//
// Copyright (c) Microsoft. All rights reserved.
// Licensed under the MIT license. See LICENSE.md file in the project root for full license information.
//

#include "stdafx.h"
#include "Basics.h"
#include "BestGpu.h"

#ifndef CPUONLY

#include "GPUMatrix.h"
#include "GPUMatrixCUDAKernels.cuh"
#include "GPUSparseMatrix.h"
#include "GPUTensor.h"
#include "CommonMatrix.h"
#define TENSOR_OPS_DECL __device__ __host__
#include "TensorOps.h"
#include "device_launch_parameters.h"
#include <cuda.h>
#include <cuda_runtime.h>
#include <curand.h>
#include <curand_kernel.h>
#include "cublas_v2.h"
#include <assert.h>
#include <memory>
#include "CntkBatchNormalization.cuh"
#include "Convolution.cuh"

#pragma comment(lib, "cudart.lib") // instruct linker to reference these libs
#pragma comment(lib, "cublas.lib")
#pragma comment(lib, "cusparse.lib")
#pragma comment(lib, "curand.lib")

#pragma warning(disable : 4267) // conversion from 'size_t' to 'unsigned int'; happens in CUDA <<<a,b>>> syntax if a and b are size_t
#pragma warning(disable : 4127) // conditional expression is constant; "if (sizeof(ElemType)==sizeof(float))" triggers this
#pragma warning(disable : 4702) // unreachable code; triggered for unknown reasons

#define DEFAULT_THREAD_PER_DIM 16

#define UNCONST(t, c, uc) GPUMatrix<t>& uc = const_cast<GPUMatrix<t>&>(c);

#ifdef _WIN32
// thread local storage to access the current stream, initalize to default stream
__declspec(thread)
#endif
    cudaStream_t t_stream = cudaStreamDefault;

#define DEFAULT_THREAD_PER_DIM 16

extern int _ConvertSMVer2Cores(int major, int minor); // forward declaration

// SetStream - set the stream that will be used by the GPU routines
void MATH_API SetStream(cudaStream_t stream)
{
    t_stream = stream;
}

// GetStream - get the stream that will be used by the GPU routines
cudaStream_t MATH_API GetStream()
{
    return t_stream;
}

// Helper macro patterns for elemtwise methods
#define DEF_ELEMWISE_INPLACE_FUNC(f)                                      \
    template <class ElemType>                                             \
    GPUMatrix<ElemType>& GPUMatrix<ElemType>::Inplace##f()                \
    {                                                                     \
        performElementWiseFunction(ElementWiseOperator::op##f, Data()); \
        return *this;                                                     \
    }
#define DEF_ELEMWISE_ASSIGN_FUNC(f)                                                       \
    template <class ElemType>                                                             \
    GPUMatrix<ElemType>& GPUMatrix<ElemType>::Assign##f##Of(const GPUMatrix<ElemType>& a) \
    {                                                                                     \
        if (a.IsEmpty())                                                                  \
            LogicError("Assign##f##Of: Matrix a is empty.");                              \
        if (this != &a)                                                                   \
            RequireSize(a.GetNumRows(), a.GetNumCols());                                       \
        performElementWiseFunction(ElementWiseOperator::op##f, a.Data());               \
        return *this;                                                                     \
    }

template <>
const char* CudaErrString<cudaError_t>(cudaError_t x)
{
    cudaDeviceSynchronize();
    return cudaGetErrorString(x);
}
template <>
const char* CudaErrString<cublasStatus_t>(cublasStatus_t e)
{
    cudaDeviceSynchronize();
    switch (e)
    {
    case CUBLAS_STATUS_SUCCESS:          return "CUBLAS_STATUS_SUCCESS";
    case CUBLAS_STATUS_NOT_INITIALIZED:  return "CUBLAS_STATUS_NOT_INITIALIZED";
    case CUBLAS_STATUS_ALLOC_FAILED:     return "CUBLAS_STATUS_ALLOC_FAILED";
    case CUBLAS_STATUS_INVALID_VALUE:    return "CUBLAS_STATUS_INVALID_VALUE";
    case CUBLAS_STATUS_ARCH_MISMATCH:    return "CUBLAS_STATUS_ARCH_MISMATCH";
    case CUBLAS_STATUS_MAPPING_ERROR:    return "CUBLAS_STATUS_MAPPING_ERROR";
    case CUBLAS_STATUS_EXECUTION_FAILED: return "CUBLAS_STATUS_EXECUTION_FAILED";
    case CUBLAS_STATUS_INTERNAL_ERROR:   return "CUBLAS_STATUS_INTERNAL_ERROR";
    case CUBLAS_STATUS_NOT_SUPPORTED:    return "CUBLAS_STATUS_NOT_SUPPORTED";
    case CUBLAS_STATUS_LICENSE_ERROR:    return "CUBLAS_STATUS_LICENSE_ERROR";
    default:                             return "(look for CUBLAS_STATUS_xxx in cublas_api.h)";
    }
}
template <>
const char* CudaErrString<curandStatus>(curandStatus)
{
    cudaDeviceSynchronize();
    return "(see curand.h & look for curandStatus or CURAND_STATUS_xxx)";
}

namespace Microsoft { namespace MSR { namespace CNTK {

template <typename AllocatedElemType>
AllocatedElemType* TracingGPUMemoryAllocator::Allocate(int deviceId, size_t numRows, size_t numCols)
{
    if (IsTraceEnabled())
    {
        auto freeAndTotalMemory = GetFreeAndTotalMemoryInMBs(deviceId);
        fprintf(stderr, "Allocating Matrix<%s> (Rows = %d, Cols = %d) buffer on DeviceId = %d; GPU Memory Free = %d MB of %d MB\n", typeid(AllocatedElemType).name(), (int)numRows, (int)numCols, (int)deviceId, (int)freeAndTotalMemory.first, (int)freeAndTotalMemory.second);
        Microsoft::MSR::CNTK::DebugUtil::PrintCallStack();
    }

    AllocatedElemType* deviceBufferPtr = AllocateNoTrace<AllocatedElemType>(deviceId, numRows * numCols);

    if (IsTraceEnabled())
    {
        fprintf(stderr, "Allocated DeviceData = %p\n", (void*) deviceBufferPtr);
    }

    return deviceBufferPtr;
}

template <typename AllocatedElemType>
AllocatedElemType* TracingGPUMemoryAllocator::Allocate(int deviceId, size_t numElements)
{
    if (IsTraceEnabled())
    {
        auto freeAndTotalMemory = GetFreeAndTotalMemoryInMBs(deviceId);
        fprintf(stderr, "Allocating array<%s> (NumElements = %d) on DeviceId = %d; GPU Memory Free = %d MB of %d MB\n", typeid(AllocatedElemType).name(), (int)numElements, (int)deviceId, (int)freeAndTotalMemory.first, (int)freeAndTotalMemory.second);
        Microsoft::MSR::CNTK::DebugUtil::PrintCallStack();
    }

    AllocatedElemType* deviceBufferPtr = AllocateNoTrace<AllocatedElemType>(deviceId, numElements);
    
    if (IsTraceEnabled())
    {
        fprintf(stderr, "Allocated DeviceData = %p\n", (void*)deviceBufferPtr);
    }

    return deviceBufferPtr;
}

template <typename AllocatedElemType>
void TracingGPUMemoryAllocator::Free(int deviceId, AllocatedElemType* bufferPtr, bool ignoreCUDARetCode /*= false*/)
{
    PrepareDevice(deviceId);
    if (ignoreCUDARetCode)
        cudaFree((void*) bufferPtr);
    else
        CUDA_CALL(cudaFree((void*) bufferPtr));

    if (IsTraceEnabled())
    {
        auto freeAndTotalMemory = GetFreeAndTotalMemoryInMBs(deviceId);
        fprintf(stderr, "Freed buffer<%s> DeviceData = %p on DeviceId = %d; GPU Memory Free = %d MB of %d MB\n", typeid(AllocatedElemType).name(), (void*) bufferPtr, (int) deviceId, (int) freeAndTotalMemory.first, (int) freeAndTotalMemory.second);
        Microsoft::MSR::CNTK::DebugUtil::PrintCallStack();
    }
}

template <typename AllocatedElemType>
AllocatedElemType* TracingGPUMemoryAllocator::AllocateNoTrace(int deviceId, size_t numElements)
{
    AllocatedElemType* deviceBufferPtr;

    PrepareDevice(deviceId);
    CUDA_CALL(cudaMalloc((void**) &deviceBufferPtr, sizeof(AllocatedElemType) * numElements));

    return deviceBufferPtr;
}

std::pair<size_t, size_t> TracingGPUMemoryAllocator::GetFreeAndTotalMemoryInMBs(int deviceId)
{
    PrepareDevice(deviceId);

    size_t free, total;
    CUDA_CALL(cudaMemGetInfo(&free, &total));

    size_t numBytesPerMB = 1 << 20;
    return {free / numBytesPerMB, total / numBytesPerMB};
}

// PrepareDevice - Setup the correct cuda context for an operation
// deviceId - the device on which the operation will take place
void PrepareDevice(DEVICEID_TYPE deviceId)
{
    static DEVICEID_TYPE currentDevice = DEVICEID_NOTYETDETERMINED;
    // and if we last set the device to be this device we are good
    if (deviceId == currentDevice)
        return;
    CUDA_CALL(cudaSetDevice(deviceId));
    currentDevice = deviceId;
}

#pragma region DeviceBoundNumber class

template <class ElemType>
DeviceBoundNumber<ElemType>::DeviceBoundNumber(const DeviceBoundNumber<ElemType>& /*deepCopy*/)
{
    NOT_IMPLEMENTED;
}

template <class ElemType>
DeviceBoundNumber<ElemType>::DeviceBoundNumber(DeviceBoundNumber<ElemType>&& shallowCopy)
{
    ShallowCopyFrom(shallowCopy.m_data, shallowCopy.m_computeDevice);
    shallowCopy.m_data = NULL;
}

template <class ElemType>
void DeviceBoundNumber<ElemType>::ShallowCopyFrom(ElemType* newVal, int newValsDevceId)
{
    m_computeDevice = newValsDevceId;
    m_data = newVal;
}

template <class ElemType>
DeviceBoundNumber<ElemType>::~DeviceBoundNumber()
{
    if (m_data != NULL)
    {
        if (m_computeDevice < 0)
        {
            delete m_data;
            m_data = NULL;
        }
        else
        {
            TracingGPUMemoryAllocator::Free<ElemType>(m_computeDevice, m_data);
        }
    }
}

#pragma endregion DeviceBoundNumber class

#pragma region Helper functions
template <class ElemType>
cublasHandle_t _initCUBLAS(int devId)
{
    PrepareDevice((DEVICEID_TYPE) devId);
    cublasHandle_t cuHandle;
    CUBLAS_CALL(cublasCreate(&cuHandle));
    return cuHandle;
}

template <class ElemType>
void GPUMatrix<ElemType>::SetDevice(DEVICEID_TYPE deviceId)
{
    assert(deviceId >= 0);
    CUDA_CALL(cudaSetDevice(deviceId));
}

// PrepareDevice - Setup the correct cuda context for an operation
// deviceId - the device on which the operation will take place
//            defaults to -1, which means use matrices current device
template <class ElemType>
DEVICEID_TYPE GPUMatrix<ElemType>::PrepareDevice(DEVICEID_TYPE deviceId /*=-1*/) const
{
    // if default value use current compute device
    DEVICEID_TYPE newId = deviceId >= 0 ? deviceId : GetComputeDeviceId();

    Microsoft::MSR::CNTK::PrepareDevice(newId);
    return newId;
}

template <class ElemType>
ElemType* GPUMatrix<ElemType>::CopyToArray() const
{
    size_t numElements = GetNumElements();
    if (numElements != 0)
    {
        PrepareDevice();
        ElemType* pArray = new ElemType[numElements];
        CUDA_CALL(cudaMemcpy(pArray, Data(), sizeof(ElemType) * m_numRows * m_numCols, cudaMemcpyDeviceToHost));
        return pArray;
    }
    else
    {
        return NULL;
    }
}

//memory will be allocated by the callee if not enough but need to be deleted by the caller after it's done
//return number of elements copied
template <class ElemType>
size_t GPUMatrix<ElemType>::CopyToArray(ElemType*& arrayCopyTo, size_t& currentArraySize) const
{
    size_t numElements = GetNumElements();

    if (numElements > currentArraySize)
    {
        delete arrayCopyTo;
        arrayCopyTo = new ElemType[numElements];
        currentArraySize = numElements;
    }

    if (numElements != 0)
    {
        PrepareDevice();
        CUDA_CALL(cudaMemcpy(arrayCopyTo, Data(), sizeof(ElemType) * numElements, cudaMemcpyDeviceToHost));
    }

    return numElements;
}

template <typename ElemType>
void GPUMatrix<ElemType>::CopySection(size_t numRows, size_t numCols, ElemType* dst, size_t colStride) const
{
    CUBLAS_CALL(cublasGetMatrix((int) numRows, (int) numCols, sizeof(ElemType),
                                Data(), (int) GetNumRows(), dst, (int) colStride));
}
template <class ElemType>
void GPUMatrix<ElemType>::ChangeDeviceTo(DEVICEID_TYPE to_id)
{
    if (to_id == CPUDEVICE)
        LogicError("to_id must be valid GPU");
    if (GetComputeDeviceId() == to_id)
        return;

    ElemType* d_dst = TracingGPUMemoryAllocator::Allocate<ElemType>(to_id, m_numRows, m_numCols);

    SetSizeAllocated(m_numRows * m_numCols);

    // check to make sure we have something to copy (on init we often have zero sized allocations)
    if (GetSizeAllocated() > 0)
    {
        // first try peer access
        int canAccessPeer = false;
        CUDA_CALL(cudaDeviceCanAccessPeer(&canAccessPeer, to_id, GetComputeDeviceId()));
        if (canAccessPeer)
        {
            cudaError_t cudaStatus = cudaDeviceEnablePeerAccess(GetComputeDeviceId(), 0);
            if (cudaStatus != cudaErrorPeerAccessAlreadyEnabled)
            {
                CUDA_CALL(cudaStatus);
            }
            CUDA_CALL(cudaMemcpyPeer(d_dst, to_id, Data(), GetComputeDeviceId(), sizeof(ElemType) * m_numRows * m_numCols));
        }
        else
        {
            // peer access didn't work, just copy normal
            // make this more efficient by keeping some buffers available for each copy
            ElemType* h_dst = NULL;
            PrepareDevice();
            CUDA_CALL(cudaMallocHost((void**) &h_dst, sizeof(ElemType) * m_numRows * m_numCols));
            CUDA_CALL(cudaMemcpy(h_dst, Data(), sizeof(ElemType) * m_numRows * m_numCols, cudaMemcpyDeviceToHost));
            PrepareDevice((DEVICEID_TYPE) to_id);
            CUDA_CALL(cudaMemcpy(d_dst, h_dst, sizeof(ElemType) * m_numRows * m_numCols, cudaMemcpyHostToDevice));
            CUDA_CALL(cudaFreeHost(h_dst));
        }
    }

    TracingGPUMemoryAllocator::Free<ElemType>(GetComputeDeviceId(), Buffer());
    SetBuffer(d_dst, m_numRows * m_numCols * sizeof(ElemType));

    PrepareDevice((DEVICEID_TYPE) to_id);
    SetComputeDeviceId(to_id);
}

template <class ElemType>
void GPUMatrix<ElemType>::performElementWiseFunction(ElementWiseOperator kind, const ElemType* src)
{
    PrepareDevice();
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    switch (kind)
    {
    case ElementWiseOperator::opSigmoid:
    {
        PROFILE_CUDA_STREAM("_elementWiseSigmoidOnCuda", t_stream);
        _elementWiseSigmoidOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    case ElementWiseOperator::opTanh:
    {
        PROFILE_CUDA_STREAM("_elementWiseTanhOnCuda", t_stream);
        _elementWiseTanhOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    case ElementWiseOperator::opSqrt:
    {
        PROFILE_CUDA_STREAM("_elementWiseSqrtOnCuda", t_stream);
        _elementWiseSqrtOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    case ElementWiseOperator::opExp:
    {
        PROFILE_CUDA_STREAM("_elementWiseExpOnCuda", t_stream);
        _elementWiseExpOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    case ElementWiseOperator::opLog:
    {
        PROFILE_CUDA_STREAM("_elementWiseLogOnCuda", t_stream);
        _elementWiseLogOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    case ElementWiseOperator::opAbs:
    {
        PROFILE_CUDA_STREAM("_elementWiseAbsOnCuda", t_stream);
        _elementWiseAbsOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    case ElementWiseOperator::opLinearRectifierDerivative:
    {
        PROFILE_CUDA_STREAM("_elementWiseLinRectDerivativeOnCuda", t_stream);
        _elementWiseLinRectDerivativeOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    case ElementWiseOperator::opCosine:
    {
        PROFILE_CUDA_STREAM("_elementWiseCosineOnCuda", t_stream);
        _elementWiseCosineOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    case ElementWiseOperator::opNegativeSine:
    {
        PROFILE_CUDA_STREAM("_elementWiseNegativeSineOnCuda", t_stream);
        _elementWiseNegativeSineOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    case ElementWiseOperator::opSigmoidDerivative:
    {
        PROFILE_CUDA_STREAM("_elementWiseSigmoidDerivativeOnCuda", t_stream);
        _elementWiseSigmoidDerivativeOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(src, Data(), N);
        break;
    }
    default: LogicError("performElementWiseFunction: unexpected op code %d", (int)kind);
    }
}

#pragma endregion Helper functions

#pragma region Constructors and Destructor

// should only be used by constructors
template <class ElemType>
void GPUMatrix<ElemType>::ZeroInit(int deviceId)
{
    BaseMatrix<ElemType>::ZeroInit();
    SetComputeDeviceId(deviceId);
}

template <class ElemType>
GPUMatrix<ElemType>::GPUMatrix(int deviceId)
{
    ZeroInit(deviceId);
};

template <class ElemType>
GPUMatrix<ElemType>::GPUMatrix(const size_t numRows, const size_t numCols, int deviceId)
{
    ZeroInit(deviceId);
    m_numRows = numRows;
    m_numCols = numCols;
    SetSizeAllocated(GetNumElements());

    if (GetNumElements() != 0)
    {
        SetBuffer(TracingGPUMemoryAllocator::Allocate<ElemType>(GetComputeDeviceId(), m_numRows, m_numCols), GetNumElements() * sizeof(ElemType));
        CUDA_CALL(cudaMemset(Buffer(), 0, sizeof(ElemType) * GetSizeAllocated()));
    }
};

template <class ElemType>
GPUMatrix<ElemType>::GPUMatrix(const size_t numRows, const size_t numCols, int deviceId, ElemType* pArray, const size_t matrixFlags)
{
    ZeroInit(deviceId);
    SetValue(numRows, numCols, deviceId, pArray, matrixFlags);
};

template <class ElemType>
GPUMatrix<ElemType>::GPUMatrix(const GPUMatrix<ElemType>& deepCopyFrom)
{
    ZeroInit();
	SetValue(deepCopyFrom);
}

template <class ElemType>
GPUMatrix<ElemType>::GPUMatrix(GPUMatrix<ElemType>&& moveFrom)
{
    ShallowCopyFrom(moveFrom);
    moveFrom.ZeroValues();
}

//assignment operator, deep copy
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::operator=(const GPUMatrix<ElemType>& deepCopyFrom)
{
    if (this != &deepCopyFrom)
    {
        SetValue(deepCopyFrom);
    }
    return *this;
}

//move assignment operator, shallow copy
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::operator=(GPUMatrix<ElemType>&& moveFrom)
{
    if (this != &moveFrom)
    {
        ShallowCopyFrom(moveFrom);
        moveFrom.ZeroValues();
    }
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>::~GPUMatrix(void)
{
}

// TODO: This should be in the storage object.
// Clear will clear your storage, zeroinit just drops it on the ground.
template <class ElemType>
void GPUMatrix<ElemType>::Clear()
{
    VerifyWritable(__func__);
    //if (OwnBuffer() && m_pArray != NULL)
    if (m_sob != nullptr)
    {
        if (GetComputeDeviceId()>= 0)
        {
            // BUG: We do not check the CUDA return code for cudaFree here since this may get called
            // during processExit when cudaFree will fail. The destruction of CUDA objects during
            // process exit must be avoided
            ReleaseStorageMemory();
        }
    }

    ZeroInit(GetComputeDeviceId());
}
#pragma endregion Constructors and Destructor

template <class ElemType>
std::unique_ptr<GPUMatrix<ElemType>> GPUMatrix<ElemType>::GetOrCreateWorkspace() const
{
    // REVIEW alexeyk: not thread-safe, fine for now.
    if (m_workspace == nullptr)
        m_workspace = std::make_unique<conc_stack<std::unique_ptr<GPUMatrix<ElemType>>>>();
    assert(m_workspace != nullptr);
    auto deviceId = GetComputeDeviceId();
    return m_workspace->pop_or_create([deviceId]()
                                      {
                                          return std::make_unique<GPUMatrix<ElemType>>(deviceId);
                                      });
}

template <class ElemType>
void GPUMatrix<ElemType>::ReleaseWorkspace(std::unique_ptr<GPUMatrix<ElemType>> src) const
{
    assert(m_workspace != nullptr);
    m_workspace->push(std::move(src));
}

#pragma region Basic Operators
template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::ColumnSlice(size_t startColumn, size_t numCols) const
{
    if (startColumn + numCols > GetNumCols())
        InvalidArgument("The slice (%d+%d) is out of range of the source matrix (%d).", (int) startColumn, (int) numCols, (int) GetNumCols());

    GPUMatrix<ElemType> slice(GetComputeDeviceId());

    slice.ShallowCopyFrom(*this);
    slice.m_numCols = numCols;
    slice.m_sliceViewOffset = m_sliceViewOffset + startColumn * GetNumRows();

    return slice;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignColumnSlice(const GPUMatrix<ElemType>& fromMatrix, size_t startColumn, size_t numCols)
{
    if (numCols == 0)
        LogicError("The slice cannot have 0 columns.");

    if (startColumn + numCols > fromMatrix.GetNumCols())
        InvalidArgument("The slice (%d+%d) is out of range of the source matrix (%d).", (int) startColumn, (int) numCols, (int) fromMatrix.GetNumCols());

    Clear();

    ShallowCopyFrom(fromMatrix);
    m_numCols = numCols;
    m_sliceViewOffset = fromMatrix.m_sliceViewOffset + startColumn * GetNumRows();

    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::SetColumnSlice(const GPUMatrix<ElemType>& fromMatrix, size_t startColumn, size_t numCols)
{
    if (startColumn + numCols > GetNumCols())
        LogicError("The slice is out of range of the destination matrix.");
    if (numCols > fromMatrix.GetNumCols())
        InvalidArgument("The slice (%d) is out of range of the source matrix (%d).", (int) numCols, (int) fromMatrix.GetNumCols());
    if (m_numRows != fromMatrix.m_numRows)
        LogicError("The number of rows in source and destination matrices do not match");

    if (m_numRows * numCols > 0) // TODO: remove if unnecessary
        CUDA_CALL(cudaMemcpy(Data() + m_sliceViewOffset + LocateColumn(startColumn), fromMatrix.Data(), sizeof(ElemType) * m_numRows * numCols, cudaMemcpyDeviceToDevice));
    return *this;
}

template <class ElemType>
void GPUMatrix<ElemType>::CopyColumnsStrided(const GPUMatrix<ElemType>& fromMatrix, size_t numCols, size_t srcNumColsStride, size_t destNumColsStride)
{
    if ((((numCols - 1) * srcNumColsStride) + 1) > fromMatrix.m_numCols)
        LogicError("The numCols to copy and srcNumColsStride specified is out of range of the source matrix.");
    if ((((numCols - 1) * destNumColsStride) + 1) > m_numCols)
        LogicError("The numCols to copy and srcNumColsStride specified is out of range of the destination matrix.");
    if (m_numRows != fromMatrix.m_numRows)
        LogicError("The number of rows in source and destination matrices do not match");

    if ((m_numRows * numCols) > 0)
    {
        // Launch a kernel to do the strided copy
        CUDA_LONG N = (CUDA_LONG)(m_numRows * numCols);
        int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
        PrepareDevice();
        PROFILE_CUDA_STREAM("_copyColumnsStrided", t_stream);
        _copyColumnsStrided<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), fromMatrix.Data(), N, (CUDA_LONG) m_numRows, (CUDA_LONG) destNumColsStride, (CUDA_LONG) srcNumColsStride);
    }
}

