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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 the Groovy facade for Redberry. It contains the classes and categories defining DSL features and syntax notations for common routines from redebrry-core and redberry-physics.
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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.groovy

import cc.redberry.core.context.CC
import cc.redberry.core.indices.StructureOfIndices
import cc.redberry.core.parser.ParseTokenSimpleTensor
import cc.redberry.core.parser.preprocessor.GeneralIndicesInsertion
import cc.redberry.core.tensor.SimpleTensor
import cc.redberry.core.tensor.Tensor
import cc.redberry.core.transformations.*
import cc.redberry.core.transformations.collect.CollectTransformation
import cc.redberry.core.transformations.expand.ExpandAllTransformation
import cc.redberry.core.transformations.expand.ExpandDenominatorTransformation
import cc.redberry.core.transformations.expand.ExpandNumeratorTransformation
import cc.redberry.core.transformations.expand.ExpandTransformation
import cc.redberry.core.transformations.factor.FactorTransformation
import cc.redberry.core.transformations.fractions.GetDenominatorTransformation
import cc.redberry.core.transformations.fractions.GetNumeratorTransformation
import cc.redberry.core.transformations.fractions.TogetherTransformation
import cc.redberry.core.utils.ByteBackedBitArray

/**
 * Groovy facade for Redberry transformations and utility methods.
 *
 * @author Dmitry Bolotin
 * @author Stanislav Poslavsky
 */
class RedberryStatic {
    /**
     * Expands out products and positive integer powers.
     * @see ExpandTransformation
     */
    public static final Transformation Expand = new Transformation() {
        @Override
        Tensor transform(Tensor t) { ExpandTransformation.expand(t) }

        Transformation getAt(Transformation... transformations) { new ExpandTransformation(transformations) }
    }

    /**
     * Expands out all products and integer powers in any part of expression.
     * @see ExpandAllTransformation
     */
    public static final Transformation ExpandAll = new Transformation() {
        @Override
        Tensor transform(Tensor t) { ExpandAllTransformation.expandAll(t) }

        Transformation getAt(Transformation... transformations) { new ExpandAllTransformation(transformations) }
    }

    /**
     * Expands out products and powers that appear as denominators.
     * @see ExpandNumeratorTransformation
     */
    public static final Transformation ExpandNumerator = new Transformation() {
        @Override
        Tensor transform(Tensor t) { ExpandNumeratorTransformation.expandNumerator(t) }

        Transformation getAt(Transformation... transformations) { new ExpandNumeratorTransformation(transformations) }
    }

    /**
     * Expands out products and powers that appear in the numerator.
     * @see ExpandDenominatorTransformation
     */
    public static final Transformation ExpandDenominator = new Transformation() {
        @Override
        Tensor transform(Tensor t) { ExpandDenominatorTransformation.expandDenominator(t) }

        Transformation getAt(Transformation... transformations) { new ExpandDenominatorTransformation(transformations) }
    }

    /**
     * Collects terms by pattern
     */
    public static final StaticCollect Collect = new StaticCollect();

    private final static class StaticCollect {
        Transformation getAt(SimpleTensor var) {
            return new CollectTransformation(var);
        }

        Transformation getProperty(String var) {
            use(Redberry) {
                return new CollectTransformation(var.t);
            }
        }

        Transformation getAt(Collection args) {
            use(Redberry) {
                return new CollectTransformation(* args.collect { (it instanceof String) ? it.t : it });
            }
        }
    }

    /**
     * Gives a partial derivative.
     * @see DifferentiateTransformation
     */
    public static final StaticDifferentiate Differentiate = new StaticDifferentiate();

    private final static class StaticDifferentiate {
        Transformation getAt(SimpleTensor var) {
            return new DifferentiateTransformation(var);
        }

        Transformation getProperty(String var) {
            use(Redberry) {
                return new DifferentiateTransformation(var.t);
            }
        }

        Transformation getAt(Collection args) {
            use(Redberry) {
                int i;
                def vars = []
                def transformations = []
                args.each { arg ->
                    if (arg instanceof String) arg = arg.t

                    if (arg instanceof SimpleTensor)
                        vars.add(arg)
                    else if (arg instanceof Transformation)
                        transformations.add(arg)
                    else
                        throw new IllegalArgumentException();
                }
                return new DifferentiateTransformation(transformations as Transformation[], vars as SimpleTensor[]);
            }
        }
    }

    /**
     * Eliminates metrics and Kronecker deltas
     * @see EliminateMetricsTransformation
     */
    public static final Transformation EliminateMetrics = EliminateMetricsTransformation.ELIMINATE_METRICS

