Aurora/src/Function1D.cpp

#include "Function1D.h"
#include "Function2D.h"
#include "Function.h"

//必须在Eigen之前
#include "AuroraDefs.h"
#include "Matrix.h"

#include <cstddef>
#include <cstdint>
#include <cstring>
#include <cmath>
#include <iostream>

#include <Eigen/Core>
#include <Eigen/Eigen>
#include <Eigen/Dense>
#include <Eigen/SVD>
#include <mkl_lapack.h>
#include <sys/types.h>

using namespace Aurora;

namespace {
    const int COMPLEX_STRIDE = 2;
    const int REAL_STRIDE = 1;
    const int SAME_STRIDE = 1;
    const double VALUE_ONE = 1.0;
    const ushort CONVERT_AND_VALUE = 15;
    const ushort CONVERT_AND_VALUE_2 = 2047;
    const ushort CONVERT_MUL_VALUE = 2048;

    uint CONVERT_ADD_VALUE = UINT32_MAX - 4095;

    inline void convertValue(double aValue ,double* des){
      double value = aValue;
      ushort *exponentPtr = (ushort *)&value;
      exponentPtr[0] = (exponentPtr[0] >> 11) & CONVERT_AND_VALUE;
      exponentPtr[1] = (exponentPtr[1] >> 11) & CONVERT_AND_VALUE;
      exponentPtr[2] = (exponentPtr[2] >> 11) & CONVERT_AND_VALUE;
      exponentPtr[3] = (exponentPtr[3] >> 11) & CONVERT_AND_VALUE;
      double signValue = aValue;
      short *signPtr = (short *)&signValue;
      uint sign_bit[4] = {
          (uint)(signPtr[0] < 0 ? 1 : 0), (uint)(signPtr[1] < 0 ? 1 : 0),
          (uint)(signPtr[2] < 0 ? 1 : 0), (uint)(signPtr[3] < 0 ? 1 : 0)};
      double fraction3Value = aValue;
      ushort *fraction3Ptr = (ushort *)&fraction3Value;
      fraction3Ptr[0] &= CONVERT_AND_VALUE_2;
      fraction3Ptr[1] &= CONVERT_AND_VALUE_2;
      fraction3Ptr[2] &= CONVERT_AND_VALUE_2;
      fraction3Ptr[3] &= CONVERT_AND_VALUE_2;
      uint hidden_bit[4] = {
          sign_bit[0] * (!exponentPtr[0] ? 1 : 0) * CONVERT_MUL_VALUE +
              ((!sign_bit[0] && exponentPtr[0]) ? 1 : 0) * CONVERT_MUL_VALUE,
          sign_bit[1] * (!exponentPtr[1] ? 1 : 0) * 2048 +
              ((!sign_bit[1] && exponentPtr[1]) ? 1 : 0) * CONVERT_MUL_VALUE,
          sign_bit[2] * (!exponentPtr[2] ? 1 : 0) * CONVERT_MUL_VALUE +
              ((!sign_bit[2] && exponentPtr[2]) ? 1 : 0) * CONVERT_MUL_VALUE,
          sign_bit[3] * (!exponentPtr[3] ? 1 : 0) * 2048 +
              ((!sign_bit[3] && exponentPtr[3]) ? 1 : 0) * CONVERT_MUL_VALUE,
      };
      int outputPtr[4] = {0};
      uint temp = fraction3Ptr[0] + hidden_bit[0] + sign_bit[0] * CONVERT_ADD_VALUE;
      outputPtr[0] = exponentPtr[0] > 1 ? (temp << (exponentPtr[0] - 1))
                                  : (temp >> std::abs(exponentPtr[0] - 1));
      temp = fraction3Ptr[1] + hidden_bit[1] + sign_bit[1] * CONVERT_ADD_VALUE;
      outputPtr[1] = exponentPtr[1] > 1 ? (temp << (exponentPtr[1] - 1))
                                  : (temp >> std::abs(exponentPtr[1] - 1));
      temp = fraction3Ptr[2] + hidden_bit[2] + sign_bit[2] * CONVERT_ADD_VALUE;
      outputPtr[2] = exponentPtr[2] > 1 ? (temp << (exponentPtr[2] - 1))
                                  : (temp >> std::abs(exponentPtr[2] - 1));
      temp = fraction3Ptr[3] + hidden_bit[3] + sign_bit[3] * CONVERT_ADD_VALUE;
      outputPtr[3] = exponentPtr[3] > 1 ? (temp << (exponentPtr[3] - 1))
                                  : (temp >> std::abs(exponentPtr[3] - 1));
    des[0] = outputPtr[0];
    des[1] = outputPtr[1];
    des[2] = outputPtr[2];
    des[3] = outputPtr[3];