//for each column of a, we assign all rows of a to this starting from startIndex
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignToRowSliceValuesOf(const GPUMatrix<ElemType>& a, const size_t startIndex, const size_t numRows)
{
    if (a.IsEmpty())
        LogicError("AddToRowSliceValuesOf: input matrix a is empty.");

    if (a.GetNumRows() != numRows)
        LogicError("AddToRowSliceValuesOf: a.GetNumRows() != numRows.");

    if (startIndex + numRows > GetNumRows())
        LogicError("AddToRowSliceValuesOf: startIndex + numRows exceeds GetNumRows().");

    if (a.GetNumCols() != GetNumCols())
        LogicError("AddToRowSliceValuesOf: columns does not match.");

    CUDA_LONG N = (CUDA_LONG) a.GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_assignToRowSliceValuesOf", t_stream);
    _assignToRowSliceValuesOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, (CUDA_LONG) startIndex, (CUDA_LONG) GetNumRows(), (CUDA_LONG) a.GetNumRows());
    return *this;
}

//for each column of a, we assign numRows starting from startIndex to this
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignRowSliceValuesOf(const GPUMatrix<ElemType>& a, const size_t startIndex, const size_t numRows)
{
    if (a.IsEmpty())
        LogicError("AssignRowSliceValuesOf: input matrix a is empty.");

    if (startIndex + numRows > a.GetNumRows())
        LogicError("AssignRowSliceValuesOf: startIndex + numRows exceeds a.GetNumRows().");

    RequireSize(numRows, a.GetNumCols());

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_assignRowSliceValuesOf", t_stream);
    _assignRowSliceValuesOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, (CUDA_LONG) startIndex, (CUDA_LONG) numRows, (CUDA_LONG) a.GetNumRows());
    return *this;
}

//for the row slice of this starting from startIndex we add a to it.
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddToRowSliceValuesOf(const GPUMatrix<ElemType>& a, const size_t startIndex, const size_t numRows)
{
    if (a.IsEmpty())
        LogicError("AddToRowSliceValuesOf: input matrix a is empty.");

    if (a.GetNumRows() != numRows)
        LogicError("AddToRowSliceValuesOf: a.GetNumRows() != numRows.");

    if (startIndex + numRows > GetNumRows())
        LogicError("AddToRowSliceValuesOf: startIndex + numRows exceeds GetNumRows().");

    if (a.GetNumCols() != GetNumCols())
        LogicError("AddToRowSliceValuesOf: columns does not match.");

    CUDA_LONG N = (CUDA_LONG) a.GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_addToRowSliceValuesOf", t_stream);
    _addToRowSliceValuesOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, (CUDA_LONG) startIndex, (CUDA_LONG) GetNumRows(), (CUDA_LONG) a.GetNumRows());
    return *this;
}

//for each column of this, we add row slice of a starting from startIndex
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddWithRowSliceValuesOf(const GPUMatrix<ElemType>& a, const size_t startIndex, const size_t numRows)
{
    if (a.IsEmpty())
        LogicError("AddWithRowSliceValuesOf: input matrix a is empty.");

    if (GetNumRows() != numRows)
        LogicError("AddWithRowSliceValuesOf: GetNumRows() != numRows.");

    if (startIndex + numRows > a.GetNumRows())
        LogicError("AddWithRowSliceValuesOf: startIndex + numRows exceeds a.GetNumRows().");

    if (a.GetNumCols() != GetNumCols())
        LogicError("AddWithRowSliceValuesOf: columns does not match.");

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_addWithRowSliceValuesOf", t_stream);
    _addWithRowSliceValuesOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, (CUDA_LONG) startIndex, (CUDA_LONG) GetNumRows(), (CUDA_LONG) a.GetNumRows());
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::Diagonal() const
{
    size_t m = GetNumRows();
    size_t n = GetNumCols();
    if (m != n)
        LogicError("Diagonal can be called only for square matrix. (rows=%d, cols=%d)", (int) m, (int) n);

    GPUMatrix<ElemType> diag(1, n, GetComputeDeviceId());

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_assignToDiagonalValuesOf", t_stream);
    _assignToDiagonalValuesOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(diag.Data(), Data(), N, (CUDA_LONG) n);
    return diag;
}

// c = c - 1.0 for a specific position
template <class ElemType>
void GPUMatrix<ElemType>::MinusOneAt(GPUMatrix<ElemType>& c, const size_t position)
{
    assert(position < c.GetNumElements());

    CUDA_LONG n = (CUDA_LONG) c.GetNumElements();
    CUDA_LONG p = (CUDA_LONG) position;

    int blocksPerGrid = (int) ceil(1.0 * n / GridDim::maxThreadsPerBlock);
    c.PrepareDevice();
    PROFILE_CUDA_STREAM("_minusOneAt", t_stream);
    _minusOneAt<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(c.Data(), p, n);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignRepeatOf(const GPUMatrix<ElemType>& a, const size_t numRowRepeats, const size_t numColRepeats)
{
    if (this == &a)
        LogicError("AssignRepeatOf: a is the same as [this]. Does not support inplace repeat.");

    if (a.IsEmpty())
        LogicError("AssignRepeatOf: Matrix a is empty.");

    RequireSize(a.GetNumRows() * numRowRepeats, a.GetNumCols() * numColRepeats);

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    CUDA_LONG n = (CUDA_LONG) a.GetNumCols(), m = (CUDA_LONG) a.GetNumRows();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_assignRepeatOf", t_stream);
    _assignRepeatOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, m, n, (CUDA_LONG) GetNumRows());
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddToRowRepeatValuesOf(const GPUMatrix<ElemType>& a, const size_t numRepeats)
{
    if (a.IsEmpty())
        LogicError("AddToRowRepeatValuesOf: input matrix a is empty.");

    if (a.GetNumRows() != GetNumRows() * numRepeats)
        LogicError("AddToRowSliceValuesOf: a.GetNumRows() != GetNumRows() * numRepeats.");

    RequireSize(a.GetNumRows() / numRepeats, a.GetNumCols());

    CUDA_LONG N = (CUDA_LONG) a.GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_addToRowRepeatValuesOf", t_stream);
    _addToRowRepeatValuesOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, (CUDA_LONG) a.GetNumRows(), (CUDA_LONG) a.GetNumCols(), (CUDA_LONG) GetNumRows());
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignPositiveAndShiftedNegSample(const GPUMatrix<ElemType>& a, const size_t posNumber, const size_t negNumber, const size_t shiftNumber)
{
    if (this == &a)
        LogicError("AssignPositiveAndShiftedNegSample: a is the same as [this]. Does not support inplace assignment.");

    if (a.IsEmpty())
        LogicError("AssignPositiveAndShiftedNegSample: Matrix a is empty.");

    RequireSize(a.GetNumRows() * (posNumber + negNumber), a.GetNumCols());

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    CUDA_LONG n = (CUDA_LONG) a.GetNumCols(), m = (CUDA_LONG) a.GetNumRows();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_assignPositiveAndShiftedNegSample", t_stream);
    _assignPositiveAndShiftedNegSample<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, m, n, (CUDA_LONG) GetNumRows(), posNumber, shiftNumber);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddFoldedPositiveAndShiftedNegSample(const GPUMatrix<ElemType>& a, const size_t posNumber, const size_t negNumber, const size_t shiftNumber)
{
    if (this == &a)
        LogicError("AddFoldedPositiveAndShiftedNegSample: a is the same as [this]. Does not support inplace assignment.");

    if (a.IsEmpty())
        LogicError("AddFoldedPositiveAndShiftedNegSample: Matrix a is empty.");

    if (a.GetNumRows() != GetNumRows() * (posNumber + negNumber) || a.GetNumCols() != GetNumCols())
        LogicError("AddFoldedPositiveAndShiftedNegSample: dimensions mismatch.");

    CUDA_LONG N = (CUDA_LONG) a.GetNumElements();
    CUDA_LONG n = (CUDA_LONG) a.GetNumCols(), m = (CUDA_LONG) a.GetNumRows();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_addFoldedPositiveAndShiftedNegSample", t_stream);
    _addFoldedPositiveAndShiftedNegSample<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, m, n, (CUDA_LONG) GetNumRows(), posNumber, shiftNumber);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::Transpose() const
{
    if (IsEmpty())
        LogicError("Transpose: Matrix is empty.");

    GPUMatrix<ElemType> c(GetComputeDeviceId());
    c.AssignTransposeOf(*this);
    return c;
}

// GetCublasHandle - get a cublas handle for the given GPU, should only need one per GPU
// computeDevice - The compute device for which the cublas handle is desired
// returns: cublas handle
// NOTE: we currently don't bother to ever free the CUBLAS handle, it will be freed automatically by CUDA when the process ends
template <class ElemType>
cublasHandle_t GPUMatrix<ElemType>::GetCublasHandle(int computeDevice /*=-1*/)
{
    // if the compute device is not passed, get the current device from CUDA
    if (computeDevice < 0)
        cudaGetDevice(&computeDevice);

    if (computeDevice < 0 || computeDevice >= MaxGpus)
        LogicError("GetCublasHandle: Maximum GPU exceeded");
    cublasHandle_t cuHandle = s_cuHandle[computeDevice];
    if (cuHandle == NULL)
    {
        s_cuHandle[computeDevice] = cuHandle = _initCUBLAS<ElemType>(computeDevice);
    }
    CUBLAS_CALL(cublasSetStream(cuHandle, t_stream));

    return cuHandle;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignTransposeOf(const GPUMatrix<ElemType>& a)
{
    if (this == &a)
        LogicError("AssignTransposeOf: a is the same as [this]. Does not support inplace transpose.");

    if (a.IsEmpty())
        LogicError("AssignTransposeOf: Matrix a is empty.");

    if (GetNumRows() != a.GetNumCols() || GetNumCols() != a.GetNumRows())
        RequireSize(a.GetNumCols(), a.GetNumRows());

    cublasHandle_t cuHandle = GetCublasHandle(a.GetComputeDeviceId());
    cublasOperation_t transA = CUBLAS_OP_T;
    cublasOperation_t transB = CUBLAS_OP_T;
    int m = (int) a.m_numCols;
    int n = (int) a.m_numRows;
    ElemType alpha = 1;
    ElemType beta = 0;
    cublasStatus_t st;
    if (sizeof(ElemType) == sizeof(float))
    {
        PROFILE_CUDA_STREAM("cublasSgeam", t_stream);
        st = cublasSgeam(cuHandle, transA, transB, m, n, reinterpret_cast<float*>(&alpha), reinterpret_cast<float*>(a.Data()), (int)a.m_numRows, reinterpret_cast<float*>(&beta), reinterpret_cast<float*>(a.Data()), (int)a.m_numRows, reinterpret_cast<float*>(Data()), (int)m_numRows);
    }
    else if (sizeof(ElemType) == sizeof(double))
    {
        PROFILE_CUDA_STREAM("cublasDgeam", t_stream);
        st = cublasDgeam(cuHandle, transA, transB, m, n, reinterpret_cast<double*>(&alpha), reinterpret_cast<double*>(a.Data()), (int)a.m_numRows, reinterpret_cast<double*>(&beta), reinterpret_cast<double*>(a.Data()), (int)a.m_numRows, reinterpret_cast<double*>(Data()), (int)m_numRows);
    }
    else
        RuntimeError("Unsupported template argument in GPUMatrix");
    if (st != CUBLAS_STATUS_SUCCESS)
        RuntimeError("AssignTransposeOf failed");
    m_numRows = a.m_numCols;
    m_numCols = a.m_numRows;
    return *this;
}

template <class ElemType>
__global__ void _doGatherColumnsOf(ElemType* us, size_t usStride, const ElemType beta, const ElemType* idx, size_t idxStride, const ElemType* a, size_t aStride, size_t aCols, const ElemType alpha, CUDA_LONG numElements)
{
    CUDA_LONG id = GridDim::GetLinearThreadId();
    if (id >= numElements) // note: there are no __syncthread() calls inside
        return;

    // id = i + jOut * usStride;
    // Each thread processes one element of the output matrix.
    CUDA_LONG i    = id % usStride; // row index into 'us' and 'a'
    CUDA_LONG jOut = id / usStride; // col index into 'us' and 'idx'

    auto jInF = idx[jOut * idxStride]; // this is the column we need to get
    if (jInF < 0)                      // negative index means gap
        return;
    size_t jIn = (size_t)jInF;
    if (jIn >= aCols)
        return; // actually a failure

    const ElemType&  ra = a[    i + jIn  *  aStride  ];
    ElemType&       rus = us[id/*i + jOut * usStride*/];

    ElemType res = ra * alpha;
    if (beta != 0)
        res += rus * beta;
    rus = res;
}

// *this[:,j] = a[:,idx[j]] * alpha + *this[:,j] * beta
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::DoGatherColumnsOf(ElemType beta, const GPUMatrix<ElemType>& idx, const GPUMatrix<ElemType>& a, ElemType alpha)
{
    if (idx.GetNumRows() != 1) // index is 1-dimensional only
        InvalidArgument("DoGatherColumnsOf: Map must be a row vector.");

    if (beta == 0)
        RequireSize(a.GetNumRows(), idx.GetNumCols()); // output has same column format as a, but number of columns comes from idx
    else
        VerifySize(a.GetNumRows(), idx.GetNumCols());

    if (idx.GetComputeDeviceId() != a.GetComputeDeviceId() || GetComputeDeviceId() != a.GetComputeDeviceId())
        InvalidArgument("All matrices must be on the same GPU");
    a.PrepareDevice();

    // launch the kernel
    CUDA_LONG NN = (CUDA_LONG)GetNumElements(); // linear space identifying each individual input element
    
    GridDim grid(NN);
    PROFILE_CUDA_STREAM("_doGatherColumnsOf", t_stream);
    _doGatherColumnsOf<ElemType><<<grid.m_blocksPerGrid, grid.m_threadsPerBlock, 0, t_stream>>>(Data(), GetNumRows(), beta, idx.Data(), idx.GetNumRows(), a.Data(), a.GetNumRows(), a.GetNumCols(), alpha, grid.m_N);

    // Note: The following fails silently (no error, immediate or delayed) for numcols = 10000 under CUDA 7.0.
    //_doGatherColumnsOf<ElemType><<<GetNumCols(), GetNumRows(), 0, t_stream>>>(Data(), GetNumRows(), beta, idx.Data(), idx.GetNumRows(), a.Data(), a.GetNumRows(), a.GetNumCols(), alpha);

    return *this;
}

template <class ElemType>
__global__ void _doScatterColumnsOf(ElemType* us, size_t usStride, size_t usCols, const ElemType* idx, size_t idxStride, const ElemType* a, size_t aStride, const ElemType alpha, CUDA_LONG numElements)
{
    CUDA_LONG id = GridDim::GetLinearThreadId();
    if (id >= numElements) // note: there are no __syncthread() calls inside
        return;

    // id = i + jIn  *  aStride
    // Each thread processes one element of a
    CUDA_LONG i   = id % aStride; // row index into 'a' and 'us'
    CUDA_LONG jIn = id / aStride; // col index into 'a' and 'idx'

    auto jOutF = idx[jIn * idxStride]; // this is the column we copy/add into
    if (jOutF < 0)                     // negative index means gap
        return;
    size_t jOut = (size_t)jOutF;
    if (jOut >= usCols)
        return; // actually a failure  --TODO: This should not be necessary. Why is it?

    const ElemType&  ra =  a[id/*i + jIn  *  aStride*/];
    ElemType&       rus = us[    i + jOut * usStride  ];

    ElemType res = ra * alpha;
    if (res != 0)             // avoid memory conflict if e.g. an entire column has no gradient
        atomicAdd(&rus, res); // rus += res;
    // Note: atomicAdd() is supposed to be fast in case of no conflict (the simple case of Scatter())
}

// little helper for debugging
template <class ElemType>
static void Peek(const GPUMatrix<ElemType>& m, const char* which)
{
    size_t rows = m.GetNumRows();
    size_t cols = m.GetNumCols();
    ElemType buf[10000] = { 0 };
    size_t n = min(rows * cols, _countof(buf));
    CUDA_CALL(cudaMemcpy(buf, m.Data(), sizeof(ElemType) * n, cudaMemcpyDeviceToHost));
    UNUSED(which); UNUSED(rows); UNUSED(cols); sin(1.0f); // set breakpoint here
    //CUDA_CALL(cudaMemcpy(const_cast<ElemType*>(m.Data()), buf, sizeof(ElemType) * n, cudaMemcpyHostToDevice));
}

// *this[:,idx[j]] = a[:,j] * alpha + *this[:,idx[j]] * beta
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::DoScatterColumnsOf(ElemType beta, const GPUMatrix<ElemType>& idx, const GPUMatrix<ElemType>& a, ElemType alpha)
{
    if (idx.GetNumRows() != 1) // index is 1-dimensional only
        InvalidArgument("DoScatterColumnsOf: Map must be a row vector.");
    if (idx.GetNumCols() != a.GetNumCols())
        InvalidArgument("DoScatterColumnsOf: Map must have width of input vector.");
    if (a.GetNumRows() != GetNumRows())
        InvalidArgument("DoScatterColumnsOf: Output must have same height as input vector.");

    if (idx.GetComputeDeviceId() != a.GetComputeDeviceId() || GetComputeDeviceId() != a.GetComputeDeviceId())
        InvalidArgument("All matrices must be on the same GPU");
    a.PrepareDevice();

    auto& us = *this;

    // pre-scale with beta upfront
    // Scatter may add more than one source column to the same target, so we must pre-scale with beta, and then just keep adding.
    Scale(beta, us); // if beta is 0, then this will be a memset()

    // launch the kernel
    CUDA_LONG NN = (CUDA_LONG)(a.GetNumElements()); // linear space identifying each individual input element
    GridDim grid(NN);
    PROFILE_CUDA_STREAM("_doScatterColumnsOf", t_stream);
    _doScatterColumnsOf<ElemType><<<grid.m_blocksPerGrid, grid.m_threadsPerBlock, 0, t_stream>>>(Data(), GetNumRows(), GetNumCols(), idx.Data(), idx.GetNumRows(), a.Data(), a.GetNumRows(), alpha, NN);

    //_doScatterColumnsOf<ElemType><<<a.GetNumCols(), a.GetNumRows(), 0, t_stream>>>(Data(), GetNumRows(), GetNumCols(), idx.Data(), idx.GetNumRows(), a.Data(), a.GetNumRows(), alpha, NN);

    return *this;
}

template <class ElemType>
void GPUMatrix<ElemType>::SetValue(const ElemType v)
{
    if (IsEmpty())
        return;

    CUDA_LONG N = (CUDA_LONG) GetNumElements();

    // Check if value is zero, which can be set using cudaMemset
    bool isZero = true;
    const char* valArray = reinterpret_cast<const char*>(&v);

    for (int i = 0; i < sizeof(ElemType); i++)
    {
        if (valArray[i] != 0)
        {
            isZero = false;
            break;
        }
    }

    if (isZero)
    {
        CUDA_CALL(cudaMemset(Data(), 0, N * sizeof(ElemType)));
    }
    else
    {
        int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
        PrepareDevice();
        PROFILE_CUDA_STREAM("_setValue", t_stream);
        _setValue<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), v, N);
    }
}

template <class ElemType>
void GPUMatrix<ElemType>::SetValue(const ElemType* d_v) // d_v is pointer to the the value in GPU memory
{
    if (IsEmpty())
        LogicError("SetValue: Matrix is empty.");

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_setValue", t_stream);
    _setValue<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), d_v, N);
}

template <class ElemType>
void GPUMatrix<ElemType>::MaskColumnsValue(const GPUMatrix<char>& columnsMask, ElemType val)
{
    if (GetNumCols() != columnsMask.GetNumCols())
        RuntimeError("Matrix and column mask must have equal number of columns");

    if (GetComputeDeviceId() != columnsMask.GetComputeDeviceId())
        RuntimeError("Matrix and column mask must be on the same device");

    int blocksPerGrid = (int) GetNumCols();
    PrepareDevice();
    PROFILE_CUDA_STREAM("_maskColumnsValue", t_stream);
    _maskColumnsValue<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), columnsMask.Data(), (CUDA_LONG) GetNumCols(), (CUDA_LONG) GetNumRows(), val);
}

template <class ElemType>
void GPUMatrix<ElemType>::SetColumn(const ElemType* colPointer, size_t colInd)
{
    if (IsEmpty())
        LogicError("SetValue: Matrix is empty.");
    if (colPointer == NULL)
        return;
    CUDA_CALL(cudaMemcpy(Data() + LocateColumn(colInd), colPointer, sizeof(ElemType) * m_numRows, cudaMemcpyHostToDevice));
}

template <class ElemType>
void GPUMatrix<ElemType>::SetColumn(const GPUMatrix<ElemType>& valMat, size_t colInd)
{
    if (IsEmpty())
        LogicError("SetColumn: Matrix is empty.");
    if (valMat.GetNumCols() != 1)
        LogicError("SetColumn: only support one column matrix now.");
    CUDA_CALL(cudaMemcpy(Data() + LocateColumn(colInd), valMat.Data(), sizeof(ElemType) * m_numRows, cudaMemcpyDeviceToDevice));
}

template <class ElemType>
void GPUMatrix<ElemType>::SetValue(const GPUMatrix<ElemType>& deepCopyFrom)
{
    if (this == &deepCopyFrom)
        return;

	SetValue(deepCopyFrom.GetNumRows(), deepCopyFrom.GetNumCols(), deepCopyFrom.GetComputeDeviceId(), deepCopyFrom.Data(), matrixFlagSetValueOnDevice);
}

template <class ElemType>
void GPUMatrix<ElemType>::SetValue(const size_t numRows, const size_t numCols, int deviceId, ElemType* pArray, size_t matrixFlags)
{
    // handle externally managed case
	// BUGBUG: This is super super ugly, and needs to be fixed, but if matrixFlags has the right value, then we can't free anything,
    // and everything gets wonky. This should be fixed, and would go away if it is made a shared_ptr.
    if (matrixFlags & matrixFlagDontOwnBuffer)
    {
        // free the existing array if it used to be an owned array
        if ( Buffer() != NULL)
        {
            TracingGPUMemoryAllocator::Free<ElemType>(GetComputeDeviceId(), Buffer());
        }
        m_numRows = numRows;
        m_numCols = numCols;
        SetBuffer(pArray, GetNumElements() * sizeof(ElemType), true);
        SetSizeAllocated(GetNumElements());
        SetFormat(matrixFormatDense);
        SetComputeDeviceId(deviceId);
    }
    else
    {
        // if the devices are different move it now
        if (GetComputeDeviceId() != deviceId && deviceId >= 0)
        {
            Clear();
            ZeroInit(deviceId);
        }

        // now RequireSize/allocate as necessary
        RequireSize(numRows, numCols);

        // copy over the content to the buffer
        PrepareDevice();
        if (pArray != NULL)
        {
            if (!(matrixFlags & matrixFormatRowMajor))
            {
                CUDA_CALL(cudaMemcpy(Data(), pArray, sizeof(ElemType) * GetNumElements(), (matrixFlags & matrixFlagSetValueOnDevice) ? cudaMemcpyDeviceToDevice : cudaMemcpyHostToDevice));
            }
            else // row major: must transpose (this is not meant to be efficient, but very useful for defining inline matrices for test code)
            {
                vector<ElemType> transposed(GetNumElements());
                for (size_t i = 0; i < numRows; i++)
                    for (size_t j = 0; j < numCols; j++)
                        transposed[i + numRows * j] = pArray[j + numCols * i];
                CUDA_CALL(cudaMemcpy(Data(), transposed.data(), sizeof(ElemType) * GetNumElements(), (matrixFlags & matrixFlagSetValueOnDevice) ? cudaMemcpyDeviceToDevice : cudaMemcpyHostToDevice));
            }
        }
    }
    SetFormat(matrixFormatDense);
}

template <class ElemType>
void GPUMatrix<ElemType>::SetDiagonalValue(const ElemType v)
{
    CUDA_LONG N = (CUDA_LONG) GetNumRows();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_setDiagonalValue", t_stream);
    _setDiagonalValue<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), v, N, (CUDA_LONG) GetNumRows());
}

template <class ElemType>
void GPUMatrix<ElemType>::SetDiagonalValue(const GPUMatrix<ElemType>& vector)
{
    if (IsEmpty() || vector.IsEmpty())
        LogicError("SetDiagonalValue: Matrix is empty.");

    if (GetNumRows() != GetNumCols())
        LogicError("SetDiagonalValue: NumRows and NumCols do not agree.");

    if (vector.GetNumRows() != 1 && vector.GetNumCols() != 1)
        LogicError("SetDiagonalValue: input vector must be a vector.");

    if (vector.GetNumElements() == 1) // reduce to simple form
        SetDiagonalValue(vector.Data()[0]);

    else if (vector.GetNumRows() != GetNumRows())
        LogicError("SetDiagonalValue: input vector's dimension does not agree with [this].");
    else
    {
        CUDA_LONG N = (CUDA_LONG) GetNumRows();
        int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
        PrepareDevice();
        PROFILE_CUDA_STREAM("_setDiagonalValueFromVector", t_stream);
        _setDiagonalValueFromVector<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), vector.Data(), N);
    }
}

template <class ElemType>
void GPUMatrix<ElemType>::SetUniformRandomValue(const ElemType low, const ElemType high, unsigned long seed)
{
    PrepareDevice();
    CreateCurandObject(seed, __FUNCTION__); // TODO call ResetCurandObject() instead?

