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    #include "misc.h"
    #include "cublas_wrapper.h"
    #include <iostream>
    #include <iomanip>
    #include <stdio.h>
    
    
    /*
    
     *      preconditioner.h
     *
     *      This file contains different preconditioner implementations. They are all implementations of the abstract
    
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     *      type Preconditioner. It is the users responsibility to check wether a preconditioner solves the 2D or
    
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     *      the 3D problem.
     *
     *      @author Simon Schoelly
     *
     */
    
    /*
     *      Abstract preconditioner class. Provides two methods that have to be implemented:
     *      init: initialzes the preconditioner before the first run
     *      run: solves M\b
     *
     *      @param FT Field Type - Either float or double
    
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     *
    
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     */
    template<class FT>
    class Preconditioner {
    public:
            virtual void init (int const m, FT const alpha, cublasHandle_t cublas_handle, cusparseHandle_t cusparse_handle) = 0;
            virtual void run  (FT const * const b, FT * const x) = 0;
            virtual void run2 (FT const * const b, FT * const x) = 0;
            virtual void run3 (FT const * const b, FT * const x) = 0;
            virtual void run_t(FT const * const b, FT * const x) = 0;
    
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    };
    
    
    /*
     *      Kernel that performs the thomas algorithm. Used for ThomasPreconditioner and SpikeThomasPreconditioner.
     *
     *      @param FT Field Type - Either float or double
     *      @param m grid size i.e. M is of size mxm
     *      @param m >= block_size >= 1 the size of a block that is inverted. For the ThomasPreconditioner this is of size m
     *      @param num_blocks the number of blocks that we invert
     *      @param alpha > 0.
     *      @param beta = sqrt(alpha)
     *      @param c_prime coefficients for the thomas algorithm that where precualculated
     *      @param b != NULL input vector of size m*num_blocks*block_size
     *      @param x != NULL output vector of size m*num_blocks*block_size
     *
    
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     *      @return M\X
     *
    
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     */
    template<class FT>
    __global__ void thomas_kernel(int const m, int block_size, int num_blocks, FT const alpha, FT const beta, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x) {
    
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    	int tid = blockIdx.x * blockDim.x + threadIdx.x;
    
    	if (tid >= m*num_blocks) {
    	  return;
    	}
    
            int start = (tid / m) * block_size * m + (tid % m);
    
            FT work_buffer_reg = b[start] * beta / (FT(2) + alpha);
    
            x[start] = work_buffer_reg;
            for (int i = 1; i < block_size; ++i) {
            	int j = start + i*m;
                work_buffer_reg  = (b[j] * beta + work_buffer_reg) / (FT(2) + alpha + dev_c_prime[i-1]);
    			x[j] = work_buffer_reg;
            }
    
            for (int i = block_size-2; i >= 0; --i) {
            	int j = start + i*m;
            	work_buffer_reg = x[j] - dev_c_prime[i] * work_buffer_reg;
                x[j] = work_buffer_reg;
            }
    }
    
    
    template<class FT>
    __global__ void thomas_kernel_trans(int const m, int block_size, int num_blocks, FT const alpha, FT const beta,
    		FT const * const __restrict__ dev_c_prime,
    		FT const * const __restrict__ b,
    		FT       * const __restrict__ x) {
    
    	// dev_c_prime - precalculated factors
    	// b - input
    	// x - output
    
    
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    	__shared__ FT sh_x[THREADS+1][THREADS];
    
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    	int tid_l = threadIdx.x;
    	int bid   =  blockIdx.x;
    	//int tid   =  blockIdx.x * blockDim.x + threadIdx.x;
    	FT  work_buffer_reg = 0.0;
    
    	//if (bid != 0) return;
    
