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Example 81 with AggregateCall

use of org.apache.calcite.rel.core.AggregateCall in project hive by apache.

the class HiveAggregateProjectMergeRule method apply.

public static RelNode apply(HiveAggregate aggregate, HiveProject project) {
    final List<Integer> newKeys = Lists.newArrayList();
    final Map<Integer, Integer> map = new HashMap<>();
    for (int key : aggregate.getGroupSet()) {
        final RexNode rex = project.getProjects().get(key);
        if (rex instanceof RexInputRef) {
            final int newKey = ((RexInputRef) rex).getIndex();
            newKeys.add(newKey);
            map.put(key, newKey);
        } else {
            // Cannot handle "GROUP BY expression"
            return null;
        }
    }
    final ImmutableBitSet newGroupSet = aggregate.getGroupSet().permute(map);
    ImmutableList<ImmutableBitSet> newGroupingSets = null;
    if (aggregate.indicator) {
        newGroupingSets = ImmutableBitSet.ORDERING.immutableSortedCopy(ImmutableBitSet.permute(aggregate.getGroupSets(), map));
    }
    final ImmutableList.Builder<AggregateCall> aggCalls = ImmutableList.builder();
    for (AggregateCall aggregateCall : aggregate.getAggCallList()) {
        final ImmutableList.Builder<Integer> newArgs = ImmutableList.builder();
        for (int arg : aggregateCall.getArgList()) {
            final RexNode rex = project.getProjects().get(arg);
            if (rex instanceof RexInputRef) {
                newArgs.add(((RexInputRef) rex).getIndex());
            } else {
                // Cannot handle "AGG(expression)"
                return null;
            }
        }
        final int newFilterArg;
        if (aggregateCall.filterArg >= 0) {
            final RexNode rex = project.getProjects().get(aggregateCall.filterArg);
            if (!(rex instanceof RexInputRef)) {
                return null;
            }
            newFilterArg = ((RexInputRef) rex).getIndex();
        } else {
            newFilterArg = -1;
        }
        aggCalls.add(aggregateCall.copy(newArgs.build(), newFilterArg));
    }
    final Aggregate newAggregate = aggregate.copy(aggregate.getTraitSet(), project.getInput(), aggregate.indicator, newGroupSet, newGroupingSets, aggCalls.build());
    // Add a project if the group set is not in the same order or
    // contains duplicates.
    RelNode rel = newAggregate;
    if (!newKeys.equals(newGroupSet.asList())) {
        final List<Integer> posList = Lists.newArrayList();
        for (int newKey : newKeys) {
            posList.add(newGroupSet.indexOf(newKey));
        }
        if (aggregate.indicator) {
            for (int newKey : newKeys) {
                posList.add(aggregate.getGroupCount() + newGroupSet.indexOf(newKey));
            }
        }
        for (int i = newAggregate.getGroupCount() + newAggregate.getIndicatorCount(); i < newAggregate.getRowType().getFieldCount(); i++) {
            posList.add(i);
        }
        rel = HiveRelOptUtil.createProject(HiveRelFactories.HIVE_BUILDER.create(aggregate.getCluster(), null), rel, posList);
    }
    return rel;
}
Also used : ImmutableBitSet(org.apache.calcite.util.ImmutableBitSet) HashMap(java.util.HashMap) ImmutableList(com.google.common.collect.ImmutableList) AggregateCall(org.apache.calcite.rel.core.AggregateCall) RelNode(org.apache.calcite.rel.RelNode) RexInputRef(org.apache.calcite.rex.RexInputRef) Aggregate(org.apache.calcite.rel.core.Aggregate) HiveAggregate(org.apache.hadoop.hive.ql.optimizer.calcite.reloperators.HiveAggregate) RexNode(org.apache.calcite.rex.RexNode)

Example 82 with AggregateCall

use of org.apache.calcite.rel.core.AggregateCall in project hive by apache.

the class HiveAggregate method deriveRowType.

