import itertools
import pytest
import numpy as np
from numpy.testing import (
assert_, assert_equal, assert_array_equal, assert_almost_equal,
assert_raises, suppress_warnings, assert_raises_regex, assert_allclose
)
# Setup for optimize einsum
chars = 'abcdefghij'
sizes = np.array([2, 3, 4, 5, 4, 3, 2, 6, 5, 4, 3])
global_size_dict = dict(zip(chars, sizes))
class TestEinsum:
def test_einsum_errors(self):
for do_opt in [True, False]:
# Need enough arguments
assert_raises(ValueError, np.einsum, optimize=do_opt)
assert_raises(ValueError, np.einsum, "", optimize=do_opt)
# subscripts must be a string
assert_raises(TypeError, np.einsum, 0, 0, optimize=do_opt)
# out parameter must be an array
assert_raises(TypeError, np.einsum, "", 0, out='test',
optimize=do_opt)
# order parameter must be a valid order
assert_raises(ValueError, np.einsum, "", 0, order='W',
optimize=do_opt)
# casting parameter must be a valid casting
assert_raises(ValueError, np.einsum, "", 0, casting='blah',
optimize=do_opt)
# dtype parameter must be a valid dtype
assert_raises(TypeError, np.einsum, "", 0, dtype='bad_data_type',
optimize=do_opt)
# other keyword arguments are rejected
assert_raises(TypeError, np.einsum, "", 0, bad_arg=0,
optimize=do_opt)
# issue 4528 revealed a segfault with this call
assert_raises(TypeError, np.einsum, *(None,)*63, optimize=do_opt)
# number of operands must match count in subscripts string
assert_raises(ValueError, np.einsum, "", 0, 0, optimize=do_opt)
assert_raises(ValueError, np.einsum, ",", 0, [0], [0],
optimize=do_opt)
assert_raises(ValueError, np.einsum, ",", [0], optimize=do_opt)
# can't have more subscripts than dimensions in the operand
assert_raises(ValueError, np.einsum, "i", 0, optimize=do_opt)
assert_raises(ValueError, np.einsum, "ij", [0, 0], optimize=do_opt)
assert_raises(ValueError, np.einsum, "...i", 0, optimize=do_opt)
assert_raises(ValueError, np.einsum, "i...j", [0, 0], optimize=do_opt)
assert_raises(ValueError, np.einsum, "i...", 0, optimize=do_opt)
assert_raises(ValueError, np.einsum, "ij...", [0, 0], optimize=do_opt)
# invalid ellipsis
assert_raises(ValueError, np.einsum, "i..", [0, 0], optimize=do_opt)
assert_raises(ValueError, np.einsum, ".i...", [0, 0], optimize=do_opt)
assert_raises(ValueError, np.einsum, "j->..j", [0, 0], optimize=do_opt)
assert_raises(ValueError, np.einsum, "j->.j...", [0, 0], optimize=do_opt)
# invalid subscript character
assert_raises(ValueError, np.einsum, "i%...", [0, 0], optimize=do_opt)
assert_raises(ValueError, np.einsum, "...j$", [0, 0], optimize=do_opt)
assert_raises(ValueError, np.einsum, "i->&", [0, 0], optimize=do_opt)
# output subscripts must appear in input
assert_raises(ValueError, np.einsum, "i->ij", [0, 0], optimize=do_opt)
# output subscripts may only be specified once
assert_raises(ValueError, np.einsum, "ij->jij", [[0, 0], [0, 0]],
optimize=do_opt)
# dimensions much match when being collapsed
assert_raises(ValueError, np.einsum, "ii",
np.arange(6).reshape(2, 3), optimize=do_opt)
assert_raises(ValueError, np.einsum, "ii->i",
np.arange(6).reshape(2, 3), optimize=do_opt)
# broadcasting to new dimensions must be enabled explicitly
assert_raises(ValueError, np.einsum, "i", np.arange(6).reshape(2, 3),
optimize=do_opt)
assert_raises(ValueError, np.einsum, "i->i", [[0, 1], [0, 1]],
out=np.arange(4).reshape(2, 2), optimize=do_opt)
with assert_raises_regex(ValueError, "'b'"):
# gh-11221 - 'c' erroneously appeared in the error message
a = np.ones((3, 3, 4, 5, 6))
b = np.ones((3, 4, 5))
np.einsum('aabcb,abc', a, b)
# Check order kwarg, asanyarray allows 1d to pass through
assert_raises(ValueError, np.einsum, "i->i", np.arange(6).reshape(-1, 1),
optimize=do_opt, order='d')
def test_einsum_views(self):
# pass-through
for do_opt in [True, False]:
a = np.arange(6)
a.shape = (2, 3)
b = np.einsum("...", a, optimize=do_opt)
assert_(b.base is a)
b = np.einsum(a, [Ellipsis], optimize=do_opt)
assert_(b.base is a)
b = np.einsum("ij", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, a)
b = np.einsum(a, [0, 1], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, a)
# output is writeable whenever input is writeable
b = np.einsum("...", a, optimize=do_opt)
assert_(b.flags['WRITEABLE'])
a.flags['WRITEABLE'] = False
b = np.einsum("...", a, optimize=do_opt)
assert_(not b.flags['WRITEABLE'])
# transpose
a = np.arange(6)
a.shape = (2, 3)
b = np.einsum("ji", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, a.T)
b = np.einsum(a, [1, 0], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, a.T)
# diagonal
a = np.arange(9)
