@Test
public void test2() {
Tensor t = parse("A*(B*A+C*K)*F", "^i", "_j");
Indices indices = ParserIndices.parseSimple("^i_j");
Tensor e = Tensors.parse("A^{i}_{a}*F^{b}_{j}*(B^{a}_{c}*A^{c}_{b}+K^{c}_{b}*C^{a}_{c})");
assertIndicesParity(t.getIndices().getFree(), indices);
assertEquals(t, e);
}
@Test
public void test7() {
Tensor t = parse("A*(B+E*(R+K*U))", "^i", "_j");
Indices indices = ParserIndices.parseSimple("^i_j");
Tensor e = Tensors.parse("A^i_a*(B^a_j+E^a_b*(R^b_j+K^b_c*U^c_j))");
assertIndicesParity(t.getIndices().getFree(), indices);
assertEqualsExactly(t, e);
}
@Test
public void test8() {
for (int i = 0; i < 100; ++i) {
CC.resetTensorNames();
Tensor t = parse("L*L*(L-1)*A*B", "^ijpq", "_pqrs", "A", "B");
Indices indices = ParserIndices.parseSimple("^ijpq_pqrs");
assertIndicesParity(t.getIndices().getFree(), indices.getFree());
}
}
static IndexMappingProvider createPort(IndexMappingProvider opu, Tensor from, Tensor to) {
if (from.hashCode() != to.hashCode()) return IndexMappingProvider.Util.EMPTY_PROVIDER;
if (from.getClass() != to.getClass()) {
Tensor nonComplex;
// Processing case -2*(1/2)*g_mn -> g_mn
if (from instanceof Product && !(to instanceof Product)) {
if (from.size() != 2) return IndexMappingProvider.Util.EMPTY_PROVIDER;
if ((nonComplex = extractNonComplexFactor(from)) != null)
return new MinusIndexMappingProviderWrapper(createPort(opu, nonComplex, to));
return IndexMappingProvider.Util.EMPTY_PROVIDER;
}
// Processing case g_mn -> -2*(1/2)*g_mn
if (to instanceof Product && !(from instanceof Product)) {
if (to.size() != 2) return IndexMappingProvider.Util.EMPTY_PROVIDER;
if ((nonComplex = extractNonComplexFactor(to)) != null)
return new MinusIndexMappingProviderWrapper(createPort(opu, from, nonComplex));
return IndexMappingProvider.Util.EMPTY_PROVIDER;
}
return IndexMappingProvider.Util.EMPTY_PROVIDER;
}
IndexMappingProviderFactory factory = map.get(from.getClass());
if (factory == null) throw new RuntimeException("Unsupported tensor type: " + from.getClass());
return factory.create(opu, from, to);
}
@Test
public void performance() {
Tensor t =
parse(
"(1/10)*L*L*HATK^{\\delta}*DELTA^{\\mu\\nu\\alpha\\beta}*HATK^{\\gamma}*n_{\\sigma}*n_{\\lambda}*R^{\\sigma}_{\\alpha\\beta\\gamma}*R^{\\lambda}_{\\mu\\nu\\delta} + "
+ "L*L*(L-1)*(L-1)*(L-2)*HATK^{\\beta\\gamma\\delta}*DELTA^{\\alpha}*HATK^{\\mu\\nu}*n_{\\sigma}*n_{\\lambda}*((2/45)*R^{\\lambda}_{\\alpha\\delta\\nu}*R^{\\sigma}_{\\beta\\mu\\gamma}-(1/120)*R^{\\lambda}_{\\delta\\alpha\\nu}*R^{\\sigma}_{\\beta\\mu\\gamma}) +"
+ "L*L*(L-1)*HATK^{\\delta}*DELTA^{\\alpha\\beta\\gamma}*HATK^{\\mu\\nu}*n_{\\sigma}*n_{\\lambda}*(-(1/10)*R^{\\lambda}_{\\mu\\gamma\\nu}*R^{\\sigma}_{\\alpha\\delta\\beta}+(1/15)*R^{\\lambda}_{\\delta\\alpha\\nu}*R^{\\sigma}_{\\beta\\mu\\gamma}+(1/60)*R^{\\lambda}_{\\beta\\delta\\nu}*R^{\\sigma}_{\\gamma\\mu\\alpha})+"
