File size: 25,748 Bytes
712dbf0 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 |
// Copyright © 2023-2024 Apple Inc.
#include <variant>
#include <nanobind/nanobind.h>
#include <nanobind/stl/pair.h>
#include <nanobind/stl/string.h>
#include <nanobind/stl/variant.h>
#include <nanobind/stl/vector.h>
#include "mlx/linalg.h"
#include "python/src/small_vector.h"
namespace mx = mlx::core;
namespace nb = nanobind;
using namespace nb::literals;
void init_linalg(nb::module_& parent_module) {
auto m = parent_module.def_submodule(
"linalg", "mlx.core.linalg: linear algebra routines.");
m.def(
"norm",
[](const mx::array& a,
const std::variant<std::monostate, int, double, std::string>& ord_,
const std::variant<std::monostate, int, std::vector<int>>& axis_,
const bool keepdims,
const mx::StreamOrDevice stream) {
std::optional<std::vector<int>> axis = std::nullopt;
if (auto pv = std::get_if<int>(&axis_); pv) {
axis = std::vector<int>{*pv};
} else if (auto pv = std::get_if<std::vector<int>>(&axis_); pv) {
axis = *pv;
}
if (std::holds_alternative<std::monostate>(ord_)) {
return mx::linalg::norm(a, axis, keepdims, stream);
} else {
if (auto pv = std::get_if<std::string>(&ord_); pv) {
return mx::linalg::norm(a, *pv, axis, keepdims, stream);
}
double ord;
if (auto pv = std::get_if<int>(&ord_); pv) {
ord = *pv;
} else {
ord = std::get<double>(ord_);
}
return mx::linalg::norm(a, ord, axis, keepdims, stream);
}
},
nb::arg(),
"ord"_a = nb::none(),
"axis"_a = nb::none(),
"keepdims"_a = false,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def norm(a: array, /, ord: Union[None, int, float, str] = None, axis: Union[None, int, list[int]] = None, keepdims: bool = False, *, stream: Union[None, Stream, Device] = None) -> array"),
R"pbdoc(
Matrix or vector norm.
This function computes vector or matrix norms depending on the value of
the ``ord`` and ``axis`` parameters.
Args:
a (array): Input array. If ``axis`` is ``None``, ``a`` must be 1-D or 2-D,
unless ``ord`` is ``None``. If both ``axis`` and ``ord`` are ``None``, the
2-norm of ``a.flatten`` will be returned.
ord (int, float or str, optional): Order of the norm (see table under ``Notes``).
If ``None``, the 2-norm (or Frobenius norm for matrices) will be computed
along the given ``axis``. Default: ``None``.
axis (int or list(int), optional): If ``axis`` is an integer, it specifies the
axis of ``a`` along which to compute the vector norms. If ``axis`` is a
2-tuple, it specifies the axes that hold 2-D matrices, and the matrix
norms of these matrices are computed. If `axis` is ``None`` then
either a vector norm (when ``a`` is 1-D) or a matrix norm (when ``a`` is
2-D) is returned. Default: ``None``.
keepdims (bool, optional): If ``True``, the axes which are normed over are
left in the result as dimensions with size one. Default ``False``.
Returns:
array: The output containing the norm(s).
Notes:
For values of ``ord < 1``, the result is, strictly speaking, not a
mathematical norm, but it may still be useful for various numerical
purposes.
The following norms can be calculated:
===== ============================ ==========================
ord norm for matrices norm for vectors
===== ============================ ==========================
None Frobenius norm 2-norm
'fro' Frobenius norm --
'nuc' nuclear norm --
inf max(sum(abs(x), axis=1)) max(abs(x))
-inf min(sum(abs(x), axis=1)) min(abs(x))
0 -- sum(x != 0)
1 max(sum(abs(x), axis=0)) as below
-1 min(sum(abs(x), axis=0)) as below
2 2-norm (largest sing. value) as below
-2 smallest singular value as below
other -- sum(abs(x)**ord)**(1./ord)
===== ============================ ==========================
The Frobenius norm is given by [1]_:
:math:`||A||_F = [\sum_{i,j} abs(a_{i,j})^2]^{1/2}`
The nuclear norm is the sum of the singular values.