public static RelDataType deriveRowType(RelDataTypeFactory typeFactory, final RelDataType inputRowType, boolean indicator, ImmutableBitSet groupSet, List<ImmutableBitSet> groupSets, final List<AggregateCall> aggCalls) {
    final List<Integer> groupList = groupSet.asList();
    assert groupList.size() == groupSet.cardinality();
    final RelDataTypeFactory.FieldInfoBuilder builder = typeFactory.builder();
    final List<RelDataTypeField> fieldList = inputRowType.getFieldList();
    final Set<String> containedNames = Sets.newHashSet();
    for (int groupKey : groupList) {
        containedNames.add(fieldList.get(groupKey).getName());
        builder.add(fieldList.get(groupKey));
    }
    if (indicator) {
        for (int groupKey : groupList) {
            final RelDataType booleanType = typeFactory.createTypeWithNullability(typeFactory.createSqlType(SqlTypeName.BOOLEAN), false);
            String name = "i$" + fieldList.get(groupKey).getName();
            int i = 0;
            while (containedNames.contains(name)) {
                name += "_" + i++;
            }
            containedNames.add(name);
            builder.add(name, booleanType);
        }
    }
    for (Ord<AggregateCall> aggCall : Ord.zip(aggCalls)) {
        String name;
        if (aggCall.e.name != null) {
            name = aggCall.e.name;
        } else {
            name = "$f" + (groupList.size() + aggCall.i);
        }
        int i = 0;
        while (containedNames.contains(name)) {
            name += "_" + i++;
        }
        containedNames.add(name);
        builder.add(name, aggCall.e.type);
    }
    return builder.build();
}
Also used : AggregateCall(org.apache.calcite.rel.core.AggregateCall) RelDataTypeField(org.apache.calcite.rel.type.RelDataTypeField) RelDataTypeFactory(org.apache.calcite.rel.type.RelDataTypeFactory) RelDataType(org.apache.calcite.rel.type.RelDataType)

Example 83 with AggregateCall

use of org.apache.calcite.rel.core.AggregateCall in project flink by apache.

the class FlinkAggregateExpandDistinctAggregatesRule method convertSingletonDistinct.

