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Adds nuclear norm support (#1894)

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* adjust norm unit test tolerance
This commit is contained in:
Abe Leininger 2025-03-04 15:26:02 -06:00 committed by GitHub
parent 9680f72cca
commit 3835a428c5
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GPG Key ID: B5690EEEBB952194
11 changed files with 260 additions and 55 deletions
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43
mlx/backend/cpu/svd.cpp
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@ -8,7 +8,7 @@
namespace mlx::core {
template <typename T>
void svd_impl(const array& a, array& u, array& s, array& vt) {
void svd_impl(const array& a, T* u_data, T* s_data, T* vt_data) {
// Lapack uses the column-major convention. To avoid having to transpose
// the input and then transpose the outputs, we swap the indices/sizes of the
// matrices and take advantage of the following identity (see
@ -35,13 +35,8 @@ void svd_impl(const array& a, array& u, array& s, array& vt) {
array in(a.shape(), a.dtype(), nullptr, {});
copy(a, in, a.flags().row_contiguous ? CopyType::Vector : CopyType::General);
// Allocate outputs.
u.set_data(allocator::malloc_or_wait(u.nbytes()));
s.set_data(allocator::malloc_or_wait(s.nbytes()));
vt.set_data(allocator::malloc_or_wait(vt.nbytes()));
static constexpr auto job_u = "V";
static constexpr auto job_vt = "V";
auto job_u = (u_data && vt_data) ? "V" : "N";
auto job_vt = (u_data && vt_data) ? "V" : "N";
static constexpr auto range = "A";
// Will contain the number of singular values after the call has returned.
@ -56,6 +51,7 @@ void svd_impl(const array& a, array& u, array& s, array& vt) {
static const int ignored_int = 0;
static const T ignored_float = 0;
static T ignored_output = 0;
int info;
@ -109,12 +105,12 @@ void svd_impl(const array& a, array& u, array& s, array& vt) {
/* il = */ &ignored_int,
/* iu = */ &ignored_int,
/* ns = */ &ns,
/* s = */ s.data<T>() + K * i,
/* s = */ s_data + K * i,
// According to the identity above, lapack will write Vᵀᵀ as U.
/* u = */ vt.data<T>() + N * N * i,
/* u = */ vt_data ? vt_data + N * N * i : &ignored_output,
/* ldu = */ &ldu,
// According to the identity above, lapack will write Uᵀ as Vᵀ.
/* vt = */ u.data<T>() + M * M * i,
/* vt = */ u_data ? u_data + M * M * i : &ignored_output,
/* ldvt = */ &ldvt,
/* work = */ static_cast<T*>(scratch.buffer.raw_ptr()),
/* lwork = */ &lwork,
@ -136,15 +132,36 @@ void svd_impl(const array& a, array& u, array& s, array& vt) {
}
}
template <typename T>
void compute_svd(const array& a, bool compute_uv, std::vector<array>& outputs) {
if (compute_uv) {
array& u = outputs[0];
array& s = outputs[1];
array& vt = outputs[2];
u.set_data(allocator::malloc_or_wait(u.nbytes()));
s.set_data(allocator::malloc_or_wait(s.nbytes()));
vt.set_data(allocator::malloc_or_wait(vt.nbytes()));
svd_impl<T>(a, u.data<T>(), s.data<T>(), vt.data<T>());
} else {
array& s = outputs[0];
s.set_data(allocator::malloc_or_wait(s.nbytes()));
svd_impl<T>(a, nullptr, s.data<T>(), nullptr);
}
}
void SVD::eval_cpu(
const std::vector<array>& inputs,
std::vector<array>& outputs) {
switch (inputs[0].dtype()) {
case float32:
svd_impl<float>(inputs[0], outputs[0], outputs[1], outputs[2]);
compute_svd<float>(inputs[0], compute_uv_, outputs);
break;
case float64:
svd_impl<double>(inputs[0], outputs[0], outputs[1], outputs[2]);
compute_svd<double>(inputs[0], compute_uv_, outputs);
break;
default:
throw std::runtime_error(

