Examples of Symmetries

cc.redberry.core.combinatorics.Symmetries
This class is a representation of {@link Symmetry} set. It holds a set ofsymmetries and provides common functionality: adding {@code Symmetry} anditerating over all possible symmetries, which can be generated by compositions of keeping symmetries. Also, it watches that all keeping symmetries are consistent, i.e. it throws {@link InconsistentGeneratorsException}when trying to add symmetry, which is inconsistent with already added symmetries. All adding combinatorics must have the same dimension, which specified at initialization. For more details see method summary. @see Symmetry @see PermutationsSpanIterator @author Dmitry Bolotin @author Stanislav Poslavsky
cc.redberry.core.combinatorics.symmetries.Symmetries

This interface is a representation of a set of symmetries, which takes into account possible compositions of symmetries in this set. More formally, set contains no element s, which can be expressed as s=s1*s2*s3*...*sN, where {s1,s2,s3,...,sN} are elements of this set. So, this interface models the mathematical basis of subgroup of symmetric group. It contains the identity symmetry by default.

All symmetries, keeping by this set must be consistent. It means, that all of them must have similar dimension (see {@link #dimension()}); next, if we denote symmetry as pair (permutation, sign), there is no any symmetry (p,s) and subset of symmetries {(p1,s1),(p2,s2),...,<(pN,sN)}, such that p = p1*p2*p3*...*pN, but s != s1*s2*s3*...*sN. Method {@link #add(cc.redberry.core.combinatorics.Symmetry)} throws {@link InconsistentGeneratorsException}if its argument is inconsistent with existing symmetries in set.

Iterator returned by this set iterates over all possible compositions of symmetries from set, i.e. it works as {@link PermutationsSpanIterator}. To extract only the basis symmetries, a special method {@link #getBasisSymmetries() }introduced. This method returns an unmodifiable list of basis symmetries.

Objects of this type can be created via static factory methods in {@link SymmetriesFactory}.
@author Dmitry Bolotin @author Stanislav Poslavsky @see SymmetriesFactory @see Symmetry @see PermutationsSpanIterator @see InconsistentGeneratorsException

Examples of cc.redberry.core.combinatorics.Symmetries

    private final Symmetries symmetries;
    private short[] diffIds = null;


    IndicesSymmetries(IndicesTypeStructure indicesTypeStructure) {
        this.indicesTypeStructure = indicesTypeStructure;
        this.symmetries = new Symmetries(indicesTypeStructure.size());
    }

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Examples of cc.redberry.core.combinatorics.Symmetries

    private final Symmetries symmetries;
    private short[] diffIds = null;


    IndicesSymmetries(IndicesTypeStructure indicesTypeStructure) {
        this.indicesTypeStructure = indicesTypeStructure;
        this.symmetries = new Symmetries(indicesTypeStructure.size());
    }

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Examples of cc.redberry.core.combinatorics.Symmetries

    public Tensor transform(Tensor tensor) {
        if (!tensor.getIndices().getFreeIndices().equalsIgnoreOrder(indices))
            return tensor;
        if (symmetries.isEmpty())
            return TensorNumber.createZERO();
        Symmetries tensorSymmetries = IndexMappingUtils.getSymmetriesFromMappings(indices, tensor, allowDiffStates);


        List<Tensor> generatedTensors = new ArrayList<>();
        List<Permutation> generatedPermutations = new ArrayList<>();
        OUT:
        for (Permutation permutation : symmetries) {

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Examples of cc.redberry.core.combinatorics.Symmetries

//        for (IndexMappingBufferImpl buffer : buffers)
//            symmetries.add(getSymmetryFromMapping(indices, buffer));
//        return symmetries;
//    }
    public static Symmetries getSymmetriesFromMappings(Indices indices, OutputPortUnsafe<IndexMappingBuffer> buffers) {
        Symmetries symmetries = new Symmetries(indices.size());
        IndexMappingBuffer buffer;
        while ((buffer = buffers.take()) != null)
            symmetries.add(getSymmetryFromMapping(indices, buffer));
        return symmetries;
    }

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Examples of cc.redberry.core.combinatorics.symmetries.Symmetries

    public static Symmetry getSymmetryFromMapping(final int[] indices, IndexMappingBuffer indexMappingBuffer) {
        return getSymmetryFromMapping1(IndicesUtils.getIndicesNames(indices), indexMappingBuffer);
    }


    public static Symmetries getSymmetriesFromMappings(final int[] indices, MappingsPort mappingsPort) {
        Symmetries symmetries = SymmetriesFactory.createSymmetries(indices.length);
        int[] indicesNames = IndicesUtils.getIndicesNames(indices);
        IndexMappingBuffer buffer;
        while ((buffer = mappingsPort.take()) != null)
            symmetries.add(getSymmetryFromMapping1(indicesNames, buffer));
        return symmetries;
    }