    }

    inline void convertValue2(short* aValue ,double* des){
      ushort exponentPtr[4] = {(ushort)aValue[0],(ushort)aValue[1],(ushort)aValue[2],(ushort)aValue[3]};
      exponentPtr[0] = (exponentPtr[0] >> 11) & CONVERT_AND_VALUE;
      exponentPtr[1] = (exponentPtr[1] >> 11) & CONVERT_AND_VALUE;
      exponentPtr[2] = (exponentPtr[2] >> 11) & CONVERT_AND_VALUE;
      exponentPtr[3] = (exponentPtr[3] >> 11) & CONVERT_AND_VALUE;
      short signPtr [4] = {aValue[0],aValue[1],aValue[2],aValue[3]};
      uint sign_bit[4] = {
          (uint)(signPtr[0] < 0 ? 1 : 0), (uint)(signPtr[1] < 0 ? 1 : 0),
          (uint)(signPtr[2] < 0 ? 1 : 0), (uint)(signPtr[3] < 0 ? 1 : 0)};
      ushort fraction3Ptr[4] = {(ushort)aValue[0],(ushort)aValue[1],(ushort)aValue[2],(ushort)aValue[3]};
      fraction3Ptr[0] &= CONVERT_AND_VALUE_2;
      fraction3Ptr[1] &= CONVERT_AND_VALUE_2;
      fraction3Ptr[2] &= CONVERT_AND_VALUE_2;
      fraction3Ptr[3] &= CONVERT_AND_VALUE_2;
      uint hidden_bit[4] = {
          sign_bit[0] * (!exponentPtr[0] ? 1 : 0) * CONVERT_MUL_VALUE +
              ((!sign_bit[0] && exponentPtr[0]) ? 1 : 0) * CONVERT_MUL_VALUE,
          sign_bit[1] * (!exponentPtr[1] ? 1 : 0) * 2048 +
              ((!sign_bit[1] && exponentPtr[1]) ? 1 : 0) * CONVERT_MUL_VALUE,
          sign_bit[2] * (!exponentPtr[2] ? 1 : 0) * CONVERT_MUL_VALUE +
              ((!sign_bit[2] && exponentPtr[2]) ? 1 : 0) * CONVERT_MUL_VALUE,
          sign_bit[3] * (!exponentPtr[3] ? 1 : 0) * 2048 +
              ((!sign_bit[3] && exponentPtr[3]) ? 1 : 0) * CONVERT_MUL_VALUE,
      };
      int outputPtr[4] = {0};
      uint temp = fraction3Ptr[0] + hidden_bit[0] + sign_bit[0] * CONVERT_ADD_VALUE;
      outputPtr[0] = exponentPtr[0] > 1 ? (temp << (exponentPtr[0] - 1)): temp;
      temp = fraction3Ptr[1] + hidden_bit[1] + sign_bit[1] * CONVERT_ADD_VALUE;
      outputPtr[1] = exponentPtr[1] > 1 ? (temp << (exponentPtr[1] - 1)): temp;
      temp = fraction3Ptr[2] + hidden_bit[2] + sign_bit[2] * CONVERT_ADD_VALUE;
      outputPtr[2] = exponentPtr[2] > 1 ? (temp << (exponentPtr[2] - 1)): temp;
      temp = fraction3Ptr[3] + hidden_bit[3] + sign_bit[3] * CONVERT_ADD_VALUE;
      outputPtr[3] = exponentPtr[3] > 1 ? (temp << (exponentPtr[3] - 1)): temp;
    des[0] = outputPtr[0];
    des[1] = outputPtr[1];
    des[2] = outputPtr[2];
    des[3] = outputPtr[3];

    }
}


Aurora::Matrix Aurora::complex(const Aurora::Matrix &matrix) {
    if (matrix.getValueType() == Complex) {
        std::cerr<<"complex not support complex value type"<<std::endl;
        return matrix;
    }
    auto output = malloc(matrix.getDataSize() ,true);
    memset(output, 0, (matrix.getDataSize() * sizeof(std::complex<double>)));
    cblas_dcopy(matrix.getDataSize(), matrix.getData(), REAL_STRIDE, (double *) output, COMPLEX_STRIDE);
    return Aurora::Matrix::New((double *) output, matrix.getDimSize(0), matrix.getDimSize(1), matrix.getDimSize(2),
                               Complex);
}

