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Einsum (#1269)
* einsum initial * fix comma break * sum axis was wrong * small cleanups * python binding * changed bindings to resemble numpy * remove todo comment * comment changes * add count of operands/inputs * fail fast if operands list is empty * ignore comma if no output * einsum path matching numpy * getting somewhere with path * remove print * it passes the first test * moved einsum tests to seperate file * seperated einsum path * moved einsum naive * remove space from equation * fast fail if no operands passed * update tests and remove printf * small cleanup * some more cleanups * removed python helper file * ack * utilize std for finding min in vector * duplicate def * remove the tuple as it was unreadable * moved einsum_naive back to ops * remaining isn't needed * avoid creating another set * cleanup * greedy path, start of naive einsum * more einsum * fix some bugs * some more fixes, tests pass * benchmark * some simplify * fix einsum and test Co-authored-by: Angelos Katharopoulos <a_katharopoulos@apple.com> * add a bunch more tests and fix a bunch more bugs * some docs nits --------- Co-authored-by: dc-dc-dc <dgcruz983@gmail.com> Co-authored-by: Angelos Katharopoulos <a_katharopoulos@apple.com>
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Awni Hannun
318
python/tests/test_einsum.py
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318
python/tests/test_einsum.py
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# Copyright © 2024 Apple Inc.
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import unittest
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import mlx.core as mx
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import mlx_tests
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import numpy as np
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class TestEinsum(mlx_tests.MLXTestCase):
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def test_simple_path(self):
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a = mx.zeros((5, 5))
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path = mx.einsum_path("ii", a)
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self.assertEqual(path[0], [(0,)])
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path = mx.einsum_path("ij->i", a)
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self.assertEqual(path[0], [(0,)])
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path = mx.einsum_path("ii->i", a)
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self.assertEqual(path[0], [(0,)])
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a = mx.zeros((5, 8))
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b = mx.zeros((8, 3))
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path = mx.einsum_path("ij,jk", a, b)
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self.assertEqual(path[0], [(0, 1)])
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path = mx.einsum_path("ij,jk -> ijk", a, b)
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self.assertEqual(path[0], [(0, 1)])
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a = mx.zeros((5, 8))
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b = mx.zeros((8, 3))
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c = mx.zeros((3, 7))
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path = mx.einsum_path("ij,jk,kl", a, b, c)
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self.assertEqual(path[0], [(0, 1), (0, 1)])
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a = mx.zeros((5, 8))
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b = mx.zeros((8, 10))
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c = mx.zeros((10, 7))
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path = mx.einsum_path("ij,jk,kl", a, b, c)
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self.assertEqual(path[0], [(1, 2), (0, 1)])
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def test_longer_paths(self):
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chars = "abcdefghijklmopqABC"
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sizes = [2, 3, 4, 5, 4, 3, 2, 6, 5, 4, 3, 2, 5, 7, 4, 3, 2, 3, 4]
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dim_dict = {c: s for c, s in zip(chars, sizes)}
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cases = [
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"eb,cb,fb->cef",
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"dd,fb,be,cdb->cef",
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"dd,fb,be,cdb->cef",
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"bca,cdb,dbf,afc->",
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"dcc,fce,ea,dbf->ab",
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"dcc,fce,ea,dbf->ab",
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]
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for case in cases:
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subscripts = case[: case.find("->")].split(",")
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inputs = []
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for s in subscripts:
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shape = [dim_dict[c] for c in s]
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inputs.append(np.ones(shape))
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np_path = np.einsum_path(case, *inputs)
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inputs = [mx.array(i) for i in inputs]
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mx_path = mx.einsum_path(case, *inputs)
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self.assertEqual(np_path[0][1:], mx_path[0])
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def test_simple_einsum(self):
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a = mx.arange(4 * 4).reshape(4, 4)
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a_mx = mx.einsum("ii->i", a)
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a_np = np.einsum("ii->i", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 2 * 2).reshape(2, 2, 2)
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a_mx = mx.einsum("iii->i", a)
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a_np = np.einsum("iii->i", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 2 * 3 * 3).reshape(2, 2, 3, 3)
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a_mx = mx.einsum("iijj->ij", a)
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a_np = np.einsum("iijj->ij", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 2 * 3 * 3).reshape(2, 3, 2, 3)
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a_mx = mx.einsum("ijij->ij", a)
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a_np = np.einsum("ijij->ij", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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# Test some simple reductions
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a = mx.arange(2 * 2).reshape(2, 2)
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a_mx = mx.einsum("ii", a)
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a_np = np.einsum("ii", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 4).reshape(2, 4)
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a_mx = mx.einsum("ij->", a)
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a_np = np.einsum("ij->", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 4).reshape(2, 4)
