Examples with AggregateOperator org.apache.sysml.runtime.matrix.operators.AggregateOperator used on opensource projects

Example 11 with AggregateOperator

use of org.apache.sysml.runtime.matrix.operators.AggregateOperator in project incubator-systemml by apache.

the class InstructionUtils method parseAggregateTernaryOperator.

public static AggregateTernaryOperator parseAggregateTernaryOperator(String opcode, int numThreads) {
    CorrectionLocationType corr = opcode.equalsIgnoreCase("tak+*") ? CorrectionLocationType.LASTCOLUMN : CorrectionLocationType.LASTROW;
    AggregateOperator agg = new AggregateOperator(0, KahanPlus.getKahanPlusFnObject(), true, corr);
    IndexFunction ixfun = opcode.equalsIgnoreCase("tak+*") ? ReduceAll.getReduceAllFnObject() : ReduceRow.getReduceRowFnObject();
    return new AggregateTernaryOperator(Multiply.getMultiplyFnObject(), agg, ixfun, numThreads);
}

Example 12 with AggregateOperator

use of org.apache.sysml.runtime.matrix.operators.AggregateOperator in project incubator-systemml by apache.

the class InstructionUtils method parseBasicAggregateUnaryOperator.

public static AggregateUnaryOperator parseBasicAggregateUnaryOperator(String opcode, int numThreads) {
    AggregateUnaryOperator aggun = null;
    if (opcode.equalsIgnoreCase("uak+")) {
        AggregateOperator agg = new AggregateOperator(0, KahanPlus.getKahanPlusFnObject(), true, CorrectionLocationType.LASTCOLUMN);
        aggun = new AggregateUnaryOperator(agg, ReduceAll.getReduceAllFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uark+")) {
        // RowSums
        AggregateOperator agg = new AggregateOperator(0, KahanPlus.getKahanPlusFnObject(), true, CorrectionLocationType.LASTCOLUMN);
        aggun = new AggregateUnaryOperator(agg, ReduceCol.getReduceColFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uack+")) {
        // ColSums
        AggregateOperator agg = new AggregateOperator(0, KahanPlus.getKahanPlusFnObject(), true, CorrectionLocationType.LASTROW);
        aggun = new AggregateUnaryOperator(agg, ReduceRow.getReduceRowFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uasqk+")) {
        AggregateOperator agg = new AggregateOperator(0, KahanPlusSq.getKahanPlusSqFnObject(), true, CorrectionLocationType.LASTCOLUMN);
        aggun = new AggregateUnaryOperator(agg, ReduceAll.getReduceAllFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uarsqk+")) {
        // RowSums
        AggregateOperator agg = new AggregateOperator(0, KahanPlusSq.getKahanPlusSqFnObject(), true, CorrectionLocationType.LASTCOLUMN);
        aggun = new AggregateUnaryOperator(agg, ReduceCol.getReduceColFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uacsqk+")) {
        // ColSums
        AggregateOperator agg = new AggregateOperator(0, KahanPlusSq.getKahanPlusSqFnObject(), true, CorrectionLocationType.LASTROW);
        aggun = new AggregateUnaryOperator(agg, ReduceRow.getReduceRowFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uamean")) {
        // Mean
        AggregateOperator agg = new AggregateOperator(0, Mean.getMeanFnObject(), true, CorrectionLocationType.LASTTWOCOLUMNS);
        aggun = new AggregateUnaryOperator(agg, ReduceAll.getReduceAllFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uarmean")) {
        // RowMeans
        AggregateOperator agg = new AggregateOperator(0, Mean.getMeanFnObject(), true, CorrectionLocationType.LASTTWOCOLUMNS);
        aggun = new AggregateUnaryOperator(agg, ReduceCol.getReduceColFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uacmean")) {
        // ColMeans
        AggregateOperator agg = new AggregateOperator(0, Mean.getMeanFnObject(), true, CorrectionLocationType.LASTTWOROWS);
        aggun = new AggregateUnaryOperator(agg, ReduceRow.getReduceRowFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uavar")) {
        // Variance
        CM varFn = CM.getCMFnObject(AggregateOperationTypes.VARIANCE);
        CorrectionLocationType cloc = CorrectionLocationType.LASTFOURCOLUMNS;
        AggregateOperator agg = new AggregateOperator(0, varFn, true, cloc);
        aggun = new AggregateUnaryOperator(agg, ReduceAll.getReduceAllFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uarvar")) {
        // RowVariances
