def test_reshape():
array = ImmutableDenseNDimArray(range(50), 50)
assert array.shape == (50,)
assert array.rank() == 1
array = array.reshape(5, 5, 2)
assert array.shape == (5, 5, 2)
assert array.rank() == 3
assert len(array) == 50
def test_reshape():
array = ImmutableDenseNDimArray(range(50), 50)
assert array.shape == (50, )
assert array.rank() == 1
array = array.reshape(5, 5, 2)
assert array.shape == (5, 5, 2)
assert array.rank() == 3
assert len(array) == 50
def test_ndim_array_initiation():
arr_with_one_element = ImmutableDenseNDimArray([23])
assert len(arr_with_one_element) == 1
assert arr_with_one_element[0] == 23
assert arr_with_one_element[:] == [23]
assert arr_with_one_element.rank() == 1
arr_with_symbol_element = ImmutableDenseNDimArray([Symbol('x')])
assert len(arr_with_symbol_element) == 1
assert arr_with_symbol_element[0] == Symbol('x')
assert arr_with_symbol_element[:] == [Symbol('x')]
assert arr_with_symbol_element.rank() == 1
number5 = 5
vector = ImmutableDenseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector.rank() == 1
vector = ImmutableSparseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector._sparse_array == Dict()
assert vector.rank() == 1
n_dim_array = ImmutableDenseNDimArray(range(3**4), (
3,
3,
3,
3,
))
assert len(n_dim_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == (3, 3, 3, 3)
assert n_dim_array.rank() == 4
array_shape = (3, 3, 3, 3)
sparse_array = ImmutableSparseNDimArray.zeros(*array_shape)
assert len(sparse_array._sparse_array) == 0
assert len(sparse_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == array_shape
assert n_dim_array.rank() == 4
one_dim_array = ImmutableDenseNDimArray([2, 3, 1])
assert len(one_dim_array) == 3
assert one_dim_array.shape == (3, )
assert one_dim_array.rank() == 1
assert one_dim_array.tolist() == [2, 3, 1]
shape = (3, 3)
array_with_many_args = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_many_args) == 3 * 3
assert array_with_many_args.shape == shape
assert array_with_many_args[0, 0] == 0
assert array_with_many_args.rank() == 2
def test_ndim_array_initiation():
arr_with_one_element = ImmutableDenseNDimArray([23])
assert len(arr_with_one_element) == 1
assert arr_with_one_element[0] == 23
assert arr_with_one_element[:] == [23]
assert arr_with_one_element.rank() == 1
arr_with_symbol_element = ImmutableDenseNDimArray([Symbol('x')])
assert len(arr_with_symbol_element) == 1
assert arr_with_symbol_element[0] == Symbol('x')
assert arr_with_symbol_element[:] == [Symbol('x')]
assert arr_with_symbol_element.rank() == 1
number5 = 5
vector = ImmutableDenseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5,)
assert vector.rank() == 1
vector = ImmutableSparseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5,)
assert vector._sparse_array == Dict()
assert vector.rank() == 1
n_dim_array = ImmutableDenseNDimArray(range(3**4), (3, 3, 3, 3,))
assert len(n_dim_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == (3, 3, 3, 3)
assert n_dim_array.rank() == 4
array_shape = (3, 3, 3, 3)
sparse_array = ImmutableSparseNDimArray.zeros(*array_shape)
assert len(sparse_array._sparse_array) == 0
assert len(sparse_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == array_shape
assert n_dim_array.rank() == 4
one_dim_array = ImmutableDenseNDimArray([2, 3, 1])
assert len(one_dim_array) == 3
assert one_dim_array.shape == (3,)
assert one_dim_array.rank() == 1
assert one_dim_array.tolist() == [2, 3, 1]
