cavis/libnd4j/include/ops/declarable/helpers/cuda/lup.cu

/*******************************************************************************
 * Copyright (c) 2015-2018 Skymind, Inc.
 *
 * This program and the accompanying materials are made available under the
 * terms of the Apache License, Version 2.0 which is available at
 * https://www.apache.org/licenses/LICENSE-2.0.
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
 * License for the specific language governing permissions and limitations
 * under the License.
 *
 * SPDX-License-Identifier: Apache-2.0
 ******************************************************************************/

//
//  @author raver119@gmail.com
//

#include <ops/declarable/helpers/top_k.h>
#include <MmulHelper.h>
#include <NDArrayFactory.h>
#include <Status.h>
#include <ConstantTadHelper.h>
#include <ShapeUtils.h>
//#include <ops/declarable/generic/helpers/BroadcastHelper.h>

#include <cusolverDn.h>
#include <cuda_exception.h>

namespace nd4j {
namespace ops {
namespace helpers {

// ------------------------------------------------------------------------------------------------------------------ //
//  invert the second diagonal for lower diagonal matrix
    template<typename T>
    static __global__ void
    invertKernelLow(void *invertedBuf, Nd4jLong *invertedShape, void *inputBuf, Nd4jLong *inputShape, Nd4jLong n) {
        T* inverted = reinterpret_cast<T *>(invertedBuf);
        T* input = reinterpret_cast<T*>(inputBuf);

        auto start = threadIdx.x + blockIdx.x * blockDim.x;
        auto step = blockDim.x * gridDim.x;

        for (int i = start + 1; i < n; i += step) {
            Nd4jLong pos[] = {i, i - 1};
            Nd4jLong posX[] = {i, i};
            Nd4jLong posY[] = {i - 1, i - 1};
            auto xIndex = shape::getOffset(inputShape, pos);
            auto dxIndex = shape::getOffset(inputShape, posX);
            auto dyIndex = shape::getOffset(inputShape, posY);
            auto zIndex = shape::getOffset(invertedShape, pos);
            // invert lower triangular matrix
            inverted[zIndex] = -input[xIndex] / (input[dxIndex] * input[dyIndex]);
//            math::atomics::nd4j_atomicAdd(&inverted[zIndex], - input[xIndex] * inverted[iIndex] / input[dIndex]);
        }
    }
// ------------------------------------------------------------------------------------------------------------------ //
// invert diagonal vals to upper diagonal matrix
    template<typename T>
    static __global__ void
    upvertKernel(void *invertedBuf, Nd4jLong *invertedShape, void *inputBuf, Nd4jLong *inputShape, Nd4jLong n) {
        T *inverted = reinterpret_cast<T *>(invertedBuf);
        T *input = reinterpret_cast<T *>(inputBuf);

        auto start = threadIdx.x + blockIdx.x * blockDim.x;
        auto step = blockDim.x * gridDim.x;

        for (int i = start; i < n; i += step) {
            Nd4jLong pos[] = {i, i};
            auto xIndex = shape::getOffset(inputShape, pos);
            auto zIndex = shape::getOffset(invertedShape, pos);
//            math::atomics::nd4j_atomicDiv(&inverted[zIndex], input[xIndex]);
            // invert diagonal elements
            inverted[zIndex] /= input[xIndex];
        }
    }

// ------------------------------------------------------------------------------------------------------------------ //
//  invert upper second diagonal
    template<typename T>
    static __global__ void
    upvertKernelUp(void *invertedBuf, Nd4jLong *invertedShape, void *inputBuf, Nd4jLong *inputShape, Nd4jLong n) {

        __shared__ T* inverted;
        __shared__ T* input;
        if (threadIdx.x == 0) {
            inverted = reinterpret_cast<T *>(invertedBuf);
            input = reinterpret_cast<T *>(inputBuf);
        }
        __syncthreads();

        auto start = threadIdx.x + blockIdx.x * blockDim.x;
        auto step = blockDim.x * gridDim.x;

        for (int i = start; i < n - 1; i += step) {
            Nd4jLong pos[] = {i, i + 1};
            Nd4jLong posX[] = {i + 1, i + 1};
            auto xIndex = shape::getOffset(inputShape, pos);
            auto iIndex = shape::getOffset(invertedShape, posX);
            auto zIndex = shape::getOffset(invertedShape, pos);
            // invert upper matrix
            math::atomics::nd4j_atomicAdd(&inverted[zIndex], -input[xIndex] * inverted[iIndex]); // / input[yIndex]);
            //inputMatrix->t<T>(i, i + 1) * invertedMatrix->t<T>(i + 1, i + 1) / inputMatrix->t<T>(i, i)
        }
    }

// ------------------------------------------------------------------------------------------------------------------ //
    template<typename T>
    static __global__ void
    invertLowKernel(void *invertedBuf, Nd4jLong *invertedShape, void *inputBuf, Nd4jLong *inputShape, Nd4jLong n) {

        T *inverted = reinterpret_cast<T *>(invertedBuf);
        T *input = reinterpret_cast<T *>(inputBuf);
        if (threadIdx.x == 0) {
            inverted = reinterpret_cast<T *>(invertedBuf);
            input = reinterpret_cast<T *>(inputBuf);
        }
        __syncthreads();

        auto tid = blockIdx.x * blockDim.x + threadIdx.x;
        auto step = gridDim.x * blockDim.x;

        for (int i = tid + 2; i < n; i += step) {
            for (int j = i - 2; j >= 0; --j)
                for (int k = 0; k < i; k++) {
                    Nd4jLong posZ[] = {i, j};
                    Nd4jLong posY[] = {k, j};
                    Nd4jLong posX[] = {i, k};
                    Nd4jLong posD[] = {i, i};

                    auto xIndex = shape::getOffset(inputShape, posX);
                    auto yIndex = shape::getOffset(invertedShape, posY);
                    auto dIndex = shape::getOffset(inputShape, posD);
                    auto zIndex = shape::getOffset(invertedShape, posZ);
                    // invert non-diagonal elements
                    math::atomics::nd4j_atomicAdd(&inverted[zIndex], -inverted[yIndex] * input[xIndex] / input[dIndex]);
                }
        }
    }

