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+import itertools
+import sys
+import platform
+
+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
+ )
+
+try:
+ COMPILERS = np.show_config(mode="dicts")["Compilers"]
+ USING_CLANG_CL = COMPILERS["c"]["name"] == "clang-cl"
+except TypeError:
+ USING_CLANG_CL = False
+
+# 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_object_errors(self):
+ # Exceptions created by object arithmetic should
+ # successfully propagate
+
+ class CustomException(Exception):
+ pass
+
+ class DestructoBox:
+
+ def __init__(self, value, destruct):
+ self._val = value
+ self._destruct = destruct
+
+ def __add__(self, other):
+ tmp = self._val + other._val
+ if tmp >= self._destruct:
+ raise CustomException
+ else:
+ self._val = tmp
+ return self
+
+ def __radd__(self, other):
+ if other == 0:
+ return self
+ else:
+ return self.__add__(other)
+
+ def __mul__(self, other):
+ tmp = self._val * other._val
+ if tmp >= self._destruct:
+ raise CustomException
+ else:
+ self._val = tmp
+ return self
+
+ def __rmul__(self, other):
+ if other == 0:
+ return self
+ else:
+ return self.__mul__(other)
+
+ a = np.array([DestructoBox(i, 5) for i in range(1, 10)],
+ dtype='object').reshape(3, 3)
+
+ # raised from unbuffered_loop_nop1_ndim2
+ assert_raises(CustomException, np.einsum, "ij->i", a)
+
+ # raised from unbuffered_loop_nop1_ndim3
+ b = np.array([DestructoBox(i, 100) for i in range(0, 27)],
+ dtype='object').reshape(3, 3, 3)
+ assert_raises(CustomException, np.einsum, "i...k->...", b)
+
+ # raised from unbuffered_loop_nop2_ndim2
+ b = np.array([DestructoBox(i, 55) for i in range(1, 4)],
+ dtype='object')
+ assert_raises(CustomException, np.einsum, "ij, j", a, b)
+
+ # raised from unbuffered_loop_nop2_ndim3
+ assert_raises(CustomException, np.einsum, "ij, jh", a, a)
+
+ # raised from PyArray_EinsteinSum
+ assert_raises(CustomException, np.einsum, "ij->", a)
+
+ 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))
+
+ @np._no_nep50_warning()
+ def check_einsum_sums(self, dtype, do_opt=False):
+ dtype = np.dtype(dtype)
+ # 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)
+ b = np.sum(a, axis=-1)
+ if hasattr(b, 'astype'):
+ b = b.astype(dtype)
+ assert_equal(np.einsum("i->", a, optimize=do_opt), b)
+ assert_equal(np.einsum(a, [0], [], optimize=do_opt), b)
+
+ for n in range(1, 17):
+ a = np.arange(2*3*n, dtype=dtype).reshape(2, 3, n)
+ b = np.sum(a, axis=-1)
+ if hasattr(b, 'astype'):
+ b = b.astype(dtype)
+ assert_equal(np.einsum("...i->...", a, optimize=do_opt), b)
+ assert_equal(np.einsum(a, [Ellipsis, 0], [Ellipsis], optimize=do_opt), b)
+
+ # sum(a, axis=0)
+ for n in range(1, 17):
+ a = np.arange(2*n, dtype=dtype).reshape(2, n)
+ b = np.sum(a, axis=0)
+ if hasattr(b, 'astype'):
+ b = b.astype(dtype)
+ assert_equal(np.einsum("i...->...", a, optimize=do_opt), b)
+ assert_equal(np.einsum(a, [0, Ellipsis], [Ellipsis], optimize=do_opt), b)
+
+ for n in range(1, 17):
+ a = np.arange(2*3*n, dtype=dtype).reshape(2, 3, n)
+ b = np.sum(a, axis=0)
+ if hasattr(b, 'astype'):
+ b = b.astype(dtype)
+ assert_equal(np.einsum("i...->...", a, optimize=do_opt), b)
+ assert_equal(np.einsum(a, [0, Ellipsis], [Ellipsis], optimize=do_opt), b)
+
+ # trace(a)
+ for n in range(1, 17):
+ a = np.arange(n*n, dtype=dtype).reshape(n, n)
