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Redberry is an open source computer algebra system designed for tensor manipulation. It implements basic computer algebra system routines as well as complex tools for real computations in physics. This is Redberry core, which contains the implementation of the basic computer algebra routines and general-purpose transformations.
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/*
 * Redberry: symbolic tensor computations.
 *
 * Copyright (c) 2010-2013:
 *   Stanislav Poslavsky   
 *   Bolotin Dmitriy       
 *
 * 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 .
 */
package cc.redberry.core.indexmapping;

import cc.redberry.core.number.Complex;
import cc.redberry.core.tensor.*;
import cc.redberry.core.tensor.functions.*;

import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Set;

/**
 * Provides static methods for creating mappings of indices.
 *
 * @author Dmitry Bolotin
 * @author Stanislav Poslavsky
 * @since 1.0
 */
public final class IndexMappings {

    private IndexMappings() {
    }

    /**
     * Creates output port of mappings of two simple tensors and do not takes into account the arguments of fields.
     *
     * @param from from tensor
     * @param to   to tensor
     * @return port of mappings of indices
     */
    public static MappingsPort simpleTensorsPort(SimpleTensor from, SimpleTensor to) {
        final IndexMappingProvider provider = ProviderSimpleTensor.FACTORY_SIMPLETENSOR.create(IndexMappingProvider.Util.singleton(new IndexMappingBufferImpl()), from, to);
        provider.tick();
        return new MappingsPortRemovingContracted(provider);
    }

    /**
     * Creates output port of mappings of two products of tensors represented as arrays of multipliers, where
     * each multiplier of {@code from} will be mapped on the multiplier of {@code to} at the same
     * position. Such ordering can be obtained via {@link cc.redberry.core.transformations.substitutions.ProductsBijectionsPort}.
     * In contrast to {@link #createPort(cc.redberry.core.tensor.Tensor, cc.redberry.core.tensor.Tensor)}, this method
     * will fully handles mappings of free indices on contracted ones (like e.g. _i^j -> _k^k).
     *
     * @param from from tensor
     * @param to   to tensor
     * @return port of mappings of indices
     */
    public static MappingsPort createBijectiveProductPort(Tensor[] from, Tensor[] to) {
        if (from.length != to.length)
            throw new IllegalArgumentException("From length != to length.");
        if (from.length == 0)
            return IndexMappingProvider.Util.singleton(new IndexMappingBufferImpl());
        if (from.length == 1)
            return createPort(from[0], to[0]);
        return new MappingsPortRemovingContracted(new SimpleProductMappingsPort(IndexMappingProvider.Util.singleton(new IndexMappingBufferImpl()), from, to));
    }

    /**
     * Creates output port of mappings of tensor {@code from} on tensor {@code to}.
     *
     * @param from from tensor
     * @param to   to tensor
     * @return output port of mappings
     */
    public static MappingsPort createPort(Tensor from, Tensor to) {
        return createPort(new IndexMappingBufferImpl(), from, to);
    }

    /**
     * Creates output port of mappings of tensor {@code from} on tensor {@code to} with specified
     * mappings rules defined in specified {@link IndexMappingBuffer}.
     *
     * @param buffer initial mapping rules
     * @param from   from tensor
     * @param to     to tensor
     * @return output port of mapping
     */
    public static MappingsPort createPort(final IndexMappingBuffer buffer,
                                          final Tensor from, final Tensor to) {
        final IndexMappingProvider provider = createPort(IndexMappingProvider.Util.singleton(buffer), from, to);
        provider.tick();
        return new MappingsPortRemovingContracted(provider);
    }

    /**
     * Returns the first mapping of tensor {@code from} on tensor {@code to}.
     *
     * @param from from tensor
     * @param to   to tensor
     * @return mapping of indices of tensor {@code from} on tensor {@code to}
     */
    public static IndexMappingBuffer getFirst(Tensor from, Tensor to) {
        return createPort(from, to).take();
    }

    /**
     * Returns {@code true} if there is mapping of tensor {@code from} on tensor {@code to}.
     *
     * @param from from tensor
     * @param to   to tensor
     * @return {@code true} if there is mapping of tensor {@code from} on tensor {@code to}
     */
    public static boolean mappingExists(Tensor from, Tensor to) {
        return getFirst(from, to) != null;
    }

    /**
     * Returns {@code true} if specified mapping is one of mappings of tensor {@code from} on tensor {@code to}.
     *
     * @param buffer mapping
     * @param from   from tensor
     * @param to     to tensor
     * @return Returns {@code true} if specified mapping is one of mappings of indices of tensor {@code from} on tensor {@code to}.
     */
    public static boolean testMapping(Tensor from, Tensor to, IndexMappingBuffer buffer) {
        return createPort(new IndexMappingBufferTester(buffer), from, to).take() != null;
    }

    private static Tensor extractNonComplexFactor(Tensor t) {
        Product p = (Product) t;
        if (p.getFactor().isMinusOne())
            return p.get(1);
        else
            return null;
    }

    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);
    }

    private static final Map map;

    static {
        map = new HashMap<>();
        map.put(SimpleTensor.class, ProviderSimpleTensor.FACTORY_SIMPLETENSOR);
        map.put(TensorField.class, ProviderSimpleTensor.FACTORY_TENSORFIELD);
        map.put(Product.class, ProviderProduct.FACTORY);
        map.put(Sum.class, ProviderSum.FACTORY);
        map.put(Expression.class, ProviderSum.FACTORY);
        map.put(Complex.class, ProviderComplex.FACTORY);
        map.put(Power.class, ProviderPower.INSTANCE);

        map.put(Sin.class, ProviderFunctions.ODD_FACTORY);
        map.put(ArcSin.class, ProviderFunctions.ODD_FACTORY);
        map.put(Tan.class, ProviderFunctions.ODD_FACTORY);
        map.put(ArcTan.class, ProviderFunctions.ODD_FACTORY);

        map.put(Cos.class, ProviderFunctions.EVEN_FACTORY);
        map.put(ArcCos.class, ProviderFunctions.EVEN_FACTORY);
        map.put(Cot.class, ProviderFunctions.EVEN_FACTORY);
        map.put(ArcCot.class, ProviderFunctions.EVEN_FACTORY);
    }

    private static Set getAllMappings(MappingsPort opu) {
        Set res = new HashSet<>();
        IndexMappingBuffer c;
        while ((c = opu.take()) != null)
            res.add(c);
        return res;
    }

    /**
     * Returns a set of all possible mappings of tensor {@code from} on tensor {@code to}.
     *
     * @param from from tensor
     * @param to   to tensor
     * @return a set of all possible mappings of tensor {@code from} on tensor {@code to}
     */
    public static Set getAllMappings(Tensor from, Tensor to) {
        return getAllMappings(IndexMappings.createPort(from, to));
    }
}