a.shape = (3, 3)
b = np.einsum("ii->i", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a[i, i] for i in range(3)])
b = np.einsum(a, [0, 0], [0], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a[i, i] for i in range(3)])
# diagonal with various ways of broadcasting an additional dimension
a = np.arange(27)
a.shape = (3, 3, 3)
b = np.einsum("...ii->...i", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [[x[i, i] for i in range(3)] for x in a])
b = np.einsum(a, [Ellipsis, 0, 0], [Ellipsis, 0], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [[x[i, i] for i in range(3)] for x in a])
b = np.einsum("ii...->...i", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [[x[i, i] for i in range(3)]
for x in a.transpose(2, 0, 1)])
b = np.einsum(a, [0, 0, Ellipsis], [Ellipsis, 0], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [[x[i, i] for i in range(3)]
for x in a.transpose(2, 0, 1)])
b = np.einsum("...ii->i...", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a[:, i, i] for i in range(3)])
b = np.einsum(a, [Ellipsis, 0, 0], [0, Ellipsis], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a[:, i, i] for i in range(3)])
b = np.einsum("jii->ij", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a[:, i, i] for i in range(3)])
b = np.einsum(a, [1, 0, 0], [0, 1], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a[:, i, i] for i in range(3)])
b = np.einsum("ii...->i...", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a.transpose(2, 0, 1)[:, i, i] for i in range(3)])
b = np.einsum(a, [0, 0, Ellipsis], [0, Ellipsis], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a.transpose(2, 0, 1)[:, i, i] for i in range(3)])
b = np.einsum("i...i->i...", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a.transpose(1, 0, 2)[:, i, i] for i in range(3)])
b = np.einsum(a, [0, Ellipsis, 0], [0, Ellipsis], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a.transpose(1, 0, 2)[:, i, i] for i in range(3)])
b = np.einsum("i...i->...i", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [[x[i, i] for i in range(3)]
for x in a.transpose(1, 0, 2)])
b = np.einsum(a, [0, Ellipsis, 0], [Ellipsis, 0], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [[x[i, i] for i in range(3)]
for x in a.transpose(1, 0, 2)])
# triple diagonal
a = np.arange(27)
a.shape = (3, 3, 3)
b = np.einsum("iii->i", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a[i, i, i] for i in range(3)])
b = np.einsum(a, [0, 0, 0], [0], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, [a[i, i, i] for i in range(3)])
# swap axes
a = np.arange(24)
a.shape = (2, 3, 4)
b = np.einsum("ijk->jik", a, optimize=do_opt)
assert_(b.base is a)
assert_equal(b, a.swapaxes(0, 1))
b = np.einsum(a, [0, 1, 2], [1, 0, 2], optimize=do_opt)
assert_(b.base is a)
assert_equal(b, a.swapaxes(0, 1))
def check_einsum_sums(self, dtype, do_opt=False):
# Check various sums. Does many sizes to exercise unrolled loops.
# sum(a, axis=-1)
for n in range(1, 17):
a = np.arange(n, dtype=dtype)
assert_equal(np.einsum("i->", a, optimize=do_opt),
np.sum(a, axis=-1).astype(dtype))
assert_equal(np.einsum(a, [0], [], optimize=do_opt),
np.sum(a, axis=-1).astype(dtype))
for n in range(1, 17):
a = np.arange(2*3*n, dtype=dtype).reshape(2, 3, n)
assert_equal(np.einsum("...i->...", a, optimize=do_opt),
np.sum(a, axis=-1).astype(dtype))
assert_equal(np.einsum(a, [Ellipsis, 0], [Ellipsis], optimize=do_opt),
np.sum(a, axis=-1).astype(dtype))
# sum(a, axis=0)
for n in range(1, 17):
a = np.arange(2*n, dtype=dtype).reshape(2, n)
assert_equal(np.einsum("i...->...", a, optimize=do_opt),
np.sum(a, axis=0).astype(dtype))
assert_equal(np.einsum(a, [0, Ellipsis], [Ellipsis], optimize=do_opt),
np.sum(a, axis=0).astype(dtype))
for n in range(1, 17):
a = np.arange(2*3*n, dtype=dtype).reshape(2, 3, n)
assert_equal(np.einsum("i...->...", a, optimize=do_opt),
np.sum(a, axis=0).astype(dtype))
assert_equal(np.einsum(a, [0, Ellipsis], [Ellipsis], optimize=do_opt),
np.sum(a, axis=0).astype(dtype))
# trace(a)
for n in range(1, 17):
a = np.arange(n*n, dtype=dtype).reshape(n, n)
assert_equal(np.einsum("ii", a, optimize=do_opt),
np.trace(a).astype(dtype))
assert_equal(np.einsum(a, [0, 0], optimize=do_opt),
np.trace(a).astype(dtype))
# gh-15961: should accept numpy int64 type in subscript list
np_array = np.asarray([0, 0])
assert_equal(np.einsum(a, np_array, optimize=do_opt),
np.trace(a).astype(dtype))
assert_equal(np.einsum(a, list(np_array), optimize=do_opt),
np.trace(a).astype(dtype))
# multiply(a, b)
assert_equal(np.einsum("..., ...", 3, 4), 12) # scalar case