    	// read first patch of input data
    	#pragma unroll
    	for (int i = 0; i < THREADS; i++) {
    		//sh_b[tid_l][i] = b[ tid_l + m*(i+bid*THREADS) + 0*THREADS ];
    		sh_x[tid_l][i] = b[ tid_l + m*(i+bid*THREADS) + 0*THREADS ];
    	}
    
    
    	for (int l = 0; l < M/THREADS; l++) {
    		#pragma unroll
    		for (int i = 0; i < THREADS; ++i) {
    			//FT b_l     = sh_b[i][tid_l];
    			FT b_l     = sh_x[i][tid_l];
    			FT c_prime = dev_c_prime[l*THREADS+i-1];
    			work_buffer_reg  = (b_l * beta + work_buffer_reg) / (FT(2) + alpha + c_prime);
    			sh_x[i][tid_l] = work_buffer_reg;
    //			if (tid_l == 0) printf(" x = %.10f - %.10f - %.10f - %.10f \n",sh_b	[i][tid_l],sh_b[i][tid_l+1],sh_x[i][tid_l],sh_x[i][tid_l+1]);
    
    		}
    
    		// save temp res and get new input data
    		if ( l < (M/THREADS - 1) ) {
    			#pragma unroll
    			for (int i = 0; i < THREADS; i++) {
    								 x[ tid_l + m*(i+bid*THREADS) +  l   *THREADS ] = sh_x[tid_l][i];
    				sh_x[tid_l][i] = b[ tid_l + m*(i+bid*THREADS) + (l+1)*THREADS ];
    				//sh_b[tid_l][i] = b[ tid_l + m*(i+bid*THREADS) + (l+1)*THREADS ];
    			}
    		}
    	}
    
        // backward
    //	if (tid_l == 0) printf("\n");
    
    	int level = M/THREADS - 1;
    	#pragma unroll
    	for (int i = THREADS-2; i >= 0; --i) {
    		FT x_l = sh_x[i][tid_l];
    		work_buffer_reg = x_l - dev_c_prime[level*THREADS+i] * work_buffer_reg;
    		sh_x[i][tid_l] = work_buffer_reg;
    //		if (tid_l == 0) printf(" x = %.10f - %.10f\n",sh_x[i][tid_l],sh_x[i][tid_l+1]);
    
    	}
    
    	for (int l = level; l >= 1 ; l--) {
    		// save temp res and get new input data
    		#pragma unroll
    		for (int i = 0; i < THREADS; i++) {
    							 x[ tid_l + m*(i+bid*THREADS) +  l   *THREADS ] = sh_x[tid_l][i];
    			sh_x[tid_l][i] = x[ tid_l + m*(i+bid*THREADS) + (l-1)*THREADS ];
    		}
    
    		#pragma unroll
    		for (int i = THREADS-1; i >= 0; --i) {
    			FT x_l = sh_x[i][tid_l];
    			work_buffer_reg = x_l - dev_c_prime[(l-1)*THREADS+i] * work_buffer_reg;
    			sh_x[i][tid_l] = work_buffer_reg;
    //			if (tid_l == 0) printf(" x = %.10f - %.10f\n",sh_x[i][tid_l],sh_x[i][tid_l+1]);
    		}
    	}
    
    	// write last patch of output data
    	#pragma unroll
    	for (int i = 0; i < THREADS; i++) {
    		x[ tid_l + m*(i+bid*THREADS) + 0*THREADS ] = sh_x[tid_l][i];
    	}
    
    
    }
    
    
    
    
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    // Thomas algorithm with storing intermediate results in shared memory - saves one global memory read and global memory write into x - compare with previous Thomas kernel
    
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    template<class FT>
    __global__ void thomas_kernel2(int const m, int block_size, int num_blocks, FT const alpha, FT const beta, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x) {
    
    	extern __shared__ FT xs[];
    
            int tid   = blockIdx.x * blockDim.x + threadIdx.x;
    
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    	int tid_l = threadIdx.x;
    
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            if (tid >= m*num_blocks) {
              return;
            }
    
            int start = (tid / m) * block_size * m + (tid % m);
    
