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// Copyright © 2023 Apple Inc.
#include "doctest/doctest.h"
#include "mlx/mlx.h"
using namespace mlx::core;
TEST_CASE("test fft basics") {
array x(1.0);
CHECK_THROWS(fft::fft(x));
CHECK_THROWS(fft::ifft(x));
x = array({1.0});
auto y = fft::fft(x);
CHECK_EQ(y.dtype(), complex64);
CHECK_EQ(y.size(), x.size());
CHECK_EQ(y.item<complex64_t>(), complex64_t{1.0f, 0.0f});
y = fft::ifft(x);
CHECK_EQ(y.dtype(), complex64);
CHECK_EQ(y.size(), x.size());
CHECK_EQ(y.item<complex64_t>(), complex64_t{1.0f, 0.0f});
x = array({complex64_t{1.0f, 1.0f}}, complex64);
y = fft::fft(x);
CHECK_EQ(y.size(), x.size());
CHECK_EQ(y.item<complex64_t>(), complex64_t{1.0f, 1.0f});
y = fft::ifft(x);
CHECK_EQ(y.dtype(), complex64);
CHECK_EQ(y.size(), x.size());
CHECK_EQ(y.item<complex64_t>(), complex64_t{1.0f, 1.0f});
{
x = array({0.0f, 1.0f, 2.0f, 3.0f});
y = fft::fft(x);
std::initializer_list<complex64_t> expected = {
{6.0, 0.0},
{-2.0, 2.0},
{-2.0, 0.0},
{-2.0, -2.0},
};
CHECK_EQ(y.size(), x.size());
CHECK(array_equal(y, array(expected)).item<bool>());
y = fft::ifft(x);
std::initializer_list<complex64_t> expected_inv = {
{1.5, 0.0},
{-0.5, -0.5},
{-0.5, 0.0},
{-0.5, 0.5},
};
CHECK(array_equal(y, array(expected_inv)).item<bool>());
}
{
std::initializer_list<complex64_t> vals = {
{1.0f, 1.0f}, {2.0f, 1.0f}, {1.0f, 2.0f}, {2.0f, 2.0f}};
x = array(vals);
y = fft::fft(x);
std::initializer_list<complex64_t> expected = {
{6.0, 6.0},
{-1.0, -1.0},
{-2.0, 0.0},
{1.0, -1.0},
};
CHECK_EQ(y.size(), x.size());
CHECK(array_equal(y, array(expected)).item<bool>());
CHECK(array_equal(fft::ifft(y), x).item<bool>());
}
// Specify axes
{
x = array({0.0f, 1.0f, 2.0f, 3.0f}, {2, 2});
std::initializer_list<complex64_t> expected_0 = {
{2.0, 0.0},
{4.0, 0.0},
{-2.0, 0.0},
{-2.0, 0.0},
};
y = fft::fft(x, 0);
CHECK(array_equal(y, array(expected_0, {2, 2})).item<bool>());
CHECK(array_equal(fft::ifft(y, 0), x).item<bool>());
std::initializer_list<complex64_t> expected_1 = {
{1.0, 0.0},
{-1.0, 0.0},
{5.0, 0.0},
{-1.0, 0.0},
};
y = fft::fft(x, 1);
CHECK(array_equal(y, array(expected_1, {2, 2})).item<bool>());
CHECK(array_equal(fft::ifft(y, 1), x).item<bool>());
}
}
TEST_CASE("test real ffts") {
auto x = array({1.0});
auto y = fft::rfft(x);
CHECK_EQ(y.dtype(), complex64);
CHECK_EQ(y.size(), x.size());
CHECK_EQ(y.item<complex64_t>(), complex64_t{1.0f, 0.0f});
{
x = array({0.0f, 1.0f, 2.0f, 3.0f});
y = fft::rfft(x);
std::initializer_list<complex64_t> expected = {
{6.0, 0.0}, {-2.0, 2.0}, {-2.0, -0.0}};
CHECK_EQ(y.size(), x.size() / 2 + 1);
CHECK(array_equal(y, array(expected)).item<bool>());
}
x = array(complex64_t{1, 1});
CHECK_THROWS(fft::irfft(x));
x = array({complex64_t{0, 1}, complex64_t{1, 0}});
y = fft::irfft(x);
CHECK_EQ(y.size(), 2);
CHECK_EQ(y.dtype(), float32);
CHECK(array_equal(y, array({0.5f, -0.5f})).item<bool>());
}
TEST_CASE("test fftn") {
auto x = zeros({5, 5, 5});
CHECK_THROWS_AS(fft::fftn(x, {}, {0, 3}), std::invalid_argument);
CHECK_THROWS_AS(fft::fftn(x, {}, {0, -4}), std::invalid_argument);
CHECK_THROWS_AS(fft::fftn(x, {}, {0, 0}), std::invalid_argument);
CHECK_THROWS_AS(fft::fftn(x, {5, 5, 5}, {0}), std::invalid_argument);
CHECK_THROWS_AS(fft::fftn(x, {0}, {}, {}), std::invalid_argument);
CHECK_THROWS_AS(fft::fftn(x, {1, -1}, {}, {}), std::invalid_argument);