for n in range(1, 17):
a = np.arange(3 * n, dtype=dtype).reshape(3, n)
b = np.arange(2 * 3 * n, dtype=dtype).reshape(2, 3, n)
assert_equal(np.einsum("..., ...", a, b, optimize=do_opt),
np.multiply(a, b))
assert_equal(np.einsum(a, [Ellipsis], b, [Ellipsis], optimize=do_opt),
np.multiply(a, b))
# inner(a,b)
for n in range(1, 17):
a = np.arange(2 * 3 * n, dtype=dtype).reshape(2, 3, n)
b = np.arange(n, dtype=dtype)
assert_equal(np.einsum("...i, ...i", a, b, optimize=do_opt), np.inner(a, b))
assert_equal(np.einsum(a, [Ellipsis, 0], b, [Ellipsis, 0], optimize=do_opt),
np.inner(a, b))
for n in range(1, 11):
a = np.arange(n * 3 * 2, dtype=dtype).reshape(n, 3, 2)
b = np.arange(n, dtype=dtype)
assert_equal(np.einsum("i..., i...", a, b, optimize=do_opt),
np.inner(a.T, b.T).T)
assert_equal(np.einsum(a, [0, Ellipsis], b, [0, Ellipsis], optimize=do_opt),
np.inner(a.T, b.T).T)
# outer(a,b)
for n in range(1, 17):
a = np.arange(3, dtype=dtype)+1
b = np.arange(n, dtype=dtype)+1
assert_equal(np.einsum("i,j", a, b, optimize=do_opt),
np.outer(a, b))
assert_equal(np.einsum(a, [0], b, [1], optimize=do_opt),
np.outer(a, b))
# Suppress the complex warnings for the 'as f8' tests
with suppress_warnings() as sup:
sup.filter(np.ComplexWarning)
# matvec(a,b) / a.dot(b) where a is matrix, b is vector
for n in range(1, 17):
a = np.arange(4*n, dtype=dtype).reshape(4, n)
b = np.arange(n, dtype=dtype)
assert_equal(np.einsum("ij, j", a, b, optimize=do_opt),
np.dot(a, b))
assert_equal(np.einsum(a, [0, 1], b, [1], optimize=do_opt),
np.dot(a, b))
c = np.arange(4, dtype=dtype)
np.einsum("ij,j", a, b, out=c,
dtype='f8', casting='unsafe', optimize=do_opt)
assert_equal(c,
np.dot(a.astype('f8'),
b.astype('f8')).astype(dtype))
c[...] = 0
np.einsum(a, [0, 1], b, [1], out=c,
dtype='f8', casting='unsafe', optimize=do_opt)
assert_equal(c,
np.dot(a.astype('f8'),
b.astype('f8')).astype(dtype))
for n in range(1, 17):
a = np.arange(4*n, dtype=dtype).reshape(4, n)
b = np.arange(n, dtype=dtype)
assert_equal(np.einsum("ji,j", a.T, b.T, optimize=do_opt),
np.dot(b.T, a.T))
assert_equal(np.einsum(a.T, [1, 0], b.T, [1], optimize=do_opt),
np.dot(b.T, a.T))
c = np.arange(4, dtype=dtype)
np.einsum("ji,j", a.T, b.T, out=c,
dtype='f8', casting='unsafe', optimize=do_opt)
assert_equal(c,
np.dot(b.T.astype('f8'),
a.T.astype('f8')).astype(dtype))
c[...] = 0
np.einsum(a.T, [1, 0], b.T, [1], out=c,
dtype='f8', casting='unsafe', optimize=do_opt)
assert_equal(c,
np.dot(b.T.astype('f8'),
a.T.astype('f8')).astype(dtype))
# matmat(a,b) / a.dot(b) where a is matrix, b is matrix
for n in range(1, 17):
if n < 8 or dtype != 'f2':
a = np.arange(4*n, dtype=dtype).reshape(4, n)
b = np.arange(n*6, dtype=dtype).reshape(n, 6)
assert_equal(np.einsum("ij,jk", a, b, optimize=do_opt),
np.dot(a, b))
assert_equal(np.einsum(a, [0, 1], b, [1, 2], optimize=do_opt),
np.dot(a, b))
for n in range(1, 17):
a = np.arange(4*n, dtype=dtype).reshape(4, n)
b = np.arange(n*6, dtype=dtype).reshape(n, 6)
c = np.arange(24, dtype=dtype).reshape(4, 6)
np.einsum("ij,jk", a, b, out=c, dtype='f8', casting='unsafe',
optimize=do_opt)
assert_equal(c,
np.dot(a.astype('f8'),
b.astype('f8')).astype(dtype))
c[...] = 0
np.einsum(a, [0, 1], b, [1, 2], out=c,
dtype='f8', casting='unsafe', optimize=do_opt)
assert_equal(c,
np.dot(a.astype('f8'),
b.astype('f8')).astype(dtype))
# matrix triple product (note this is not currently an efficient
# way to multiply 3 matrices)
a = np.arange(12, dtype=dtype).reshape(3, 4)
b = np.arange(20, dtype=dtype).reshape(4, 5)
c = np.arange(30, dtype=dtype).reshape(5, 6)
if dtype != 'f2':
assert_equal(np.einsum("ij,jk,kl", a, b, c, optimize=do_opt),
a.dot(b).dot(c))
assert_equal(np.einsum(a, [0, 1], b, [1, 2], c, [2, 3],
optimize=do_opt), a.dot(b).dot(c))
d = np.arange(18, dtype=dtype).reshape(3, 6)
np.einsum("ij,jk,kl", a, b, c, out=d,
dtype='f8', casting='unsafe', optimize=do_opt)
tgt = a.astype('f8').dot(b.astype('f8'))
tgt = tgt.dot(c.astype('f8')).astype(dtype)
assert_equal(d, tgt)
d[...] = 0
np.einsum(a, [0, 1], b, [1, 2], c, [2, 3], out=d,
dtype='f8', casting='unsafe', optimize=do_opt)
tgt = a.astype('f8').dot(b.astype('f8'))
tgt = tgt.dot(c.astype('f8')).astype(dtype)
assert_equal(d, tgt)
# tensordot(a, b)
if np.dtype(dtype) != np.dtype('f2'):
a = np.arange(60, dtype=dtype).reshape(3, 4, 5)
b = np.arange(24, dtype=dtype).reshape(4, 3, 2)
assert_equal(np.einsum("ijk, jil -> kl", a, b),
np.tensordot(a, b, axes=([1, 0], [0, 1])))
assert_equal(np.einsum(a, [0, 1, 2], b, [1, 0, 3], [2, 3]),
np.tensordot(a, b, axes=([1, 0], [0, 1])))
