def test_contraction_structure_Mul_and_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
i_ji = x[i]**(y[j] * x[i])
assert get_contraction_structure(i_ji) == {None: set([i_ji])}
ij_i = (x[i] * y[j])**(y[i])
assert get_contraction_structure(ij_i) == {None: set([ij_i])}
j_ij_i = x[j] * (x[i] * y[j])**(y[i])
assert get_contraction_structure(j_ij_i) == {(j, ): set([j_ij_i])}
j_i_ji = x[j] * x[i]**(y[j] * x[i])
assert get_contraction_structure(j_i_ji) == {(j, ): set([j_i_ji])}
ij_exp_kki = x[i] * y[j] * exp(y[i] * y[k, k])
result = get_contraction_structure(ij_exp_kki)
expected = {
(i, ):
set([ij_exp_kki]),
ij_exp_kki: [{
None:
set([exp(y[i] * y[k, k])]),
exp(y[i] * y[k, k]): [{
None: set([y[i] * y[k, k]]),
y[i] * y[k, k]: [{
(k, ): set([y[k, k]])
}]
}]
}]
}
assert result == expected
def test_ufunc_support():
f = Function("f")
g = Function("g")
x = IndexedBase("x")
y = IndexedBase("y")
i, j = Idx("i"), Idx("j")
a = symbols("a")
assert get_indices(f(x[i])) == (set([i]), {})
assert get_indices(f(x[i], y[j])) == (set([i, j]), {})
assert get_indices(f(y[i]) * g(x[i])) == (set(), {})
assert get_indices(f(a, x[i])) == (set([i]), {})
assert get_indices(f(a, y[i], x[j]) * g(x[i])) == (set([j]), {})
assert get_indices(g(f(x[i]))) == (set([i]), {})
assert get_contraction_structure(f(x[i])) == {None: set([f(x[i])])}
assert get_contraction_structure(f(y[i]) * g(x[i])) == {
(i, ): set([f(y[i]) * g(x[i])])
}
assert get_contraction_structure(f(y[i]) * g(f(x[i]))) == {
(i, ): set([f(y[i]) * g(f(x[i]))])
}
assert get_contraction_structure(f(x[j], y[i]) * g(x[i])) == {
(i, ): set([f(x[j], y[i]) * g(x[i])])
}
def test_ufunc_support():
f = Function('f')
g = Function('g')
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
a = symbols('a')
assert get_indices(f(x[i])) == (set([i]), {})
assert get_indices(f(x[i], y[j])) == (set([i, j]), {})
assert get_indices(f(y[i]) * g(x[i])) == (set(), {})
assert get_indices(f(a, x[i])) == (set([i]), {})
assert get_indices(f(a, y[i], x[j]) * g(x[i])) == (set([j]), {})
assert get_indices(g(f(x[i]))) == (set([i]), {})
assert get_contraction_structure(f(x[i])) == {None: set([f(x[i])])}
assert get_contraction_structure(f(y[i]) * g(x[i])) == {
(i, ): set([f(y[i]) * g(x[i])])
}
assert get_contraction_structure(f(y[i]) * g(f(x[i]))) == {
(i, ): set([f(y[i]) * g(f(x[i]))])
}
assert get_contraction_structure(f(x[j], y[i]) * g(x[i])) == {
(i, ): set([f(x[j], y[i]) * g(x[i])])
}
def test_contraction_structure_Add_in_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
s_ii_jj_s = (1 + x[i, i])**(1 + y[j, j])
expected = {
None:
set([s_ii_jj_s]),
s_ii_jj_s: [{
None: set([S.One]),
(i, ): set([x[i, i]])
}, {
None: set([S.One]),
(j, ): set([y[j, j]])
}]
}
result = get_contraction_structure(s_ii_jj_s)
assert result == expected
s_ii_jk_s = (1 + x[i, i])**(1 + y[j, k])
expected_2 = {
None: set([(x[i, i] + 1)**(y[j, k] + 1)]),
s_ii_jk_s: [{
None: set([S.One]),
(i, ): set([x[i, i]])
}]
}
result_2 = get_contraction_structure(s_ii_jk_s)
assert result_2 == expected_2
def test_contraction_structure_Mul_and_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
i_ji = x[i]**(y[j]*x[i])
assert get_contraction_structure(i_ji) == {None: set([i_ji])}
ij_i = (x[i]*y[j])**(y[i])
assert get_contraction_structure(ij_i) == {None: set([ij_i])}
j_ij_i = x[j]*(x[i]*y[j])**(y[i])
assert get_contraction_structure(j_ij_i) == {(j,): set([j_ij_i])}
j_i_ji = x[j]*x[i]**(y[j]*x[i])
assert get_contraction_structure(j_i_ji) == {(j,): set([j_i_ji])}
ij_exp_kki = x[i]*y[j]*exp(y[i]*y[k, k])
result = get_contraction_structure(ij_exp_kki)
expected = {
(i,): set([ij_exp_kki]),
ij_exp_kki: [{