// Test 2D FFT
{
x = array({0.0f, 1.0f, 2.0f, 3.0f}, {2, 2});
std::initializer_list<complex64_t> expected = {
{6.0, 0.0},
{-2.0, 0.0},
{-4.0, 0.0},
{0.0, 0.0},
};
auto y = fft::fft2(x);
CHECK(array_equal(y, array(expected, {2, 2})).item<bool>());
CHECK(array_equal(fft::ifft2(y), x).item<bool>());
}
// Test 3D FFT
{
x = reshape(arange(8, float32), {2, 2, 2});
std::initializer_list<complex64_t> expected = {
{28.0, 0.0},
{-4.0, 0.0},
{-8.0, 0.0},
{0.0, 0.0},
{-16.0, 0.0},
{0.0, 0.0},
{0.0, 0.0},
{0.0, 0.0},
};
auto y = fft::fftn(x);
CHECK(array_equal(y, array(expected, {2, 2, 2})).item<bool>());
CHECK(array_equal(fft::ifftn(y), x).item<bool>());
x = reshape(arange(20, float32), {5, 4});
y = fft::rfftn(x);
CHECK_EQ(y.shape(), Shape{5, 3});
y = fft::rfftn(x, {1, 0});
CHECK_EQ(y.shape(), Shape{3, 4});
x = reshape(arange(20, float32), {5, 4});
y = fft::irfftn(x);
CHECK_EQ(y.shape(), Shape{5, 6});
y = fft::irfftn(x, {1, 0});
CHECK_EQ(y.shape(), Shape{8, 4});
}
// Check the types of real ffts
{
x = zeros({5, 5}, float32);
auto y = fft::rfft2(x);
CHECK_EQ(y.shape(), Shape{5, 3});
CHECK_EQ(y.dtype(), complex64);
y = fft::rfftn(x);
CHECK_EQ(y.shape(), Shape{5, 3});
CHECK_EQ(y.dtype(), complex64);
x = zeros({5, 5}, complex64);
y = fft::irfft2(x);
CHECK_EQ(y.shape(), Shape{5, 8});
CHECK_EQ(y.dtype(), float32);
y = fft::irfftn(x);
CHECK_EQ(y.shape(), Shape{5, 8});
CHECK_EQ(y.dtype(), float32);
}
}
TEST_CASE("test fft with provided shape") {
auto x = ones({5, 5});
auto y = fft::fft(x, 7, 0);
CHECK_EQ(y.shape(), Shape{7, 5});
y = fft::fft(x, 3, 0);
CHECK_EQ(y.shape(), Shape{3, 5});
y = fft::fft(x, 7, 1);
CHECK_EQ(y.shape(), Shape{5, 7});
y = fft::fft(x, 3, 1);
CHECK_EQ(y.shape(), Shape{5, 3});
y = fft::rfft(x, 7, 0);
CHECK_EQ(y.shape(), Shape{4, 5});
y = fft::rfft(x, 3, 0);
CHECK_EQ(y.shape(), Shape{2, 5});
y = fft::rfft(x, 3, 1);
CHECK_EQ(y.shape(), Shape{5, 2});
}
TEST_CASE("test fft vmap") {
auto fft_fn = [](array x) { return fft::fft(x); };
auto x = reshape(arange(8), {2, 4});
auto y = vmap(fft_fn)(x);
CHECK(array_equal(y, fft::fft(x)).item<bool>());
y = vmap(fft_fn, 1, 1)(x);
CHECK(array_equal(y, fft::fft(x, 0)).item<bool>());
auto rfft_fn = [](array x) { return fft::rfft(x); };
y = vmap(rfft_fn)(x);
CHECK(array_equal(y, fft::rfft(x)).item<bool>());
y = vmap(rfft_fn, 1, 1)(x);
CHECK(array_equal(y, fft::rfft(x, 0)).item<bool>());
}
TEST_CASE("test fft grads") {
// Regular
auto fft_fn = [](array x) { return fft::fft(x); };
auto cotangent = astype(arange(10), complex64);
auto vjp_out = vjp(fft_fn, zeros_like(cotangent), cotangent).second;
CHECK(array_equal(fft::ifft(cotangent) * 10, vjp_out).item<bool>());
auto tangent = astype(arange(10), complex64);
auto jvp_out = jvp(fft_fn, zeros_like(tangent), tangent).second;
CHECK(array_equal(fft::fft(tangent), jvp_out).item<bool>());
// Inverse
auto ifft_fn = [](array x) { return fft::ifft(x); };
vjp_out = vjp(ifft_fn, zeros_like(cotangent), cotangent).second;
CHECK(array_equal(fft::fft(cotangent) * 0.1, vjp_out).item<bool>());
jvp_out = jvp(ifft_fn, zeros_like(tangent), tangent).second;
CHECK(array_equal(fft::ifft(tangent), jvp_out).item<bool>());
// Real
auto rfft_fn = [](array x) { return fft::rfft(x); };
cotangent = astype(arange(6), complex64);
vjp_out = vjp(rfft_fn, zeros({10}), cotangent).second;
array mask({1.0, 0.5, 0.5, 0.5, 0.5, 1.0}, complex64);
