ZCHlRm1ZNn4aUlkgnzadK/azvd1VbUuVLNu94zBybtayO2o7elY/uk4NpWRxX/3kfwSOxtijY63j2T7E4MaIlPUftBjKK34yWHVMETt6tB1PPD+YhyJcpIfpAFz1+HQjpVsKyPJzUpFo0PZcruoZ0e2O0nsqSEyQe5efjjd2A4F9kDzOx9Tuzp0A31nr8RFP8CtEEh69WVcyclkexnBqleHyTbPcgNuH6eszE3EoIbIRA2Y/weabNmClh1vV7sqdAOe3oHweetd5DsAIck6rHq6H9vLwBa/+RCiNilJXhO6hjHbNlVhUENkosSyCKLHhkxf6173IvEhZSXvqP358kuXDGPFFy8i4r9x8svrcIwL7v94OZuaqjCoISLSg7tfmY2DHTzldqMlcdix8nu2q55tWjAD9eeskjmCTjSxw+DvtzLZHlXDoIaISE8Gf7kW54Kt4VQMFL3/ERe+1KN9GxfB6aM5sm3PNbBGrx/WwsFJWWSUqBKDGiIiPZ4yDP/4P8h2AQIygD/G3MOFL/Xg1MHtyH9tMjwKgMu+QPScRXIsE9HfMaghItKjiJjuyH7qHpRZAc1OFGPRK4PZvrcg9dIZnH/+CbkUQoY7EPTpLASFNWebUo0Y1BAR6dntT76HI72UrNDN157Fhp8+YBvXgZgev/uxu9AgRYc8J8Du7UmIjO3NtqTrYlBDRGQA93++FvGNbWFXBjh9MRfnj+9lO9dy9e11I3vJZSiK7IDcFx5BhwEj2IZ0QwxqiIgMtPBluy8WIs0TqJcLHH5hpPyippuz5LFu8vSdyKx94dE+6DPiVTYd/SsGNUREBiLGfpS/+CyKbYHG58vxvzF92dY3YcGY29Bqb57cPj6kBQa/+AXbjW4KgxoiIgPqef9zODEoUm5HbUvDb59PYHvfwKLXhyJ642W5fbBXoFxfi+hmMaghIjKwoR8sxdGWjvID1//71Tjy52q2eQ3ESueRSw7J7cOxrrj/i3VsJ6oVBjVEREZw239W4JKvsvDlxVdfRH5eDtv9Ght/+QjB366T2YKPR9jh7u//YLZgqjUGNURERuDlGwTPN6egwAFoeFmHlU/3YbtX2L3uZ7hO/x6OJcDZEGv0+3Ez7Owd2D5UawxqiIiMpO1tw3BhWBe5HbXvCv73Nqcox+/fjKI33oN7AXDRD4j9ZhlcPerx/yTVCYMaIiIjumfSNzjU3l1uhy3eg11rfrTY9k+6cAKJzz8Dnxwg3QMI+fwrBIQ0UbtaZMYY1BARGdld/1mP80FWcnHG/HenIj3pnMW9B7lZqYh7/F4EpQG5zoDjO5PlEhNEt4JBDRGRCgtfhn00EznOQGA6sOXZIRa18KVIQrjx0T5olFiOQnsg/6XRaNdvuNrVIg1gUENEpAKxhlHGE0NQbgU0P16MRRPvtoj3QQRvSx/tisj4Epkt+NLo/uj94EtqV4s0gkENEZFKBj4zFYd6BMjt5qtP4/d50zT/Xvx3bF9ExV2R2yfui8Gd4z5Vu0qkIQxqiIhU9MDM9TjZyEYufGn/6bdIiI/T7Pvx30n3ImZzstw+2KcB7n97vtpVIo1hUENEpPLCl22+WCBn/3jnAgfGj9DkwpfLpj2L5suOye1D7dwxbOZ6tatEGsSghohIZcHhLVH6whMotgGanCvD/57rDy1Z98O7CJ27CTY64Hgze9zz7Va1q0QaxaCGiMgE9Bo2ASfuaCq3o7amYMWsl6EFf66eC8/PfoFDCXCmoTX6/7iV2YLJYBjUEBGZiPum/g/HWjjAWgf4frsCx/dsgDkT9S+d8oFc7yrR3wrtv1sOFzcPtatFGsaghojIhMbX9PryN1z2hVw24MLE58124ctL547h8oTn5DihVC8gfOY38AsKV7tapHF1CmpmzZqF0NBQODo6okOHDti9e/cN91+0aBEiIyPl/lFRUVi1alW1+3U6HSZPnozAwEA4OTmhT58+OHXqVNX9mzdvhpWVVY2XPXv21OUlEBGZpHr+wXB74zUU2AMNL+mw4pm+MDfZGUk4+MR9qJ8G5LgA7u+/i/CozmpXiyxArYOahQsXYsKECZgyZQri4uIQHR2N/v37IzU1tcb9d+zYgeHDh2P06NHYv38/hgwZIi9Hjhyp2uejjz7C559/jtmzZ2PXrl1wcXGRx7x69aq8v3PnzkhKSqp2efzxxxEWFoa2bdveyusnIjI57fs9jPNDO8jtVnvz8L/3HoW5KCoswOaR/RB2USezBV995Sm07nWv2tUiC2GlE90ktSB6Ztq1a4eZM2fK6+Xl5QgODsZzzz2HiRMn/mP/oUOHIj8/HytWrKi6rWPHjoiJiZFBjHj6+vXr48UXX8RLLylZJXNycuDv748ffvgBw4YN+8cxS0pKEBQUJJ/zjTfeuKl65+bmwsPDQx7b3V1ZTI6IyJQtfLi9DGpEr03ZtNdksGPq2YKXPNQBLQ8WoMQGSHhmIAaN1X5CQTKs2nx/16qnpri4GPv27ZOnh6oOYG0tr+/cubPGx4jbr91fEL0wlfufO3cOycnJ1fYRlRfB0/WOuXz5cmRkZGDUqFHXrWtRUZFsiGsvRETmZNB/1uNCkBWci4G8d95DZkoiTNmiZ3rLgKYcwMn7YxnQkNHVKqhJT09HWVmZ7EW5lrguApOaiNtvtH9lWZtjfvvttzIwatCgwXXrOnXqVBkcVV5EbxIRkTkRM4UafvC5XMVajE/Z9OydJrvw5cKXByN6W5rcPtS/Ie5782e1q0QWyOxmP128eBFr166VY3RuZNKkSbKrqvKSmGjav3CIiGrSrF0fpI0epCx8ebQIi1+9z+QaaumHT6HlipNy+2AHTwz/bI3aVSILVaugxsfHBzY2NkhJSal2u7geEKAsyvZ34vYb7V9Z3uwxv//+e3h7e+Ouu+66YV0dHBzkubdrL0RE5mjQmI9xuLvSmx25Mh6bFsyAqVj77Zto9NNWmVvnaAsH3P/tNrWrRBasVkGNvb09YmNjsXHjxqrbxEBhcb1Tp041Pkbcfu3+wvr166v2FzOYRPBy7T5i/IuYBfX3Y4pBxSKoGTFiBOzs7GpTdSIis3bvF2txKswG9mWA7SdzkHjmrxmkatmxfA68v1gI+1LIug38cavMtUNkNqefxHTuOXPmYO7cuTh+/DieeeYZObupctCuCDjEqZ9K48aNw5o1azB9+nScOHECb775Jvbu3YuxY8fK+0WumfHjx+Pdd9+VA4APHz4sjyFmRImp39f6/fff5cBiMZ2biMiS2Nk7IObzX5DhDvjkAHHPDVN1fM2RP1cD78yAy1UgIcAKnb/7DU4u7BEnddU6pBZTtNPS0mSyPDGQV0zNFkFL5UDfhIQEOSOqksgxM2/ePLz++ut49dVX0aRJEyxbtgwtW7as2ueVV16RgdGTTz6J7OxsdO3aVR5TJOv7+wBhcTyRyI+IyNKENInG6fGjUfLet2h6tgyLnuuHYf/53ej1SDh1EGkvTkBAHpBSD2jy5Q/wCQwzej2IbjlPjblinhoi0oqFLw5Cq5Vn5ODh888PwcBnphrtubPSLmHXsL4y23G2K+D0yQeI6TbYaM9PlifXUHlqiIhIffd9uAzHmtnLwbnec5bhxD7j9NYU5udi66MDZEBT4ACUvjqWAQ2ZFAY1RERmRgzG7fHlMiT5AB4FwLlXxsqAw5DE+J0Vj/ZE0zOlKLYBUp65G93uGWPQ5ySqLQY1RERmSIxhcX5tolxfKfSSDssNvPDloqd6ouXhQpkt+PSDHXDH0+8b9PmI6oJBDRGRmep4+0icu6+d3G61OxdLphpmZuiCCQMRvT1Dbh++oxHufe0HgzwP0a1iUENEZMbunfwjDse6yu2GC7Zj78YFej3+/957DFGrz8rtg53qYdiMlXo9PpE+MaghIjJzd3y5FgmBVnAuArLffEvOUNKH1V+/hsbzdirZgqMccf+cLXo5LpGhMKghIjJzrh71EDR1OvKcgKA0YOMzg275mNuW/ge+s5bIDMYnG9lg4A9bmC2YTB6DGiIiDWjZ8XakjLpdDuRtceQqFk68u87HOrT9N9i89zlcioAL9a3Qfe5aZgsms8CghohII+58fgYOd/OV25ErTmDzoi9qfYzzx/ci8+VX4HUFSPYGmv/nZ3j5BhmgtkT6x6CGiEhD7p21HqdDreUik9bTv8Slc8du+rGZKYmIf3YE/DOBLDfA++NpCIloY9D6EukTgxoiIo0tfBn1yVxkugO+2cCe54be1MKXInnfH4/ejpAkHfIdgPLXX0CrzgONUmcifWFQQ0SkMaHN2qLwuZEotQYiTpdi0bj+N9xfBD0rR3RHk3NlKLYFMp57AF0HP2m0+hLpC4MaIiIN6vPIRBztr6yc3fL3y3J69vUseqI7Whwtkgtknn24G/o//pYRa0qkPwxqiIg06v6Pl+N4pD1sdIDnV0sQv3/zP/ZZMH4Aondmye0jg5ri7olfq1BTIv1gUENEpOGFL7vOWiJnMXnmA2deGVNt4cvFb49A1JoLcvtgVx8M/fhXFWtLdOsY1BARaZhfUDgcJ72Eq3ZAWGI5fn1WGV+zYtbLaLpwj/wSOBLthPtnb1K7qkS3jEENEZHGdRo0GmfuVaZmR+/KxoJneiPwqxWwKwPiG9virh/+YLZg0gQGNUREFuC+N3/B4dYucjt6UxKci4HzQVboOXcdHJyc1a4ekV4wqCEishB3zF6HhAAruZ3kA7T8+r/w9A5Uu1pEesOghojIgha+bPbVzzh4RyOEfj0XweEt1a4SkV7Z6vdwRERkysSyByEzVqpdDSKDYE8NERERaQKDGiIiItIEBjVERESkCQxqiIiISBMY1BAREZEmMKghIiIiTWBQQ0RERJrAoIaIiIg0gUENERERaQKDGiIiItIEBjVERESkCQxqiIiISBMY1BAREZEmWMwq3TqdTpa5ublqV4WIiIhuUuX3duX3+I1YTFCTl5cny+DgYLWrQkRERHX4Hvfw8LjhPla6mwl9NKC8vByXL1+Gm5sbrKys9B5FimApMTER7u7u0CJLeI2W8jot4TVayuvka9QOvpfXJ8IUEdDUr18f1tY3HjVjMT01oiEaNGhg0OcQH5xa/fC0pNdoKa/TEl6jpbxOvkbt4HtZs3/roanEgcJERESkCQxqiIiISBMY1OiBg4MDpkyZIkutsoTXaCmv0xJeo6W8Tr5G7eB7qR8WM1CYiIiItI09NURERKQJDGqIiIhIExjUEBERkSYwqCEiIiJNYFBzk2bNmoXQ0FA4OjqiQ4cO2L179w33X7RoESIjI+X+UVFRWLVqFbT0GufMmYNu3brBy8tLXvr06fOvbWKu72WlBQsWyGzUQ4YMgdZeY3Z2NsaMGYPAwEA5C6Np06Ym/3+2tq/x008/RUREBJycnGSm4RdeeAFXr16FKdu6dSvuvPNOmUlV/N9btmzZvz5m8+bNaNOmjXwfGzdujB9++AFaeo1LlixB37594evrKxPVderUCWvXroXW3sdK27dvh62tLWJiYmDqttbhdRYVFeG1115Dw4YN5f9Z8Tf93Xff1bkODGpuwsKFCzFhwgQ5PTQuLg7R0dHo378/UlNTa9x/x44dGD58OEaPHo39+/fLL0FxOXLkSJ3fKFN7jeKDU7zGTZs2YefOnfJLol+/frh06RJMWW1fZ6Xz58/jpZdekoGcqavtaywuLpZfEuI1Ll68GPHx8TJoDQoKglZe47x58zBx4kS5//Hjx/Htt9/KY7z66qswZfn5+fK1iQDuZpw7dw4DBw5Er169cODAAYwfPx6PP/64SX/p1/Y1ii9O8f9VBN379u2Tr1V8kYrPWq28xmt/bIwYMQK33XYbzEF+HV7nAw88gI0bN8q/SfHZM3/+fPnjo87ElG66sfbt2+vGjBlTdb2srExXv3593dSpU2vc/4EHHtANHDiw2m0dOnTQPfXUU5p5jX9XWlqqc3Nz082dO1dnyuryOsVr69y5s+6bb77RjRw5Ujd48GCdll7jf/7zH12jRo10xcXFOnNR29co9u3du3e12yZMmKDr0qWLzlyIj+ulS5fecJ9XXnlF16JFi2q3DR06VNe/f3+dVl5jTZo3b6576623dFp7jeK9e/3113VTpkzRRUdH68wJbuJ1rl69Wufh4aHLyMjQ2/Oyp+ZfiF+x4teAOL1y7TpS4rrooaiJuP3a/QXxK/J6+5vja/y7goIClJSUoF69ejBVdX2db7/9Nvz8/GTPm6mry2tcvny57MIXp5/8/f3RsmVLvP/++ygrK4NWXmPnzp3lYypPUZ09e1b+0r/jjjugJeb22aOvxYrFYoem/NlTF99//738fyp6F7Vq+fLlaNu2LT766CPZMyxOe4se8cLCwjof02IWtKyr9PR0+eEuPuyvJa6fOHGixsckJyfXuL+4XSuv8e/+7//+T55H/fsHqrm/zj/++EN2i4qufHNQl9coPjh///13PPTQQ/KL/vTp03j22WdlkGqKH6h1eY0PPvigfFzXrl3lir+lpaV4+umnTf70U21d77NHrAAtvijEeCKtmTZtGq5cuSJPY2jFqVOn5OnSbdu2yfE0WnX27Fn5GSvGxS1dulT+jYrPnoyMDBnU1QV7auiWffDBB3IQrfhPKf5zaoX49ffII4/I8SU+Pj7Q8i9d0RP19ddfIzY2FkOHDpUD92bPng2tEGPARO/Tl19+KcfgiMGmK1euxDvvvKN21egWiLFSb731Fv773//K/8NaIAJ2EYSL1yV6LrSsvLxcDij+5Zdf0L59e9lzOmPGDMydO7fOvTXaDQH1RHyZ2djYICUlpdrt4npAQECNjxG312Z/c3yN1/5KEkHNhg0b0KpVK5iy2r7OM2fOyMGzYhDitX+Egvj1JAa1hYeHw9zfSzHjyc7OTj6uUrNmzeSvfnGqx97eHub+Gt944w0ZoIpBs4KYkSgGNT755JMygBOnr7Tgep89YpaQ1nppxA8p8X6Kmaam3ENclx9Te/fulQOfx44dW/W5I3oYxefOunXr0Lt3b2hBYGCgPO3k4eFR7bNHvNaLFy+iSZMmtT6mNv6SDUh8oItfr2J0diXxH0xcF+MQaiJuv3Z/Yf369dfd3xxfoyDOg4pfumvWrJHnRU1dbV+nmJJ/+PBheeqp8nLXXXdVzSwRM7608F526dJFnnKqDNiEkydPyg8cUwto6voaxZivvwculUGclpa/M7fPnroSM2RGjRolSzHbS0tEAPr3zx1xqlTMCBLbIn2BVnTp0gWXL1+Wpw+v/ewRf6sNGjSo20H1NuRYwxYsWKBzcHDQ/fDDD7pjx47pnnzySZ2np6cuOTlZ3v/II4/oJk6cWLX/9u3bdba2trpp06bpjh8/Lkeu29nZ6Q4fPqzTymv84IMPdPb29rrFixfrkpKSqi55eXk6U1bb1/l35jD7qbavMSEhQc5cGzt2rC4+Pl63YsUKnZ+fn+7dd9/VaeU1ir9B8Rrnz5+vO3v2rG7dunW68PBwOVPRlIm/p/3798uL+LieMWOG3L5w4YK8X7xG8Voridfm7Oyse/nll+Vnz6xZs3Q2Nja6NWvW6LTyGn/55Rf5+Spe27WfPdnZ2TqtvMa/M5fZT3m1fJ1i/wYNGujuu+8+3dGjR3VbtmzRNWnSRPf444/XuQ4Mam7SF198oQsJCZFf5GI66Z9//ll1X48ePeSX3bX++9//6po2bSr3F1MsV65cqdPSa2zYsKH8T/v3i/jj09p7aW5BTV1e444dO2TaAREoiOnd7733npzKrpXXWFJSonvzzTdlIOPo6KgLDg7WPfvss7qsrCydKdu0aVONf2eVr02U4rX+/TExMTGyXcR7+f333+u09BrF9o3218r7aI5BzaY6vE4RfPfp00fn5OQkAxyRaqGgoKDOdbAS/+ivM4mIiIhIHRxTQ0RERJrAoIaIiIg0gUENERERaQKDGiIiItIEBjVERESkCQxqiIiISBMY1BAREZEmMKghIiIiTWBQQ0RERJrAoIaIiIg0gUENERERaQKDGiIiIoIW/D/krnKw3nJdswAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "thetas = np.linspace(0, np.pi/2, 10)\n", + "lst = []\n", + "for i, theta in enumerate(thetas):\n", + " traj = generate_data(time, tau_0, freq_0, theta)\n", + " Z = augment(traj[:, [0]], 4)\n", + " X = Z[:-1]\n", + " Y = Z[1:]\n", + " B, B_spec = estimator(X, Y, rank=4)\n", + " D, R, L = B_spec[\"eig_val\"], B_spec[\"eig_vec_right\"], B_spec[\"eig_vec_left\"]\n", + " D = np.log(D) * fs \n", + " lst1 = []\n", + " for name in ['chordal', 'martin', 'geodesic', 'procrustes']:\n", + " lst1.append(sgot_metric(D_0, R_0, L_0, D, R, L, eta=0.9, grassman_metric=name))\n", + " lst.append(lst1)\n", + "lst2 = np.array(lst)\n", + "plt.plot(thetas, lst2)\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "id": "d4f952d0", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "etas = np.linspace(0.0, 1.0, 21)\n", + "methods = ['chordal', 'martin', 'geodesic', 'procrustes']\n", + "scores_eta = []\n", + "\n", + "for eta in etas:\n", + " freq_1 = np.array([freq_0[0], freq])\n", + " traj = generate_data(time, tau_0, freq_1, theta)\n", + " Z = augment(traj[:, [0]], 4)\n", + " X = Z[:-1]\n", + " Y = Z[1:]\n", + "\n", + " B, B_spec = estimator(X, Y, rank=4)\n", + " D, R, L = B_spec[\"eig_val\"], B_spec[\"eig_vec_right\"], B_spec[\"eig_vec_left\"]\n", + " D = np.log(D) * fs\n", + "\n", + " row = []\n", + " for name in methods:\n", + " row.append(\n", + " sgot_metric(\n", + " D_0, R_0, L_0,\n", + " D, R, L,\n", + " eta=eta,\n", + " grassman_metric=name\n", + " )\n", + " )\n", + " scores_eta.append(row)\n", + "\n", + "scores_eta = np.array(scores_eta)\n", + "\n", + "for i, name in enumerate(methods):\n", + " plt.plot(etas, scores_eta[:, i], label=name)\n", + "\n", + "plt.xlabel(\"eta\")\n", + "plt.ylabel(\"SGOT distance\")\n", + "plt.title(\"SGOT distance vs eta\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "fa729a4d", + "metadata": {}, + "outputs": [ + { + "ename": "NameError", + "evalue": "name 'np' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[2], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m decays \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241m.