mirror of
https://github.com/ml-explore/mlx.git
synced 2025-11-04 10:38:10 +08:00
linalg.norm (#187)
* implemented vector_norm in cpp added linalg to mlx * implemented vector_norm python binding * renamed vector_norm to norm, implemented norm without provided ord * completed the implementation of the norm * added tests * removed unused import in linalg.cpp * updated python bindings * added some tests for python bindings * handling inf, -inf as numpy does, more extensive tests of compatibility with numpy * added better docs and examples * refactored mlx.linalg.norm bindings * reused existing util for implementation of linalg.norm * more tests * fixed a bug with no ord and axis provided * removed unused imports * some style and API consistency updates to linalg norm * remove unused includes * fix python tests * fixed a bug with frobenius norm of a complex-valued matrix * complex for vector too --------- Co-authored-by: Awni Hannun <awni@apple.com>
This commit is contained in:
Gabrijel Boduljak
committed by
GitHub
GitHub
parent
447bc089b9
commit
6b0d30bb85
@@ -11,6 +11,7 @@ pybind11_add_module(
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/stream.cpp
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/transforms.cpp
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/random.cpp
|
||||
${CMAKE_CURRENT_SOURCE_DIR}/linalg.cpp
|
||||
)
|
||||
|
||||
if (NOT MLX_PYTHON_BINDINGS_OUTPUT_DIRECTORY)
|
||||
|
||||
180
python/src/linalg.cpp
Normal file
180
python/src/linalg.cpp
Normal file
@@ -0,0 +1,180 @@
|
||||
// Copyright © 2023 Apple Inc.
|
||||
|
||||
#include <variant>
|
||||
|
||||
#include <pybind11/pybind11.h>
|
||||
#include <pybind11/stl.h>
|
||||
|
||||
#include "mlx/linalg.h"
|
||||
|
||||
#include "python/src/load.h"
|
||||
#include "python/src/utils.h"
|
||||
|
||||
namespace py = pybind11;
|
||||
using namespace py::literals;
|
||||
|
||||
using namespace mlx::core;
|
||||
using namespace mlx::core::linalg;
|
||||
|
||||
void init_linalg(py::module_& parent_module) {
|
||||
py::options options;
|
||||
options.disable_function_signatures();
|
||||
|
||||
auto m = parent_module.def_submodule(
|
||||
"linalg", "mlx.core.linalg: linear algebra routines.");
|
||||
|
||||
m.def(
|
||||
"norm",
|
||||
[](const 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 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 norm(a, axis, keepdims, stream);
|
||||
} else {
|
||||
if (auto pv = std::get_if<std::string>(&ord_); pv) {
|
||||
return 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 norm(a, ord, axis, keepdims, stream);
|
||||
}
|
||||
},
|
||||
"a"_a,
|
||||
py::pos_only(),
|
||||
"ord"_a = none,
|
||||
"axis"_a = none,
|
||||
"keepdims"_a = false,
|
||||
py::kw_only(),
|
||||
"stream"_a = none,
|
||||
R"pbdoc(
|
||||
norm(a: array, /, ord: Union[None, scalar, str] = None, axis: Union[None, int, List[int]] = None, keepdims: bool = False, *, stream: Union[None, Stream, Device] = None) -> array
|
||||
|
||||
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 (scalar 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 --
|
||||
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)
|
||||
===== ============================ ==========================
|
||||
|
||||
.. warning::
|
||||
Nuclear norm and norms based on singular values are not yet implemented.
|
||||
|
||||
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");
|
||||
}
|
||||
@@ -15,6 +15,7 @@ void init_ops(py::module_&);
|
||||
void init_transforms(py::module_&);
|
||||
void init_random(py::module_&);
|
||||
void init_fft(py::module_&);
|
||||
void init_linalg(py::module_&);
|
||||
|
||||
PYBIND11_MODULE(core, m) {
|
||||
m.doc() = "mlx: A framework for machine learning on Apple silicon.";
|
||||
@@ -29,5 +30,6 @@ PYBIND11_MODULE(core, m) {
|
||||
init_transforms(m);
|
||||
init_random(m);
|
||||
init_fft(m);
|
||||
init_linalg(m);
|
||||
m.attr("__version__") = TOSTRING(_VERSION_);
|
||||
}
|
||||
|
||||
Reference in New Issue
Block a user