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a_mx = mx.einsum("ij->i", a)
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a_np = np.einsum("ij->i", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 4).reshape(2, 4)
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a_mx = mx.einsum("ij->j", a)
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a_np = np.einsum("ij->j", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 2 * 2).reshape(2, 2, 2)
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a_mx = mx.einsum("iii->", a)
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a_np = np.einsum("iii->", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 2 * 3 * 3).reshape(2, 3, 2, 3)
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a_mx = mx.einsum("ijij->j", a)
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a_np = np.einsum("ijij->j", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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# Test some simple transposes
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a = mx.arange(2 * 4).reshape(2, 4)
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a_mx = mx.einsum("ij", a)
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a_np = np.einsum("ij", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 4).reshape(2, 4)
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a_mx = mx.einsum("ij->ji", a)
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a_np = np.einsum("ij->ji", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.arange(2 * 3 * 4).reshape(2, 3, 4)
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a_mx = mx.einsum("ijk->jki", a)
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a_np = np.einsum("ijk->jki", a)
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self.assertTrue(np.array_equal(a_mx, a_np))
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def test_two_input_einsum(self):
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# Matmul
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a = mx.full((2, 8), 1.0)
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b = mx.full((8, 2), 1.0)
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a_mx = mx.einsum("ik,kj", a, b)
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a_np = np.einsum("ik,kj", a, b)
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self.assertTrue(np.array_equal(a_mx, a_np))
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# Matmul + transpose
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a = mx.full((2, 8), 1.0)
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b = mx.full((8, 3), 1.0)
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a_mx = mx.einsum("ik,kj->ji", a, b)
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a_np = np.einsum("ik,kj->ji", a, b)
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self.assertTrue(np.array_equal(a_mx, a_np))
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# Inner product
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a = mx.full((4,), 1.0)
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b = mx.full((4,), 1.0)
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a_mx = mx.einsum("i,i", a, b)
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a_np = np.einsum("i,i", a, b)
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self.assertTrue(np.array_equal(a_mx, a_np))
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# Outer product
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a = mx.full((4,), 0.5)
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b = mx.full((6,), 2.0)
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a_mx = mx.einsum("i,j->ij", a, b)
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a_np = np.einsum("i,j->ij", a, b)
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self.assertTrue(np.array_equal(a_mx, a_np))
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# Elementwise multiply
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a = mx.full((2, 8), 1.0)
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b = mx.full((2, 8), 1.0)
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a_mx = mx.einsum("ij,ij->ij", a, b)
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a_np = np.einsum("ij,ij->ij", a, b)
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self.assertTrue(np.array_equal(a_mx, a_np))
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# Medley
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a = mx.full((2, 8, 3, 5), 1.0)
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b = mx.full((3, 7, 5, 2), 1.0)
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a_mx = mx.einsum("abcd,fgda->bfca", a, b)
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a_np = np.einsum("abcd,fgda->bfca", a, b)
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self.assertTrue(np.array_equal(a_mx, a_np))
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def test_sum_first(self):
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a = mx.full((5, 8), 1.0)
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b = mx.full((8, 2), 1.0)
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a_mx = mx.einsum("ab,bc->c", a, b)
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a_np = np.einsum("ab,bc->c", a, b)
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self.assertTrue(np.array_equal(a_mx, a_np))
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def test_broadcasting(self):
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a = mx.full((5, 1), 1.0)
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b = mx.full((8, 2), 1.0)
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a_mx = mx.einsum("ab,bc->c", a, b)
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return
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a_np = np.einsum("ab,bc->c", a, b)
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self.assertTrue(np.array_equal(a_mx, a_np))
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a = mx.random.uniform(shape=(5, 1, 3, 1))
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b = mx.random.uniform(shape=(1, 7, 1, 2))
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a_mx = mx.einsum("abcd,cdab->abcd", a, b)
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a_np = np.einsum("abcd,cdab->abcd", a, b)
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self.assertTrue(np.allclose(a_mx, a_np))
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def test_attention(self):
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q = mx.random.uniform(shape=(2, 3, 4, 5))
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k = mx.random.uniform(shape=(2, 3, 4, 5))
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v = mx.random.uniform(shape=(2, 3, 4, 5))
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s = mx.einsum("itjk,iujk->ijtu", q, k)
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out_mx = mx.einsum("ijtu,iujk->itjk", s, v)
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s = np.einsum("itjk,iujk->ijtu", q, k)
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out_np = np.einsum("ijtu,iujk->itjk", s, v)
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self.assertTrue(np.allclose(out_mx, out_np))
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def test_multi_input_einsum(self):
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a = mx.ones((3, 4, 5))