55
mlx/linalg.cpp
View File

@ -102,8 +102,21 @@ inline array matrix_norm(
dtype,
s);
} else if (ord == 2.0 || ord == -2.0) {
throw std::runtime_error(
"[linalg::norm] Singular value norms are not implemented.");
row_axis = (axis[0] < 0) ? axis[0] + a.ndim() : axis[0];
col_axis = (axis[1] < 0) ? axis[1] + a.ndim() : axis[1];
auto a_matrix = (row_axis > col_axis)
? moveaxis(moveaxis(a, row_axis, -1, s), col_axis, -1, s)
: moveaxis(moveaxis(a, col_axis, -1, s), row_axis, -2, s);
a_matrix = svd(a_matrix, false, s).at(0);
a_matrix = (ord == 2.0) ? max(a_matrix, -1, false, s)
: min(a_matrix, -1, false, s);
if (keepdims) {
std::vector<int> sorted_axes = (row_axis < col_axis)
? std::vector<int>{row_axis, col_axis}
: std::vector<int>{col_axis, row_axis};
a_matrix = expand_dims(a_matrix, sorted_axes, s);
}
return astype(a_matrix, dtype, s);
} else {
std::ostringstream msg;
msg << "[linalg::norm] Invalid ord " << ord << " for matrix norm.";
@ -120,8 +133,19 @@ inline array matrix_norm(
if (ord == "f" || ord == "fro") {
return l2_norm(a, axis, keepdims, s);
} else if (ord == "nuc") {
throw std::runtime_error(
"[linalg::norm] Nuclear norm not yet implemented.");
int row_axis = (axis[0] < 0) ? axis[0] + a.ndim() : axis[0];
int col_axis = (axis[1] < 0) ? axis[1] + a.ndim() : axis[1];
auto a_matrix = (row_axis > col_axis)
? moveaxis(moveaxis(a, row_axis, -1, s), col_axis, -1, s)
: moveaxis(moveaxis(a, col_axis, -1, s), row_axis, -2, s);
a_matrix = sum(svd(a_matrix, false, s).at(0), -1, false, s);
if (keepdims) {
std::vector<int> sorted_axes = (row_axis < col_axis)
? std::vector<int>{row_axis, col_axis}
: std::vector<int>{col_axis, row_axis};
a_matrix = expand_dims(a_matrix, sorted_axes, s);
}
return a_matrix;
} else {
std::ostringstream msg;
msg << "[linalg::norm] Invalid ord value '" << ord << "' for matrix norm.";
@ -214,7 +238,8 @@ std::pair<array, array> qr(const array& a, StreamOrDevice s /* = {} */) {
return std::make_pair(out[0], out[1]);
}
std::vector<array> svd(const array& a, StreamOrDevice s /* = {} */) {
std::vector<array>
svd(const array& a, bool compute_uv, StreamOrDevice s /* = {} */) {
check_cpu_stream(s, "[linalg::svd]");
check_float(a.dtype(), "[linalg::svd]");
@ -230,14 +255,22 @@ std::vector<array> svd(const array& a, StreamOrDevice s /* = {} */) {
const auto n = a.shape(-1);
const auto rank = a.ndim();
auto u_shape = a.shape();
u_shape[rank - 2] = m;
u_shape[rank - 1] = m;
auto s_shape = a.shape();
s_shape.pop_back();
s_shape[rank - 2] = std::min(m, n);
if (!compute_uv) {
return {array(
std::move(s_shape),
std::move(a.dtype()),
std::make_shared<SVD>(to_stream(s), compute_uv),
{a})};
}
auto u_shape = a.shape();
u_shape[rank - 2] = m;
u_shape[rank - 1] = m;
auto vt_shape = a.shape();
vt_shape[rank - 2] = n;
vt_shape[rank - 1] = n;
@ -245,7 +278,7 @@ std::vector<array> svd(const array& a, StreamOrDevice s /* = {} */) {
return array::make_arrays(
{u_shape, s_shape, vt_shape},
{a.dtype(), a.dtype(), a.dtype()},
std::make_shared<SVD>(to_stream(s)),
std::make_shared<SVD>(to_stream(s), compute_uv),
{a});
}
@ -323,7 +356,7 @@ array pinv(const array& a, StreamOrDevice s /* = {} */) {
int m = a.shape(-2);
int n = a.shape(-1);
int k = std::min(m, n);
auto outs = linalg::svd(a, s);
auto outs = linalg::svd(a, true, s);
array U = outs[0];
array S = outs[1];
array V = outs[2];