// ------------------------------------------------------------------------------------------------------------------ //
// Invertion of upper triangular matrix non-diagonal elements when main and second diagonals already processed
    template<typename T>
    static __global__ void
    invertUpKernel(void *invertedBuf, Nd4jLong *invertedShape, void *inputBuf, Nd4jLong *inputShape, Nd4jLong n) {
        __shared__ T* inverted;
        __shared__ T* input;

        if (threadIdx.x == 0) {
            inverted = reinterpret_cast<T *>(invertedBuf);;
            input = reinterpret_cast<T *>(inputBuf);
        }
        __syncthreads();
        auto tid = blockIdx.x * blockDim.x + threadIdx.x;
        auto step = blockDim.x * gridDim.x;

        for (int i = (int)n - tid - 2; i >= 0; i -= step) {
            for (int j = i + 2; j < (int)n; j++)
                for (int k = i; k < (int)n; k++) {
                    Nd4jLong posZ[] = {i, j};
                    Nd4jLong posY[] = {k, j};
                    Nd4jLong posX[] = {i, k};
                    // inversion with Joardan Gauss transformation
                    auto xIndex = shape::getOffset(inputShape, posX);
                    auto yIndex = shape::getOffset(invertedShape, posY);
                    auto zIndex = shape::getOffset(invertedShape, posZ);
                    // invert upper non-diagonal elements
                    math::atomics::nd4j_atomicAdd(&inverted[zIndex], -inverted[yIndex] * input[xIndex]);
                }
        }
    }

// ------------------------------------------------------------------------------------------------------------------ //
// procedure to invert lower-triangular matrix.
// In current case lower triangular matrix has main diagonal with general values
//
    template<typename T>
    static void invertLowerMatrix_(LaunchContext *context, NDArray *inputMatrix, NDArray *invertedMatrix) {
        int n = inputMatrix->rows();
        invertedMatrix->setIdentity();

        if (inputMatrix->isIdentityMatrix()) return;

        auto stream = context->getCudaStream();

        // invert lower matrix
        // invert main diagonal
        upvertKernel<T><<<1, n, 512, *stream>>>(invertedMatrix->specialBuffer(), invertedMatrix->specialShapeInfo(), inputMatrix->specialBuffer(), inputMatrix->specialShapeInfo(), n);
        // invert the second diagonal
        invertKernelLow<T><<<1, n, 512, *stream>>>(invertedMatrix->specialBuffer(), invertedMatrix->specialShapeInfo(), inputMatrix->specialBuffer(), inputMatrix->specialShapeInfo(), n);
        // invert non-diagonal elements
        invertLowKernel<T><<<n, n, 512, *stream>>>(invertedMatrix->specialBuffer(), invertedMatrix->specialShapeInfo(), inputMatrix->specialBuffer(), inputMatrix->specialShapeInfo(), n);
    }

// ------------------------------------------------------------------------------------------------------------------ //
// caller for invert lower matrix routine
    void invertLowerMatrix(LaunchContext *context, NDArray *inputMatrix, NDArray *invertedMatrix) {
        NDArray::prepareSpecialUse({invertedMatrix}, {inputMatrix});
        BUILD_SINGLE_SELECTOR(inputMatrix->dataType(), invertLowerMatrix_, (context, inputMatrix, invertedMatrix), FLOAT_NATIVE);
        NDArray::registerSpecialUse({invertedMatrix}, {inputMatrix});
    }

// ------------------------------------------------------------------------------------------------------------------ //
// procedure to invert upper-triangular matrix.
// In current case upper triangular matrix has main diagonal with all ones on it.
    template<typename T>
    static void invertUpperMatrix_(LaunchContext *context, NDArray* inputMatrix, NDArray* invertedMatrix) {
        int n = inputMatrix->rows();
        invertedMatrix->setIdentity();
        auto stream = context->getCudaStream();
        if (inputMatrix->isIdentityMatrix()) { // the inverse for I is I
            return;
        }

        // invert upper matrix
        // invert the second diagonal
        upvertKernelUp<T><<<1, n, 512, *stream >>>(invertedMatrix->specialBuffer(), invertedMatrix->specialShapeInfo(),
                inputMatrix->specialBuffer(), inputMatrix->specialShapeInfo(), n);

        // invert other elements
        invertUpKernel<T><<<n, n, 512, *stream >>>(invertedMatrix->specialBuffer(), invertedMatrix->specialShapeInfo(),inputMatrix->specialBuffer(), inputMatrix->specialShapeInfo(), n);
    }

// ------------------------------------------------------------------------------------------------------------------ //
//  invertion of upper triangular matrix - runner routine
    void invertUpperMatrix(LaunchContext *context, NDArray *inputMatrix, NDArray *invertedMatrix) {
        NDArray::prepareSpecialUse({invertedMatrix}, {inputMatrix});
        BUILD_SINGLE_SELECTOR(invertedMatrix->dataType(), invertUpperMatrix_, (context, inputMatrix, invertedMatrix), FLOAT_NATIVE);
        NDArray::prepareSpecialUse({invertedMatrix}, {inputMatrix});
    }

// ------------------------------------------------------------------------------------------------------------------ //
    // determinant kernel - accumulation product of all values on the main diagonal
    template<typename T>
    static __global__ void determinantKernel(T *compound, T *result, Nd4jLong len) {
        auto start = blockIdx.x * blockDim.x + threadIdx.x;
        auto step = blockDim.x * gridDim.x;
        for (auto i = start; i < len; i += step) {
            auto pos = i * len + i; //shape::getOffset(0, shape::shapeOf(shape), shape::stride(shape), di, 2);
            // multiply all diagonal elements
            math::atomics::nd4j_atomicMul(&result[0], compound[pos]);
        }
    }

