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# Copyright © 2024 Apple Inc.
import unittest
import mlx.core as mx
import mlx_tests
import numpy as np
class TestEinsum(mlx_tests.MLXTestCase):
def test_simple_path(self):
a = mx.zeros((5, 5))
path = mx.einsum_path("ii", a)
self.assertEqual(path[0], [(0,)])
path = mx.einsum_path("ij->i", a)
self.assertEqual(path[0], [(0,)])
path = mx.einsum_path("ii->i", a)
self.assertEqual(path[0], [(0,)])
a = mx.zeros((5, 8))
b = mx.zeros((8, 3))
path = mx.einsum_path("ij,jk", a, b)
self.assertEqual(path[0], [(0, 1)])
path = mx.einsum_path("ij,jk -> ijk", a, b)
self.assertEqual(path[0], [(0, 1)])
a = mx.zeros((5, 8))
b = mx.zeros((8, 3))
c = mx.zeros((3, 7))
path = mx.einsum_path("ij,jk,kl", a, b, c)
self.assertEqual(path[0], [(0, 1), (0, 1)])
a = mx.zeros((5, 8))
b = mx.zeros((8, 10))
c = mx.zeros((10, 7))
path = mx.einsum_path("ij,jk,kl", a, b, c)
self.assertEqual(path[0], [(1, 2), (0, 1)])
def test_longer_paths(self):
chars = "abcdefghijklmopqABC"
sizes = [2, 3, 4, 5, 4, 3, 2, 6, 5, 4, 3, 2, 5, 7, 4, 3, 2, 3, 4]
dim_dict = {c: s for c, s in zip(chars, sizes)}
cases = [
"eb,cb,fb->cef",
"dd,fb,be,cdb->cef",
"dd,fb,be,cdb->cef",
"bca,cdb,dbf,afc->",
"dcc,fce,ea,dbf->ab",
"dcc,fce,ea,dbf->ab",
]
for case in cases:
subscripts = case[: case.find("->")].split(",")
inputs = []
for s in subscripts:
shape = [dim_dict[c] for c in s]
inputs.append(np.ones(shape))
np_path = np.einsum_path(case, *inputs)
inputs = [mx.array(i) for i in inputs]
mx_path = mx.einsum_path(case, *inputs)
self.assertEqual(np_path[0][1:], mx_path[0])
def test_simple_einsum(self):
a = mx.arange(4 * 4).reshape(4, 4)
a_mx = mx.einsum("ii->i", a)
a_np = np.einsum("ii->i", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 2 * 2).reshape(2, 2, 2)
a_mx = mx.einsum("iii->i", a)
a_np = np.einsum("iii->i", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 2 * 3 * 3).reshape(2, 2, 3, 3)
a_mx = mx.einsum("iijj->ij", a)
a_np = np.einsum("iijj->ij", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 2 * 3 * 3).reshape(2, 3, 2, 3)
a_mx = mx.einsum("ijij->ij", a)
a_np = np.einsum("ijij->ij", a)
self.assertTrue(np.array_equal(a_mx, a_np))
# Test some simple reductions
a = mx.arange(2 * 2).reshape(2, 2)
a_mx = mx.einsum("ii", a)
a_np = np.einsum("ii", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 4).reshape(2, 4)
a_mx = mx.einsum("ij->", a)
a_np = np.einsum("ij->", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 4).reshape(2, 4)
a_mx = mx.einsum("ij->i", a)
a_np = np.einsum("ij->i", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 4).reshape(2, 4)
a_mx = mx.einsum("ij->j", a)
a_np = np.einsum("ij->j", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 2 * 2).reshape(2, 2, 2)
a_mx = mx.einsum("iii->", a)
a_np = np.einsum("iii->", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 2 * 3 * 3).reshape(2, 3, 2, 3)
a_mx = mx.einsum("ijij->j", a)
a_np = np.einsum("ijij->j", a)
self.assertTrue(np.array_equal(a_mx, a_np))
# Test some simple transposes
a = mx.arange(2 * 4).reshape(2, 4)
a_mx = mx.einsum("ij", a)