6
mlx/linalg.h
View File

@ -62,7 +62,11 @@ norm(const array& a, int axis, bool keepdims = false, StreamOrDevice s = {}) {
std::pair<array, array> qr(const array& a, StreamOrDevice s = {});
std::vector<array> svd(const array& a, StreamOrDevice s = {});
std::vector<array>
svd(const array& a, bool compute_uv, StreamOrDevice s /* = {} */);
inline std::vector<array> svd(const array& a, StreamOrDevice s = {}) {
return svd(a, true, s);
}
array inv(const array& a, StreamOrDevice s = {});

3
mlx/primitives.cpp
View File

@ -4940,7 +4940,8 @@ std::pair<std::vector<array>, std::vector<int>> SVD::vmap(
const std::vector<int>& axes) {
auto ax = axes[0] >= 0 ? 0 : -1;
auto a = axes[0] > 0 ? moveaxis(inputs[0], axes[0], 0, stream()) : inputs[0];
return {{linalg::svd(a, stream())}, {ax, ax, ax}};
std::vector<int> new_axes(compute_uv_ ? 3 : 1, ax);
return {linalg::svd(a, compute_uv_, stream()), std::move(new_axes)};
}
std::pair<std::vector<array>, std::vector<int>> Inverse::vmap(

9
mlx/primitives.h
View File

@ -2287,7 +2287,8 @@ class QRF : public Primitive {
/* SVD primitive. */
class SVD : public Primitive {
public:
explicit SVD(Stream stream) : Primitive(stream) {}
explicit SVD(Stream stream, bool compute_uv)
: Primitive(stream), compute_uv_(compute_uv) {}
void eval_cpu(const std::vector<array>& inputs, std::vector<array>& outputs)
override;
@ -2296,6 +2297,12 @@ class SVD : public Primitive {
DEFINE_VMAP()
DEFINE_PRINT(SVD)
auto state() const {
return compute_uv_;
}
private:
bool compute_uv_;
};
/* Matrix inversion primitive. */

2
mlx/random.cpp
View File

@ -244,7 +244,7 @@ array multivariate_normal(
// Compute the square-root of the covariance matrix, using the SVD
auto covariance = astype(cov, float32, stream);
auto SVD = linalg::svd(covariance, stream);
auto SVD = linalg::svd(covariance, true, stream);
auto std = astype(
matmul(
multiply(

26
python/src/linalg.cpp
View File

@ -92,6 +92,7 @@ void init_linalg(nb::module_& parent_module) {
===== ============================ ==========================
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)
@ -102,9 +103,6 @@ void init_linalg(nb::module_& parent_module) {
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}`
@ -206,15 +204,22 @@ void init_linalg(nb::module_& parent_module) {
)pbdoc");
m.def(
"svd",
[](const mx::array& a, mx::StreamOrDevice s /* = {} */) {
const auto result = mx::linalg::svd(a, s);
return nb::make_tuple(result.at(0), result.at(1), result.at(2));
[](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, *, stream: Union[None, Stream, Device] = None) -> Tuple[array, array, array]"),
"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.
@ -224,12 +229,15 @@ void init_linalg(nb::module_& parent_module) {
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:
tuple(array, array, array): The ``U``, ``S``, and ``Vt`` matrices, such that
``A = U @ diag(S) @ Vt``
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",