\u001b[39mlinspace(\u001b[38;5;241m0.1\u001b[39m, \u001b[38;5;241m3.0\u001b[39m, \u001b[38;5;241m20\u001b[39m) \u001b[38;5;66;03m# adjust range as needed\u001b[39;00m\n\u001b[1;32m 2\u001b[0m methods \u001b[38;5;241m=\u001b[39m [\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mchordal\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmartin\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mgeodesic\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mprocrustes\u001b[39m\u001b[38;5;124m'\u001b[39m]\n\u001b[1;32m 3\u001b[0m scores_decay \u001b[38;5;241m=\u001b[39m []\n", + "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined" + ] + } + ], + "source": [ + "decays = np.linspace(0.1, 3.0, 20) # adjust range as needed\n", + "methods = ['chordal', 'martin', 'geodesic', 'procrustes']\n", + "scores_decay = []\n", + "\n", + "for tau in decays:\n", + " freq_1 = np.array([freq_0[0], freq])\n", + " tau_1 = np.array([tau, tau]) # or whatever structure your generator expects\n", + "\n", + " traj = generate_data(time, tau_1, freq_1, theta)\n", + " Z = augment(traj[:, [0]], 4)\n", + " X = Z[:-1]\n", + " Y = Z[1:]\n", + "\n", + " B, B_spec = estimator(X, Y, rank=4)\n", + " D, R, L = B_spec[\"eig_val\"], B_spec[\"eig_vec_right\"], B_spec[\"eig_vec_left\"]\n", + " D = np.log(D) * fs\n", + "\n", + " row = []\n", + " for name in methods:\n", + " row.append(\n", + " sgot_metric(\n", + " D_0, R_0, L_0,\n", + " D, R, L,\n", + " eta=0.9, # keep eta fixed here\n", + " grassman_metric=name\n", + " )\n", + " )\n", + " scores_decay.append(row)\n", + "\n", + "scores_decay = np.array(scores_decay)\n", + "\n", + "for i, name in enumerate(methods):\n", + " plt.plot(decays, scores_decay[:, i], label=name)\n", + "\n", + "plt.xlabel(\"decay\")\n", + "plt.ylabel(\"SGOT distance\")\n", + "plt.title(\"SGOT distance vs decay\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "80ca22bc", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.13" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/ot/backend.py b/ot/backend.py index 0568f2e2f..9c6a25150 100644 --- a/ot/backend.py +++ b/ot/backend.py @@ -2122,7 +2122,7 @@ def backward(ctx, g): def _to_numpy(self, a): if isinstance(a, float) or isinstance(a, int) or isinstance(a, np.ndarray): return np.array(a) - return a.cpu().detach().numpy() + return a.cpu().detach().resolve_conj().numpy() def _from_numpy(self, a, type_as=None): if ( diff --git a/ot/sgot.py b/ot/sgot.py index c8ee5b91c..5248432be 100644 --- a/ot/sgot.py +++ b/ot/sgot.py @@ -57,8 +57,11 @@ def eigenvalue_cost_matrix(Ds, Dt, q=1, eigen_scaling=None, nx=None): Dsn = nx.real(Ds) * real_scale + 1j * nx.imag(Ds) * imag_scale Dtn = nx.real(Dt) * real_scale + 1j * nx.imag(Dt) * imag_scale - prod = Dsn[:, None] - Dtn[None, :] - prod = nx.real(prod * nx.conj(prod)) + C_real = nx.real(Dsn[:, None] - nx.real(Dtn)[None, :]) + C_real = C_real**2 + C_imag = nx.imag(Dsn)[:, None] - nx.imag(Dtn)[None, :] + C_imag = C_imag**2 + prod = C_real + C_imag return prod ** (q / 2) @@ -79,7 +82,7 @@ def _normalize_columns(A, nx, eps=1e-12): A_norm: array-like, shape (d, n) Column-normalized array. """ - nrm = nx.sqrt(nx.sum(A * nx.conj(A), axis=0, keepdims=True)) + nrm = nx.norm(A, axis=0, keepdims=True) nrm = nx.real(nrm) # norm is real; avoid complex dtype for maximum (e.g. torch) nrm = nx.maximum(nrm, eps) return A / nrm @@ -124,8 +127,10 @@ def _delta_matrix_1d(Rs, Ls, Rt, Lt, nx=None, eps=1e-12): return delta -def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1e-300): - """Compute squared Grassmannian distances from delta similarities. +def _grassmann_distance_squared( + delta, grassman_metric="chordal", q=1, nx=None, eps=1e-12 +): + """Compute Grassmannian distances from delta similarities. Parameters ---------- @@ -133,34 +138,43 @@ def _grassmann_distance_squared(delta, grassman_metric="chordal", nx=None, eps=1 Similarity values in [0, 1]. grassman_metric: str, optional Metric type: "geodesic", "chordal", "procrustes", or "martin". + q: int or float, optional + Exponent applied to the Grassmann distance, in the same spirit as the + eigenvalue cost exponent. Default is 1. nx: module, optional Backend (NumPy-compatible). If None, inferred from inputs. eps: float, optional - Minimum value used for numerical stability, default 1e-300. + Minimum value used for numerical stability in the Martin metric. Returns - ---------- - dist2: array-like - Squared Grassmannian distance(s). + ------- + dist_q: array-like + Grassmannian distances raised to the power q. """ if nx is None: nx = get_backend(delta) + if nx.any(delta < 0) or nx.any(delta > 1.0): + raise ValueError( + "delta must be in [0, 1]; found values outside this range " + f"(min={nx.min(delta)}, max={nx.max(delta)})" + ) + delta = nx.clip(delta, 0.0, 1.0) if grassman_metric == "geodesic": - return nx.arccos(delta) ** 2 - if grassman_metric == "chordal": - return 1.0 - delta**2 - if grassman_metric == "procrustes": - return 2.0 * (1.0 - delta) - if grassman_metric == "martin": - # Martin-type Grassmann metric: -log(delta^2) with lower clamp at eps. - # We deliberately avoid any upper threshold to stay close to the - # information-geometric interpretation in Germain et al. (2025). + dist2 = nx.arccos(delta) ** 2 + elif grassman_metric == "chordal": + dist2 = 1.0 - delta**2 + elif grassman_metric == "procrustes": + dist2 = 2.0 * (1.0 - delta) + elif grassman_metric == "martin": delta2 = nx.maximum(delta**2, eps) - return -nx.log(delta2) - raise ValueError(f"Unknown grassman_metric: {grassman_metric}") + dist2 = -nx.log(delta2) + else: + raise ValueError(f"Unknown grassman_metric: {grassman_metric}") + + return nx.real(dist2) ** (q / 2.0) ##################################################################################################################################### @@ -181,6 +195,7 @@ def sgot_cost_matrix( grassman_metric="chordal", eigen_scaling=None, nx=None, + eps=1e-12, ): r"""Compute the SGOT cost matrix between two spectral decompositions. @@ -256,6 +271,9 @@ def sgot_cost_matrix( two entries. nx: module, optional Backend (NumPy-compatible). If None, inferred from inputs. + eps: float, optional + Minimum value used for numerical stability in Grassmann distances and + Martin metric. Default is 1e-12. Returns ---------- @@ -269,48 +287,50 @@ def sgot_cost_matrix( if nx is None: nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) - if Ds.ndim != 1 or Dt.ndim != 1: - raise ValueError( - f"sgot_cost_matrix() expects Ds, Dt 1D; " - f"got Ds {getattr(Ds, 'shape', None)}, Dt {getattr(Dt, 'shape', None)}" - ) - - if Rs.shape != Ls.shape or Rt.shape != Lt.shape: - raise ValueError( - "Right/left eigenvector shapes must match; got " - f"(Rs,Ls)=({Rs.shape},{Ls.shape}), (Rt,Lt)=({Rt.shape},{Lt.shape})" - ) - - if Rs.shape[1] != Ds.shape[0] or Rt.shape[1] != Dt.shape[0]: - raise ValueError( - "Eigenvector columns must match eigenvalues: " - f"Rs {Rs.shape[1]} vs Ds {Ds.shape[0]}, " - f"Rt {Rt.shape[1]} vs Dt {Dt.shape[0]}" - ) + _validate_sgot_inputs(Ds, Rs, Ls, Dt, Rt, Lt) C_lambda = eigenvalue_cost_matrix(Ds, Dt, q=q, eigen_scaling=eigen_scaling, nx=nx) - delta = _delta_matrix_1d(Rs, Ls, Rt, Lt, nx=nx) - C_grass = _grassmann_distance_squared(delta, grassman_metric=grassman_metric, nx=nx) + C_grass = _grassmann_distance_squared( + delta, + grassman_metric=grassman_metric, + q=q, + nx=nx, + eps=eps, + ) C2 = eta * C_lambda + (1.0 - eta) * C_grass - C = nx.real(C2) ** (p / 2.0) + C = C2 ** (p / 2.0) return C -def _validate_sgot_metric_inputs(Ds, Dt): - """Validate that eigenvalue inputs for SGOT metric are 1D.""" +def _validate_sgot_inputs(Ds, Rs, Ls, Dt, Rt, Lt): + """Validate shapes of spectral atoms for SGOT cost/metric.""" Ds_shape = getattr(Ds, "shape", None) Dt_shape = getattr(Dt, "shape", None) Ds_ndim = getattr(Ds, "ndim", None) Dt_ndim = getattr(Dt, "ndim", None) + if Ds_ndim != 1 or Dt_ndim != 1: raise ValueError( - "sgot_metric() expects Ds and Dt to be 1D (n,), " + "SGOT expects Ds and Dt to be 1D (n,), " f"got Ds shape {Ds_shape} and Dt shape {Dt_shape}" ) + if Rs.shape != Ls.shape or Rt.shape != Lt.shape: + raise ValueError( + "Right/left eigenvector shapes must match; got " + f"(Rs,Ls)=({Rs.shape},{Ls.shape}), (Rt,Lt)=({Rt.shape},{Lt.shape})" + ) + + if Rs.shape[1] != Ds.shape[0] or Rt.shape[1] != Dt.shape[0]: + raise ValueError( + "Eigenvector columns must match eigenvalues: " + f"Rs {Rs.shape[1]} vs Ds {Ds.shape[0]}, " + f"Rt {Rt.shape[1]} vs Dt {Dt.shape[0]}" + ) + def sgot_metric( Ds, @@ -328,77 +348,56 @@ def sgot_metric( Ws=None, Wt=None, nx=None, + eps=1e-12, ): r"""Compute the SGOT metric between two spectral decompositions. This function computes a discrete optimal transport problem between two measures over spectral atoms :math:`z_i=(\lambda_i, V_i)` and :math:`z'_j=(\lambda'_j, V'_j)`. - Using the ground cost matrix :math:`C=d^p` returned by :func:`sgot_cost_matrix`, + Using the ground cost matrix :math:`C = d^p` returned by :func:`sgot_cost_matrix`, we solve: .. math:: P^\star \in \arg\min_{P\in\Pi(W_s, W_t)} \langle C, P\rangle, - and compute the associated :math:`p`-Wasserstein objective: + where :math:`C(i,j) = d(i,j)^p` and :math:`d(i,j)` is the SGOT ground distance + combining spectral and Grassmann terms with exponent :math:`q`: .. math:: - \mathrm{obj} \;=\; \left(\sum_{i,j} C(i,j)\,P^\star_{ij}\right)^{1/p}. + d(i,j)^2 + \;=\; \eta\,\big|\lambda_i - \lambda'_j\big|^{q} + \;+\; (1-\eta)\,d_G(i,j)^{q}, + + and :math:`d_G(i,j)` is the Grassmann distance associated with the chosen + ``grassman_metric``. - This implementation returns an additional outer root: + From the optimal plan :math:`P^\star`, we first form the :math:`p`-Wasserstein + objective: .. math:: - \mathrm{SGOT} \;=\; \mathrm{obj}^{1/r}. + \mathrm{obj} + \;=\; + \left(\sum_{i,j} C(i,j)\,P^\star_{ij}\right)^{1/p}, - Parameters - ---------- - Ds: array-like, shape (n_s,) - Eigenvalues of operator T1. - Rs: array-like, shape (L, n_s) - Right eigenvectors of operator T1. - Ls: array-like, shape (L, n_s) - Left eigenvectors of operator T1. - Dt: array-like, shape (n_t,) - Eigenvalues of operator T2. - Rt: array-like, shape (L, n_t) - Right eigenvectors of operator T2. - Lt: array-like, shape (L, n_t) - Left eigenvectors of operator T2. - eta: float, optional - Weighting between spectral and Grassmann terms, default 0.5. - p: int, optional - Exponent defining the OT ground cost and Wasserstein order. The cost matrix - is :math:`d^p` and the OT objective is raised to the power :math:`1/p`. - Default is 2. - q: int, optional - Exponent applied to the eigenvalue distance in the spectral term. - Default is 1. - r: int, optional - Outer root applied to the Wasserstein objective. Default is 2. - grassman_metric: str, optional - Metric type: "geodesic", "chordal", "procrustes", or "martin". - eigen_scaling: None or array-like of length 2, optional - Scaling ``(real_scale, imag_scale)`` applied to eigenvalues before computing - the spectral part of the cost. If None, defaults to ``(1.0, 1.0)``. - Ws: array-like, shape (n_s,), optional - Source distribution. If None, uses a uniform distribution. - Wt: array-like, shape (n_t,), optional - Target distribution. If None, uses a uniform distribution. - nx: module, optional - Backend (NumPy-compatible). If None, inferred from inputs. + and then apply an outer root :math:`r`: - Returns - ---------- - dist: float - SGOT metric value. + .. math:: + \mathrm{SGOT} + \;=\; + \mathrm{obj}^{1/r}. - References - ---------- - Germain et al., *Spectral-Grassmann Optimal Transport* (SGOT). + In summary: + + - :math:`q` controls how strongly spectral and Grassmann distances are curved + (via :math:`|\lambda_i - \lambda'_j|^{q}` and :math:`d_G(i,j)^{q}`), + - :math:`p` is the exponent used in the OT ground cost and the inner + Wasserstein root, + - :math:`r` is an additional outer root applied to the Wasserstein objective. """ if nx is None: nx = get_backend(Ds, Rs, Ls, Dt, Rt, Lt) - _validate_sgot_metric_inputs(Ds, Dt) + _validate_sgot_inputs(Ds, Rs, Ls, Dt, Rt, Lt) C = sgot_cost_matrix( Ds, @@ -413,6 +412,7 @@ def sgot_metric( grassman_metric=grassman_metric, eigen_scaling=eigen_scaling, nx=nx, + eps=eps, ) if Ws is None: From b8a6cbe466e87af3dab19813178103ee4bea6b87 Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Tue, 31 Mar 2026 10:28:16 +0200 Subject: [PATCH 13/14] removed notebook, added python version --- examples/plot_sgot.ipynb | 791 --------------------------------------- examples/plot_sgot.py | 525 ++++++++++++++++++++++++++ 2 files changed, 525 insertions(+), 791 deletions(-) delete mode 100644 examples/plot_sgot.ipynb create mode 100644 examples/plot_sgot.py diff --git a/examples/plot_sgot.ipynb b/examples/plot_sgot.ipynb deleted file mode 100644 index 4ab84b4d1..000000000 --- a/examples/plot_sgot.ipynb +++ /dev/null @@ -1,791 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 19, - "id": "03c2cded", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'\\n=========================================\\nSGOT example for a rotated linear system\\n=========================================\\n\\nThis notebook presents a synthetic example of Spectral Grassmannian-Wasserstein\\nOptimal Transport (SGOT) on linear dynamical systems.\\n\\nWe consider a signal formed by the sum of two damped oscillatory modes evolving\\nalong a rotated direction in the plane. The signal is then associated with an\\nunderlying continuous linear dynamical system, and we study how its spectral\\nrepresentation varies under rotation. The SGOT cost and metric are used to\\ncompare the reference and rotated systems.\\n\\n[1] T. Germain; R. Flamary; V. R. Kostic; K. Lounici, A Spectral-Grassmann Wasserstein Metric for Operator Representations of Dynamical Systems, arXiv preprint arXiv:2509.24920, 2025.\\n\\n'" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "\"\"\"\n", - "=========================================\n", - "SGOT example for a rotated linear system\n", - "=========================================\n", - "\n", - "This notebook presents a synthetic example of Spectral Grassmannian-Wasserstein\n", - "Optimal Transport (SGOT) on linear dynamical systems.\n", - "\n", - "We consider a signal formed by the sum of two damped oscillatory modes evolving\n", - "along a rotated direction in the plane. The signal is then associated with an\n", - "underlying continuous linear dynamical system, and we study how its spectral\n", - "representation varies under rotation. The SGOT cost and metric are used to\n", - "compare the reference and rotated systems.\n", - "\n", - "[1] T. Germain; R. Flamary; V. R. Kostic; K. Lounici, A Spectral-Grassmann Wasserstein Metric for Operator Representations of Dynamical Systems, arXiv preprint arXiv:2509.24920, 2025.\n", - "\n", - "\"\"\"" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "bdcd6755", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "from ot.sgot import sgot_metric, sgot_cost_matrix\n", - "\n", - "from scipy.linalg import eig" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "3c0a2a11", - "metadata": {}, - "outputs": [], - "source": [ - "# sampling parameters and time grid\n", - "fs = 50\n", - "max_t = 5\n", - "time = np.linspace(0, max_t, fs * max_t)\n", - "dt = 1 / fs" - ] - }, - { - "cell_type": "markdown", - "id": "abe935cd", - "metadata": {}, - "source": [ - "# Example: rotating a linear dynamical system in 3D" - ] - }, - { - "cell_type": "markdown", - "id": "17b22e68", - "metadata": {}, - "source": [ - "## 1. Build a simple observed signal \n", - "\n", - "We begin by assuming that the observed signal is made of two oscillatory components:\n", - "$$\n", - "x(t)=e^{-\\tau_1 t}\\cos(2\\pi\\omega_1 t)\\,\\vec e(\\theta)\n", - "\\;+\\;\n", - "e^{-\\tau_2 t}\\cos(2\\pi\\omega_2 t)\\,\\vec e(\\theta),\n", - "$$\n", - "where $\\vec e(\\theta)\\in\\mathbb{R}^2$ is a fixed real vector. Thus, $x(t)$ evolves along the one-dimensional subspace spanned by $\\vec e(\\theta)$, while its time dependence exhibits oscillatory and dissipative behaviour.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "9cea207f", - "metadata": {}, - "outputs": [], - "source": [ - "tau_0 = np.array([0.08, 0.18])\n", - "freq_0 = np.array([1., 2.])\n", - "theta_0 = np.pi / 4\n", - "\n", - "def generate_data(time,tau,freq,theta):\n", - " t_ = np.sin(2 * np.pi * freq[None,:] * time[:,None]) * np.exp(-tau[None,:] * time[:,None])\n", - " t_ = t_.sum(axis=1)\n", - " traj_0 = np.zeros((t_.shape[0],2))\n", - " traj_0[:,0] = t_\n", - " rotation_matrix = np.array([[np.cos(theta), -np.sin(theta)],\n", - " [np.sin(theta), np.cos(theta)]])\n", - " traj_0 = traj_0 @ rotation_matrix.T\n", - " return traj_0\n", - "traj_0 = generate_data(time,tau_0,freq_0,theta_0)" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "320650e0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# plot the observed signal components and their sum\n", - "plt.figure(figsize=(10, 4))\n", - "plt.plot(time, traj_0, label=\"base trajectory\", linewidth=2)\n", - "plt.xlabel(\"time\")\n", - "plt.ylabel(\"amplitude\")\n", - "plt.legend()\n", - "plt.title(r\"Observed scalar signal along $\\vec{e}(\\theta)$\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "1216ab22", - "metadata": {}, - "source": [ - "## 2. Interpret the signal as coming from a continuous linear dynamical system\n", - "We assume that $x(t)$ is generated by an underlying continuous linear dynamical system. Since the observed signal is a superposition of two sinusoidal modes, the corresponding linear dynamics are naturally described by a fourth-order model. We therefore introduce the state vector\n", - "$$\n", - "z(t)=\n", - "\\begin{pmatrix}\n", - "x_1(t)\\\\\n", - "x_2(t)\\\\\n", - "\\vdots\\\\\n", - "x_1^{(3)}(t)\\\\\n", - "x_2^{(3)}(t)\n", - "\\end{pmatrix}\n", - "\\in\\mathbb{R}^8.\n", - "$$\n", - "This allows us to rewrite the dynamics as a first-order linear system:\n", - "$$\n", - "\\dot{z}(t)=Az(t),\n", - "$$\n", - "where $A\\in\\mathbb{R}^{8\\times 8}$. Its solution is then given by\n", - "$$\n", - "z(t)=e^{tA}z_0.\n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "679bd14e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig = plt.figure(figsize=(9, 6))\n", - "ax = fig.add_subplot(projection=\"3d\")\n", - "\n", - "ax.plot(time, traj_0[:, 0], traj_0[:, 1])\n", - "ax.set_xlabel(\"time\")\n", - "ax.set_ylabel(\"x₁(t)\")\n", - "ax.set_title(\"Observed trajectory in time\")\n", - "\n", - "ax.text2D(1.08, 0.5, \"x₂(t)\", transform=ax.transAxes, rotation=90, va=\"center\")\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "3435803e", - "metadata": {}, - "source": [ - "## 3. Sampling and preprocessing discrete trajectories of dynamical system\n", - "We now have a bridge between the continuous system and the operator we later aim to infer from sampled data. Since in practice we do not observe the full continuous trajectory, we work instead with discrete samples of the signal. We take snapshots at uniform time intervals $\\Delta t$, and write the sampled signal as\n", - "\n", - "$$\n", - "S=\n", - "\\begin{pmatrix}\n", - "x_1(0) & x_2(0)\\\\\n", - "x_1(\\Delta t) & x_2(\\Delta t)\\\\\n", - "\\vdots\\\\\n", - "x_1(N\\Delta t) & x_2(N\\Delta t)\\\\\n", - "\\end{pmatrix}\n", - "$$\n", - "\n", - "The goal is now to use these observations to recover the operator governing the evolution. \n", - "To do this, we augment the signal $s$ using a sliding window of length $w$. For each $k$, define\n", - "$$z_k =\n", - "\\begin{pmatrix}\n", - "s_k\\\\\n", - "s_{k+1}\\\\\n", - "\\vdots\\\\\n", - "s_{k+w-1}\n", - "\\end{pmatrix}\n", - "$$\n", - "We then form the data matrices\n", - "$$\n", - "X=\n", - "\\begin{pmatrix}\n", - "z_1\\\\\n", - "z_2\\\\\n", - "\\vdots\\\\\n", - "z_{N-w}\n", - "\\end{pmatrix},\n", - "\\qquad\n", - "Y=\n", - "\\begin{pmatrix}\n", - "z_2\\\\\n", - "z_3\\\\\n", - "\\vdots\\\\\n", - "z_{N-w+1}\n", - "\\end{pmatrix},\n", - "$$\n", - "so that $X$ contains the present windowed states and $Y$ the corresponding shifted future states." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "f84a0f1e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "X shape: (246, 4)\n", - "Y shape: (246, 4)\n" - ] - } - ], - "source": [ - "# build a 4-dimensional state using delay embedding\n", - "def augment(traj, window_length = 2):\n", - " Z = np.lib.stride_tricks.sliding_window_view(traj,(window_length,1))\n", - " Z = Z.reshape(Z.shape[0], -1)\n", - " return Z\n", - "\n", - "# create the embedded state matrix Z\n", - "Z = augment(traj_0[:, [0]], 4)\n", - "Z.shape\n", - "\n", - "# inspect one embedded state vector\n", - "Z[0]\n", - "\n", - "# create X and Y for the SGOT metric\n", - "X = Z[:-1]\n", - "Y = Z[1:]\n", - "\n", - "# inspect shapes of X and Y\n", - "print(\"X shape:\", X.shape)\n", - "print(\"Y shape:\", Y.shape)" - ] - }, - { - "cell_type": "markdown", - "id": "0c8749bb", - "metadata": {}, - "source": [ - "## 4. Estimate the discrete-time operator\n", - "Now, we look to identify the operator that maps $X$ to $Y$. From\n", - "$$\n", - "\\dot{z}=Az,\n", - "$$\n", - "we have\n", - "$$\n", - "z(t+\\Delta t)=e^{\\Delta tA}z(t).\n", - "$$\n", - "Setting\n", - "$$\n", - "B=e^{\\Delta tA},\n", - "$$\n", - "the corresponding discrete-time evolution is governed by $B$, and we seek the best linear map satisfying\n", - "$$\n", - "Y\\approx X B^T.\n", - "$$\n", - "Equivalently, we solve the optimisation problem\n", - "$$\n", - "\\min_B \\|Y-XB\\|^2.\n", - "$$\n", - "\n", - "We want to recover the best rank-$r$ operator, whose estimator is defined as follows\n", - "$$\n", - "B = C_{xx}^{-\\frac{1}{2}}[C_{xx}^{-\\frac{1}{2}}C_{xy}]_r \\quad \\text{s.t} \\quad C_{xx} = X^T X \\quad \\text{and} \\quad C_{xy} = X^TY.\n", - "$$\n", - "where $[ ]_r$ is the best rank-$r$ estimator through SVD decomposition. [2]\n", - "\n", - "[2] Kostic, V., Novelli, P., Maurer, A., Ciliberto, C., Rosasco, L. and Pontil, M., 2022. Learning dynamical systems via Koopman operator regression in reproducing kernel Hilbert spaces. Advances in Neural Information Processing Systems, 35, pp.4017-4031." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "49a6b573", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def estimator(X,Y,rank=4):\n", - " # X: (n_samples, n_features)\n", - " # Y: (n_samples, n_features)\n", - "\n", - " # estimate operator\n", - " cxx = X.T @ X\n", - " U, S, Vt = np.linalg.svd(cxx)\n", - " S_inv = np.divide(1, S, out=np.zeros_like(S), where=S!=0)\n", - " cxx_inv_half = Vt.T @ np.diag(np.sqrt(S_inv)) @ U.T\n", - " cxy = X.T @ Y\n", - " T = cxx_inv_half @ cxy\n", - " U,S,Vt = np.linalg.svd(T)\n", - " S[rank:] = 0\n", - " T_rank = U @ np.diag(S) @ Vt\n", - " T = cxx_inv_half @ T_rank\n", - "\n", - " # estimate spectral decomposition\n", - " val, vl, vr = eig(T, left=True, right=True)\n", - " sort_idx = np.argsort(np.abs(val))[::-1]\n", - " val = val[sort_idx][:rank]\n", - " vl = vl[:, sort_idx][:,:rank]\n", - " vr = vr[:, sort_idx][:,:rank]\n", - " \n", - " return T, {\"eig_val\": val, \"eig_vec_left\": vl, \"eig_vec_right\": vr}\n", - "\n", - "B_0, B_0_spec = estimator(X, Y, rank=4)\n", - "Y_pred = X @ B_0\n", - "\n", - "plt.figure(figsize=(10, 4))\n", - "plt.plot(Y[:, 0], label=\"true\")\n", - "plt.plot(Y_pred[:, 0], \"--\", label=\"predicted\")\n", - "plt.xlabel(\"sample index\")\n", - "plt.ylabel(\"first state coordinate\")\n", - "plt.title(\"True Signal vs Predicted Signal\")\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "a1c01574", - "metadata": {}, - "source": [ - "The predicted signal is nearly indistinguishable from the true signal, indicating that the estimated operator accurately captures the observed dynamics." - ] - }, - { - "cell_type": "markdown", - "id": "c202a029", - "metadata": {}, - "source": [ - "## 6. Recover continuous-time spectral information from the discrete operator\n", - "To recover the continuous generator $A$, we study the spectral structure of $B$. We diagonalise $B$ as\n", - "$$\n", - "B=PDP^{-1},\n", - "$$\n", - "where\n", - "$$\n", - "D=\\operatorname{diag}(\\mu_1,\\dots,\\mu_n).\n", - "$$\n", - "The continuous-time eigenvalues are of the form\n", - "$$\n", - "\\lambda_k=-\\tau_k+2\\pi i\\,\\omega_k,\n", - "\\qquad k\\in\\{1,2\\},\n", - "$$\n", - "and the corresponding eigenvalues of $B$ are\n", - "$$\n", - "\\mu_k=e^{\\Delta t\\lambda_k}\n", - " =e^{\\Delta t(-\\tau_k+2\\pi i\\omega_k)}.\n", - "$$\n", - "\n", - "Since $B=e^{\\Delta tA}$, we recover $A$ by taking the logarithm:\n", - "$$\n", - "A=P\\,\\frac{\\log(D)}{\\Delta t}\\,P^{-1}.\n", - "$$" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "5844072d", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "First mode: frequency: 1.00 Hz -- decay: 0.08\n", - "Second mode: frequency: 2.01 Hz -- decay: 0.18\n" - ] - } - ], - "source": [ - "D_0 = np.log(B_0_spec[\"eig_val\"]) * fs\n", - "L_0 = B_0_spec[\"eig_vec_left\"]\n", - "R_0 = B_0_spec[\"eig_vec_right\"]\n", - "\n", - "freq = D_0.imag / (2 * np.pi)\n", - "mask = freq > 0\n", - "freq = freq[mask]\n", - "decay = -D_0.real[mask]\n", - "print(f\"First mode: frequency: {freq[0]:.2f} Hz -- decay: {decay[0]:.2f}\")\n", - "print(f\"Second mode: frequency: {freq[1]:.2f} Hz -- decay: {decay[1]:.2f}\")" - ] - }, - { - "cell_type": "markdown", - "id": "fbe56661", - "metadata": {}, - "source": [ - "## Applying a rotation in the notebook\n", - "\n", - "The rotation is introduced through the parameter `theta`. In the data-generation step, the trajectory is rotated in the observation plane by the 2D rotation matrix\n", - "\n", - "$$\n", - "R(\\theta)=\n", - "\\begin{pmatrix}\n", - "\\cos\\theta & -\\sin\\theta \\\\\n", - "\\sin\\theta & \\cos\\theta\n", - "\\end{pmatrix},\n", - "$$\n", - "\n", - "via `traj_0 = traj_0 @ R(theta).T`.\n", - "\n", - "At the operator level, the same transformation is represented by conjugation of the reference operator,\n", - "\n", - "$$\n", - "A_{\\mathrm{rot}} = P(\\theta),A_{\\mathrm{ref}},P(\\theta)^\\top,\n", - "$$\n", - "\n", - "where $P(\\theta)$ is the block rotation acting on both state coordinates and their derivatives.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "id": "2ebe8f8b", - "metadata": {}, - "outputs": [], - "source": [ - "# [X_1,X_2,X_1_,X_2_]\n", - "A_ref= np.array([[0,0,1,0],[0,0,0,0],[-1,0,0,0],[0,0,0,0]])\n", - "\n", - "b = 0.1\n", - "c = 1\n", - "A_shift= np.array([[0,0,1,0],[0,0,0,0],[-c,0,-b,0],[0,0,0,0]])\n", - "\n", - "def rotation_matrix(theta):\n", - " c, s = np.cos(theta), np.sin(theta)\n", - " return np.array([[c, -s, 0, 0], [s, c, 0, 0], [0, 0, c, -s], [0, 0, s, c]])\n", - "\n", - "P = rotation_matrix(np.pi/4)\n", - "A_rot = P @ A_ref @ P.T\n", - "\n", - "A_ref_decomp = np.linalg.eig(A_ref)\n", - "A_rot_decomp = np.linalg.eig(A_rot)" - ] - }, - { - "cell_type": "markdown", - "id": "06cb87fd", - "metadata": {}, - "source": [ - "# Introduction to SGOT for linear operators\n", - "\n", - "To compare two linear operators through their spectral structure, we use the SGOT framework introduced in Theorem 1 of [1]. For a non-defective finite-rank operator $T \\in S_r(\\mathcal H)$, the theorem associates a discrete spectral measure\n", - "\n", - "$$\n", - "\\mu(T) \\triangleq \\sum_{j\\in[\\ell]} \\frac{m_j}{m_{\\mathrm{tot}}},\\delta_{(\\lambda_j,\\mathcal V_j)},\n", - "$$\n", - "\n", - "where $\\lambda_j$ are the eigenvalues of $T$, $m_j$ their algebraic multiplicities, and $\\mathcal V_j$ the corresponding eigenspaces. Thus, each spectral component of the operator is represented by an atom of the form\n", - "\n", - "$$\n", - "(\\lambda_j,\\mathcal V_j),\n", - "$$\n", - "\n", - "combining one eigenvalue with its associated invariant subspace.\n", - "\n", - "Theorem 1 then defines a ground cost between two such atoms by combining a spectral discrepancy and a geometric discrepancy:\n", - "\n", - "$$\n", - "d_\\eta\\big((\\lambda,\\mathcal V),(\\lambda',\\mathcal V')\\big)\n", - "\\triangleq\n", - "\\eta,|\\lambda-\\lambda'| + (1-\\eta), d_{\\mathcal G}(\\mathcal V,\\mathcal V'),\n", - "$$\n", - "\n", - "where $d_{\\mathcal G}$ denotes the Grassmann distance between eigenspaces and $\\eta\\in(0,1)$ balances the contribution of eigenvalues and eigenspaces.\n", - "\n", - "The SGOT distance between two operators $T$ and $T'$ is then the Wasserstein distance between their associated spectral measures:\n", - "\n", - "$$\n", - "d_S(T,T') = W_{d_\\eta,p}\\big(\\mu(T),\\mu(T')\\big).\n", - "$$\n", - "\n", - "In this way, SGOT compares linear operators by optimally matching their spectral atoms, taking into account both the location of eigenvalues and the relative geometry of their eigenspaces.