    cudaEvent_t done = nullptr;
    CUDA_CALL(cudaEventCreate(&done));
    if (sizeof(ElemType) == sizeof(float))
    {
        PROFILE_CUDA("curandGenerateUniform");
        CURAND_CALL(curandGenerateUniform(((curandGenerator_t*)s_curandGenerator)[0], reinterpret_cast<float*>(Data()), GetNumElements()));
    }
    else
    {
        PROFILE_CUDA("curandGenerateUniformDouble");
        CURAND_CALL(curandGenerateUniformDouble(((curandGenerator_t*)s_curandGenerator)[0], reinterpret_cast<double*>(Data()), GetNumElements()));
    }
    // Wait for curand* to complete before continuing
    CUDA_CALL(cudaEventRecord(done));
    CUDA_CALL(cudaEventSynchronize(done));
    // CURAND_CALL(curandDestroyGenerator(gen));
    CUDA_CALL(cudaEventDestroy(done));

    size_t N = GetNumElements();
    size_t blocksPerGrid = (size_t) ceil(N / (double) GridDim::maxThreadsPerBlock);

    PROFILE_CUDA_STREAM("_rescaleToRange", t_stream);
    _rescaleToRange<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), N, low, high);
}

template <class ElemType>
void GPUMatrix<ElemType>::SetGaussianRandomValue(const ElemType mean, const ElemType sigma, unsigned long seed)
{
    PrepareDevice();
    CreateCurandObject(seed, __FUNCTION__); // TODO call ResetCurandObject() instead?

    if (sizeof(ElemType) == sizeof(float))
    {
        PROFILE_CUDA("curandGenerateNormal");
        CURAND_CALL(curandGenerateNormal(((curandGenerator_t*)s_curandGenerator)[0], reinterpret_cast<float*>(Data()), GetNumElements(), (float)mean, (float)sigma));
    }
    else
    {
        PROFILE_CUDA("curandGenerateNormalDouble");
        CURAND_CALL(curandGenerateNormalDouble(((curandGenerator_t*)s_curandGenerator)[0], reinterpret_cast<double*>(Data()), GetNumElements(), (double)mean, (double)sigma));
    }
    // CURAND_CALL(curandDestroyGenerator(gen));
}

//maskRate: percentage of values masked out (similar to dropout rate)
//scaleValue: which scale value to set to the left ones (unmasked items).
template <class ElemType>
void GPUMatrix<ElemType>::SetUniformRandomMask(const ElemType maskRate, const ElemType scaleValue, unsigned long seed)
{
    PrepareDevice();
    CreateCurandObject(seed, __FUNCTION__); // TODO call ResetCurandObject() instead?

    cudaEvent_t done = nullptr;
    CUDA_CALL(cudaEventCreate(&done));
    if (sizeof(ElemType) == sizeof(float))
    {
        PROFILE_CUDA("curandGenerateUniform");
        CURAND_CALL(curandGenerateUniform((((curandGenerator_t*)s_curandGenerator)[0]), reinterpret_cast<float*>(Data()), GetNumElements()));
    }
    else
    {
        PROFILE_CUDA("curandGenerateUniformDouble");
        CURAND_CALL(curandGenerateUniformDouble((((curandGenerator_t*)s_curandGenerator)[0]), reinterpret_cast<double*>(Data()), GetNumElements()));
    }

    // Wait for curand* to complete before continuing
    CUDA_CALL(cudaEventRecord(done));
    CUDA_CALL(cudaEventSynchronize(done));
    CUDA_CALL(cudaEventDestroy(done));
    // CURAND_CALL(curandDestroyGenerator(gen));

    size_t N = GetNumElements();
    size_t blocksPerGrid = (size_t) ceil(N / (double) GridDim::maxThreadsPerBlock);
    PROFILE_CUDA_STREAM("_setMaskAndScale", t_stream);
    _setMaskAndScale<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), N, maskRate, scaleValue);
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::Adagrad(GPUMatrix<ElemType>& gradients, const bool needAveMultiplier)
{
    size_t numColsNeeded = gradients.GetNumCols();
    if (needAveMultiplier)
        numColsNeeded += gradients.GetNumCols();

    if (IsEmpty() || GetNumCols() < numColsNeeded)
    {
        RequireSize(gradients.GetNumRows(), numColsNeeded);
        SetValue(0.0);
    }

    assert(GetNumRows() == gradients.GetNumRows() && GetNumCols() == numColsNeeded);

    size_t n = gradients.GetNumElements();

    ElemType* multipliers = nullptr;
    if (needAveMultiplier)
        multipliers = Data() + n; // temp memory used to store multipliers,

    int blocksPerGrid = (n + GridDim::maxThreadsPerBlock - 1) / GridDim::maxThreadsPerBlock;
    {
        // BUGBUG: Should this use CUDA streams?
        PROFILE_CUDA("_adagrad");
        _adagrad<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock>>>(Data(), gradients.Data(), n, multipliers);
    }

    if (!needAveMultiplier)
        return 1;

    cublasHandle_t cuHandle = GetCublasHandle(GetComputeDeviceId());
    if (sizeof(ElemType) == sizeof(float))
    {
        float aveMultiplier = 0;
        PROFILE_CUDA_STREAM("cublasSasum", t_stream);
        CUBLAS_CALL(cublasSasum(cuHandle, (CUDA_LONG) n, reinterpret_cast<float*>(multipliers), 1, &aveMultiplier));
        return (ElemType) aveMultiplier / n;
    }
    else
    {
        double aveMultiplier = 0;
        PROFILE_CUDA_STREAM("cublasDasum", t_stream);
        CUBLAS_CALL(cublasDasum(cuHandle, (CUDA_LONG) n, reinterpret_cast<double*>(multipliers), 1, &aveMultiplier));
        return (ElemType) aveMultiplier / n;
    }
}

template <class ElemType>
void GPUMatrix<ElemType>::FSAdagrad(GPUMatrix<ElemType>& gradients,
                                    GPUMatrix<ElemType>& functionValues,
                                    ElemType learnRatePerSample,
                                    ElemType momentum,
                                    ElemType adaWeight,
                                    ElemType adaMul)
{
    size_t numColsNeeded = 2 * gradients.GetNumCols();

    if (IsEmpty() || (GetNumCols() < numColsNeeded))
    {
        RequireSize(gradients.GetNumRows(), numColsNeeded);
        SetValue(0.0);
    }

    assert((GetNumRows() == gradients.GetNumRows()) && (GetNumCols() == numColsNeeded));

    size_t n = gradients.GetNumElements();
    int blocksPerGrid = (n + GridDim::maxThreadsPerBlock - 1) / GridDim::maxThreadsPerBlock;
    PROFILE_CUDA("_fsadagrad");
    _fsadagrad<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock>>>(n, gradients.Data(), Data(), Data()+ n, functionValues.Data(),
                                                                         learnRatePerSample, momentum, adaWeight, adaMul);
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::RmsProp(GPUMatrix<ElemType>& gradients,
                                      ElemType RMS_GAMMA,
                                      ElemType RMS_WGT_INC,
                                      ElemType RMS_WGT_MAX,
                                      ElemType RMS_WGT_DEC,
                                      ElemType RMS_WGT_MIN,
                                      const bool needAveMultiplier)
{
    const ElemType floor = 1e-6f;
    static ElemType* upd_gpu = (ElemType*) 0;

    size_t n = gradients.GetNumElements();
    int blocksPerGrid = (GetNumElements() + GridDim::maxThreadsPerBlock - 1) / GridDim::maxThreadsPerBlock;

    size_t numColsNeeded = gradients.GetNumCols() * 3;
    if (needAveMultiplier)
        numColsNeeded += gradients.GetNumCols();

    if (IsEmpty() || GetNumCols() < numColsNeeded)
    {
        RequireSize(gradients.GetNumRows(), numColsNeeded);
        SetValue(0.0);

        ElemType* avars = Data();         // accumulated variances for RMS scaling
        ElemType* signs = Data() + n;     // sign of previous gradient
        ElemType* steps = Data() + 2 * n; // current step size
        // Data()+3*n is temp memory used to store multipliers, no need to initialize

        PROFILE_CUDA("_rmsprop_init");
        _rmsprop_init<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock>>>(avars, signs, steps, gradients.Data(), n);
    }
    assert(GetNumRows() == gradients.GetNumRows() && GetNumCols() == numColsNeeded);

    ElemType* avars = Data();         // accumulated variances for RMS scaling
    ElemType* signs = Data() + n;     // sign of previous gradient
    ElemType* steps = Data() + 2 * n; // current step size

    ElemType* multipliers = nullptr;
    if (needAveMultiplier)
        multipliers = Data() + 3 * n; // temp memory used to store multipliers,

    if (!upd_gpu)
    {
        const ElemType upd[] = {
            2, 2, 0,
            2, 2, 0,
            1, 1, 1,
            2, 2, 0,
            1, 2, 1,
            0, 2, 2,
            1, 1, 1,
            0, 2, 2,
            0, 2, 2,
        };

        upd_gpu = TracingGPUMemoryAllocator::Allocate<ElemType>(GetComputeDeviceId(), 27);
        CUDA_CALL(cudaMemcpy(upd_gpu, upd, sizeof(ElemType) * _countof(upd), cudaMemcpyHostToDevice));
    }

    {
        PROFILE_CUDA("_rmsprop");
        _rmsprop<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock>>>(avars, signs, steps, gradients.Data(), n,
                                                                       RMS_GAMMA, RMS_WGT_INC, RMS_WGT_MAX, RMS_WGT_DEC, RMS_WGT_MIN,
                                                                       floor, upd_gpu, multipliers);
    }

    if (!needAveMultiplier)
        return 1;

    cublasHandle_t cuHandle = GetCublasHandle(GetComputeDeviceId());
    if (sizeof(ElemType) == sizeof(float))
    {
        float aveMultiplier = 0;
        PROFILE_CUDA_STREAM("cublasSasum", t_stream);
        CUBLAS_CALL(cublasSasum(cuHandle, (CUDA_LONG) n, reinterpret_cast<float*>(multipliers), 1, &aveMultiplier));
        return aveMultiplier / n;
    }
    else
    {
        double aveMultiplier = 0;
        PROFILE_CUDA_STREAM("cublasDasum", t_stream);
        CUBLAS_CALL(cublasDasum(cuHandle, (CUDA_LONG) n, reinterpret_cast<double*>(multipliers), 1, &aveMultiplier));
        return (ElemType) aveMultiplier / n;
    }
}

template <class ElemType>
void GPUMatrix<ElemType>::Reshape(const size_t numRows, const size_t numCols)
{
    assert(numRows * numCols == GetNumElements());
    if (numRows * numCols != GetNumElements())
        InvalidArgument("Reshape: total number of elements does not match.");

    m_numRows = numRows;
    m_numCols = numCols;
}

template <class ElemType>
void GPUMatrix<ElemType>::RequireSize(const size_t numRows, const size_t numCols, bool growOnly)
{
    if (GetNumRows() != numRows || GetNumCols() != numCols)
        Resize(numRows, numCols, growOnly);
}

template <class ElemType>
void GPUMatrix<ElemType>::Resize(const size_t numRows, const size_t numCols, bool growOnly)
{
    VerifyResizable(__func__);

    if (GetNumRows() == numRows && GetNumCols() == numCols)
        return;

    m_numRows = numRows;
    m_numCols = numCols;

    size_t numElements = GetNumElements();
    if (numElements > GetSizeAllocated() || (!growOnly && numElements != GetSizeAllocated()))
    {
        if (IsEmpty())
        {
            SetSizeAllocated(0);
            SetBuffer(nullptr, 0);
        }
        else
        {
            if (Buffer())
            {
                TracingGPUMemoryAllocator::Free<ElemType>(GetComputeDeviceId(), Buffer());
            }
            SetSizeAllocated(numElements);
            SetBuffer(TracingGPUMemoryAllocator::Allocate<ElemType>(GetComputeDeviceId(), m_numRows, m_numCols), numElements * sizeof(ElemType));
            CUDA_CALL(cudaMemset(Buffer(), 0, sizeof(ElemType) * GetSizeAllocated()));
        }
    }
    m_sliceViewOffset = 0;
}

template <class ElemType>
size_t GPUMatrix<ElemType>::LocateElement(const size_t row, const size_t col) const
{
    assert(row < m_numRows && col < m_numCols);
    return LocateColumn(col) + row; // matrix in column-wise storage
}

template <class ElemType>
size_t GPUMatrix<ElemType>::LocateColumn(const size_t col) const
{
    assert(col < GetNumCols());
    return col * m_numRows; // matrix in column-wise storage
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::Get00Element() const
{
    ElemType res = 0;
    CUDA_CALL(cudaMemcpy(&res, Data(), sizeof(ElemType), cudaMemcpyDeviceToHost));
    return res;
}
#pragma endregion Basic Operators

#pragma region Member BLAS Functions
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::operator+=(ElemType alpha)
{
    if (IsEmpty())
        LogicError("operator+=: Matrix is empty.");
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PROFILE_CUDA_STREAM("_addValue", t_stream);
    _addValue<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), alpha, N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::operator+(ElemType alpha) const
{
    if (IsEmpty())
        LogicError("operator+: Matrix is empty.");

    GPUMatrix<ElemType> c(*this);
    c += alpha;
    return c;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignSumOf(const ElemType alpha, const GPUMatrix<ElemType>& a)
{
    SetValue(a);
    (*this) += alpha;
    return (*this);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::operator+=(const GPUMatrix<ElemType>& a)
{
    ScaleAndAdd(1, a, *this);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::operator+(const GPUMatrix<ElemType>& a) const
{
    if (GetNumElements() == 1)
    {
        GPUMatrix<ElemType> c(a);
        c += Get00Element();
        return c;
    }
    else if (a.GetNumElements() == 1)
    {
        GPUMatrix<ElemType> c(*this);
        c += a.Get00Element();
        return c;
    }
    else
    {
        GPUMatrix<ElemType> c(*this); // this implementation will introduce a copy overhead. but make resue of the code
        c += a;
        return c;
    }
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignSumOf(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b)
{
    SetValue(a);
    (*this) += b;
    return (*this);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::operator-=(ElemType alpha)
{
    if (IsEmpty())
        LogicError("operato-=: Matrix is empty.");
    return operator+=(-1 * alpha);
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::operator-(ElemType alpha) const
{
    if (IsEmpty())
        LogicError("operator-: Matrix is empty.");
    return operator+(-1 * alpha);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignDifferenceOf(const ElemType alpha, const GPUMatrix<ElemType>& a)
{
    RequireSize(a.m_numRows, a.m_numCols);
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_assignDifferenceOf1", t_stream);
    _assignDifferenceOf1<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), alpha, a.Data(), N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignDifferenceOf(const GPUMatrix<ElemType>& a, const ElemType alpha)
{
    RequireSize(a.m_numRows, a.m_numCols);
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_assignDifferenceOf2", t_stream);
    _assignDifferenceOf2<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), alpha, a.Data(), N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::operator-=(const GPUMatrix<ElemType>& a)
{
    ScaleAndAdd(-1, a, *this);

    return *this;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::operator-(const GPUMatrix<ElemType>& a) const
{
    GPUMatrix<ElemType> c(*this); // this implementation will introduce a copy overhead. but make resue of the code
    c -= a;
    return c;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignDifferenceOf(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b)
{
    if (this != &a)
    {
        RequireSize(a.GetNumRows(), a.GetNumCols());
        SetValue(a);
    }
    (*this) -= b;
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::operator*=(ElemType alpha)
{
    Scale(alpha, *this);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::operator*(ElemType alpha) const
{
    GPUMatrix<ElemType> c(GetNumRows(), GetNumCols(), GetComputeDeviceId());
    Scale(alpha, *this, c);
    return c;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignProductOf(const ElemType alpha, const GPUMatrix<ElemType>& a)
{
    Scale(alpha, a, *this);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignProductOf(const GPUMatrix<ElemType>& a, const bool transposeA, const GPUMatrix<ElemType>& b, const bool transposeB)
{
    if (a.GetNumElements() == 1)
    {
        if (transposeB)
            AssignTransposeOf(b);
        (*this) *= a.Get00Element();
    }
    else if (b.GetNumElements() == 1)
    {
        if (transposeA)
            AssignTransposeOf(a);
        (*this) *= b.Get00Element();
    }
    else
        Multiply(a, transposeA, b, transposeB, *this);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::operator*(const GPUMatrix<ElemType>& a) const
{
    const GPUMatrix<ElemType>& us = *this;
    if (GetNumElements() == 1)
    {
        GPUMatrix<ElemType> c(GetComputeDeviceId());
        c.AssignProductOf(Get00Element(), a);
        return c;
    }
    else if (a.GetNumElements() == 1)
    {
        GPUMatrix<ElemType> c(GetComputeDeviceId());
        c.AssignProductOf(a.Get00Element(), us);
        return c;
    }
    else
    {
        GPUMatrix<ElemType> c(GetNumRows(), a.GetNumCols(), GetComputeDeviceId());
        Multiply(*this, a, c);
        return c;
    }
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::operator/=(ElemType alpha)
{
    (*this) *= 1 / alpha;
    return (*this);
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::operator/(ElemType alpha) const
{
    return ((*this) * (1 / alpha));
}

//element-wise power
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::operator^=(ElemType alpha)
{
    GPUMatrix<ElemType>& us = *this;
    ElementWisePower(alpha, us, us);
    return us;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::operator^(ElemType alpha) const
{
    GPUMatrix<ElemType> c(GetNumRows(), GetNumCols(), GetComputeDeviceId());
    ElementWisePower(alpha, *this, c);
    return c;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignElementPowerOf(const GPUMatrix<ElemType>& a, const ElemType power)
{
    ElementWisePower(power, a, *this);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddElementProductOf(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("AddElementProductOf: Matrix is empty.");

    assert(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols());
    if (!(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols()))
        InvalidArgument("The input matrix dimensions do not match.");

    if (!(a.GetNumRows() == GetNumRows() && a.GetNumCols() == GetNumCols()))
        InvalidArgument("The input matrix dimensions do not match [this].");

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_addElementProductOf", t_stream);
    _addElementProductOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), b.Data(), N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::ColumnElementMultiplyWith(const GPUMatrix<ElemType>& a)
{
    if (a.IsEmpty() || IsEmpty())
        LogicError("ColumnElementMultiplyWith: Matrix is empty.");

    if (!(a.GetNumRows() == GetNumRows() && a.GetNumCols() == 1))
        InvalidArgument("ColumnElementMultiplyWith: The input matrix should be a col vector and match [this]'s rows.");

    CUDA_LONG N = (CUDA_LONG) a.GetNumRows();
    CUDA_LONG M = (CUDA_LONG) GetNumCols();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_columnElementMultiplyWith", t_stream);
    _columnElementMultiplyWith<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, M);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::RowElementMultiplyWith(const GPUMatrix<ElemType>& a)
{
    if (a.IsEmpty() || IsEmpty())
        LogicError("RowElementMultiplyWith: Matrix is empty.");

    if (!(a.GetNumRows() == 1 && a.GetNumCols() == GetNumCols()))
        InvalidArgument("RowElementMultiplyWith: The input matrix should be a row vector and match [this]'s columns.");

    CUDA_LONG N = (CUDA_LONG) GetNumRows();
    CUDA_LONG M = (CUDA_LONG) a.GetNumCols();
    int blocksPerGrid = (int) ceil(1.0 * M / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_rowElementMultiplyWith", t_stream);
    _rowElementMultiplyWith<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, M);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::RowElementDivideBy(const GPUMatrix<ElemType>& a)
{
    if (a.IsEmpty() || IsEmpty())
        LogicError("RowElementDivideBy: Matrix is empty.");

    if (!(a.GetNumRows() == 1 && a.GetNumCols() == GetNumCols()))
        InvalidArgument("RowElementDivideBy: The input matrix should be a row vector and match [this]'s columns.");

    CUDA_LONG N = (CUDA_LONG) GetNumRows();
    CUDA_LONG M = (CUDA_LONG) a.GetNumCols();
    int blocksPerGrid = (int) ceil(1.0 * M / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_rowElementDivideBy", t_stream);
    _rowElementDivideBy<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, M);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::ColumnElementDivideBy(const GPUMatrix<ElemType>& a)
{
    if (a.IsEmpty() || IsEmpty())
        LogicError("ColumnElementDivideBy: Matrix is empty.");

    if (!(a.GetNumRows() == GetNumRows() && a.GetNumCols() == 1))
        InvalidArgument("ColumnElementDivideBy: The input matrix should be a col vector and match [this]'s rows.");

    CUDA_LONG N = (CUDA_LONG) a.GetNumRows();
    CUDA_LONG M = (CUDA_LONG) GetNumCols();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_ColumnElementDivideBy", t_stream);
    _ColumnElementDivideBy<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N, M);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::ElementInverse()
{
    if (IsEmpty())
        LogicError("ElementInverse: Matrix is empty.");

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_elemInverse", t_stream);
    _elemInverse<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignElementInverseOf(const GPUMatrix<ElemType>& a)
{
    SetValue(a);
    return ElementInverse();
}

DEF_ELEMWISE_INPLACE_FUNC(Sigmoid)

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignSigmoidOf(const GPUMatrix<ElemType>& a)
{
    RequireSize(a.GetNumRows(), a.GetNumCols());
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_assignSigmoidOf", t_stream);
    // _elementWIseSigmoidOnCuda has an implementation that avoids possible overflow errors, but has a slight accuracy regression.
#if 0
    _elementWiseSigmoidOnCuda<<<blocksPerGrid, threadsPerBlock, 0, t_stream>>>(a.Data(), Data(), N);
#else
    _assignSigmoidOf<<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(a.Data(), Data(), N);
#endif
    return *this;
}

DEF_ELEMWISE_INPLACE_FUNC(SigmoidDerivative)
DEF_ELEMWISE_ASSIGN_FUNC(SigmoidDerivative)

template <class ElemType>
void GPUMatrix<ElemType>::AssignNoiseContrastiveEstimation(const GPUMatrix<ElemType>& a,
                                                           const GPUMatrix<ElemType>& b, const GPUMatrix<ElemType>& bias, size_t sampleCount, GPUMatrix<ElemType>& tmp, GPUMatrix<ElemType>& c)
//this:   samples+probs
// a  :   hidden
// b  :   embedding
// tmp:   softmax
// c  :   loglikelihood
{
    UNCONST(ElemType, a, my_a);
    UNCONST(ElemType, b, my_b);
    UNCONST(ElemType, bias, my_bias);

    // a: dim * minibatch
    // b: dim * |vocab|
    int p = 512;
    int width = a.GetNumRows(); // dimension of hidden vector

    while (p / 2 > width)
        p = p / 2;

    {
        PROFILE_CUDA("_computeNceOutput");
        _computeNceOutput<ElemType><<<GetNumElements() / 2, p>>>(
            Data(),
            sampleCount,
            m_numRows / 2,
            my_a.Data(), // a
            a.GetNumRows(),
            my_b.Data(), // b
            my_bias.Data(),
            tmp.Data()); // tmp
    }

    p = 512;
    while (p / 2 > GetNumElements() / 2)
        p = p / 2;

    {
        PROFILE_CUDA("_assignNoiseContrastiveEstimation");
        // summing up objective must be done in one block
        _assignNoiseContrastiveEstimation<ElemType><<<1, p>>>(
            Data(),
            sampleCount,
            m_numRows / 2,
            my_a.Data(),
            a.GetNumCols(),
            my_b.Data(),
            tmp.Data(),
            c.Data());
    }
}

template <class ElemType>
void GPUMatrix<ElemType>::AssignNCEDerivative(GPUMatrix<ElemType>& tmp, const GPUMatrix<ElemType>& a,
                                              const GPUMatrix<ElemType>& b, size_t inputIndex, GPUMatrix<ElemType>& c)
{
    UNCONST(ElemType, a, my_a);
    UNCONST(ElemType, b, my_b);

    int p = 512;
    int width = a.GetNumRows();
    while (p / 2 > width)
        p = p / 2;