33
python/tests/test_linalg.py
View File

@ -12,11 +12,11 @@ import numpy as np
class TestLinalg(mlx_tests.MLXTestCase):
def test_norm(self):
vector_ords = [None, 0.5, 0, 1, 2, 3, -1, float("inf"), -float("inf")]
matrix_ords = [None, "fro", -1, 1, float("inf"), -float("inf")]
matrix_ords = [None, "fro", "nuc", -1, 1, -2, 2, float("inf"), -float("inf")]
for shape in [(3,), (2, 3), (2, 3, 3)]:
x_mx = mx.arange(1, math.prod(shape) + 1).reshape(shape)
x_np = np.arange(1, math.prod(shape) + 1).reshape(shape)
x_mx = mx.arange(1, math.prod(shape) + 1, dtype=mx.float32).reshape(shape)
x_np = np.arange(1, math.prod(shape) + 1, dtype=np.float32).reshape(shape)
# Test when at least one axis is provided
for num_axes in range(1, len(shape)):
if num_axes == 1:
@ -26,11 +26,14 @@ class TestLinalg(mlx_tests.MLXTestCase):
for axis in itertools.combinations(range(len(shape)), num_axes):
for keepdims in [True, False]:
for o in ords:
stream = (
mx.cpu if o in ["nuc", -2, 2] else mx.default_device()
)
out_np = np.linalg.norm(
x_np, ord=o, axis=axis, keepdims=keepdims
)
out_mx = mx.linalg.norm(
x_mx, ord=o, axis=axis, keepdims=keepdims
x_mx, ord=o, axis=axis, keepdims=keepdims, stream=stream
)
with self.subTest(
shape=shape, ord=o, axis=axis, keepdims=keepdims
@ -133,20 +136,38 @@ class TestLinalg(mlx_tests.MLXTestCase):
def test_svd_decomposition(self):
A = mx.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]], dtype=mx.float32)
U, S, Vt = mx.linalg.svd(A, stream=mx.cpu)
U, S, Vt = mx.linalg.svd(A, compute_uv=True, stream=mx.cpu)
self.assertTrue(
mx.allclose(U[:, : len(S)] @ mx.diag(S) @ Vt, A, rtol=1e-5, atol=1e-7)
)
S = mx.linalg.svd(A, compute_uv=False, stream=mx.cpu)
self.assertTrue(
mx.allclose(
mx.linalg.norm(S), mx.linalg.norm(A, ord="fro"), rtol=1e-5, atol=1e-7
)
)
# Multiple matrices
B = A + 10.0
AB = mx.stack([A, B])
Us, Ss, Vts = mx.linalg.svd(AB, stream=mx.cpu)
Us, Ss, Vts = mx.linalg.svd(AB, compute_uv=True, stream=mx.cpu)
for M, U, S, Vt in zip([A, B], Us, Ss, Vts):
self.assertTrue(
mx.allclose(U[:, : len(S)] @ mx.diag(S) @ Vt, M, rtol=1e-5, atol=1e-7)
)
Ss = mx.linalg.svd(AB, compute_uv=False, stream=mx.cpu)
for M, S in zip([A, B], Ss):
self.assertTrue(
mx.allclose(
mx.linalg.norm(S),
mx.linalg.norm(M, ord="fro"),
rtol=1e-5,
atol=1e-7,
)
)
def test_inverse(self):
A = mx.array([[1, 2, 3], [6, -5, 4], [-9, 8, 7]], dtype=mx.float32)
A_inv = mx.linalg.inv(A, stream=mx.cpu)