c = np.arange(10, dtype=dtype).reshape(5, 2)
np.einsum("ijk,jil->kl", a, b, out=c,
dtype='f8', casting='unsafe', optimize=do_opt)
assert_equal(c, np.tensordot(a.astype('f8'), b.astype('f8'),
axes=([1, 0], [0, 1])).astype(dtype))
c[...] = 0
np.einsum(a, [0, 1, 2], b, [1, 0, 3], [2, 3], out=c,
dtype='f8', casting='unsafe', optimize=do_opt)
assert_equal(c, np.tensordot(a.astype('f8'), b.astype('f8'),
axes=([1, 0], [0, 1])).astype(dtype))
# logical_and(logical_and(a!=0, b!=0), c!=0)
a = np.array([1, 3, -2, 0, 12, 13, 0, 1], dtype=dtype)
b = np.array([0, 3.5, 0., -2, 0, 1, 3, 12], dtype=dtype)
c = np.array([True, True, False, True, True, False, True, True])
assert_equal(np.einsum("i,i,i->i", a, b, c,
dtype='?', casting='unsafe', optimize=do_opt),
np.logical_and(np.logical_and(a != 0, b != 0), c != 0))
assert_equal(np.einsum(a, [0], b, [0], c, [0], [0],
dtype='?', casting='unsafe'),
np.logical_and(np.logical_and(a != 0, b != 0), c != 0))
a = np.arange(9, dtype=dtype)
assert_equal(np.einsum(",i->", 3, a), 3*np.sum(a))
assert_equal(np.einsum(3, [], a, [0], []), 3*np.sum(a))
assert_equal(np.einsum("i,->", a, 3), 3*np.sum(a))
assert_equal(np.einsum(a, [0], 3, [], []), 3*np.sum(a))
# Various stride0, contiguous, and SSE aligned variants
for n in range(1, 25):
a = np.arange(n, dtype=dtype)
if np.dtype(dtype).itemsize > 1:
assert_equal(np.einsum("...,...", a, a, optimize=do_opt),
np.multiply(a, a))
assert_equal(np.einsum("i,i", a, a, optimize=do_opt), np.dot(a, a))
assert_equal(np.einsum("i,->i", a, 2, optimize=do_opt), 2*a)
assert_equal(np.einsum(",i->i", 2, a, optimize=do_opt), 2*a)
assert_equal(np.einsum("i,->", a, 2, optimize=do_opt), 2*np.sum(a))
assert_equal(np.einsum(",i->", 2, a, optimize=do_opt), 2*np.sum(a))
assert_equal(np.einsum("...,...", a[1:], a[:-1], optimize=do_opt),
np.multiply(a[1:], a[:-1]))
assert_equal(np.einsum("i,i", a[1:], a[:-1], optimize=do_opt),
np.dot(a[1:], a[:-1]))
assert_equal(np.einsum("i,->i", a[1:], 2, optimize=do_opt), 2*a[1:])
assert_equal(np.einsum(",i->i", 2, a[1:], optimize=do_opt), 2*a[1:])
assert_equal(np.einsum("i,->", a[1:], 2, optimize=do_opt),
2*np.sum(a[1:]))
assert_equal(np.einsum(",i->", 2, a[1:], optimize=do_opt),
2*np.sum(a[1:]))
# An object array, summed as the data type
a = np.arange(9, dtype=object)
b = np.einsum("i->", a, dtype=dtype, casting='unsafe')
assert_equal(b, np.sum(a))
assert_equal(b.dtype, np.dtype(dtype))
b = np.einsum(a, [0], [], dtype=dtype, casting='unsafe')
assert_equal(b, np.sum(a))
assert_equal(b.dtype, np.dtype(dtype))
# A case which was failing (ticket #1885)
p = np.arange(2) + 1
q = np.arange(4).reshape(2, 2) + 3
r = np.arange(4).reshape(2, 2) + 7
assert_equal(np.einsum('z,mz,zm->', p, q, r), 253)
# singleton dimensions broadcast (gh-10343)
p = np.ones((10,2))
q = np.ones((1,2))
assert_array_equal(np.einsum('ij,ij->j', p, q, optimize=True),
np.einsum('ij,ij->j', p, q, optimize=False))
assert_array_equal(np.einsum('ij,ij->j', p, q, optimize=True),
[10.] * 2)
# a blas-compatible contraction broadcasting case which was failing
# for optimize=True (ticket #10930)
x = np.array([2., 3.])
y = np.array([4.])
assert_array_equal(np.einsum("i, i", x, y, optimize=False), 20.)
assert_array_equal(np.einsum("i, i", x, y, optimize=True), 20.)
# all-ones array was bypassing bug (ticket #10930)
p = np.ones((1, 5)) / 2
q = np.ones((5, 5)) / 2
for optimize in (True, False):
assert_array_equal(np.einsum("...ij,...jk->...ik", p, p,
optimize=optimize),
np.einsum("...ij,...jk->...ik", p, q,
optimize=optimize))
assert_array_equal(np.einsum("...ij,...jk->...ik", p, q,
optimize=optimize),
np.full((1, 5), 1.25))
# Cases which were failing (gh-10899)
x = np.eye(2, dtype=dtype)
y = np.ones(2, dtype=dtype)
assert_array_equal(np.einsum("ji,i->", x, y, optimize=optimize),
[2.]) # contig_contig_outstride0_two
assert_array_equal(np.einsum("i,ij->", y, x, optimize=optimize),
[2.]) # stride0_contig_outstride0_two
assert_array_equal(np.einsum("ij,i->", x, y, optimize=optimize),
[2.]) # contig_stride0_outstride0_two
def test_einsum_sums_int8(self):
self.check_einsum_sums('i1')
def test_einsum_sums_uint8(self):
self.check_einsum_sums('u1')
def test_einsum_sums_int16(self):
self.check_einsum_sums('i2')
def test_einsum_sums_uint16(self):
self.check_einsum_sums('u2')
def test_einsum_sums_int32(self):
self.check_einsum_sums('i4')
self.check_einsum_sums('i4', True)
def test_einsum_sums_uint32(self):
self.check_einsum_sums('u4')
self.check_einsum_sums('u4', True)
def test_einsum_sums_int64(self):
self.check_einsum_sums('i8')
def test_einsum_sums_uint64(self):