+ "L*L*(L-1)*(L-1)*HATK^{\\gamma\\delta}*DELTA^{\\alpha\\beta}*HATK^{\\mu\\nu}*n_{\\sigma}*n_{\\lambda}*(-(1/20)*R^{\\lambda}_{\\mu\\beta\\nu}*R^{\\sigma}_{\\delta\\alpha\\gamma}+(1/180)*R^{\\lambda}_{\\alpha\\nu\\beta}*R^{\\sigma}_{\\gamma\\delta\\mu}-(7/360)*R^{\\lambda}_{\\mu\\gamma\\nu}*R^{\\sigma}_{\\alpha\\delta\\beta}-(1/240)*R^{\\lambda}_{\\delta\\beta\\nu}*R^{\\sigma}_{\\gamma\\alpha\\mu}-(1/120)*R^{\\lambda}_{\\beta\\gamma\\nu}*R^{\\sigma}_{\\alpha\\delta\\mu}-(1/30)*R^{\\lambda}_{\\delta\\beta\\nu}*R^{\\sigma}_{\\alpha\\gamma\\mu})+"
+ "L*L*(L-1)*HATK^{\\mu\\nu}*DELTA^{\\alpha\\beta\\gamma}*HATK^{\\delta}*n_{\\sigma}*n_{\\lambda}*((7/120)*R^{\\lambda}_{\\beta\\gamma\\nu}*R^{\\sigma}_{\\mu\\alpha\\delta}-(3/40)*R^{\\lambda}_{\\beta\\gamma\\delta}*R^{\\sigma}_{\\mu\\alpha\\nu}+(1/120)*R^{\\lambda}_{\\delta\\gamma\\nu}*R^{\\sigma}_{\\alpha\\beta\\mu})+"
+ "L*L*HATK^{\\mu}*DELTA^{\\alpha\\beta\\gamma}*HATK^{\\nu}*{\\nu}_{\\lambda}*(-(1/8)*R_{\\beta\\gamma}*R^{\\lambda}_{\\nu\\alpha\\mu}+(3/20)*R_{\\beta\\gamma}*R^{\\lambda}_{\\mu\\alpha\\nu}+(3/40)*R_{\\alpha\\mu}*R^{\\lambda}_{\\beta\\gamma\\nu}+(1/40)*R^{\\sigma}_{\\beta\\gamma\\mu}*R^{\\lambda}_{\\nu\\alpha\\sigma}-(3/20)*R^{\\sigma}_{\\alpha\\beta\\mu}*R^{\\lambda}_{\\gamma\\nu\\sigma}+(1/10)*R^{\\sigma}_{\\alpha\\beta\\nu}*R^{\\lambda}_{\\gamma\\mu\\sigma})+"
+ "L*L*(L-1)*HATK^{\\gamma}*DELTA^{\\alpha\\beta}*HATK^{\\mu\\nu}*n_{\\lambda}*((1/20)*R_{\\alpha\\nu}*R^{\\lambda}_{\\gamma\\beta\\mu}+(1/20)*R_{\\alpha\\gamma}*R^{\\lambda}_{\\mu\\beta\\nu}+(1/10)*R_{\\alpha\\beta}*R^{\\lambda}_{\\mu\\gamma\\nu}+(1/20)*R^{\\sigma}_{\\alpha\\nu\\gamma}*R^{\\lambda}_{\\sigma\\beta\\mu}-(1/60)*R^{\\sigma}_{\\mu\\alpha\\nu}*R^{\\lambda}_{\\beta\\sigma\\gamma}+(1/10)*R^{\\sigma}_{\\alpha\\beta\\gamma}*R^{\\lambda}_{\\mu\\sigma\\nu}-(1/12)*R^{\\sigma}_{\\alpha\\beta\\nu}*R^{\\lambda}_{\\mu\\sigma\\gamma})+"
+ "L*L*(L-1)*(L-1)*HATK^{\\alpha\\beta}*DELTA^{\\gamma}*HATK^{\\mu\\nu}*n_{\\lambda}*((1/60)*R_{\\alpha\\mu}*R^{\\lambda}_{\\beta\\nu\\gamma}-(1/20)*R_{\\alpha\\mu}*R^{\\lambda}_{\\gamma\\nu\\beta}+(1/120)*R_{\\alpha\\beta}*R^{\\lambda}_{\\mu\\nu\\gamma}+(3/40)*R_{\\alpha\\gamma}*R^{\\lambda}_{\\nu\\beta\\mu}+(1/20)*R^{\\sigma}_{\\gamma\\mu\\alpha}*R^{\\lambda}_{\\nu\\sigma\\beta}+(1/120)*R^{\\sigma}_{\\alpha\\mu\\gamma}*R^{\\lambda}_{\\beta\\nu\\sigma}-(1/40)*R^{\\sigma}_{\\alpha\\mu\\gamma}*R^{\\lambda}_{\\sigma\\nu\\beta}+(1/40)*R^{\\sigma}_{\\alpha\\mu\\beta}*R^{\\lambda}_{\\sigma\\nu\\gamma}-(1/20)*R^{\\sigma}_{\\alpha\\mu\\beta}*R^{\\lambda}_{\\gamma\\nu\\sigma}-(1/40)*R^{\\sigma}_{\\mu\\beta\\nu}*R^{\\lambda}_{\\gamma\\sigma\\alpha})+"
+ "L*L*(L-1)*HATK^{\\alpha\\beta}*DELTA^{\\mu\\nu}*HATK^{\\gamma}*n_{\\lambda}*((1/20)*R^{\\sigma}_{\\mu\\nu\\beta}*R^{\\lambda}_{\\gamma\\sigma\\alpha}-(7/60)*R^{\\sigma}_{\\beta\\mu\\alpha}*R^{\\lambda}_{\\gamma\\nu\\sigma}+(1/20)*R^{\\sigma}_{\\beta\\mu\\alpha}*R^{\\lambda}_{\\sigma\\nu\\gamma}+(1/10)*R^{\\sigma}_{\\mu\\beta\\gamma}*R^{\\lambda}_{\\nu\\alpha\\sigma}+(1/60)*R^{\\sigma}_{\\mu\\beta\\gamma}*R^{\\lambda}_{\\alpha\\nu\\sigma}+(7/120)*R_{\\alpha\\beta}*R^{\\lambda}_{\\nu\\gamma\\mu}+(11/60)*R_{\\beta\\mu}*R^{\\lambda}_{\\nu\\alpha\\gamma})",