Aurora::Matrix Aurora::real(const Aurora::Matrix &matrix) {
    if (matrix.getValueType() == Normal) {
        std::cerr<<"real only support complex value type"<<std::endl;
        return matrix;
    }
    auto output = (double *) malloc(matrix.getDataSize());
    memset(output, 0, (matrix.getDataSize() * sizeof(double)));
    cblas_dcopy(matrix.getDataSize(), matrix.getData(),COMPLEX_STRIDE , (double *) output, REAL_STRIDE);
    return Aurora::Matrix::New((double *) output, matrix.getDimSize(0), matrix.getDimSize(1), matrix.getDimSize(2));
}

Aurora::Matrix Aurora::imag(const Aurora::Matrix &matrix) {
    if (matrix.getValueType() == Normal) {
        std::cerr<<"imag only support complex value type"<<std::endl;
        return matrix;
    }
    auto output = malloc(matrix.getDataSize());
    memset(output, 0, (matrix.getDataSize() * sizeof(double)));
    cblas_dcopy(matrix.getDataSize(), matrix.getData()+1,COMPLEX_STRIDE , (double *) output, REAL_STRIDE);
    return Aurora::Matrix::New((double *) output, matrix.getDimSize(0), matrix.getDimSize(1), matrix.getDimSize(2));
}

Aurora::Matrix Aurora::ceil(const Aurora::Matrix &matrix) {
    auto output = malloc(matrix.getDataSize());
    //for real part
    vdCeilI(matrix.getDataSize(), matrix.getData(), SAME_STRIDE, output, SAME_STRIDE);
    if (matrix.getValueType() == Complex) {
        //for imag part
        vdCeilI(matrix.getDataSize(), matrix.getData() + 1, SAME_STRIDE, output + 1, SAME_STRIDE);
    }
    return Aurora::Matrix::New(output, matrix);
}

Aurora::Matrix Aurora::ceil(const Aurora::Matrix &&matrix) {
    //for real part
    vdCeilI(matrix.getDataSize(), matrix.getData(), SAME_STRIDE, matrix.getData(), SAME_STRIDE);
    if (matrix.getValueType() == Complex) {
        //for imag part
        vdCeilI(matrix.getDataSize(), matrix.getData() + 1, SAME_STRIDE, matrix.getData() + 1, SAME_STRIDE);
    }
    return matrix;
}

Aurora::Matrix Aurora::round(const Aurora::Matrix &matrix) {
    auto output = malloc(matrix.getDataSize());
    //for real part
    vdRoundI(matrix.getDataSize(), matrix.getData(), SAME_STRIDE, output, SAME_STRIDE);
    if (matrix.getValueType() == Complex) {
        //for imag part
        vdRoundI(matrix.getDataSize(), matrix.getData() + 1, SAME_STRIDE, output + 1, SAME_STRIDE);
    }
    return Aurora::Matrix::New(output, matrix);
}

Aurora::Matrix Aurora::round(const Aurora::Matrix &&matrix) {
    //for real part
    vdRoundI(matrix.getDataSize(), matrix.getData(), SAME_STRIDE, matrix.getData(), SAME_STRIDE);
    if (matrix.getValueType() == Complex) {
        //for imag part
        vdRoundI(matrix.getDataSize(), matrix.getData() + 1, SAME_STRIDE, matrix.getData() + 1, SAME_STRIDE);
    }
    return matrix;
}

Aurora::Matrix Aurora::sqrt(const Aurora::Matrix& matrix) {

    if (matrix.getValueType() != Complex) {
        auto output = malloc(matrix.getDataSize());
        vdSqrtI(matrix.getDataSize(), matrix.getData(), SAME_STRIDE, output, SAME_STRIDE);
        return Aurora::Matrix::New(output, matrix);
    }
    std::cerr<<"sqrt not support complex"<<std::endl;
    return Aurora::Matrix();
}

Aurora::Matrix Aurora::sqrt(Aurora::Matrix&& matrix) {
    if (matrix.getValueType() != Complex) {
        vdSqrtI(matrix.getDataSize(), matrix.getData(), SAME_STRIDE, matrix.getData(), SAME_STRIDE);
        return matrix;
    }
    std::cerr<<"sqrt not support complex"<<std::endl;
    return Aurora::Matrix();
}