Both the Frobenius and nuclear norm orders are only defined for
matrices and raise a ``ValueError`` when ``a.ndim != 2``.
References:
.. [1] G. H. Golub and C. F. Van Loan, *Matrix Computations*,
Baltimore, MD, Johns Hopkins University Press, 1985, pg. 15
Examples:
>>> import mlx.core as mx
>>> from mlx.core import linalg as la
>>> a = mx.arange(9) - 4
>>> a
array([-4, -3, -2, ..., 2, 3, 4], dtype=int32)
>>> b = a.reshape((3,3))
>>> b
array([[-4, -3, -2],
[-1, 0, 1],
[ 2, 3, 4]], dtype=int32)
>>> la.norm(a)
array(7.74597, dtype=float32)
>>> la.norm(b)
array(7.74597, dtype=float32)
>>> la.norm(b, 'fro')
array(7.74597, dtype=float32)
>>> la.norm(a, float("inf"))
array(4, dtype=float32)
>>> la.norm(b, float("inf"))
array(9, dtype=float32)
>>> la.norm(a, -float("inf"))
array(0, dtype=float32)
>>> la.norm(b, -float("inf"))
array(2, dtype=float32)
>>> la.norm(a, 1)
array(20, dtype=float32)
>>> la.norm(b, 1)
array(7, dtype=float32)
>>> la.norm(a, -1)
array(0, dtype=float32)
>>> la.norm(b, -1)
array(6, dtype=float32)
>>> la.norm(a, 2)
array(7.74597, dtype=float32)
>>> la.norm(a, 3)
array(5.84804, dtype=float32)
>>> la.norm(a, -3)
array(0, dtype=float32)
>>> c = mx.array([[ 1, 2, 3],
... [-1, 1, 4]])
>>> la.norm(c, axis=0)
array([1.41421, 2.23607, 5], dtype=float32)
>>> la.norm(c, axis=1)
array([3.74166, 4.24264], dtype=float32)
>>> la.norm(c, ord=1, axis=1)
array([6, 6], dtype=float32)
>>> m = mx.arange(8).reshape(2,2,2)
>>> la.norm(m, axis=(1,2))
array([3.74166, 11.225], dtype=float32)
>>> la.norm(m[0, :, :]), LA.norm(m[1, :, :])
(array(3.74166, dtype=float32), array(11.225, dtype=float32))
)pbdoc");
m.def(
"qr",
&mx::linalg::qr,
"a"_a,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def qr(a: array, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array]"),
R"pbdoc(
The QR factorization of the input matrix.
This function supports arrays with at least 2 dimensions. The matrices
which are factorized are assumed to be in the last two dimensions of
the input.
Args:
a (array): Input array.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
tuple(array, array): ``Q`` and ``R`` matrices such that ``Q @ R = a``.
Example:
>>> A = mx.array([[2., 3.], [1., 2.]])
>>> Q, R = mx.linalg.qr(A, stream=mx.cpu)
>>> Q
array([[-0.894427, -0.447214],
[-0.447214, 0.894427]], dtype=float32)
>>> R
array([[-2.23607, -3.57771],
[0, 0.447214]], dtype=float32)
)pbdoc");
m.def(
"svd",
[](const mx::array& a,
bool compute_uv /* = true */,
mx::StreamOrDevice s /* = {} */) -> nb::object {
const auto result = mx::linalg::svd(a, compute_uv, s);
if (result.size() == 1) {
return nb::cast(result.at(0));
} else {
return nb::make_tuple(result.at(0), result.at(1), result.at(2));
}
},
"a"_a,
"compute_uv"_a = true,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def svd(a: array, compute_uv: bool = True, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array, array]"),
R"pbdoc(
The Singular Value Decomposition (SVD) of the input matrix.
This function supports arrays with at least 2 dimensions. When the input
has more than two dimensions, the function iterates over all indices of the first
a.ndim - 2 dimensions and for each combination SVD is applied to the last two indices.
Args:
a (array): Input array.
compute_uv (bool, optional): If ``True``, return the ``U``, ``S``, and ``Vt`` components.