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out_mx = mx.einsum("ijk,lmk,ijf->lf", a, a, a)
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out_np = np.einsum("ijk,lmk,ijf->lf", a, a, a)
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self.assertTrue(np.allclose(out_mx, out_np))
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def test_opt_einsum_test_cases(self):
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# Test cases from
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# https://github.com/dgasmith/opt_einsum/blob/c826bb7df16f470a69f7bf90598fc27586209d11/opt_einsum/tests/test_contract.py#L11
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tests = [
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# Test hadamard-like products
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"a,ab,abc->abc",
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"a,b,ab->ab",
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# Test index-transformations
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"ea,fb,gc,hd,abcd->efgh",
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"ea,fb,abcd,gc,hd->efgh",
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"abcd,ea,fb,gc,hd->efgh",
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# Test complex contractions
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"acdf,jbje,gihb,hfac,gfac,gifabc,hfac",
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"cd,bdhe,aidb,hgca,gc,hgibcd,hgac",
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"abhe,hidj,jgba,hiab,gab",
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"bde,cdh,agdb,hica,ibd,hgicd,hiac",
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"chd,bde,agbc,hiad,hgc,hgi,hiad",
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"chd,bde,agbc,hiad,bdi,cgh,agdb",
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"bdhe,acad,hiab,agac,hibd",
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# Test collapse
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"ab,ab,c->",
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"ab,ab,c->c",
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"ab,ab,cd,cd->",
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"ab,ab,cd,cd->ac",
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"ab,ab,cd,cd->cd",
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"ab,ab,cd,cd,ef,ef->",
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# Test outer prodcuts
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"ab,cd,ef->abcdef",
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"ab,cd,ef->acdf",
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"ab,cd,de->abcde",
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"ab,cd,de->be",
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"ab,bcd,cd->abcd",
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"ab,bcd,cd->abd",
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# Random test cases that have previously failed
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"eb,cb,fb->cef",
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"dd,fb,be,cdb->cef",
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"bca,cdb,dbf,afc->",
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"dcc,fce,ea,dbf->ab",
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"fdf,cdd,ccd,afe->ae",
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"abcd,ad",
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"ed,fcd,ff,bcf->be",
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"baa,dcf,af,cde->be",
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"bd,db,eac->ace",
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"fff,fae,bef,def->abd",
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"efc,dbc,acf,fd->abe",
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# Inner products
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"ab,ab",
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"ab,ba",
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"abc,abc",
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"abc,bac",
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"abc,cba",
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# GEMM test cases
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"ab,bc",
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"ab,cb",
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"ba,bc",
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"ba,cb",
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"abcd,cd",
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"abcd,ab",
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"abcd,cdef",
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"abcd,cdef->feba",
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"abcd,efdc",
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# Inner then dot
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"aab,bc->ac",
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"ab,bcc->ac",
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"aab,bcc->ac",
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"baa,bcc->ac",
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"aab,ccb->ac",
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# Randomly build test caes
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"aab,fa,df,ecc->bde",
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"ecb,fef,bad,ed->ac",
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"bcf,bbb,fbf,fc->",
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"bb,ff,be->e",
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"bcb,bb,fc,fff->",
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"fbb,dfd,fc,fc->",
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"afd,ba,cc,dc->bf",
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"adb,bc,fa,cfc->d",
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"bbd,bda,fc,db->acf",
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"dba,ead,cad->bce",
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"aef,fbc,dca->bde",
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]
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size_dict = dict(zip("abcdefghij", [2, 3, 4, 5, 2, 3, 4, 5, 2, 3]))
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def inputs_for_case(test_case):
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inputs = test_case.split("->")[0].split(",")
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return [
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mx.random.uniform(shape=tuple(size_dict[c] for c in inp))
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for inp in inputs
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]
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for test_case in tests:
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inputs = inputs_for_case(test_case)
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np_out = np.einsum(test_case, *inputs)
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mx_out = mx.einsum(test_case, *inputs)
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self.assertTrue(np.allclose(mx_out, np_out, rtol=1e-4, atol=1e-4))
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if __name__ == "__main__":
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unittest.main()
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