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non square qr (#1783)

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This commit is contained in:
Awni Hannun
2025-01-21 14:07:47 -08:00
committed by GitHub
parent 1f4c127fb9
commit e6a7ab9675
3 changed files with 37 additions and 15 deletions
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25
mlx/backend/common/qrf.cpp
View File

@@ -41,7 +41,7 @@ template <typename T>
void qrf_impl(const array& a, array& q, array& r) {
const int M = a.shape(-2);
const int N = a.shape(-1);
const int lda = std::max(M, N);
const int lda = M;
size_t num_matrices = a.size() / (M * N);
int num_reflectors = std::min(M, N);
auto tau =
@@ -89,13 +89,16 @@ void qrf_impl(const array& a, array& q, array& r) {
allocator::free(work);
r.set_data(allocator::malloc_or_wait(r.nbytes()));
copy_inplace(in, r, CopyType::General);
for (int i = 0; i < num_matrices; ++i) {
// Zero lower triangle
/// num_reflectors x N
for (int j = 0; j < r.shape(-2); ++j) {
for (int k = 0; k < j; ++k) {
r.data<T>()[i * N * M + j * N + k] = 0;
r.data<T>()[i * N * num_reflectors + j * N + k] = 0;
}
for (int k = j; k < r.shape(-1); ++k) {
r.data<T>()[i * N * num_reflectors + j * N + k] =
in.data<T>()[i * N * M + j + k * M];
}
}
}
@@ -104,7 +107,7 @@ void qrf_impl(const array& a, array& q, array& r) {
lwork = -1;
lpack<T>::xorgqr(
&M,
&N,
&num_reflectors,
&num_reflectors,
nullptr,
&lda,
@@ -120,7 +123,7 @@ void qrf_impl(const array& a, array& q, array& r) {
// Compute Q
lpack<T>::xorgqr(
&M,
&N,
&num_reflectors,
&num_reflectors,
in.data<float>() + M * N * i,
&lda,
@@ -131,7 +134,15 @@ void qrf_impl(const array& a, array& q, array& r) {
}
q.set_data(allocator::malloc_or_wait(q.nbytes()));
copy_inplace(in, q, CopyType::General);
for (int i = 0; i < num_matrices; ++i) {
// M x num_reflectors
for (int j = 0; j < q.shape(-2); ++j) {
for (int k = 0; k < q.shape(-1); ++k) {
q.data<T>()[i * M * num_reflectors + j * num_reflectors + k] =
in.data<T>()[i * N * M + j + k * M];
}
}
}
// Cleanup
allocator::free(work);

12
mlx/linalg.cpp
View File

@@ -187,13 +187,13 @@ std::pair<array, array> qr(const array& a, StreamOrDevice s /* = {} */) {
<< a.ndim() << " dimensions.";
throw std::invalid_argument(msg.str());
}
if (a.shape(-1) != a.shape(-2)) {
throw std::invalid_argument(
"[linalg::qr] Support for non-square matrices NYI.");
}
int k = std::min(a.shape(-2), a.shape(-1));
auto q_shape = a.shape();
q_shape.back() = k;
auto r_shape = a.shape();
r_shape[r_shape.size() - 2] = k;
auto out = array::make_arrays(
{a.shape(), a.shape()},
{std::move(q_shape), std::move(r_shape)},
{a.dtype(), a.dtype()},
std::make_shared<QRF>(to_stream(s)),
{astype(a, a.dtype(), s)});

15
python/tests/test_linalg.py
View File

@@ -103,7 +103,7 @@ class TestLinalg(mlx_tests.MLXTestCase):
Q, R = mx.linalg.qr(A, stream=mx.cpu)
out = Q @ R
self.assertTrue(mx.allclose(out, A))
out = Q @ Q
out = Q.T @ Q
self.assertTrue(mx.allclose(out, mx.eye(2), rtol=1e-5, atol=1e-7))
self.assertTrue(mx.allclose(mx.tril(R, -1), mx.zeros_like(R)))
self.assertEqual(Q.dtype, mx.float32)
@@ -116,10 +116,21 @@ class TestLinalg(mlx_tests.MLXTestCase):
for a, q, r in zip(A, Q, R):
out = q @ r
self.assertTrue(mx.allclose(out, a))
out = q @ q
out = q.T @ q
self.assertTrue(mx.allclose(out, mx.eye(2), rtol=1e-5, atol=1e-7))
self.assertTrue(mx.allclose(mx.tril(r, -1), mx.zeros_like(r)))
# Non square matrices
for shape in [(4, 8), (8, 4)]:
A = mx.random.uniform(shape=shape)
Q, R = mx.linalg.qr(A, stream=mx.cpu)
out = Q @ R
self.assertTrue(mx.allclose(out, A, rtol=1e-4, atol=1e-6))
out = Q.T @ Q
self.assertTrue(
mx.allclose(out, mx.eye(min(A.shape)), rtol=1e-4, atol=1e-6)
)
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)