auto expected = fft::irfft(cotangent * mask, 10, 0) * 10;
CHECK(array_equal(expected, vjp_out).item<bool>());
tangent = astype(arange(10), float32);
jvp_out = jvp(rfft_fn, zeros_like(tangent), tangent).second;
CHECK(array_equal(fft::rfft(tangent), jvp_out).item<bool>());
// Inverse real
auto irfft_fn = [](array x) { return fft::irfft(x); };
cotangent = astype(arange(10), float32);
vjp_out = vjp(irfft_fn, astype(zeros({6}), complex64), cotangent).second;
mask = array({0.1, 0.2, 0.2, 0.2, 0.2, 0.1}, float32);
expected = fft::rfft(cotangent) * mask;
CHECK(array_equal(expected, vjp_out).item<bool>());
tangent = astype(arange(10), complex64);
jvp_out = jvp(irfft_fn, zeros_like(tangent), tangent).second;
CHECK(array_equal(fft::irfft(tangent), jvp_out).item<bool>());
// Check ND vjps run properly
vjp_out = vjp([](array x) { return fft::fftn(x); },
astype(zeros({5, 5}), complex64),
astype(zeros({5, 5}), complex64))
.second;
CHECK_EQ(vjp_out.shape(), Shape{5, 5});
vjp_out = vjp([](array x) { return fft::ifftn(x); },
astype(zeros({5, 5}), complex64),
astype(zeros({5, 5}), complex64))
.second;
CHECK_EQ(vjp_out.shape(), Shape{5, 5});
vjp_out = vjp([](array x) { return fft::rfftn(x); },
zeros({5, 9}),
astype(zeros({5, 5}), complex64))
.second;
CHECK_EQ(vjp_out.shape(), Shape{5, 9});
vjp_out = vjp([](array x) { return fft::irfftn(x); },
astype(zeros({5, 5}), complex64),
zeros({5, 8}))
.second;
CHECK_EQ(vjp_out.shape(), Shape{5, 5});
}
TEST_CASE("test fftshift and ifftshift") {
// Test 1D array with even length
auto x = arange(8);
auto y = fft::fftshift(x);
CHECK_EQ(y.shape(), x.shape());
// print y
CHECK(array_equal(y, array({4, 5, 6, 7, 0, 1, 2, 3})).item<bool>());
// Test 1D array with odd length
x = arange(7);
y = fft::fftshift(x);
CHECK_EQ(y.shape(), x.shape());
CHECK(array_equal(y, array({4, 5, 6, 0, 1, 2, 3})).item<bool>());
// Test 2D array
x = reshape(arange(16), {4, 4});
y = fft::fftshift(x);
auto expected =
array({10, 11, 8, 9, 14, 15, 12, 13, 2, 3, 0, 1, 6, 7, 4, 5}, {4, 4});
CHECK(array_equal(y, expected).item<bool>());
// Test with specific axes
y = fft::fftshift(x, {0});
expected =
array({8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7}, {4, 4});
CHECK(array_equal(y, expected).item<bool>());
y = fft::fftshift(x, {1});
expected =
array({2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13}, {4, 4});
CHECK(array_equal(y, expected).item<bool>());
// Test ifftshift (inverse operation)
x = arange(8);
y = fft::ifftshift(x);
CHECK_EQ(y.shape(), x.shape());
CHECK(array_equal(y, array({4, 5, 6, 7, 0, 1, 2, 3})).item<bool>());
// Test ifftshift with odd length (different from fftshift)
x = arange(7);
y = fft::ifftshift(x);
CHECK_EQ(y.shape(), x.shape());
CHECK(array_equal(y, array({3, 4, 5, 6, 0, 1, 2})).item<bool>());
// Test 2D ifftshift
x = reshape(arange(16), {4, 4});
y = fft::ifftshift(x);
expected =
array({10, 11, 8, 9, 14, 15, 12, 13, 2, 3, 0, 1, 6, 7, 4, 5}, {4, 4});
CHECK(array_equal(y, expected).item<bool>());
// Test error cases
CHECK_THROWS_AS(fft::fftshift(x, {3}), std::invalid_argument);
CHECK_THROWS_AS(fft::fftshift(x, {-5}), std::invalid_argument);
CHECK_THROWS_AS(fft::ifftshift(x, {3}), std::invalid_argument);
CHECK_THROWS_AS(fft::ifftshift(x, {-5}), std::invalid_argument);
}
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