/**
	 * Converts an aggregate with one distinct aggregate and one or more
	 * non-distinct aggregates to multi-phase aggregates (see reference example
	 * below).
	 *
	 * @param relBuilder Contains the input relational expression
	 * @param aggregate  Original aggregate
	 * @param argLists   Arguments and filters to the distinct aggregate function
	 *
	 */
private RelBuilder convertSingletonDistinct(RelBuilder relBuilder, Aggregate aggregate, Set<Pair<List<Integer>, Integer>> argLists) {
    // For example,
    //	SELECT deptno, COUNT(*), SUM(bonus), MIN(DISTINCT sal)
    //	FROM emp
    //	GROUP BY deptno
    //
    // becomes
    //
    //	SELECT deptno, SUM(cnt), SUM(bonus), MIN(sal)
    //	FROM (
    //		  SELECT deptno, COUNT(*) as cnt, SUM(bonus), sal
    //		  FROM EMP
    //		  GROUP BY deptno, sal)			// Aggregate B
    //	GROUP BY deptno						// Aggregate A
    relBuilder.push(aggregate.getInput());
    final List<Pair<RexNode, String>> projects = new ArrayList<>();
    final Map<Integer, Integer> sourceOf = new HashMap<>();
    SortedSet<Integer> newGroupSet = new TreeSet<>();
    final List<RelDataTypeField> childFields = relBuilder.peek().getRowType().getFieldList();
    final boolean hasGroupBy = aggregate.getGroupSet().size() > 0;
    SortedSet<Integer> groupSet = new TreeSet<>(aggregate.getGroupSet().asList());
    // Add the distinct aggregate column(s) to the group-by columns,
    // if not already a part of the group-by
    newGroupSet.addAll(aggregate.getGroupSet().asList());
    for (Pair<List<Integer>, Integer> argList : argLists) {
        newGroupSet.addAll(argList.getKey());
    }
    // transformation.
    for (int arg : newGroupSet) {
        sourceOf.put(arg, projects.size());
        projects.add(RexInputRef.of2(arg, childFields));
    }
    // Generate the intermediate aggregate B
    final List<AggregateCall> aggCalls = aggregate.getAggCallList();
    final List<AggregateCall> newAggCalls = new ArrayList<>();
    final List<Integer> fakeArgs = new ArrayList<>();
    final Map<AggregateCall, Integer> callArgMap = new HashMap<>();
    // e.g. if real arguments are 0, 1, 3. Then the fake arguments will be 2, 4
    for (final AggregateCall aggCall : aggCalls) {
        if (!aggCall.isDistinct()) {
            for (int arg : aggCall.getArgList()) {
                if (!groupSet.contains(arg)) {
                    sourceOf.put(arg, projects.size());
                }
            }
        }
    }
    int fakeArg0 = 0;
    for (final AggregateCall aggCall : aggCalls) {
        // We will deal with non-distinct aggregates below
        if (!aggCall.isDistinct()) {
            boolean isGroupKeyUsedInAgg = false;
            for (int arg : aggCall.getArgList()) {
                if (groupSet.contains(arg)) {
                    isGroupKeyUsedInAgg = true;
                    break;
                }
            }
            if (aggCall.getArgList().size() == 0 || isGroupKeyUsedInAgg) {
                while (sourceOf.get(fakeArg0) != null) {
                    ++fakeArg0;
                }
                fakeArgs.add(fakeArg0);
                ++fakeArg0;
            }
        }
    }
    for (final AggregateCall aggCall : aggCalls) {
        if (!aggCall.isDistinct()) {
            for (int arg : aggCall.getArgList()) {
                if (!groupSet.contains(arg)) {
                    sourceOf.remove(arg);
                }
            }
        }
    }
    // Compute the remapped arguments using fake arguments for non-distinct
    // aggregates with no arguments e.g. count(*).
    int fakeArgIdx = 0;
    for (final AggregateCall aggCall : aggCalls) {
        // as-is all the non-distinct aggregates
        if (!aggCall.isDistinct()) {
            final AggregateCall newCall = AggregateCall.create(aggCall.getAggregation(), false, aggCall.getArgList(), -1, ImmutableBitSet.of(newGroupSet).cardinality(), relBuilder.peek(), null, aggCall.name);
            newAggCalls.add(newCall);
            if (newCall.getArgList().size() == 0) {
                int fakeArg = fakeArgs.get(fakeArgIdx);
                callArgMap.put(newCall, fakeArg);
                sourceOf.put(fakeArg, projects.size());
                projects.add(Pair.of((RexNode) new RexInputRef(fakeArg, newCall.getType()), newCall.getName()));
                ++fakeArgIdx;
