float sigmoid(float x)
{
    return (1 / (1 + exp(-x)));
}

float sigmoid_dy_dz(float x)
{
    return (x * (1.0 - x));
}

float tanh_dy_dz(float x)
{
    return (1.0 - x*x);
}

//對每一行進行softmax
void softmax(float *x, int row, int column)
{
    for (int j = 0; j < row; ++j)
    {
        float max
 
 = 0.0;
        float sum = 0.0;
        for (int k = 0; k < column; ++k)
            if (max < x[k + j*column])
                max = x[k + j*column];
        for (int k = 0; k < column; ++k)
        {
            x[k + j*column] = exp(x[k + j*column] - max);    // prevent data overflow
            sum += x[k + j*column];
        }
        for
 
 (int k = 0; k < column; ++k) x[k + j*column] /= sum;
    }
}   //row*column