from sympy.core import symbols, S, Pow, Function from sympy.functions import exp from sympy.testing.pytest import raises from sympy.tensor.indexed import Idx, IndexedBase from sympy.tensor.index_methods import IndexConformanceException from sympy.tensor.index_methods import (get_contraction_structure, get_indices) def test_trivial_indices(): x, y = symbols('x y') assert get_indices(x) == (set(), {}) assert get_indices(x*y) == (set(), {}) assert get_indices(x + y) == (set(), {}) assert get_indices(x**y) == (set(), {}) def test_get_indices_Indexed(): x = IndexedBase('x') i, j = Idx('i'), Idx('j') assert get_indices(x[i, j]) == ({i, j}, {}) assert get_indices(x[j, i]) == ({j, i}, {}) def test_get_indices_Idx(): f = Function('f') i, j = Idx('i'), Idx('j') assert get_indices(f(i)*j) == ({i, j}, {}) assert get_indices(f(j, i)) == ({j, i}, {}) assert get_indices(f(i)*i) == (set(), {}) def test_get_indices_mul(): x = IndexedBase('x') y = IndexedBase('y') i, j = Idx('i'), Idx('j') assert get_indices(x[j]*y[i]) == ({i, j}, {}) assert get_indices(x[i]*y[j]) == ({i, j}, {}) def test_get_indices_exceptions(): x = IndexedBase('x') y = IndexedBase('y') i, j = Idx('i'), Idx('j') raises(IndexConformanceException, lambda: get_indices(x[i] + y[j])) def test_scalar_broadcast(): x = IndexedBase('x') y = IndexedBase('y') i, j = Idx('i'), Idx('j') assert get_indices(x[i] + y[i, i]) == ({i}, {}) assert get_indices(x[i] + y[j, j]) == ({i}, {}) def test_get_indices_add(): x = IndexedBase('x') y = IndexedBase('y') A = IndexedBase('A') i, j, k = Idx('i'), Idx('j'), Idx('k') assert get_indices(x[i] + 2*y[i]) == ({i}, {}) assert get_indices(y[i] + 2*A[i, j]*x[j]) == ({i}, {}) assert get_indices(y[i] + 2*(x[i] + A[i, j]*x[j])) == ({i}, {}) assert get_indices(y[i] + x[i]*(A[j, j] + 1)) == ({i}, {}) assert get_indices( y[i] + x[i]*x[j]*(y[j] + A[j, k]*x[k])) == ({i}, {}) def test_get_indices_Pow(): x = IndexedBase('x') y = IndexedBase('y') A = IndexedBase('A') i, j, k = Idx('i'), Idx('j'), Idx('k') assert get_indices(Pow(x[i], y[j])) == ({i, j}, {}) assert get_indices(Pow(x[i, k], y[j, k])) == ({i, j, k}, {}) assert get_indices(Pow(A[i, k], y[k] + A[k, j]*x[j])) == ({i, k}, {}) assert get_indices(Pow(2, x[i])) == get_indices(exp(x[i])) # test of a design decision, this may change: assert get_indices(Pow(x[i], 2)) == ({i}, {}) 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: {x[i]*y[j]}} assert get_contraction_structure(x[i] + y[j]) == {None: {x[i], y[j]}} assert get_contraction_structure(x[i]*y[i]) == {(i,): {x[i]*y[i]}} assert get_contraction_structure( 1 + x[i]*y[i]) == {None: {S.One}, (i,): {x[i]*y[i]}} assert get_contraction_structure(x[i]**y[i]) == {None: {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: {y[i]}, (j,): {A[i, j]*x[j]}} assert get_contraction_structure(expr1) == d1 expr2 = expr1*A[k, i] + x[k] d2 = {None: {x[k]}, (i,): {expr1*A[k, i]}, expr1*A[k, i]: [d1]} assert get_contraction_structure(expr2) == d2 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_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: {i_ji}} ij_i = (x[i]*y[j])**(y[i]) assert get_contraction_structure(ij_i) == {None: {ij_i}} j_ij_i = x[j]*(x[i]*y[j])**(y[i]) assert get_contraction_structure(j_ij_i) == {(j,): {j_ij_i}} j_i_ji = x[j]*x[i]**(y[j]*x[i]) assert get_contraction_structure(j_i_ji) == {(j,): {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,): {ij_exp_kki}, ij_exp_kki: [{ None: {exp(y[i]*y[k, k])}, exp(y[i]*y[k, k]): [{ None: {y[i]*y[k, k]}, y[i]*y[k, k]: [{(k,): {y[k, k]}}] }]} ] } 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: {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 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])) == ({i}, {}) assert get_indices(f(x[i], y[j])) == ({i, j}, {}) assert get_indices(f(y[i])*g(x[i])) == (set(), {}) assert get_indices(f(a, x[i])) == ({i}, {}) assert get_indices(f(a, y[i], x[j])*g(x[i])) == ({j}, {}) assert get_indices(g(f(x[i]))) == ({i}, {}) assert get_contraction_structure(f(x[i])) == {None: {f(x[i])}} assert get_contraction_structure( f(y[i])*g(x[i])) == {(i,): {f(y[i])*g(x[i])}} assert get_contraction_structure( f(y[i])*g(f(x[i]))) == {(i,): {f(y[i])*g(f(x[i]))}} assert get_contraction_structure( f(x[j], y[i])*g(x[i])) == {(i,): {f(x[j], y[i])*g(x[i])}}