def test_ndim_array_converting():
dense_array = ImmutableDenseNDimArray([1, 2, 3, 4], (2, 2))
alist = dense_array.tolist()
alist == [[1, 2], [3, 4]]
matrix = dense_array.tomatrix()
assert (isinstance(matrix, Matrix))
for i in range(len(dense_array)):
assert dense_array[i] == matrix[i]
assert matrix.shape == dense_array.shape
assert ImmutableDenseNDimArray(matrix) == dense_array
assert ImmutableDenseNDimArray(matrix.as_immutable()) == dense_array
assert ImmutableDenseNDimArray(matrix.as_mutable()) == dense_array
sparse_array = ImmutableSparseNDimArray([1, 2, 3, 4], (2, 2))
alist = sparse_array.tolist()
assert alist == [[1, 2], [3, 4]]
matrix = sparse_array.tomatrix()
assert(isinstance(matrix, SparseMatrix))
for i in range(len(sparse_array)):
assert sparse_array[i] == matrix[i]
assert matrix.shape == sparse_array.shape
assert ImmutableSparseNDimArray(matrix) == sparse_array
assert ImmutableSparseNDimArray(matrix.as_immutable()) == sparse_array
assert ImmutableSparseNDimArray(matrix.as_mutable()) == sparse_array
def test_diff_and_applyfunc():
from sympy.abc import x, y, z
md = ImmutableDenseNDimArray([[x, y], [x * z, x * y * z]])
assert md.diff(x) == ImmutableDenseNDimArray([[1, 0], [z, y * z]])
assert diff(md, x) == ImmutableDenseNDimArray([[1, 0], [z, y * z]])
sd = ImmutableSparseNDimArray(md)
assert sd == ImmutableSparseNDimArray([x, y, x * z, x * y * z], (2, 2))
assert sd.diff(x) == ImmutableSparseNDimArray([[1, 0], [z, y * z]])
assert diff(sd, x) == ImmutableSparseNDimArray([[1, 0], [z, y * z]])
mdn = md.applyfunc(lambda x: x * 3)
assert mdn == ImmutableDenseNDimArray([[3 * x, 3 * y],
[3 * x * z, 3 * x * y * z]])
assert md != mdn
sdn = sd.applyfunc(lambda x: x / 2)
assert sdn == ImmutableSparseNDimArray([[x / 2, y / 2],
[x * z / 2, x * y * z / 2]])
assert sd != sdn
sdp = sd.applyfunc(lambda x: x + 1)
assert sdp == ImmutableSparseNDimArray([[x + 1, y + 1],
[x * z + 1, x * y * z + 1]])
assert sd != sdp
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_converting():
dense_array = ImmutableDenseNDimArray([1, 2, 3, 4], (2, 2))
alist = dense_array.tolist()
alist == [[1, 2], [3, 4]]
matrix = dense_array.tomatrix()
assert (isinstance(matrix, Matrix))
for i in range(len(dense_array)):
assert dense_array[dense_array._get_tuple_index(i)] == matrix[i]
assert matrix.shape == dense_array.shape
assert ImmutableDenseNDimArray(matrix) == dense_array
assert ImmutableDenseNDimArray(matrix.as_immutable()) == dense_array
assert ImmutableDenseNDimArray(matrix.as_mutable()) == dense_array
sparse_array = ImmutableSparseNDimArray([1, 2, 3, 4], (2, 2))
alist = sparse_array.tolist()
assert alist == [[1, 2], [3, 4]]
matrix = sparse_array.tomatrix()
assert (isinstance(matrix, SparseMatrix))
for i in range(len(sparse_array)):
assert sparse_array[sparse_array._get_tuple_index(i)] == matrix[i]
assert matrix.shape == sparse_array.shape
assert ImmutableSparseNDimArray(matrix) == sparse_array
assert ImmutableSparseNDimArray(matrix.as_immutable()) == sparse_array
assert ImmutableSparseNDimArray(matrix.as_mutable()) == sparse_array
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_diff_and_applyfunc():
from sympy.abc import x, y, z
md = ImmutableDenseNDimArray([[x, y], [x*z, x*y*z]])
assert md.diff(x) == ImmutableDenseNDimArray([[1, 0], [z, y*z]])