            FT work_buffer_reg = b[start] * beta / (FT(2) + alpha);
    
            xs[tid_l * block_size + 0 + tid_l] = work_buffer_reg;
            for (int i = 1; i < block_size; ++i) {
                    int j = start + i*m;
                    work_buffer_reg  = (b[j] * beta + work_buffer_reg) / (FT(2) + alpha + dev_c_prime[i-1]);
                    xs[ tid_l * block_size + i + tid_l ] = work_buffer_reg;
            }
    
    
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            FT x_reg = work_buffer_reg;
    
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            x[start + (block_size-1)*m] = x_reg;
            for (int i = block_size-2; i >= 0; --i) {
                    int j = start + i*m;
                    x_reg = xs[tid_l * block_size + i + tid_l] - dev_c_prime[i] * x_reg;
                    x[j] = x_reg;
            }
    }
    
    
    
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    // Thomas algorithm that calculates cprime on the fly - eliminates reading of the cprime from global memory - SHARED MEMORY will become the bottleneck - reduces amount of blocks that can sit on one Streaming Multiprocessor
    
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    template<class FT>
    __global__ void thomas_kernel3(int const m, int block_size, int num_blocks, FT const alpha, FT const beta, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x) {
    
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    	int tid   = blockIdx.x * blockDim.x + threadIdx.x;
            int tid_l = threadIdx.x;
    
    	if (tid >= m*num_blocks) {
              return;
            }
    
    	//__shared__ FT d [32][33];
    	//__shared__ FT xs[32][34];
    
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    	extern __shared__ FT shared_pool[];
    
    	FT *shared_pool_p = shared_pool;
    
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    	FT *d = &shared_pool_p[ 0 ];
    	FT *xs= &shared_pool_p[ blockDim.x * (m+1) ]; // shared memory size: 2 * threads_per_block * (m+1) * sizeof(FT)
    
    	// tridiag(gamma,delta,gamma) x = b
    
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    	FT delta = beta + (FT(2) / beta);  // value on diag
            FT gama  = FT(-1) / beta;
    	FT gama2 = gama*gama;
    
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    	FT d_reg;
    
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    	FT x_reg;
    
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            d_reg     = FT(1) / delta;
    
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            d[tid_l * block_size + 0 + tid_l] = d_reg;  //d[tid][0] = d_reg;
    
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            int start = (tid / m) * block_size * m + (tid % m);
    	x_reg = b[start];
    
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    	xs[tid_l * block_size + 0 + tid_l] = x_reg; //xs[tid][0] = x_reg;
    
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    	for (int i = 1; i < block_size; ++i) {
    
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    		int j = start + i*m;
    
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    		x_reg     = b[j] - gama * x_reg * d_reg;
    
    
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    		d_reg     = FT(1) / ( delta - gama2 * d_reg ); // d_reg = d[tid][i-1]
    
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    	        d[tid_l * block_size + i + tid_l] = d_reg; //d[tid][i] = d_reg;
    
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    		//x_reg     = b[j] - gama * x_reg * d_reg;
    		xs[tid_l * block_size + i + tid_l] = x_reg; //xs[tid][i] = x_reg;
    
    
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    	}
    
    	x_reg = x_reg * d_reg;
    	x[start + (block_size - 1) * m] = x_reg;
    
    	for (int i = block_size-2; i >= 0; --i) {
    		int j = start + i*m;
    
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    		//x_reg = (xs[tid][i] - gama * x_reg) * d[tid][i];
    
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    		x_reg = (xs[tid_l * block_size + i + tid_l] - gama * x_reg) * d[tid_l * block_size + i + tid_l];
    		x[j]  = x_reg;
    
    
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    	}
    }
    
    
    /*
     *      Preconditioner for the 2D problem. Uses the thomas algorithm to invert M.
     *
     *      @param FT Field Type - Either float or double
    