        CM varFn = CM.getCMFnObject(AggregateOperationTypes.VARIANCE);
        CorrectionLocationType cloc = CorrectionLocationType.LASTFOURCOLUMNS;
        AggregateOperator agg = new AggregateOperator(0, varFn, true, cloc);
        aggun = new AggregateUnaryOperator(agg, ReduceCol.getReduceColFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uacvar")) {
        // ColVariances
        CM varFn = CM.getCMFnObject(AggregateOperationTypes.VARIANCE);
        CorrectionLocationType cloc = CorrectionLocationType.LASTFOURROWS;
        AggregateOperator agg = new AggregateOperator(0, varFn, true, cloc);
        aggun = new AggregateUnaryOperator(agg, ReduceRow.getReduceRowFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("ua+")) {
        AggregateOperator agg = new AggregateOperator(0, Plus.getPlusFnObject());
        aggun = new AggregateUnaryOperator(agg, ReduceAll.getReduceAllFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uar+")) {
        // RowSums
        AggregateOperator agg = new AggregateOperator(0, Plus.getPlusFnObject());
        aggun = new AggregateUnaryOperator(agg, ReduceCol.getReduceColFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uac+")) {
        // ColSums
        AggregateOperator agg = new AggregateOperator(0, Plus.getPlusFnObject());
        aggun = new AggregateUnaryOperator(agg, ReduceRow.getReduceRowFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("ua*")) {
        AggregateOperator agg = new AggregateOperator(1, Multiply.getMultiplyFnObject());
        aggun = new AggregateUnaryOperator(agg, ReduceAll.getReduceAllFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uamax")) {
        AggregateOperator agg = new AggregateOperator(Double.NEGATIVE_INFINITY, Builtin.getBuiltinFnObject("max"));
        aggun = new AggregateUnaryOperator(agg, ReduceAll.getReduceAllFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uamin")) {
        AggregateOperator agg = new AggregateOperator(Double.POSITIVE_INFINITY, Builtin.getBuiltinFnObject("min"));
        aggun = new AggregateUnaryOperator(agg, ReduceAll.getReduceAllFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uatrace")) {
        AggregateOperator agg = new AggregateOperator(0, Plus.getPlusFnObject());
        aggun = new AggregateUnaryOperator(agg, ReduceDiag.getReduceDiagFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uaktrace")) {
        AggregateOperator agg = new AggregateOperator(0, KahanPlus.getKahanPlusFnObject(), true, CorrectionLocationType.LASTCOLUMN);
        aggun = new AggregateUnaryOperator(agg, ReduceDiag.getReduceDiagFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uarmax")) {
        AggregateOperator agg = new AggregateOperator(Double.NEGATIVE_INFINITY, Builtin.getBuiltinFnObject("max"));
        aggun = new AggregateUnaryOperator(agg, ReduceCol.getReduceColFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uarimax")) {
        AggregateOperator agg = new AggregateOperator(Double.NEGATIVE_INFINITY, Builtin.getBuiltinFnObject("maxindex"), true, CorrectionLocationType.LASTCOLUMN);
        aggun = new AggregateUnaryOperator(agg, ReduceCol.getReduceColFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uarmin")) {
        AggregateOperator agg = new AggregateOperator(Double.POSITIVE_INFINITY, Builtin.getBuiltinFnObject("min"));
        aggun = new AggregateUnaryOperator(agg, ReduceCol.getReduceColFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uarimin")) {
        AggregateOperator agg = new AggregateOperator(Double.POSITIVE_INFINITY, Builtin.getBuiltinFnObject("minindex"), true, CorrectionLocationType.LASTCOLUMN);
        aggun = new AggregateUnaryOperator(agg, ReduceCol.getReduceColFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uacmax")) {
        AggregateOperator agg = new AggregateOperator(Double.NEGATIVE_INFINITY, Builtin.getBuiltinFnObject("max"));
        aggun = new AggregateUnaryOperator(agg, ReduceRow.getReduceRowFnObject(), numThreads);
    } else if (opcode.equalsIgnoreCase("uacmin")) {
        AggregateOperator agg = new AggregateOperator(Double.POSITIVE_INFINITY, Builtin.getBuiltinFnObject("min"));
        aggun = new AggregateUnaryOperator(agg, ReduceRow.getReduceRowFnObject(), numThreads);
    }
    return aggun;
}