Aurora::Matrix Aurora::abs(const Aurora::Matrix &matrix) {
    auto output = malloc(matrix.getDataSize());
    if (matrix.getValueType()==Normal){
        vdAbsI(matrix.getDataSize(), matrix.getData(), SAME_STRIDE, output, SAME_STRIDE);
    }
    else{
        vzAbsI(matrix.getDataSize(), (std::complex<double> *)matrix.getData(), SAME_STRIDE,output, SAME_STRIDE);
    }
    return Aurora::Matrix::New(output, matrix.getDimSize(0), matrix.getDimSize(1), matrix.getDimSize(2));
}

Aurora::Matrix Aurora::abs(Aurora::Matrix&& matrix) {
    if (matrix.getValueType()==Normal){
        vdAbsI(matrix.getDataSize(), matrix.getData(), SAME_STRIDE, matrix.getData(), SAME_STRIDE);
        return matrix;
    }
    //TODO：考虑尝试是不是使用realloc缩短已分配的内存的方式重用matrix
    else{
        auto output = malloc(matrix.getDataSize());
        vzAbsI(matrix.getDataSize(), (std::complex<double> *)matrix.getData(), SAME_STRIDE,output, SAME_STRIDE);
        return Aurora::Matrix::New(output, matrix.getDimSize(0), matrix.getDimSize(1), matrix.getDimSize(2));
    }

}

Aurora::Matrix Aurora::sign(const Aurora::Matrix &matrix) {
    if (matrix.getValueType()==Normal){
        auto ret = matrix.deepCopy();
        Eigen::Map<Eigen::VectorXd> retV(ret.getData(),ret.getDataSize());
        retV = retV.array().sign();
        return ret;
    }
    else{
        //sign(x) = x./abs(x)，前提是 x 为复数。
        auto output = malloc(matrix.getDataSize(),true);
        Matrix absMatrix = abs(matrix);
        vdDivI(matrix.getDataSize(), matrix.getData(),COMPLEX_STRIDE,
                absMatrix.getData(), REAL_STRIDE,output,COMPLEX_STRIDE);
        vdDivI(matrix.getDataSize(), matrix.getData()+1,COMPLEX_STRIDE,
               absMatrix.getData(), REAL_STRIDE,output+1,COMPLEX_STRIDE);
        return Aurora::Matrix::New(output, matrix);
    }
}

Aurora::Matrix Aurora::sign(Aurora::Matrix&& matrix) {
    if (matrix.getValueType()==Normal){
        Eigen::Map<Eigen::VectorXd> retV(matrix.getData(),matrix.getDataSize());
        retV = retV.array().sign();
        return matrix;
    }
    else{
        //sign(x) = x./abs(x)，前提是 x 为复数。
        Matrix absMatrix = abs(matrix);
        vdDivI(matrix.getDataSize(), matrix.getData(),COMPLEX_STRIDE,
               absMatrix.getData(), REAL_STRIDE,matrix.getData(),COMPLEX_STRIDE);
        vdDivI(matrix.getDataSize(), matrix.getData()+1,COMPLEX_STRIDE,
               absMatrix.getData(), REAL_STRIDE,matrix.getData()+1,COMPLEX_STRIDE);
        return matrix;
    }
}

Matrix Aurora::interp1(const Matrix& aX, const Matrix& aV, const Matrix& aX1, InterpnMethod aMethod)
{
    const int nx = aX.getDimSize(0);
    const int ny = 1;
    int nx1 = aX1.getDimSize(0);
    std::shared_ptr<double> resultData = std::shared_ptr<double>(Aurora::malloc(nx1), Aurora::free);
    std::vector<int> resultInfo = {nx1};
    Aurora::Matrix result(resultData, resultInfo);
    DFTaskPtr task ;
    int status = dfdNewTask1D(&task, nx, aX.getData(), DF_NO_HINT, ny, aV.getData(), DF_NO_HINT);
    if (status != DF_STATUS_OK)
    {
        return Matrix();
    }
    MKL_INT sorder;
    MKL_INT stype;
    if (aMethod == InterpnMethod::Spline)
    {
        sorder = DF_PP_CUBIC;
        stype = DF_PP_BESSEL;
    }
    else
    {
        sorder = DF_PP_LINEAR;
        stype = DF_PP_BESSEL;
    }
    double* scoeffs = Aurora::malloc(ny * (nx-1) * sorder);
     status = dfdEditPPSpline1D(task, sorder,DF_PP_NATURAL , DF_BC_NOT_A_KNOT, 0, DF_NO_IC, 0, scoeffs, DF_NO_HINT);
    if (status != DF_STATUS_OK)
    {
        return Matrix();
    }
    status = dfdConstruct1D( task, DF_PP_SPLINE, DF_METHOD_STD );
    if (status != DF_STATUS_OK)
    {
        return Matrix();
    }

    int dorder = 1;
    status = dfdInterpolate1D(task, DF_INTERP, DF_METHOD_PP, nx1, aX1.getData(), DF_NO_HINT, 1, &dorder,
                              DF_NO_APRIORI_INFO, resultData.get(), DF_MATRIX_STORAGE_ROWS, nullptr);

    status = dfDeleteTask(&task);