    PROFILE_CUDA("_assignNceDerivativeNew");
    _assignNceDerivativeNew<ElemType><<<(tmp.GetNumElements() + p - 1) / p, p>>>(
        Data(),
        tmp.GetNumCols(),
        m_numRows / 2,
        my_a.Data(),
        a.GetNumRows(),
        my_b.Data(),
        tmp.Data(),
        c.Data(),
        inputIndex);
}

template <class ElemType>
void GPUMatrix<ElemType>::AssignSoftmaxSum(const GPUMatrix<ElemType>& a, GPUMatrix<ElemType>& c)
{
    UNCONST(ElemType, a, my_a);

    int p = 512;
    int width = a.GetNumRows();
    while (p / 2 > width)
        p = p / 2;

    PROFILE_CUDA("_assignSoftmaxSum");
    _assignSoftmaxSum<ElemType><<<1, p>>>(
        my_a.Data(),
        width,
        Data(),
        c.Data());
}

template <class ElemType>
void GPUMatrix<ElemType>::AssignNCEUnnormalizedEval(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c)
{
    assert(a.GetComputeDeviceId() == b.GetComputeDeviceId());
    assert(GetNumRows() == a.GetNumRows());
    assert(GetNumCols() == b.GetNumRows());
    assert(a.GetNumCols() == b.GetNumRows());
    UNUSED(a);
    UNUSED(b);
    UNUSED(c); // TODO: this function seems like a stub
    /*
        EnsureAuxMemory();
        int p = 512;
        int width = a.GetNumCols();
        while (p / 2 > width) p = p / 2;

        // this kernel need be launched in nnz blocks
        _sparseInnerProductDenseTimesDense<ElemType> << <m_nz, p >> >(
        m_dVal,
        m_buf,
        m_dCol,
        m_nz,
        GetNumRows(),
        a.Buffer(),
        b.Buffer(),
        b.GetNumRows(),
        m_res);

        // sum up the results
        _reductionSum32<ElemType> << <1, 32 >> >(m_res, c.Buffer(), m_nz);*/
}

DEF_ELEMWISE_INPLACE_FUNC(Tanh)
DEF_ELEMWISE_ASSIGN_FUNC(Tanh)

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::InplaceLogSoftmax(const bool isColWise)
{
    if (IsEmpty())
        LogicError("InplaceLogSoftmax: Matrix is empty.");

    PrepareDevice();
    if (isColWise)
    {
        CUDA_LONG N = (CUDA_LONG) GetNumCols(); // one kernel per column
        int blocksPerGrid = (int) ceil(N * 1.0 / GridDim::maxThreadsPerBlock);
        PROFILE_CUDA_STREAM("_logSoftMaxColWise", t_stream);
        _logSoftMaxColWise<<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), (CUDA_LONG) m_numCols, (CUDA_LONG) m_numRows);
    }
    else
    {
        CUDA_LONG N = (CUDA_LONG) GetNumRows(); // one kernel per column
        int blocksPerGrid = (int) ceil(N * 1.0 / GridDim::maxThreadsPerBlock);
        PROFILE_CUDA_STREAM("_logSoftMaxRowWise", t_stream);
        _logSoftMaxRowWise<<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), (CUDA_LONG) m_numCols, (CUDA_LONG) m_numRows);
    }
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignLogSoftmaxOf(const GPUMatrix<ElemType>& a, const bool isColWise)
{
    RequireSize(a.GetNumRows(), a.GetNumCols());
    if (isColWise)
    {
        PrepareDevice();
        CUDA_LONG N = (CUDA_LONG) GetNumCols();
        CUDA_LONG M = (CUDA_LONG) GetNumRows();
        PROFILE_CUDA_STREAM("_assignColumnwiseLogSoftmaxOf", t_stream);
        _assignColumnwiseLogSoftmaxOf<<<N, 512, 0, t_stream>>>(a.Data(), Data(), N, M);
    }
    else
    {
        NOT_IMPLEMENTED;
    }

    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::InplaceHardmax(const bool isColWise)
{
    return AssignHardmaxOf(*this, isColWise);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignHardmaxOf(const GPUMatrix<ElemType>& a, const bool isColWise)
{
    RequireSize(a.GetNumRows(), a.GetNumCols());
    if (isColWise)
    {
        PrepareDevice();
        CUDA_LONG N = (CUDA_LONG) GetNumCols();
        CUDA_LONG M = (CUDA_LONG) GetNumRows();
        PROFILE_CUDA_STREAM("_assignColumnwiseHardmaxOf", t_stream);
        _assignColumnwiseHardmaxOf<<<N, 512, 0, t_stream>>>(a.Data(), Data(), N, M);
    }
    else
    {
        NOT_IMPLEMENTED;
    }

    return *this;
}

DEF_ELEMWISE_INPLACE_FUNC(Sqrt)
DEF_ELEMWISE_ASSIGN_FUNC(Sqrt)

DEF_ELEMWISE_INPLACE_FUNC(Exp)
DEF_ELEMWISE_ASSIGN_FUNC(Exp)

DEF_ELEMWISE_INPLACE_FUNC(Log)
DEF_ELEMWISE_ASSIGN_FUNC(Log)

DEF_ELEMWISE_INPLACE_FUNC(Abs)
DEF_ELEMWISE_ASSIGN_FUNC(Abs)

DEF_ELEMWISE_INPLACE_FUNC(LinearRectifierDerivative)
DEF_ELEMWISE_ASSIGN_FUNC(LinearRectifierDerivative)

DEF_ELEMWISE_INPLACE_FUNC(Cosine)
DEF_ELEMWISE_ASSIGN_FUNC(Cosine)

DEF_ELEMWISE_INPLACE_FUNC(NegativeSine)
DEF_ELEMWISE_ASSIGN_FUNC(NegativeSine)

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::InplaceTruncateBottom(const ElemType threshold)
{
    return AssignTruncateBottomOf(*this, threshold);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignTruncateBottomOf(const GPUMatrix<ElemType>& a, const ElemType threshold)
{
    if (a.IsEmpty())
        LogicError("AssignTruncateBottomOf: Matrix a is empty.");

    if (this != &a)
    {
        RequireSize(a.GetNumRows(), a.GetNumCols());
    }

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(N * 1.0 / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_assignTruncateBottom", t_stream);
    _assignTruncateBottom<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), threshold, N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::InplaceTruncateTop(const ElemType threshold)
{
    return AssignTruncateTopOf(*this, threshold);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignTruncateTopOf(const GPUMatrix<ElemType>& a, const ElemType threshold)
{
    if (a.IsEmpty())
        LogicError("AssignTruncateTopOf: Matrix a is empty.");

    if (this != &a)
    {
        RequireSize(a.GetNumRows(), a.GetNumCols());
    }

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(N * 1.0 / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_assignTruncateTop", t_stream);
    _assignTruncateTop<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), threshold, N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::InplaceTruncate(const ElemType threshold)
{
    if (IsEmpty())
        LogicError("InplaceTruncate: Matrix is empty.");

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(N * 1.0 / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_inplaceTruncate", t_stream);
    _inplaceTruncate<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), threshold, N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::InplaceSoftThreshold(const ElemType threshold)
{
    if (IsEmpty())
        LogicError("InplaceSoftThreshold: Matrix is empty.");

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(N * 1.0 / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_inplaceSoftThreshold", t_stream);
    _inplaceSoftThreshold<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), threshold, N);
    return *this;
}
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::SetToZeroIfAbsLessThan(const ElemType threshold)
{
    if (IsEmpty())
        LogicError("SetToZeroIfAbsLessThan: Matrix is empty.");
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(N * 1.0 / GridDim::maxThreadsPerBlock);
    PrepareDevice();
    PROFILE_CUDA_STREAM("_setToZeroIfAbsLessThan", t_stream);
    _setToZeroIfAbsLessThan<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), threshold, N);
    return *this;
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::SumOfAbsElements() const
{
    if (IsEmpty())
        LogicError("SumOfAbsElements: Matrix is empty");

    cublasHandle_t cuHandle = GetCublasHandle(GetComputeDeviceId());
    if (sizeof(ElemType) == sizeof(float))
    {
        float res = 0;
        PROFILE_CUDA_STREAM("cublasSasum", t_stream);
        CUBLAS_CALL(cublasSasum(cuHandle, (CUDA_LONG) GetNumElements(), reinterpret_cast<float*>(Data()), 1, &res));
        return res;
    }
    else
    {
        double res = 0;
        PROFILE_CUDA_STREAM("cublasDasum", t_stream);
        CUBLAS_CALL(cublasDasum(cuHandle, (CUDA_LONG) GetNumElements(), reinterpret_cast<double*>(Data()), 1, &res));
        return ElemType(res);
    }
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::SumOfElements() const
{
    if (IsEmpty())
        LogicError("SumOfElements: Matrix is empty");

    ElemType* d_sum = TracingGPUMemoryAllocator::Allocate<ElemType>(GetComputeDeviceId(), 1);
    ElemType h_sum;

    // WARNING: THIS kernel is not the most efficient way!
    {
        PROFILE_CUDA_STREAM("_reductionSum", t_stream);
        _reductionSum<ElemType><<<1, 1024, 0, t_stream>>>(Data(), d_sum, (CUDA_LONG) GetNumElements());
    }
    CUDA_CALL(cudaMemcpy(&h_sum, d_sum, sizeof(ElemType), cudaMemcpyDeviceToHost));
    TracingGPUMemoryAllocator::Free<ElemType>(GetComputeDeviceId(), d_sum);
    return h_sum;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignSumOfElements(const GPUMatrix<ElemType>& a)
{
    if (a.IsEmpty())
        LogicError("AssignSumOfElements: Matrix a is empty");

    RequireSize(1, 1);

    PrepareDevice();
    PROFILE_CUDA("_reductionSumAndAssign");
    // WARNING: THIS kernel is not the most efficient way!
    // BUGBUG: Should this use CUDA streams (t_stream)?
    _reductionSumAndAssign<ElemType><<<1, 1024>>>(Data(), a.Data(), (CUDA_LONG) a.GetNumElements(), (CUDA_LONG) GetNumElements());
    return (*this);
}

template <class ElemType>
DeviceBoundNumber<ElemType> GPUMatrix<ElemType>::Sum_AsDeviceBoundNum() const
{
    if (IsEmpty())
        LogicError("Matrix is empty");
    ElemType* d_sum = TracingGPUMemoryAllocator::Allocate<ElemType>(GetComputeDeviceId(), 1);

    // WARNING: THIS kernel is not the most efficient way!
    {
        PROFILE_CUDA_STREAM("_reductionSum", t_stream);
        _reductionSum<ElemType><<<1, 1024, 0, t_stream>>>(Data(), d_sum, (CUDA_LONG) GetNumElements());
    }
    DeviceBoundNumber<ElemType> result;
    result.ShallowCopyFrom(d_sum, GetComputeDeviceId());
    return result;
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::Max() const
{
    cublasHandle_t cuHandle = GetCublasHandle(GetComputeDeviceId());
    ElemType res;
    if (sizeof(ElemType) == sizeof(float))
    {
        int resInd = 0;
        {
            PROFILE_CUDA_STREAM("cublasIsamax", t_stream);
            cublasIsamax(cuHandle, (CUDA_LONG)GetNumElements(), reinterpret_cast<float*>(Data()), 1, &resInd);
        }
        resInd--;
        CUDA_CALL(cudaMemcpy(reinterpret_cast<float*>(&res), reinterpret_cast<float*>(Data()+ resInd), sizeof(float), cudaMemcpyDeviceToHost));
        return res;
    }
    else
    {
        int resInd = 0;
        {
            PROFILE_CUDA_STREAM("cublasIdamax", t_stream);
            cublasIdamax(cuHandle, (CUDA_LONG)GetNumElements(), reinterpret_cast<double*>(Data()), 1, &resInd);
        }
        resInd--;
        CUDA_CALL(cudaMemcpy(reinterpret_cast<double*>(&res), Data()+ resInd, sizeof(float), cudaMemcpyDeviceToHost));
        return res;
    }
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::ElementMultiplyWith(const GPUMatrix<ElemType>& a)
{
    if (IsEmpty() || a.IsEmpty())
        LogicError("ElementMultiplyWith: Matrix is empty.");

    GPUMatrix<ElemType>& us = *this;
    assert(us.GetNumRows() == a.GetNumRows() && us.GetNumCols() == a.GetNumCols());
    if (us.GetNumRows() != a.GetNumRows() || us.GetNumCols() != a.GetNumCols())
        InvalidArgument("The matrix dimensions do not match.");

    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(((double) N) / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_elemMul", t_stream);
    _elemMul<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignElementProductOf(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("AssignElementProductOf: Matrix is empty.");

    assert(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols());
    if (!(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols()))
        InvalidArgument("The input matrix dimensions do not match.");

    RequireSize(a.GetNumRows(), a.GetNumCols());
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(((double) N) / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_assignElementProductOf", t_stream);
    _assignElementProductOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), b.Data(), N);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::ElementDivideBy(const GPUMatrix<ElemType>& a)
{
    return AssignElementDivisionOf(*this, a);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignElementDivisionOf(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("AssignElementDivisionOf: Matrix is empty.");

    assert(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols());
    if (!(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols()))
        InvalidArgument("The input matrix dimensions do not match.");

    RequireSize(a.GetNumRows(), a.GetNumCols());
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(((double) N) / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_assignElementDivisionOf", t_stream);
    _assignElementDivisionOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), b.Data(), N);
    return *this;
}

template <class ElemType>
bool GPUMatrix<ElemType>::IsEqualTo(const GPUMatrix<ElemType>& a, const ElemType threshold /*= 1e-8*/) const
{
    return AreEqual(*this, a, threshold);
}

template <class ElemType>
void GPUMatrix<ElemType>::VectorSum(const GPUMatrix<ElemType>& a, GPUMatrix<ElemType>& c, const bool isColWise)
{
    if (a.GetComputeDeviceId() != c.GetComputeDeviceId())
    {
        InvalidArgument("All matrices must be on the same GPU");
    }

    a.PrepareDevice();

    if (a.IsEmpty())
        LogicError("VectorSum:  Input matrix is empty.");

    const CUDA_LONG n = (CUDA_LONG) a.GetNumRows();
    const CUDA_LONG m = (CUDA_LONG) a.GetNumCols();
    assert(m > 0 && n > 0); // converting from size_t to int may cause overflow

    int blocksPerGrid = 0;
    if (isColWise) // col-wise
    {
        c.RequireSize(1, m);
        blocksPerGrid = (int) ceil(1.0 * m / GridDim::maxThreadsPerBlock);
    }
    else
    {
        c.RequireSize(n, 1);
        blocksPerGrid = (int) ceil(1.0 * n / GridDim::maxThreadsPerBlock);
    }

    PROFILE_CUDA_STREAM("_vectorSum", t_stream);
    _vectorSum<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(c.Data(), a.Data(), n, m, isColWise);
}
template <class ElemType>
void GPUMatrix<ElemType>::VectorNorm1(GPUMatrix<ElemType>& c, const bool isColWise) const
{
    if (IsEmpty())
        LogicError("VectorNorm1: Matrix is empty.");

    const CUDA_LONG n = (CUDA_LONG) GetNumRows();
    const CUDA_LONG m = (CUDA_LONG) GetNumCols();
    assert(m > 0 && n > 0); // converting from size_t to int may cause overflow

    PrepareDevice();
    c.ChangeDeviceTo(GetComputeDeviceId());

    int blocksPerGrid = 0;
    if (isColWise) // col-wise
    {
        c.RequireSize(1, m);
        blocksPerGrid = (int) ceil(1.0 * m / GridDim::maxThreadsPerBlock);
    }
    else
    {
        c.RequireSize(n, 1);
        blocksPerGrid = (int) ceil(1.0 * n / GridDim::maxThreadsPerBlock);
    }

    PROFILE_CUDA_STREAM("_vectorNorm1", t_stream);
    _vectorNorm1<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(c.Data(), Data(), n, m, isColWise);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignVectorNorm1Of(GPUMatrix<ElemType>& a, const bool isColWise)
{
    a.VectorNorm1(*this, isColWise);
    return *this;
}

template <class ElemType>
void GPUMatrix<ElemType>::VectorNorm2(GPUMatrix<ElemType>& c, const bool isColWise) const
{
    if (IsEmpty())
        LogicError("VectorNorm2: Matrix is empty.");

    const CUDA_LONG n = (CUDA_LONG) GetNumRows();
    const CUDA_LONG m = (CUDA_LONG) GetNumCols();
    assert(m > 0 && n > 0); // converting from size_t to int may cause overflow

    PrepareDevice();
    c.ChangeDeviceTo(GetComputeDeviceId());

    int blocksPerGrid = 0;
    if (isColWise) // col-wise
    {
        c.RequireSize(1, m);
        blocksPerGrid = (int) ceil(1.0 * m / GridDim::maxThreadsPerBlock);
    }
    else
    {
        c.RequireSize(n, 1);
        c.ChangeDeviceTo(GetComputeDeviceId());
        blocksPerGrid = (int) ceil(1.0 * n / GridDim::maxThreadsPerBlock);
    }

    PROFILE_CUDA_STREAM("_vectorNorm2", t_stream);
    _vectorNorm2<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(c.Data(), Data(), n, m, isColWise);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignVectorNorm2Of(GPUMatrix<ElemType>& a, const bool isColWise)
{
    a.VectorNorm2(*this, isColWise);
    return *this;
}

template <class ElemType>
void GPUMatrix<ElemType>::VectorNormInf(GPUMatrix<ElemType>& c, const bool isColWise) const
{
    if (IsEmpty())
        LogicError("VectorMax: Matrix is empty.");

    // this implementation is not efficient
    GPUMatrix<ElemType> tmp(GetComputeDeviceId());
    GPUMatrix<ElemType> tmp1(GetComputeDeviceId());
    tmp.AssignAbsOf((*this));
    tmp.VectorMax(tmp1, c, isColWise);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignVectorNormInfOf(GPUMatrix<ElemType>& a, const bool isColWise)
{
    a.VectorNormInf(*this, isColWise);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignInnerProductOf(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, const bool isColWise)
{
    InnerProduct(a, b, *this, isColWise);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignKhatriRaoProductOf(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("AssignKhatriRaoProductOf: Matrix is empty.");

    CUDA_LONG cols = a.GetNumCols();
    assert(cols == b.GetNumCols());
    if (!(cols == b.GetNumCols()))
        InvalidArgument("AssignKhatriRaoProductOf: The input matrix dimensions do not match.");

    CUDA_LONG rowsA = (CUDA_LONG) a.GetNumRows();
    CUDA_LONG rowsB = (CUDA_LONG) b.GetNumRows();
    RequireSize(rowsA * rowsB, cols);
    float N = (float) GetNumElements();
    int blocksPerGrid = (int) ceil(N / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_assignKhatriRaoProductOf", t_stream);
    _assignKhatriRaoProductOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), b.Data(), rowsA, rowsB, cols);
    return *this;
}

//column-wise reshaped product. Used to compute KhatriRaoProduct Gradient
//   this = reshape each column of a from (K1xK2,1) to (K1, K2)
//   if each column of a is not transposed, each (K1, K2) times each column of b (K2, frames).
//   the output is a (K1, frames) matrix
//   if each column of a is tranposed, each (K1, K2)^T times each column of b(K1, frames) and output is (K2, frames)
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddColumnReshapeProductOf(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, const bool transposeAColumn)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("AddColumnReshapeProductOf: Matrix is empty.");

    CUDA_LONG cols = a.GetNumCols();
    assert(cols == b.GetNumCols());
    if (!(cols == b.GetNumCols()))
        InvalidArgument("AddColumnReshapeProductOf: The input matrix dimensions do not match.");

    CUDA_LONG rowsA = (CUDA_LONG) a.GetNumRows();
    CUDA_LONG rowsB = (CUDA_LONG) b.GetNumRows();
    if (rowsA % rowsB != 0)
        InvalidArgument("AddColumnReshapeProductOf: number of rows in a should be multiples of that in b.");

    CUDA_LONG rowsC = rowsA / rowsB;
    if (rowsC != GetNumRows() || cols != GetNumCols())
        InvalidArgument("AddColumnReshapeProductOf: This matrix does not have the right size.");

    float N = (float) GetNumElements();
    int blocksPerGrid = (int) ceil(N / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_addColumnReshapeProductOf", t_stream);
    _addColumnReshapeProductOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), b.Data(), rowsB, rowsC, cols, transposeAColumn);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddWithScaleOf(ElemType alpha, const GPUMatrix<ElemType>& a)
{
    ScaleAndAdd(alpha, a, *this);
    return *this;
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::FrobeniusNorm() const
{
    if (IsEmpty())
        LogicError("FrobeniusNorm: Matrix is empty.");

    ElemType* d_sum = TracingGPUMemoryAllocator::Allocate<ElemType>(GetComputeDeviceId(), 1);

    ElemType h_sum = 0;
    // WARNING: THIS kernel is not the most efficient way!
    {
        PROFILE_CUDA_STREAM("_reductionSum2", t_stream);
        _reductionSum2<ElemType><<<1, 1024, 0, t_stream>>>(Data(), d_sum, (CUDA_LONG) GetNumElements(), true);
    }
    CUDA_CALL(cudaMemcpy(&h_sum, d_sum, sizeof(ElemType), cudaMemcpyDeviceToHost));
    TracingGPUMemoryAllocator::Free<ElemType>(GetComputeDeviceId(), d_sum);

    return (h_sum);
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignFrobeniusNormOf(const GPUMatrix<ElemType>& a)
{
    if (a.IsEmpty())
        LogicError("AssignFrobeniusNormOf: Matrix a is empty.");

    RequireSize(1, 1);

    PrepareDevice();
    // WARNING: THIS kernel is not the most efficient way!
    PROFILE_CUDA_STREAM("_reductionSum2", t_stream);
    _reductionSum2<ElemType><<<1, 1024, 0, t_stream>>>(a.Data(), Data(), (CUDA_LONG) a.GetNumElements(), true);

    return *this;
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::MatrixNormInf() const
{
    if (IsEmpty())
        LogicError("MatrixNorm1: Matrix is empty.");

    ElemType* d_maxAbs = TracingGPUMemoryAllocator::Allocate<ElemType>(GetComputeDeviceId(), 1);

    ElemType h_maxAbs = 0;
    // WARNING: THIS kernel is not the most efficient way!
    {
        PROFILE_CUDA_STREAM("_reductionMatrixNormInf", t_stream);
        _reductionMatrixNormInf<ElemType><<<1, 1024, 0, t_stream>>>(Data(), d_maxAbs, (CUDA_LONG) GetNumElements());
    }
    CUDA_CALL(cudaMemcpy(&h_maxAbs, d_maxAbs, sizeof(ElemType), cudaMemcpyDeviceToHost));
    TracingGPUMemoryAllocator::Free<ElemType>(GetComputeDeviceId(), d_maxAbs);
    return h_maxAbs;
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::MatrixNorm1() const
{
    if (IsEmpty())
        LogicError("MatrixNorm1: Matrix is empty.");
    return SumOfAbsElements();
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::MatrixNorm0() const
{
    if (IsEmpty())
        LogicError("MatrixNorm0: Matrix is empty.");

    ElemType* d_nz = TracingGPUMemoryAllocator::Allocate<ElemType>(GetComputeDeviceId(), 1);
    ElemType h_nz = 0;
    // WARNING: THIS kernel is not the most efficient way!
    {
        PROFILE_CUDA_STREAM("_reductionMatrixNorm0", t_stream);
        _reductionMatrixNorm0<ElemType><<<1, 1024, 0, t_stream>>>(Data(), d_nz, (CUDA_LONG) GetNumElements());
    }
    CUDA_CALL(cudaMemcpy(&h_nz, d_nz, sizeof(ElemType), cudaMemcpyDeviceToHost));
    TracingGPUMemoryAllocator::Free<ElemType>(GetComputeDeviceId(), d_nz);
    return h_nz;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignSignOf(const GPUMatrix<ElemType>& a)
{
    if (a.IsEmpty())
        LogicError("AssignSignOf: Matrix a is empty.");

    if (this != &a)
        RequireSize(a.GetNumRows(), a.GetNumCols());

    PrepareDevice();
    int blocksPerGrid = (int) ceil(1.0 * GetNumElements() / GridDim::maxThreadsPerBlock);
    PROFILE_CUDA_STREAM("_assignSignOf", t_stream);
    _assignSignOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), (CUDA_LONG) GetNumElements());
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddSignOf(const GPUMatrix<ElemType>& a)
{
    if (a.IsEmpty())
        LogicError("AddSignOf: Matrix a is empty.");

    if (this != &a)
        RequireSize(a.GetNumRows(), a.GetNumCols());

    PrepareDevice();
    int blocksPerGrid = (int) ceil(1.0 * GetNumElements() / GridDim::maxThreadsPerBlock);
    PROFILE_CUDA_STREAM("_addSignOf", t_stream);
    _addSignOf<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), (CUDA_LONG) GetNumElements());
    return *this;
}

template <class ElemType>
void GPUMatrix<ElemType>::VectorMax(GPUMatrix<ElemType>& maxIndexes, GPUMatrix<ElemType>& maxValues, const bool isColWise) const
{
    if (IsEmpty())
        LogicError("VectorMax: Matrix is empty.");

    const GPUMatrix<ElemType>& us = *this;
    const CUDA_LONG m = (CUDA_LONG) GetNumRows();
    const CUDA_LONG n = (CUDA_LONG) GetNumCols();
    assert(m > 0 && n > 0); // converting from size_t to int may cause overflow

    PrepareDevice();
    if (isColWise)
    {
        maxValues.RequireSize(1, n);
        maxIndexes.RequireSize(1, n);

        int blocksPerGrid = n; // we'll have 1 block processing 1 column
        PROFILE_CUDA_STREAM("_vectorMaxMinReduce", t_stream);
        _vectorMaxMinReduce<ElemType, true><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(us.Data(), maxIndexes.Data(), maxValues.Data(), m, n);

        /*int blocksPerGrid=(int)ceil(1.0*n/GridDim::maxThreadsPerBlock);
            _vectorMax<ElemType><<<blocksPerGrid,GridDim::maxThreadsPerBlock,0,t_stream>>>(us.Data(),maxIndexes.Data(),maxValues.Data(),m,n,isColWise);*/
    }
    else
    {
        maxValues.RequireSize(m, 1);
        maxIndexes.RequireSize(m, 1);
        int blocksPerGrid = (int) ceil(1.0 * m / GridDim::maxThreadsPerBlock);
        PROFILE_CUDA_STREAM("_vectorMax", t_stream);
        _vectorMax<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(us.Data(), maxIndexes.Data(), maxValues.Data(), m, n, isColWise);
    }
}

__global__ void _initIndicesForSort(uint64_t* indexes, CUDA_LONG crow, CUDA_LONG ccol)
{
    CUDA_LONG id = blockDim.x * blockIdx.x + threadIdx.x;
    if (id >= crow * ccol)
        return;
    uint32_t irow = id % crow;
    uint32_t icol = id / crow;
    indexes[id] = (static_cast<uint64_t>(irow) << 32) | icol;
}

template <class ElemType>
void GPUMatrix<ElemType>::VectorMax(GPUMatrix<ElemType>& maxIndexes, GPUMatrix<ElemType>& maxValues, const bool isColWise, int topK) const
{
    if (IsEmpty())
        LogicError("VectorMax: Matrix is empty.");

    if (topK == 1)
    {
        VectorMax(maxIndexes, maxValues, isColWise);
        return;
    }

    if (!isColWise)
        RuntimeError("Row-wise TopK max is not supported.");

    const GPUMatrix<ElemType>& us = *this;
    const CUDA_LONG m = (CUDA_LONG) GetNumRows();
    const CUDA_LONG n = (CUDA_LONG) GetNumCols();
    assert(topK <= m);
    assert(m > 0 && n > 0); // converting from size_t to int may cause overflow

    PrepareDevice();
    maxValues.RequireSize(topK, n);
    maxIndexes.RequireSize(topK, n);

    // To sort matrix columns we use 2-pass _stable_ sort algorithm:
    // 1. Sort by values (descending) with corresponding row/col indexes.
    // 2. Sort by col indices (ascending) with corresponding values/row indices.
    // Indices are stored as 64-bit ints where low 32 bits represent column and high 32 bits - row index.
    // On the second pass only first 32 bits of the index are used in sorting, so SortPairs has
    // begin_bit and end_bit set accordingly.