sd = ImmutableSparseNDimArray(md)
assert sd == ImmutableSparseNDimArray([x, y, x*z, x*y*z], (2, 2))
assert sd.diff(x) == ImmutableSparseNDimArray([[1, 0], [z, y*z]])
mdn = md.applyfunc(lambda x: x*3)
assert mdn == ImmutableDenseNDimArray([[3*x, 3*y], [3*x*z, 3*x*y*z]])
assert md != mdn
sdn = sd.applyfunc(lambda x: x/2)
assert sdn == ImmutableSparseNDimArray([[x/2, y/2], [x*z/2, x*y*z/2]])
assert sd != sdn
def test_slices():
md = ImmutableDenseNDimArray(range(10, 34), (2, 3, 4))
assert md[:] == ImmutableDenseNDimArray(range(10, 34), (2, 3, 4))
assert md[:, :, 0].tomatrix() == Matrix([[10, 14, 18], [22, 26, 30]])
assert md[0, 1:2, :].tomatrix() == Matrix([[14, 15, 16, 17]])
assert md[0, 1:3, :].tomatrix() == Matrix([[14, 15, 16, 17], [18, 19, 20, 21]])
assert md[:, :, :] == md
sd = ImmutableSparseNDimArray(range(10, 34), (2, 3, 4))
assert sd == ImmutableSparseNDimArray(md)
assert sd[:] == ImmutableSparseNDimArray(range(10, 34), (2, 3, 4))
assert sd[:, :, 0].tomatrix() == Matrix([[10, 14, 18], [22, 26, 30]])
assert sd[0, 1:2, :].tomatrix() == Matrix([[14, 15, 16, 17]])
assert sd[0, 1:3, :].tomatrix() == Matrix([[14, 15, 16, 17], [18, 19, 20, 21]])
assert sd[:, :, :] == sd
def test_calculation():
a = ImmutableDenseNDimArray([1] * 9, (3, 3))
b = ImmutableDenseNDimArray([9] * 9, (3, 3))
c = a + b
for i in c:
assert i == ImmutableDenseNDimArray([10, 10, 10])
assert c == ImmutableDenseNDimArray([10] * 9, (3, 3))
assert c == ImmutableSparseNDimArray([10] * 9, (3, 3))
c = b - a
for i in c:
assert i == ImmutableDenseNDimArray([8, 8, 8])
assert c == ImmutableDenseNDimArray([8] * 9, (3, 3))
assert c == ImmutableSparseNDimArray([8] * 9, (3, 3))
def test_symbolic_indexing():
x, y, z, w = symbols("x y z w")
M = ImmutableDenseNDimArray([[x, y], [z, w]])
i, j = symbols("i, j")
Mij = M[i, j]
assert isinstance(Mij, Indexed)
Ms = ImmutableSparseNDimArray([[2, 3 * x], [4, 5]])
msij = Ms[i, j]
assert isinstance(msij, Indexed)
for oi, oj in [(0, 0), (0, 1), (1, 0), (1, 1)]:
assert Mij.subs({i: oi, j: oj}) == M[oi, oj]
assert msij.subs({i: oi, j: oj}) == Ms[oi, oj]
A = IndexedBase("A", (0, 2))
assert A[0, 0].subs(A, M) == x
assert A[i, j].subs(A, M) == M[i, j]
assert M[i, j].subs(M, A) == A[i, j]
assert isinstance(M[3 * i - 2, j], Indexed)
assert M[3 * i - 2, j].subs({i: 1, j: 0}) == M[1, 0]
assert isinstance(M[i, 0], Indexed)
assert M[i, 0].subs(i, 0) == M[0, 0]
assert M[0, i].subs(i, 1) == M[0, 1]
assert M[i, j].diff(x) == ImmutableDenseNDimArray([[1, 0], [0, 0]])[i, j]
assert Ms[i, j].diff(x) == ImmutableSparseNDimArray([[0, 3], [0, 0]])[i, j]
Mo = ImmutableDenseNDimArray([1, 2, 3])
assert Mo[i].subs(i, 1) == 2
Mos = ImmutableSparseNDimArray([1, 2, 3])
assert Mos[i].subs(i, 1) == 2
raises(ValueError, lambda: M[i, 2])
raises(ValueError, lambda: M[i, -1])
raises(ValueError, lambda: M[2, i])
raises(ValueError, lambda: M[-1, i])
raises(ValueError, lambda: Ms[i, 2])
raises(ValueError, lambda: Ms[i, -1])
raises(ValueError, lambda: Ms[2, i])
raises(ValueError, lambda: Ms[-1, i])
def test_op_priority():
from sympy.abc import x
md = ImmutableDenseNDimArray([1, 2, 3])
e1 = (1 + x) * md
e2 = md * (1 + x)
assert e1 == ImmutableDenseNDimArray([1 + x, 2 + 2 * x, 3 + 3 * x])
assert e1 == e2
sd = ImmutableSparseNDimArray([1, 2, 3])