    Aurora::free(scoeffs);
    return result;
}

Matrix Aurora::repmat(const Matrix& aMatrix,int aRowTimes, int aColumnTimes)
{
    if(aRowTimes < 1 || aColumnTimes < 1 || aMatrix.getDims() > 2 || aMatrix.isNull())
    {
        return Matrix();
    }
    int complexStep = aMatrix.getValueType();
    int originalDataSize = aMatrix.getDataSize() * complexStep;
    double* resultData = Aurora::malloc(originalDataSize * aRowTimes * aColumnTimes);
    int row = aMatrix.getDimSize(0);
    int column = aMatrix.getDimSize(1);
    double* originalData = aMatrix.getData();
    double* resultDataTemp = resultData;
    for(int i=0; i<column; ++i)
    {
        for(int j=1; j<=aRowTimes; ++j)
        {
            cblas_dcopy(row*complexStep,originalData, 1, resultDataTemp, 1);
            resultDataTemp += row*complexStep;
        }
        originalData += row*complexStep;
    }

    resultDataTemp = resultData;
    int step = originalDataSize * aRowTimes;
    for(int i=1; i<aColumnTimes; ++i)
    {
        cblas_dcopy(step, resultData, 1, resultData + i*step, 1);
    }

    std::vector<int> resultInfo;
    resultInfo.push_back(aRowTimes * row);
    column = aColumnTimes*column;
    if (column > 1)
    {
        resultInfo.push_back(column);
    }

    return Matrix(std::shared_ptr<double>(resultData, Aurora::free),resultInfo, aMatrix.getValueType());
}

Matrix Aurora::repmat(const Matrix& aMatrix,int aRowTimes, int aColumnTimes, int aSliceTimes)
{
    if(aRowTimes < 1 || aColumnTimes < 1 || aSliceTimes < 1 || aMatrix.getDims() > 2 || aMatrix.isNull())
    {
        return Matrix();
    }

    int complexStep = aMatrix.getValueType();
    Matrix resultTemp = Aurora::repmat(aMatrix, aRowTimes, aColumnTimes);
    int resultTempDataSize = resultTemp.getDataSize() * complexStep;
    double* resultData = Aurora::malloc(resultTempDataSize * aSliceTimes);
    std::copy(resultTemp.getData(), resultTemp.getData() + resultTempDataSize, resultData);
    for(int i=1; i<aSliceTimes; ++i)
    {
        cblas_dcopy(resultTempDataSize, resultData, 1, resultData + i*resultTempDataSize, 1);
    }
    std::vector<int> resultInfo;
    int row = resultTemp.getDimSize(0);
    int column = resultTemp.getDimSize(1);
    resultInfo.push_back(row);
    if (column > 1 || aSliceTimes > 1)
    {
        resultInfo.push_back(column);
    }
    if (aSliceTimes > 1)
    {
        resultInfo.push_back(aSliceTimes);
    }

    return Matrix(std::shared_ptr<double>(resultData, Aurora::free), resultInfo, aMatrix.getValueType());
}


Matrix Aurora::polyval(const Matrix &aP, const Matrix &aX) {
    auto result = malloc(aX.getDataSize());
    auto powArg = new double[aP.getDataSize()];
    for (int j = aP.getDataSize(), i = 0; j > 0; --j, ++i) {
        powArg[i] = (double) (j - 1);
    }
    auto temp = new double[aP.getDataSize()];
    for (int i = 0; i < aX.getDataSize(); ++i) {
        vdPowI(aP.getDataSize(), aX.getData() + i, 0, powArg, 1, temp, 1);
        vdMul(aP.getDataSize(), aP.getData(), temp, temp);
        Eigen::Map<Eigen::VectorXd> vd(temp,aP.getDataSize());
        result[i] = vd.array().sum();
    }
    delete[] powArg;
    delete[] temp;

    return Matrix::New(result,aX);
}

Matrix Aurora::log(const Matrix& aMatrix, int aBaseNum)
{
    size_t size = aMatrix.getDataSize();
    double* data = Aurora::malloc(size);
    vdLn(size, aMatrix.getData(), data);
    if(aBaseNum != -1)
    {
        double baseNum = aBaseNum;
        double temp;
        vdLn(1, &baseNum, &temp);
        for (size_t i = 0; i < size; i++)
        {
            data[i] /= temp;
        }
    }
    return Matrix::New(data, aMatrix);
}