// ------------------------------------------------------------------------------------------------------------------ //
    // determinant logarithm - accumulation sum of all logarithm values on the main diagonal. All in logarithic values
    // should be positive
    template<typename T>
    static __global__ void determinantLogKernel(T *compound, T *result, Nd4jLong len) {
        auto start = blockIdx.x * blockDim.x + threadIdx.x;
        auto step = blockDim.x * gridDim.x;
        for (auto i = start; i < len; i += step) {
            auto pos = i * len + i; //shape::getOffset(0, shape::shapeOf(shape), shape::stride(shape), di, 2);
            // sum logs of all diagonal elements
            math::atomics::nd4j_atomicAdd(result, math::nd4j_log<T,T>(math::nd4j_abs(compound[pos])));
        }
    }

// ------------------------------------------------------------------------------------------------------------------ //
    // kernel to copy matrix with given shape to compound tensor with given pos
    // output - a N-D tensor buffer with rank not less than 2, input - 2D square n x n matrix with n = rowLen
    template<typename T, typename F>
    static __global__ void
    fillMatrix(void *output, Nd4jLong *outShape, void *input, Nd4jLong *inputShape, Nd4jLong pos, Nd4jLong rowLen) {
        __shared__ F *matrix;
        __shared__ T *inputBuf;
        __shared__ Nd4jLong inputLen;
        __shared__ Nd4jLong n2;

        if (threadIdx.x == 0) {
            matrix = reinterpret_cast<F*>(output);
            inputBuf = reinterpret_cast<T*>(input);
            inputLen = shape::length(inputShape);
            n2 = rowLen * rowLen;
        }
        __syncthreads();

        auto start = blockIdx.x * blockDim.x + threadIdx.x;
        auto step = blockDim.x * gridDim.x;

        for (int k = pos + start, j = start; j < n2; k += step, j += step) {
            auto xIndex = shape::getIndexOffset(k, inputShape);
            matrix[j] = (F) inputBuf[xIndex];
        }
    }

// ------------------------------------------------------------------------------------------------------------------ //
// same as above, but without type conversion
    template<typename T>
    static __global__ void
    returnMatrix(void *output, Nd4jLong *outputShape, void *input, Nd4jLong *inputShape, Nd4jLong pos, Nd4jLong rowLen) {
        __shared__ T* matrix;
        __shared__ T* outputBuf;
        __shared__ Nd4jLong outputLen;
        __shared__ Nd4jLong n2;

        if (threadIdx.x == 0) {
            matrix = reinterpret_cast<T *>(input);
            outputBuf = reinterpret_cast<T *>(output);
            outputLen = shape::length(inputShape);
            n2 = rowLen * rowLen;
        }
        __syncthreads();
        auto start = blockIdx.x * blockDim.x + threadIdx.x;
        auto step = blockDim.x * gridDim.x;

        for (int k = pos + start, j = start; j < n2; k += step, j += step) {
            auto zIndex = shape::getIndexOffset(k, outputShape);
            outputBuf[zIndex] = matrix[j];
        }
    }

// ------------------------------------------------------------------------------------------------------------------ //
    // fill up permutaion matrix kernel. Permutation matrix filled with zeros and ones
    template<typename F>
    static __global__ void fillUpPermutation(void *output, Nd4jLong *shape, int *source, int rowNum) {
        F *permutation = reinterpret_cast<F *>(output);

        auto start = blockIdx.x * blockDim.x + threadIdx.x;
        auto step = blockDim.x * gridDim.x;
        for (auto i = start; i < rowNum; i += step) {
            int val = source[i] - 1;
            Nd4jLong posF[] = {i, val};
            auto pos = shape::getOffset(shape, posF);
            permutation[pos] = F(1.f);
        }
    }

// ------------------------------------------------------------------------------------------------------------------ //
    // LUP decomposition runner - using CUBLAS SOLVER
    // if permutation is given, then using LUP decomposition, LU decomposition otherwise
    // L - lower triangular, U - upper triangular, P - permutation matricies
    // PA = LU
    //
    // input - A matrix nxn
    // compound - C matrix L + U - I, or main diagonal and lower - L matrix, from the 2nd diagonal - U matrix
    template<typename T, typename I>
    static void lup_(LaunchContext *context, NDArray *input, NDArray *compound, NDArray *permutation) {
        auto stream = context->getCudaStream();
        auto n = input->rows();
        cusolverDnHandle_t cusolverH = nullptr;
        // create solver handle
        cusolverStatus_t status = cusolverDnCreate(&cusolverH);
        if (CUSOLVER_STATUS_SUCCESS != status) {
            throw cuda_exception::build("Cannot create cuSolver handle", status);
        }
        // set solver stream
        status = cusolverDnSetStream(cusolverH, *stream);
        if (CUSOLVER_STATUS_SUCCESS != status) {
            throw cuda_exception::build("Cannot set up stream for cuda solver", status);
        }
        int lwork = 0;
        int *d_info = nullptr;
        // allocate memory for permutation vector
        auto err = cudaMalloc((void **) &d_info, sizeof(int));
        if (err) {
            throw cuda_exception::build("helpers::lup_: Cannot allocate memory for solver info buffer", err);
        }

        DataType dtype = input->dataType();
        switch (dtype) { // there are two implementations with cublas for LUP decomposition - double and float

            case DataType::DOUBLE: {
                double *d_work = nullptr;
                // compute internal buffer size
                double *matrix = reinterpret_cast<double *>(input->specialBuffer());
                status = cusolverDnDgetrf_bufferSize(
                        cusolverH,
                        n,
                        n,
                        matrix,
                        n,
                        &lwork);
                if (CUSOLVER_STATUS_SUCCESS != status) {
                    throw cuda_exception::build("helpers::lup_: Cannot create cuSolver handle", status);
                }

                err = cudaMalloc((void **) &d_work, sizeof(float) * lwork);
                if (err) {
                    throw cuda_exception::build("helpers::lup_: Cannot allocate memory for solver data buffer",
                                                err);
                }

                if (permutation == nullptr) {
                    status = cusolverDnDgetrf(
                            cusolverH,
                            n,
                            n,
                            matrix,
                            n,
                            d_work,
                            nullptr,
                            d_info);