"^ijpq",
"_pqrs",
"HATK",
"DELTA");
Indices indices = ParserIndices.parseSimple("^ijpq_pqrs");
assertIndicesParity(t.getIndices().getFree(), indices.getFree());
}
public static Tensor symmetrize(SimpleTensor tensor, int[] freeIndices, Symmetries symmetries) {
if (symmetries.isEmpty()) return tensor;
int[] tempI = freeIndices.clone();
int[] allFreeIndices = tensor.getIndices().getFree().getAllIndices().copy();
Arrays.sort(tempI);
Arrays.sort(allFreeIndices);
int[] diff = MathUtils.intSetDifference(tempI, allFreeIndices);
System.arraycopy(freeIndices, 0, allFreeIndices, 0, freeIndices.length);
System.arraycopy(diff, 0, allFreeIndices, freeIndices.length, diff.length);
SumBuilder builder = new SumBuilder();
Tensor temp;
for (Symmetry symmetry : symmetries) {
temp =
applyIndexMapping(tensor, allFreeIndices, permute(allFreeIndices, symmetry), new int[0]);
if (symmetry.isAntiSymmetry()) temp = negate(temp);
builder.put(temp);
}
temp = builder.build();
if (temp instanceof Sum) {
// retrieving factor
Complex factor = null, tempF;
for (int i = temp.size() - 1; i >= 0; --i) {
if (temp.get(i) instanceof Product) {
tempF = ((Product) temp.get(i)).getFactor();
assert tempF.isInteger();
tempF = tempF.abs();
} else tempF = Complex.ONE;
if (factor == null) factor = tempF;
assert factor.equals(tempF);
}
if (!factor.isOne())
temp = FastTensors.multiplySumElementsOnFactor((Sum) temp, factor.reciprocal());
return multiply(new Complex(new Rational(1, temp.size())), temp);
}
return temp;
}
@Test
public void test4() {
Tensor t = parse("a*b*A*c*B*C", "^ij", "_pq", "a", "b", "c", "d");
Indices indices = ParserIndices.parseSimple("^ij_pq");
assertIndicesParity(t.getIndices().getFree(), indices);
}
@Test
public void test3() {
Tensor t = parse("A^{\\alpha n}*B*C", "^ij", "_pq");
assertIndicesParity(t.getIndices().getFree(), ParserIndices.parseSimple("^{\\alpha n i j}_pq"));
}
@Test
public void test1() {
Tensor t = parse("A*B*C", "^i", "_j", "A", "B", "C");
Indices indices = ParserIndices.parseSimple("^i_j");
assertIndicesParity(t.getIndices().getFree(), indices);
}
@Test
public void test10() {
Tensor t = parse("A=2*B+A*B", "^i", "_j");
Indices indices = ParserIndices.parseSimple("^i_j");
assertIndicesParity(t.getIndices().getFree(), indices.getFree());
}
@Test
public void test9() {
Tensor t = parse("a*A*B+((1/2)*a+b)*A*(A+B*(A+X*A))*c", "^a", "_b", "A", "B");
Indices indices = ParserIndices.parseSimple("^a_b");
assertIndicesParity(t.getIndices().getFree(), indices.getFree());
}
@Test
public void test6() {
Tensor t = parse("a*(b+a)*A*(c+d)*B*C", "^ij", "_pq", "A", "B", "C", "F");
Indices indices = ParserIndices.parseSimple("^ij_pq");
assertIndicesParity(t.getIndices().getFree(), indices);
}