Matrix Aurora::exp(const Matrix& aMatrix)
{
    size_t size = aMatrix.getDataSize();
    double* data;
    if (aMatrix.isComplex())
    {
        data = Aurora::malloc(size, true);
        vzExp(size, (MKL_Complex16*)aMatrix.getData(), (MKL_Complex16*)data);
    }
    else
    {
        data = Aurora::malloc(size);
        vdExp(size, aMatrix.getData(), data);
    }
    return Matrix::New(data, aMatrix);
}

Matrix Aurora::mod(const Matrix& aMatrix, double aValue)
{
    if(aMatrix.isComplex() || aMatrix.isNull())
    {
        return Matrix();
    }

    size_t size = aMatrix.getDataSize();
    double* matrixData = aMatrix.getData();
    double* resultData = Aurora::malloc(size);
    for(size_t i=0; i<size; ++i)
    {
        resultData[i] = fmod(matrixData[i], aValue);
    }

    return Matrix::New(resultData, aMatrix);
}

Matrix Aurora::acos(const Matrix& aMatrix)
{
    if(aMatrix.isComplex() || aMatrix.isNull())
    {
        return Matrix();
    }

    size_t size = aMatrix.getDataSize();
    double* matrixData = aMatrix.getData();
    double* resultData = Aurora::malloc(size);
    vdAcos(size, matrixData, resultData);
    return Matrix::New(resultData, aMatrix);
}

Matrix Aurora::acosd(const Matrix& aMatrix)
{
    if(aMatrix.isComplex() || aMatrix.isNull())
    {
        return Matrix();
    }

    size_t size = aMatrix.getDataSize();
    double* matrixData = aMatrix.getData();
    double* resultData = Aurora::malloc(size);
    vdAcos(size, matrixData, resultData);
    for(size_t i=0; i<size; ++i)
    {
        resultData[i] = resultData[i] * 180 / PI;
    }
    return Matrix::New(resultData, aMatrix);
}

Matrix Aurora::conj(const Matrix& aMatrix)
{
    if(!aMatrix.isComplex())
    {
        return Matrix::copyFromRawData(aMatrix.getData(),aMatrix.getDimSize(0),aMatrix.getDimSize(1),aMatrix.getDimSize(2));
    }
    size_t size = aMatrix.getDataSize();
    double* data = malloc(size,true);
    vzConj(size,(MKL_Complex16*)aMatrix.getData(), (MKL_Complex16*)data);
    return Matrix::New(data, aMatrix);
}

double Aurora::norm(const Matrix& aMatrix, NormMethod aNormMethod)
{
    if(aMatrix.isNull())
    {
        return NAN;
    }

    size_t size = aMatrix.getDataSize();
    if(aMatrix.isComplex())
    {
        size*=2;
    }
    int column = aMatrix.getDimSize(1);
    int row = aMatrix.getDimSize(0);
    if (aNormMethod == NormMethod::Norm1)
    {
        double value = 0;
        for(int i=0; i<column; ++i)
        {
            double temp = Aurora::sum(abs(aMatrix($,i,$).toMatrix())).getData()[0];
            if(temp > value)
            {
                value = temp;
            }
        }
        return value;
    }
    else if(aNormMethod == NormMethod::NormF)
    {
        return cblas_dnrm2(size, aMatrix.getData(), 1);
    }
    else if(aNormMethod == NormMethod::Norm2)
    {
        //columns > 1
        if(aMatrix.getDimSize(1) > 1)
        {
            if(aMatrix.isComplex())
            {
                Eigen::Map<Eigen::MatrixXcd> eMatrix((MKL_Complex16*)aMatrix.getData(), row, column);
                Eigen::JacobiSVD<Eigen::MatrixXcd> svd(eMatrix, Eigen::ComputeThinU | Eigen::ComputeThinV);
                return svd.singularValues()(0);
            }
            else
            {
                Eigen::Map<Eigen::MatrixXd> eMatrix(aMatrix.getData(), row, column);
                Eigen::JacobiSVD<Eigen::MatrixXd> svd(eMatrix, Eigen::ComputeThinU | Eigen::ComputeThinV);
                return svd.singularValues()(0);
            }
        }
        else
        {
            return cblas_dnrm2(size, aMatrix.getData(), 1);
        }
    }