    CUDA_LONG celt = static_cast<CUDA_LONG>(GetNumElements());
    ElemType* inVal = us.Data();
    ElemType* outVal1 = nullptr;
    ElemType* outVal2 = nullptr;
    uint64_t* inIdx = nullptr;
    uint64_t* outIdx = nullptr;
    // Determine temp buffer size needed for SortPairsDescending to sort values on the first pass.
    size_t cbtemp = 0;
    // If first param is nullptr then no actual work is done except writing result to cbtemp.
    {
        PROFILE_CUDA_STREAM("SortPairsDescending", t_stream);
        CUDA_CALL(cub::DeviceRadixSort::SortPairsDescending(nullptr, cbtemp, inVal, outVal1, inIdx, outIdx, celt, 0, sizeof(ElemType) * 8, t_stream));
    }
    size_t ctemp1 = (cbtemp + sizeof(ElemType) - 1) / sizeof(ElemType);
    // Determine temp buffer size needed for SortPairs to sort indices on the second pass.
    cbtemp = 0;
    {
        PROFILE_CUDA_STREAM("SortPairs", t_stream);
        CUDA_CALL(cub::DeviceRadixSort::SortPairs(nullptr, cbtemp, outIdx, inIdx, outVal1, outVal2, celt, 0, 32, t_stream));
    }
    size_t ctemp2 = (cbtemp + sizeof(ElemType) - 1) / sizeof(ElemType);
    size_t ctemp = std::max(ctemp1, ctemp2);
    cbtemp = ctemp * sizeof(ElemType);
    // ElemType count needed to store indices, accounting for natural alignment for uint64_t type.
    size_t cidx = ((celt + 1) * sizeof(uint64_t) - 1 + sizeof(ElemType) - 1) / sizeof(ElemType);
    // Get temp workspace.
    auto workspace = GetOrCreateWorkspace();
    // RequireSize to store: output values for the 1st and 2nd passes, input indices, output indices, and temp storage.
    workspace->RequireSize(m, 2 * n + (2 * cidx + ctemp + m - 1) / m);
    outVal1 = workspace->Data();
    outVal2 = outVal1 + celt;
    inIdx = reinterpret_cast<uint64_t*>(outVal2 + celt);
    // Align indices pointer if needed.
    size_t cbAlign = reinterpret_cast<size_t>(inIdx) % sizeof(uint64_t);
    if (cbAlign != 0)
        reinterpret_cast<uint8_t*&>(inIdx) += sizeof(uint64_t) - cbAlign;
    outIdx = inIdx + celt;
    void* ptmp = outIdx + celt;
    assert(reinterpret_cast<ElemType*>(reinterpret_cast<uint8_t*>(ptmp) + cbtemp) <= workspace->Data()+ workspace->GetNumElements());

    // Initialize indices.
    const int ThreadsPerBlock = 128;
    int cblock = (celt + ThreadsPerBlock - 1) / ThreadsPerBlock;
    {
        PROFILE_CUDA_STREAM("_initIndicesForSort", t_stream);
        _initIndicesForSort<<<cblock, ThreadsPerBlock, 0, t_stream>>>(inIdx, m, n);
    }
    // Sort by values.
    {
        PROFILE_CUDA_STREAM("SortPairsDescending", t_stream);
        CUDA_CALL(cub::DeviceRadixSort::SortPairsDescending(ptmp, cbtemp, inVal, outVal1, inIdx, outIdx, celt, 0, sizeof(ElemType) * 8, t_stream));
    }
    // Sort by column indices. outIdx contains indices after the first pass so it's used as an input.
    {
        PROFILE_CUDA_STREAM("SortPairs", t_stream);
        CUDA_CALL(cub::DeviceRadixSort::SortPairs(ptmp, cbtemp, outIdx, inIdx, outVal1, outVal2, celt, 0, 32, t_stream));
    }
    // Copy results.
    cblock = (topK * n + ThreadsPerBlock - 1) / ThreadsPerBlock;
    {
        PROFILE_CUDA_STREAM("_copyTopKResults", t_stream);
        _copyTopKResults<<<cblock, ThreadsPerBlock, 0, t_stream>>>(inIdx, outVal2, maxIndexes.Data(), maxValues.Data(), m, n, topK);
    }

    ReleaseWorkspace(std::move(workspace));

}

template <class ElemType>
void GPUMatrix<ElemType>::VectorMin(GPUMatrix<ElemType>& minIndexes, GPUMatrix<ElemType>& minValues, const bool isColWise) const
{
    if (IsEmpty())
        LogicError("VectorMax: Matrix is empty.");

    const GPUMatrix<ElemType>& us = *this;
    const int m = (int) GetNumRows();
    const int n = (int) GetNumCols();

    assert(m > 0 && n > 0); // converting from size_t to int may cause overflow
    PrepareDevice();
    if (isColWise)
    {
        minValues.RequireSize(1, n);
        minIndexes.RequireSize(1, n);

        int blocksPerGrid = n; // we'll have 1 block processing 1 column
        PROFILE_CUDA_STREAM("_vectorMaxMinReduce", t_stream);
        _vectorMaxMinReduce<ElemType, false><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(us.Data(), minIndexes.Data(), minValues.Data(), m, n);

        /*
            int blocksPerGrid=(int)ceil(1.0*n/GridDim::maxThreadsPerBlock);
            _vectorMin<ElemType><<<blocksPerGrid,GridDim::maxThreadsPerBlock,0,t_stream>>>(us.Data(),minIndexes.Data(),minValues.Data(),m,n,isColWise);*/
    }
    else
    {
        minValues.RequireSize(m, 1);
        minIndexes.RequireSize(m, 1);
        int blocksPerGrid = (int) ceil(1.0 * m / GridDim::maxThreadsPerBlock);
        PROFILE_CUDA_STREAM("_vectorMin", t_stream);
        _vectorMin<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(us.Data(), minIndexes.Data(), minValues.Data(), m, n, isColWise);
    }
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignNumOfDiff(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, bool searchInCol)
{
    if (a.GetNumCols() != b.GetNumCols())
        InvalidArgument("AssignNumOfDiff: a and b must have the same number of columns.");
    if (!searchInCol && a.GetNumRows() != b.GetNumRows())
        InvalidArgument("AssignNumOfDiff: a and b must have the same number of rows.");

    RequireSize(1, 1); // result should be one element

    PrepareDevice();
    if (!searchInCol)
    {
        // int blocksPerGrid=(int)ceil(1.0*a.GetNumElements()/GridDim::maxThreadsPerBlock);
        // _assignNumOfDiff<ElemType><<<blocksPerGrid,GridDim::maxThreadsPerBlock,0,t_stream>>>(a.Data(), b.Data(), Data(), a.GetNumElements());
        PROFILE_CUDA_STREAM("_assignNumOfDiff", t_stream);
        _assignNumOfDiff<ElemType><<<1, 1024, 0, t_stream>>>(a.Data(), b.Data(), Data(), (CUDA_LONG) a.GetNumElements());
    }
    else
    {
        const int blockSize = 1024;
        PROFILE_CUDA_STREAM("_assignNumOfDiffCol", t_stream);
        _assignNumOfDiffCol<blockSize><<<1, blockSize, 0, t_stream>>>(a.Data(), b.Data(), Data(),
                                                                      static_cast<CUDA_LONG>(b.GetNumRows()), static_cast<CUDA_LONG>(a.GetNumCols()));
    }
    return *this;
}

#pragma endregion Member BLAS Functions

#pragma region Other helper functions
template <class ElemType>
void GPUMatrix<ElemType>::Print(const char* /*matrixName*/, size_t /*rowStart*/, size_t /*rowEnd*/, size_t /*colStart*/, size_t /*colEnd*/) const
{
    NOT_IMPLEMENTED;
}

template <class ElemType>
void GPUMatrix<ElemType>::Print(const char* matrixName /*=nullptr*/) const
{
    Print(matrixName, 0, GetNumRows() - 1, 0, GetNumCols() - 1);
}

//helpfer function used for convolution neural network
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignPackedConvolutionInput(const GPUMatrix<ElemType>& inputSubBatch,
                                                                       const size_t inputWidth, const size_t inputHeight, const size_t inputChannels,
                                                                       const size_t outputWidth, const size_t outputHeight, const size_t outputChannels,
                                                                       const size_t kernelWidth, const size_t kernelHeight, const size_t horizontalSubsample, const size_t verticalSubsample,
                                                                       const bool zeroPadding)
{
    assert(verticalSubsample <= kernelHeight && horizontalSubsample <= kernelWidth);

    size_t packedInputRows = kernelWidth * kernelHeight * inputChannels;
    size_t packedInputColsPerSample = outputWidth * outputHeight;
    size_t smallBatchSize = inputSubBatch.GetNumCols();
    RequireSize(packedInputRows, packedInputColsPerSample * smallBatchSize);
    if (zeroPadding)
        SetValue((ElemType) 0);

    PrepareDevice();
    int numThreadPerBlock = GridDim::maxThreadsPerBlock;
#if 1
    int blocksPerGrid = (smallBatchSize * inputWidth * inputHeight * inputChannels + numThreadPerBlock - 1) / numThreadPerBlock;
#else
    dim3 blocksPerGrid((inputWidth * inputHeight * inputChannels + numThreadPerBlock - 1) / numThreadPerBlock, smallBatchSize);
#endif
    PROFILE_CUDA_STREAM("_assignPackedConvolutionInput", t_stream);
    _assignPackedConvolutionInput<<<blocksPerGrid, numThreadPerBlock, 0, t_stream>>>(Data(),
                                                                                     inputSubBatch.Data(),
                                                                                     smallBatchSize,
                                                                                     inputWidth, inputHeight, inputChannels,
                                                                                     outputWidth, outputHeight, outputChannels,
                                                                                     kernelWidth, kernelHeight, horizontalSubsample, verticalSubsample, zeroPadding);

    return *this;
}

//helpfer function used for convolution neural network
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::UnpackConvolutionInput(GPUMatrix<ElemType>& inputSubBatch,
                                                                 const size_t inputWidth, const size_t inputHeight, const size_t inputChannels,
                                                                 const size_t outputWidth, const size_t outputHeight, const size_t outputChannels,
                                                                 const size_t kernelWidth, const size_t kernelHeight, const size_t horizontalSubsample, const size_t verticalSubsample,
                                                                 const bool zeroPadding) const
{
    assert(verticalSubsample <= kernelHeight && horizontalSubsample <= kernelWidth);

    size_t smallBatchSize = inputSubBatch.GetNumCols();

    PrepareDevice();
    int numThreadPerBlock = GridDim::maxThreadsPerBlock;
#if 1
    int blocksPerGrid = (smallBatchSize * inputWidth * inputHeight * inputChannels + numThreadPerBlock - 1) / numThreadPerBlock;
#else
    dim3 blocksPerGrid((inputWidth * inputHeight * inputChannels + numThreadPerBlock - 1) / numThreadPerBlock, smallBatchSize);
#endif
    PROFILE_CUDA_STREAM("_unpackConvolutionInput", t_stream);
    _unpackConvolutionInput<<<blocksPerGrid, numThreadPerBlock, 0, t_stream>>>(Data(),
                                                                               inputSubBatch.Data(),
                                                                               smallBatchSize,
                                                                               inputWidth, inputHeight, inputChannels,
                                                                               outputWidth, outputHeight, outputChannels,
                                                                               kernelWidth, kernelHeight, horizontalSubsample, verticalSubsample, zeroPadding);

    return inputSubBatch;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignMaxPoolingResult(const GPUMatrix<ElemType>& inputBatch, const size_t channels,
                                                                 const size_t inputWidth, const size_t inputHeight, const size_t inputSizePerSample,
                                                                 const size_t outputWidth, const size_t outputHeight, const size_t outputSizePerSample,
                                                                 const size_t windowWidth, const size_t windowHeight, const size_t horizontalSubsample, const size_t verticalSubsample)
{
    assert(verticalSubsample <= windowHeight && horizontalSubsample <= windowWidth);

    unsigned int batchSize = inputBatch.GetNumCols();
    RequireSize(outputSizePerSample, batchSize);

    int numThreadPerBlock = GridDim::maxThreadsPerBlock;
    int blocksPerGrid = (batchSize * outputSizePerSample + numThreadPerBlock - 1) / numThreadPerBlock;

    PrepareDevice();
    PROFILE_CUDA_STREAM("_assignMaxPoolingResult", t_stream);
    _assignMaxPoolingResult<<<blocksPerGrid, numThreadPerBlock, 0, t_stream>>>(Data(), inputBatch.Data(), batchSize, channels,
                                                                               inputWidth, inputHeight, inputSizePerSample,
                                                                               outputWidth, outputHeight, outputSizePerSample,
                                                                               windowWidth, windowHeight, horizontalSubsample, verticalSubsample);

    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddMaxPoolingGradient(const GPUMatrix<ElemType>& outputGradientBatch, const GPUMatrix<ElemType>& inputBatch, const GPUMatrix<ElemType>& outputBatch,
                                                                const size_t channels,
                                                                const size_t inputWidth, const size_t inputHeight, const size_t inputSizePerSample,
                                                                const size_t outputWidth, const size_t outputHeight, const size_t outputSizePerSample,
                                                                const size_t windowWidth, const size_t windowHeight, const size_t horizontalSubsample, const size_t verticalSubsample)
{
    assert(verticalSubsample <= windowHeight && horizontalSubsample <= windowWidth);

    unsigned int batchSize = outputGradientBatch.GetNumCols();
    int numThreadPerBlock = GridDim::maxThreadsPerBlock;

    PrepareDevice();

    int blocksPerGrid = (batchSize * inputSizePerSample + numThreadPerBlock - 1) / numThreadPerBlock;
    PROFILE_CUDA_STREAM("_addMaxPoolingGradient", t_stream);
    _addMaxPoolingGradient<<<blocksPerGrid, numThreadPerBlock, 0, t_stream>>>(Data(), outputGradientBatch.Data(), inputBatch.Data(), outputBatch.Data(), batchSize, channels,
                                                                              inputWidth, inputHeight, inputSizePerSample,
                                                                              outputWidth, outputHeight, outputSizePerSample,
                                                                              windowWidth, windowHeight, horizontalSubsample, verticalSubsample);

    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignAveragePoolingResult(const GPUMatrix<ElemType>& inputBatch, const size_t channels,
                                                                     const size_t inputWidth, const size_t inputHeight, const size_t inputSizePerSample,
                                                                     const size_t outputWidth, const size_t outputHeight, const size_t outputSizePerSample,
                                                                     const size_t windowWidth, const size_t windowHeight, const size_t horizontalSubsample, const size_t verticalSubsample)
{
    assert(verticalSubsample <= windowHeight && horizontalSubsample <= windowWidth);

    unsigned int batchSize = inputBatch.GetNumCols();
    RequireSize(outputSizePerSample, batchSize);

    int numThreadPerBlock = GridDim::maxThreadsPerBlock;
    int blocksPerGrid = (batchSize * outputSizePerSample + numThreadPerBlock - 1) / numThreadPerBlock;

    PrepareDevice();
    PROFILE_CUDA_STREAM("_assignAveragePoolingResult", t_stream);
    _assignAveragePoolingResult<<<blocksPerGrid, numThreadPerBlock, 0, t_stream>>>(Data(), inputBatch.Data(), batchSize, channels,
                                                                                   inputWidth, inputHeight, inputSizePerSample,
                                                                                   outputWidth, outputHeight, outputSizePerSample,
                                                                                   windowWidth, windowHeight, horizontalSubsample, verticalSubsample);

    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AddAveragePoolingGradient(const GPUMatrix<ElemType>& outputGradientBatch,
                                                                    const size_t channels,
                                                                    const size_t inputWidth, const size_t inputHeight, const size_t inputSizePerSample,
                                                                    const size_t outputWidth, const size_t outputHeight, const size_t outputSizePerSample,
                                                                    const size_t windowWidth, const size_t windowHeight, const size_t horizontalSubsample, const size_t verticalSubsample)
{
    assert(verticalSubsample <= windowHeight && horizontalSubsample <= windowWidth);

    size_t batchSize = outputGradientBatch.GetNumCols();
    int numThreadPerBlock = GridDim::maxThreadsPerBlock;

    PrepareDevice();
    PROFILE_CUDA_STREAM("_addAveragePoolingGradient", t_stream);
    size_t blocksPerGrid = (batchSize * inputSizePerSample + numThreadPerBlock - 1) / numThreadPerBlock;
    _addAveragePoolingGradient<<<blocksPerGrid, numThreadPerBlock, 0, t_stream>>>(Data(), outputGradientBatch.Data(), (CUDA_LONG) batchSize, channels,
                                                                                  inputWidth, inputHeight, inputSizePerSample,
                                                                                  outputWidth, outputHeight, outputSizePerSample,
                                                                                  windowWidth, windowHeight, horizontalSubsample, verticalSubsample);

    return *this;
}

#pragma endregion Other helper functions

template <class ElemType>
void GPUMatrix<ElemType>::ConvolutionForward(const GPUMatrix<ElemType>& kernel, const GPUMatrix<int>& mpRowCol, const GPUMatrix<int>& mpRowIwht,
                                             const GPUMatrix<int>& mpRowRun, const GPUMatrix<int>& runs, GPUMatrix<ElemType>& output) const
{
    const int BlockSize = 128;
    auto gdim = dim3((output.GetNumRows() + BlockSize - 1)/ BlockSize, std::min((int)GetNumCols(), 65535));
    PrepareDevice();
    PROFILE_CUDA_STREAM("kConvolutionForward", t_stream);
    kConvolutionForward<<<gdim, BlockSize, 0, t_stream>>>((int)GetNumCols(), kernel.Data(), mpRowCol.Data(), mpRowIwht.Data(), mpRowRun.Data(),
                                                            runs.Data(), Data(), (int)GetNumRows(), output.Data(), (int)output.GetNumRows());
}

template <class ElemType>
void GPUMatrix<ElemType>::ConvolutionBackwardData(const GPUMatrix<ElemType>& kernel, const GPUMatrix<int>& mpRowCol, const GPUMatrix<int>& mpRowIwht,
                                                  const GPUMatrix<int>& mpRowRun, const GPUMatrix<int>& runs, GPUMatrix<ElemType>& grad) const
{
    const int BlockSize = 128;
    auto gdim = dim3((GetNumRows() + BlockSize - 1)/ BlockSize, std::min((int)GetNumCols(), 65535));
    PrepareDevice();
    PROFILE_CUDA_STREAM("kConvolutionBackwardData", t_stream);
    kConvolutionBackwardData<<<gdim, BlockSize, 0, t_stream>>>((int)GetNumCols(), kernel.Data(), mpRowCol.Data(), mpRowIwht.Data(), mpRowRun.Data(),
                                                                 runs.Data(), Data(), (int)GetNumRows(), grad.Data(), (int)grad.GetNumRows());
}

template <class ElemType>
void GPUMatrix<ElemType>::ConvolutionBackwardKernel(const GPUMatrix<ElemType>& in, const GPUMatrix<int>& mpRowCol, const GPUMatrix<int>& mpRowIwht,
                                                    const GPUMatrix<int>& mpRowRun, const GPUMatrix<int>& runs, GPUMatrix<ElemType>& kernelGrad) const
{
    const int BlockSize = 128;
    auto gdim = dim3((GetNumRows() + BlockSize - 1)/ BlockSize, std::min((int)GetNumCols(), 65535));
    PrepareDevice();
    PROFILE_CUDA_STREAM("kConvolutionBackwardKernel", t_stream);
    kConvolutionBackwardKernel<<<gdim, BlockSize, 0, t_stream>>>((int)GetNumCols(), (int)in.GetNumRows(), (int)GetNumRows(),
                                                                   in.Data(), mpRowCol.Data(), mpRowIwht.Data(), mpRowRun.Data(),
                                                                   runs.Data(), Data(), kernelGrad.Data());
}

template <class ElemType>
void GPUMatrix<ElemType>::MaxPoolingForward(const GPUMatrix<int>& mpRowCol, const GPUMatrix<int>& mpRowIndices, const GPUMatrix<int>& indices, GPUMatrix<ElemType>& output) const
{
    const int BlockSize = 128;
    auto gdim = dim3((output.GetNumRows() + BlockSize - 1)/ BlockSize, std::min((int)GetNumCols(), 65535));
    PrepareDevice();
    PROFILE_CUDA_STREAM("kMaxPoolingForward", t_stream);
    kMaxPoolingForward<<<gdim, BlockSize, 0, t_stream>>>((int)GetNumCols(), mpRowCol.Data(), mpRowIndices.Data(), indices.Data(),
                                                           Data(), (int)GetNumRows(), output.Data(), (int)output.GetNumRows());
}

template <class ElemType>
void GPUMatrix<ElemType>::MaxPoolingBackward(const GPUMatrix<ElemType>& out, const GPUMatrix<ElemType>& in,
                                             const GPUMatrix<int>& mpRowCol, const GPUMatrix<int>& mpRowIndices, const GPUMatrix<int>& indices,
                                             GPUMatrix<ElemType>& grad) const
{
    const int BlockSize = 128;
    auto gdim = dim3((GetNumRows() + BlockSize - 1)/ BlockSize, std::min((int)GetNumCols(), 65535));
    PrepareDevice();
    PROFILE_CUDA_STREAM("kMaxPoolingBackward", t_stream);
    kMaxPoolingBackward<<<gdim, BlockSize, 0, t_stream>>>((int)GetNumCols(), out.Data(), in.Data(),
                                                            mpRowCol.Data(), mpRowIndices.Data(), indices.Data(),
                                                            Data(), (int)GetNumRows(), grad.Data(), (int)grad.GetNumRows());
}

template <class ElemType>
void GPUMatrix<ElemType>::AveragePoolingForward(const GPUMatrix<int>& mpRowCol, const GPUMatrix<int>& mpRowIndices, const GPUMatrix<int>& indices, GPUMatrix<ElemType>& output) const
{
    const int BlockSize = 128;
    auto gdim = dim3((output.GetNumRows() + BlockSize - 1)/ BlockSize, std::min((int)GetNumCols(), 65535));
    PrepareDevice();
    PROFILE_CUDA_STREAM("kAveragePoolingForward", t_stream);
    kAveragePoolingForward<<<gdim, BlockSize, 0, t_stream>>>((int)GetNumCols(), mpRowCol.Data(), mpRowIndices.Data(), indices.Data(),
                                                               Data(), (int)GetNumRows(), output.Data(), (int)output.GetNumRows());
}

template <class ElemType>
void GPUMatrix<ElemType>::AveragePoolingBackward(const GPUMatrix<int>& mpRowCol, const GPUMatrix<int>& mpRowIndices, const GPUMatrix<int>& indices, GPUMatrix<ElemType>& grad) const
{
    const int BlockSize = 128;
    auto gdim = dim3((GetNumRows() + BlockSize - 1)/ BlockSize, std::min((int)GetNumCols(), 65535));
    PrepareDevice();
    PROFILE_CUDA_STREAM("kAveragePoolingBackward", t_stream);
    kAveragePoolingBackward<<<gdim, BlockSize, 0, t_stream>>>((int)GetNumCols(), mpRowCol.Data(), mpRowIndices.Data(), indices.Data(),
                                                                Data(), (int)GetNumRows(), grad.Data(), (int)grad.GetNumRows());
}

template <class ElemType>
void GPUMatrix<ElemType>::BatchNormalizationForward(const GPUMatrix<ElemType>& scale, const GPUMatrix<ElemType>& bias, double expAvgFactor, double blendFactor,
                                                    GPUMatrix<ElemType>& runMean, GPUMatrix<ElemType>& runInvStdDev, GPUMatrix<ElemType>& out, double epsilon,
                                                    GPUMatrix<ElemType>& saveMean, GPUMatrix<ElemType>& saveInvStdDev) const
{
    assert((GetNumRows() % scale.GetNumRows()) == 0);

    bool spatial = GetNumRows() != scale.GetNumRows();
    size_t vectorSize = GetNumRows();
    size_t spatialSize = spatial ? (GetNumRows() / scale.GetNumRows()) : 1;
    size_t batchSize = GetNumCols();

    assert(0 < vectorSize && vectorSize <= std::numeric_limits<int>::max());
    assert(0 < batchSize  && batchSize  <= std::numeric_limits<int>::max());