self.check_einsum_sums('u8')
def test_einsum_sums_float16(self):
self.check_einsum_sums('f2')
def test_einsum_sums_float32(self):
self.check_einsum_sums('f4')
def test_einsum_sums_float64(self):
self.check_einsum_sums('f8')
self.check_einsum_sums('f8', True)
def test_einsum_sums_longdouble(self):
self.check_einsum_sums(np.longdouble)
def test_einsum_sums_cfloat64(self):
self.check_einsum_sums('c8')
self.check_einsum_sums('c8', True)
def test_einsum_sums_cfloat128(self):
self.check_einsum_sums('c16')
def test_einsum_sums_clongdouble(self):
self.check_einsum_sums(np.clongdouble)
def test_einsum_misc(self):
# This call used to crash because of a bug in
# PyArray_AssignZero
a = np.ones((1, 2))
b = np.ones((2, 2, 1))
assert_equal(np.einsum('ij...,j...->i...', a, b), [[[2], [2]]])
assert_equal(np.einsum('ij...,j...->i...', a, b, optimize=True), [[[2], [2]]])
# Regression test for issue #10369 (test unicode inputs with Python 2)
assert_equal(np.einsum(u'ij...,j...->i...', a, b), [[[2], [2]]])
assert_equal(np.einsum('...i,...i', [1, 2, 3], [2, 3, 4]), 20)
assert_equal(np.einsum(u'...i,...i', [1, 2, 3], [2, 3, 4]), 20)
assert_equal(np.einsum('...i,...i', [1, 2, 3], [2, 3, 4],
optimize=u'greedy'), 20)
# The iterator had an issue with buffering this reduction
a = np.ones((5, 12, 4, 2, 3), np.int64)
b = np.ones((5, 12, 11), np.int64)
assert_equal(np.einsum('ijklm,ijn,ijn->', a, b, b),
np.einsum('ijklm,ijn->', a, b))
assert_equal(np.einsum('ijklm,ijn,ijn->', a, b, b, optimize=True),
np.einsum('ijklm,ijn->', a, b, optimize=True))
# Issue #2027, was a problem in the contiguous 3-argument
# inner loop implementation
a = np.arange(1, 3)
b = np.arange(1, 5).reshape(2, 2)
c = np.arange(1, 9).reshape(4, 2)
assert_equal(np.einsum('x,yx,zx->xzy', a, b, c),
[[[1, 3], [3, 9], [5, 15], [7, 21]],
[[8, 16], [16, 32], [24, 48], [32, 64]]])
assert_equal(np.einsum('x,yx,zx->xzy', a, b, c, optimize=True),
[[[1, 3], [3, 9], [5, 15], [7, 21]],
[[8, 16], [16, 32], [24, 48], [32, 64]]])
# Ensure explicitly setting out=None does not cause an error
# see issue gh-15776 and issue gh-15256
assert_equal(np.einsum('i,j', [1], [2], out=None), [[2]])
def test_subscript_range(self):
# Issue #7741, make sure that all letters of Latin alphabet (both uppercase & lowercase) can be used
# when creating a subscript from arrays
a = np.ones((2, 3))
b = np.ones((3, 4))
np.einsum(a, [0, 20], b, [20, 2], [0, 2], optimize=False)
np.einsum(a, [0, 27], b, [27, 2], [0, 2], optimize=False)
np.einsum(a, [0, 51], b, [51, 2], [0, 2], optimize=False)
assert_raises(ValueError, lambda: np.einsum(a, [0, 52], b, [52, 2], [0, 2], optimize=False))
assert_raises(ValueError, lambda: np.einsum(a, [-1, 5], b, [5, 2], [-1, 2], optimize=False))
def test_einsum_broadcast(self):
# Issue #2455 change in handling ellipsis
# remove the 'middle broadcast' error
# only use the 'RIGHT' iteration in prepare_op_axes
# adds auto broadcast on left where it belongs
# broadcast on right has to be explicit
# We need to test the optimized parsing as well
A = np.arange(2 * 3 * 4).reshape(2, 3, 4)
B = np.arange(3)
ref = np.einsum('ijk,j->ijk', A, B, optimize=False)
for opt in [True, False]:
assert_equal(np.einsum('ij...,j...->ij...', A, B, optimize=opt), ref)
assert_equal(np.einsum('ij...,...j->ij...', A, B, optimize=opt), ref)
assert_equal(np.einsum('ij...,j->ij...', A, B, optimize=opt), ref) # used to raise error
A = np.arange(12).reshape((4, 3))
B = np.arange(6).reshape((3, 2))
ref = np.einsum('ik,kj->ij', A, B, optimize=False)
for opt in [True, False]:
assert_equal(np.einsum('ik...,k...->i...', A, B, optimize=opt), ref)
assert_equal(np.einsum('ik...,...kj->i...j', A, B, optimize=opt), ref)
assert_equal(np.einsum('...k,kj', A, B, optimize=opt), ref) # used to raise error
assert_equal(np.einsum('ik,k...->i...', A, B, optimize=opt), ref) # used to raise error
dims = [2, 3, 4, 5]
a = np.arange(np.prod(dims)).reshape(dims)
v = np.arange(dims[2])
ref = np.einsum('ijkl,k->ijl', a, v, optimize=False)
for opt in [True, False]:
assert_equal(np.einsum('ijkl,k', a, v, optimize=opt), ref)
assert_equal(np.einsum('...kl,k', a, v, optimize=opt), ref) # used to raise error
assert_equal(np.einsum('...kl,k...', a, v, optimize=opt), ref)
J, K, M = 160, 160, 120
A = np.arange(J * K * M).reshape(1, 1, 1, J, K, M)
B = np.arange(J * K * M * 3).reshape(J, K, M, 3)
ref = np.einsum('...lmn,...lmno->...o', A, B, optimize=False)
for opt in [True, False]:
assert_equal(np.einsum('...lmn,lmno->...o', A, B,
optimize=opt), ref) # used to raise error
def test_einsum_fixedstridebug(self):
