def test_sparse():
sparse_array = Arraypy((2, 2), 'sparse')
assert len(sparse_array) == 2 * 2
# dictionary where all data is
assert len(sparse_array._output) == 0
# it's empty, even thought Arraypy knows that 'empty' data is zero
if sys.version_info[0] >= 3:
for i in sparse_array:
assert i == 0
else:
idx = sparse_array.start_index
for i in range(len(sparse_array.start_index)):
assert sparse_array[idx] == 0
idx = sparse_array.next_index(idx)
sparse_array[0, 0] = 123
assert len(sparse_array._output) == 1
assert sparse_array[0, 0] == 123
# when element in sparse array become zero it will disappear from
# dictionary
sparse_array[0, 0] = 0
assert len(sparse_array._output) == 0
assert sparse_array[0, 0] == 0
def dw(omega, args):
"""Return a skew-symmetric tensor of type (0, p+1).
Indexes the output tensor will start as well as the input tensor (array).
If the input parameters of the same type, they must be equal to the initial
indexes.
Examples:
=========
>>> from tensor_analysis.tensor_fields import dw
>>> from sympy import symbols
>>> from tensor_analysis.arraypy import Arraypy
>>> x1, x2, x3 = symbols('x1 x2 x3')
omega - differential form, differential which is calculated.
It's can be a skew-symmetric tensor of type (0,p) or an array arraypy:
>>> omega=Arraypy([2,3,1]).to_tensor((-1,-1))
>>> omega[1,2]=x3
>>> omega[1,3]=-x2
>>> omega[2,1]=-x3
>>> omega[2,3]=x1
>>> omega[3,1]=x2
>>> omega[3,2]=-x1
args it's a list of symbol arguments of differential form.
It's can be in list, array of arraypy or contravariant tensor.
External differential of a differential forms:
>>> domega=dw(omega, [x1,x2,x3])
>>> print(domega)
0 0 0
0 0 3
0 -3 0
0 0 -3
0 0 0
3 0 0
0 3 0
-3 0 0
0 0 0
>>> domega.type_pq
(0, 3)
"""
# Handling of a vector of arguments
check_vector_of_arguments(args)
# The definition of the start index of args
if isinstance(args, list):
idx_args = 0
else:
idx_args = args.start_index[0]
# Handling of a differential form
if not isinstance(omega, (TensorArray, Arraypy)):
raise ValueError(
"The type of differential form must be TensorArray or Arraypy")
if omega.rank > 1:
if not is_asymmetric(omega):
raise ValueError("The differential form must be a skew-symmetric")
idx_omega = omega.start_index[0]
# Define the start index in the output tensor
if isinstance(omega, type(args)) and idx_omega != idx_args:
raise ValueError("The start index of the differential form and \
vector of arguments must be equal")
idx_st = idx_omega
# Creating the output array in accordance with start indexes
n = omega.shape[0] # the dimensionality of the input array
p = len(omega.shape) # the rank of the input array
valence_ind = [(-1) for k in range(p + 1)]
d_omega = Arraypy([p + 1, n, idx_st]).to_tensor(valence_ind)
# Calculation
idx = d_omega.start_index
if isinstance(args, (TensorArray, Arraypy)):
args = args.to_list()
for i in range(len(d_omega)):
# tuple_list_indx it's list of tuple. Example:[(0, 1), (0, 1), (0, 0)]
tuple_list_indx = [
delete_index_from_list(
idx,
f) for f in range(
len(idx))]
for k in range(p + 1):
d_omega[idx] += Add(((-1)**k) * diff(omega[tuple_list_indx[k]],
args[idx[k] - idx_st]))
idx = d_omega.next_index(idx)
# Output
return d_omega
def test_next_index():
array = Arraypy((2, 2), 'Py')
assert array.next_index((0, 0)) == (0, 1)
assert array.next_index((0, 1)) == (1, 0)
assert array.next_index((1, 0)) == (1, 1)
assert array.next_index((1, 1)) == (0, 0)
def dw(omega, args):
"""Return a skew-symmetric tensor of type (0, p+1).
Indexes the output tensor will start as well as the input tensor (array).
If the input parameters of the same type, they must be equal to the initial
indexes.
Examples:
=========
>>> from tensor_analysis.tensor_fields import dw
>>> from sympy import symbols
>>> from tensor_analysis.arraypy import Arraypy
>>> x1, x2, x3 = symbols('x1 x2 x3')
omega - differential form, differential which is calculated.
It's can be a skew-symmetric tensor of type (0,p) or an array arraypy:
>>> omega=Arraypy([2,3,1]).to_tensor((-1,-1))
>>> omega[1,2]=x3
>>> omega[1,3]=-x2
>>> omega[2,1]=-x3
>>> omega[2,3]=x1
>>> omega[3,1]=x2
>>> omega[3,2]=-x1
args it's a list of symbol arguments of differential form.
It's can be in list, array of arraypy or contravariant tensor.
External differential of a differential forms:
>>> domega=dw(omega, [x1,x2,x3])
>>> print(domega)
0 0 0
0 0 3
0 -3 0
0 0 -3
0 0 0
3 0 0
0 3 0
-3 0 0
0 0 0
>>> domega.type_pq
(0, 3)
"""
# Handling of a vector of arguments
check_vector_of_arguments(args)
# The definition of the start index of args
if isinstance(args, list):
idx_args = 0
else:
idx_args = args.start_index[0]
# Handling of a differential form
if not isinstance(omega, (TensorArray, Arraypy)):
raise ValueError(
"The type of differential form must be TensorArray or Arraypy")
if omega.rank > 1:
if not is_asymmetric(omega):
raise ValueError("The differential form must be a skew-symmetric")
idx_omega = omega.start_index[0]
# Define the start index in the output tensor
if isinstance(omega, type(args)) and idx_omega != idx_args:
raise ValueError("The start index of the differential form and \
vector of arguments must be equal")
idx_st = idx_omega
# Creating the output array in accordance with start indexes
n = omega.shape[0] # the dimensionality of the input array
p = len(omega.shape) # the rank of the input array
valence_ind = [(-1) for k in range(p + 1)]
d_omega = Arraypy([p + 1, n, idx_st]).to_tensor(valence_ind)
# Calculation
idx = d_omega.start_index
if isinstance(args, (TensorArray, Arraypy)):
args = args.to_list()
for i in range(len(d_omega)):
# tuple_list_indx it's list of tuple. Example:[(0, 1), (0, 1), (0, 0)]
tuple_list_indx = [
delete_index_from_list(idx, f) for f in range(len(idx))
]
for k in range(p + 1):
d_omega[idx] += Add(
((-1)**k) *
diff(omega[tuple_list_indx[k]], args[idx[k] - idx_st]))
idx = d_omega.next_index(idx)
# Output
return d_omega