    /**
     * Expands out product of sums and positive integer powers and
     * permanently eliminates metric and Kronecker deltas
     */
    public static final Transformation ExpandAndEliminate = new TransformationCollection(
            new ExpandTransformation(EliminateMetricsTransformation.ELIMINATE_METRICS),
            EliminateMetricsTransformation.ELIMINATE_METRICS)

    /**
     * Gives the numerator of expression.
     * @see GetNumeratorTransformation
     */
    public static final Transformation Numerator = GetNumeratorTransformation.GET_NUMERATOR

    /**
     * Gives the denominator of expression.
     * @see GetDenominatorTransformation
     */
    public static final Transformation Denominator = GetDenominatorTransformation.GET_DENOMINATOR

    /**
     * Removes parts of expressions, which are zero because of the symmetries (symmetric and antisymmetric at the same time).
     * @see EliminateFromSymmetriesTransformation
     */
    public static final Transformation EliminateFromSymmetries = EliminateFromSymmetriesTransformation.ELIMINATE_FROM_SYMMETRIES;

    /**
     * Puts terms in a sum over a common denominator, and cancels factors in the result.
     * @see TogetherTransformation
     */
    public static final Transformation Together = TogetherTransformation.TOGETHER;

    /**
     * Puts terms in a sum over a common denominator, and cancels all symbolic factors in the result.
     * @see TogetherTransformation
     */
    public static final Transformation TogetherFactor = TogetherTransformation.TOGETHER_FACTOR;

    /**
     * Replaces complex numbers in the expression to their complex conjugation.
     * @see ComplexConjugateTransformation
     */
    public static final Transformation Conjugate = ComplexConjugateTransformation.COMPLEX_CONJUGATE;

    /**
     * Gives the numerical value of expression.
     * @see ToNumericTransformation
     */
    public static final Transformation Numeric = ToNumericTransformation.TO_NUMERIC;

    /**
     * Collects similar scalar factors in products.
     * @see CollectNonScalarsTransformation
     */
    public static final Transformation CollectScalars = CollectScalarFactorsTransformation.COLLECT_SCALAR_FACTORS

    /**
     * Puts terms in a sum together factoring out all scalars in each term.
     * @see CollectNonScalarsTransformation
     */
    public static final Transformation CollectNonScalars = CollectNonScalarsTransformation.COLLECT_NON_SCALARS;

    /**
     * Factors a polynomial over the integers.
     * @see FactorTransformation
     */
    public static final Transformation Factor = FactorTransformation.FACTOR;


    /*
     * Matrices definition
     */

    static GeneralIndicesInsertion indicesInsertion = new GeneralIndicesInsertion();
    static {
        CC.current().getParseManager().defaultParserPreprocessors.add(indicesInsertion);
    }

    /**
     * Tells Redberry to consider specified tensors as matrices and use matrix multiplication rules
     * @param objs input
     * @see GeneralIndicesInsertion
     */
    public static void defineMatrices(Object... objs) {
        def bufferOfTensors = [], bufferOfDescriptors = [];
        objs.each { obj ->
            if (obj instanceof MatrixDescriptor)
                bufferOfDescriptors << obj
            else {
                if (bufferOfDescriptors) {
                    bufferOfTensors.each { it -> defineMatrices(it, * bufferOfDescriptors) }
                    bufferOfTensors = []
                    bufferOfDescriptors = []
                }
                bufferOfTensors << obj
            }
        }
        bufferOfTensors.each { it -> defineMatrix(it, * bufferOfDescriptors) }
        //int index = objs.findIndexOf { it instanceof MatrixDescriptor }
        //objs[0..
                def type = descriptor.type.type
                if (allTypesCounts[type] != 0)
                    throw new IllegalArgumentException()
                allTypesCounts[type] = descriptor.lower + descriptor.upper
                allStates[type] = new ByteBackedBitArray(allTypesCounts[type])
                for (int i = 0; i < descriptor.upper; ++i)
                    allStates[type].set(i)
            }
            st[0] = new StructureOfIndices(allTypesCounts, allStates);
            descriptors.each {
                indicesInsertion.addInsertionRule(CC.getNameManager().mapNameDescriptor(token.name, st),
                        it.type)
            }
        }
    }

    /*
     * Utilities
     */

    /**
     * Evaluates closure, and returns a time in milliseconds used
     * @param closure do stuff
     * @return time spent in calculation
     */
    public static long timing(Closure closure, stdout = true) {
        long start = System.currentTimeMillis();
        closure.call();
        long stop = System.currentTimeMillis();
        if (stdout) println('Time: ' + (stop - start) + ' ms.')
        return (stop - start)
    }
}