                    if (status != CUSOLVER_STATUS_SUCCESS) {
                        throw cuda_exception::build("helpers::lup_: LU factorization is failed due ",
                                                    status);
                    }
                }
                else {
                    NDArray permutVector('c', {n}, nd4j::DataType::INT32, context);
                    int* permutationBuf = permutVector.dataBuffer()->specialAsT<int>();
                    status = cusolverDnDgetrf(
                            cusolverH,
                            n,
                            n,
                            matrix,
                            n,
                            d_work,
                            permutationBuf,
                            d_info);
                    if (status != CUSOLVER_STATUS_SUCCESS) {
                        throw cuda_exception::build("helpers::lup_: LU factorization is failed due ",
                                                    status);
                    }

                    if (permutation->rankOf() == 2) {
                        fillUpPermutation<double> <<< n, n, 1024, *stream >>>
                                                                  (permutation->specialBuffer(), permutation->specialShapeInfo(), permutationBuf, n);
                    }
                    else {
                        permutVector.tickWriteDevice();
                        input->tickWriteDevice();
                        compound->assign(input);
                        permutation->assign(permutVector);
                    }
                }
                err = cudaFree(d_work);
                if (err) {
                    throw cuda_exception::build("helpers::lup_: Cannot deallocate memory for solver data buffer",
                                                err);
                }
            }
                break;
            case DataType::FLOAT32: {
                float *matrix = reinterpret_cast<float*>(input->specialBuffer());
                float *d_work = nullptr;

                status = cusolverDnSgetrf_bufferSize(
                        cusolverH,
                        n,
                        n,
                        matrix,
                        n,
                        &lwork);
                if (CUSOLVER_STATUS_SUCCESS != status) {
                    throw cuda_exception::build("helpers::lup_: Cannot create cuSolver handle", status);
                }

                err = cudaMalloc((void **) &d_work, sizeof(float) * lwork);
                if (err) {
                    throw cuda_exception::build("helpers::lup_: Cannot allocate memory for solver data buffer",
                                                err);
                }

                if (permutation == nullptr)
                    status = cusolverDnSgetrf(
                            cusolverH,
                            n,
                            n,
                            matrix,
                            n,
                            d_work,
                            nullptr,
                            d_info);
                else {
                    NDArray permutVector('c', {n}, DataType::INT32, context);
                    int *permutationBuf = reinterpret_cast<int *>(permutVector.specialBuffer());
                    status = cusolverDnSgetrf(
                            cusolverH,
                            n,
                            n,
                            matrix,
                            n,
                            d_work,
                            permutationBuf,
                            d_info);
                    if (permutation->rankOf() == 2) {
                        fillUpPermutation<I> <<< n, n, 128, *stream >>>
                                                             (permutation->specialBuffer(), permutation->specialShapeInfo(), permutationBuf, n);
                        permutation->tickWriteDevice();
                    }
                    else {
                        input->tickWriteDevice();
                        compound->assign(input);
                        permutation->assign(permutVector);
                    }
                }
                err = cudaFree(d_work);
                if (err) {
                    throw cuda_exception::build("helpers::lup_: Cannot deallocate memory for solver data buffer",
                                                err);
                }

            }
        }
        if (CUSOLVER_STATUS_SUCCESS != status) {
            throw cuda_exception::build("helpers::lup_: Cannot make LU decomposition", status);
        }
        err = cudaFree(d_info);
        if (err) {
            throw cuda_exception::build("helpers::lup_: Cannot deallocate memory for solver info buffer", err);
        }
        cusolverDnDestroy(cusolverH);
//        NDArray::registerSpecialUse({input}, {input});
        input->tickWriteDevice();
    }
// ------------------------------------------------------------------------------------------------------------------ //

    BUILD_DOUBLE_TEMPLATE(template void lup_,(LaunchContext * context, NDArray * input, NDArray * output, NDArray * permutation), FLOAT_NATIVE, INDEXING_TYPES);

    template <typename T>
    static __device__ void  swapRows(T* matrix, Nd4jLong* shape, Nd4jLong theFirst, Nd4jLong theSecond, Nd4jLong n) {
        if (theFirst != theSecond) {
            for (auto i = 0; i < n; i++) {
                Nd4jLong theFirstPos[] = {theFirst, i};
                Nd4jLong theSecondPos[] = {theSecond, i};
                auto theFirstIndex = shape::getOffset(shape, theFirstPos, 0);
                auto theSecondIndex = shape::getOffset(shape, theSecondPos, 0);
                math::nd4j_swap(matrix[theFirstIndex], matrix[theSecondIndex]);
            }
        }
    }

    template <typename T>
    static __device__ void processColumns(Nd4jLong currentRow, Nd4jLong rowNum, T* compoundBuf, Nd4jLong* compoundShape) {
        Nd4jLong xDiag[] = {currentRow, currentRow};
        auto diagIndex = shape::getOffset(compoundShape, xDiag, 0);
        for (auto j = currentRow + 1; j < rowNum; j++) {
            Nd4jLong xRow[] = {j, currentRow};
            auto rowIndex = shape::getOffset(compoundShape, xRow, 0);
            compoundBuf[rowIndex] /= compoundBuf[diagIndex]; //output->t<T>(i, i);
            for (auto k = currentRow + 1; k < rowNum; k++) {
                Nd4jLong yRow[] = {j, k};
                Nd4jLong yCol[] = {currentRow, k};
                auto rowIndexY = shape::getOffset(compoundShape, yRow, 0);
                auto colIndex = shape::getOffset(compoundShape, yCol, 0);
                compoundBuf[rowIndexY] -= compoundBuf[rowIndex] * compoundBuf[colIndex];
            }
        }
    }

    template <typename T>
    __device__ Nd4jLong argmaxCol(Nd4jLong column, T* compoundBuffer, Nd4jLong* compoundShape) {
        auto rowNum = shape::sizeAt(compoundShape, 0);
        Nd4jLong xInitial[] = {column, column};
        auto xInitialIndex = shape::getOffset(compoundShape, xInitial, 0);
        auto maxValue = T(0); //nd4j::math::nd4j_abs(compoundBuffer[xInitialIndex]);
        auto result = -1LL;

