Project a symmetric matrix onto the space of symmetric matrices with eigenvalues larger or equal to `vmin`. Parameters ---------- S : array_like (n, d, d) or (d, d) The input symmetric matrix or matrices. nx : module, optional The numerical backend module to
(S, nx=None, vmin=0.0)
| 1386 | |
| 1387 | |
| 1388 | def proj_SDP(S, nx=None, vmin=0.0): |
| 1389 | """ |
| 1390 | Project a symmetric matrix onto the space of symmetric matrices with |
| 1391 | eigenvalues larger or equal to `vmin`. |
| 1392 | |
| 1393 | Parameters |
| 1394 | ---------- |
| 1395 | S : array_like (n, d, d) or (d, d) |
| 1396 | The input symmetric matrix or matrices. |
| 1397 | nx : module, optional |
| 1398 | The numerical backend module to use. If not provided, the backend will |
| 1399 | be fetched from the input matrix `S`. |
| 1400 | vmin : float, optional |
| 1401 | The minimum value for the eigenvalues. Eigenvalues below this value will |
| 1402 | be clipped to vmin. |
| 1403 | |
| 1404 | .. note:: This function is backend-compatible and will work on arrays |
| 1405 | from all compatible backends. |
| 1406 | |
| 1407 | Returns |
| 1408 | ------- |
| 1409 | P : ndarray (n, d, d) or (d, d) |
| 1410 | The projected symmetric positive definite matrix. |
| 1411 | |
| 1412 | """ |
| 1413 | if nx is None: |
| 1414 | nx = get_backend(S) |
| 1415 | |
| 1416 | w, P = nx.eigh(S) |
| 1417 | w = nx.clip(w, vmin, None) |
| 1418 | |
| 1419 | if len(S.shape) == 2: # input was (d, d) |
| 1420 | return P @ nx.diag(w) @ P.T |
| 1421 | |
| 1422 | else: # input was (n, d, d): broadcasting |
| 1423 | Q = nx.einsum("ijk,ik->ijk", P, w) # Q[i] = P[i] @ diag(w[i]) |
| 1424 | # R[i] = Q[i] @ P[i].T |
| 1425 | return nx.einsum("ijk,ikl->ijl", Q, nx.transpose(P, (0, 2, 1))) |
| 1426 | |
| 1427 | |
| 1428 | def exp_bures(Sigma, S, nx=None): |
no test coverage detected