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270 lines
8.7 KiB
C++
270 lines
8.7 KiB
C++
// Copyright © 2023-2024 Apple Inc.
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#include "doctest/doctest.h"
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#include <cmath>
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#include "mlx/mlx.h"
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using namespace mlx::core;
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using namespace mlx::core::linalg;
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TEST_CASE("[mlx.core.linalg.norm] no ord") {
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// Zero dimensions
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array x(2.0);
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CHECK_EQ(norm(x).item<float>(), 2.0f);
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CHECK_THROWS(norm(x, 0));
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x = array({1, 2, 3});
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float expected = std::sqrt(1 + 4 + 9);
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CHECK_EQ(norm(x).item<float>(), doctest::Approx(expected));
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CHECK_EQ(norm(x, 0, false).item<float>(), doctest::Approx(expected));
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CHECK_EQ(norm(x, -1, false).item<float>(), doctest::Approx(expected));
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CHECK_EQ(norm(x, -1, true).ndim(), 1);
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CHECK_THROWS(norm(x, 1));
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x = reshape(arange(9), {3, 3});
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expected =
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std::sqrt(0 + 1 + 2 * 2 + 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6 + 7 * 7 + 8 * 8);
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CHECK_EQ(norm(x).item<float>(), doctest::Approx(expected));
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CHECK_EQ(
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norm(x, std::vector<int>{0, 1}).item<float>(), doctest::Approx(expected));
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CHECK(allclose(
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norm(x, 0, false),
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array(
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{std::sqrt(0 + 3 * 3 + 6 * 6),
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std::sqrt(1 + 4 * 4 + 7 * 7),
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std::sqrt(2 * 2 + 5 * 5 + 8 * 8)}))
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.item<bool>());
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CHECK(allclose(
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norm(x, 1, false),
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array(
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{std::sqrt(0 + 1 + 2 * 2),
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std::sqrt(3 * 3 + 4 * 4 + 5 * 5),
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std::sqrt(6 * 6 + 7 * 7 + 8 * 8)}))
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.item<bool>());
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x = reshape(arange(18), {2, 3, 3});
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CHECK(allclose(
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norm(x, 2, false),
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array(
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{
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std::sqrt(0 + 1 + 2 * 2),
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std::sqrt(3 * 3 + 4 * 4 + 5 * 5),
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std::sqrt(6 * 6 + 7 * 7 + 8 * 8),
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std::sqrt(9 * 9 + 10 * 10 + 11 * 11),
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std::sqrt(12 * 12 + 13 * 13 + 14 * 14),
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std::sqrt(15 * 15 + 16 * 16 + 17 * 17),
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},
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{2, 3}))
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.item<bool>());
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CHECK(allclose(
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norm(x, std::vector<int>{1, 2}, false),
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array(
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{std::sqrt(
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0 + 1 + 2 * 2 + 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6 + 7 * 7 +
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8 * 8),
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std::sqrt(
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9 * 9 + 10 * 10 + 11 * 11 + 12 * 12 + 13 * 13 + 14 * 14 +
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15 * 15 + 16 * 16 + 17 * 17)},
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{2}))
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.item<bool>());
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CHECK_THROWS(norm(x, std::vector<int>{0, 1, 2}));
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}
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TEST_CASE("[mlx.core.linalg.norm] double ord") {
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CHECK_THROWS(norm(array(0), 2.0));
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array x({1, 2, 3});
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float expected = std::sqrt(1 + 4 + 9);
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CHECK_EQ(norm(x, 2.0).item<float>(), doctest::Approx(expected));
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CHECK_EQ(norm(x, 2.0, 0).item<float>(), doctest::Approx(expected));
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CHECK_THROWS(norm(x, 2.0, 1));
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expected = 1 + 2 + 3;
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CHECK_EQ(norm(x, 1.0).item<float>(), doctest::Approx(expected));
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expected = 3;
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CHECK_EQ(norm(x, 0.0).item<float>(), doctest::Approx(expected));
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expected = 3;
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CHECK_EQ(
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norm(x, std::numeric_limits<double>::infinity()).item<float>(),
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doctest::Approx(expected));
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expected = 1;
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CHECK_EQ(
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norm(x, -std::numeric_limits<double>::infinity()).item<float>(),
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doctest::Approx(expected));
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x = reshape(arange(9), {3, 3});
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CHECK(allclose(
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norm(x, 2.0, 0, false),
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array(
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{std::sqrt(0 + 3 * 3 + 6 * 6),
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std::sqrt(1 + 4 * 4 + 7 * 7),
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std::sqrt(2 * 2 + 5 * 5 + 8 * 8)}))
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.item<bool>());
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CHECK(allclose(
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norm(x, 2.0, 1, false),
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array(
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{sqrt(0 + 1 + 2 * 2),
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sqrt(3 * 3 + 4 * 4 + 5 * 5),
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sqrt(6 * 6 + 7 * 7 + 8 * 8)}))
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.item<bool>());
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CHECK_EQ(
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norm(x, 1.0, std::vector<int>{0, 1}).item<float>(),
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doctest::Approx(15.0));
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CHECK_EQ(
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norm(x, 1.0, std::vector<int>{1, 0}).item<float>(),
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doctest::Approx(21.0));
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CHECK_EQ(
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norm(x, -1.0, std::vector<int>{0, 1}).item<float>(),
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doctest::Approx(9.0));
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CHECK_EQ(
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norm(x, -1.0, std::vector<int>{1, 0}).item<float>(),
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doctest::Approx(3.0));
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CHECK_EQ(
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norm(x, 1.0, std::vector<int>{0, 1}, true).shape(),
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std::vector<int>{1, 1});
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CHECK_EQ(
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norm(x, 1.0, std::vector<int>{1, 0}, true).shape(),
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std::vector<int>{1, 1});
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CHECK_EQ(
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norm(x, -1.0, std::vector<int>{0, 1}, true).shape(),
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std::vector<int>{1, 1});