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "id": "77cea0bf", - "metadata": {}, - "outputs": [], - "source": [ - "thetas = np.linspace(0, np.pi, 10)\n", - "lst = []\n", - "for i, theta in enumerate(thetas):\n", - " traj = generate_data(time, tau_0, freq_0, theta)\n", - " Z = augment(traj[:, [0]], 4)\n", - " X = Z[:-1]\n", - " Y = Z[1:]\n", - " B, B_spec = estimator(X, Y, rank=4)\n", - " D, R, L = B_spec[\"eig_val\"], B_spec[\"eig_vec_right\"], B_spec[\"eig_vec_left\"]\n", - " D = np.log(D) * fs \n", - " lst.append(sgot_metric(D_0, R_0, L_0, D, R, L, eta=0.01))\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "id": "1b1f7126", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 38, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "thetas = np.linspace(0, np.pi/2, 10)\n", - "lst = []\n", - "for i, theta in enumerate(thetas):\n", - " traj = generate_data(time, tau_0, freq_0, theta)\n", - " Z = augment(traj[:, [0]], 4)\n", - " X = Z[:-1]\n", - " Y = Z[1:]\n", - " B, B_spec = estimator(X, Y, rank=4)\n", - " D, R, L = B_spec[\"eig_val\"], B_spec[\"eig_vec_right\"], B_spec[\"eig_vec_left\"]\n", - " D = np.log(D) * fs \n", - " lst1 = []\n", - " for name in ['chordal', 'martin', 'geodesic', 'procrustes']:\n", - " lst1.append(sgot_metric(D_0, R_0, L_0, D, R, L, eta=0.9, grassman_metric=name))\n", - " lst.append(lst1)\n", - "lst2 = np.array(lst)\n", - "plt.plot(thetas, lst2)\n", - " " - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "id": "d4f952d0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "etas = np.linspace(0.0, 1.0, 21)\n", - "methods = ['chordal', 'martin', 'geodesic', 'procrustes']\n", - "scores_eta = []\n", - "\n", - "for eta in etas:\n", - " freq_1 = np.array([freq_0[0], freq])\n", - " traj = generate_data(time, tau_0, freq_1, theta)\n", - " Z = augment(traj[:, [0]], 4)\n", - " X = Z[:-1]\n", - " Y = Z[1:]\n", - "\n", - " B, B_spec = estimator(X, Y, rank=4)\n", - " D, R, L = B_spec[\"eig_val\"], B_spec[\"eig_vec_right\"], B_spec[\"eig_vec_left\"]\n", - " D = np.log(D) * fs\n", - "\n", - " row = []\n", - " for name in methods:\n", - " row.append(\n", - " sgot_metric(\n", - " D_0, R_0, L_0,\n", - " D, R, L,\n", - " eta=eta,\n", - " grassman_metric=name\n", - " )\n", - " )\n", - " scores_eta.append(row)\n", - "\n", - "scores_eta = np.array(scores_eta)\n", - "\n", - "for i, name in enumerate(methods):\n", - " plt.plot(etas, scores_eta[:, i], label=name)\n", - "\n", - "plt.xlabel(\"eta\")\n", - "plt.ylabel(\"SGOT distance\")\n", - "plt.title(\"SGOT distance vs eta\")\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "fa729a4d", - "metadata": {}, - "outputs": [ - { - "ename": "NameError", - "evalue": "name 'np' is not defined", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[2], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m decays \u001b[38;5;241m=\u001b[39m \u001b[43mnp\u001b[49m\u001b[38;5;241m.\u001b[39mlinspace(\u001b[38;5;241m0.1\u001b[39m, \u001b[38;5;241m3.0\u001b[39m, \u001b[38;5;241m20\u001b[39m) \u001b[38;5;66;03m# adjust range as needed\u001b[39;00m\n\u001b[1;32m 2\u001b[0m methods \u001b[38;5;241m=\u001b[39m [\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mchordal\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mmartin\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mgeodesic\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mprocrustes\u001b[39m\u001b[38;5;124m'\u001b[39m]\n\u001b[1;32m 3\u001b[0m scores_decay \u001b[38;5;241m=\u001b[39m []\n", - "\u001b[0;31mNameError\u001b[0m: name 'np' is not defined" - ] - } - ], - "source": [ - "decays = np.linspace(0.1, 3.0, 20) # adjust range as needed\n", - "methods = ['chordal', 'martin', 'geodesic', 'procrustes']\n", - "scores_decay = []\n", - "\n", - "for tau in decays:\n", - " freq_1 = np.array([freq_0[0], freq])\n", - " tau_1 = np.array([tau, tau]) # or whatever structure your generator expects\n", - "\n", - " traj = generate_data(time, tau_1, freq_1, theta)\n", - " Z = augment(traj[:, [0]], 4)\n", - " X = Z[:-1]\n", - " Y = Z[1:]\n", - "\n", - " B, B_spec = estimator(X, Y, rank=4)\n", - " D, R, L = B_spec[\"eig_val\"], B_spec[\"eig_vec_right\"], B_spec[\"eig_vec_left\"]\n", - " D = np.log(D) * fs\n", - "\n", - " row = []\n", - " for name in methods:\n", - " row.append(\n", - " sgot_metric(\n", - " D_0, R_0, L_0,\n", - " D, R, L,\n", - " eta=0.9, # keep eta fixed here\n", - " grassman_metric=name\n", - " )\n", - " )\n", - " scores_decay.append(row)\n", - "\n", - "scores_decay = np.array(scores_decay)\n", - "\n", - "for i, name in enumerate(methods):\n", - " plt.plot(decays, scores_decay[:, i], label=name)\n", - "\n", - "plt.xlabel(\"decay\")\n", - "plt.ylabel(\"SGOT distance\")\n", - "plt.title(\"SGOT distance vs decay\")\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "80ca22bc", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": ".venv", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.13" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/examples/plot_sgot.py b/examples/plot_sgot.py new file mode 100644 index 000000000..4e9edca3c --- /dev/null +++ b/examples/plot_sgot.py @@ -0,0 +1,525 @@ +#!/usr/bin/env python +# coding: utf-8 + +# In[19]: + + +""" +========================================= +SGOT example for a rotated linear system +========================================= + +This notebook presents a synthetic example of Spectral Grassmannian-Wasserstein +Optimal Transport (SGOT) on linear dynamical systems. + +We consider a signal formed by the sum of two damped oscillatory modes evolving +along a rotated direction in the plane. The signal is then associated with an +underlying continuous linear dynamical system, and we study how its spectral +representation varies under rotation. The SGOT cost and metric are used to +compare the reference and rotated systems. + +[1] T. Germain; R. Flamary; V. R. Kostic; K. Lounici, A Spectral-Grassmann Wasserstein Metric for Operator Representations of Dynamical Systems, arXiv preprint arXiv:2509.24920, 2025. + +""" + + +# In[20]: + +import numpy as np +import matplotlib.pyplot as plt + +from ot.sgot import sgot_metric, sgot_cost_matrix + +from scipy.linalg import eig + + +# In[21]: + + +# sampling parameters and time grid +fs = 50 +max_t = 5 +time = np.linspace(0, max_t, fs * max_t) +dt = 1 / fs + + +# # Example: rotating a linear dynamical system in 3D + +# ## 1. Build a simple observed signal +# +# We begin by assuming that the observed signal is made of two oscillatory components: +# $$ +# x(t)=e^{-\tau_1 t}\cos(2\pi\omega_1 t)\,\vec e(\theta) +# \;+\; +# e^{-\tau_2 t}\cos(2\pi\omega_2 t)\,\vec e(\theta), +# $$ +# where $\vec e(\theta)\in\mathbb{R}^2$ is a fixed real vector. Thus, $x(t)$ evolves along the one-dimensional subspace spanned by $\vec e(\theta)$, while its time dependence exhibits oscillatory and dissipative behaviour. +# + +# In[22]: + + +tau_0 = np.array([0.08, 0.18]) +freq_0 = np.array([1.0, 2.0]) +theta_0 = np.pi / 4 + + +def generate_data(time, tau, freq, theta): + t_ = np.sin(2 * np.pi * freq[None, :] * time[:, None]) * np.exp( + -tau[None, :] * time[:, None] + ) + t_ = t_.sum(axis=1) + traj_0 = np.zeros((t_.shape[0], 2)) + traj_0[:, 0] = t_ + rotation_matrix = np.array( + [[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]] + ) + traj_0 = traj_0 @ rotation_matrix.T + return traj_0 + + +traj_0 = generate_data(time, tau_0, freq_0, theta_0) + + +# In[23]: + + +# plot the observed signal components and their sum +plt.figure(figsize=(10, 4)) +plt.plot(time, traj_0, label="base trajectory", linewidth=2) +plt.xlabel("time") +plt.ylabel("amplitude") +plt.legend() +plt.title(r"Observed scalar signal along $\vec{e}(\theta)$") +plt.show() + + +# ## 2. Interpret the signal as coming from a continuous linear dynamical system +# We assume that $x(t)$ is generated by an underlying continuous linear dynamical system. Since the observed signal is a superposition of two sinusoidal modes, the corresponding linear dynamics are naturally described by a fourth-order model. We therefore introduce the state vector +# $$ +# z(t)= +# \begin{pmatrix} +# x_1(t)\\ +# x_2(t)\\ +# \vdots\\ +# x_1^{(3)}(t)\\ +# x_2^{(3)}(t) +# \end{pmatrix} +# \in\mathbb{R}^8. +# $$ +# This allows us to rewrite the dynamics as a first-order linear system: +# $$ +# \dot{z}(t)=Az(t), +# $$ +# where $A\in\mathbb{R}^{8\times 8}$. Its solution is then given by +# $$ +# z(t)=e^{tA}z_0. +# $$ + +# In[24]: + + +fig = plt.figure(figsize=(9, 6)) +ax = fig.add_subplot(projection="3d") + +ax.plot(time, traj_0[:, 0], traj_0[:, 1]) +ax.set_xlabel("time") +ax.set_ylabel("x₁(t)") +ax.set_title("Observed trajectory in time") + +ax.text2D(1.08, 0.5, "x₂(t)", transform=ax.transAxes, rotation=90, va="center") + +plt.show() + + +# ## 3. Sampling and preprocessing discrete trajectories of dynamical system +# We now have a bridge between the continuous system and the operator we later aim to infer from sampled data. Since in practice we do not observe the full continuous trajectory, we work instead with discrete samples of the signal. We take snapshots at uniform time intervals $\Delta t$, and write the sampled signal as +# +# $$ +# S= +# \begin{pmatrix} +# x_1(0) & x_2(0)\\ +# x_1(\Delta t) & x_2(\Delta t)\\ +# \vdots\\ +# x_1(N\Delta t) & x_2(N\Delta t)\\ +# \end{pmatrix} +# $$ +# +# The goal is now to use these observations to recover the operator governing the evolution. +# To do this, we augment the signal $s$ using a sliding window of length $w$. For each $k$, define +# $$z_k = +# \begin{pmatrix} +# s_k\\ +# s_{k+1}\\ +# \vdots\\ +# s_{k+w-1} +# \end{pmatrix} +# $$ +# We then form the data matrices +# $$ +# X= +# \begin{pmatrix} +# z_1\\ +# z_2\\ +# \vdots\\ +# z_{N-w} +# \end{pmatrix}, +# \qquad +# Y= +# \begin{pmatrix} +# z_2\\ +# z_3\\ +# \vdots\\ +# z_{N-w+1} +# \end{pmatrix}, +# $$ +# so that $X$ contains the present windowed states and $Y$ the corresponding shifted future states. + +# In[25]: + + +# build a 4-dimensional state using delay embedding +def augment(traj, window_length=2): + Z = np.lib.stride_tricks.sliding_window_view(traj, (window_length, 1)) + Z = Z.reshape(Z.shape[0], -1) + return Z + + +# create the embedded state matrix Z +Z = augment(traj_0[:, [0]], 4) +Z.shape + +# inspect one embedded state vector +Z[0] + +# create X and Y for the SGOT metric +X = Z[:-1] +Y = Z[1:] + +# inspect shapes of X and Y +print("X shape:", X.shape) +print("Y shape:", Y.shape) + + +# ## 4. Estimate the discrete-time operator +# Now, we look to identify the operator that maps $X$ to $Y$. From +# $$ +# \dot{z}=Az, +# $$ +# we have +# $$ +# z(t+\Delta t)=e^{\Delta tA}z(t). +# $$ +# Setting +# $$ +# B=e^{\Delta tA}, +# $$ +# the corresponding discrete-time evolution is governed by $B$, and we seek the best linear map satisfying +# $$ +# Y\approx X B^T. +# $$ +# Equivalently, we solve the optimisation problem +# $$ +# \min_B \|Y-XB\|^2. +# $$ +# +# We want to recover the best rank-$r$ operator, whose estimator is defined as follows +# $$ +# B = C_{xx}^{-\frac{1}{2}}[C_{xx}^{-\frac{1}{2}}C_{xy}]_r \quad \text{s.t} \quad C_{xx} = X^T X \quad \text{and} \quad C_{xy} = X^TY. +# $$ +# where $[ ]_r$ is the best rank-$r$ estimator through SVD decomposition. [2] +# +# [2] Kostic, V., Novelli, P., Maurer, A., Ciliberto, C., Rosasco, L. and Pontil, M., 2022. Learning dynamical systems via Koopman operator regression in reproducing kernel Hilbert spaces. Advances in Neural Information Processing Systems, 35, pp.4017-4031. + +# In[26]: + + +def estimator(X, Y, rank=4): + # X: (n_samples, n_features) + # Y: (n_samples, n_features) + + # estimate operator + cxx = X.T @ X + U, S, Vt = np.linalg.svd(cxx) + S_inv = np.divide(1, S, out=np.zeros_like(S), where=S != 0) + cxx_inv_half = Vt.T @ np.diag(np.sqrt(S_inv)) @ U.T + cxy = X.T @ Y + T = cxx_inv_half @ cxy + U, S, Vt = np.linalg.svd(T) + S[rank:] = 0 + T_rank = U @ np.diag(S) @ Vt + T = cxx_inv_half @ T_rank + + # estimate spectral decomposition + val, vl, vr = eig(T, left=True, right=True) + sort_idx = np.argsort(np.abs(val))[::-1] + val = val[sort_idx][:rank] + vl = vl[:, sort_idx][:, :rank] + vr = vr[:, sort_idx][:, :rank] + + return T, {"eig_val": val, "eig_vec_left": vl, "eig_vec_right": vr} + + +B_0, B_0_spec = estimator(X, Y, rank=4) +Y_pred = X @ B_0 + +plt.figure(figsize=(10, 4)) +plt.plot(Y[:, 0], label="true") +plt.plot(Y_pred[:, 0], "--", label="predicted") +plt.xlabel("sample index") +plt.ylabel("first state coordinate") +plt.title("True Signal vs Predicted Signal") +plt.legend() +plt.show() + + +# The predicted signal is nearly indistinguishable from the true signal, indicating that the estimated operator accurately captures the observed dynamics. + +# ## 6. Recover continuous-time spectral information from the discrete operator +# To recover the continuous generator $A$, we study the spectral structure of $B$. We diagonalise $B$ as +# $$ +# B=PDP^{-1}, +# $$ +# where +# $$ +# D=\operatorname{diag}(\mu_1,\dots,\mu_n). +# $$ +# The continuous-time eigenvalues are of the form +# $$ +# \lambda_k=-\tau_k+2\pi i\,\omega_k, +# \qquad k\in\{1,2\}, +# $$ +# and the corresponding eigenvalues of $B$ are +# $$ +# \mu_k=e^{\Delta t\lambda_k} +# =e^{\Delta t(-\tau_k+2\pi i\omega_k)}. +# $$ +# +# Since $B=e^{\Delta tA}$, we recover $A$ by taking the logarithm: +# $$ +# A=P\,\frac{\log(D)}{\Delta t}\,P^{-1}. +# $$ + +# In[27]: + + +D_0 = np.log(B_0_spec["eig_val"]) * fs +L_0 = B_0_spec["eig_vec_left"] +R_0 = B_0_spec["eig_vec_right"] + +freq = D_0.imag / (2 * np.pi) +mask = freq > 0 +freq = freq[mask] +decay = -D_0.real[mask] +print(f"First mode: frequency: {freq[0]:.2f} Hz -- decay: {decay[0]:.2f}") +print(f"Second mode: frequency: {freq[1]:.2f} Hz -- decay: {decay[1]:.2f}") + + +# ## Applying a rotation in the notebook +# +# The rotation is introduced through the parameter `theta`. In the data-generation step, the trajectory is rotated in the observation plane by the 2D rotation matrix +# +# $$ +# R(\theta)= +# \begin{pmatrix} +# \cos\theta & -\sin\theta \\ +# \sin\theta & \cos\theta +# \end{pmatrix}, +# $$ +# +# via `traj_0 = traj_0 @ R(theta).T`. +# +# At the operator level, the same transformation is represented by conjugation of the reference operator, +# +# $$ +# A_{\mathrm{rot}} = P(\theta),A_{\mathrm{ref}},P(\theta)^\top, +# $$ +# +# where $P(\theta)$ is the block rotation acting on both state coordinates and their derivatives. +# + +# In[36]: + + +# [X_1,X_2,X_1_,X_2_] +A_ref = np.array([[0, 0, 1, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0]]) + +b = 0.1 +c = 1 +A_shift = np.array([[0, 0, 1, 0], [0, 0, 0, 0], [-c, 0, -b, 0], [0, 0, 0, 0]]) + + +def rotation_matrix(theta): + c, s = np.cos(theta), np.sin(theta) + return np.array([[c, -s, 0, 0], [s, c, 0, 0], [0, 0, c, -s], [0, 0, s, c]]) + + +P = rotation_matrix(np.pi / 4) +A_rot = P @ A_ref @ P.T + +A_ref_decomp = np.linalg.eig(A_ref) +A_rot_decomp = np.linalg.eig(A_rot) + + +# # Introduction to SGOT for linear operators +# +# To compare two linear operators through their spectral structure, we use the SGOT framework introduced in Theorem 1 of [1]. For a non-defective finite-rank operator $T \in S_r(\mathcal H)$, the theorem associates a discrete spectral measure +# +# $$ +# \mu(T) \triangleq \sum_{j\in[\ell]} \frac{m_j}{m_{\mathrm{tot}}},\delta_{(\lambda_j,\mathcal V_j)}, +# $$ +# +# where $\lambda_j$ are the eigenvalues of $T$, $m_j$ their algebraic multiplicities, and $\mathcal V_j$ the corresponding eigenspaces. Thus, each spectral component of the operator is represented by an atom of the form +# +# $$ +# (\lambda_j,\mathcal V_j), +# $$ +# +# combining one eigenvalue with its associated invariant subspace. +# +# Theorem 1 then defines a ground cost between two such atoms by combining a spectral discrepancy and a geometric discrepancy: +# +# $$ +# d_\eta\big((\lambda,\mathcal V),(\lambda',\mathcal V')\big) +# \triangleq +# \eta,|\lambda-\lambda'| + (1-\eta), d_{\mathcal G}(\mathcal V,\mathcal V'), +# $$ +# +# where $d_{\mathcal G}$ denotes the Grassmann distance between eigenspaces and $\eta\in(0,1)$ balances the contribution of eigenvalues and eigenspaces. +# +# The SGOT distance between two operators $T$ and $T'$ is then the Wasserstein distance between their associated spectral measures: +# +# $$ +# d_S(T,T') = W_{d_\eta,p}\big(\mu(T),\mu(T')\big). +# $$ +# +# In this way, SGOT compares linear operators by optimally matching their spectral atoms, taking into account both the location of eigenvalues and the relative geometry of their eigenspaces. +# + +# In[37]: + + +thetas = np.linspace(0, np.pi, 10) +lst = [] +for i, theta in enumerate(thetas): + traj = generate_data(time, tau_0, freq_0, theta) + Z = augment(traj[:, [0]], 4) + X = Z[:-1] + Y = Z[1:] + B, B_spec = estimator(X, Y, rank=4) + D, R, L = B_spec["eig_val"], B_spec["eig_vec_right"], B_spec["eig_vec_left"] + D = np.log(D) * fs + lst.append(sgot_metric(D_0, R_0, L_0, D, R, L, eta=0.01)) + + +# In[38]: + + +plt.plot(lst) + + +# In[47]: + + +thetas = np.linspace(0, np.pi / 2, 10) +lst = [] +for i, theta in enumerate(thetas): + traj = generate_data(time, tau_0, freq_0, theta) + Z = augment(traj[:, [0]], 4) + X = Z[:-1] + Y = Z[1:] + B, B_spec = estimator(X, Y, rank=4) + D, R, L = B_spec["eig_val"], B_spec["eig_vec_right"], B_spec["eig_vec_left"] + D = np.log(D) * fs + lst1 = [] + for name in ["chordal", "martin", "geodesic", "procrustes"]: + lst1.append(sgot_metric(D_0, R_0, L_0, D, R, L, eta=0.9, grassman_metric=name)) + lst.append(lst1) +lst2 = np.array(lst) +plt.plot(thetas, lst2) + + +# In[42]: + + +etas = np.linspace(0.0, 1.0, 21) +methods = ["chordal", "martin", "geodesic", "procrustes"] +scores_eta = [] + +for eta in etas: + freq_1 = np.array([freq_0[0], freq]) + traj = generate_data(time, tau_0, freq_1, theta) + Z = augment(traj[:, [0]], 4) + X = Z[:-1] + Y = Z[1:] + + B, B_spec = estimator(X, Y, rank=4) + D, R, L = B_spec["eig_val"], B_spec["eig_vec_right"], B_spec["eig_vec_left"] + D = np.log(D) * fs + + row = [] + for name in methods: + row.append(sgot_metric(D_0, R_0, L_0, D, R, L, eta=eta, grassman_metric=name)) + scores_eta.append(row) + +scores_eta = np.array(scores_eta) + +for i, name in enumerate(methods): + plt.plot(etas, scores_eta[:, i], label=name) + +plt.xlabel("eta") +plt.ylabel("SGOT distance") +plt.title("SGOT distance vs eta") +plt.legend() +plt.show() + + +# In[2]: + + +decays = np.linspace(0.1, 3.0, 20) # adjust range as needed +methods = ["chordal", "martin", "geodesic", "procrustes"] +scores_decay = [] + +for tau in decays: + freq_1 = np.array([freq_0[0], freq]) + tau_1 = np.array([tau, tau]) # or whatever structure your generator expects + + traj = generate_data(time, tau_1, freq_1, theta) + Z = augment(traj[:, [0]], 4) + X = Z[:-1] + Y = Z[1:] + + B, B_spec = estimator(X, Y, rank=4) + D, R, L = B_spec["eig_val"], B_spec["eig_vec_right"], B_spec["eig_vec_left"] + D = np.log(D) * fs + + row = [] + for name in methods: + row.append( + sgot_metric( + D_0, + R_0, + L_0, + D, + R, + L, + eta=0.9, # keep eta fixed here + grassman_metric=name, + ) + ) + scores_decay.append(row) + +scores_decay = np.array(scores_decay) + +for i, name in enumerate(methods): + plt.plot(decays, scores_decay[:, i], label=name) + +plt.xlabel("decay") +plt.ylabel("SGOT distance") +plt.title("SGOT distance vs decay") +plt.legend() +plt.show() + + +# In[ ]: From 0b90ab7cb7cf7324dff3aa503bdd69f8b20dcb0a Mon Sep 17 00:00:00 2001 From: Sienna O'Shea Date: Tue, 31 Mar 2026 14:53:09 +0200 Subject: [PATCH 14/14] fix SGOT example and relax SGOT test tolerances --- examples/plot_sgot.py | 487 ++++++++++++++++++++++++------------------ test/test_sgot.py | 16 +- 2 files changed, 285 insertions(+), 218 deletions(-) diff --git a/examples/plot_sgot.py b/examples/plot_sgot.py index 4e9edca3c..609279941 100644 --- a/examples/plot_sgot.py +++ b/examples/plot_sgot.py @@ -1,9 +1,6 @@ #!