If ``False``, return only the ``S`` array. Default: ``True``.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
Union[tuple(array, ...), array]:
If compute_uv is ``True`` returns the ``U``, ``S``, and ``Vt`` matrices, such that
``A = U @ diag(S) @ Vt``. If compute_uv is ``False`` returns singular values array ``S``.
)pbdoc");
m.def(
"inv",
&mx::linalg::inv,
"a"_a,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def inv(a: array, *, stream: Union[None, Stream, Device] = None) -> array"),
R"pbdoc(
Compute the inverse of a square matrix.
This function supports arrays with at least 2 dimensions. When the input
has more than two dimensions, the inverse is computed for each matrix
in the last two dimensions of ``a``.
Args:
a (array): Input array.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: ``ainv`` such that ``dot(a, ainv) = dot(ainv, a) = eye(a.shape[0])``
)pbdoc");
m.def(
"tri_inv",
&mx::linalg::tri_inv,
"a"_a,
"upper"_a = false,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def tri_inv(a: array, upper: bool = False, *, stream: Union[None, Stream, Device] = None) -> array"),
R"pbdoc(
Compute the inverse of a triangular square matrix.
This function supports arrays with at least 2 dimensions. When the input
has more than two dimensions, the inverse is computed for each matrix
in the last two dimensions of ``a``.
Args:
a (array): Input array.
upper (bool, optional): Whether the array is upper or lower triangular. Defaults to ``False``.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: ``ainv`` such that ``dot(a, ainv) = dot(ainv, a) = eye(a.shape[0])``
)pbdoc");
m.def(
"cholesky",
&mx::linalg::cholesky,
"a"_a,
"upper"_a = false,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def cholesky(a: array, upper: bool = False, *, stream: Union[None, Stream, Device] = None) -> array"),
R"pbdoc(
Compute the Cholesky decomposition of a real symmetric positive semi-definite matrix.
This function supports arrays with at least 2 dimensions. When the input
has more than two dimensions, the Cholesky decomposition is computed for each matrix
in the last two dimensions of ``a``.
If the input matrix is not symmetric positive semi-definite, behaviour is undefined.
Args:
a (array): Input array.
upper (bool, optional): If ``True``, return the upper triangular Cholesky factor.
If ``False``, return the lower triangular Cholesky factor. Default: ``False``.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: If ``upper = False``, it returns a lower triangular ``L`` matrix such
that ``L @ L.T = a``. If ``upper = True``, it returns an upper triangular
``U`` matrix such that ``U.T @ U = a``.
)pbdoc");
m.def(
"cholesky_inv",
&mx::linalg::cholesky_inv,
"a"_a,
"upper"_a = false,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def cholesky_inv(L: array, upper: bool = False, *, stream: Union[None, Stream, Device] = None) -> array"),
R"pbdoc(
Compute the inverse of a real symmetric positive semi-definite matrix using it's Cholesky decomposition.
Let :math:`\mathbf{A}` be a real symmetric positive semi-definite matrix and :math:`\mathbf{L}` its Cholesky decomposition such that:
.. math::
\begin{aligned}
\mathbf{A} = \mathbf{L}\mathbf{L}^T
\end{aligned}
This function computes :math:`\mathbf{A}^{-1}`.
This function supports arrays with at least 2 dimensions. When the input
has more than two dimensions, the Cholesky inverse is computed for each matrix
in the last two dimensions of :math:`\mathbf{L}`.
If the input matrix is not a triangular matrix behaviour is undefined.
Args:
L (array): Input array.
upper (bool, optional): If ``True``, return the upper triangular Cholesky factor.
If ``False``, return the lower triangular Cholesky factor. Default: ``False``.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: :math:`\mathbf{A^{-1}}` where :math:`\mathbf{A} = \mathbf{L}\mathbf{L}^T`.
)pbdoc");
m.def(
"pinv",
&mx::linalg::pinv,
"a"_a,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def pinv(a: array, *, stream: Union[None, Stream, Device] = None) -> array"),
R"pbdoc(
Compute the (Moore-Penrose) pseudo-inverse of a matrix.
