Examples with Pair com.sri.ai.util.base.Pair used on opensource projects

Example 26 with Pair

use of com.sri.ai.util.base.Pair in project aic-expresso by aic-sri-international.

the class PolynomialSummation method sum.

/**
 * Compute the sum for the summation of a polynomial.
 *
 * @param indexOfSummation
 *        the index variable of the summation.
 * @param lowerBoundExclusive
 *        the lower bound of the summation.
 * @param upperBoundInclusive
 *        the upper bound of the summation.
 * @param summand
 *        the polynomial to be summed.
 * @return the sum of the given summation.
 */
public static Polynomial sum(Expression indexOfSummation, Expression lowerBoundExclusive, Expression upperBoundInclusive, Polynomial summand) {
    Polynomial result;
    List<Expression> indexVariable = Arrays.asList(indexOfSummation);
    Polynomial summandAsPolynomialOfIndex = DefaultPolynomial.make(summand, indexVariable);
    int n = summandAsPolynomialOfIndex.degree();
    // 
    // collect the t coefficients
    List<Expression> tCoefficients = new ArrayList<>(n);
    for (int i = 0; i <= n; i++) {
        tCoefficients.add(Expressions.ZERO);
    }
    for (int i = 0; i < summandAsPolynomialOfIndex.numberOfTerms(); i++) {
        Monomial term = summandAsPolynomialOfIndex.getMonomials().get(i);
        tCoefficients.set(term.getPowerOfFactor(indexOfSummation).intValue(), term.getCoefficient(indexVariable));
    }
    // 
    // compute polynomials R_i(x) = (x + l)^i for each i
    Expression indexOfSummationPlusLowerBound = new DefaultFunctionApplication(PLUS_FUNCTOR, Arrays.asList(indexOfSummation, lowerBoundExclusive));
    Polynomial indexOfSummationPlusLowerBoundPolynomial = DefaultPolynomial.make(indexOfSummationPlusLowerBound, indexVariable);
    List<Polynomial> rPolynomials = new ArrayList<>(n);
    rPolynomials.add(DefaultPolynomial.make(Expressions.ONE, indexVariable));
    rPolynomials.add(indexOfSummationPlusLowerBoundPolynomial);
    for (int i = 2; i <= n; i++) {
        rPolynomials.add(rPolynomials.get(i - 1).times(indexOfSummationPlusLowerBoundPolynomial));
    }
    Map<Pair<Integer, Integer>, Expression> indexedRCoefficient = new LinkedHashMap<>();
    for (int i = 0; i <= n; i++) {
        Polynomial rPolynomial = rPolynomials.get(i);
        for (int q = 0; q <= i; q++) {
            Pair<Integer, Integer> indexKey = new Pair<>(i, q);
            Monomial rqxq = rPolynomial.getMapFromSignatureToMonomial().get(Arrays.asList(new Rational(q)));
            if (rqxq == null) {
                indexedRCoefficient.put(indexKey, Expressions.ZERO);
            } else {
                indexedRCoefficient.put(indexKey, rqxq.getCoefficient(indexVariable));
            }
        }
    }
    // 
    // compute "constants" (may contain variables other than x)
    // s_i,q,j =   t_i*R_{i,q}/(q+1) (-1)^j choose(q+1,j) B_j
    // where R_{i,q}(x) is the coefficient in R_i(x) multiplying x^q.
    Map<Triple<Integer, Integer, Integer>, Polynomial> sConstants = new LinkedHashMap<>();
    for (int i = 0; i <= n; i++) {
        Expression ti = tCoefficients.get(i);
        for (int q = 0; q <= i; q++) {
            Expression riq = indexedRCoefficient.get(new Pair<>(i, q));
            Expression tiByriq = new DefaultFunctionApplication(TIMES_FUNCTOR, Arrays.asList(ti, riq));
            for (int j = 0; j <= q; j++) {
                Triple<Integer, Integer, Integer> indexKey = new Triple<>(i, q, j);
                Expression qPlus1 = Expressions.makeSymbol(q + 1);
                Expression minus1PowerJ = Expressions.makeSymbol(j % 2 == 0 ? 1 : -1);
                Expression chooseQplus1J = Expressions.makeSymbol(Util.binomialCoefficient(q + 1, j));
                Expression bernoulliJ = Expressions.makeSymbol(BernoulliNumber.computeFirst(j));
                Expression sConstant = new DefaultFunctionApplication(TIMES_FUNCTOR, Arrays.asList(new DefaultFunctionApplication(DIVISION_FUNCTOR, Arrays.asList(tiByriq, qPlus1)), minus1PowerJ, chooseQplus1J, bernoulliJ));
                sConstants.put(indexKey, DefaultPolynomial.make(sConstant, indexVariable));
            }
        }
    }
    // 
    // compute polynomials, for each q, j,   V_{q + 1 -j}  = (u - l)^{q + 1 - j}
    Expression upperBoundMinusLowerBound = new DefaultFunctionApplication(MINUS_FUNCTOR, Arrays.asList(upperBoundInclusive, lowerBoundExclusive));
    Polynomial upperBoundMinusLowerBoundPolynomial = DefaultPolynomial.make(upperBoundMinusLowerBound, indexVariable);
    Map<Integer, Polynomial> vValues = new LinkedHashMap<>();
    for (int q = 0; q <= n; q++) {
        for (int j = 0; j <= q; j++) {
            Integer exponent = q + 1 - j;
            if (!vValues.containsKey(exponent)) {
                vValues.put(exponent, upperBoundMinusLowerBoundPolynomial.exponentiate(exponent));
            }
        }
    }
    // 
    // Compute the w values and construct the final result.
    Polynomial ws = DefaultPolynomial.make(Expressions.ZERO, indexVariable);
    for (int i = 0; i <= n; i++) {
        for (int q = 0; q <= i; q++) {
            for (int j = 0; j <= q; j++) {
                Triple<Integer, Integer, Integer> sConstantKey = new Triple<>(i, q, j);
                Integer valueKey = q + 1 - j;
                Polynomial sConstant = sConstants.get(sConstantKey);
                Polynomial vValue = vValues.get(valueKey);
                Polynomial w = sConstant.times(vValue);
                ws = ws.add(w);
            }
        }
    }
    List<Expression> generalizedVariables = DefaultPolynomial.extractGeneralizedVariables(ws);
    if (generalizedVariables.size() > 0) {
        // Simplify in the context of the contained generalized variables
        // and then return as a single constant factor (i.e. the index variable should not be present).
        ws = DefaultPolynomial.make(ws, generalizedVariables);
    }
    result = DefaultPolynomial.make(ws, indexVariable);
    return result;
}