Example 13 with AggregateOperator

use of org.apache.sysml.runtime.matrix.operators.AggregateOperator in project incubator-systemml by apache.

the class AggregateBinaryCPInstruction method parseInstruction.

public static AggregateBinaryCPInstruction parseInstruction(String str) {
    CPOperand in1 = new CPOperand("", ValueType.UNKNOWN, DataType.UNKNOWN);
    CPOperand in2 = new CPOperand("", ValueType.UNKNOWN, DataType.UNKNOWN);
    CPOperand out = new CPOperand("", ValueType.UNKNOWN, DataType.UNKNOWN);
    String[] parts = InstructionUtils.getInstructionPartsWithValueType(str);
    String opcode = parts[0];
    if (!opcode.equalsIgnoreCase("ba+*")) {
        throw new DMLRuntimeException("AggregateBinaryInstruction.parseInstruction():: Unknown opcode " + opcode);
    }
    InstructionUtils.checkNumFields(parts, 4);
    in1.split(parts[1]);
    in2.split(parts[2]);
    out.split(parts[3]);
    int k = Integer.parseInt(parts[4]);
    AggregateOperator agg = new AggregateOperator(0, Plus.getPlusFnObject());
    AggregateBinaryOperator aggbin = new AggregateBinaryOperator(Multiply.getMultiplyFnObject(), agg, k);
    return new AggregateBinaryCPInstruction(aggbin, in1, in2, out, opcode, str);
}

Example 14 with AggregateOperator

use of org.apache.sysml.runtime.matrix.operators.AggregateOperator in project incubator-systemml by apache.

the class LibMatrixAgg method groupedAggregate.

public static void groupedAggregate(MatrixBlock groups, MatrixBlock target, MatrixBlock weights, MatrixBlock result, int numGroups, Operator op, int k) {
    // fall back to sequential version if necessary
    boolean rowVector = (target.getNumRows() == 1 && target.getNumColumns() > 1);
    if (k <= 1 || (long) target.rlen * target.clen < PAR_NUMCELL_THRESHOLD || rowVector || target.clen == 1) {
        groupedAggregate(groups, target, weights, result, numGroups, op);
        return;
    }
    if (!(op instanceof CMOperator || op instanceof AggregateOperator)) {
        throw new DMLRuntimeException("Invalid operator (" + op + ") encountered while processing groupedAggregate.");
    }
    // preprocessing (no need to check isThreadSafe)
    result.sparse = false;
    result.allocateDenseBlock();
    // (currently: parallelization over columns to avoid additional memory requirements)
    try {
        ExecutorService pool = CommonThreadPool.get(k);
        ArrayList<GrpAggTask> tasks = new ArrayList<>();
        int blklen = (int) (Math.ceil((double) target.clen / k));
        for (int i = 0; i < k & i * blklen < target.clen; i++) tasks.add(new GrpAggTask(groups, target, weights, result, numGroups, op, i * blklen, Math.min((i + 1) * blklen, target.clen)));
        List<Future<Object>> taskret = pool.invokeAll(tasks);
        pool.shutdown();
        for (Future<Object> task : taskret) // error handling
        task.get();
    } catch (Exception ex) {
        throw new DMLRuntimeException(ex);
    }
    // postprocessing
    result.recomputeNonZeros();
    result.examSparsity();
}

Example 15 with AggregateOperator

use of org.apache.sysml.runtime.matrix.operators.AggregateOperator in project incubator-systemml by apache.

the class LibMatrixCUDA method unaryAggregate.