        for (auto rowCounter = column; rowCounter < rowNum; rowCounter++) {
            Nd4jLong xPos[] = {rowCounter, column};
            auto xIndex = shape::getOffset(compoundShape, xPos, 0);
            if (nd4j::math::nd4j_abs(compoundBuffer[xIndex]) > maxValue) {
                maxValue = nd4j::math::nd4j_max(maxValue, nd4j::math::nd4j_abs(compoundBuffer[xIndex]));
                result = rowCounter;
            }
        }
        return result;
    }

        template <typename T, typename I>
    static __device__ int  luNN(T* matrix, Nd4jLong* shape, I* permutation, Nd4jLong* permuShape, Nd4jLong n) {

        for (auto i = 0; i < n - 1; i++) {
            auto pivotIndex = argmaxCol(i, matrix, shape);
            if (pivotIndex < 0) {
                return -1;//throw std::runtime_error("helpers::luNN_: input matrix is singular.");
            }
            math::nd4j_swap(permutation[shape::getIndexOffset(i, permuShape)], permutation[shape::getIndexOffset(pivotIndex, permuShape)]);
            swapRows(matrix, shape, (Nd4jLong)i, pivotIndex, n);

            processColumns(i, n, matrix, shape);
        }
        return 0;
    }

    template <typename T, typename I>
    static __global__ void luBatchedKernel(T* outputBuf, Nd4jLong* outputShape, I* permutations, Nd4jLong* permuShape,
         Nd4jLong* outputTadShape, Nd4jLong* outputTadOffsets, Nd4jLong* permuTadShape, Nd4jLong* permuTadOffsets,
         Nd4jLong batchNum) {

        auto start = blockIdx.x * blockDim.x + threadIdx.x;
        auto step = blockDim.x * gridDim.x;

        for (auto b = start; b < batchNum; b += step) {
            T* matrix = outputBuf + outputTadOffsets[b];
            I* permutation = permutations + permuTadOffsets[b];

            if (0 != luNN(matrix, outputTadShape, permutation, permuTadShape, shape::length(permuTadShape))) break;
        }
    }

    template <typename T, typename I>
    static void lu_(LaunchContext * context, NDArray* input, NDArray* output, NDArray* permutationVectors) {
        auto n = input->sizeAt(-1);
        auto stream = context->getCudaStream();
        NDArray iota('c', {n}, permutationVectors->dataType());// = NDArrayFactory::create(); // <int>('c', {n});
        iota.linspace(0); iota.syncToDevice();

        output->assign(input); // fill up output tensor with zeros
//        output->tickWriteDevice();
        permutationVectors->applyTrueBroadcast(nd4j::BroadcastOpsTuple::Assign(), iota, *permutationVectors, true, nullptr);
//        permutationVectors->tickWriteDevice();
        auto tads = ConstantTadHelper::getInstance()->tadForDimensions(output->shapeInfo(), {-2, -1});
        auto permutaionTads = ConstantTadHelper::getInstance()->tadForDimensions(output->shapeInfo(), {-1});
        auto batchNum = tads.numberOfTads();
        luBatchedKernel<T,I><<<batchNum, 256, 1024, *stream>>>(reinterpret_cast<T*>(output->platformBuffer()),
                output->specialShapeInfo(), reinterpret_cast<I*>(permutationVectors->platformBuffer()),
                permutationVectors->specialShapeInfo(), tads.specialShapeInfo(), tads.specialOffsets(),
                permutaionTads.specialShapeInfo(), permutaionTads.specialOffsets(), batchNum);
    }

    void lu(LaunchContext* context, NDArray* input, NDArray* output, NDArray* permutations) {
        NDArray::prepareSpecialUse({output, permutations}, {input});
        BUILD_DOUBLE_SELECTOR(input->dataType(), permutations->dataType(), lu_, (context, input, output, permutations), FLOAT_NATIVE, INDEXING_TYPES);
        NDArray::registerSpecialUse({output, permutations}, {input});
    }
// ------------------------------------------------------------------------------------------------------------------ //
    template<typename T>
    static int determinant_(nd4j::LaunchContext *context, NDArray *input, NDArray *output) {
        Nd4jLong n = input->sizeAt(-1);
        Nd4jLong n2 = n * n;
        std::vector<int> dims();
        auto packX = ConstantTadHelper::getInstance()->tadForDimensions(input->getShapeInfo(), {input->rankOf() - 2, input->rankOf() - 1});
        //auto packZ = ConstantTadHelper::getInstance()->tadForDimensions(output->shapeInfo(), {output->rankOf() - 1});
//        DataType dtype = input->dataType();
//        if (dtype != DataType::DOUBLE)
//            dtype = DataType::FLOAT32;
        auto matrix = NDArrayFactory::create(input->ordering(), {n, n}, DataTypeUtils::fromT<T>(), context); //, block.getWorkspace());
        auto det = NDArrayFactory::create<T>(1);
        auto stream = context->getCudaStream();
        NDArray::prepareSpecialUse({output}, {input});
        dim3 launchDims(256, 256, 1024);
        output->assign(1.f);
        for (int e = 0; e < output->lengthOf(); e++) {
            Nd4jLong pos = e * n2;
//            if (matrix.dataType() == input->dataType())
            fillMatrix<T, T><<<launchDims.x, launchDims.y, launchDims.z, *stream>>>(matrix.specialBuffer(), matrix.specialShapeInfo(), input->specialBuffer(), input->specialShapeInfo(), pos, n);
//            else
//                fillMatrix<T, float><<<launchDims.x, launchDims.y, launchDims.z, *stream>>>(matrix.specialBuffer(), matrix.specialShapeInfo(), input->specialBuffer(), input->specialShapeInfo(), pos, n);
            lup_<T, int>(context, &matrix, nullptr, nullptr);
//            else
//                lup_<float>(context, &matrix, nullptr, nullptr);
            auto offset = shape::getIndexOffset(e, output->shapeInfo());
            auto inputBuf = reinterpret_cast<T *>(matrix.specialBuffer());
            auto outputBuf = reinterpret_cast<T *>(output->specialBuffer()) + offset;
//            if (matrix.dataType() == input->dataType())
            determinantKernel<T> << < launchDims.x, launchDims.y, launchDims.z, *stream >> >
                                                                                (inputBuf, outputBuf, n);
//            else
//                determinantKernel<T, float><<<launchDims.x, launchDims.y, launchDims.z, *stream >>> (inputBuf, outputBuf, n);
        }
        NDArray::registerSpecialUse({output}, {input});