# Issue #4485 obscure einsum bug
# This case revealed a bug in nditer where it reported a stride
# as 'fixed' (0) when it was in fact not fixed during processing
# (0 or 4). The reason for the bug was that the check for a fixed
# stride was using the information from the 2D inner loop reuse
# to restrict the iteration dimensions it had to validate to be
# the same, but that 2D inner loop reuse logic is only triggered
# during the buffer copying step, and hence it was invalid to
# rely on those values. The fix is to check all the dimensions
# of the stride in question, which in the test case reveals that
# the stride is not fixed.
#
# NOTE: This test is triggered by the fact that the default buffersize,
# used by einsum, is 8192, and 3*2731 = 8193, is larger than that
# and results in a mismatch between the buffering and the
# striding for operand A.
A = np.arange(2 * 3).reshape(2, 3).astype(np.float32)
B = np.arange(2 * 3 * 2731).reshape(2, 3, 2731).astype(np.int16)
es = np.einsum('cl, cpx->lpx', A, B)
tp = np.tensordot(A, B, axes=(0, 0))
assert_equal(es, tp)
# The following is the original test case from the bug report,
# made repeatable by changing random arrays to aranges.
A = np.arange(3 * 3).reshape(3, 3).astype(np.float64)
B = np.arange(3 * 3 * 64 * 64).reshape(3, 3, 64, 64).astype(np.float32)
es = np.einsum('cl, cpxy->lpxy', A, B)
tp = np.tensordot(A, B, axes=(0, 0))
assert_equal(es, tp)
def test_einsum_fixed_collapsingbug(self):
# Issue #5147.
# The bug only occurred when output argument of einssum was used.
x = np.random.normal(0, 1, (5, 5, 5, 5))
y1 = np.zeros((5, 5))
np.einsum('aabb->ab', x, out=y1)
idx = np.arange(5)
y2 = x[idx[:, None], idx[:, None], idx, idx]
assert_equal(y1, y2)
def test_einsum_failed_on_p9_and_s390x(self):
# Issues gh-14692 and gh-12689
# Bug with signed vs unsigned char errored on power9 and s390x Linux
tensor = np.random.random_sample((10, 10, 10, 10))
x = np.einsum('ijij->', tensor)
y = tensor.trace(axis1=0, axis2=2).trace()
assert_allclose(x, y)
def test_einsum_all_contig_non_contig_output(self):
# Issue gh-5907, tests that the all contiguous special case
# actually checks the contiguity of the output
x = np.ones((5, 5))
out = np.ones(10)[::2]
correct_base = np.ones(10)
correct_base[::2] = 5
# Always worked (inner iteration is done with 0-stride):
np.einsum('mi,mi,mi->m', x, x, x, out=out)
assert_array_equal(out.base, correct_base)
# Example 1:
out = np.ones(10)[::2]
np.einsum('im,im,im->m', x, x, x, out=out)
assert_array_equal(out.base, correct_base)
# Example 2, buffering causes x to be contiguous but
# special cases do not catch the operation before:
out = np.ones((2, 2, 2))[..., 0]
correct_base = np.ones((2, 2, 2))
correct_base[..., 0] = 2
x = np.ones((2, 2), np.float32)
np.einsum('ij,jk->ik', x, x, out=out)
assert_array_equal(out.base, correct_base)
@pytest.mark.parametrize("dtype",
np.typecodes["AllFloat"] + np.typecodes["AllInteger"])
def test_different_paths(self, dtype):
# Test originally added to cover broken float16 path: gh-20305
# Likely most are covered elsewhere, at least partially.
dtype = np.dtype(dtype)
# Simple test, designed to excersize most specialized code paths,
# note the +0.5 for floats. This makes sure we use a float value
# where the results must be exact.
arr = (np.arange(7) + 0.5).astype(dtype)
scalar = np.array(2, dtype=dtype)
# contig -> scalar:
res = np.einsum('i->', arr)
assert res == arr.sum()
# contig, contig -> contig:
res = np.einsum('i,i->i', arr, arr)
assert_array_equal(res, arr * arr)
# noncontig, noncontig -> contig:
res = np.einsum('i,i->i', arr.repeat(2)[::2], arr.repeat(2)[::2])
assert_array_equal(res, arr * arr)
# contig + contig -> scalar
assert np.einsum('i,i->', arr, arr) == (arr * arr).sum()
# contig + scalar -> contig (with out)
out = np.ones(7, dtype=dtype)
res = np.einsum('i,->i', arr, dtype.type(2), out=out)
assert_array_equal(res, arr * dtype.type(2))
# scalar + contig -> contig (with out)
res = np.einsum(',i->i', scalar, arr)
assert_array_equal(res, arr * dtype.type(2))
# scalar + contig -> scalar
res = np.einsum(',i->', scalar, arr)
# Use einsum to compare to not have difference due to sum round-offs:
assert res == np.einsum('i->', scalar * arr)
# contig + scalar -> scalar
res = np.einsum('i,->', arr, scalar)
# Use einsum to compare to not have difference due to sum round-offs:
assert res == np.einsum('i->', scalar * arr)
# contig + contig + contig -> scalar
arr = np.array([0.5, 0.5, 0.25, 4.5, 3.], dtype=dtype)
res = np.einsum('i,i,i->', arr, arr, arr)
assert_array_equal(res, (arr * arr * arr).sum())
# four arrays:
res = np.einsum('i,i,i,i->', arr, arr, arr, arr)
assert_array_equal(res, (arr * arr * arr * arr).sum())
def test_small_boolean_arrays(self):