e3 = (1 + x) * sd
e4 = sd * (1 + x)
assert e3 == ImmutableDenseNDimArray([1 + x, 2 + 2 * x, 3 + 3 * x])
assert e3 == e4
def test_ndim_array_converting():
dense_array = ImmutableDenseNDimArray([1, 2, 3, 4], (2, 2))
alist = dense_array.tolist()
alist == [[1, 2], [3, 4]]
matrix = dense_array.tomatrix()
assert (isinstance(matrix, Matrix))
for i in range(len(dense_array)):
assert dense_array[i] == matrix[i]
assert matrix.shape == dense_array.shape
sparse_array = ImmutableSparseNDimArray([1, 2, 3, 4], (2, 2))
alist = sparse_array.tolist()
assert alist == [[1, 2], [3, 4]]
matrix = sparse_array.tomatrix()
assert (isinstance(matrix, SparseMatrix))
for i in range(len(sparse_array)):
assert sparse_array[i] == matrix[i]
assert matrix.shape == sparse_array.shape
def test_sparse():
sparse_array = ImmutableSparseNDimArray([0, 0, 0, 1], (2, 2))
assert len(sparse_array) == 2 * 2
# dictionary where all data is, only non-zero entries are actually stored:
assert len(sparse_array._sparse_array) == 1
assert list(sparse_array) == [0, 0, 0, 1]
for i, j in zip(sparse_array, [0, 0, 0, 1]):
assert i == j
def sparse_assignment():
sparse_array[0, 0] = 123
assert len(sparse_array._sparse_array) == 1
raises(TypeError, sparse_assignment)
assert len(sparse_array._sparse_array) == 1
assert sparse_array[0, 0] == 0
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 test_rebuild_immutable_arrays():
sparr = ImmutableSparseNDimArray(range(10, 34), (2, 3, 4))
densarr = ImmutableDenseNDimArray(range(10, 34), (2, 3, 4))
assert sparr == sparr.func(*sparr.args)
assert densarr == densarr.func(*densarr.args)
def test_rebuild_immutable_arrays():
sparr = ImmutableSparseNDimArray(range(10, 34), (2, 3, 4))
densarr = ImmutableDenseNDimArray(range(10, 34), (2, 3, 4))
assert sparr == sparr.func(*sparr.args)
assert densarr == densarr.func(*densarr.args)
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 test_sparse():
sparse_array = ImmutableSparseNDimArray([0, 0, 0, 1], (2, 2))
assert len(sparse_array) == 2 * 2
# dictionary where all data is, only non-zero entries are actually stored:
assert len(sparse_array._sparse_array) == 1
assert sparse_array.tolist() == [[0, 0], [0, 1]]
for i, j in zip(sparse_array, [[0, 0], [0, 1]]):
assert i == ImmutableSparseNDimArray(j)
def sparse_assignment():
sparse_array[0, 0] = 123
assert len(sparse_array._sparse_array) == 1
raises(TypeError, sparse_assignment)
assert len(sparse_array._sparse_array) == 1
assert sparse_array[0, 0] == 0
assert sparse_array / 0 == ImmutableSparseNDimArray(
[[S.NaN, S.NaN], [S.NaN, S.ComplexInfinity]], (2, 2))
# test for large scale sparse array
# equality test
assert ImmutableSparseNDimArray.zeros(
100000, 200000) == ImmutableSparseNDimArray.zeros(100000, 200000)
# __mul__ and __rmul__
a = ImmutableSparseNDimArray({200001: 1}, (100000, 200000))
assert a * 3 == ImmutableSparseNDimArray({200001: 3}, (100000, 200000))
assert 3 * a == ImmutableSparseNDimArray({200001: 3}, (100000, 200000))
assert a * 0 == ImmutableSparseNDimArray({}, (100000, 200000))
assert 0 * a == ImmutableSparseNDimArray({}, (100000, 200000))
# __div__
assert a / 3 == ImmutableSparseNDimArray({200001: Rational(1, 3)},
(100000, 200000))
# __neg__
assert -a == ImmutableSparseNDimArray({200001: -1}, (100000, 200000))