        return Status::OK();
    }

        int determinant(nd4j::LaunchContext *context, NDArray *input, NDArray *output) {
            NDArray::prepareSpecialUse({output}, {input});
            BUILD_SINGLE_SELECTOR(input->dataType(), return determinant_, (context, input, output), FLOAT_NATIVE);
            NDArray::registerSpecialUse({output}, {input});
        }

        template<typename T>
        int logAbsDeterminant_(LaunchContext *context, NDArray *input, NDArray *output) {
            Nd4jLong n = input->sizeAt(-1);
            Nd4jLong n2 = n * n;
            std::vector<int> dims();
            auto packX = ConstantTadHelper::getInstance()->tadForDimensions(input->getShapeInfo(), {input->rankOf() - 2, input->rankOf() - 1});
            //auto packZ = ConstantTadHelper::getInstance()->tadForDimensions(output->shapeInfo(), {output->rankOf() - 1});
            DataType dtype = input->dataType();
            if (dtype != DataType::DOUBLE)
                dtype = DataType::FLOAT32;

            auto matrix = NDArrayFactory::create(input->ordering(), {n, n}, dtype, context); //, block.getWorkspace());
            auto det = NDArrayFactory::create<T>(1);
            auto stream = context->getCudaStream();
            NDArray::prepareSpecialUse({output}, {input});
            dim3 launchDims(256, 256, 1024);
            output->assign(0.f);
            for (int e = 0; e < output->lengthOf(); e++) {
                Nd4jLong pos = e * n2;
//            if (matrix.dataType() == input->dataType())
                fillMatrix<T, T><<<launchDims.x, launchDims.y, launchDims.z, *stream>>>(matrix.specialBuffer(), matrix.specialShapeInfo(), input->specialBuffer(), input->specialShapeInfo(), pos, n);
//            else
//                fillMatrix<T, float><<<launchDims.x, launchDims.y, launchDims.z, *stream>>>(matrix.specialBuffer(), matrix.specialShapeInfo(), input->specialBuffer(), input->specialShapeInfo(), pos, n);

//            if (matrix.dataType() == input->dataType())
                lup_<T, int>(context, &matrix, nullptr, nullptr);
//            else
//                lup_<float>(context, &matrix, nullptr, nullptr);
                auto offset = shape::getIndexOffset(e, output->shapeInfo());
                auto inputBuf = reinterpret_cast<T *>(matrix.specialBuffer());
                auto outputBuf = reinterpret_cast<T *>(output->specialBuffer()) + offset;
//            if (matrix.dataType() == input->dataType())
                determinantLogKernel<T><<<launchDims.x, launchDims.y, launchDims.z, *stream>>>(inputBuf, outputBuf, n);
//            else
//                determinantLogKernel<T, float><<<launchDims.x, launchDims.y, launchDims.z, *stream >>> (inputBuf, outputBuf, n);
            }
            NDArray::registerSpecialUse({output}, {input});

            return Status::OK();

            return ND4J_STATUS_OK;
        }

        int logAbsDeterminant(nd4j::LaunchContext *context, NDArray *input, NDArray *output) {
            NDArray::prepareSpecialUse({output}, {input});
            BUILD_SINGLE_SELECTOR(input->dataType(), return logAbsDeterminant_, (context, input, output), FLOAT_NATIVE);
            NDArray::registerSpecialUse({output}, {input});
        }

        template<typename T>
        static __global__ void
        fillLowerUpperKernel(void *lowerBuf, Nd4jLong *lowerShape, void *upperBuf, Nd4jLong *upperShape,
                             void *matrixBuf, Nd4jLong *matrixShape, Nd4jLong n) {

            __shared__ T *lowerMatrix;
            __shared__ T *upperMatrix;
            __shared__ T *matrix;

            if (threadIdx.x == 0) {
                lowerMatrix = reinterpret_cast<T *>(lowerBuf);
                upperMatrix = reinterpret_cast<T *>(upperBuf);
                matrix = reinterpret_cast<T *>(matrixBuf);
            }
            __syncthreads();

            for (int k = blockIdx.x; k < n; k += gridDim.x) {  // and then put all values under main diagonal on to it
                for (int j = threadIdx.x; j < n; j += blockDim.x) {
                    Nd4jLong posX[] = {k, j};
                    Nd4jLong posD[] = {j, j};
                    auto xPos = shape::getOffset(lowerShape, posX);
                    auto yPos = shape::getOffset(upperShape, posX);
                    auto iPos = shape::getOffset(matrixShape, posX);
                    auto dPos = shape::getOffset(matrixShape, posD);
                    if (k >= j)
                        lowerMatrix[xPos] = matrix[iPos];//(k, j);
                    else
                        upperMatrix[yPos] = matrix[iPos]; //k, j);
                }
            }
        }

        template<typename T>
        static int inverse_(nd4j::LaunchContext *context, NDArray *input, NDArray *output) {
            auto n = input->sizeAt(-1);
            auto n2 = n * n;
            auto dtype = DataTypeUtils::fromT<T>(); //input->dataType();
//            if (dtype != DataType::DOUBLE)
//                dtype = DataType::FLOAT32;
            NDArray matrix = NDArrayFactory::create('c', {n, n}, dtype, context);
            NDArray upper = NDArrayFactory::create('c', {n, n}, dtype, context);
            NDArray lower = NDArrayFactory::create('c', {n, n}, dtype, context);
            NDArray compound = NDArrayFactory::create('c', {n, n}, dtype, context);
            NDArray permutation = NDArrayFactory::create('c', {n, n}, dtype, context);
            auto packX = nd4j::ConstantTadHelper::getInstance()->tadForDimensions(input->getShapeInfo(),
                                                                                  {input->rankOf() - 2,
                                                                                   input->rankOf() - 1});
            auto packZ = nd4j::ConstantTadHelper::getInstance()->tadForDimensions(output->getShapeInfo(),
                                                                                  {output->rankOf() - 2,
                                                                                   output->rankOf() - 1});
            auto stream = context->getCudaStream();