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     *
    
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     */
    template<class FT>
    class ThomasPreconditioner : public Preconditioner<FT> {
    private:
            FT *c_prime;
            int m;
            FT alpha, beta;
            cublasHandle_t cublas_handle;
            FT *b_trans;
    
            bool USE_IMPLICIT_TRANSPOSE;
            int thomas_kernel_block_size;
    public:
            ThomasPreconditioner(bool useImplicitTranspose) {
            	this->USE_IMPLICIT_TRANSPOSE = useImplicitTranspose;
            }
    
            virtual void init(int const m, FT const alpha, cublasHandle_t cublas_handle, cusparseHandle_t cusparse_handle) {
                    this->m = m;
                    this->alpha = alpha;
                    beta = sqrt(alpha);
                    this-> cublas_handle = cublas_handle;
    
                    FT *host_c_prime = new FT[m];
    
                    host_c_prime[0] = FT(-1) / (alpha + FT(2));
                    for (int i = 1; i < m; ++i) {
                            host_c_prime[i] = FT(-1) / (host_c_prime[i-1] + FT(2) + alpha);
                    }
    
                    cudaMalloc((void **) &c_prime, m*sizeof(FT));
                    cudaMemcpy(c_prime, host_c_prime, m*sizeof(FT), cudaMemcpyHostToDevice);
    
                    delete[] host_c_prime;
    
                    cudaMalloc((void **) &b_trans, m*m*sizeof(FT));
    
                    int minGridSize;
    
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                    cudaOccupancyMaxPotentialBlockSize(&minGridSize, &thomas_kernel_block_size, thomas_kernel<FT>, 0, m);
    
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                    thomas_kernel_block_size /= 8;
            }
    
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            virtual void run(FT const * const b, FT * const x) {
    
            	if (!USE_IMPLICIT_TRANSPOSE) {
    
            		FT block_count = divide_and_round_up(m, thomas_kernel_block_size);
                    FT threads_per_block = thomas_kernel_block_size;
    
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                    cublas_transpose(cublas_handle, m, b, b_trans);
    
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                    FT *y_trans = x;
    
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                    thomas_kernel<FT><<<block_count, threads_per_block >>> (m, m, 1, alpha, beta, c_prime, b_trans, y_trans);
    
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                    FT *y = b_trans;
    
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                    cublas_transpose(cublas_handle, m, y_trans, y);
    
    
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                    thomas_kernel<FT><<<block_count, threads_per_block >>> (m, m, 1, alpha, beta, c_prime, y, x);
    
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                    //std::cout << "Tk 1 - cublas trans " << std::endl;
    
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            	} else {
    
            		FT block_count = divide_and_round_up(m, thomas_kernel_block_size);
                    FT threads_per_block = thomas_kernel_block_size;
    
                    thomas_kernel_trans<FT><<<M/THREADS, THREADS >>>             (m, m, 1, alpha, beta, c_prime, b, b_trans);
                    FT const * const b_trans_const = b_trans;
                    thomas_kernel      <FT><<<block_count, threads_per_block >>> (m, m, 1, alpha, beta, c_prime, b_trans_const, x);
                  //thomas_kernel      <FT><<<block_count, threads_per_block >>> (m, m, 1, alpha, beta, c_prime, b_trans, x);
    
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                    //std::cout << "Tk 1 - implicit trans " << std::endl;
    
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            	}
            }
    
            virtual void run_t(FT const * const b, FT * const x) {
            }
    
    
    
            virtual void run2(FT const * const b, FT * const x) {
    
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            }
    
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            virtual void run3(FT const * const b, FT * const x) {
            }
    
    
    
            ~ThomasPreconditioner() {
                    cudaFree(b_trans);
                    cudaFree(c_prime);
            }
    
    };
    