29
python/tests/test_vmap.py
View File

@ -316,33 +316,56 @@ class TestVmap(mlx_tests.MLXTestCase):
def test_vmap_svd(self):
a = mx.random.uniform(shape=(3, 4, 2))
cpu_svd = lambda x: mx.linalg.svd(x, stream=mx.cpu)
cpu_svd_full = lambda x: mx.linalg.svd(x, compute_uv=True, stream=mx.cpu)
cpu_svd_singular = lambda x: mx.linalg.svd(x, compute_uv=False, stream=mx.cpu)
# Vmap over the first axis (this is already supported natively by the primitive).
Us, Ss, Vts = mx.vmap(cpu_svd, in_axes=(0,))(a)
Us, Ss, Vts = mx.vmap(cpu_svd_full, in_axes=(0,))(a)
self.assertEqual(Us.shape, (a.shape[0], a.shape[1], a.shape[1]))
self.assertEqual(Ss.shape, (a.shape[0], a.shape[2]))
self.assertEqual(Vts.shape, (a.shape[0], a.shape[2], a.shape[2]))
Sv = mx.vmap(cpu_svd_singular, in_axes=(0,))(a)
self.assertEqual(Sv.shape, (a.shape[0], a.shape[2]))
for i in range(a.shape[0]):
M = a[i]
U, S, Vt = Us[i], Ss[i], Vts[i]
self.assertTrue(
mx.allclose(U[:, : len(S)] @ mx.diag(S) @ Vt, M, rtol=1e-5, atol=1e-7)
)
self.assertTrue(
mx.allclose(
mx.linalg.norm(Sv[i]),
mx.linalg.norm(M, ord="fro"),
rtol=1e-5,
atol=1e-7,
)
)
# Vmap over the second axis.
Us, Ss, Vts = mx.vmap(cpu_svd, in_axes=(1,))(a)
Us, Ss, Vts = mx.vmap(cpu_svd_full, in_axes=(1,))(a)
self.assertEqual(Us.shape, (a.shape[1], a.shape[0], a.shape[0]))
self.assertEqual(Ss.shape, (a.shape[1], a.shape[2]))
self.assertEqual(Vts.shape, (a.shape[1], a.shape[2], a.shape[2]))
Sv = mx.vmap(cpu_svd_singular, in_axes=(1,))(a)
self.assertEqual(Sv.shape, (a.shape[1], a.shape[2]))
for i in range(a.shape[1]):
M = a[:, i, :]
U, S, Vt = Us[i], Ss[i], Vts[i]
self.assertTrue(
mx.allclose(U[:, : len(S)] @ mx.diag(S) @ Vt, M, rtol=1e-5, atol=1e-7)
)
self.assertTrue(
mx.allclose(
mx.linalg.norm(Sv[i]),
mx.linalg.norm(M, ord="fro"),
rtol=1e-5,
atol=1e-7,
)
)
def test_vmap_inverse(self):
mx.random.seed(42)