            for (auto i = 0LL; i < packX.numberOfTads(); i++) {
                fillMatrix<T, T><<<1, n2, 1024, *stream>>>(matrix.specialBuffer(), matrix.specialShapeInfo(), input->specialBuffer(), input->specialShapeInfo(), i * n2, n);
                matrix.tickWriteDevice();
                //compound.assign(matrix);
//            if (matrix.dataType() == input->dataType())
                lup_<T, int>(context, &matrix, nullptr, nullptr);
                fillLowerUpperKernel<T><<<n, n, 1024, *stream>>>(lower.specialBuffer(), lower.specialShapeInfo(), upper.specialBuffer(), upper.specialShapeInfo(), matrix.specialBuffer(), matrix.specialShapeInfo(), n);
                lower.tickWriteDevice();
                upper.tickWriteDevice();
//                lower.printIndexedBuffer("LOWER");
//                upper.printIndexedBuffer("UPPER");
                matrix.assign(0);
                invertUpperMatrix(context, &upper, &matrix); // U^{-1}
                matrix.tickWriteDevice();
//                matrix.printIndexedBuffer("Upper Inverted");
                compound.assign(0);
                invertLowerMatrix(context, &lower, &compound); // L{-1}
                compound.tickWriteDevice();
//                compound.printIndexedBuffer("Lower Inverted");
//                matrix.tickWriteDevice();
//                compound.tickWriteDevice();
                nd4j::MmulHelper::mmul(&matrix, &compound, &upper, 1.0, 0.0);
                upper.tickWriteDevice();
//                upper.printIndexedBuffer("Full inverted");
                returnMatrix<T> <<<1, n2, 1024, *stream>>>(output->specialBuffer(), output->specialShapeInfo(), upper.specialBuffer(), upper.specialShapeInfo(), i * n2, n);
            }
            return Status::OK();
        }

        int inverse(nd4j::LaunchContext *context, NDArray *input, NDArray *output) {
            NDArray::prepareSpecialUse({output}, {input});
            BUILD_SINGLE_SELECTOR(input->dataType(), return inverse_, (context, input, output), FLOAT_NATIVE);
            NDArray::registerSpecialUse({output}, {input});
        }

        bool checkCholeskyInput(nd4j::LaunchContext *context, NDArray const *input) {
            return true;
        }

        template<typename F>
        __global__ void fillBatchKernel(F **dArrayBatch, F *buf, Nd4jLong *offsets, Nd4jLong batchSize) {
            auto start = blockIdx.x * blockDim.x + threadIdx.x;
            auto step = blockDim.x * gridDim.x;

            for (auto i = start; i < batchSize; i += step) {
                dArrayBatch[i] = buf + offsets[i];
            }
        }

        template<typename F>
        __global__ void
        adjustResultsKernel(F *dArray, Nd4jLong *shape, Nd4jLong *offsets, Nd4jLong batchSize, Nd4jLong n) {
            //auto i = blockIdx.x * blockDim.x + threadIdx.x;
            Nd4jLong *shapeOf = shape::shapeOf(shape);
            Nd4jLong *strideOf = shape::stride(shape);

            for (auto i = blockIdx.x; i < batchSize; i += gridDim.x) {
                auto current = dArray + offsets[i];
                for (auto r = threadIdx.x; r < n; r += blockDim.x) {
                    for (auto c = r + 1; c < n; c++) {
                        Nd4jLong posRC[] = {r, c};
                        auto pos = r * n + c; //shape::getOffset(0, shapeOf, strideOf, posRC, 2);
                        current[pos] = 0.;
                    }
                }
            }
        }

        template<typename F>
        int cholesky__(LaunchContext *context, NDArray *input, NDArray *output, bool inplace) {
            if (!inplace)
                output->assign(input);
            auto tempOutput =output->dup();
            cusolverDnHandle_t handle = nullptr;
            auto n = input->sizeAt(-1);
            auto n2 = n * n;
            NDArray::prepareSpecialUse({output}, {input});
            auto status = cusolverDnCreate(&handle);
            if (CUSOLVER_STATUS_SUCCESS != status) {
                throw cuda_exception::build("helpers::cholesky_: Cannot create solver handle", status);
            }
            F **dArrayBatch = nullptr;
            auto packX = nd4j::ConstantTadHelper::getInstance()->tadForDimensions(tempOutput.getShapeInfo(),
                                                                                  {tempOutput.rankOf() - 2,
                                                                                   tempOutput.rankOf() - 1});
            const Nd4jLong batchSize = packX.numberOfTads();
            int *dInfoArray = nullptr;
            auto err = cudaMalloc((void **) &dArrayBatch, sizeof(F *) * batchSize);
            if (err) {
                throw cuda_exception::build("helpers::cholesky_: Cannot allocate memory for solver batch data buffer",
                                            err);
            }
            err = cudaMalloc((void **) &dInfoArray, sizeof(int) * batchSize);
            if (err) {
                throw cuda_exception::build("helpers::cholesky_: Cannot allocate memory for solver errors buffer", err);
            }
            auto stream = context->getCudaStream();
            fillBatchKernel<F> << < 1, batchSize, 128, *stream >> >
                                                       (dArrayBatch, reinterpret_cast<F *>(tempOutput.specialBuffer()), packX.specialOffsets(), batchSize);

            status = cusolverDnSetStream(handle, *stream);
            if (CUSOLVER_STATUS_SUCCESS != status) {
                throw cuda_exception::build("helpers::cholesky_: Cannot set stream to solver handle", status);
            }
            const cublasFillMode_t uplo = CUBLAS_FILL_MODE_UPPER;
            if (input->dataType() == DataType::DOUBLE)
                status = cusolverDnDpotrfBatched(
                        handle,
                        uplo,
                        n,
                        (double **) dArrayBatch,
                        n,
                        dInfoArray,
                        batchSize);
            else
                status = cusolverDnSpotrfBatched(
                        handle,
                        uplo,
                        n,
                        (float **) dArrayBatch,
                        n,
                        dInfoArray,
                        batchSize);