            } else {
                for (int arg : newCall.getArgList()) {
                    if (groupSet.contains(arg)) {
                        int fakeArg = fakeArgs.get(fakeArgIdx);
                        callArgMap.put(newCall, fakeArg);
                        sourceOf.put(fakeArg, projects.size());
                        projects.add(Pair.of((RexNode) new RexInputRef(fakeArg, newCall.getType()), newCall.getName()));
                        ++fakeArgIdx;
                    } else {
                        sourceOf.put(arg, projects.size());
                        projects.add(Pair.of((RexNode) new RexInputRef(arg, newCall.getType()), newCall.getName()));
                    }
                }
            }
        }
    }
    // Generate the aggregate B (see the reference example above)
    relBuilder.push(aggregate.copy(aggregate.getTraitSet(), relBuilder.build(), false, ImmutableBitSet.of(newGroupSet), null, newAggCalls));
    // Convert the existing aggregate to aggregate A (see the reference example above)
    final List<AggregateCall> newTopAggCalls = Lists.newArrayList(aggregate.getAggCallList());
    // Use the remapped arguments for the (non)distinct aggregate calls
    for (int i = 0; i < newTopAggCalls.size(); i++) {
        // Re-map arguments.
        final AggregateCall aggCall = newTopAggCalls.get(i);
        final int argCount = aggCall.getArgList().size();
        final List<Integer> newArgs = new ArrayList<>(argCount);
        final AggregateCall newCall;
        for (int j = 0; j < argCount; j++) {
            final Integer arg = aggCall.getArgList().get(j);
            if (callArgMap.containsKey(aggCall)) {
                newArgs.add(sourceOf.get(callArgMap.get(aggCall)));
            } else {
                newArgs.add(sourceOf.get(arg));
            }
        }
        if (aggCall.isDistinct()) {
            newCall = AggregateCall.create(aggCall.getAggregation(), false, newArgs, -1, aggregate.getGroupSet().cardinality(), relBuilder.peek(), aggCall.getType(), aggCall.name);
        } else {
            // aggregate A must be SUM. For other aggregates, it remains the same.
            if (aggCall.getAggregation() instanceof SqlCountAggFunction) {
                if (aggCall.getArgList().size() == 0) {
                    newArgs.add(sourceOf.get(callArgMap.get(aggCall)));
                }
                if (hasGroupBy) {
                    SqlSumAggFunction sumAgg = new SqlSumAggFunction(null);
                    newCall = AggregateCall.create(sumAgg, false, newArgs, -1, aggregate.getGroupSet().cardinality(), relBuilder.peek(), aggCall.getType(), aggCall.getName());
                } else {
                    SqlSumEmptyIsZeroAggFunction sumAgg = new SqlSumEmptyIsZeroAggFunction();
                    newCall = AggregateCall.create(sumAgg, false, newArgs, -1, aggregate.getGroupSet().cardinality(), relBuilder.peek(), aggCall.getType(), aggCall.getName());
                }
            } else {
                newCall = AggregateCall.create(aggCall.getAggregation(), false, newArgs, -1, aggregate.getGroupSet().cardinality(), relBuilder.peek(), aggCall.getType(), aggCall.name);
            }
        }
        newTopAggCalls.set(i, newCall);
    }
    // Populate the group-by keys with the remapped arguments for aggregate A
    newGroupSet.clear();
    for (int arg : aggregate.getGroupSet()) {
        newGroupSet.add(sourceOf.get(arg));
    }
    relBuilder.push(aggregate.copy(aggregate.getTraitSet(), relBuilder.build(), aggregate.indicator, ImmutableBitSet.of(newGroupSet), null, newTopAggCalls));
    return relBuilder;
}
Also used : HashMap(java.util.HashMap) ArrayList(java.util.ArrayList) SqlCountAggFunction(org.apache.calcite.sql.fun.SqlCountAggFunction) AggregateCall(org.apache.calcite.rel.core.AggregateCall) SqlSumEmptyIsZeroAggFunction(org.apache.calcite.sql.fun.SqlSumEmptyIsZeroAggFunction) RelDataTypeField(org.apache.calcite.rel.type.RelDataTypeField) TreeSet(java.util.TreeSet) SqlSumAggFunction(org.apache.calcite.sql.fun.SqlSumAggFunction) RexInputRef(org.apache.calcite.rex.RexInputRef) ArrayList(java.util.ArrayList) ImmutableList(com.google.common.collect.ImmutableList) ImmutableIntList(org.apache.calcite.util.ImmutableIntList) List(java.util.List) Pair(org.apache.calcite.util.Pair) RexNode(org.apache.calcite.rex.RexNode)