Example 27 with Pair

use of com.sri.ai.util.base.Pair in project aic-expresso by aic-sri-international.

the class AbstractSingleVariableNumericConstraintFeasibilityRegionStepSolver method makeUpperBoundsAndStrictness.

/**
 * A method setting {@link #upperBoundsIncludingImplicitOnes} and {@link #fromUpperBoundsIncludingImplicitOnesToStrictness}
 * from constraint and variable's type.
 * @param context
 */
protected void makeUpperBoundsAndStrictness(Context context) {
    AbstractSingleVariableConstraint abstractSingleVariableConstraint = (AbstractSingleVariableConstraint) constraint;
    FunctionIterator<Expression, Pair<Expression, Boolean>> upperBoundsFromPositiveNormalizedAtomsIterator = functionIterator(predicateIterator(abstractSingleVariableConstraint.getPositiveNormalizedAtoms(), e -> e.hasFunctor(LESS_THAN)), // strict
    e -> processExplicitUpperBoundAndStrictnessPair(e.get(1), true, context));
    FunctionIterator<Expression, Pair<Expression, Boolean>> upperBoundsFromNegativeNormalizedAtomsIterator = functionIterator(predicateIterator(abstractSingleVariableConstraint.getNegativeNormalizedAtoms(), // not (X > Y) <=> X <= Y, so Y is a non-strict upper bound
    e -> e.hasFunctor(GREATER_THAN)), // non-strict
    e -> processExplicitUpperBoundAndStrictnessPair(e.get(1), false, context));
    Pair<Expression, Boolean> typeUpperBound = getTypeUpperBoundAndStrictness(context);
    Iterator<Pair<Expression, Boolean>> upperBoundsAndStrictnessIterator = new NestedIterator<>(upperBoundsFromPositiveNormalizedAtomsIterator, upperBoundsFromNegativeNormalizedAtomsIterator, typeUpperBound);
    upperBoundsIncludingImplicitOnes = arrayList();
    fromUpperBoundsIncludingImplicitOnesToStrictness = map();
    for (Pair<Expression, Boolean> boundAndStrictness : in(upperBoundsAndStrictnessIterator)) {
        Expression bound = boundAndStrictness.first;
        upperBoundsIncludingImplicitOnes.add(bound);
        Boolean strictness = boundAndStrictness.second;
        Boolean previousStrictness = fromUpperBoundsIncludingImplicitOnesToStrictness.get(bound);
        if (previousStrictness == null || (!previousStrictness && strictness)) {
            // if no strictness information so far, store current one; otherwise, only need to change it if previous occurrences were non-strict and this one is strict
            fromUpperBoundsIncludingImplicitOnesToStrictness.put(bound, strictness);
        }
    }
}

Example 28 with Pair

use of com.sri.ai.util.base.Pair in project aic-expresso by aic-sri-international.

the class TupleValuedFreeVariablesSimplifier method simplify.