a_np = np.einsum("ij", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 4).reshape(2, 4)
a_mx = mx.einsum("ij->ji", a)
a_np = np.einsum("ij->ji", a)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.arange(2 * 3 * 4).reshape(2, 3, 4)
a_mx = mx.einsum("ijk->jki", a)
a_np = np.einsum("ijk->jki", a)
self.assertTrue(np.array_equal(a_mx, a_np))
def test_two_input_einsum(self):
# Matmul
a = mx.full((2, 8), 1.0)
b = mx.full((8, 2), 1.0)
a_mx = mx.einsum("ik,kj", a, b)
a_np = np.einsum("ik,kj", a, b)
self.assertTrue(np.array_equal(a_mx, a_np))
# Matmul + transpose
a = mx.full((2, 8), 1.0)
b = mx.full((8, 3), 1.0)
a_mx = mx.einsum("ik,kj->ji", a, b)
a_np = np.einsum("ik,kj->ji", a, b)
self.assertTrue(np.array_equal(a_mx, a_np))
# Inner product
a = mx.full((4,), 1.0)
b = mx.full((4,), 1.0)
a_mx = mx.einsum("i,i", a, b)
a_np = np.einsum("i,i", a, b)
self.assertTrue(np.array_equal(a_mx, a_np))
# Outer product
a = mx.full((4,), 0.5)
b = mx.full((6,), 2.0)
a_mx = mx.einsum("i,j->ij", a, b)
a_np = np.einsum("i,j->ij", a, b)
self.assertTrue(np.array_equal(a_mx, a_np))
# Elementwise multiply
a = mx.full((2, 8), 1.0)
b = mx.full((2, 8), 1.0)
a_mx = mx.einsum("ij,ij->ij", a, b)
a_np = np.einsum("ij,ij->ij", a, b)
self.assertTrue(np.array_equal(a_mx, a_np))
# Medley
a = mx.full((2, 8, 3, 5), 1.0)
b = mx.full((3, 7, 5, 2), 1.0)
a_mx = mx.einsum("abcd,fgda->bfca", a, b)
a_np = np.einsum("abcd,fgda->bfca", a, b)
self.assertTrue(np.array_equal(a_mx, a_np))
def test_sum_first(self):
a = mx.full((5, 8), 1.0)
b = mx.full((8, 2), 1.0)
a_mx = mx.einsum("ab,bc->c", a, b)
a_np = np.einsum("ab,bc->c", a, b)
self.assertTrue(np.array_equal(a_mx, a_np))
def test_broadcasting(self):
a = mx.full((5, 1), 1.0)
b = mx.full((8, 2), 1.0)
a_mx = mx.einsum("ab,bc->c", a, b)
return
a_np = np.einsum("ab,bc->c", a, b)
self.assertTrue(np.array_equal(a_mx, a_np))
a = mx.random.uniform(shape=(5, 1, 3, 1))
b = mx.random.uniform(shape=(1, 7, 1, 2))
a_mx = mx.einsum("abcd,cdab->abcd", a, b)
a_np = np.einsum("abcd,cdab->abcd", a, b)
self.assertTrue(np.allclose(a_mx, a_np))
def test_attention(self):
q = mx.random.uniform(shape=(2, 3, 4, 5))
k = mx.random.uniform(shape=(2, 3, 4, 5))
v = mx.random.uniform(shape=(2, 3, 4, 5))
s = mx.einsum("itjk,iujk->ijtu", q, k)
out_mx = mx.einsum("ijtu,iujk->itjk", s, v)
s = np.einsum("itjk,iujk->ijtu", q, k)
out_np = np.einsum("ijtu,iujk->itjk", s, v)
self.assertTrue(np.allclose(out_mx, out_np))
def test_multi_input_einsum(self):
a = mx.ones((3, 4, 5))
out_mx = mx.einsum("ijk,lmk,ijf->lf", a, a, a)
out_np = np.einsum("ijk,lmk,ijf->lf", a, a, a)
self.assertTrue(np.allclose(out_mx, out_np))
def test_opt_einsum_test_cases(self):
# Test cases from
# https://github.com/dgasmith/opt_einsum/blob/c826bb7df16f470a69f7bf90598fc27586209d11/opt_einsum/tests/test_contract.py#L11
tests = [
# Test hadamard-like products
"a,ab,abc->abc",
"a,b,ab->ab",
# Test index-transformations
"ea,fb,gc,hd,abcd->efgh",
"ea,fb,abcd,gc,hd->efgh",
"abcd,ea,fb,gc,hd->efgh",
# Test complex contractions
"acdf,jbje,gihb,hfac,gfac,gifabc,hfac",
"cd,bdhe,aidb,hgca,gc,hgibcd,hgac",
