Java tutorial
/* * Redberry: symbolic tensor computations. * * Copyright (c) 2010-2013: * Stanislav Poslavsky <stvlpos@mail.ru> * Bolotin Dmitriy <bolotin.dmitriy@gmail.com> * * This file is part of Redberry. * * Redberry is free software: you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * Redberry is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with Redberry. If not, see <http://www.gnu.org/licenses/>. */ package cc.redberry.physics.oneloopdiv; import cc.redberry.core.indices.IndicesBuilder; import cc.redberry.core.number.Complex; import cc.redberry.core.tensor.*; import cc.redberry.core.tensor.iterator.FromChildToParentIterator; import cc.redberry.core.tensor.ApplyIndexMapping; import cc.redberry.core.transformations.expand.ExpandTransformation; import cc.redberry.core.transformations.Transformation; import cc.redberry.core.utils.TensorUtils; import org.apache.commons.math3.util.ArithmeticUtils; import java.util.ArrayList; import java.util.List; /** * @author Dmitry Bolotin * @author Stanislav Poslavsky */ public final class Averaging implements Transformation { private final SimpleTensor const_n; public Averaging(SimpleTensor const_n) { this.const_n = const_n; } private static Tensor average(final int[] indices) { if (indices.length == 0) return Complex.ONE; if (indices.length == 2) return Tensors.createMetricOrKronecker(indices[0], indices[1]); SumBuilder sb = new SumBuilder(); for (int i = 1; i < indices.length; ++i) { int[] suffix = new int[indices.length - 2]; System.arraycopy(indices, 1, suffix, 0, i - 1); System.arraycopy(indices, i + 1, suffix, i - 1, indices.length - i - 1); sb.put(Tensors.multiply(Tensors.createMetricOrKronecker(indices[0], indices[i]), average(suffix))); } return sb.build(); } @Override public Tensor transform(Tensor tensor) { if (tensor instanceof Sum || tensor instanceof Expression) { int i; Tensor tensorCurrent, tempResult; Tensor[] newSumElements = new Tensor[tensor.size()]; boolean needRebuild = false; for (i = tensor.size() - 1; i >= 0; --i) { tensorCurrent = tensor.get(i); tempResult = transform(tensorCurrent); if (tensorCurrent != tempResult) needRebuild = true; newSumElements[i] = tempResult; } if (needRebuild) return tensor.getFactory().create(newSumElements); else return tensor; } if (tensor instanceof Product) { int i; int count = 0; Tensor current, old; IndicesBuilder ib = new IndicesBuilder(); List<Tensor> newProductElements = new ArrayList<>(); for (i = tensor.size() - 1; i >= 0; --i) { current = tensor.get(i); if (isN(current)) { ib.append(current); ++count; } else { if (TensorUtils.isScalar(current)) { FromChildToParentIterator iterator = new FromChildToParentIterator(current); Tensor temp; boolean flag = false; while ((temp = iterator.next()) != null) { if (isN(temp)) { flag = true; break; } } if (!flag) { newProductElements.add(current); continue; } if (!(current instanceof Power) || !TensorUtils.isInteger(current.get(1)) || ((Complex) current.get(1)).intValue() != 2) throw new IllegalArgumentException(); Tensor[] bases = { current.get(0), current.get(0) }; bases[1] = ApplyIndexMapping.renameDummy(bases[1], TensorUtils.getAllIndicesNamesT(tensor).toArray()); flag = false; for (Tensor base : bases) { for (Tensor t : base) { if (isN(t)) { ib.append(t); ++count; flag = true; } else newProductElements.add(t); } } if (!flag) throw new IllegalArgumentException("Expand first"); } else newProductElements.add(current); } } if (count == 0) return tensor; if (count % 2 != 0) return Complex.ZERO; // System.out.println(count); count = count / 2; Tensor result = average(ib.getIndices().getAllIndices().copy()); long factor = ArithmeticUtils.pow((long) 2, count) * ArithmeticUtils.factorial(count + 1);//may be BigInteger? Complex number = new Complex((long) factor).reciprocal(); result = ExpandTransformation.expand(result); newProductElements.add(number); newProductElements.add(result); return Tensors.multiply(newProductElements.toArray(new Tensor[newProductElements.size()])); } if (tensor instanceof Power) { Tensor nBase = transform(tensor.get(0)); if (nBase == tensor.get(0)) return tensor; return Tensors.pow(nBase, tensor.get(1)); } return tensor; } private boolean isN(Tensor t) { return t instanceof SimpleTensor && ((SimpleTensor) t).getName() == const_n.getName(); } }