shape = (3, 3)
array_with_many_args = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_many_args) == 3 * 3
assert array_with_many_args.shape == shape
assert array_with_many_args[0, 0] == 0
assert array_with_many_args.rank() == 2
def test_ndim_array_initiation():
arr_with_no_elements = ImmutableDenseNDimArray([], shape=(0, ))
assert len(arr_with_no_elements) == 0
assert arr_with_no_elements.rank() == 1
raises(ValueError, lambda: ImmutableDenseNDimArray([0], shape=(0, )))
raises(ValueError, lambda: ImmutableDenseNDimArray([1, 2, 3], shape=(0, )))
raises(ValueError, lambda: ImmutableDenseNDimArray([], shape=()))
raises(ValueError, lambda: ImmutableSparseNDimArray([0], shape=(0, )))
raises(ValueError,
lambda: ImmutableSparseNDimArray([1, 2, 3], shape=(0, )))
raises(ValueError, lambda: ImmutableSparseNDimArray([], shape=()))
arr_with_one_element = ImmutableDenseNDimArray([23])
assert len(arr_with_one_element) == 1
assert arr_with_one_element[0] == 23
assert arr_with_one_element[:] == ImmutableDenseNDimArray([23])
assert arr_with_one_element.rank() == 1
arr_with_symbol_element = ImmutableDenseNDimArray([Symbol('x')])
assert len(arr_with_symbol_element) == 1
assert arr_with_symbol_element[0] == Symbol('x')
assert arr_with_symbol_element[:] == ImmutableDenseNDimArray([Symbol('x')])
assert arr_with_symbol_element.rank() == 1
number5 = 5
vector = ImmutableDenseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector.rank() == 1
vector = ImmutableSparseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5, )
assert vector._sparse_array == Dict()
assert vector.rank() == 1
n_dim_array = ImmutableDenseNDimArray(range(3**4), (
3,
3,
3,
3,
))
assert len(n_dim_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == (3, 3, 3, 3)
assert n_dim_array.rank() == 4
array_shape = (3, 3, 3, 3)
sparse_array = ImmutableSparseNDimArray.zeros(*array_shape)
assert len(sparse_array._sparse_array) == 0
assert len(sparse_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == array_shape
assert n_dim_array.rank() == 4
one_dim_array = ImmutableDenseNDimArray([2, 3, 1])
assert len(one_dim_array) == 3
assert one_dim_array.shape == (3, )
assert one_dim_array.rank() == 1
assert one_dim_array.tolist() == [2, 3, 1]
shape = (3, 3)
array_with_many_args = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_many_args) == 3 * 3
assert array_with_many_args.shape == shape
assert array_with_many_args[0, 0] == 0
assert array_with_many_args.rank() == 2
shape = (long(3), long(3))
array_with_long_shape = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_long_shape) == 3 * 3
assert array_with_long_shape.shape == shape
assert array_with_long_shape[long(0), long(0)] == 0
assert array_with_long_shape.rank() == 2
vector_with_long_shape = ImmutableDenseNDimArray(range(5), long(5))
assert len(vector_with_long_shape) == 5
assert vector_with_long_shape.shape == (long(5), )
assert vector_with_long_shape.rank() == 1
raises(ValueError, lambda: vector_with_long_shape[long(5)])
from sympy.abc import x
for ArrayType in [ImmutableDenseNDimArray, ImmutableSparseNDimArray]:
rank_zero_array = ArrayType(x)
assert len(rank_zero_array) == 1
assert rank_zero_array.shape == ()
assert rank_zero_array.rank() == 0
assert rank_zero_array[()] == x
raises(ValueError, lambda: rank_zero_array[0])
def permutedims(expr, perm):
"""
Permutes the indices of an array.
Parameter specifies the permutation of the indices.