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Examples of cc.redberry.core.combinatorics.symmetries.Symmetries

    public static Symmetries findIndicesSymmetries(SimpleIndices indices, Tensor tensor) {
        return getSymmetriesFromMappings(indices.getAllIndices().copy(), IndexMappings.createPort(tensor, tensor));
    }


    public static Symmetries getIndicesSymmetriesForIndicesWithSameStates(final int[] indices, Tensor tensor) {
        Symmetries total = findIndicesSymmetries(indices, tensor);
        Symmetries symmetries = SymmetriesFactory.createSymmetries(indices.length);
        int i;
        OUT:
        for (Symmetry s : total) {
            for (i = 0; i < indices.length; ++i)
                if (IndicesUtils.getRawStateInt(indices[i]) != IndicesUtils.getRawStateInt(indices[s.newIndexOf(i)]))
                    continue OUT;
            symmetries.add(s);
        }
        return symmetries;
    }

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Examples of cc.redberry.core.combinatorics.symmetries.Symmetries

    public static Symmetry getSymmetryFromMapping(final int[] indices, IndexMappingBuffer indexMappingBuffer) {
        return getSymmetryFromMapping1(IndicesUtils.getIndicesNames(indices), indexMappingBuffer);
    }


    public static Symmetries getSymmetriesFromMappings(final int[] indices, MappingsPort mappingsPort) {
        Symmetries symmetries = SymmetriesFactory.createSymmetries(indices.length);
        int[] indicesNames = IndicesUtils.getIndicesNames(indices);
        IndexMappingBuffer buffer;
        while ((buffer = mappingsPort.take()) != null)
            symmetries.add(getSymmetryFromMapping1(indicesNames, buffer));
        return symmetries;
    }

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Examples of cc.redberry.core.combinatorics.symmetries.Symmetries

    private static Map<IntArray, Boolean> getEpsilonSymmetries(int indicesSize) {
        Map<IntArray, Boolean> symmetries = cachedLeviCivitaSymmetries.get(indicesSize);
        if (symmetries != null)
            return symmetries;
        symmetries = new HashMap<>();
        Symmetries ss = SymmetriesFactory.createSymmetries(indicesSize);
        ss.addUnsafe(new Symmetry(Combinatorics.createTransposition(indicesSize, 0, 1), true));
        if (indicesSize % 2 == 0)
            ss.addUnsafe(new Symmetry(Combinatorics.createCycle(indicesSize), true));
        else
            ss.addUnsafe(new Symmetry(Combinatorics.createCycle(indicesSize), false));
        for (Symmetry symmetry : ss)
            symmetries.put(symmetry.getPermutation(), symmetry.isAntiSymmetry());
        cachedLeviCivitaSymmetries.put(indicesSize, symmetries);
        return symmetries;
    }

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Examples of cc.redberry.core.combinatorics.symmetries.Symmetries

    }


    public static Tensor symmetrizeUpperLowerIndices(Tensor tensor, boolean multiplyOnSymmetryFactor) {
        Indices indices = IndicesFactory.create(tensor.getIndices().getFree());
        int[] indicesArray = indices.getAllIndices().copy();
        Symmetries symmetries = TensorUtils.getIndicesSymmetriesForIndicesWithSameStates(indicesArray, tensor);
        int lowerCount = indices.getLower().length(), upperCount = indices.getUpper().length();


        IntPermutationsGenerator lowIndicesPermutationsGenerator,
                upperIndicesPermutationGenerator;
        SumBuilder sumBuilder = new SumBuilder();

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Examples of cc.redberry.core.combinatorics.symmetries.Symmetries

        int[] _sortPermutation = ArraysUtils.quickSortP(sortedIndicesNames);
        return getSymmetryFromMapping1(sortedIndicesNames, _sortPermutation, mapping);
    }


    public static Symmetries getSymmetriesFromMappings(final int[] indices, MappingsPort mappingsPort) {
        Symmetries symmetries = SymmetriesFactory.createSymmetries(indices.length);
        int[] sortedIndicesNames = IndicesUtils.getIndicesNames(indices);
        int[] sortPermutation = ArraysUtils.quickSortP(sortedIndicesNames);
        Mapping buffer;
        while ((buffer = mappingsPort.take()) != null)
            symmetries.add(getSymmetryFromMapping1(sortedIndicesNames, sortPermutation, buffer));
        return symmetries;
    }

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