+ b = np.trace(a)
+ if hasattr(b, 'astype'):
+ b = b.astype(dtype)
+ assert_equal(np.einsum("ii", a, optimize=do_opt), b)
+ assert_equal(np.einsum(a, [0, 0], optimize=do_opt), b)
+
+ # 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), b)
+ assert_equal(np.einsum(a, list(np_array), optimize=do_opt), b)
+
+ # 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)
+ neg_val = -2 if dtype.kind != "u" else np.iinfo(dtype).max - 1
+ a = np.array([1, 3, neg_val, 0, 12, 13, 0, 1], dtype=dtype)
+ b = np.array([0, 3.5, 0., neg_val, 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))
+ if hasattr(b, "dtype"):
+ # Can be a python object when dtype is object
+ assert_equal(b.dtype, np.dtype(dtype))
+
+ b = np.einsum(a, [0], [], dtype=dtype, casting='unsafe')
+ assert_equal(b, np.sum(a))
+ if hasattr(b, "dtype"):
+ # Can be a python object when dtype is object
+ 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):
+ if (
+ (sys.platform == 'darwin' and platform.machine() == 'x86_64')
+ or
+ USING_CLANG_CL
+ ):
+ pytest.xfail('Fails on macOS x86-64 and when using clang-cl '
+ 'with Meson, see gh-23838')
+ self.check_einsum_sums('i1')
+
+ def test_einsum_sums_uint8(self):
+ if (
+ (sys.platform == 'darwin' and platform.machine() == 'x86_64')
+ or
+ USING_CLANG_CL
+ ):
+ pytest.xfail('Fails on macOS x86-64 and when using clang-cl '
+ 'with Meson, see gh-23838')
+ 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_sums_object(self):
+ self.check_einsum_sums('object')
+ self.check_einsum_sums('object', True)
+
+ 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('ij...,j...->i...', a, b), [[[2], [2]]])
+ assert_equal(np.einsum('...i,...i', [1, 2, 3], [2, 3, 4]), 20)
+ assert_equal(np.einsum('...i,...i', [1, 2, 3], [2, 3, 4],
+ optimize='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_object_loop(self):
+
+ class Mult:
+ def __mul__(self, other):
+ return 42
+
+ objMult = np.array([Mult()])
+ objNULL = np.ndarray(buffer = b'\0' * np.intp(0).itemsize, shape=1, dtype=object)
+
+ with pytest.raises(TypeError):
+ np.einsum("i,j", [1], objNULL)
+ with pytest.raises(TypeError):
+ np.einsum("i,j", objNULL, [1])
+ assert np.einsum("i,j", objMult, objMult) == 42
+
+ 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 exercise 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')
+ 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')
+ 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_path_type_input_internal_trace(self):
+ #gh-20962
+ path_test = self.build_operands('cab,cdd->ab')
+ exp_path = ['einsum_path', (1,), (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_path_type_input_invalid(self):
+ path_test = self.build_operands('ab,bc,cd,de->ae')
+ exp_path = ['einsum_path', (2, 3), (0, 1)]
+ assert_raises(RuntimeError, np.einsum, *path_test, optimize=exp_path)
+ assert_raises(
+ RuntimeError, np.einsum_path, *path_test, optimize=exp_path)
+
+ path_test = self.build_operands('a,a,a->a')
+ exp_path = ['einsum_path', (1,), (0, 1)]
+ assert_raises(RuntimeError, np.einsum, *path_test, optimize=exp_path)
+ assert_raises(
+ RuntimeError, np.einsum_path, *path_test, optimize=exp_path)
+
+ 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)
generated by cgit v1.2.3 (git 2.47.1) at 2025-07-27 05:49:59 +0000