            if (CUSOLVER_STATUS_SUCCESS != status) {
                throw cuda_exception::build("helpers::cholesky_: Cholesky factorization failed for batch", status);
            }
            adjustResultsKernel<F> << < batchSize, n2, 128, *stream >> >
                                                            (reinterpret_cast<F *>(tempOutput.specialBuffer()), packX.specialShapeInfo(), packX.specialOffsets(), batchSize, n);

            err = cudaFree(dArrayBatch);
            if (err) {
                throw cuda_exception::build("helpers::cholesky_: Cannot deallocate memory for solver batch data buffer",
                                            err);
            }
            err = cudaFree(dInfoArray);
            if (err) {
                throw cuda_exception::build("helpers::cholesky_: Cannot allocate memory for solver errors buffer", err);
            }

            if (!inplace)
                output->assign(tempOutput);
            else
                input->assign(tempOutput);

            NDArray::registerSpecialUse({output}, {input});
            return Status::OK();
        }

//    template <typename T>
        int cholesky_(LaunchContext *context, NDArray *input, NDArray *output, bool inplace) {
            NDArray::prepareSpecialUse({output}, {input});
            if (input->dataType() == DataType::DOUBLE)
                cholesky__<double>(context, input, output, inplace);
            else if (input->dataType() == DataType::FLOAT32)
                cholesky__<float>(context, input, output, inplace);
            else {
                std::unique_ptr<NDArray> tempOutput(
                        NDArrayFactory::create_('c', input->getShapeAsVector(), DataType::FLOAT32, context));
                tempOutput->assign(input);
                cholesky__<float>(context, tempOutput.get(), tempOutput.get(), true);
                output->assign(tempOutput.get());
            }
            NDArray::registerSpecialUse({output}, {input});
            return Status::OK();
        }

        int cholesky(nd4j::LaunchContext *context, NDArray *input, NDArray *output, bool inplace) {
//        BUILD_SINGLE_SELECTOR(input->dataType(), return cholesky_, (context, input, output, inplace), FLOAT_TYPES);
            return cholesky_(context, input, output, inplace);
        }
//    BUILD_SINGLE_TEMPLATE(template int cholesky_, (LaunchContext* context, NDArray* input, NDArray* output, bool inplace), FLOAT_TYPES);
        BUILD_SINGLE_TEMPLATE(template int inverse_, (nd4j::LaunchContext * context, NDArray * input, NDArray * output),
                              FLOAT_NATIVE);

        template<typename T>
        __global__ void
        logDetKernel(T *inputBuf, Nd4jLong *inputShape, Nd4jLong batchNum, Nd4jLong *tadShape, Nd4jLong *tadOffsets,
                     T *outputBuf, Nd4jLong *outputShape) {

            __shared__ int n;
            if (threadIdx.x == 0) {
                n = shape::sizeAt(inputShape, -1); // * shape::sizeAt(inputShape, -1);
            }
            __syncthreads();

            T *output = outputBuf;
            T *input = inputBuf;

            for (auto i = blockIdx.x; i < batchNum; i += gridDim.x) {
                T *current = input + tadOffsets[i];

                auto zIndex = shape::getIndexOffset(i, outputShape);
                for (auto e = threadIdx.x; e < n; e += blockDim.x) {
                    Nd4jLong diag[] = {e, e};
                    auto xIndex = shape::getOffset(tadShape, diag);
                    math::atomics::nd4j_atomicAdd(&output[zIndex],math::nd4j_log<T, T>(current[xIndex] * current[xIndex]));
                }
            }
        }

        template<typename T>
        int logdetFunctor_(nd4j::LaunchContext *context, NDArray *input, NDArray *output) {
            NDArray::prepareSpecialUse({output}, {input});
            auto n2 = input->sizeAt(-1) * input->sizeAt(-2);
            auto stream = context->getCudaStream();
            NDArray tempOutput(*input);

            cholesky(context, input, &tempOutput, false);

            auto outputBuf = output->dataBuffer()->specialAsT<T>(); //reinterpret_cast<T*>(output->specialBuffer()); // + e * n2; // + e * n2;
            auto inputBuf = tempOutput.dataBuffer()->specialAsT<T>(); //reinterpret_cast<T*>(tempOutput.specialBuffer());
            output->nullify();
            auto packX = nd4j::ConstantTadHelper::getInstance()->tadForDimensions(tempOutput.getShapeInfo(),
                                                                                  {tempOutput.rankOf() - 2,
                                                                                   tempOutput.rankOf() - 1});
            logDetKernel<T> <<<128, 512, 256, *stream>>>(inputBuf, tempOutput.specialShapeInfo(),
                    packX.numberOfTads(), packX.specialShapeInfo(),
                    packX.specialOffsets(), outputBuf, output->specialShapeInfo());
            output->tickWriteDevice();
            NDArray::registerSpecialUse({output}, {input});
            return Status::OK();
        }

        int logdetFunctor(nd4j::LaunchContext *context, NDArray *input, NDArray *output) {
            BUILD_SINGLE_SELECTOR(output->dataType(), return logdetFunctor_, (context, input, output), FLOAT_NATIVE);
        }

        /*
         * lup - batched input, batched outputs
         * */
        int lup(LaunchContext *context, NDArray *input, NDArray *compound, NDArray *permutation) {
            BUILD_DOUBLE_SELECTOR(input->dataType(), permutation->dataType(), lup_,(context, input, compound, permutation), FLOAT_NATIVE, INDEXING_TYPES);
            return Status::OK();
        }

//        BUILD_SINGLE_TEMPLATE(template int logdetFunctor_,
//                              (nd4j::LaunchContext * context, NDArray * input, NDArray * output), FLOAT_NATIVE);
    }
}
}