82
tests/linalg_tests.cpp
View File

@ -100,7 +100,7 @@ TEST_CASE("[mlx.core.linalg.norm] double ord") {
norm(x, -std::numeric_limits<double>::infinity()).item<float>(),
doctest::Approx(expected));
x = reshape(arange(9), {3, 3});
x = reshape(arange(9, float32), {3, 3});
CHECK(allclose(
norm(x, 2.0, 0, false),
@ -129,10 +129,34 @@ TEST_CASE("[mlx.core.linalg.norm] double ord") {
CHECK_EQ(
norm(x, -1.0, std::vector<int>{1, 0}).item<float>(),
doctest::Approx(3.0));
CHECK_EQ(
norm(x, 2.0, std::vector<int>{0, 1}, false, Device::cpu).item<float>(),
doctest::Approx(14.226707));
CHECK_EQ(
norm(x, 2.0, std::vector<int>{1, 0}, false, Device::cpu).item<float>(),
doctest::Approx(14.226707));
CHECK_EQ(
norm(x, -2.0, std::vector<int>{0, 1}, false, Device::cpu).item<float>(),
doctest::Approx(0.0));
CHECK_EQ(
norm(x, -2.0, std::vector<int>{1, 0}, false, Device::cpu).item<float>(),
doctest::Approx(0.0));
CHECK_EQ(norm(x, 1.0, std::vector<int>{0, 1}, true).shape(), Shape{1, 1});
CHECK_EQ(norm(x, 1.0, std::vector<int>{1, 0}, true).shape(), Shape{1, 1});
CHECK_EQ(norm(x, -1.0, std::vector<int>{0, 1}, true).shape(), Shape{1, 1});
CHECK_EQ(norm(x, -1.0, std::vector<int>{1, 0}, true).shape(), Shape{1, 1});
CHECK_EQ(
norm(x, 2.0, std::vector<int>{0, 1}, true, Device::cpu).shape(),
Shape{1, 1});
CHECK_EQ(
norm(x, 2.0, std::vector<int>{1, 0}, true, Device::cpu).shape(),
Shape{1, 1});
CHECK_EQ(
norm(x, -2.0, std::vector<int>{0, 1}, true, Device::cpu).shape(),
Shape{1, 1});
CHECK_EQ(
norm(x, -2.0, std::vector<int>{1, 0}, true, Device::cpu).shape(),
Shape{1, 1});
CHECK_EQ(
norm(x, -1.0, std::vector<int>{-2, -1}, false).item<float>(),
@ -140,8 +164,14 @@ TEST_CASE("[mlx.core.linalg.norm] double ord") {
CHECK_EQ(
norm(x, 1.0, std::vector<int>{-2, -1}, false).item<float>(),
doctest::Approx(15.0));
CHECK_EQ(
norm(x, -2.0, std::vector<int>{-2, -1}, false, Device::cpu).item<float>(),
doctest::Approx(0.0));
CHECK_EQ(
norm(x, 2.0, std::vector<int>{-2, -1}, false, Device::cpu).item<float>(),
doctest::Approx(14.226707));
x = reshape(arange(18), {2, 3, 3});
x = reshape(arange(18, float32), {2, 3, 3});
CHECK_THROWS(norm(x, 2.0, std::vector{0, 1, 2}));
CHECK(allclose(
norm(x, 3.0, 0),
@ -199,13 +229,31 @@ TEST_CASE("[mlx.core.linalg.norm] double ord") {
.item<bool>());
CHECK(allclose(norm(x, -1.0, std::vector<int>{1, 2}), array({9, 36}))
.item<bool>());
CHECK(allclose(
norm(x, 2.0, std::vector<int>{0, 1}, false, Device::cpu),
array({22.045408, 24.155825, 26.318918}))
.item<bool>());
CHECK(allclose(
norm(x, 2.0, std::vector<int>{1, 2}, false, Device::cpu),
array({14.226707, 39.759212}))
.item<bool>());
CHECK(allclose(
norm(x, -2.0, std::vector<int>{0, 1}, false, Device::cpu),
array({3, 2.7378995, 2.5128777}))
.item<bool>());
CHECK(allclose(
norm(x, -2.0, std::vector<int>{1, 2}, false, Device::cpu),
array({4.979028e-16, 7.009628e-16}),
/* rtol = */ 1e-5,
/* atol = */ 1e-6)
.item<bool>());
}
TEST_CASE("[mlx.core.linalg.norm] string ord") {
array x({1, 2, 3});
CHECK_THROWS(norm(x, "fro"));
x = reshape(arange(9), {3, 3});
x = reshape(arange(9, float32), {3, 3});
CHECK_THROWS(norm(x, "bad ord"));
CHECK_EQ(
@ -214,8 +262,11 @@ TEST_CASE("[mlx.core.linalg.norm] string ord") {
CHECK_EQ(
norm(x, "fro", std::vector<int>{0, 1}).item<float>(),
doctest::Approx(14.2828568570857));
CHECK_EQ(
norm(x, "nuc", std::vector<int>{0, 1}, false, Device::cpu).item<float>(),
doctest::Approx(15.491934));
x = reshape(arange(18), {2, 3, 3});
x = reshape(arange(18, float32), {2, 3, 3});
CHECK(allclose(
norm(x, "fro", std::vector<int>{0, 1}),
array({22.24859546, 24.31049156, 26.43860813}))
@ -240,6 +291,18 @@ TEST_CASE("[mlx.core.linalg.norm] string ord") {
norm(x, "f", std::vector<int>{2, 1}),
array({14.28285686, 39.7617907}))
.item<bool>());
CHECK(allclose(
norm(x, "nuc", std::vector<int>{0, 1}, false, Device::cpu),
array({25.045408, 26.893724, 28.831797}))
.item<bool>());
CHECK(allclose(
norm(x, "nuc", std::vector<int>{1, 2}, false, Device::cpu),
array({15.491934, 40.211937}))
.item<bool>());
CHECK(allclose(
norm(x, "nuc", std::vector<int>{-2, -1}, false, Device::cpu),
array({15.491934, 40.211937}))
.item<bool>());
}
TEST_CASE("test QR factorization") {
@ -271,7 +334,7 @@ TEST_CASE("test SVD factorization") {
const auto prng_key = random::key(42);
const auto A = mlx::core::random::normal({5, 4}, prng_key);
const auto outs = linalg::svd(A, Device::cpu);
const auto outs = linalg::svd(A, true, Device::cpu);
CHECK_EQ(outs.size(), 3);
const auto& U = outs[0];
@ -291,6 +354,15 @@ TEST_CASE("test SVD factorization") {
CHECK_EQ(U.dtype(), float32);
CHECK_EQ(S.dtype(), float32);
CHECK_EQ(Vt.dtype(), float32);
// Test singular values
const auto& outs_sv = linalg::svd(A, false, Device::cpu);
const auto SV = outs_sv[0];
CHECK_EQ(SV.shape(), Shape{4});
CHECK_EQ(SV.dtype(), float32);
CHECK(allclose(norm(SV), norm(A, "fro")).item<bool>());
}
TEST_CASE("test matrix inversion") {