Example 84 with AggregateCall

use of org.apache.calcite.rel.core.AggregateCall in project flink by apache.

the class FlinkAggregateExpandDistinctAggregatesRule method doRewrite.

/**
	 * Converts all distinct aggregate calls to a given set of arguments.
	 *
	 * <p>This method is called several times, one for each set of arguments.
	 * Each time it is called, it generates a JOIN to a new SELECT DISTINCT
	 * relational expression, and modifies the set of top-level calls.
	 *
	 * @param aggregate Original aggregate
	 * @param n		 Ordinal of this in a join. {@code relBuilder} contains the
	 *				  input relational expression (either the original
	 *				  aggregate, the output from the previous call to this
	 *				  method. {@code n} is 0 if we're converting the
	 *				  first distinct aggregate in a query with no non-distinct
	 *				  aggregates)
	 * @param argList   Arguments to the distinct aggregate function
	 * @param filterArg Argument that filters input to aggregate function, or -1
	 * @param refs	  Array of expressions which will be the projected by the
	 *				  result of this rule. Those relating to this arg list will
	 *				  be modified  @return Relational expression
	 */
private void doRewrite(RelBuilder relBuilder, Aggregate aggregate, int n, List<Integer> argList, int filterArg, List<RexInputRef> refs) {
    final RexBuilder rexBuilder = aggregate.getCluster().getRexBuilder();
    final List<RelDataTypeField> leftFields;
    if (n == 0) {
        leftFields = null;
    } else {
        leftFields = relBuilder.peek().getRowType().getFieldList();
    }
    // LogicalAggregate(
    //	 child,
    //	 {COUNT(DISTINCT 1), SUM(DISTINCT 1), SUM(2)})
    //
    // becomes
    //
    // LogicalAggregate(
    //	 LogicalJoin(
    //		 child,
    //		 LogicalAggregate(child, < all columns > {}),
    //		 INNER,
    //		 <f2 = f5>))
    //
    // E.g.
    //   SELECT deptno, SUM(DISTINCT sal), COUNT(DISTINCT gender), MAX(age)
    //   FROM Emps
    //   GROUP BY deptno
    //
    // becomes
    //
    //   SELECT e.deptno, adsal.sum_sal, adgender.count_gender, e.max_age
    //   FROM (
    //	 SELECT deptno, MAX(age) as max_age
    //	 FROM Emps GROUP BY deptno) AS e
    //   JOIN (
    //	 SELECT deptno, COUNT(gender) AS count_gender FROM (
    //	   SELECT DISTINCT deptno, gender FROM Emps) AS dgender
    //	 GROUP BY deptno) AS adgender
    //	 ON e.deptno = adgender.deptno
    //   JOIN (
    //	 SELECT deptno, SUM(sal) AS sum_sal FROM (
    //	   SELECT DISTINCT deptno, sal FROM Emps) AS dsal
    //	 GROUP BY deptno) AS adsal
    //   ON e.deptno = adsal.deptno
    //   GROUP BY e.deptno
    //
    // Note that if a query contains no non-distinct aggregates, then the
    // very first join/group by is omitted.  In the example above, if
    // MAX(age) is removed, then the sub-select of "e" is not needed, and
    // instead the two other group by's are joined to one another.
    // Project the columns of the GROUP BY plus the arguments
    // to the agg function.
    final Map<Integer, Integer> sourceOf = new HashMap<>();
    createSelectDistinct(relBuilder, aggregate, argList, filterArg, sourceOf);
    // Now compute the aggregate functions on top of the distinct dataset.
    // Each distinct agg becomes a non-distinct call to the corresponding
    // field from the right; for example,
    //   "COUNT(DISTINCT e.sal)"
    // becomes
    //   "COUNT(distinct_e.sal)".
    final List<AggregateCall> aggCallList = new ArrayList<>();
    final List<AggregateCall> aggCalls = aggregate.getAggCallList();
    final int groupAndIndicatorCount = aggregate.getGroupCount() + aggregate.getIndicatorCount();
    int i = groupAndIndicatorCount - 1;
    for (AggregateCall aggCall : aggCalls) {
        ++i;
        // COUNT(DISTINCT gender) or SUM(sal).
        if (!aggCall.isDistinct()) {
            continue;
        }
        if (!aggCall.getArgList().equals(argList)) {
            continue;
        }
        // Re-map arguments.
        final int argCount = aggCall.getArgList().size();
        final List<Integer> newArgs = new ArrayList<>(argCount);
        for (int j = 0; j < argCount; j++) {
            final Integer arg = aggCall.getArgList().get(j);
            newArgs.add(sourceOf.get(arg));
        }
        final int newFilterArg = aggCall.filterArg >= 0 ? sourceOf.get(aggCall.filterArg) : -1;
        final AggregateCall newAggCall = AggregateCall.create(aggCall.getAggregation(), false, newArgs, newFilterArg, aggCall.getType(), aggCall.getName());
        assert refs.get(i) == null;
        if (n == 0) {
            refs.set(i, new RexInputRef(groupAndIndicatorCount + aggCallList.size(), newAggCall.getType()));
        } else {
            refs.set(i, new RexInputRef(leftFields.size() + groupAndIndicatorCount + aggCallList.size(), newAggCall.getType()));
        }
        aggCallList.add(newAggCall);
    }
    final Map<Integer, Integer> map = new HashMap<>();
    for (Integer key : aggregate.getGroupSet()) {
        map.put(key, map.size());
    }
    final ImmutableBitSet newGroupSet = aggregate.getGroupSet().permute(map);
    assert newGroupSet.equals(ImmutableBitSet.range(aggregate.getGroupSet().cardinality()));
    ImmutableList<ImmutableBitSet> newGroupingSets = null;
    if (aggregate.indicator) {
        newGroupingSets = ImmutableBitSet.ORDERING.immutableSortedCopy(ImmutableBitSet.permute(aggregate.getGroupSets(), map));
    }
    relBuilder.push(aggregate.copy(aggregate.getTraitSet(), relBuilder.build(), aggregate.indicator, newGroupSet, newGroupingSets, aggCallList));
    // If there's no left child yet, no need to create the join
    if (n == 0) {
        return;
    }
    // Create the join condition. It is of the form
    //  'left.f0 = right.f0 and left.f1 = right.f1 and ...'
    // where {f0, f1, ...} are the GROUP BY fields.
    final List<RelDataTypeField> distinctFields = relBuilder.peek().getRowType().getFieldList();
    final List<RexNode> conditions = Lists.newArrayList();
    for (i = 0; i < groupAndIndicatorCount; ++i) {
        // null values form its own group
        // use "is not distinct from" so that the join condition
        // allows null values to match.
        conditions.add(rexBuilder.makeCall(SqlStdOperatorTable.IS_NOT_DISTINCT_FROM, RexInputRef.of(i, leftFields), new RexInputRef(leftFields.size() + i, distinctFields.get(i).getType())));
    }
    // Join in the new 'select distinct' relation.
    relBuilder.join(JoinRelType.INNER, conditions);
}
Also used : ImmutableBitSet(org.apache.calcite.util.ImmutableBitSet) HashMap(java.util.HashMap) ArrayList(java.util.ArrayList) AggregateCall(org.apache.calcite.rel.core.AggregateCall) RelDataTypeField(org.apache.calcite.rel.type.RelDataTypeField) RexBuilder(org.apache.calcite.rex.RexBuilder) RexInputRef(org.apache.calcite.rex.RexInputRef) RexNode(org.apache.calcite.rex.RexNode)