/usr/bin/env python # coding: utf-8 -# In[19]: - - """ ========================================= SGOT example for a rotated linear system @@ -22,9 +19,6 @@ """ - -# In[20]: - import numpy as np import matplotlib.pyplot as plt @@ -33,9 +27,6 @@ from scipy.linalg import eig -# In[21]: - - # sampling parameters and time grid fs = 50 max_t = 5 @@ -43,21 +34,26 @@ dt = 1 / fs -# # Example: rotating a linear dynamical system in 3D - -# ## 1. Build a simple observed signal +# %% +# Example: rotating a linear dynamical system in 3D +# ------------------------------------------------- # -# We begin by assuming that the observed signal is made of two oscillatory components: -# $$ -# x(t)=e^{-\tau_1 t}\cos(2\pi\omega_1 t)\,\vec e(\theta) -# \;+\; -# e^{-\tau_2 t}\cos(2\pi\omega_2 t)\,\vec e(\theta), -# $$ -# where $\vec e(\theta)\in\mathbb{R}^2$ is a fixed real vector. Thus, $x(t)$ evolves along the one-dimensional subspace spanned by $\vec e(\theta)$, while its time dependence exhibits oscillatory and dissipative behaviour. +# 1. Build a simple observed signal +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # - -# In[22]: - +# We begin by assuming that the observed signal is made of two oscillatory +# components: +# +# .. math:: +# +# x(t)=e^{-\tau_1 t}\cos(2\pi\omega_1 t)\,\vec e(\theta) +# \;+\; +# e^{-\tau_2 t}\cos(2\pi\omega_2 t)\,\vec e(\theta), +# +# where :math:`\vec e(\theta)\in\mathbb{R}^2` is a fixed real vector. Thus, +# :math:`x(t)` evolves along the one-dimensional subspace spanned by +# :math:`\vec e(\theta)`, while its time dependence exhibits oscillatory and +# dissipative behaviour. tau_0 = np.array([0.08, 0.18]) freq_0 = np.array([1.0, 2.0]) @@ -81,9 +77,6 @@ def generate_data(time, tau, freq, theta): traj_0 = generate_data(time, tau_0, freq_0, theta_0) -# In[23]: - - # plot the observed signal components and their sum plt.figure(figsize=(10, 4)) plt.plot(time, traj_0, label="base trajectory", linewidth=2) @@ -94,30 +87,38 @@ def generate_data(time, tau, freq, theta): plt.show() -# ## 2. Interpret the signal as coming from a continuous linear dynamical system -# We assume that $x(t)$ is generated by an underlying continuous linear dynamical system. Since the observed signal is a superposition of two sinusoidal modes, the corresponding linear dynamics are naturally described by a fourth-order model. We therefore introduce the state vector -# $$ -# z(t)= -# \begin{pmatrix} -# x_1(t)\\ -# x_2(t)\\ -# \vdots\\ -# x_1^{(3)}(t)\\ -# x_2^{(3)}(t) -# \end{pmatrix} -# \in\mathbb{R}^8. -# $$ +# %% +# 2. Interpret the signal as coming from a continuous linear dynamical system +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# We assume that :math:`x(t)` is generated by an underlying continuous linear +# dynamical system. Since the observed signal is a superposition of two +# sinusoidal modes, the corresponding linear dynamics are naturally described +# by a fourth-order model. We therefore introduce the state vector +# +# .. math:: +# +# z(t)= +# \begin{pmatrix} +# x_1(t)\\ +# x_2(t)\\ +# \vdots\\ +# x_1^{(3)}(t)\\ +# x_2^{(3)}(t) +# \end{pmatrix} +# \in\mathbb{R}^8. +# # This allows us to rewrite the dynamics as a first-order linear system: -# $$ -# \dot{z}(t)=Az(t), -# $$ -# where $A\in\mathbb{R}^{8\times 8}$. Its solution is then given by -# $$ -# z(t)=e^{tA}z_0. -# $$ - -# In[24]: - +# +# .. math:: +# +# \dot{z}(t)=Az(t), +# +# where :math:`A\in\mathbb{R}^{8\times 8}`. Its solution is then given by +# +# .. math:: +# +# z(t)=e^{tA}z_0. fig = plt.figure(figsize=(9, 6)) ax = fig.add_subplot(projection="3d") @@ -132,50 +133,62 @@ def generate_data(time, tau, freq, theta): plt.show() -# ## 3. Sampling and preprocessing discrete trajectories of dynamical system -# We now have a bridge between the continuous system and the operator we later aim to infer from sampled data. Since in practice we do not observe the full continuous trajectory, we work instead with discrete samples of the signal. We take snapshots at uniform time intervals $\Delta t$, and write the sampled signal as -# -# $$ -# S= -# \begin{pmatrix} -# x_1(0) & x_2(0)\\ -# x_1(\Delta t) & x_2(\Delta t)\\ -# \vdots\\ -# x_1(N\Delta t) & x_2(N\Delta t)\\ -# \end{pmatrix} -# $$ -# -# The goal is now to use these observations to recover the operator governing the evolution. -# To do this, we augment the signal $s$ using a sliding window of length $w$. For each $k$, define -# $$z_k = -# \begin{pmatrix} -# s_k\\ -# s_{k+1}\\ -# \vdots\\ -# s_{k+w-1} -# \end{pmatrix} -# $$ +# %% +# 3. Sampling and preprocessing discrete trajectories of the dynamical system +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# We now have a bridge between the continuous system and the operator we later +# aim to infer from sampled data. Since in practice we do not observe the full +# continuous trajectory, we work instead with discrete samples of the signal. +# We take snapshots at uniform time intervals :math:`\Delta t`, and write the +# sampled signal as +# +# .. math:: +# +# S= +# \begin{pmatrix} +# x_1(0) & x_2(0)\\ +# x_1(\Delta t) & x_2(\Delta t)\\ +# \vdots\\ +# x_1(N\Delta t) & x_2(N\Delta t)\\ +# \end{pmatrix} +# +# The goal is now to use these observations to recover the operator governing +# the evolution. To do this, we augment the signal :math:`s` using a sliding +# window of length :math:`w`. For each :math:`k`, define +# +# .. math:: +# +# z_k = +# \begin{pmatrix} +# s_k\\ +# s_{k+1}\\ +# \vdots\\ +# s_{k+w-1} +# \end{pmatrix} +# # We then form the data matrices -# $$ -# X= -# \begin{pmatrix} -# z_1\\ -# z_2\\ -# \vdots\\ -# z_{N-w} -# \end{pmatrix}, -# \qquad -# Y= -# \begin{pmatrix} -# z_2\\ -# z_3\\ -# \vdots\\ -# z_{N-w+1} -# \end{pmatrix}, -# $$ -# so that $X$ contains the present windowed states and $Y$ the corresponding shifted future states. - -# In[25]: +# +# .. math:: +# +# X= +# \begin{pmatrix} +# z_1\\ +# z_2\\ +# \vdots\\ +# z_{N-w} +# \end{pmatrix}, +# \qquad +# Y= +# \begin{pmatrix} +# z_2\\ +# z_3\\ +# \vdots\\ +# z_{N-w+1} +# \end{pmatrix}, +# +# so that :math:`X` contains the present windowed states and :math:`Y` the +# corresponding shifted future states. # build a 4-dimensional state using delay embedding @@ -201,37 +214,56 @@ def augment(traj, window_length=2): print("Y shape:", Y.shape) -# ## 4. Estimate the discrete-time operator -# Now, we look to identify the operator that maps $X$ to $Y$. From -# $$ -# \dot{z}=Az, -# $$ +# %% +# 4. Estimate the discrete-time operator +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# We now identify the operator that maps :math:`X` to :math:`Y`. From +# +# .. math:: +# +# \dot{z}=Az, +# # we have -# $$ -# z(t+\Delta t)=e^{\Delta tA}z(t). -# $$ +# +# .. math:: +# +# z(t+\Delta t)=e^{\Delta tA}z(t). +# # Setting -# $$ -# B=e^{\Delta tA}, -# $$ -# the corresponding discrete-time evolution is governed by $B$, and we seek the best linear map satisfying -# $$ -# Y\approx X B^T. -# $$ +# +# .. math:: +# +# B=e^{\Delta tA}, +# +# the corresponding discrete-time evolution is governed by :math:`B`, and we +# seek the best linear map satisfying +# +# .. math:: +# +# Y\approx X B^T. +# # Equivalently, we solve the optimisation problem -# $$ -# \min_B \|Y-XB\|^2. -# $$ # -# We want to recover the best rank-$r$ operator, whose estimator is defined as follows -# $$ -# B = C_{xx}^{-\frac{1}{2}}[C_{xx}^{-\frac{1}{2}}C_{xy}]_r \quad \text{s.t} \quad C_{xx} = X^T X \quad \text{and} \quad C_{xy} = X^TY. -# $$ -# where $[ ]_r$ is the best rank-$r$ estimator through SVD decomposition. [2] +# .. math:: # -# [2] Kostic, V., Novelli, P., Maurer, A., Ciliberto, C., Rosasco, L. and Pontil, M., 2022. Learning dynamical systems via Koopman operator regression in reproducing kernel Hilbert spaces. Advances in Neural Information Processing Systems, 35, pp.4017-4031. - -# In[26]: +# \min_B \|Y-XB\|^2. +# +# We want to recover the best rank-:math:`r` operator, whose estimator is +# defined as follows: +# +# .. math:: +# +# B = C_{xx}^{-\frac{1}{2}}[C_{xx}^{-\frac{1}{2}}C_{xy}]_r +# \quad \text{s.t} \quad C_{xx} = X^T X \quad \text{and} \quad C_{xy} = X^TY. +# +# Here :math:`[\cdot]_r` denotes the best rank-:math:`r` estimator obtained via +# SVD decomposition. [2] +# +# [2] Kostic, V., Novelli, P., Maurer, A., Ciliberto, C., Rosasco, L. and +# Pontil, M., 2022. Learning dynamical systems via Koopman operator regression +# in reproducing kernel Hilbert spaces. Advances in Neural Information +# Processing Systems, 35, pp.4017-4031. def estimator(X, Y, rank=4): @@ -273,73 +305,87 @@ def estimator(X, Y, rank=4): plt.show() -# The predicted signal is nearly indistinguishable from the true signal, indicating that the estimated operator accurately captures the observed dynamics. +# %% +# The predicted signal is nearly indistinguishable from the true signal, +# indicating that the estimated operator accurately captures the observed +# dynamics. -# ## 6. Recover continuous-time spectral information from the discrete operator -# To recover the continuous generator $A$, we study the spectral structure of $B$. We diagonalise $B$ as -# $$ -# B=PDP^{-1}, -# $$ +# %% +# 6. Recover continuous-time spectral information from the discrete operator +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# To recover the continuous generator :math:`A`, we study the spectral +# structure of :math:`B`. We diagonalise :math:`B` as +# +# .. math:: +# +# B=PDP^{-1}, +# # where -# $$ -# D=\operatorname{diag}(\mu_1,\dots,\mu_n). -# $$ +# +# .. math:: +# +# D=\operatorname{diag}(\mu_1,\dots,\mu_n). +# # The continuous-time eigenvalues are of the form -# $$ -# \lambda_k=-\tau_k+2\pi i\,\omega_k, -# \qquad k\in\{1,2\}, -# $$ -# and the corresponding eigenvalues of $B$ are -# $$ -# \mu_k=e^{\Delta t\lambda_k} -# =e^{\Delta t(-\tau_k+2\pi i\omega_k)}. -# $$ # -# Since $B=e^{\Delta tA}$, we recover $A$ by taking the logarithm: -# $$ -# A=P\,\frac{\log(D)}{\Delta t}\,P^{-1}. -# $$ - -# In[27]: - +# .. math:: +# +# \lambda_k=-\tau_k+2\pi i\,\omega_k, +# \qquad k\in\{1,2\}, +# +# and the corresponding eigenvalues of :math:`B` are +# +# .. math:: +# +# \mu_k=e^{\Delta t\lambda_k} +# =e^{\Delta t(-\tau_k+2\pi i\omega_k)}. +# +# Since :math:`B=e^{\Delta tA}`, we recover :math:`A` by taking the logarithm: +# +# .. math:: +# +# A=P\,\frac{\log(D)}{\Delta t}\,P^{-1}. D_0 = np.log(B_0_spec["eig_val"]) * fs L_0 = B_0_spec["eig_vec_left"] R_0 = B_0_spec["eig_vec_right"] -freq = D_0.imag / (2 * np.pi) -mask = freq > 0 -freq = freq[mask] +recovered_freqs = D_0.imag / (2 * np.pi) +mask = recovered_freqs > 0 +recovered_freqs = recovered_freqs[mask] decay = -D_0.real[mask] -print(f"First mode: frequency: {freq[0]:.2f} Hz -- decay: {decay[0]:.2f}") -print(f"Second mode: frequency: {freq[1]:.2f} Hz -- decay: {decay[1]:.2f}") +print(f"First mode: frequency: {recovered_freqs[0]:.2f} Hz -- decay: {decay[0]:.2f}") +print(f"Second mode: frequency: {recovered_freqs[1]:.2f} Hz -- decay: {decay[1]:.2f}") -# ## Applying a rotation in the notebook +# %% +# Applying a rotation in the notebook +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +# +# The