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Eigenvalues and eigenvectors (#1334)

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* initial eigvalsh

* add compute_vectors

* add compute_vectors_

* return a pair

* add eigh to return only eigenvectors

* fixed typo

* merge merge Eighvalsh and Eigh into a single primitive

* use the same primate with the flag

* fix primatives

* use MULTI

* fix eval_gpu

* fix decleration

* rename EighPrimitive to Eigh

* tests

* tests

* fix rebase and format

* cleanup lapack

* format

* add cblas.h

---------

Co-authored-by: Awni Hannun <awni@apple.com>
This commit is contained in:
Kashif Rasul
2024-10-22 21:18:48 +02:00
committed by GitHub
parent c26208f67d
commit 3ddc07e936
23 changed files with 434 additions and 86 deletions
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81
python/src/linalg.cpp
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@@ -405,4 +405,85 @@ void init_linalg(nb::module_& parent_module) {
Returns:
array: The cross product of ``a`` and ``b`` along the specified axis.
)pbdoc");
m.def(
"eigvalsh",
&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 array& a, const std::string UPLO, StreamOrDevice s) {
// TODO avoid cast?
auto result = eigh(a, UPLO, s);
return nb::make_tuple(result.first, result.second);
},
"a"_a,
"UPLO"_a = "L",
nb::kw_only(),
"stream"_a = nb::none(),
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");
}