This function calculates a generalized inverse of a matrix using its
singular-value decomposition. This function supports arrays with at least 2 dimensions.
When the input has more than two dimensions, the inverse is computed for each
matrix in the last two dimensions of ``a``.
Args:
a (array): Input array.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: ``aplus`` such that ``a @ aplus @ a = a``
)pbdoc");
m.def(
"cross",
&mx::linalg::cross,
"a"_a,
"b"_a,
"axis"_a = -1,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def cross(a: array, b: array, axis: int = -1, *, stream: Union[None, Stream, Device] = None) -> array"),
R"pbdoc(
Compute the cross product of two arrays along a specified axis.
The cross product is defined for arrays with size 2 or 3 in the
specified axis. If the size is 2 then the third value is assumed
to be zero.
Args:
a (array): Input array.
b (array): Input array.
axis (int, optional): Axis along which to compute the cross
product. Default: ``-1``.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: The cross product of ``a`` and ``b`` along the specified axis.
)pbdoc");
m.def(
"eigvals",
&mx::linalg::eigvals,
"a"_a,
nb::kw_only(),
"stream"_a = nb::none(),
R"pbdoc(
Compute the eigenvalues of a square matrix.
This function differs from :func:`numpy.linalg.eigvals` in that the
return type is always complex even if the eigenvalues are all real.
This function supports arrays with at least 2 dimensions. When the
input has more than two dimensions, the eigenvalues are computed for
each matrix in the last two dimensions.
Args:
a (array): The input array.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: The eigenvalues (not necessarily in order).
Example:
>>> A = mx.array([[1., -2.], [-2., 1.]])
>>> eigenvalues = mx.linalg.eigvals(A, stream=mx.cpu)
>>> eigenvalues
array([3+0j, -1+0j], dtype=complex64)
)pbdoc");
m.def(
"eig",
[](const mx::array& a, mx::StreamOrDevice s) {
auto result = mx::linalg::eig(a, s);
return nb::make_tuple(result.first, result.second);
},
"a"_a,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def eig(a: array, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array]"),
R"pbdoc(
Compute the eigenvalues and eigenvectors of a square matrix.
This function differs from :func:`numpy.linalg.eig` in that the
return type is always complex even if the eigenvalues are all real.
This function supports arrays with at least 2 dimensions. When the input
has more than two dimensions, the eigenvalues and eigenvectors are
computed for each matrix in the last two dimensions.
Args:
a (array): The input array.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
Tuple[array, array]:
A tuple containing the eigenvalues and the normalized right
eigenvectors. The column ``v[:, i]`` is the eigenvector
corresponding to the i-th eigenvalue.
Example:
>>> A = mx.array([[1., -2.], [-2., 1.]])
>>> w, v = mx.linalg.eig(A, stream=mx.cpu)
>>> w
array([3+0j, -1+0j], dtype=complex64)
>>> v
array([[0.707107+0j, 0.707107+0j],
[-0.707107+0j, 0.707107+0j]], dtype=complex64)
)pbdoc");
m.def(
"eigvalsh",
&mx::linalg::eigvalsh,
"a"_a,
"UPLO"_a = "L",
nb::kw_only(),
"stream"_a = nb::none(),
R"pbdoc(
Compute the eigenvalues of a complex Hermitian or real symmetric matrix.
This function supports arrays with at least 2 dimensions. When the
input has more than two dimensions, the eigenvalues are computed for
each matrix in the last two dimensions.
Args:
a (array): Input array. Must be a real symmetric or complex
Hermitian matrix.
UPLO (str, optional): Whether to use the upper (``"U"``) or
lower (``"L"``) triangle of the matrix. Default: ``"L"``.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: The eigenvalues in ascending order.
Note:
The input matrix is assumed to be symmetric (or Hermitian). Only
the selected triangle is used. No checks for symmetry are performed.
Example:
>>> A = mx.array([[1., -2.], [-2., 1.]])