    return 0;
}

Matrix Aurora::transpose(const Matrix& aMatrix)
{
    //not surpport for 3 dims.
    if(aMatrix.isNull() || aMatrix.getDimSize(2) > 1)
    {
        return Matrix();
    }
    size_t size = aMatrix.getDataSize();
    int row = aMatrix.getDimSize(0);
    int col = aMatrix.getDimSize(1);
    double* resultData;
    double* data = aMatrix.getData();
    if(aMatrix.isComplex())
    {
        resultData = Aurora::malloc(size, true);
        mkl_zomatcopy('C', 'T',row ,col, 1.0, (MKL_Complex16*)data, row, (MKL_Complex16*)resultData, col);
    }
    else
    {
        resultData = Aurora::malloc(size);
        mkl_domatcopy('C', 'T',row ,col, 1.0, data, row, resultData, col);
    }

    return Matrix::New(resultData,col,row,1,aMatrix.getValueType());
}

Matrix Aurora::horzcat(const Matrix& aMatrix1, const Matrix& aMatrix2)
{
    if(aMatrix1.isNull() || aMatrix2.isNull() || aMatrix1.getDims() !=2 || aMatrix2.getDims() !=2 ||
       aMatrix1.getDimSize(0) != aMatrix2.getDimSize(0) || aMatrix1.getValueType() != aMatrix2.getValueType())
    {
        return Matrix();
    }
    int column1 = aMatrix1.getDimSize(1);
    int column2 = aMatrix2.getDimSize(1);
    int row = aMatrix1.getDimSize(0);
    size_t size1= aMatrix1.getDataSize();
    size_t size2= aMatrix2.getDataSize();
    double* resultData = Aurora::malloc(size1 + size2,aMatrix1.getValueType());
    cblas_dcopy(size1, aMatrix1.getData(), 1, resultData, 1);
    cblas_dcopy(size2, aMatrix2.getData(), 1, resultData + size1, 1);

    return Matrix::New(resultData, row, column1+column2, 1, aMatrix1.getValueType());
}

Matrix Aurora::vecnorm(const Matrix& aMatrix, NormMethod aNormMethod, int aDim)
{
    //only surpport aDim = 1 for now.
    if(aDim != 1 || aNormMethod == NormMethod::NormF || aMatrix.isNull())
    {
        return Matrix();
    }
    int column = aMatrix.getDimSize(1);
    double* resultData = Aurora::malloc(column);
    for(int i=0; i<column; ++i)
    {
        resultData[i] = norm(aMatrix($,i,$).toMatrix(), aNormMethod);
    }

    return Matrix::New(resultData,column);
}

Matrix Aurora::linspace(double aStart, double aEnd, int aNum)
{
    double step = (aEnd - aStart) / (aNum - 1);
    double* resultData = Aurora::malloc(aNum);
    for (int i = 0; i < aNum; i++)
    {
        resultData[i] = aStart + step * i;
    }

    return Matrix::New(resultData,aNum);
}

Matrix Aurora::auroraUnion(const Matrix& aMatrix1, const Matrix& aMatrix2)
{
    if(aMatrix1.isNull() || aMatrix2.isNull() || aMatrix1.isComplex() || aMatrix2.isComplex())
    {
        return Matrix();
    }

    size_t size1= aMatrix1.getDataSize();
    size_t size2= aMatrix2.getDataSize();
    double* resultData = Aurora::malloc(size1 + size2);
    cblas_dcopy(size1, aMatrix1.getData(), 1, resultData, 1);
    cblas_dcopy(size2, aMatrix2.getData(), 1, resultData + size1, 1);
    std::vector<double> vector(resultData,  resultData + size1 + size2);
    Aurora::free(resultData);
    std::sort(vector.begin(), vector.end());
    auto last = std::unique(vector.begin(), vector.end());
    vector.erase(last, vector.end());

    return Matrix::copyFromRawData(vector.data(),vector.size());
}

Matrix Aurora::intersect(const Matrix& aMatrix1, const Matrix& aMatrix2)
{
    if(aMatrix1.isNull() || aMatrix2.isNull() || aMatrix1.isComplex() || aMatrix2.isComplex())
    {
        return Matrix();
    }