// ********************************************************************/
// ******** End of TRANSPOSE SELF MATRIX MULTIPLY Functions ***********/
// ********************************************************************/
// ********************************************************************/
// ****************  UNARY AGGREGATE Functions ************************/
// ********************************************************************/
/**
 * Entry point to perform Unary aggregate operations on the GPU.
 * The execution context object is used to allocate memory for the GPU.
 *
 * @param ec       Instance of {@link ExecutionContext}, from which the output variable will be allocated
 * @param gCtx     a valid {@link GPUContext}
 * @param instName name of the invoking instruction to record{@link Statistics}.
 * @param in1      input matrix
 * @param output   output matrix/scalar name
 * @param op       Instance of {@link AggregateUnaryOperator} which encapsulates the direction of reduction/aggregation and the reduction operation.
 */
public static void unaryAggregate(ExecutionContext ec, GPUContext gCtx, String instName, MatrixObject in1, String output, AggregateUnaryOperator op) {
    if (ec.getGPUContext(0) != gCtx)
        throw new DMLRuntimeException("GPU : Invalid internal state, the GPUContext set with the ExecutionContext is not the same used to run this LibMatrixCUDA function");
    if (LOG.isTraceEnabled()) {
        LOG.trace("GPU : unaryAggregate" + ", GPUContext=" + gCtx);
    }
    final int REDUCTION_ALL = 1;
    final int REDUCTION_ROW = 2;
    final int REDUCTION_COL = 3;
    final int REDUCTION_DIAG = 4;
    // A kahan sum implemention is not provided. is a "uak+" or other kahan operator is encountered,
    // it just does regular summation reduction.
    final int OP_PLUS = 1;
    final int OP_PLUS_SQ = 2;
    final int OP_MEAN = 3;
    final int OP_VARIANCE = 4;
    final int OP_MULTIPLY = 5;
    final int OP_MAX = 6;
    final int OP_MIN = 7;
    final int OP_MAXINDEX = 8;
    final int OP_MININDEX = 9;
    // Sanity Checks
    if (!in1.getGPUObject(gCtx).isAllocated())
        throw new DMLRuntimeException("Internal Error - The input is not allocated for a GPU Aggregate Unary:" + in1.getGPUObject(gCtx).isAllocated());
    boolean isSparse = in1.getGPUObject(gCtx).isSparse();
    IndexFunction indexFn = op.indexFn;
    AggregateOperator aggOp = op.aggOp;
    // Convert Reduction direction to a number
    int reductionDirection = -1;
    if (indexFn instanceof ReduceAll) {
        reductionDirection = REDUCTION_ALL;
    } else if (indexFn instanceof ReduceRow) {
        reductionDirection = REDUCTION_ROW;
    } else if (indexFn instanceof ReduceCol) {
        reductionDirection = REDUCTION_COL;
    } else if (indexFn instanceof ReduceDiag) {
        reductionDirection = REDUCTION_DIAG;
    } else {
        throw new DMLRuntimeException("Internal Error - Invalid index function type, only reducing along rows, columns, diagonals or all elements is supported in Aggregate Unary operations");
    }
    if (reductionDirection == -1)
        throw new DMLRuntimeException("Internal Error - Incorrect type of reduction direction set for aggregate unary GPU instruction");
    // Convert function type to a number
    int opIndex = -1;
    if (aggOp.increOp.fn instanceof KahanPlus) {
        opIndex = OP_PLUS;
    } else if (aggOp.increOp.fn instanceof KahanPlusSq) {
        opIndex = OP_PLUS_SQ;
    } else if (aggOp.increOp.fn instanceof Mean) {
        opIndex = OP_MEAN;
    } else if (aggOp.increOp.fn instanceof CM) {
        if (((CM) aggOp.increOp.fn).getAggOpType() != CMOperator.AggregateOperationTypes.VARIANCE)
            throw new DMLRuntimeException("Internal Error - Invalid Type of CM operator for Aggregate Unary operation on GPU");
        opIndex = OP_VARIANCE;
    } else if (aggOp.increOp.fn instanceof Plus) {
        opIndex = OP_PLUS;
    } else if (aggOp.increOp.fn instanceof Multiply) {
        opIndex = OP_MULTIPLY;
    } else if (aggOp.increOp.fn instanceof Builtin) {
        Builtin b = (Builtin) aggOp.increOp.fn;
        switch(b.bFunc) {
            case MAX:
                opIndex = OP_MAX;
                break;
            case MIN:
                opIndex = OP_MIN;
                break;
            case MAXINDEX:
                opIndex = OP_MAXINDEX;