Examples
========
>>> from sympy.abc import x, y, z, t
>>> from sympy import sin
>>> from sympy import Array, permutedims
>>> a = Array([[x, y, z], [t, sin(x), 0]])
>>> a
[[x, y, z], [t, sin(x), 0]]
>>> permutedims(a, (1, 0))
[[x, t], [y, sin(x)], [z, 0]]
If the array is of second order, ``transpose`` can be used:
>>> from sympy import transpose
>>> transpose(a)
[[x, t], [y, sin(x)], [z, 0]]
Examples on higher dimensions:
>>> b = Array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
>>> permutedims(b, (2, 1, 0))
[[[1, 5], [3, 7]], [[2, 6], [4, 8]]]
>>> permutedims(b, (1, 2, 0))
[[[1, 5], [2, 6]], [[3, 7], [4, 8]]]
``Permutation`` objects are also allowed:
>>> from sympy.combinatorics import Permutation
>>> permutedims(b, Permutation([1, 2, 0]))
[[[1, 5], [2, 6]], [[3, 7], [4, 8]]]
"""
from sympy.tensor.array import SparseNDimArray
if not isinstance(expr, NDimArray):
expr = ImmutableDenseNDimArray(expr)
from sympy.combinatorics import Permutation
if not isinstance(perm, Permutation):
perm = Permutation(list(perm))
if perm.size != expr.rank():
raise ValueError("wrong permutation size")
# Get the inverse permutation:
iperm = ~perm
new_shape = perm(expr.shape)
if isinstance(expr, SparseNDimArray):
return type(expr)({
tuple(perm(expr._get_tuple_index(k))): v
for k, v in expr._sparse_array.items()
}, new_shape)
indices_span = perm([range(i) for i in expr.shape])
new_array = [None] * len(expr)
for i, idx in enumerate(itertools.product(*indices_span)):
t = iperm(idx)
new_array[i] = expr[t]
return type(expr)(new_array, new_shape)
def test_ndim_array_initiation():
arr_with_no_elements = ImmutableDenseNDimArray([], shape=(0,))
assert len(arr_with_no_elements) == 0
assert arr_with_no_elements.rank() == 1
raises(ValueError, lambda: ImmutableDenseNDimArray([0], shape=(0,)))
raises(ValueError, lambda: ImmutableDenseNDimArray([1, 2, 3], shape=(0,)))
raises(ValueError, lambda: ImmutableDenseNDimArray([], shape=()))
raises(ValueError, lambda: ImmutableSparseNDimArray([0], shape=(0,)))
raises(ValueError, lambda: ImmutableSparseNDimArray([1, 2, 3], shape=(0,)))
raises(ValueError, lambda: ImmutableSparseNDimArray([], shape=()))
arr_with_one_element = ImmutableDenseNDimArray([23])
assert len(arr_with_one_element) == 1
assert arr_with_one_element[0] == 23
assert arr_with_one_element[:] == [23]
assert arr_with_one_element.rank() == 1
arr_with_symbol_element = ImmutableDenseNDimArray([Symbol('x')])
assert len(arr_with_symbol_element) == 1
assert arr_with_symbol_element[0] == Symbol('x')
assert arr_with_symbol_element[:] == [Symbol('x')]
assert arr_with_symbol_element.rank() == 1
number5 = 5
vector = ImmutableDenseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5,)
assert vector.rank() == 1
vector = ImmutableSparseNDimArray.zeros(number5)
assert len(vector) == number5
assert vector.shape == (number5,)
assert vector._sparse_array == Dict()
assert vector.rank() == 1
n_dim_array = ImmutableDenseNDimArray(range(3**4), (3, 3, 3, 3,))
assert len(n_dim_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == (3, 3, 3, 3)
assert n_dim_array.rank() == 4
array_shape = (3, 3, 3, 3)
sparse_array = ImmutableSparseNDimArray.zeros(*array_shape)
assert len(sparse_array._sparse_array) == 0
assert len(sparse_array) == 3 * 3 * 3 * 3
assert n_dim_array.shape == array_shape
assert n_dim_array.rank() == 4
one_dim_array = ImmutableDenseNDimArray([2, 3, 1])
assert len(one_dim_array) == 3
assert one_dim_array.shape == (3,)
assert one_dim_array.rank() == 1
assert one_dim_array.tolist() == [2, 3, 1]
shape = (3, 3)
array_with_many_args = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_many_args) == 3 * 3
assert array_with_many_args.shape == shape
assert array_with_many_args[0, 0] == 0
assert array_with_many_args.rank() == 2
shape = (long(3), long(3))
array_with_long_shape = ImmutableSparseNDimArray.zeros(*shape)
assert len(array_with_long_shape) == 3 * 3
assert array_with_long_shape.shape == shape
assert array_with_long_shape[long(0), long(0)] == 0
assert array_with_long_shape.rank() == 2
vector_with_long_shape = ImmutableDenseNDimArray(range(5), long(5))
assert len(vector_with_long_shape) == 5
assert vector_with_long_shape.shape == (long(5),)
assert vector_with_long_shape.rank() == 1
raises(ValueError, lambda: vector_with_long_shape[long(5)])
from sympy.abc import x
rank_zero_array = ImmutableDenseNDimArray(x)
assert len(rank_zero_array) == 1
assert rank_zero_array.shape == ()
assert rank_zero_array.rank() == 0
assert rank_zero_array[()] == x
assert rank_zero_array[0] == x
def permutedims(expr, perm=None, index_order_old=None, index_order_new=None):
"""
Permutes the indices of an array.