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CHECK_EQ(
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norm(x, -1.0, std::vector<int>{1, 0}, true).shape(),
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std::vector<int>{1, 1});
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CHECK_EQ(
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norm(x, -1.0, std::vector<int>{-2, -1}, false).item<float>(),
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doctest::Approx(9.0));
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CHECK_EQ(
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norm(x, 1.0, std::vector<int>{-2, -1}, false).item<float>(),
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doctest::Approx(15.0));
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x = reshape(arange(18), {2, 3, 3});
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CHECK_THROWS(norm(x, 2.0, std::vector{0, 1, 2}));
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CHECK(allclose(
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norm(x, 3.0, 0),
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array(
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{9.,
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10.00333222,
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11.02199456,
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12.06217728,
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13.12502645,
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14.2094363,
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15.31340617,
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16.43469751,
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17.57113899},
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{3, 3}))
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.item<bool>());
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CHECK(allclose(
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norm(x, 3.0, 2),
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array(
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{2.08008382,
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6.,
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10.23127655,
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14.5180117,
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18.82291607,
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23.13593104},
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{2, 3}))
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.item<bool>());
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CHECK(
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allclose(
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norm(x, 0.0, 0), array({1., 2., 2., 2., 2., 2., 2., 2., 2.}, {3, 3}))
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.item<bool>());
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CHECK(allclose(norm(x, 0.0, 1), array({2., 3., 3., 3., 3., 3.}, {2, 3}))
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.item<bool>());
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CHECK(allclose(norm(x, 0.0, 2), array({2., 3., 3., 3., 3., 3.}, {2, 3}))
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.item<bool>());
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CHECK(allclose(
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norm(x, 1.0, 0),
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array({9., 11., 13., 15., 17., 19., 21., 23., 25.}, {3, 3}))
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.item<bool>());
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CHECK(allclose(norm(x, 1.0, 1), array({9., 12., 15., 36., 39., 42.}, {2, 3}))
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.item<bool>());
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CHECK(allclose(norm(x, 1.0, 2), array({3., 12., 21., 30., 39., 48.}, {2, 3}))
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.item<bool>());
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CHECK(allclose(norm(x, 1.0, std::vector<int>{0, 1}), array({21., 23., 25.}))
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.item<bool>());
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CHECK(allclose(norm(x, 1.0, std::vector<int>{1, 2}), array({15., 42.}))
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.item<bool>());
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CHECK(allclose(norm(x, -1.0, std::vector<int>{0, 1}), array({9., 11., 13.}))
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.item<bool>());
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CHECK(allclose(norm(x, -1.0, std::vector<int>{1, 2}), array({9., 36.}))
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.item<bool>());
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CHECK(allclose(norm(x, -1.0, std::vector<int>{1, 0}), array({9., 12., 15.}))
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.item<bool>());
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CHECK(allclose(norm(x, -1.0, std::vector<int>{2, 1}), array({3, 30}))
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.item<bool>());
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CHECK(allclose(norm(x, -1.0, std::vector<int>{1, 2}), array({9, 36}))
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.item<bool>());
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}
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TEST_CASE("[mlx.core.linalg.norm] string ord") {
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array x({1, 2, 3});
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CHECK_THROWS(norm(x, "fro"));
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x = reshape(arange(9), {3, 3});
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CHECK_THROWS(norm(x, "bad ord"));
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CHECK_EQ(
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norm(x, "f", std::vector<int>{0, 1}).item<float>(),
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doctest::Approx(14.2828568570857));
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CHECK_EQ(
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norm(x, "fro", std::vector<int>{0, 1}).item<float>(),
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doctest::Approx(14.2828568570857));
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x = reshape(arange(18), {2, 3, 3});
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CHECK(allclose(
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norm(x, "fro", std::vector<int>{0, 1}),
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array({22.24859546, 24.31049156, 26.43860813}))
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.item<bool>());
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CHECK(allclose(
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norm(x, "fro", std::vector<int>{1, 2}),
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array({14.28285686, 39.7617907}))
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.item<bool>());
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CHECK(allclose(
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norm(x, "f", std::vector<int>{0, 1}),
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array({22.24859546, 24.31049156, 26.43860813}))
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.item<bool>());
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CHECK(allclose(
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norm(x, "f", std::vector<int>{1, 0}),
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array({22.24859546, 24.31049156, 26.43860813}))
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.item<bool>());
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CHECK(allclose(
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norm(x, "f", std::vector<int>{1, 2}),
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array({14.28285686, 39.7617907}))
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.item<bool>());
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CHECK(allclose(
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norm(x, "f", std::vector<int>{2, 1}),
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array({14.28285686, 39.7617907}))
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.item<bool>());
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}
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TEST_CASE("test QR factorization") {
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// 0D and 1D throw
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CHECK_THROWS(linalg::qr(array(0.0)));
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CHECK_THROWS(linalg::qr(array({0.0, 1.0})));
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// Unsupported types throw
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CHECK_THROWS(linalg::qr(array({0, 1}, {1, 2})));
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array A = array({{2., 3., 1., 2.}, {2, 2}});
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auto [Q, R] = linalg::qr(A, Device::cpu);
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auto out = matmul(Q, R);
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CHECK(allclose(out, A).item<bool>());
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out = matmul(Q, Q);
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CHECK(allclose(out, eye(2), 1e-5, 1e-7).item<bool>());
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CHECK(allclose(tril(R, -1), zeros_like(R)).item<bool>());
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CHECK_EQ(Q.dtype(), float32);
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CHECK_EQ(R.dtype(), float32);
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}
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