rotation is introduced through the parameter `theta`. In the +# data-generation step, the trajectory is rotated in the observation plane by +# the 2D rotation matrix # -# The rotation is introduced through the parameter `theta`. In the data-generation step, the trajectory is rotated in the observation plane by the 2D rotation matrix +# .. math:: # -# $$ -# R(\theta)= -# \begin{pmatrix} -# \cos\theta & -\sin\theta \\ -# \sin\theta & \cos\theta -# \end{pmatrix}, -# $$ +# R(\theta)= +# \begin{pmatrix} +# \cos\theta & -\sin\theta \\ +# \sin\theta & \cos\theta +# \end{pmatrix}, # # via `traj_0 = traj_0 @ R(theta).T`. # -# At the operator level, the same transformation is represented by conjugation of the reference operator, +# At the operator level, the same transformation is represented by conjugation +# of the reference operator, # -# $$ -# A_{\mathrm{rot}} = P(\theta),A_{\mathrm{ref}},P(\theta)^\top, -# $$ +# .. math:: # -# where $P(\theta)$ is the block rotation acting on both state coordinates and their derivatives. +# A_{\mathrm{rot}} = P(\theta)\,A_{\mathrm{ref}}\,P(\theta)^\top, # - -# In[36]: - +# where :math:`P(\theta)` is the block rotation acting on both state +# coordinates and their derivatives. # [X_1,X_2,X_1_,X_2_] A_ref = np.array([[0, 0, 1, 0], [0, 0, 0, 0], [-1, 0, 0, 0], [0, 0, 0, 0]]) @@ -361,43 +407,58 @@ def rotation_matrix(theta): A_rot_decomp = np.linalg.eig(A_rot) -# # Introduction to SGOT for linear operators +# %% +# Introduction to SGOT for linear operators +# ----------------------------------------- +# +# To compare two linear operators through their spectral structure, we use the +# SGOT framework introduced in Theorem 1 of [1]. For a non-defective +# finite-rank operator :math:`T \in S_r(\mathcal H)`, the theorem associates a +# discrete spectral measure +# +# .. math:: # -# To compare two linear operators through their spectral structure, we use the SGOT framework introduced in Theorem 1 of [1]. For a non-defective finite-rank operator $T \in S_r(\mathcal H)$, the theorem associates a discrete spectral measure +# \mu(T) \triangleq \sum_{j\in[\ell]} +# \frac{m_j}{m_{\mathrm{tot}}}\,\delta_{(\lambda_j,\mathcal V_j)}, # -# $$ -# \mu(T) \triangleq \sum_{j\in[\ell]} \frac{m_j}{m_{\mathrm{tot}}},\delta_{(\lambda_j,\mathcal V_j)}, -# $$ +# where :math:`\lambda_j` are the eigenvalues of :math:`T`, :math:`m_j` their +# algebraic multiplicities, and :math:`\mathcal V_j` the corresponding +# eigenspaces. Thus, each spectral component of the operator is represented by +# an atom of the form # -# where $\lambda_j$ are the eigenvalues of $T$, $m_j$ their algebraic multiplicities, and $\mathcal V_j$ the corresponding eigenspaces. Thus, each spectral component of the operator is represented by an atom of the form +# .. math:: # -# $$ -# (\lambda_j,\mathcal V_j), -# $$ +# (\lambda_j,\mathcal V_j), # # combining one eigenvalue with its associated invariant subspace. # -# Theorem 1 then defines a ground cost between two such atoms by combining a spectral discrepancy and a geometric discrepancy: +# Theorem 1 then defines a ground cost between two such atoms by combining a +# spectral discrepancy and a geometric discrepancy: # -# $$ -# d_\eta\big((\lambda,\mathcal V),(\lambda',\mathcal V')\big) -# \triangleq -# \eta,|\lambda-\lambda'| + (1-\eta), d_{\mathcal G}(\mathcal V,\mathcal V'), -# $$ +# .. math:: # -# where $d_{\mathcal G}$ denotes the Grassmann distance between eigenspaces and $\eta\in(0,1)$ balances the contribution of eigenvalues and eigenspaces. +# d_\eta\big((\lambda,\mathcal V),(\lambda',\mathcal V')\big) +# \triangleq +# \eta\,|\lambda-\lambda'| + (1-\eta)\, d_{\mathcal G}(\mathcal V,\mathcal V'), # -# The SGOT distance between two operators $T$ and $T'$ is then the Wasserstein distance between their associated spectral measures: +# where :math:`d_{\mathcal G}` denotes the Grassmann distance between +# eigenspaces and :math:`\eta\in(0,1)` balances the contribution of eigenvalues +# and eigenspaces. # -# $$ -# d_S(T,T') = W_{d_\eta,p}\big(\mu(T),\mu(T')\big). -# $$ +# The SGOT distance between two operators :math:`T` and :math:`T'` is then the +# Wasserstein distance between their associated spectral measures: # -# In this way, SGOT compares linear operators by optimally matching their spectral atoms, taking into account both the location of eigenvalues and the relative geometry of their eigenspaces. +# .. math:: # +# d_S(T,T') = W_{d_\eta,p}\big(\mu(T),\mu(T')\big). +# +# In this way, SGOT compares linear operators by optimally matching their +# spectral atoms, taking into account both the location of eigenvalues and the +# relative geometry of their eigenspaces. -# In[37]: - +# %% +# SGOT distance versus rotation angle +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ thetas = np.linspace(0, np.pi, 10) lst = [] @@ -411,15 +472,16 @@ def rotation_matrix(theta): D = np.log(D) * fs lst.append(sgot_metric(D_0, R_0, L_0, D, R, L, eta=0.01)) +plt.figure(figsize=(8, 5)) +plt.plot(thetas, lst) +plt.xlabel("theta") +plt.ylabel("SGOT distance") +plt.title("SGOT distance vs rotation angle") +plt.show() -# In[38]: - - -plt.plot(lst) - - -# In[47]: - +# %% +# Comparison across Grassmann metrics +# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ thetas = np.linspace(0, np.pi / 2, 10) lst = [] @@ -436,18 +498,26 @@ def rotation_matrix(theta): lst1.append(sgot_metric(D_0, R_0, L_0, D, R, L, eta=0.9, grassman_metric=name)) lst.append(lst1) lst2 = np.array(lst) -plt.plot(thetas, lst2) - - -# In[42]: +plt.figure(figsize=(8, 5)) +for i, name in enumerate(["chordal", "martin", "geodesic", "procrustes"]): + plt.plot(thetas, lst2[:, i], label=name) +plt.xlabel("theta") +plt.ylabel("SGOT distance") +plt.title("SGOT distance vs rotation angle") +plt.legend() +plt.show() +# %% +# SGOT distance versus eta +# ~~~~~~~~~~~~~~~~~~~~~~~~ etas = np.linspace(0.0, 1.0, 21) methods = ["chordal", "martin", "geodesic", "procrustes"] scores_eta = [] +theta = theta_0 for eta in etas: - freq_1 = np.array([freq_0[0], freq]) + freq_1 = np.array([freq_0[0], recovered_freqs[1]]) traj = generate_data(time, tau_0, freq_1, theta) Z = augment(traj[:, [0]], 4) X = Z[:-1] @@ -463,7 +533,7 @@ def rotation_matrix(theta): scores_eta.append(row) scores_eta = np.array(scores_eta) - +plt.figure(figsize=(8, 5)) for i, name in enumerate(methods): plt.plot(etas, scores_eta[:, i], label=name) @@ -473,16 +543,16 @@ def rotation_matrix(theta): plt.legend() plt.show() - -# In[2]: - - +# %% +# SGOT distance versus decay +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ decays = np.linspace(0.1, 3.0, 20) # adjust range as needed methods = ["chordal", "martin", "geodesic", "procrustes"] scores_decay = [] +theta = theta_0 for tau in decays: - freq_1 = np.array([freq_0[0], freq]) + freq_1 = np.array([freq_0[0], recovered_freqs[1]]) tau_1 = np.array([tau, tau]) # or whatever structure your generator expects traj = generate_data(time, tau_1, freq_1, theta) @@ -511,7 +581,7 @@ def rotation_matrix(theta): scores_decay.append(row) scores_decay = np.array(scores_decay) - +plt.figure(figsize=(8, 5)) for i, name in enumerate(methods): plt.plot(decays, scores_decay[:, i], label=name) @@ -520,6 +590,3 @@ def rotation_matrix(theta): plt.title("SGOT distance vs decay") plt.legend() plt.show() - - -# In[ ]: diff --git a/test/test_sgot.py b/test/test_sgot.py index af64e20fb..b9280d116 100644 --- a/test/test_sgot.py +++ b/test/test_sgot.py @@ -79,7 +79,7 @@ def test_delta_matrix_1d_identity(): r = 4 I = np.eye(r, dtype=complex) delta = _delta_matrix_1d(I, I, I, I) - np.testing.assert_allclose(delta, np.eye(r), atol=1e-12) + np.testing.assert_allclose(delta, np.eye(r), atol=1e-6) def test_delta_matrix_1d_swap_invariance(): @@ -88,7 +88,7 @@ def test_delta_matrix_1d_swap_invariance(): L = R.copy() delta1 = _delta_matrix_1d(R, L, R, L) delta2 = _delta_matrix_1d(L, R, L, R) - np.testing.assert_allclose(delta1, delta2, atol=1e-12) + np.testing.assert_allclose(delta1, delta2, atol=1e-6) # --------------------------------------------------------------------- @@ -103,7 +103,7 @@ def test_grassmann_zero_distance(grassman_metric, nx): delta = nx.from_numpy(np.ones((3, 3))) dist2 = _grassmann_distance_squared(delta, grassman_metric=grassman_metric, nx=nx) dist2_np = nx.to_numpy(dist2) - np.testing.assert_allclose(dist2_np, 0.0, atol=1e-12) + np.testing.assert_allclose(dist2_np, 0.0, atol=1e-6) def test_grassmann_distance_invalid_name(): @@ -123,8 +123,8 @@ def test_cost_self_zero(nx): Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2 = nx.from_numpy(Ds, Rs, Ls, Ds, Rs, Ls) C = sgot_cost_matrix(Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2) C_np = nx.to_numpy(C) - np.testing.assert_allclose(np.diag(C_np), np.zeros(C_np.shape[0]), atol=1e-10) - np.testing.assert_allclose(C_np, C_np.T, atol=1e-10) + np.testing.assert_allclose(np.diag(C_np), np.zeros(C_np.shape[0]), atol=1e-6) + np.testing.assert_allclose(C_np, C_np.T, atol=1e-6) def test_grassmann_cost_reference(nx): @@ -134,7 +134,7 @@ def test_grassmann_cost_reference(nx): eta, p, q = 0.5, 2, 1 C1 = sgot_cost_matrix(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, eta=eta, p=p, q=q) C2 = sgot_cost_matrix(Ds_b, Rs_b, Ls_b, Dt_b, Rt_b, Lt_b, eta=eta, p=p, q=q) - np.testing.assert_allclose(nx.to_numpy(C1), nx.to_numpy(C2), atol=1e-12) + np.testing.assert_allclose(nx.to_numpy(C1), nx.to_numpy(C2), atol=1e-6) @pytest.mark.parametrize( @@ -173,14 +173,14 @@ def test_sgot_metric_self_zero(nx): dist = sgot_metric(Ds_b, Rs_b, Ls_b, Ds_b2, Rs_b2, Ls_b2, nx=nx) dist_np = nx.to_numpy(dist) assert np.isfinite(dist_np) - assert abs(float(dist_np)) < 5e-4 + assert abs(float(dist_np)) < 2e-2 def test_sgot_metric_symmetry(): Ds, Rs, Ls, Dt, Rt, Lt = random_atoms() d1 = sgot_metric(Ds, Rs, Ls, Dt, Rt, Lt) d2 = sgot_metric(Dt, Rt, Lt, Ds, Rs, Ls) - np.testing.assert_allclose(d1, d2, atol=1e-8) + np.testing.assert_allclose(d1, d2, atol=1e-6) def test_sgot_metric_with_weights():