    // If expAvgFactor == 0 && blendFactor == 1 then we don't need to compute current minibatch statistics.
    if (expAvgFactor > 0 || blendFactor < 1)
    {
        if (spatial)
        {
            PROFILE_CUDA_STREAM("ComputeSpatialBatchMeanAndInvStdDev", t_stream);
            Call<ComputeSpatialBatchMeanAndInvStdDev, ElemType>(spatialSize, vectorSize, spatialSize, batchSize, Data(),
                                                                expAvgFactor, runMean.Data(), runInvStdDev.Data(), epsilon,
                                                                saveMean.Data(), saveInvStdDev.Data(), GetStream());
        }
        else
        {
            PROFILE_CUDA_STREAM("ComputeBatchMeanAndInvStdDev", t_stream);
            Call<ComputeBatchMeanAndInvStdDev, ElemType>(vectorSize, vectorSize, batchSize, Data(),
                                                         expAvgFactor, runMean.Data(), runInvStdDev.Data(), epsilon,
                                                         saveMean.Data(), saveInvStdDev.Data(), GetStream());
        }
    }
    // When:
    //     blendFactor == 1 - use running mean/var instead of the current minibatch mean/var.
    // 0 < blendFactor <  1 - blend running mean/var with mean/var of the current minibatch: saveMean = (1 - blendFactor) * saveMean + blendFactor * runMean
    //     blendFactor == 0 - use mean/var of the current minibatch.
    if (blendFactor < 1)
    {
        if (blendFactor > 0)
        {
            // REVIEW alexeyk: can be rolled into NormalizeBatchTraining to save bandwidth.
            Scale((ElemType)(1 - blendFactor), saveMean);
            ScaleAndAdd((ElemType)blendFactor, runMean, saveMean);
            Scale((ElemType)(1 - blendFactor), saveInvStdDev);
            ScaleAndAdd((ElemType)blendFactor, runInvStdDev, saveInvStdDev);
        }
        PROFILE_CUDA_STREAM("NormalizeBatchTraining", t_stream);
        Call<NormalizeBatchTraining, ElemType>(spatial ? spatialSize : vectorSize, vectorSize, spatialSize, batchSize,
                                               spatial, Data(), out.Data(), scale.Data(), bias.Data(),
                                               saveMean.Data(), saveInvStdDev.Data(), GetStream());
    }
    else
    {
        PROFILE_CUDA_STREAM("NormalizeBatchTraining", t_stream);
        Call<NormalizeBatchTraining, ElemType>(spatial ? spatialSize : vectorSize, vectorSize, spatialSize, batchSize,
                                               spatial, Data(), out.Data(), scale.Data(), bias.Data(),
                                               runMean.Data(), runInvStdDev.Data(), GetStream());
    }
}

template <class ElemType>
void GPUMatrix<ElemType>::BatchNormalizationBackward(const GPUMatrix<ElemType>& in, GPUMatrix<ElemType>& grad, const GPUMatrix<ElemType>& scale, 
                                                     const GPUMatrix<ElemType>& saveMean, const GPUMatrix<ElemType>& saveInvStdDev,
                                                     GPUMatrix<ElemType>& scaleGrad, GPUMatrix<ElemType>& biasGrad) const
{
    assert((GetNumRows() % scale.GetNumRows()) == 0);

    bool spatial = GetNumRows() != scale.GetNumRows();
    size_t vectorSize = GetNumRows();
    size_t spatialSize = spatial ? (GetNumRows() / scale.GetNumRows()) : 1;
    size_t batchSize = GetNumCols();

    assert(0 < vectorSize && vectorSize <= std::numeric_limits<int>::max());
    assert(0 < batchSize  && batchSize  <= std::numeric_limits<int>::max());

    if (spatial)
    {
        PROFILE_CUDA_STREAM("ComputeSpatialScaleAndBiasGradients", t_stream);
        Call<ComputeSpatialScaleAndBiasGradients, ElemType>(spatialSize, vectorSize, spatialSize, batchSize, in.Data(), Data(), scaleGrad.Data(), biasGrad.Data(),
                                                            saveMean.Data(), saveInvStdDev.Data(), GetStream());
    }
    else
    {
        PROFILE_CUDA_STREAM("ComputeScaleAndBiasGradients", t_stream);
        Call<ComputeScaleAndBiasGradients, ElemType>(vectorSize, vectorSize, batchSize, in.Data(), Data(), scaleGrad.Data(), biasGrad.Data(),
                                                     saveMean.Data(), saveInvStdDev.Data(), GetStream());
    }
    PROFILE_CUDA_STREAM("BackpropagateBatchNormGradients", t_stream);
    Call<BackpropagateBatchNormGradients, ElemType>(spatial ? spatialSize : vectorSize, vectorSize, spatialSize, batchSize, spatial,
                                                    in.Data(), Data(), grad.Data(), scale.Data(), scaleGrad.Data(), biasGrad.Data(), saveMean.Data(), saveInvStdDev.Data(), GetStream());
}

#pragma region Static BLAS Functions
// float/double overloads of cublasSgemm()/cublasDgemm()
static cublasStatus_t cublas_gemm(cublasHandle_t handle, cublasOperation_t transa, cublasOperation_t transb, int m, int n, int k, const float* alpha, const float* A, int lda, const float* B, int ldb, const float* beta, float* C, int ldc)
{
    return cublasSgemm(handle, transa, transb, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc);
}
static cublasStatus_t cublas_gemm(cublasHandle_t handle, cublasOperation_t transa, cublasOperation_t transb, int m, int n, int k, const double* alpha, const double* A, int lda, const double* B, int ldb, const double* beta, double* C, int ldc)
{
    return cublasDgemm(handle, transa, transb, m, n, k, alpha, A, lda, B, ldb, beta, C, ldc);
}
static cublasStatus_t cublas_axpy(cublasHandle_t handle, int n, const float* alpha, const float* x, int incx, float* y, int incy)
{
    return cublasSaxpy(handle, n, alpha, x, incx, y, incy);
}
static cublasStatus_t cublas_axpy(cublasHandle_t handle, int n, const double* alpha, const double* x, int incx, double* y, int incy)
{
    return cublasDaxpy(handle, n, alpha, x, incx, y, incy);
}

template <class ElemType>
void GPUMatrix<ElemType>::MultiplyAndWeightedAdd(ElemType alpha, const GPUMatrix<ElemType>& a, const bool transposeA, const GPUMatrix<ElemType>& b, const bool transposeB,
                                                 ElemType beta, GPUMatrix<ElemType>& c)
{
    a.PrepareDevice();
    if ((a.GetComputeDeviceId() != b.GetComputeDeviceId()) || (b.GetComputeDeviceId() != c.GetComputeDeviceId())) // different GPUs
        InvalidArgument("All matrices must be on the same GPU");

    cublasHandle_t cuHandle = GetCublasHandle(b.GetComputeDeviceId());
    cublasOperation_t transA = transposeA ? CUBLAS_OP_T : CUBLAS_OP_N;
    cublasOperation_t transB = transposeB ? CUBLAS_OP_T : CUBLAS_OP_N;
    int m = int(transposeA ? a.m_numCols : a.m_numRows);
    int n = int(transposeB ? b.m_numRows : b.m_numCols);
    int k = int(transposeA ? a.m_numRows : a.m_numCols);
    int l = int(transposeB ? b.m_numCols : b.m_numRows);

    c.RequireSize(m, n);

    if (!(m > 0 && k > 0 && l > 0 && n > 0))
        RuntimeError("!(m>0 && k>0 && l>0 && n>0)"); // converting from size_t to int may cause overflow
    if (k != l)
        RuntimeError("matrix dim mismatch in MultiplyAndWeightedAdd");

    PROFILE_CUDA_STREAM("cublas_gemm", t_stream);
    CUBLAS_CALL(cublas_gemm(cuHandle, transA, transB, m, n, k, &alpha, a.Data(), (int) a.m_numRows, b.Data(), (int) b.m_numRows, &beta, c.Data(), (int) c.m_numRows));
    c.m_numRows = m;
    c.m_numCols = n;
}

template <class ElemType>
void GPUMatrix<ElemType>::Multiply1x1AndWeightedAdd(ElemType alpha, const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, ElemType beta, GPUMatrix<ElemType>& c)
{
    a.PrepareDevice();
    if ((a.GetComputeDeviceId() != b.GetComputeDeviceId()) || (b.GetComputeDeviceId() != c.GetComputeDeviceId())) // different GPUs
        InvalidArgument("All matrices must be on the same GPU");
    CUDA_LONG N = (CUDA_LONG) c.GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PROFILE_CUDA_STREAM("_multiply1x1AndWeightedAdd", t_stream);
    _multiply1x1AndWeightedAdd<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(alpha, a.Data(), b.Data(), beta, c.Data(), N);
}

template <class ElemType>
void GPUMatrix<ElemType>::MultiplyAndAdd(const GPUMatrix<ElemType>& a, const bool transposeA, const GPUMatrix<ElemType>& b, const bool transposeB, GPUMatrix<ElemType>& c)
{
    return GPUMatrix<ElemType>::MultiplyAndWeightedAdd(1, a, transposeA, b, transposeB, 1, c);
}

template <class ElemType>
void GPUMatrix<ElemType>::Multiply(const GPUMatrix<ElemType>& a, const bool transposeA, const GPUMatrix<ElemType>& b, const bool transposeB, GPUMatrix<ElemType>& c)
{
    return GPUMatrix<ElemType>::MultiplyAndWeightedAdd(1, a, transposeA, b, transposeB, 0, c);
}

template <class ElemType>
void GPUMatrix<ElemType>::Multiply(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c)
{
    return GPUMatrix<ElemType>::MultiplyAndWeightedAdd(1, a, false, b, false, 0, c);
}

/// <summary>Matrix-scalar multiply with col-major matrices: c = alpha * a + c</summary>
/// if a is a column vector, add to all columns of c
/// if a is a row vector, add to all rows of c
/// if a is a scalar, add to all elements of c
/// <param name="alpha">Scalar</param>
/// <param name="a">Input matrix</param>
/// <param name="c">Resulting matrix, user is responsible for allocating this</param>
template <class ElemType>
/*static*/ void GPUMatrix<ElemType>::ScaleAndAdd(ElemType alpha, const GPUMatrix<ElemType>& a, GPUMatrix<ElemType>& c)
{
    if (a.GetComputeDeviceId() != c.GetComputeDeviceId())
    {
        InvalidArgument("All matrices must be on the same GPU");
    }
    else
    {
        if (a.IsEmpty() && c.IsEmpty())
            return;
        a.PrepareDevice();
        if (a.IsEmpty() || c.IsEmpty())
            LogicError("ScaleAndAdd:  one of the input matrices is empty.");
        // if (a.GetNumRows() != 1 && a.GetNumCols() != 1) // a is not a col or row vector
        if (a.GetNumRows() == c.GetNumRows() && a.GetNumCols() == c.GetNumCols()) // dimensions match
        {
            const int m = (int) a.GetNumRows();
            const int n = (int) a.GetNumCols();
            const int len = m * n;
            const int incx = 1;
            const int incy = 1;

            assert(m > 0 && n > 0 && len > 0); // converting from size_t to int may cause overflow
            assert((int) c.GetNumRows() == m && (int) c.GetNumCols() == n);
            if ((int) c.GetNumRows() != m || (int) c.GetNumCols() != n)
                InvalidArgument("dimension of matrix c does not match dimension of matrix a.");

            cublasHandle_t cuHandle = GetCublasHandle(a.GetComputeDeviceId());
            // TODO: Overload the call to cublas_axpy to remove these ugly if/else statements.
            if (sizeof(ElemType) == sizeof(float))
            {
                PROFILE_CUDA_STREAM("cublasSaxpy", t_stream);
                CUBLAS_CALL(cublasSaxpy(cuHandle, len, reinterpret_cast<float*>(&alpha), reinterpret_cast<float*>(a.Data()), incx, reinterpret_cast<float*>(c.Data()), incy));
            }
            else if (sizeof(ElemType) == sizeof(double))
            {
                PROFILE_CUDA_STREAM("cublasDaxpy", t_stream);
                CUBLAS_CALL(cublasDaxpy(cuHandle, len, reinterpret_cast<double*>(&alpha), reinterpret_cast<double*>(a.Data()), incx, reinterpret_cast<double*>(c.Data()), incy));
            }
            else
            {
                RuntimeError("Unsupported template argument in GPUMatrix");
            }
        }
        else if (a.GetNumElements() == 1)
        {
            CUDA_LONG N = (CUDA_LONG) c.GetNumElements();
            int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
            c.PrepareDevice();
            PROFILE_CUDA_STREAM("_scaleAndAddScalar", t_stream);
            _scaleAndAddScalar<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(c.Data(), N, alpha, a.Data(), c.Data());
        }
        else if (a.GetNumCols() == 1) // col vector, add it to all columns
        {
            CUDA_LONG m = (CUDA_LONG) c.GetNumRows();
            CUDA_LONG n = (CUDA_LONG) c.GetNumCols();
            if (m != (CUDA_LONG) a.GetNumRows())
                InvalidArgument("To add column vector, rows should match.");

            int blocksPerGrid = (int) (ceil(1.0 * m * n / GridDim::maxThreadsPerBlock));
            PROFILE_CUDA_STREAM("_matrixVectorColumnWiseAddWithThreadPerElem", t_stream);
#ifdef VALIDATION
            printf(">>>> CUDA compute device is %d\n", a.GetComputeDeviceId());
            printf(">>>> a.Data()= %p, c.Data()= %p, alpha = %f, m = %ld, n = %ld\n", a.Data(), c.Data(), alpha, m, n);
            for (int i = 0; i < 2; i++)
            {
                ElemType buffer[10] = {-1.234f};
                cudaError_t error = cudaMemcpy(buffer, !i ? a.Data(): c.Data(), sizeof(buffer), cudaMemcpyKind::cudaMemcpyDeviceToHost);
                if (error == cudaError::cudaSuccess)
                    printf("buffer valid\n");
            }
#endif

            _matrixVectorColumnWiseAddWithThreadPerElem<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(a.Data(), c.Data(), c.Data(), alpha, m, n);

        }
        else if (a.GetNumRows() == 1) // row vector, add it to all rows
        {
            cublasHandle_t cuHandle = GetCublasHandle(a.GetComputeDeviceId());
            int m = (int) c.GetNumRows();
            int n = (int) c.GetNumCols();
            assert(n == (int) a.GetNumCols());
            if (n != (int) a.GetNumCols())
                InvalidArgument("To add row vector, cols should match.");

            // TODO: Overload the call to cublas_axpy to remove these ugly if/else statements.
            if (sizeof(ElemType) == sizeof(double))
            {
                foreach_row (i, c)
                {
                    PROFILE_CUDA_STREAM("cublasDaxpy", t_stream);
                    CUBLAS_CALL(cublasDaxpy(cuHandle, n, reinterpret_cast<double*>(&alpha), reinterpret_cast<double*>(a.Data()), 1, reinterpret_cast<double*>(c.Data()+ i), m));
                }
            }
            else
            {
                foreach_row (i, c)
                {
                    PROFILE_CUDA_STREAM("cublasSaxpy", t_stream);
                    CUBLAS_CALL(cublasSaxpy(cuHandle, n, reinterpret_cast<float*>(&alpha), reinterpret_cast<float*>(a.Data()), 1, reinterpret_cast<float*>(c.Data()+ i), m));
                }
            }
        }
        else
            InvalidArgument("dimension of matrix c does not match dimension of matrix a.");
    }
}

/// <summary>Matrix-scalar multiply with col-major matrices: c = alpha * a + b</summary>
/// if a is a column vector, add to all columns of b
/// if a is a row vector, add to all rows of b
/// if a is a scalar, add to all elements of b
/// <param name="alpha">Scalar</param>
/// <param name="a">Input matrix</param>
/// <param name="b">Input matrix</param>
/// <param name="c">Resulting matrix, user is responsible for allocating this</param>
template <class ElemType>
/*static*/ void GPUMatrix<ElemType>::ScaleAndAdd(ElemType alpha, const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c)
{
    if (a.GetComputeDeviceId() != c.GetComputeDeviceId() || a.GetComputeDeviceId() != b.GetComputeDeviceId())
    {
        InvalidArgument("All matrices must be on the same GPU");
    }
    else
    {
        if (a.IsEmpty() && b.IsEmpty())
            return;
        a.PrepareDevice();
        if (a.IsEmpty() || b.IsEmpty())
            LogicError("ScaleAndAdd: One of the input matrices is empty.");
        c.RequireSize(b.GetNumRows(), b.GetNumCols());
        // if (a.GetNumRows() != 1 && a.GetNumCols() != 1) // a is not a col or row vector
        if (a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols()) // dimensions match
        {
            /*
                const int m = (int)a.GetNumRows();
                const int n = (int)a.GetNumCols();
                const int len = m * n;
                const int incx = 1;
                const int incy = 1;
                assert (m>0 && n>0 && len>0); // converting from size_t to int may cause overflow
                */
            CUDA_LONG N = (CUDA_LONG) c.GetNumElements();
            int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
            c.PrepareDevice();
            PROFILE_CUDA_STREAM("_matrixMatrixAddOnCuda", t_stream);
            _matrixMatrixAddOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(alpha, a.Data(), b.Data(), c.Data(), N);
        }
        else if (a.GetNumElements() == 1)
        {
            CUDA_LONG N = (CUDA_LONG) c.GetNumElements();
            int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
            c.PrepareDevice();
            PROFILE_CUDA_STREAM("_scaleAndAddScalar", t_stream);
            _scaleAndAddScalar<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(c.Data(), N, alpha, a.Data(), b.Data());
        }
        else if (a.GetNumCols() == 1) // col vector, add it to all columns
        {
            CUDA_LONG m = (CUDA_LONG) c.GetNumRows();
            CUDA_LONG n = (CUDA_LONG) c.GetNumCols();
            if (m != (CUDA_LONG) a.GetNumRows())
                InvalidArgument("To add column vector, rows should match.");

            int blocksPerGrid = (int) (ceil(1.0 * m * n / GridDim::maxThreadsPerBlock));
            PROFILE_CUDA_STREAM("_matrixVectorColumnWiseAddWithThreadPerElem", t_stream);
            _matrixVectorColumnWiseAddWithThreadPerElem<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(a.Data(), b.Data(), c.Data(), alpha, m, n);

        }
        else if (a.GetNumRows() == 1) // row vector, add it to all rows
        {
            CUDA_LONG m = (CUDA_LONG) c.GetNumRows();
            CUDA_LONG n = (CUDA_LONG) c.GetNumCols();
            if (m != (CUDA_LONG) a.GetNumRows())
                InvalidArgument("To add column vector, rows should match.");

            int blocksPerGrid = (int) (ceil(1.0 * m * n / GridDim::maxThreadsPerBlock));
            PROFILE_CUDA_STREAM("_matrixVectorRowWiseAddWithThreadPerElem", t_stream);
            _matrixVectorRowWiseAddWithThreadPerElem<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(a.Data(), b.Data(), c.Data(), alpha, m, n);
        }
        else
            InvalidArgument("Dimension of matrix c does not match dimension of matrix a.");
    }
}

/// <summary>c += alpha * (a-b)</summary>
/// if a, b, c  must have same dim
/// <param name="alpha">Scalar</param>
/// <param name="a">Input matrix</param>
/// <param name="b">Input matrix</param>
/// <param name="c">Resulting matrix, user is responsible for allocating this</param>
template <class ElemType>
void GPUMatrix<ElemType>::AddScaledDifference(const ElemType alpha, const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c)
{
    if (a.GetComputeDeviceId() != c.GetComputeDeviceId())
    {
        InvalidArgument("All matrices must be on the same GPU");
    }
    else
    {
        a.PrepareDevice();

        assert(a.GetNumRows() == b.GetNumRows() && a.GetNumRows() == c.GetNumRows() &&
               a.GetNumCols() == b.GetNumCols() && a.GetNumCols() == c.GetNumCols());

        if (!(a.GetNumRows() == b.GetNumRows() && a.GetNumRows() == c.GetNumRows() &&
              a.GetNumCols() == b.GetNumCols() && a.GetNumCols() == c.GetNumCols()))
        {
            InvalidArgument("AddScaledDifference: a, b, and c must have same dimension.");
        }

        if (a.IsEmpty())
            LogicError("AddScaledDifference: Input matrix a is empty.");

        CUDA_LONG n = (CUDA_LONG) a.GetNumElements();
        int blocksPerGrid = (int) ceil(1.0 * n / GridDim::maxThreadsPerBlock);
        PROFILE_CUDA_STREAM("_addScaledDifference", t_stream);
        _addScaledDifference<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(alpha, a.Data(), b.Data(), c.Data(), n);
    }
}

/// <summary> c = alpha * (a-b)</summary>
/// if a, b, c  must have same dim
/// <param name="alpha">Scalar</param>
/// <param name="a">Input matrix</param>
/// <param name="b">Input matrix</param>
/// <param name="c">Resulting matrix, user is responsible for allocating this</param>
template <class ElemType>
void GPUMatrix<ElemType>::AssignScaledDifference(const ElemType alpha, const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c)
{
    if (a.GetComputeDeviceId() != c.GetComputeDeviceId())
    {
        InvalidArgument("All matrices must be on the same GPU");
    }
    else
    {
        a.PrepareDevice();

        assert(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols());

        if (!(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols()))
            InvalidArgument("AssignScaledDifference: a, b must have same dimension.");

        if (a.IsEmpty())
            LogicError("AssignScaledDifference: Input matrix a is empty.");

        if (&c != &a && &c != &b)
            c.RequireSize(a.GetNumRows(), a.GetNumCols());