"abhe,hidj,jgba,hiab,gab",
"bde,cdh,agdb,hica,ibd,hgicd,hiac",
"chd,bde,agbc,hiad,hgc,hgi,hiad",
"chd,bde,agbc,hiad,bdi,cgh,agdb",
"bdhe,acad,hiab,agac,hibd",
# Test collapse
"ab,ab,c->",
"ab,ab,c->c",
"ab,ab,cd,cd->",
"ab,ab,cd,cd->ac",
"ab,ab,cd,cd->cd",
"ab,ab,cd,cd,ef,ef->",
# Test outer prodcuts
"ab,cd,ef->abcdef",
"ab,cd,ef->acdf",
"ab,cd,de->abcde",
"ab,cd,de->be",
"ab,bcd,cd->abcd",
"ab,bcd,cd->abd",
# Random test cases that have previously failed
"eb,cb,fb->cef",
"dd,fb,be,cdb->cef",
"bca,cdb,dbf,afc->",
"dcc,fce,ea,dbf->ab",
"fdf,cdd,ccd,afe->ae",
"abcd,ad",
"ed,fcd,ff,bcf->be",
"baa,dcf,af,cde->be",
"bd,db,eac->ace",
"fff,fae,bef,def->abd",
"efc,dbc,acf,fd->abe",
# Inner products
"ab,ab",
"ab,ba",
"abc,abc",
"abc,bac",
"abc,cba",
# GEMM test cases
"ab,bc",
"ab,cb",
"ba,bc",
"ba,cb",
"abcd,cd",
"abcd,ab",
"abcd,cdef",
"abcd,cdef->feba",
"abcd,efdc",
# Inner then dot
"aab,bc->ac",
"ab,bcc->ac",
"aab,bcc->ac",
"baa,bcc->ac",
"aab,ccb->ac",
# Randomly build test caes
"aab,fa,df,ecc->bde",
"ecb,fef,bad,ed->ac",
"bcf,bbb,fbf,fc->",
"bb,ff,be->e",
"bcb,bb,fc,fff->",
"fbb,dfd,fc,fc->",
"afd,ba,cc,dc->bf",
"adb,bc,fa,cfc->d",
"bbd,bda,fc,db->acf",
"dba,ead,cad->bce",
"aef,fbc,dca->bde",
]
size_dict = dict(zip("abcdefghij", [2, 3, 4, 5, 2, 3, 4, 5, 2, 3]))
def inputs_for_case(test_case):
inputs = test_case.split("->")[0].split(",")
return [
mx.random.uniform(shape=tuple(size_dict[c] for c in inp))
for inp in inputs
]
for test_case in tests:
inputs = inputs_for_case(test_case)
np_out = np.einsum(test_case, *inputs)
mx_out = mx.einsum(test_case, *inputs)
self.assertTrue(np.allclose(mx_out, np_out, rtol=1e-4, atol=1e-4))
def test_ellipses(self):
size_dict = dict(zip("abcdefghij", [2, 3, 4, 5, 2, 3, 4, 5, 2, 3]))
def inputs_for_case(test_case):
inputs = test_case.split("->")[0].split(",")
return [
mx.random.uniform(shape=tuple(size_dict[c] for c in inp))
for inp in inputs
]
tests = [
("abc->ab", "...c->..."),
("abcd->ad", "a...d->..."),
("abij,abgj->abig", "...ij,...gj->...ig"),
("abij,abgj->abig", "...ij,...gj->..."),
("abhh->abh", "...hh->...h"),
("abhh->abh", "...hh->...h"),
("bch,abcj->abchj", "...h,...j->...hj"),
("bc,cd->bd", "...c,cd"),
("abc,acd->bd", "...bc,...cd"),
("abcd,c->abd", "...cd,c"),
("abcd,c->abd", "...cd,c..."),
("abcd,c->abd", "...cd,c...->d..."),
("abc,b->abc", "ab...,b...->ab..."),
("abc,b->abc", "ab...,...b->ab..."),
("abc,b->abc", "ab...,b->ab..."),
("ab,bc->ac", "ab...,b...->a..."),
("ab,bc->ac", "ab...,...bc->a...c"),
("ab,bc->ac", "ab,b...->a..."),
("abcdef,defg->abcg", "...def,defg->...g"),
]
for test_case in tests:
inputs = inputs_for_case(test_case[0])
np_out = np.einsum(test_case[1], *inputs)
mx_out = mx.einsum(test_case[1], *inputs)
self.assertTrue(np.allclose(mx_out, np_out, rtol=1e-4, atol=1e-4))
error_tests = [
("abc,abc->ab", "a...b...c,a...b...c->abc"),
]
for test_case in error_tests:
inputs = inputs_for_case(test_case[0])
with self.assertRaises(ValueError):
mx.einsum(test_case[1], *inputs)
if __name__ == "__main__":
mlx_tests.MLXTestRunner()
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