public static Expression simplify(Expression expression, Context context) {
    Expression result = expression;
    // First see if we have any free variables.
    Map<Expression, Expression> freeVariablesAndTypes = Expressions.freeVariablesAndTypes(expression, context);
    if (freeVariablesAndTypes.size() > 0) {
        // Retrieve those that are tuples
        Map<Expression, TupleType> freeVariablesOfTupleType = freeVariablesAndTypes.entrySet().stream().filter(entry -> entry.getValue() != null && TupleType.isTupleType(entry.getValue())).collect(Collectors.toMap(e -> e.getKey(), e -> (TupleType) GrinderUtil.fromTypeExpressionToItsIntrinsicMeaning(e.getValue(), context)));
        if (freeVariablesOfTupleType.size() > 0) {
            final Map<Expression, List<Pair<Expression, Integer>>> freeVariableComponentsMap = constructComponentMap(freeVariablesOfTupleType, expression, context);
            // Replace the free tuple variables with their componentised forms
            // e.g. N --> (N1, N2)
            Expression componentisedExpression = expression.replaceAllOccurrences(expr -> {
                Expression replacement = expr;
                List<Pair<Expression, Integer>> replacementComponents = freeVariableComponentsMap.get(expr);
                if (replacementComponents != null) {
                    replacement = constructComponentTuple(replacementComponents);
                }
                return replacement;
            }, context);
            // Evaluate the expression with the un-componentized free tuple variables, within an extended
            // context that knows about the newly componentized variables
            Context contextExtendedWithComponentVariables = extendContextWithComponentVariables(context, freeVariablesOfTupleType, freeVariableComponentsMap);
            Expression evaluatedResult = context.getTheory().evaluate(componentisedExpression, contextExtendedWithComponentVariables);
            // Translate back the free variable components
            // e.g:
            // if N1 = 2 then 29 else 30
            // ---->
            // if get(N, 1) = 2 then 29 else 30
            final Map<Expression, Pair<Expression, Integer>> componentToFreeVariableMap = createReverseLookupMap(freeVariableComponentsMap);
            result = evaluatedResult.replaceAllOccurrences(expr -> {
                Expression replacement = expr;
                Pair<Expression, Integer> correspondingFreeVariableWithIndex = componentToFreeVariableMap.get(expr);
                if (correspondingFreeVariableWithIndex != null) {
                    replacement = Expressions.apply(FunctorConstants.GET, correspondingFreeVariableWithIndex.first, correspondingFreeVariableWithIndex.second);
                }
                return replacement;
            }, contextExtendedWithComponentVariables);
        }
    }
    return result;
}

Example 29 with Pair

use of com.sri.ai.util.base.Pair in project aic-expresso by aic-sri-international.

the class TupleValuedFreeVariablesSimplifier method constructComponentMap.

private static Map<Expression, List<Pair<Expression, Integer>>> constructComponentMap(Map<Expression, TupleType> freeVariablesOfTupleType, Expression expression, Context context) {
    Map<Expression, List<Pair<Expression, Integer>>> result = new LinkedHashMap<>();
    for (Map.Entry<Expression, TupleType> freeVariableOfTupleType : freeVariablesOfTupleType.entrySet()) {
        Expression freeVariable = freeVariableOfTupleType.getKey();
        TupleType freeVariableTupleType = freeVariableOfTupleType.getValue();
        List<Pair<Expression, Integer>> components = new ArrayList<>();
        int tupleArity = freeVariableTupleType.getArity();
        for (int i = 1; i <= tupleArity; i++) {
            String proposedComponentVariableName = freeVariable.toString() + i;
            Expression componentVariable = Expressions.makeUniqueVariable(proposedComponentVariableName, expression, context);
            components.add(new Pair<>(componentVariable, i));
        }
        result.put(freeVariable, components);
    }
    return result;
}

Example 30 with Pair

use of com.sri.ai.util.base.Pair in project aic-expresso by aic-sri-international.

the class ModelGenerator method maxMinProbability.

public static Pair<Double, Double> maxMinProbability(Bound b, Model m) {
    Context context = m.getContext();
    Theory theory = m.getTheory();
    Expression query = m.getQuery().getValue();
    Type type = context.getTypeOfRegisteredSymbol(query);
    if (type.getName().equals("Boolean")) {
        double maxProbabilityOfTrue = -1;
        double minProbabilityOfTrue = 10;
        if (b.isExtensionalBound()) {
            DefaultExtensionalBound extensionalBound = (DefaultExtensionalBound) b;
            List<Expression> listOfElements = extensionalBound.getArguments();
            for (Expression distribution : listOfElements) {
                // replace and evaluate
                Expression replacingQueryByTrue = distribution.replaceAllOccurrences(query, parse("true"), context);
                Expression evaluating = theory.evaluate(replacingQueryByTrue, context);
                // convert to double
                double value = evaluating.doubleValue();
                // update max and min
                if (value > maxProbabilityOfTrue) {
                    maxProbabilityOfTrue = value;
                }
                if (value < minProbabilityOfTrue) {
                    minProbabilityOfTrue = value;
                }
            }
            Pair<Double, Double> result = new Pair<>(minProbabilityOfTrue, maxProbabilityOfTrue);
            return result;
        } else if (b.isIntensionalBound()) {
        }
    }
    return null;
}