        CUDA_LONG n = (CUDA_LONG) a.GetNumElements();
        int blocksPerGrid = (int) ceil(1.0 * n / GridDim::maxThreadsPerBlock);
        PROFILE_CUDA_STREAM("_assignScaledDifference", t_stream);
        _assignScaledDifference<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(alpha, a.Data(), b.Data(), c.Data(), n);
    }
}

/// <summary>c += alpha * (a-b)</summary>
/// if a, b, c  must have same dim
/// <param name="alpha">1X1 matrix</param>
/// <param name="a">Input matrix</param>
/// <param name="b">Input matrix</param>
/// <param name="c">Resulting matrix, user is responsible for allocating this</param>
template <class ElemType>
void GPUMatrix<ElemType>::AddScaledDifference(const GPUMatrix<ElemType>& alpha, const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c)
{
    assert(alpha.GetNumElements() == 1);
    if (!(alpha.GetNumElements() == 1))
        InvalidArgument("AddScaledDifference: alpha must be a 1X1 matrix.");

    if (a.GetComputeDeviceId() != c.GetComputeDeviceId())
    {
        InvalidArgument("All matrices must be on the same GPU");
    }
    else
    {
        a.PrepareDevice();

        assert(a.GetNumRows() == b.GetNumRows() && a.GetNumRows() == c.GetNumRows() &&
               a.GetNumCols() == b.GetNumCols() && a.GetNumCols() == c.GetNumCols());

        if (!(a.GetNumRows() == b.GetNumRows() && a.GetNumRows() == c.GetNumRows() &&
              a.GetNumCols() == b.GetNumCols() && a.GetNumCols() == c.GetNumCols()))
        {
            InvalidArgument("AddScaledDifference: a, b, and c must have same dimension.");
        }

        if (a.IsEmpty())
            LogicError("AddScaledDifference: Input matrix a is empty.");

        CUDA_LONG n = (CUDA_LONG) a.GetNumElements();
        int blocksPerGrid = (int) ceil(1.0 * n / GridDim::maxThreadsPerBlock);
        PROFILE_CUDA_STREAM("_addScaledDifference", t_stream);
        _addScaledDifference<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(alpha.Data(), a.Data(), b.Data(), c.Data(), n);
    }
}

/// <summary> c = alpha * (a-b)</summary>
/// if a, b, c  must have same dim
/// <param name="alpha">Scalar</param>
/// <param name="a">Input matrix</param>
/// <param name="b">Input matrix</param>
/// <param name="c">Resulting matrix, user is responsible for allocating this</param>
template <class ElemType>
void GPUMatrix<ElemType>::AssignScaledDifference(const GPUMatrix<ElemType>& alpha, const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c)
{
    assert(alpha.GetNumElements() == 1);
    if (!(alpha.GetNumElements() == 1))
        InvalidArgument("AddScaledDifference: alpha must be a 1X1 matrix.");

    if (a.GetComputeDeviceId() != c.GetComputeDeviceId())
    {
        InvalidArgument("All matrices must be on the same GPU");
    }
    else
    {
        a.PrepareDevice();

        assert(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols());

        if (!(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols()))
        {
            InvalidArgument("AssignScaledDifference: a, b must have same dimension.");
        }

        if (a.IsEmpty())
            LogicError("AssignScaledDifference: Input matrix a is empty.");

        c.RequireSize(a.GetNumRows(), a.GetNumCols());

        CUDA_LONG n = (CUDA_LONG) a.GetNumElements();
        int blocksPerGrid = (int) ceil(1.0 * n / GridDim::maxThreadsPerBlock);
        PROFILE_CUDA_STREAM("_assignScaledDifference", t_stream);
        _assignScaledDifference<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(alpha.Data(), a.Data(), b.Data(), c.Data(), n);
    }
}

//c[ci,cj] += a[ai,aj]
template <class ElemType>
void GPUMatrix<ElemType>::AddElementToElement(ElemType beta, const GPUMatrix<ElemType>& a, const size_t ai, const size_t aj, GPUMatrix<ElemType>& c, const size_t ci, const size_t cj)
{
    if (ai >= a.GetNumRows() || aj >= a.GetNumCols() ||
        ci >= c.GetNumRows() || cj >= c.GetNumCols())
        InvalidArgument("AddElementToElement: Index out of range.");

    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_addElementToElement", t_stream);
    _addElementToElement<ElemType><<<1, 1, 0, t_stream>>>(beta, a.Data(), (CUDA_LONG) a.LocateElement(ai, aj), c.Data(), (CUDA_LONG) c.LocateElement(ci, cj));
}

template <class ElemType>
/*static*/ void GPUMatrix<ElemType>::Scale(ElemType alpha, GPUMatrix<ElemType>& a)
{
    if (alpha == 0) // if 0 then do not access the value, so that we can use this to multiply uninitialized matrices with beta=0
    {
        CUDA_CALL(cudaMemset(a.Data(), 0, a.m_numRows * a.m_numCols * sizeof(ElemType)));
        return;
    }

    cublasHandle_t cuHandle = GetCublasHandle(a.GetComputeDeviceId());
    // TODO: Overload the call to cublas_axpy to remove these ugly if/else statements.
    if (sizeof(ElemType) == sizeof(float))
    {
        float alph = (float) alpha;
        PROFILE_CUDA_STREAM("cublasSscal", t_stream);
        CUBLAS_CALL(cublasSscal(cuHandle, int(a.m_numRows * a.m_numCols), &alph, (float*) a.Data(), 1));
    }
    else if (sizeof(ElemType) == sizeof(double))
    {
        double alph = alpha;
        PROFILE_CUDA_STREAM("cublasDscal", t_stream);
        CUBLAS_CALL(cublasDscal(cuHandle, int(a.m_numRows * a.m_numCols), &alph, (double*) a.Data(), 1));
    }
    else
    {
        RuntimeError("Unsupported template argument in GPUMatrix");
    }
}

template <class ElemType>
/*static*/ void GPUMatrix<ElemType>::Scale(GPUMatrix<ElemType>& alpha, GPUMatrix<ElemType>& a)
{
    if (alpha.GetNumElements() != 1)
    {
        RuntimeError("Matrix alpha must be 1x1");
    }
    cublasHandle_t cuHandle = GetCublasHandle(a.GetComputeDeviceId());
    cublasSetPointerMode(cuHandle, CUBLAS_POINTER_MODE_DEVICE);
    if (sizeof(ElemType) == sizeof(float))
    {
        PROFILE_CUDA_STREAM("cublasSscal", t_stream);
        CUBLAS_CALL(cublasSscal(cuHandle, int(a.m_numRows * a.m_numCols), (float*) alpha.Data(), (float*) a.Data(), 1));
    }
    else if (sizeof(ElemType) == sizeof(double))
    {
        PROFILE_CUDA_STREAM("cublasDscal", t_stream);
        CUBLAS_CALL(cublasDscal(cuHandle, int(a.m_numRows * a.m_numCols), (double*) alpha.Data(), (double*) a.Data(), 1));
    }
    else
    {
        cublasSetPointerMode(cuHandle, CUBLAS_POINTER_MODE_HOST);
        RuntimeError("Unsupported template argument in GPUMatrix");
    }
    cublasSetPointerMode(cuHandle, CUBLAS_POINTER_MODE_HOST);
}

template <class ElemType> // c = alpha * a
/*static*/ void GPUMatrix<ElemType>::Scale(ElemType alpha, const GPUMatrix<ElemType>& a, GPUMatrix<ElemType>& c)
{
    c = a;
    Scale(alpha, c);
}

template <class ElemType>
void GPUMatrix<ElemType>::InnerProduct(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c, const bool isColWise)
{
    if (a.GetComputeDeviceId() != b.GetComputeDeviceId() || b.GetComputeDeviceId() != c.GetComputeDeviceId()) // different GPUs
        InvalidArgument("All matrices must be on the same GPU");

    if (a.IsEmpty() || b.IsEmpty())
        LogicError("Scale:  one of the input matrices is empty.");

    const int m = (int) a.GetNumRows();
    const int n = (int) a.GetNumCols();
    const int k = (int) b.GetNumRows();
    const int l = (int) b.GetNumCols();

    assert(m > 0 && n > 0 && k > 0 && l > 0); // converting from size_t to int may cause overflow
    assert(m == k && n == l);                 // converting from size_t to int may cause overflow
    if (m != k || n != l)
        InvalidArgument("Matrices a and b should have same dimension.");

    if (isColWise)
        c.RequireSize(1, n);
    else
        c.RequireSize(m, 1);

    if ((isColWise && m == 1) || !isColWise && n == 1) // in this case it's equivalent to element-wise product
    {
        c.AssignElementProductOf(a, b);
    }
    else
    {
        c.PrepareDevice();

        int blocksPerGrid = 0;
        if (isColWise) // col-wise
        {
            c.RequireSize(1, n);
            blocksPerGrid = (int) ceil(1.0 * n / GridDim::maxThreadsPerBlock);
        }
        else
        {
            c.RequireSize(m, 1);
            blocksPerGrid = (int) ceil(1.0 * m / GridDim::maxThreadsPerBlock);
        }

        PROFILE_CUDA_STREAM("_innerProduct", t_stream);
        _innerProduct<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(c.Data(), a.Data(), b.Data(), m, n, isColWise);
    }
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::InnerProductOfMatrices(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("InnerProductOfMatrices:  one of the input matrices is empty.");

    const int m = (int) a.GetNumRows();
    const int n = (int) a.GetNumCols();
    const int k = (int) b.GetNumRows();
    const int l = (int) b.GetNumCols();

    assert(m > 0 && n > 0 && k > 0 && l > 0); // converting from size_t to int may cause overflow
    assert(m == k && n == l);                 // converting from size_t to int may cause overflow
    if (m != k || n != l)
        InvalidArgument("InnerProductOfMatrices: Matrices a and b should have same dimension.");

    cublasHandle_t cuHandle = GetCublasHandle(a.GetComputeDeviceId());
    if (sizeof(ElemType) == sizeof(double))
    {
        double tmp = 0;
        PROFILE_CUDA_STREAM("cublasDdot", t_stream);
        CUBLAS_CALL(cublasDdot(cuHandle, m * n, reinterpret_cast<double*>(a.Data()), 1, reinterpret_cast<double*>(b.Data()), 1, &tmp));
        return ElemType(tmp);
        // return (ElemType)ddot((int)a.GetNumElements(), reinterpret_cast <double*>(a.Data()), 1, reinterpret_cast <double*>(b.Data()), 1);
    }
    else
    {
        float tmp = 0;
        PROFILE_CUDA_STREAM("cublasSdot", t_stream);
        CUBLAS_CALL(cublasSdot(cuHandle, m * n, reinterpret_cast<float*>(a.Data()), 1, reinterpret_cast<float*>(b.Data()), 1, &tmp));
        return tmp;
        // return (ElemType)sdot((int)a.GetNumElements(), reinterpret_cast <float*>(a.Data()), 1, reinterpret_cast <float*>(b.Data()), 1);
    }
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignInnerProductOfMatrices(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("InnerProductOfMatrices:  one of the input matrices is empty.");

    RequireSize(1, 1);

    const int m = (int) a.GetNumRows();
    const int n = (int) a.GetNumCols();
    const int k = (int) b.GetNumRows();
    const int l = (int) b.GetNumCols();

    assert(m > 0 && n > 0 && k > 0 && l > 0); // converting from size_t to int may cause overflow
    assert(m == k && n == l);                 // converting from size_t to int may cause overflow
    if (m != k || n != l)
        InvalidArgument("InnerProductOfMatrices: Matrices a and b should have same dimension.");

    cublasHandle_t cuHandle = GetCublasHandle(a.GetComputeDeviceId());
    cublasSetPointerMode(cuHandle, CUBLAS_POINTER_MODE_DEVICE);
    if (sizeof(ElemType) == sizeof(double))
    {
        PROFILE_CUDA_STREAM("cublasDdot", t_stream);
        CUBLAS_CALL(cublasDdot(cuHandle, m * n, reinterpret_cast<double*>(a.Data()), 1, reinterpret_cast<double*>(b.Data()), 1, reinterpret_cast<double*>(Data())));
    }
    else
    {
        PROFILE_CUDA_STREAM("cublasSdot", t_stream);
        CUBLAS_CALL(cublasSdot(cuHandle, m * n, reinterpret_cast<float*>(a.Data()), 1, reinterpret_cast<float*>(b.Data()), 1, reinterpret_cast<float*>(Data())));
    }
    cublasSetPointerMode(cuHandle, CUBLAS_POINTER_MODE_HOST);
    return *this;
}

template <class ElemType>
void GPUMatrix<ElemType>::ElementWisePower(ElemType alpha, const GPUMatrix<ElemType>& a, GPUMatrix<ElemType>& c)
{
    if (a.GetComputeDeviceId() != c.GetComputeDeviceId())
    {
        InvalidArgument("All matrices must be on the same GPU");
    }
    else
    {
        if (a.IsEmpty())
            LogicError("ElementWisePower:  The input matrix a is empty.");

        c.RequireSize(a.GetNumRows(), a.GetNumCols());

        a.PrepareDevice();
        CUDA_LONG N = (CUDA_LONG) a.GetNumElements();
        int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
        PROFILE_CUDA_STREAM("_elementWisePowerOnCuda", t_stream);
        _elementWisePowerOnCuda<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(alpha, a.Data(), c.Data(), N);
    }
}

template <class ElemType>
bool GPUMatrix<ElemType>::AreEqual(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, const ElemType threshold /*= 1e-8*/)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("AreEqual: one of the input matrices is empty.");

    if (a.GetNumRows() != b.GetNumRows() || a.GetNumCols() != b.GetNumCols())
        return false;

    bool bResult = false;

    long* res = new long[1];
    res[0] = 1;
    long* d_res = TracingGPUMemoryAllocator::Allocate<long>(a.GetComputeDeviceId(), 1);
    CUDA_CALL(cudaMemcpy(d_res, res, sizeof(long) * 1, cudaMemcpyHostToDevice));
    CUDA_LONG N = (CUDA_LONG) a.GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    {
        PROFILE_CUDA_STREAM("_areEqual", t_stream);
        _areEqual<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(a.Data(), b.Data(), N, threshold, d_res);
    }
    CUDA_CALL(cudaMemcpy(res, d_res, sizeof(long) * 1, cudaMemcpyDeviceToHost));
    TracingGPUMemoryAllocator::Free<long>(a.GetComputeDeviceId(), d_res);
    if (res[0] != 0)
        bResult = true;
    delete[] res;
    return bResult;
}

// see Matrix<ElemType>::TensorShuffleScaleAndAdd() for comments
template <class ElemType>
void GPUMatrix<ElemType>::TensorShuffleScaleAndAdd(ElemType keepWeight, const GPUMatrix<ElemType>& a, size_t D, size_t S, size_t M, size_t K, size_t T, ElemType scaleFactor, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c)
{
    CUDA_LONG N = (CUDA_LONG) c.GetNumElements();
    assert(N == (CUDA_LONG) a.GetNumElements() && N == (CUDA_LONG) b.GetNumElements());
    assert(a.GetComputeDeviceId() == c.GetComputeDeviceId() && b.GetComputeDeviceId() == c.GetComputeDeviceId());
    a.PrepareDevice();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PROFILE_CUDA_STREAM("_tensorShuffleScaleAndAdd", t_stream);
    _tensorShuffleScaleAndAdd<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(keepWeight, a.Data(), D, S, M, K, T, scaleFactor, b.Data(), c.Data());
}

template <class ElemType>
bool GPUMatrix<ElemType>::HasElement(const GPUMatrix<ElemType>& a, const ElemType v)
{
    if (a.IsEmpty())
        LogicError("HasElement: the input matrix is empty.");

    bool bResult = false;
    ElemType* res = new ElemType[2];
    res[0] = v;
    res[1] = 0;
    ElemType* d_res = TracingGPUMemoryAllocator::Allocate<ElemType>(a.GetComputeDeviceId(), 2);
    CUDA_CALL(cudaMemcpy(d_res, res, sizeof(ElemType) * 2, cudaMemcpyHostToDevice));
    CUDA_LONG N = (CUDA_LONG) a.GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    {
        PROFILE_CUDA_STREAM("_hasElement", t_stream);
        _hasElement<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(a.Data(), N, d_res);
    }
    CUDA_CALL(cudaMemcpy(res, d_res, sizeof(ElemType) * 2, cudaMemcpyDeviceToHost));
    TracingGPUMemoryAllocator::Free<ElemType>(a.GetComputeDeviceId(), d_res);
    if (res[1] != 0)
        bResult = true;
    else
        bResult = false;

    delete[] res;
    return bResult;
}

template <class ElemType>
void GPUMatrix<ElemType>::CreateCurandObject(unsigned long seed, const char* caller)
{
    assert(caller != nullptr);

    if (s_curandGenerator == NULL)
    {
        unsigned long long cudaSeed = (seed == USE_TIME_BASED_SEED) ? time(NULL) : seed;
        fprintf(stderr, "%s (GPU): creating curand object with seed %llu, sizeof(ElemType)==%lu\n",
                caller, cudaSeed, (unsigned long)sizeof(ElemType));
        s_curandGenerator = new curandGenerator_t;
        // Create pseudo-random number generator
        CURAND_CALL(curandCreateGenerator(&(((curandGenerator_t*) s_curandGenerator)[0]), CURAND_RNG_PSEUDO_XORWOW));
        CURAND_CALL(curandSetPseudoRandomGeneratorSeed(((curandGenerator_t*) s_curandGenerator)[0], cudaSeed));
        CURAND_CALL(curandSetGeneratorOrdering(((curandGenerator_t*) s_curandGenerator)[0], CURAND_ORDERING_PSEUDO_SEEDED));
    }
}

template <class ElemType>
void GPUMatrix<ElemType>::ResetCurandObject(unsigned long seed, const char* caller)
{
    assert(caller != nullptr);

    if (s_curandGenerator && (seed != USE_TIME_BASED_SEED))
    {
        // Note: this might be slow.
        CURAND_CALL(curandSetPseudoRandomGeneratorSeed(((curandGenerator_t*) s_curandGenerator)[0], seed));
        CURAND_CALL(curandSetGeneratorOffset(((curandGenerator_t*) s_curandGenerator)[0], 0));
    }
    else
    {
        CreateCurandObject(seed, caller);
    }
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::Ones(const size_t rows, const size_t cols, int deviceId)
{
    GPUMatrix<ElemType> c(rows, cols, deviceId); // will initialize to 0
    c.SetValue(1);
    return c;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::Zeros(const size_t rows, const size_t cols, int deviceId)
{
    GPUMatrix<ElemType> c(rows, cols, deviceId); // will initialize to 0
    // c.SetValue(0);
    return c;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::Eye(const size_t rows, int deviceId)
{
    GPUMatrix<ElemType> c(rows, rows, deviceId); // will initialize to 0
    c.SetDiagonalValue(1);
    return c;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::RandomUniform(const size_t rows, const size_t cols, int deviceId, const ElemType low, const ElemType high, unsigned long seed)
{
    GPUMatrix<ElemType> c(rows, cols, deviceId); // will initialize to 0
    c.SetUniformRandomValue(low, high, seed);
    return c;
}

template <class ElemType>
GPUMatrix<ElemType> GPUMatrix<ElemType>::RandomGaussian(const size_t rows, const size_t cols, int deviceId, const ElemType mean, const ElemType sigma, unsigned long seed)
{
    GPUMatrix<ElemType> c(rows, cols, deviceId); // will initialize to 0
    c.SetGaussianRandomValue(mean, sigma, seed);
    return c;
}

template <class ElemType>
ElemType GPUMatrix<ElemType>::GetLearnRateForBlock_Helper(const GPUMatrix<ElemType>& Gradients, const GPUMatrix<ElemType>& SmoothedGradients)
{
    ElemType* d_res = TracingGPUMemoryAllocator::Allocate<ElemType>(Gradients.GetComputeDeviceId(), 1);

    // Compute inner product of matrices and keep it on device
    const int m = (int) Gradients.GetNumRows();
    const int n = (int) Gradients.GetNumCols();
    const int k = (int) SmoothedGradients.GetNumRows();
    const int l = (int) SmoothedGradients.GetNumCols();
    assert(m > 0 && n > 0 && k > 0 && l > 0); // converting from size_t to int may cause overflow
    assert(m == k && n == l);                 // converting from size_t to int may cause overflow
    if (m != k || n != l)
        InvalidArgument("InnerProductOfMatrices: Matrices a and b should have same dimension.");

    if (sizeof(ElemType) == sizeof(double))
    {
        cublasHandle_t cuHandle = GetCublasHandle(Gradients.GetComputeDeviceId());
        cublasSetPointerMode(cuHandle, CUBLAS_POINTER_MODE_DEVICE);
        {
            PROFILE_CUDA_STREAM("cublasDdot", t_stream);
            CUBLAS_CALL(cublasDdot(cuHandle, m * n, reinterpret_cast<double*>(Gradients.Data()), 1, reinterpret_cast<double*>(SmoothedGradients.Data()), 1, reinterpret_cast<double*>(d_res)));
        }
        cublasSetPointerMode(cuHandle, CUBLAS_POINTER_MODE_HOST);
    }
    else
    {
        cublasHandle_t cuHandle = GetCublasHandle(Gradients.GetComputeDeviceId());
        cublasSetPointerMode(cuHandle, CUBLAS_POINTER_MODE_DEVICE);
        {
            PROFILE_CUDA_STREAM("cublasSdot", t_stream);
            CUBLAS_CALL(cublasSdot(cuHandle, m * n, reinterpret_cast<float*>(Gradients.Data()), 1, reinterpret_cast<float*>(SmoothedGradients.Data()), 1, reinterpret_cast<float*>(d_res)));
        }
        cublasSetPointerMode(cuHandle, CUBLAS_POINTER_MODE_HOST);
    }
    // d_res[0] should now contain inner product of matrices
    // Compute squared Frobenius norms (squared sums of elements)
    {
        PROFILE_CUDA_STREAM("_lrHelper", t_stream);
        _lrHelper<ElemType><<<1, 512, 0, t_stream>>>(Gradients.Data(), SmoothedGradients.Data(), (CUDA_LONG) Gradients.GetNumElements(), d_res);
    }
    ElemType res;
    CUDA_CALL(cudaMemcpy(&res, d_res, sizeof(ElemType), cudaMemcpyDeviceToHost));
    TracingGPUMemoryAllocator::Free<ElemType>(Gradients.GetComputeDeviceId(), d_res);
    return res;
}
// The inputs are two row vectors [a1 a2 a3 a4] [b1 b2 b3 b4]
// The outputs are one matrix of size (nt+1)*4
// The first row is just element multiplication
// The rest rows will be with shift
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignElementProductOfWithShiftNeg(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, const size_t shift, const size_t nt)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("AssignElementProductOf: Matrix is empty.");

    assert(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols());
    if (!(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols()))
        InvalidArgument("The input matrix dimensions do not match.");

    if (!(a.GetNumRows() == 1))
        InvalidArgument("The input matrix must be a row vector.");

    RequireSize(nt + 1, a.GetNumCols());
    int BS = a.GetNumCols();

    // the output matrix is of size (nt+1, BS)
    dim3 thread_tail(DEFAULT_THREAD_PER_DIM, DEFAULT_THREAD_PER_DIM);
    dim3 block_tail((nt + 1 + DEFAULT_THREAD_PER_DIM - 1) / DEFAULT_THREAD_PER_DIM, (BS + DEFAULT_THREAD_PER_DIM - 1) / DEFAULT_THREAD_PER_DIM);

    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_assignElementProductOfWithShiftNeg", t_stream);
    _assignElementProductOfWithShiftNeg<ElemType><<<block_tail, thread_tail, 0, t_stream>>>(Data(), a.Data(), b.Data(), shift, nt + 1, BS);
    //      _assignElementProductOf<ElemType> << <block_tail, thread_tail, 0, t_stream >> >(Data(), a.Data(), b.Data(), nt);

    return *this;
}

template <class ElemType>
void GPUMatrix<ElemType>::InnerProductWithShiftNeg(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c, const size_t shift, const size_t nt)
{
    if (a.GetComputeDeviceId() != b.GetComputeDeviceId() || b.GetComputeDeviceId() != c.GetComputeDeviceId()) // different GPUs
        InvalidArgument("All matrices must be on the same GPU");

    if (a.IsEmpty() || b.IsEmpty())
        LogicError("Scale:  one of the input matrices is empty.");

    const int m = (int) a.GetNumRows();
    const int n = (int) a.GetNumCols();
    const int k = (int) b.GetNumRows();
    const int l = (int) b.GetNumCols();

    assert(m > 0 && n > 0 && k > 0 && l > 0); // converting from size_t to int may cause overflow
    assert(m == k && n == l);                 // converting from size_t to int may cause overflow
    if (m != k || n != l)
        InvalidArgument("Matrices a and b should have same dimension.");

    c.RequireSize(nt + 1, n);

    if (true)
    {
        c.PrepareDevice();

        dim3 thread_tail(DEFAULT_THREAD_PER_DIM, DEFAULT_THREAD_PER_DIM);
        dim3 block_tail((nt + 1 + DEFAULT_THREAD_PER_DIM - 1) / DEFAULT_THREAD_PER_DIM, (n + DEFAULT_THREAD_PER_DIM - 1) / DEFAULT_THREAD_PER_DIM);

