def test_tensorcontraction():
from sympy.abc import a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x
B = Array(range(18), (2, 3, 3))
assert tensorcontraction(B, (1, 2)) == Array([12, 39])
C1 = Array([a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x], (2, 3, 2, 2))
assert tensorcontraction(C1, (0, 2)) == Array([[a + o, b + p], [e + s, f + t], [i + w, j + x]])
assert tensorcontraction(C1, (0, 2, 3)) == Array([a + p, e + t, i + x])
assert tensorcontraction(C1, (2, 3)) == Array([[a + d, e + h, i + l], [m + p, q + t, u + x]])
def test_issue_emerged_while_discussing_10972():
ua = Array([-1,0])
Fa = Array([[0, 1], [-1, 0]])
po = tensorproduct(Fa, ua, Fa, ua)
assert tensorcontraction(po, (1, 2), (4, 5)) == Array([[0, 0], [0, 1]])
sa = symbols('a0:144')
po = Array(sa, [2, 2, 3, 3, 2, 2])
assert tensorcontraction(po, (0, 1), (2, 3), (4, 5)) == sa[0] + sa[108] + sa[111] + sa[124] + sa[127] + sa[140] + sa[143] + sa[16] + sa[19] + sa[3] + sa[32] + sa[35]
assert tensorcontraction(po, (0, 1, 4, 5), (2, 3)) == sa[0] + sa[111] + sa[127] + sa[143] + sa[16] + sa[32]
assert tensorcontraction(po, (0, 1), (4, 5)) == Array([[sa[0] + sa[108] + sa[111] + sa[3], sa[112] + sa[115] + sa[4] + sa[7],
sa[11] + sa[116] + sa[119] + sa[8]], [sa[12] + sa[120] + sa[123] + sa[15],
sa[124] + sa[127] + sa[16] + sa[19], sa[128] + sa[131] + sa[20] + sa[23]],
[sa[132] + sa[135] + sa[24] + sa[27], sa[136] + sa[139] + sa[28] + sa[31],
sa[140] + sa[143] + sa[32] + sa[35]]])
assert tensorcontraction(po, (0, 1), (2, 3)) == Array([[sa[0] + sa[108] + sa[124] + sa[140] + sa[16] + sa[32], sa[1] + sa[109] + sa[125] + sa[141] + sa[17] + sa[33]],
[sa[110] + sa[126] + sa[142] + sa[18] + sa[2] + sa[34], sa[111] + sa[127] + sa[143] + sa[19] + sa[3] + sa[35]]])
def matrix_product(Asm, Bsm):
'''
Matrix product between 2D sympy.tensor.array
'''
assert len(Asm.shape)<3 or len(Bsm.shape)<3,\
'Attempting matrix product between 3D (or higher) arrays!'
assert Asm.shape[1] == Bsm.shape[0], 'Matrix dimensions not compatible!'
P = smarr.tensorproduct(Asm, Bsm)
Csm = smarr.tensorcontraction(P, (1, 2))
return Csm
def apply_contraction(outer_indices, tensor_indices, array):
""" Apply the contraction structure to the array of Indexed objects.
:arg outer_indices: The outer indices (i.e. any indices that are not repeated/summation indices)
:arg tensor_indices: The indices that need to be summed over.
:arg array: The Indexed arrays to apply the index contraction structure to.
"""
contracting_indices = set(tensor_indices).difference(set(outer_indices))
result = array
if contracting_indices:
for index in contracting_indices:
match = tuple(
[i for i, x in enumerate(tensor_indices) if x == index])
result = tensorcontraction(result, match)
tensor_indices = [i for i in tensor_indices if i != index]
return result
def test_codegen_array_doit():
M = MatrixSymbol("M", 2, 2)
N = MatrixSymbol("N", 2, 2)
P = MatrixSymbol("P", 2, 2)
Q = MatrixSymbol("Q", 2, 2)
M = M.as_explicit()
N = N.as_explicit()
P = P.as_explicit()
Q = Q.as_explicit()
expr = CodegenArrayTensorProduct(M, N, P, Q)
assert expr.doit() == tensorproduct(M, N, P, Q)
expr2 = CodegenArrayContraction(expr, (0, 1))
assert expr2.doit() == tensorcontraction(tensorproduct(M, N, P, Q), (0, 1))
expr2 = CodegenArrayDiagonal(expr, (0, 1))
#assert expr2 = ... # TODO: not implemented
expr = CodegenArrayTensorProduct(M, N)
exprp = CodegenArrayPermuteDims(expr, [2, 1, 3, 0])
assert exprp.doit() == permutedims(tensorproduct(M, N), [2, 1, 3, 0])
expr = CodegenArrayElementwiseAdd(M, N)
assert expr.doit() == M + N
def covariance_transform(self, *indices):
"""
Return the array associated with this tensor with indices set according
to arguments.
Parameters
----------
indices : TensorIndex
Defines the covariance and contravariance of the returned array.
Examples
--------
>>> from sympy import diag, symbols, sin
>>> from einsteinpy.symbolic.tensor import indices
>>> from einsteinpy.symbolic.metric import Metric
>>> t, r, th, ph = symbols('t r theta phi')
>>> schwarzschild = diag(1-1/r, -1/(1-1/r), -r**2, -r**2*sin(th)**2)
>>> g = Metric('g', [t, r, th, ph], schwarzschild)
>>> mu, nu = indices('mu nu', g)
>>> g.covariance_transform(mu, nu)
[[1/(1 - 1/r), 0, 0, 0], [0, 1 - 1/r, 0, 0], [0, 0, -1/r**2, 0], [0, 0, 0, -1/(r**2*sin(theta)**2)]]
"""
array = self.as_array()
for pos, idx in enumerate(indices):
if idx.is_up ^ (self.covar[pos] > 0):
if idx.is_up:
metric = idx.tensor_index_type.metric.as_inverse()
else:
metric = idx.tensor_index_type.metric.as_array()
new = tensorcontraction(tensorproduct(metric, array),
(1, 2 + pos))
permu = list(range(len(indices)))
permu[0], permu[pos] = permu[pos], permu[0]
array = permutedims(new, permu)
return array