>>> eigenvalues = mx.linalg.eigvalsh(A, stream=mx.cpu)
>>> eigenvalues
array([-1., 3.], dtype=float32)
)pbdoc");
m.def(
"eigh",
[](const mx::array& a, const std::string& UPLO, mx::StreamOrDevice s) {
auto result = mx::linalg::eigh(a, UPLO, s);
return nb::make_tuple(result.first, result.second);
},
"a"_a,
"UPLO"_a = "L",
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def eigh(a: array, UPLO: str = 'L', *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array]"),
R"pbdoc(
Compute the eigenvalues and eigenvectors of a complex Hermitian or
real symmetric matrix.
This function supports arrays with at least 2 dimensions. When the input
has more than two dimensions, the eigenvalues and eigenvectors are
computed for each matrix in the last two dimensions.
Args:
a (array): Input array. Must be a real symmetric or complex
Hermitian matrix.
UPLO (str, optional): Whether to use the upper (``"U"``) or
lower (``"L"``) triangle of the matrix. Default: ``"L"``.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
Tuple[array, array]:
A tuple containing the eigenvalues in ascending order and
the normalized eigenvectors. The column ``v[:, i]`` is the
eigenvector corresponding to the i-th eigenvalue.
Note:
The input matrix is assumed to be symmetric (or Hermitian). Only
the selected triangle is used. No checks for symmetry are performed.
Example:
>>> A = mx.array([[1., -2.], [-2., 1.]])
>>> w, v = mx.linalg.eigh(A, stream=mx.cpu)
>>> w
array([-1., 3.], dtype=float32)
>>> v
array([[ 0.707107, -0.707107],
[ 0.707107, 0.707107]], dtype=float32)
)pbdoc");
m.def(
"lu",
[](const mx::array& a, mx::StreamOrDevice s /* = {} */) {
auto result = mx::linalg::lu(a, s);
return nb::make_tuple(result.at(0), result.at(1), result.at(2));
},
"a"_a,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def lu(a: array, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array, array]"),
R"pbdoc(
Compute the LU factorization of the given matrix ``A``.
Note, unlike the default behavior of ``scipy.linalg.lu``, the pivots
are indices. To reconstruct the input use ``L[P, :] @ U`` for 2
dimensions or ``mx.take_along_axis(L, P[..., None], axis=-2) @ U``
for more than 2 dimensions.
To construct the full permuation matrix do:
.. code-block::
P = mx.put_along_axis(mx.zeros_like(L), p[..., None], mx.array(1.0), axis=-1)
Args:
a (array): Input array.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
tuple(array, array, array):
The ``p``, ``L``, and ``U`` arrays, such that ``A = L[P, :] @ U``
)pbdoc");
m.def(
"lu_factor",
&mx::linalg::lu_factor,
"a"_a,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def lu_factor(a: array, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array]"),
R"pbdoc(
Computes a compact representation of the LU factorization.
Args:
a (array): Input array.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
tuple(array, array): The ``LU`` matrix and ``pivots`` array.
)pbdoc");
m.def(
"solve",
&mx::linalg::solve,
"a"_a,
"b"_a,
nb::kw_only(),
"stream"_a = nb::none(),
nb::sig(
"def solve(a: array, b: array, *, stream: Union[None, Stream, Device] = None) -> array"),
R"pbdoc(
Compute the solution to a system of linear equations ``AX = B``.
Args:
a (array): Input array.
b (array): Input array.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: The unique solution to the system ``AX = B``.
)pbdoc");
m.def(
"solve_triangular",
&mx::linalg::solve_triangular,
"a"_a,
"b"_a,
nb::kw_only(),
"upper"_a = false,
"stream"_a = nb::none(),
nb::sig(
"def solve_triangular(a: array, b: array, *, upper: bool = False, stream: Union[None, Stream, Device] = None) -> array"),
R"pbdoc(
Computes the solution of a triangular system of linear equations ``AX = B``.
Args:
a (array): Input array.
b (array): Input array.
upper (bool, optional): Whether the array is upper or lower
triangular. Default: ``False``.
stream (Stream, optional): Stream or device. Defaults to ``None``
in which case the default stream of the default device is used.
Returns:
array: The unique solution to the system ``AX = B``.
)pbdoc");
}
|