    size_t size1= aMatrix1.getDataSize();
    size_t size2= aMatrix2.getDataSize();
    std::vector<double> vector1(aMatrix1.getData(),  aMatrix1.getData() + size1);
    std::vector<double> vector2(aMatrix2.getData(),  aMatrix2.getData() + size2);
    std::sort(vector1.begin(), vector1.end());
    std::sort(vector2.begin(), vector2.end());

    std::vector<double> intersection;
    std::set_intersection(vector1.begin(), vector1.end(),
                          vector2.begin(), vector2.end(),
                          std::back_inserter(intersection));

    return Matrix::copyFromRawData(intersection.data(), intersection.size());
}

Matrix Aurora::intersect(const Matrix& aMatrix1, const Matrix& aMatrix2, Matrix& aIa)
{
    if(aMatrix1.isNull() || aMatrix2.isNull() || aMatrix1.isComplex() || aMatrix2.isComplex())
    {
        return Matrix();
    }

    Matrix result = intersect(aMatrix1,aMatrix2);

    size_t size = result.getDataSize();
    double* iaResult = Aurora::malloc(size);
    for(size_t i=0; i<size; ++i)
    {
        for(size_t j=0; j<aMatrix1.getDataSize(); ++j)
        {
            if(aMatrix1.getData()[j] == result.getData()[i])
            {
                iaResult[i] = j + 1;
                break;
            }
        }
    }

    aIa = Matrix::New(iaResult,size);
    return result;
}

Matrix Aurora::reshape(const Matrix& aMatrix, int aRows, int aColumns, int aSlices)
{
    if(aMatrix.isNull() || (aMatrix.getDataSize() != aRows * aColumns * aSlices))
    {
        return Matrix();
    }
    return Matrix::copyFromRawData(aMatrix.getData(),aRows,aColumns,aSlices);
}
void Aurora::nantoval(Matrix& aMatrix, double val2) {
    Eigen::Map<Eigen::VectorXd> srcV(aMatrix.getData(),aMatrix.getDataSize());
    srcV = srcV.array().isNaN().select(val2,srcV);
}

void Aurora::padding(Matrix &aMatrix, int aIndex, double aValue)
{
    if(aMatrix.isNull() || !aMatrix.isVector())
    {
        std::cerr<<"padding only support vector"<<std::endl;
        return;
    }
    if (aMatrix.getDataSize()>aIndex){
        aMatrix.getData()[aIndex] = aValue;
        return;
    }
    int size = (aIndex+1);
    double* newData = malloc(size,aMatrix.isComplex());
    cblas_dcopy(aMatrix.getDataSize()*aMatrix.getValueType(),
        aMatrix.getData(),1,newData,1);
    cblas_dcopy((size-aMatrix.getDataSize())*aMatrix.getValueType(),
        &aValue,0,newData+aMatrix.getDataSize()*aMatrix.getValueType(),1);
    aMatrix = Matrix::New(newData,size,1,1,aMatrix.getValueType());
}

Matrix Aurora::convertfp16tofloat(const Matrix& aMatrix)
{

    auto input = aMatrix.getData();
    //uint16变换为float(32位)输出大小翻倍
    auto output = malloc(aMatrix.getDataSize()*4);
    size_t rows = aMatrix.getDataSize()*sizeof(double)/sizeof(short);
    size_t total_count = aMatrix.getDataSize();
    
    // #pragma omp parallel for
    for (size_t i = 0; i < total_count; i+=8) {
        //循环展开以避免过度的线程调用
        if (i  < total_count)::convertValue2((short*)(input+i), output + (i) * 4);
        if (i+1  < total_count)::convertValue2((short*)(input+i+1), output + (i+1) * 4);
        if (i+2  < total_count)::convertValue2((short*)(input+i+2), output + (i+2) * 4);
        if (i+3  < total_count)::convertValue2((short*)(input+i+3), output + (i+3) * 4);
        if (i+4  < total_count)::convertValue2((short*)(input+i+4), output + (i+4) * 4);
        if (i+5  < total_count)::convertValue2((short*)(input+i+5), output + (i+5) * 4);
        if (i+6  < total_count)::convertValue2((short*)(input+i+6), output + (i+6) * 4);
        if (i+7  < total_count)::convertValue2((short*)(input+i+7), output + (i+7) * 4);
    }
    return Matrix::New(output,aMatrix.getDimSize(0),aMatrix.getDimSize(1),aMatrix.getDimSize(2));
}