                break;
            case MININDEX:
                opIndex = OP_MININDEX;
                break;
            default:
                new DMLRuntimeException("Internal Error - Unsupported Builtin Function for Aggregate unary being done on GPU");
        }
    } else {
        throw new DMLRuntimeException("Internal Error - Aggregate operator has invalid Value function");
    }
    if (opIndex == -1)
        throw new DMLRuntimeException("Internal Error - Incorrect type of operation set for aggregate unary GPU instruction");
    int rlen = (int) in1.getNumRows();
    int clen = (int) in1.getNumColumns();
    if (isSparse) {
        // The strategy for the time being is to convert sparse to dense
        // until a sparse specific kernel is written.
        in1.getGPUObject(gCtx).sparseToDense(instName);
    // long nnz = in1.getNnz();
    // assert nnz > 0 : "Internal Error - number of non zeroes set to " + nnz + " in Aggregate Binary for GPU";
    // MatrixObject out = ec.getSparseMatrixOutputForGPUInstruction(output, nnz);
    // throw new DMLRuntimeException("Internal Error - Not implemented");
    }
    long outRLen = -1;
    long outCLen = -1;
    if (indexFn instanceof ReduceRow) {
        // COL{SUM, MAX...}
        outRLen = 1;
        outCLen = clen;
    } else if (indexFn instanceof ReduceCol) {
        // ROW{SUM, MAX,...}
        outRLen = rlen;
        outCLen = 1;
    }
    Pointer out = null;
    if (reductionDirection == REDUCTION_COL || reductionDirection == REDUCTION_ROW) {
        // Matrix output
        MatrixObject out1 = getDenseMatrixOutputForGPUInstruction(ec, instName, output, outRLen, outCLen);
        out = getDensePointer(gCtx, out1, instName);
    }
    Pointer in = getDensePointer(gCtx, in1, instName);
    int size = rlen * clen;
    // For scalars, set the scalar output in the Execution Context object
    switch(opIndex) {
        case OP_PLUS:
            {
                switch(reductionDirection) {
                    case REDUCTION_ALL:
                        {
                            double result = reduceAll(gCtx, instName, "reduce_sum", in, size);
                            ec.setScalarOutput(output, new DoubleObject(result));
                            break;
                        }
                    case REDUCTION_COL:
                        {
                            // The names are a bit misleading, REDUCTION_COL refers to the direction (reduce all elements in a column)
                            reduceRow(gCtx, instName, "reduce_row_sum", in, out, rlen, clen);
                            break;
                        }
                    case REDUCTION_ROW:
                        {
                            reduceCol(gCtx, instName, "reduce_col_sum", in, out, rlen, clen);
                            break;
                        }
                    case REDUCTION_DIAG:
                        throw new DMLRuntimeException("Internal Error - Row, Column and Diag summation not implemented yet");
                }
                break;
            }
        case OP_PLUS_SQ:
            {
                // Calculate the squares in a temporary object tmp
                Pointer tmp = gCtx.allocate(instName, size * sizeOfDataType);
                squareMatrix(gCtx, instName, in, tmp, rlen, clen);
                // Then do the sum on the temporary object and free it
                switch(reductionDirection) {
                    case REDUCTION_ALL:
                        {
                            double result = reduceAll(gCtx, instName, "reduce_sum", tmp, size);
                            ec.setScalarOutput(output, new DoubleObject(result));
                            break;
                        }
                    case REDUCTION_COL:
                        {
                            // The names are a bit misleading, REDUCTION_COL refers to the direction (reduce all elements in a column)
                            reduceRow(gCtx, instName, "reduce_row_sum", tmp, out, rlen, clen);
                            break;
                        }
                    case REDUCTION_ROW:
                        {
                            reduceCol(gCtx, instName, "reduce_col_sum", tmp, out, rlen, clen);
                            break;
                        }
                    default:
                        throw new DMLRuntimeException("Internal Error - Unsupported reduction direction for summation squared");
                }
                gCtx.cudaFreeHelper(instName, tmp);
                break;
            }
        case OP_MEAN:
            {
                switch(reductionDirection) {
                    case REDUCTION_ALL:
                        {
                            double result = reduceAll(gCtx, instName, "reduce_sum", in, size);
                            double mean = result / size;
                            ec.setScalarOutput(output, new DoubleObject(mean));
                            break;
                        }
                    case REDUCTION_COL:
                        {
                            reduceRow(gCtx, instName, "reduce_row_mean", in, out, rlen, clen);
                            break;
                        }
                    case REDUCTION_ROW:
                        {
                            reduceCol(gCtx, instName, "reduce_col_mean", in, out, rlen, clen);
                            break;
                        }
                    default:
                        throw new DMLRuntimeException("Internal Error - Unsupported reduction direction for mean");
                }
                break;
            }
        case OP_MULTIPLY:
            {
                switch(reductionDirection) {
                    case REDUCTION_ALL:
                        {
                            double result = reduceAll(gCtx, instName, "reduce_prod", in, size);
                            ec.setScalarOutput(output, new DoubleObject(result));
                            break;
                        }
                    default:
                        throw new DMLRuntimeException("Internal Error - Unsupported reduction direction for multiplication");
                }
                break;
            }
        case OP_MAX:
            {
                switch(reductionDirection) {
                    case REDUCTION_ALL:
                        {
                            double result = reduceAll(gCtx, instName, "reduce_max", in, size);
                            ec.setScalarOutput(output, new DoubleObject(result));
                            break;
                        }
                    case REDUCTION_COL:
                        {
                            reduceRow(gCtx, instName, "reduce_row_max", in, out, rlen, clen);
                            break;
                        }
                    case REDUCTION_ROW:
                        {
                            reduceCol(gCtx, instName, "reduce_col_max", in, out, rlen, clen);
                            break;
                        }
                    default:
                        throw new DMLRuntimeException("Internal Error - Unsupported reduction direction for max");
                }
                break;
            }
        case OP_MIN:
            {
                switch(reductionDirection) {
                    case REDUCTION_ALL:
                        {
                            double result = reduceAll(gCtx, instName, "reduce_min", in, size);
                            ec.setScalarOutput(output, new DoubleObject(result));
                            break;
                        }
                    case REDUCTION_COL:
                        {
                            reduceRow(gCtx, instName, "reduce_row_min", in, out, rlen, clen);
                            break;
                        }
                    case REDUCTION_ROW:
                        {
                            reduceCol(gCtx, instName, "reduce_col_min", in, out, rlen, clen);
                            break;
                        }
                    default:
                        throw new DMLRuntimeException("Internal Error - Unsupported reduction direction for min");
                }
                break;
            }
        case OP_VARIANCE:
            {
                // Temporary GPU array for
                Pointer tmp = gCtx.allocate(instName, size * sizeOfDataType);
                Pointer tmp2 = gCtx.allocate(instName, size * sizeOfDataType);
                switch(reductionDirection) {
                    case REDUCTION_ALL:
                        {
                            double result = reduceAll(gCtx, instName, "reduce_sum", in, size);