# See gh-5946.
# Use array of True embedded in False.
a = np.zeros((16, 1, 1), dtype=np.bool_)[:2]
a[...] = True
out = np.zeros((16, 1, 1), dtype=np.bool_)[:2]
tgt = np.ones((2, 1, 1), dtype=np.bool_)
res = np.einsum('...ij,...jk->...ik', a, a, out=out)
assert_equal(res, tgt)
def test_out_is_res(self):
a = np.arange(9).reshape(3, 3)
res = np.einsum('...ij,...jk->...ik', a, a, out=a)
assert res is a
def optimize_compare(self, subscripts, operands=None):
# Tests all paths of the optimization function against
# conventional einsum
if operands is None:
args = [subscripts]
terms = subscripts.split('->')[0].split(',')
for term in terms:
dims = [global_size_dict[x] for x in term]
args.append(np.random.rand(*dims))
else:
args = [subscripts] + operands
noopt = np.einsum(*args, optimize=False)
opt = np.einsum(*args, optimize='greedy')
assert_almost_equal(opt, noopt)
opt = np.einsum(*args, optimize='optimal')
assert_almost_equal(opt, noopt)
def test_hadamard_like_products(self):
# Hadamard outer products
self.optimize_compare('a,ab,abc->abc')
self.optimize_compare('a,b,ab->ab')
def test_index_transformations(self):
# Simple index transformation cases
self.optimize_compare('ea,fb,gc,hd,abcd->efgh')
self.optimize_compare('ea,fb,abcd,gc,hd->efgh')
self.optimize_compare('abcd,ea,fb,gc,hd->efgh')
def test_complex(self):
# Long test cases
self.optimize_compare('acdf,jbje,gihb,hfac,gfac,gifabc,hfac')
self.optimize_compare('acdf,jbje,gihb,hfac,gfac,gifabc,hfac')
self.optimize_compare('cd,bdhe,aidb,hgca,gc,hgibcd,hgac')
self.optimize_compare('abhe,hidj,jgba,hiab,gab')
self.optimize_compare('bde,cdh,agdb,hica,ibd,hgicd,hiac')
self.optimize_compare('chd,bde,agbc,hiad,hgc,hgi,hiad')
self.optimize_compare('chd,bde,agbc,hiad,bdi,cgh,agdb')
self.optimize_compare('bdhe,acad,hiab,agac,hibd')
def test_collapse(self):
# Inner products
self.optimize_compare('ab,ab,c->')
self.optimize_compare('ab,ab,c->c')
self.optimize_compare('ab,ab,cd,cd->')
self.optimize_compare('ab,ab,cd,cd->ac')
self.optimize_compare('ab,ab,cd,cd->cd')
self.optimize_compare('ab,ab,cd,cd,ef,ef->')
def test_expand(self):
# Outer products
self.optimize_compare('ab,cd,ef->abcdef')
self.optimize_compare('ab,cd,ef->acdf')
self.optimize_compare('ab,cd,de->abcde')
self.optimize_compare('ab,cd,de->be')
self.optimize_compare('ab,bcd,cd->abcd')
self.optimize_compare('ab,bcd,cd->abd')
def test_edge_cases(self):
# Difficult edge cases for optimization
self.optimize_compare('eb,cb,fb->cef')
self.optimize_compare('dd,fb,be,cdb->cef')
self.optimize_compare('bca,cdb,dbf,afc->')
self.optimize_compare('dcc,fce,ea,dbf->ab')
self.optimize_compare('fdf,cdd,ccd,afe->ae')
self.optimize_compare('abcd,ad')
self.optimize_compare('ed,fcd,ff,bcf->be')
self.optimize_compare('baa,dcf,af,cde->be')
self.optimize_compare('bd,db,eac->ace')
self.optimize_compare('fff,fae,bef,def->abd')
self.optimize_compare('efc,dbc,acf,fd->abe')
self.optimize_compare('ba,ac,da->bcd')
def test_inner_product(self):
# Inner products
self.optimize_compare('ab,ab')
self.optimize_compare('ab,ba')
self.optimize_compare('abc,abc')
self.optimize_compare('abc,bac')
self.optimize_compare('abc,cba')
def test_random_cases(self):
# Randomly built test cases
self.optimize_compare('aab,fa,df,ecc->bde')
self.optimize_compare('ecb,fef,bad,ed->ac')
self.optimize_compare('bcf,bbb,fbf,fc->')
self.optimize_compare('bb,ff,be->e')
self.optimize_compare('bcb,bb,fc,fff->')
self.optimize_compare('fbb,dfd,fc,fc->')
self.optimize_compare('afd,ba,cc,dc->bf')
self.optimize_compare('adb,bc,fa,cfc->d')
self.optimize_compare('bbd,bda,fc,db->acf')
self.optimize_compare('dba,ead,cad->bce')
self.optimize_compare('aef,fbc,dca->bde')
def test_combined_views_mapping(self):
# gh-10792
a = np.arange(9).reshape(1, 1, 3, 1, 3)
b = np.einsum('bbcdc->d', a)
assert_equal(b, [12])
def test_broadcasting_dot_cases(self):
# Ensures broadcasting cases are not mistaken for GEMM
a = np.random.rand(1, 5, 4)
b = np.random.rand(4, 6)
c = np.random.rand(5, 6)
d = np.random.rand(10)
self.optimize_compare('ijk,kl,jl', operands=[a, b, c])
self.optimize_compare('ijk,kl,jl,i->i', operands=[a, b, c, d])
e = np.random.rand(1, 1, 5, 4)
f = np.random.rand(7, 7)
self.optimize_compare('abjk,kl,jl', operands=[e, b, c])
self.optimize_compare('abjk,kl,jl,ab->ab', operands=[e, b, c, f])
# Edge case found in gh-11308
g = np.arange(64).reshape(2, 4, 8)
self.optimize_compare('obk,ijk->ioj', operands=[g, g])
def test_output_order(self):
# Ensure output order is respected for optimize cases, the below
# conraction should yield a reshaped tensor view
# gh-16415
a = np.ones((2, 3, 5), order='F')
b = np.ones((4, 3), order='F')
for opt in [True, False]:
tmp = np.einsum('...ft,mf->...mt', a, b, order='a', optimize=opt)
assert_(tmp.flags.f_contiguous)
tmp = np.einsum('...ft,mf->...mt', a, b, order='f', optimize=opt)
assert_(tmp.flags.f_contiguous)
tmp = np.einsum('...ft,mf->...mt', a, b, order='c', optimize=opt)
assert_(tmp.flags.c_contiguous)
tmp = np.einsum('...ft,mf->...mt', a, b, order='k', optimize=opt)
assert_(tmp.flags.c_contiguous is False)
assert_(tmp.flags.f_contiguous is False)
tmp = np.einsum('...ft,mf->...mt', a, b, optimize=opt)
assert_(tmp.flags.c_contiguous is False)
assert_(tmp.flags.f_contiguous is False)
c = np.ones((4, 3), order='C')
for opt in [True, False]:
tmp = np.einsum('...ft,mf->...mt', a, c, order='a', optimize=opt)
assert_(tmp.flags.c_contiguous)
d = np.ones((2, 3, 5), order='C')
for opt in [True, False]:
tmp = np.einsum('...ft,mf->...mt', d, c, order='a', optimize=opt)
assert_(tmp.flags.c_contiguous)
class TestEinsumPath:
def build_operands(self, string, size_dict=global_size_dict):
# Builds views based off initial operands
operands = [string]
terms = string.split('->')[0].split(',')
for term in terms:
dims = [size_dict[x] for x in term]
operands.append(np.random.rand(*dims))
return operands
def assert_path_equal(self, comp, benchmark):
# Checks if list of tuples are equivalent
ret = (len(comp) == len(benchmark))
assert_(ret)
for pos in range(len(comp) - 1):
ret &= isinstance(comp[pos + 1], tuple)
ret &= (comp[pos + 1] == benchmark[pos + 1])
assert_(ret)
def test_memory_contraints(self):
# Ensure memory constraints are satisfied
outer_test = self.build_operands('a,b,c->abc')
path, path_str = np.einsum_path(*outer_test, optimize=('greedy', 0))
self.assert_path_equal(path, ['einsum_path', (0, 1, 2)])
path, path_str = np.einsum_path(*outer_test, optimize=('optimal', 0))
self.assert_path_equal(path, ['einsum_path', (0, 1, 2)])
long_test = self.build_operands('acdf,jbje,gihb,hfac')
path, path_str = np.einsum_path(*long_test, optimize=('greedy', 0))
self.assert_path_equal(path, ['einsum_path', (0, 1, 2, 3)])
path, path_str = np.einsum_path(*long_test, optimize=('optimal', 0))
self.assert_path_equal(path, ['einsum_path', (0, 1, 2, 3)])
def test_long_paths(self):
# Long complex cases
# Long test 1
long_test1 = self.build_operands('acdf,jbje,gihb,hfac,gfac,gifabc,hfac')
path, path_str = np.einsum_path(*long_test1, optimize='greedy')
self.assert_path_equal(path, ['einsum_path',
(3, 6), (3, 4), (2, 4), (2, 3), (0, 2), (0, 1)])
path, path_str = np.einsum_path(*long_test1, optimize='optimal')
self.assert_path_equal(path, ['einsum_path',
(3, 6), (3, 4), (2, 4), (2, 3), (0, 2), (0, 1)])
# Long test 2
long_test2 = self.build_operands('chd,bde,agbc,hiad,bdi,cgh,agdb')
path, path_str = np.einsum_path(*long_test2, optimize='greedy')
print(path)
self.assert_path_equal(path, ['einsum_path',
(3, 4), (0, 3), (3, 4), (1, 3), (1, 2), (0, 1)])
path, path_str = np.einsum_path(*long_test2, optimize='optimal')
print(path)
self.assert_path_equal(path, ['einsum_path',
(0, 5), (1, 4), (3, 4), (1, 3), (1, 2), (0, 1)])
def test_edge_paths(self):
# Difficult edge cases
# Edge test1
edge_test1 = self.build_operands('eb,cb,fb->cef')
path, path_str = np.einsum_path(*edge_test1, optimize='greedy')
self.assert_path_equal(path, ['einsum_path', (0, 2), (0, 1)])
path, path_str = np.einsum_path(*edge_test1, optimize='optimal')
self.assert_path_equal(path, ['einsum_path', (0, 2), (0, 1)])
# Edge test2
edge_test2 = self.build_operands('dd,fb,be,cdb->cef')
path, path_str = np.einsum_path(*edge_test2, optimize='greedy')
self.assert_path_equal(path, ['einsum_path', (0, 3), (0, 1), (0, 1)])
path, path_str = np.einsum_path(*edge_test2, optimize='optimal')
self.assert_path_equal(path, ['einsum_path', (0, 3), (0, 1), (0, 1)])
# Edge test3
edge_test3 = self.build_operands('bca,cdb,dbf,afc->')
path, path_str = np.einsum_path(*edge_test3, optimize='greedy')
self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)])
path, path_str = np.einsum_path(*edge_test3, optimize='optimal')
self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)])
# Edge test4
edge_test4 = self.build_operands('dcc,fce,ea,dbf->ab')
path, path_str = np.einsum_path(*edge_test4, optimize='greedy')
self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 1), (0, 1)])
path, path_str = np.einsum_path(*edge_test4, optimize='optimal')
self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 2), (0, 1)])
# Edge test5
edge_test4 = self.build_operands('a,ac,ab,ad,cd,bd,bc->',
size_dict={"a": 20, "b": 20, "c": 20, "d": 20})
path, path_str = np.einsum_path(*edge_test4, optimize='greedy')
self.assert_path_equal(path, ['einsum_path', (0, 1), (0, 1, 2, 3, 4, 5)])
path, path_str = np.einsum_path(*edge_test4, optimize='optimal')
self.assert_path_equal(path, ['einsum_path', (0, 1), (0, 1, 2, 3, 4, 5)])
def test_path_type_input(self):
# Test explicit path handling
path_test = self.build_operands('dcc,fce,ea,dbf->ab')
path, path_str = np.einsum_path(*path_test, optimize=False)
self.assert_path_equal(path, ['einsum_path', (0, 1, 2, 3)])
path, path_str = np.einsum_path(*path_test, optimize=True)
self.assert_path_equal(path, ['einsum_path', (1, 2), (0, 1), (0, 1)])
exp_path = ['einsum_path', (0, 2), (0, 2), (0, 1)]
path, path_str = np.einsum_path(*path_test, optimize=exp_path)
self.assert_path_equal(path, exp_path)
# Double check einsum works on the input path
noopt = np.einsum(*path_test, optimize=False)
opt = np.einsum(*path_test, optimize=exp_path)
assert_almost_equal(noopt, opt)
def test_spaces(self):
#gh-10794
arr = np.array([[1]])
for sp in itertools.product(['', ' '], repeat=4):
# no error for any spacing
np.einsum('{}...a{}->{}...a{}'.format(*sp), arr)
def test_overlap():
a = np.arange(9, dtype=int).reshape(3, 3)
b = np.arange(9, dtype=int).reshape(3, 3)
d = np.dot(a, b)
# sanity check
c = np.einsum('ij,jk->ik', a, b)
assert_equal(c, d)
#gh-10080, out overlaps one of the operands
c = np.einsum('ij,jk->ik', a, b, out=b)
assert_equal(c, d)