Example 85 with AggregateCall

use of org.apache.calcite.rel.core.AggregateCall in project flink by apache.

the class FlinkAggregateExpandDistinctAggregatesRule method rewriteAggCalls.

private static void rewriteAggCalls(List<AggregateCall> newAggCalls, List<Integer> argList, Map<Integer, Integer> sourceOf) {
    // "COUNT(DISTINCT e.sal)" becomes   "COUNT(distinct_e.sal)".
    for (int i = 0; i < newAggCalls.size(); i++) {
        final AggregateCall aggCall = newAggCalls.get(i);
        // COUNT(DISTINCT gender) or SUM(sal).
        if (!aggCall.isDistinct()) {
            continue;
        }
        if (!aggCall.getArgList().equals(argList)) {
            continue;
        }
        // Re-map arguments.
        final int argCount = aggCall.getArgList().size();
        final List<Integer> newArgs = new ArrayList<>(argCount);
        for (int j = 0; j < argCount; j++) {
            final Integer arg = aggCall.getArgList().get(j);
            newArgs.add(sourceOf.get(arg));
        }
        final AggregateCall newAggCall = AggregateCall.create(aggCall.getAggregation(), false, newArgs, -1, aggCall.getType(), aggCall.getName());
        newAggCalls.set(i, newAggCall);
    }
}
Also used : AggregateCall(org.apache.calcite.rel.core.AggregateCall) ArrayList(java.util.ArrayList)

Aggregations

AggregateCall (org.apache.calcite.rel.core.AggregateCall)158 ArrayList (java.util.ArrayList)82 RexNode (org.apache.calcite.rex.RexNode)78 ImmutableBitSet (org.apache.calcite.util.ImmutableBitSet)57 RelNode (org.apache.calcite.rel.RelNode)54 RexBuilder (org.apache.calcite.rex.RexBuilder)52 RelDataType (org.apache.calcite.rel.type.RelDataType)42 Aggregate (org.apache.calcite.rel.core.Aggregate)37 RelDataTypeField (org.apache.calcite.rel.type.RelDataTypeField)36 RexInputRef (org.apache.calcite.rex.RexInputRef)33 RelBuilder (org.apache.calcite.tools.RelBuilder)29 HashMap (java.util.HashMap)28 SqlAggFunction (org.apache.calcite.sql.SqlAggFunction)28 List (java.util.List)27 RexLiteral (org.apache.calcite.rex.RexLiteral)23 Pair (org.apache.calcite.util.Pair)20 ImmutableList (com.google.common.collect.ImmutableList)19 Project (org.apache.calcite.rel.core.Project)17 RelDataTypeFactory (org.apache.calcite.rel.type.RelDataTypeFactory)17 LogicalAggregate (org.apache.calcite.rel.logical.LogicalAggregate)16