        PROFILE_CUDA_STREAM("_innerProductWithShiftNeg", t_stream);
        _innerProductWithShiftNeg<ElemType><<<block_tail, thread_tail, 0, t_stream>>>(c.Data(), a.Data(), b.Data(), m, n, shift, nt + 1);
    }
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::GetARowByIndex(const GPUMatrix<ElemType>& a, const size_t m)
{
    if (a.IsEmpty())
        LogicError("GetARowByIndex: Matrix is empty.");

    RequireSize(1, a.GetNumCols());

    int n = a.GetNumRows();
    int P = a.GetNumCols();

    if (m >= n)
        LogicError("GetARowByIndex: m is out of range.");

    int blocksPerGrid = (int) ceil(((double) P) / GridDim::maxThreadsPerBlock);

    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_getARowByIndex", t_stream);
    _getARowByIndex<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), n, P, m);
    //      _assignElementProductOf<ElemType> << <block_tail, thread_tail, 0, t_stream >> >(Data(), a.Data(), b.Data(), nt);
    return *this;
}

template <class ElemType>
void GPUMatrix<ElemType>::ConductRowElementMultiplyWithShift(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, GPUMatrix<ElemType>& c, const size_t shift, const bool isafixed)
{
    if (a.GetComputeDeviceId() != b.GetComputeDeviceId() || b.GetComputeDeviceId() != c.GetComputeDeviceId()) // different GPUs
        InvalidArgument("All matrices must be on the same GPU");

    if (a.IsEmpty() || b.IsEmpty())
        LogicError("Scale:  one of the input matrices is empty.");

    const int m = (int) a.GetNumRows();
    const int n = (int) a.GetNumCols();
    const int O = (int) b.GetNumRows();
    const int P = (int) b.GetNumCols();

    assert(m > 0 && n > 0 && O > 0 && P > 0); // converting from size_t to int may cause overflow
    if (m != 1 || n != P)
        InvalidArgument("Matrices a and b should have same dimension.");

    c.RequireSize(O, P);

    if (true)
    {
        c.PrepareDevice();

        dim3 thread_tail(DEFAULT_THREAD_PER_DIM, DEFAULT_THREAD_PER_DIM);
        dim3 block_tail((O + DEFAULT_THREAD_PER_DIM - 1) / DEFAULT_THREAD_PER_DIM, (P + DEFAULT_THREAD_PER_DIM - 1) / DEFAULT_THREAD_PER_DIM);

        PROFILE_CUDA_STREAM("_conductRowElementMultiplyWithShift", t_stream);
        _conductRowElementMultiplyWithShift<ElemType><<<block_tail, thread_tail, 0, t_stream>>>(c.Data(), a.Data(), b.Data(), O, P, shift, isafixed);
    }
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignElementProductOfWithShift(const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, const size_t shift)
{
    if (a.IsEmpty() || b.IsEmpty())
        LogicError("AssignElementProductOfWithShift: Matrix is empty.");

    assert(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols());
    if (!(a.GetNumRows() == b.GetNumRows() && a.GetNumCols() == b.GetNumCols()))
        InvalidArgument("The input matrix dimensions do not match.");

    // int O = a.GetNumRows();
    int P = a.GetNumCols();

    RequireSize(1, P);
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(((double) N) / GridDim::maxThreadsPerBlock);
    a.PrepareDevice();
    PROFILE_CUDA_STREAM("_assignElementProductOfWithShift", t_stream);
    _assignElementProductOfWithShift<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), a.Data(), b.Data(), shift, N);
    return *this;
}

//sequence training
template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::DropFrame(const GPUMatrix<ElemType>& label, const GPUMatrix<ElemType>& gamma, const ElemType& threshhold)
{
    if (IsEmpty())
        LogicError("DropFrame: Matrix is empty.");

    PrepareDevice();

    long N = (long) GetNumCols(); // one kernel per column
    int blocksPerGrid = (int) ceil(N * 1.0 / GridDim::maxThreadsPerBlock);
    PROFILE_CUDA_STREAM("_DropFrame", t_stream);
    _DropFrame<<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(Data(), label.Data(), gamma.Data(), threshhold, (long) m_numCols, (long) m_numRows);
    return *this;
}

template <class ElemType>
GPUMatrix<ElemType>& GPUMatrix<ElemType>::AssignSequenceError(const ElemType hsmoothingWeight, const GPUMatrix<ElemType>& label,
                                                              const GPUMatrix<ElemType>& dnnoutput, const GPUMatrix<ElemType>& gamma, ElemType alpha)
{
    if (IsEmpty())
        LogicError("AssignSequenceError: Matrix is empty.");

    PrepareDevice();

    long N = (LONG64) label.GetNumElements();
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    PROFILE_CUDA_STREAM("_AssignSequenceError", t_stream);
    _AssignSequenceError<<<blocksPerGrid, GridDim::maxThreadsPerBlock, 0, t_stream>>>(hsmoothingWeight, Data(), label.Data(), dnnoutput.Data(), gamma.Data(), alpha, N);
    return *this;
}

#pragma endregion Static BLAS Functions

/// f = logadd(f, vec) to get the logadd sum of vector elments
template <class ElemType>
ElemType GPUMatrix<ElemType>::LogSumOfElements() const
{
    if (IsEmpty())
        LogicError("SumOfElements: Matrix is empty");

    ElemType* d_sum = TracingGPUMemoryAllocator::Allocate<ElemType>(GetComputeDeviceId(), 1);

    ElemType h_sum;
    CUDA_LONG N = (CUDA_LONG) GetNumElements();
    int blocksPerGrid = (int) ceil(((double) N) / GridDim::maxThreadsPerBlock);

    {
        // BUGBUG: Should this use CUDA streams?
        PROFILE_CUDA("_reductionLogAddSum");
        _reductionLogAddSum<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock>>>(Data(),
                                                                                  d_sum, 1, N);
    }
    CUDA_CALL(cudaMemcpy(&h_sum, d_sum, sizeof(ElemType), cudaMemcpyDeviceToHost));
    TracingGPUMemoryAllocator::Free<ElemType>(GetComputeDeviceId(), d_sum);

    return h_sum;
}

template <class ElemType>
void GPUMatrix<ElemType>::RCRFBackwardCompute(
    const GPUMatrix<ElemType>& alpha, GPUMatrix<ElemType>& beta,
    const GPUMatrix<ElemType>& /*lbls*/,
    const GPUMatrix<ElemType>& pos_scores, const GPUMatrix<ElemType>& pair_scores, const int shift)
{
    if (alpha.IsEmpty() || pos_scores.IsEmpty() || pair_scores.IsEmpty())
        LogicError("RCRFBackwardCompute: one of the input matrices is empty.");

    if (alpha.GetNumRows() != pos_scores.GetNumRows() || alpha.GetNumCols() != pos_scores.GetNumCols())
        LogicError("RCRFBackwardCompute: matrix dimensions mismatched.");

    size_t iNumLab = alpha.GetNumRows();
    size_t iNumPos = alpha.GetNumCols();

    alpha.PrepareDevice();
    beta.RequireSize(iNumLab, iNumPos);

    ElemType* d_zeta = TracingGPUMemoryAllocator::Allocate<ElemType>(alpha.GetComputeDeviceId(), iNumLab);

    CUDA_LONG N = iNumLab;
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    size_t szMemSize;
    for (int t = iNumPos - 1; t >= 0; t--)
    {
        szMemSize = sizeof(ElemType) * iNumLab;
        {
            // BUGBUG: Should this use CUDA streams?
            PROFILE_CUDA("_rcrfBackwardComputeZeta");
            _rcrfBackwardComputeZeta<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, szMemSize>>>(t, iNumPos, alpha.Data(), d_zeta, pair_scores.Data(), iNumLab, shift);
        }
        szMemSize = iNumLab * 3;
        szMemSize *= sizeof(ElemType);
        {
            // BUGBUG: Should this use CUDA streams?
            PROFILE_CUDA("_rcrfBackwardCompute");
            _rcrfBackwardCompute<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, szMemSize>>>(t, iNumPos, alpha.Data(), beta.Data(),
                                                                                                  d_zeta, pair_scores.Data(), iNumLab, shift);
        }
    }
    /*
        error = cudaGetErrorString(cudaPeekAtLastError());
        printf("%s\n", error);
        error = cudaGetErrorString(cudaThreadSynchronize());
        printf("%s\n", error);
        */

    TracingGPUMemoryAllocator::Free<ElemType>(alpha.GetComputeDeviceId(), d_zeta);
}

/**
    Compute the gradient for the first order Markov transition probabilities
    It uses equations derived in R. Collobert's paper "Natural language processing (almost) from scratch"
    */
template <class ElemType>
void GPUMatrix<ElemType>::RCRFTransGrdCompute(const GPUMatrix<ElemType>& lbls,
                                              const GPUMatrix<ElemType>& alpha,
                                              const GPUMatrix<ElemType>& beta,
                                              const GPUMatrix<ElemType>& pair_scores,
                                              GPUMatrix<ElemType>& grd,
                                              const int startLbl,
                                              const int shift)
{
    assert(shift == 1);
    int iNumPos = alpha.GetNumCols();
    int iNumLab = alpha.GetNumRows();

    ElemType* d_zeta = TracingGPUMemoryAllocator::Allocate<ElemType>(alpha.GetComputeDeviceId(), iNumLab);

    CUDA_LONG N = iNumLab;
    int blocksPerGrid = (int) ceil(1.0 * N / GridDim::maxThreadsPerBlock);
    size_t szMemSize;
    for (int t = 0; t < iNumPos; t++)
    {
        szMemSize = sizeof(ElemType) * iNumLab;
        {
            // BUGBUG: Should this use CUDA streams?
            PROFILE_CUDA("_rcrfTransGrdComputeZeta");
            _rcrfTransGrdComputeZeta<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, szMemSize>>>(t - 1, iNumPos, alpha.Data(), d_zeta, pair_scores.Data(), iNumLab, startLbl, shift);
        }
        szMemSize = iNumLab * 3;
        szMemSize *= sizeof(ElemType);
        {
            // BUGBUG: Should this use CUDA streams?
            PROFILE_CUDA("_rcrfTransGrdCompute");
            _rcrfTransGrdCompute<ElemType><<<blocksPerGrid, GridDim::maxThreadsPerBlock, szMemSize>>>(t, startLbl, alpha.Data(), beta.Data(),
                                                                                                  d_zeta, pair_scores.Data(), lbls.Data(), grd.Data(), iNumPos, iNumLab, shift);
        }
    }
    TracingGPUMemoryAllocator::Free<ElemType>(alpha.GetComputeDeviceId(), d_zeta);
};

// -----------------------------------------------------------------------
// TensorView entry points from Matrix.cpp
// -----------------------------------------------------------------------

// helper to provide a vector of ones of at least the given number of elements
// TODO: Use this to implement ComputationNode::ConstOnes? Or do we even need that anymore?
template <class ElemType>
static shared_ptr<GPUMatrix<ElemType>> GetOnesVector(size_t N, DEVICEID_TYPE deviceId)
{
    // using an array of shared_ptrs because those are thread-safe. The objects themselves are immutable.
    // And using a plain array so this will never get freed, avoiding free-after-DLL-unload issues.
    static shared_ptr<GPUMatrix<ElemType>> onesCache[32]; // cache of objects
    if (deviceId >= _countof(onesCache))
        LogicError("GetOnesVector: onesCache[] too small (%d entries), increase (you need %d) and recompile.", (int) _countof(onesCache), (int) deviceId + 1);
    auto p = onesCache[deviceId];
    if (!p || p->GetNumRows() < N) // must (re-)allocate
    {
        p = make_shared<GPUMatrix<ElemType>>(GPUMatrix<ElemType>::Ones(N, 1, deviceId));
        onesCache[deviceId] = p; // this will replace the pointer thread-safely (although weird race conditions may happen where a larger entry is overwritten by a smaller one; will still run correctly)
    }
    return p;
}

// perform unary operation 'op' on a giving 'this', reinterpreting the matrices as tensors as specified by the dims and strides
// This binds the N-ariness to a template parameter N, and gets the data pointers out from the matrix objects.
template <class ElemType>
void GPUMatrix<ElemType>::TensorOp(ElemType beta, const GPUMatrix<ElemType>& a, ElemType alpha, ElementWiseOperator op, ElementWiseOperator reductionOp,
                                   const array<size_t, 2>& offsets,
                                   const SmallVector<size_t>& regularOpDims, const array<SmallVector<ptrdiff_t>, 2>& regularStrides,
                                   const SmallVector<size_t>& reducingOpDims, const array<SmallVector<ptrdiff_t>, 2>& reducingStrides)
{
    if (reductionOp != ElementWiseOperator::opSum) // TODO: enable the reduction ops
        InvalidArgument("TensorOp: Unary reduction operations other than opSum not yet implemented.");

    a.PrepareDevice();
    if (a.GetComputeDeviceId() != GetComputeDeviceId())
        InvalidArgument("All matrices must be on the same GPU");

    // special case: linear processing
    // The case statement has measurable impact for unary ops (but not for binary ops it seems, due to double mem access).
    // Linear gap-free unary ops happen so regularly that we will eliminate the case statement from the CUDA kernel, and instead expand all.
    if (regularOpDims.size() == 1 && regularStrides[0][0] == 1 && regularStrides[1][0] == 1 && reducingOpDims.size() == 0)
    {
        // special case: for copy, use cudaMemcpy() instead, or cublas_axpy()
        // TODO: We should observe if these actually make a speed difference, and if not, remove these special cases.
        if (op == ElementWiseOperator::opCopy && beta == 0 && alpha == 1)
            return CUDA_CALL(cudaMemcpy(Data()+ offsets[1], a.Data()+ offsets[0], sizeof(ElemType) * regularOpDims[0], cudaMemcpyDeviceToDevice));
        else if (op == ElementWiseOperator::opCopy && beta == 1)
        {
            cublasHandle_t handle = GetCublasHandle(GetComputeDeviceId());
            PROFILE_CUDA_STREAM("cublas_axpy", t_stream);
            CUBLAS_CALL(cublas_axpy(handle, (int)regularOpDims[0], &alpha, a.Data() + offsets[0], 1, Data() + offsets[1], 1));
            return;
        }
        else
            return LaunchUnaryTensorOp<ElemType>(beta, a.Data()+ offsets[0], Data()+ offsets[1], alpha, op, regularOpDims[0]);
    }

    // special case: reducing a matrix onto a column vector; can be done with SGEMM
    // Note: A minor risk is that with this, our own reduction function will rarely be used.
    // That function was tested to give the same results with 'double', and nearly the same with 'float' (different summation order matters).
    else if (op == ElementWiseOperator::opCopy && // we are just adding to target without any further operation
#ifdef _DEBUG
             sizeof(ElemType) == sizeof(float) && // in debug don't shortcut 'double' so we have some test of our own codepath
#endif
             regularOpDims.size() == 1 && regularStrides[0][0] == 1 && regularStrides[1][0] == 1 && // we are processing a column
             reducingOpDims.size() == 1 && reducingStrides[0][0] >= (ptrdiff_t) regularOpDims[0])   // reducing across columns and no overlap
    {
        assert(reducingStrides[1][0] == 0);
        auto ARows = regularOpDims[0];    // vertical steps
        auto ACols = reducingOpDims[0];   // horizontal steps (reduction)
        auto ALd = reducingStrides[0][0]; // horizontal step width through matrix
        cublasHandle_t cuHandle = GetCublasHandle(a.GetComputeDeviceId());
        PROFILE_CUDA_STREAM("cublas_gemm", t_stream);
        CUBLAS_CALL(cublas_gemm(cuHandle, CUBLAS_OP_N, CUBLAS_OP_N, (int) /*CRows=*/ARows, /*CCols=*/1, (int) ACols, &alpha,
                                /*A00=*/a.Data()+ offsets[0], (int) ALd,
                                /*B00=*/GetOnesVector<ElemType>(ACols, a.GetComputeDeviceId())->Data(), (int) /*BRows=*/ACols, &beta,
                                /*C00=*/Data()+ offsets[1], (int) /*CRows=*/ARows));
        return;
    }

    // TODO: Add a special case for tensor bias reduction. cudnn is ~7% faster on Image/QuickE2E.

    // regular case
    else
        return TensorOpN<ElemType, 2>(beta, array<ElemType*, 2>{a.Data(), Data()}, alpha, op, offsets, regularOpDims, regularStrides, reducingOpDims, reducingStrides);
}

// perform binary operation 'op' on a and b giving 'this', reinterpreting the matrices as tensors as specified by the dims and strides
template <class ElemType>
void GPUMatrix<ElemType>::TensorOp(ElemType beta, const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, ElemType alpha, ElementWiseOperator op, ElementWiseOperator reductionOp,
                                   const array<size_t, 3>& offsets,
                                   const SmallVector<size_t>& regularOpDims, const array<SmallVector<ptrdiff_t>, 3>& regularStrides,
                                   const SmallVector<size_t>& reducingOpDims, const array<SmallVector<ptrdiff_t>, 3>& reducingStrides)
{
    if (reductionOp != ElementWiseOperator::opSum)
        InvalidArgument("TensorOp: The only permitted binary reduction operation is opSum.");

    a.PrepareDevice();
    if (a.GetComputeDeviceId() != GetComputeDeviceId() || b.GetComputeDeviceId() != GetComputeDeviceId())
        InvalidArgument("All matrices must be on the same GPU");

    return TensorOpN<ElemType, 3>(beta, array<ElemType*, 3>{a.Data(), b.Data(), Data()}, alpha, op, offsets, regularOpDims, regularStrides, reducingOpDims, reducingStrides);
}

// perform ternary operation 'op' on a, and c giving 'this', reinterpreting the matrices as tensors as specified by the dims and strides
template <class ElemType>
void GPUMatrix<ElemType>::TensorOp(ElemType beta, const GPUMatrix<ElemType>& a, const GPUMatrix<ElemType>& b, const GPUMatrix<ElemType>& c, ElemType alpha, ElementWiseOperator op, ElementWiseOperator reductionOp,
                                   const array<size_t, 4>& offsets,
                                   const SmallVector<size_t>& regularOpDims, const array<SmallVector<ptrdiff_t>, 4>& regularStrides,
                                   const SmallVector<size_t>& reducingOpDims, const array<SmallVector<ptrdiff_t>, 4>& reducingStrides)
{
    if (reductionOp != ElementWiseOperator::opSum)
        InvalidArgument("TensorOp: The only permitted ternary reduction operation is opSum.");

    a.PrepareDevice();
    if (a.GetComputeDeviceId() != GetComputeDeviceId() || b.GetComputeDeviceId() != GetComputeDeviceId() || c.GetComputeDeviceId() != GetComputeDeviceId())
        InvalidArgument("All matrices must be on the same GPU");
    return TensorOpN<ElemType, 4>(beta, array<ElemType*, 4>{a.Data(), b.Data(), c.Data(), Data()}, alpha, op, offsets, regularOpDims, regularStrides, reducingOpDims, reducingStrides);
}

// =======================================================================
// explicit instantiations business
// =======================================================================

template class GPUMatrix<float>;
template class GPUMatrix<double>;
template class DeviceBoundNumber<float>;
template class DeviceBoundNumber<double>;

template <class ElemType>
cublasHandle_t GPUMatrix<ElemType>::s_cuHandle[GPUMatrix<ElemType>::MaxGpus] = {0};

template <class ElemType>
void* GPUMatrix<ElemType>::s_curandGenerator = NULL;

// We use Matrix<char> as the backing store for QuantizedMatrix
// Let's explicitly instantiate the methods we need for that purpose
template GPUMatrix<char>::GPUMatrix(const size_t numRows, const size_t numCols, int deviceId);
template GPUMatrix<char>::GPUMatrix(const size_t numRows, const size_t numCols, int deviceId, char* pArray, const size_t matrixFlags);
template GPUMatrix<char>::GPUMatrix(const GPUMatrix<char>&);
template GPUMatrix<char>::GPUMatrix(GPUMatrix<char>&&);
template char* GPUMatrix<char>::CopyToArray() const;
template void GPUMatrix<char>::ChangeDeviceTo(int);
template void GPUMatrix<char>::Resize(size_t, size_t, bool);
template void GPUMatrix<char>::RequireSize(size_t, size_t, bool);

template GPUMatrix<char>::~GPUMatrix();
template GPUMatrix<char> GPUMatrix<char>::ColumnSlice(size_t startColumn, size_t numCols) const;
template GPUMatrix<char>& GPUMatrix<char>::operator=(GPUMatrix<char>&&);
template GPUMatrix<char>::GPUMatrix(int);
template void GPUMatrix<char>::SetValue(const char);
template void GPUMatrix<char>::SetValue(const size_t numRows, const size_t numCols, int deviceId, char* pArray, size_t matrixFlags);
template void GPUMatrix<char>::SetValue(GPUMatrix<char> const&);

template GPUMatrix<int>::GPUMatrix(const size_t, const size_t, int, int*, const size_t);
template GPUMatrix<int>::~GPUMatrix();

template int* TracingGPUMemoryAllocator::Allocate<int>(int, size_t);
template size_t* TracingGPUMemoryAllocator::Allocate<size_t>(int, size_t);
template long* TracingGPUMemoryAllocator::Allocate<long>(int, size_t);
template char* TracingGPUMemoryAllocator::Allocate<char>(int, size_t);
template float* TracingGPUMemoryAllocator::Allocate<float>(int, size_t);
template double* TracingGPUMemoryAllocator::Allocate<double>(int, size_t);

template void TracingGPUMemoryAllocator::Free<int>(int, int*, bool);
template void TracingGPUMemoryAllocator::Free<size_t>(int, size_t*, bool);
template void TracingGPUMemoryAllocator::Free<char>(int, char*, bool);
template void TracingGPUMemoryAllocator::Free<float>(int, float*, bool);
template void TracingGPUMemoryAllocator::Free<double>(int, double*, bool);

}}}

// !!!!This is from helper_cuda.h which comes with CUDA samples!!!! Consider if it is beneficial to just include all helper_cuda.h
// TODO: This is duplicated in BestGpu.cpp
// Beginning of GPU Architecture definitions
int _ConvertSMVer2Cores(int major, int minor)
{
    // Defines for GPU Architecture types (using the SM version to determine the # of cores per SM
    typedef struct
    {
        int SM; // 0xMm (hexidecimal notation), M = SM Major version, and m = SM minor version
        int Cores;
    } sSMtoCores;

    sSMtoCores nGpuArchCoresPerSM[] =
        {
            {0x10, 8},   // Tesla Generation (SM 1.0) G80 class
            {0x11, 8},   // Tesla Generation (SM 1.1) G8x class
            {0x12, 8},   // Tesla Generation (SM 1.2) G9x class
            {0x13, 8},   // Tesla Generation (SM 1.3) GT200 class
            {0x20, 32},  // Fermi Generation (SM 2.0) GF100 class
            {0x21, 48},  // Fermi Generation (SM 2.1) GF10x class
            {0x30, 192}, // Kepler Generation (SM 3.0) GK10x class
            {0x35, 192}, // Kepler Generation (SM 3.5) GK11x class
            {-1, -1}};

    int index = 0;

    while (nGpuArchCoresPerSM[index].SM != -1)
    {
        if (nGpuArchCoresPerSM[index].SM == ((major << 4) + minor))
        {
            return nGpuArchCoresPerSM[index].Cores;
        }

        index++;
    }
    return nGpuArchCoresPerSM[7].Cores;
};
// end of GPU Architecture definitions

//inline CUDA_LONG _GetFreeMemoryOnCUDADevice(int devId)
//{
//    CUdevice cudaDevice;
//    CUresult result = cuDeviceGet(&cudaDevice, devId);
//    if(result!= CUDA_SUCCESS)
//    {
//        return 0;
//    }
//
//    // create cuda context
//    CUcontext cudaContext;
//    result = cuCtxCreate(&cudaContext, CU_CTX_SCHED_AUTO, cudaDevice);
//    if(result != CUDA_SUCCESS)
//    {
//        return 0;
//    }
//
//    // get the amount of free memory on the graphics card
//    size_t free;
//    size_t total;
//    result = cuMemGetInfo(&free, &total);
//    if (result!=CUDA_SUCCESS)
//    {
//        return 0;
//    }
//    else
//        return (CUDA_LONG)free;
//}

#endif // CPUONLY