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.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

        return symmetrizeWithoutCheck(tensor, freeIndices, symmetries, multiplyFactorial);
    }


    public static Tensor symmetrize(Tensor tensor, int[] freeIndicesNames, Permutation[] symmetries, boolean multiplyFactorial) {
        checkConsistensy(freeIndicesNames, symmetries);
        Symmetries symmetries1 = SymmetriesFactory.createSymmetries(symmetries[0].dimension());
        for (Permutation s : symmetries)
            symmetries1.add(s.asSymmetry());
        return symmetrizeWithoutCheck(tensor, freeIndicesNames, symmetries1, multiplyFactorial);
    }

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

        if (!IndicesUtils.equalsRegardlessOrder(tensor.getIndices().getFree(), freeIndicesNames))
            throw new IllegalArgumentException("Specified indices are not equal (regardless order) to the free indices of specified tensor .");


        if (symmetries.dimension() <= 1)
            return tensor;
        Symmetries tensorSymmetries = TensorUtils.findIndicesSymmetries(freeIndicesNames, tensor);
        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.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

    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

        ArraysUtils.stableSort(types, cosort);
        int[] cosortInv = Combinatorics.inverse(cosort);


        //Allocating resulting symmetries object
        //it already contains identity symmetry
        Symmetries resultingSymmetries =
                SymmetriesFactory.createSymmetries(data.length);


        int[] c;
        int position = 0, k;


        SimpleIndices sd = IndicesFactory.createSimple(null, data);
        //rescaling symmetries to the actual length and positions corresponding 
        //to the sorted indices
        for (Symmetries ss : this.symmetries) {
            final List<Symmetry> basis = ss.getBasisSymmetries();
            //iterating from 1 because zero'th element is always identity symmetry 
            for (k = 1; k < basis.size(); ++k) {
                c = new int[data.length];
                Symmetry s = basis.get(k);
                for (j = 0; j < data.length; ++j)
                    if (cosort[j] < position || cosort[j] >= position + s.dimension())
                        c[j] = j;
                    else
                        c[j] = cosortInv[s.newIndexOf(cosort[j] - position) + position];
                resultingSymmetries.addUnsafe(UnsafeCombinatorics.createUnsafe(c, s.isAntiSymmetry()));
            }
            //increasing position in the total symmetry array
            position += ss.dimension();
        }

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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

    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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