Parameter specifies the permutation of the indices.
Examples
========
>>> from sympy.abc import x, y, z, t
>>> from sympy import sin
>>> from sympy import Array, permutedims
>>> a = Array([[x, y, z], [t, sin(x), 0]])
>>> a
[[x, y, z], [t, sin(x), 0]]
>>> permutedims(a, (1, 0))
[[x, t], [y, sin(x)], [z, 0]]
If the array is of second order, ``transpose`` can be used:
>>> from sympy import transpose
>>> transpose(a)
[[x, t], [y, sin(x)], [z, 0]]
Examples on higher dimensions:
>>> b = Array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])
>>> permutedims(b, (2, 1, 0))
[[[1, 5], [3, 7]], [[2, 6], [4, 8]]]
>>> permutedims(b, (1, 2, 0))
[[[1, 5], [2, 6]], [[3, 7], [4, 8]]]
An alternative way to specify the same permutations as in the previous
lines involves passing the *old* and *new* indices, either as a list or as
a string:
>>> permutedims(b, index_order_old="cba", index_order_new="abc")
[[[1, 5], [3, 7]], [[2, 6], [4, 8]]]
>>> permutedims(b, index_order_old="cab", index_order_new="abc")
[[[1, 5], [2, 6]], [[3, 7], [4, 8]]]
``Permutation`` objects are also allowed:
>>> from sympy.combinatorics import Permutation
>>> permutedims(b, Permutation([1, 2, 0]))
[[[1, 5], [2, 6]], [[3, 7], [4, 8]]]
"""
from sympy.tensor.array import SparseNDimArray
from sympy.tensor.array.expressions.array_expressions import _ArrayExpr
from sympy.tensor.array.expressions.array_expressions import _CodegenArrayAbstract
from sympy.tensor.array.expressions.array_expressions import _permute_dims
from sympy.matrices.expressions.matexpr import MatrixSymbol
from sympy.tensor.array.expressions import PermuteDims
from sympy.tensor.array.expressions.array_expressions import get_rank
perm = PermuteDims._get_permutation_from_arguments(perm, index_order_old,
index_order_new,
get_rank(expr))
if isinstance(expr, (_ArrayExpr, _CodegenArrayAbstract, MatrixSymbol)):
return _permute_dims(expr, perm)
if not isinstance(expr, NDimArray):
expr = ImmutableDenseNDimArray(expr)
from sympy.combinatorics import Permutation
if not isinstance(perm, Permutation):
perm = Permutation(list(perm))
if perm.size != expr.rank():
raise ValueError("wrong permutation size")
# Get the inverse permutation:
iperm = ~perm
new_shape = perm(expr.shape)
if isinstance(expr, SparseNDimArray):
return type(expr)({
tuple(perm(expr._get_tuple_index(k))): v
for k, v in expr._sparse_array.items()
}, new_shape)
indices_span = perm([range(i) for i in expr.shape])
new_array = [None] * len(expr)
for i, idx in enumerate(itertools.product(*indices_span)):
t = iperm(idx)
new_array[i] = expr[t]
return type(expr)(new_array, new_shape)
def test_issue_21870():
a0 = ImmutableDenseNDimArray(0)
assert a0.rank() == 0
a1 = ImmutableDenseNDimArray(a0)
assert a1.rank() == 0