None: set([exp(y[i]*y[k, k])]),
exp(y[i]*y[k, k]): [{
None: set([y[i]*y[k, k]]),
y[i]*y[k, k]: [{(k,): set([y[k, k]])}]
}]}
]
}
assert result == expected
def test_get_contraction_structure_basic():
x = IndexedBase('x')
y = IndexedBase('y')
i, j = Idx('i'), Idx('j')
assert get_contraction_structure(x[i]*y[j]) == {None: set([x[i]*y[j]])}
assert get_contraction_structure(x[i] + y[j]) == {None: set([x[i], y[j]])}
assert get_contraction_structure(x[i]*y[i]) == {(i,): set([x[i]*y[i]])}
assert get_contraction_structure(1 + x[i]*y[i]) == {None: set([S.One]), (i,): set([x[i]*y[i]])}
assert get_contraction_structure(x[i]**y[i]) == {None: set([x[i]**y[i]])}
def test_get_contraction_structure_complex():
x = IndexedBase('x')
y = IndexedBase('y')
A = IndexedBase('A')
i, j, k = Idx('i'), Idx('j'), Idx('k')
expr1 = y[i] + A[i, j]*x[j]
d1 = {None: set([y[i]]), (j,): set([A[i, j]*x[j]])}
assert get_contraction_structure(expr1) == d1
expr2 = expr1*A[k, i] + x[k]
d2 = {None: set([x[k]]), (i,): set([expr1*A[k, i]]), expr1*A[k, i]: [d1]}
assert get_contraction_structure(expr2) == d2
def test_get_contraction_structure_complex():
x = IndexedBase('x')
y = IndexedBase('y')
A = IndexedBase('A')
i, j, k = Idx('i'), Idx('j'), Idx('k')
expr1 = y[i] + A[i, j]*x[j]
d1 = {None: set([y[i]]), (j,): set([A[i, j]*x[j]])}
assert get_contraction_structure(expr1) == d1
expr2 = expr1*A[k, i] + x[k]
d2 = {None: set([x[k]]), (i,): set([expr1*A[k, i]]), expr1*A[k, i]: [d1]}
assert get_contraction_structure(expr2) == d2
def test_get_contraction_structure_basic():
x = IndexedBase("x")
y = IndexedBase("y")
i, j = Idx("i"), Idx("j")
assert get_contraction_structure(x[i] * y[j]) == {None: set([x[i] * y[j]])}
assert get_contraction_structure(x[i] + y[j]) == {None: set([x[i], y[j]])}
assert get_contraction_structure(x[i] * y[i]) == {
(i, ): set([x[i] * y[i]])
}
assert get_contraction_structure(1 + x[i] * y[i]) == {
None: set([S.One]),
(i, ): set([x[i] * y[i]]),
}
assert get_contraction_structure(x[i]**y[i]) == {None: set([x[i]**y[i]])}
def test_get_contraction_structure_complex():
x = IndexedBase("x")
y = IndexedBase("y")
A = IndexedBase("A")
i, j, k = Idx("i"), Idx("j"), Idx("k")
expr1 = y[i] + A[i, j] * x[j]
d1 = {None: set([y[i]]), (j, ): set([A[i, j] * x[j]])}
assert get_contraction_structure(expr1) == d1
expr2 = expr1 * A[k, i] + x[k]
d2 = {
None: set([x[k]]),
(i, ): set([expr1 * A[k, i]]),
expr1 * A[k, i]: [d1]
}
assert get_contraction_structure(expr2) == d2
def test_contraction_structure_Pow_in_Pow():
x = IndexedBase("x")
y = IndexedBase("y")
z = IndexedBase("z")
i, j, k = Idx("i"), Idx("j"), Idx("k")
ii_jj_kk = x[i, i]**y[j, j]**z[k, k]
expected = {
None:
set([ii_jj_kk]),
ii_jj_kk: [
{
(i, ): set([x[i, i]])
},
{
None:
set([y[j, j]**z[k, k]]),
y[j, j]**z[k, k]: [{
(j, ): set([y[j, j]])
}, {
(k, ): set([z[k, k]])
}],
},
],
}
assert get_contraction_structure(ii_jj_kk) == expected
def test_ufunc_support():
f = Function('f')
g = Function('g')
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
a = symbols('a')
assert get_indices(f(x[i])) == (set([i]), {})
assert get_indices(f(x[i], y[j])) == (set([i, j]), {})
assert get_indices(f(y[i])*g(x[i])) == (set(), {})
assert get_indices(f(a, x[i])) == (set([i]), {})
assert get_indices(f(a, y[i], x[j])*g(x[i])) == (set([j]), {})
assert get_indices(g(f(x[i]))) == (set([i]), {})
assert get_contraction_structure(f(x[i])) == {None: set([f(x[i])])}
assert get_contraction_structure(f(y[i])*g(x[i])) == {(i,): set([f(y[i])*g(x[i])])}
assert get_contraction_structure(f(y[i])*g(f(x[i]))) == {(i,): set([f(y[i])*g(f(x[i]))])}
assert get_contraction_structure(f(x[j], y[i])*g(x[i])) == {(i,): set([f(x[j], y[i])*g(x[i])])}