                            double mean = result / size;
                            // Subtract mean from every element in the matrix
                            ScalarOperator minusOp = new RightScalarOperator(Minus.getMinusFnObject(), mean);
                            matrixScalarOp(gCtx, instName, in, mean, rlen, clen, tmp, minusOp);
                            squareMatrix(gCtx, instName, tmp, tmp2, rlen, clen);
                            double result2 = reduceAll(gCtx, instName, "reduce_sum", tmp2, size);
                            double variance = result2 / (size - 1);
                            ec.setScalarOutput(output, new DoubleObject(variance));
                            break;
                        }
                    case REDUCTION_COL:
                        {
                            reduceRow(gCtx, instName, "reduce_row_mean", in, out, rlen, clen);
                            // Subtract the row-wise mean from every element in the matrix
                            BinaryOperator minusOp = new BinaryOperator(Minus.getMinusFnObject());
                            matrixMatrixOp(gCtx, instName, in, out, rlen, clen, VectorShape.NONE.code(), VectorShape.COLUMN.code(), tmp, minusOp);
                            squareMatrix(gCtx, instName, tmp, tmp2, rlen, clen);
                            Pointer tmpRow = gCtx.allocate(instName, rlen * sizeOfDataType);
                            reduceRow(gCtx, instName, "reduce_row_sum", tmp2, tmpRow, rlen, clen);
                            ScalarOperator divideOp = new RightScalarOperator(Divide.getDivideFnObject(), clen - 1);
                            matrixScalarOp(gCtx, instName, tmpRow, clen - 1, rlen, 1, out, divideOp);
                            gCtx.cudaFreeHelper(instName, tmpRow);
                            break;
                        }
                    case REDUCTION_ROW:
                        {
                            reduceCol(gCtx, instName, "reduce_col_mean", in, out, rlen, clen);
                            // Subtract the columns-wise mean from every element in the matrix
                            BinaryOperator minusOp = new BinaryOperator(Minus.getMinusFnObject());
                            matrixMatrixOp(gCtx, instName, in, out, rlen, clen, VectorShape.NONE.code(), VectorShape.ROW.code(), tmp, minusOp);
                            squareMatrix(gCtx, instName, tmp, tmp2, rlen, clen);
                            Pointer tmpCol = gCtx.allocate(instName, clen * sizeOfDataType);
                            reduceCol(gCtx, instName, "reduce_col_sum", tmp2, tmpCol, rlen, clen);
                            ScalarOperator divideOp = new RightScalarOperator(Divide.getDivideFnObject(), rlen - 1);
                            matrixScalarOp(gCtx, instName, tmpCol, rlen - 1, 1, clen, out, divideOp);
                            gCtx.cudaFreeHelper(instName, tmpCol);
                            break;
                        }
                    default:
                        throw new DMLRuntimeException("Internal Error - Unsupported reduction direction for variance");
                }
                gCtx.cudaFreeHelper(instName, tmp);
                gCtx.cudaFreeHelper(instName, tmp2);
                break;
            }
        case OP_MAXINDEX:
            {
                switch(reductionDirection) {
                    case REDUCTION_COL:
                        throw new DMLRuntimeException("Internal Error - Column maxindex of matrix not implemented yet for GPU ");
                    default:
                        throw new DMLRuntimeException("Internal Error - Unsupported reduction direction for maxindex");
                }
            // break;
            }
        case OP_MININDEX:
            {
                switch(reductionDirection) {
                    case REDUCTION_COL:
                        throw new DMLRuntimeException("Internal Error - Column minindex of matrix not implemented yet for GPU ");
                    default:
                        throw new DMLRuntimeException("Internal Error - Unsupported reduction direction for minindex");
                }
            // break;
            }
        default:
            throw new DMLRuntimeException("Internal Error - Invalid GPU Unary aggregate function!");
    }
}