27
tests/vmap_tests.cpp
View File

@ -466,15 +466,19 @@ TEST_CASE("test vmap scatter") {
}
TEST_CASE("test vmap SVD") {
auto fun = [](std::vector<array> inputs) {
return linalg::svd(inputs.at(0), Device::cpu);
auto svd_full = [](std::vector<array> inputs) {
return linalg::svd(inputs.at(0), true, Device::cpu);
};
auto svd_singular = [](std::vector<array> inputs) {
return linalg::svd(inputs.at(0), false, Device::cpu);
};
auto a = astype(reshape(arange(24), {3, 4, 2}), float32);
// vmap over the second axis.
{
auto out = vmap(fun, /* in_axes = */ {1})({a});
auto out = vmap(svd_full, /* in_axes = */ {1})({a});
const auto& U = out.at(0);
const auto& S = out.at(1);
const auto& Vt = out.at(2);
@ -486,7 +490,7 @@ TEST_CASE("test vmap SVD") {
// vmap over the third axis.
{
auto out = vmap(fun, /* in_axes = */ {2})({a});
auto out = vmap(svd_full, /* in_axes = */ {2})({a});
const auto& U = out.at(0);
const auto& S = out.at(1);
const auto& Vt = out.at(2);
@ -495,6 +499,21 @@ TEST_CASE("test vmap SVD") {
CHECK_EQ(S.shape(), Shape{a.shape(2), a.shape(0)});
CHECK_EQ(Vt.shape(), Shape{a.shape(2), a.shape(1), a.shape(1)});
}
// test singular values
{
auto out = vmap(svd_singular, /* in_axes = */ {1})({a});
const auto& S = out.at(0);
CHECK_EQ(S.shape(), Shape{a.shape(1), a.shape(2)});
}
{
auto out = vmap(svd_singular, /* in_axes = */ {2})({a});
const auto& S = out.at(0);
CHECK_EQ(S.shape(), Shape{a.shape(2), a.shape(0)});
}
}
TEST_CASE("test vmap dynamic slices") {