def test_contraction_structure_simple_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
ii_jj = x[i, i]**y[j, j]
assert get_contraction_structure(ii_jj) == {
None: {ii_jj},
ii_jj: [
{(i,): {x[i, i]}},
{(j,): {y[j, j]}}
]
}
ii_jk = x[i, i]**y[j, k]
assert get_contraction_structure(ii_jk) == {
None: {x[i, i]**y[j, k]},
x[i, i]**y[j, k]: [
{(i,): {x[i, i]}}
]
}
def test_contraction_structure_simple_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
ii_jj = x[i, i]**y[j, j]
assert get_contraction_structure(ii_jj) == {
None: set([ii_jj]),
ii_jj: [
{(i,): set([x[i, i]])},
{(j,): set([y[j, j]])}
]
}
ii_jk = x[i, i]**y[j, k]
assert get_contraction_structure(ii_jk) == {
None: set([x[i, i]**y[j, k]]),
x[i, i]**y[j, k]: [
{(i,): set([x[i, i]])}
]
}
def test_contraction_structure_simple_Pow():
x = IndexedBase("x")
y = IndexedBase("y")
i, j, k = Idx("i"), Idx("j"), Idx("k")
ii_jj = x[i, i]**y[j, j]
assert get_contraction_structure(ii_jj) == {
None: set([ii_jj]),
ii_jj: [{
(i, ): set([x[i, i]])
}, {
(j, ): set([y[j, j]])
}],
}
ii_jk = x[i, i]**y[j, k]
assert get_contraction_structure(ii_jk) == {
None: set([x[i, i]**y[j, k]]),
x[i, i]**y[j, k]: [{
(i, ): set([x[i, i]])
}],
}
def test_contraction_structure_simple_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
ii_jj = x[i, i]**y[j, j]
assert get_contraction_structure(ii_jj) == {
None: set([ii_jj]),
ii_jj: [
{(i,): set([x[i, i]])},
{(j,): set([y[j, j]])}
]
}
def test_contraction_structure_Add_in_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
s_ii_jj_s = (1 + x[i, i])**(1 + y[j, j])
expected = {
None: set([s_ii_jj_s]),
s_ii_jj_s: [
{None: set([S.One]), (i,): set([x[i, i]])},
{None: set([S.One]), (j,): set([y[j, j]])}
]
}
result = get_contraction_structure(s_ii_jj_s)
assert result == expected
def test_contraction_structure_Add_in_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
i, j, k = Idx('i'), Idx('j'), Idx('k')
s_ii_jj_s = (1 + x[i, i])**(1 + y[j, j])
expected = {
None: {s_ii_jj_s},
s_ii_jj_s: [
{None: {S.One}, (i,): {x[i, i]}},
{None: {S.One}, (j,): {y[j, j]}}
]
}
result = get_contraction_structure(s_ii_jj_s)
assert result == expected
s_ii_jk_s = (1 + x[i, i]) ** (1 + y[j, k])
expected_2 = {
None: {(x[i, i] + 1)**(y[j, k] + 1)},
s_ii_jk_s: [
{None: {S.One}, (i,): {x[i, i]}}
]
}
result_2 = get_contraction_structure(s_ii_jk_s)
assert result_2 == expected_2
def test_contraction_structure_Pow_in_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
z = IndexedBase('z')
i, j, k = Idx('i'), Idx('j'), Idx('k')
ii_jj_kk = x[i, i]**y[j, j]**z[k, k]
expected = {
None: set([ii_jj_kk]),
ii_jj_kk: [
{(i,): set([x[i, i]])},
{
None: set([y[j, j]**z[k, k]]),
y[j, j]**z[k, k]: [
{(j,): set([y[j, j]])},
{(k,): set([z[k, k]])}
]
}
]
}
assert get_contraction_structure(ii_jj_kk) == expected
def test_contraction_structure_Pow_in_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
z = IndexedBase('z')
i, j, k = Idx('i'), Idx('j'), Idx('k')
ii_jj_kk = x[i, i]**y[j, j]**z[k, k]
expected = {
None: set([ii_jj_kk]),
ii_jj_kk: [
{(i,): set([x[i, i]])},
{
None: set([y[j, j]**z[k, k]]),
y[j, j]**z[k, k]: [
{(j,): set([y[j, j]])},
{(k,): set([z[k, k]])}
]
}
]
}
assert get_contraction_structure(ii_jj_kk) == expected
def test_contraction_structure_Pow_in_Pow():
x = IndexedBase('x')
y = IndexedBase('y')
z = IndexedBase('z')
i, j, k = Idx('i'), Idx('j'), Idx('k')
ii_jj_kk = x[i, i]**y[j, j]**z[k, k]
expected = {
None: {ii_jj_kk},
ii_jj_kk: [
{(i,): {x[i, i]}},
{
None: {y[j, j]**z[k, k]},
y[j, j]**z[k, k]: [
{(j,): {y[j, j]}},
{(k,): {z[k, k]}}
]
}
]
}
assert get_contraction_structure(ii_jj_kk) == expected