Solve the equation ``a x = b`` for ``x``. By default, use LU decomposition and forward / backward substitutions. When ``assume_a = "pos"`` use Cholesky decomposition. Parameters ---------- a : (M, M) array_like A square matrix. b : (M,) or (M, N) array_like
(a, b, sym_pos=None, assume_a="gen")
| 1200 | |
| 1201 | |
| 1202 | def solve(a, b, sym_pos=None, assume_a="gen"): |
| 1203 | """ |
| 1204 | Solve the equation ``a x = b`` for ``x``. By default, use LU |
| 1205 | decomposition and forward / backward substitutions. When ``assume_a = "pos"`` |
| 1206 | use Cholesky decomposition. |
| 1207 | |
| 1208 | Parameters |
| 1209 | ---------- |
| 1210 | a : (M, M) array_like |
| 1211 | A square matrix. |
| 1212 | b : (M,) or (M, N) array_like |
| 1213 | Right-hand side matrix in ``a x = b``. |
| 1214 | sym_pos : bool, optional |
| 1215 | Assume a is symmetric and positive definite. If ``True``, use Cholesky |
| 1216 | decomposition. |
| 1217 | |
| 1218 | .. note:: |
| 1219 | ``sym_pos`` is deprecated and will be removed in a future version. |
| 1220 | Use ``assume_a = 'pos'`` instead. |
| 1221 | |
| 1222 | assume_a : {'gen', 'pos'}, optional |
| 1223 | Type of data matrix. It is used to choose the dedicated solver. |
| 1224 | Note that Dask does not support 'her' and 'sym' types. |
| 1225 | |
| 1226 | .. versionchanged:: 2022.8.0 |
| 1227 | ``assume_a = 'pos'`` was previously defined as ``sym_pos = True``. |
| 1228 | |
| 1229 | Returns |
| 1230 | ------- |
| 1231 | x : (M,) or (M, N) Array |
| 1232 | Solution to the system ``a x = b``. Shape of the return matches the |
| 1233 | shape of `b`. |
| 1234 | |
| 1235 | See Also |
| 1236 | -------- |
| 1237 | scipy.linalg.solve |
| 1238 | """ |
| 1239 | if sym_pos is not None: |
| 1240 | warnings.warn( |
| 1241 | "The sym_pos keyword is deprecated and should be replaced by using ``assume_a = 'pos'``." |
| 1242 | "``sym_pos`` will be removed in a future version.", |
| 1243 | category=FutureWarning, |
| 1244 | ) |
| 1245 | if sym_pos: |
| 1246 | assume_a = "pos" |
| 1247 | |
| 1248 | if assume_a == "pos": |
| 1249 | l, u = _cholesky(a) |
| 1250 | elif assume_a == "gen": |
| 1251 | p, l, u = lu(a) |
| 1252 | b = p.T.dot(b) |
| 1253 | else: |
| 1254 | raise ValueError( |
| 1255 | f"{assume_a = } is not a recognized matrix structure, " |
| 1256 | "valid structures in Dask are 'pos' and 'gen'." |
| 1257 | ) |
| 1258 | |
| 1259 | uy = solve_triangular(l, b, lower=True) |
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