    
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    ///*
    // *      Kernel that performs the thomas algorithm for the 3D problem. Used for ThomasPreconditioner3
    // *
    // *      @param FT Field Type - Either float or double
    // *      @param m grid size i.e. M is of size mxm
    // *      @param n number of vectors that we invert simultanously. Usually has value m*m
    // *      @param alpha > 0.
    // *      @param alpha_23 = alpha^(2/3)
    // *      @param c_prime coefficients for the thomas algorithm that where precualculated
    // *      @param b != NULL input vector of size m*n
    // *      @param x != NULL output vector of size m*n
    // *
    // *      @return M\X
    // *
    // */
    //
    //template<class FT>
    //__global__ void thomas_kernel3D(int const m, int n, FT const alpha, FT const alpha_23, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x) {
    //
    //	int tid = blockIdx.x * blockDim.x + threadIdx.x;
    //
    //	if (tid >= n) {
    //	  return;
    //	}
    //
    //        int start = tid;
    //
    //
    //        FT work_buffer_reg = b[start] * alpha_23 / (FT(2) + alpha);
    //        x[start] = work_buffer_reg;
    //
    //        for (int i = 1; i < m; ++i) {
    //                int j = start + i*n;
    //                work_buffer_reg  = (b[j] * alpha_23 + work_buffer_reg) / (FT(2) + alpha + dev_c_prime[i-1]);
    //                x[j] = work_buffer_reg;
    //        }
    //
    //        FT x_reg = x[start + (m-1)*n];
    //        x[start + (m-1)*n] = x_reg;
    //
    //        for (int i = m-2; i >= 0; --i) {
    //                int j = start + i*n;
    //                x_reg = x[j] - dev_c_prime[i] * x_reg;
    //                x[j] = x_reg;
    //        }
    //}
    //
    //
    //template<class FT>
    //__global__ void thomas_kernel3D_X1(int const m, FT const alpha, FT const alpha_23, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x) {
    //
    //	int n = m*m;
    //	int tid = blockIdx.x * blockDim.x + threadIdx.x;
    //
    //	if (tid >= n) {
    //	  return;
    //	}
    //
    //        int start = tid;
    //
    //
    //        FT work_buffer_reg = b[start] * alpha_23 / (FT(2) + alpha);
    //        x[start] = work_buffer_reg;
    //
    //        for (int i = 1; i < m; ++i) {
    //                int j = start + i*n;
    //                work_buffer_reg  = (b[j] * alpha_23 + work_buffer_reg) / (FT(2) + alpha + dev_c_prime[i-1]);
    //                x[j] = work_buffer_reg;
    //        }
    //
    //        FT x_reg = x[start + (m-1)*n];
    //        x[start + (m-1)*n] = x_reg;
    //
    //        for (int i = m-2; i >= 0; --i) {
    //                int j = start + i*n;
    //                x_reg = x[j] - dev_c_prime[i] * x_reg;
    //                x[j] = x_reg;
    //        }
    //}
    //
    //
    //template<class FT>
    //__global__ void thomas_kernel3D_X2(int const m, FT const alpha, FT const alpha_23, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x) {
    //
    //	int n = m*m;
    //	int tid = blockIdx.x * blockDim.x + threadIdx.x;
    //
    //	if (tid >= n) {
    //	  return;
    //	}
    //
    //        int start = (n) * (tid/m) + (tid % m); // + (i * m)
    //
    //
    //        FT work_buffer_reg = b[start] * alpha_23 / (FT(2) + alpha);
    //        x[start] = work_buffer_reg;
    //
    //        for (int i = 1; i < m; ++i) {
    //                int j = start + i*m;
    //                work_buffer_reg  = (b[j] * alpha_23 + work_buffer_reg) / (FT(2) + alpha + dev_c_prime[i-1]);
    //                x[j] = work_buffer_reg;
    //        }
    //
    //        FT x_reg = x[start + (m-1)*m];
    //        x[start + (m-1)*m] = x_reg;
    //
    //        for (int i = m-2; i >= 0; --i) {
    //                int j = start + i*m;
    //                x_reg = x[j] - dev_c_prime[i] * x_reg;
    //                x[j] = x_reg;
    //        }
    //}
    //
    //
    //
    //template<class FT>
    //__global__ void thomas_kernel3D_XT(int const m, FT const alpha, FT const alpha_23, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x) {
    //
    //	//#define TILE_SIZE 2
    //	//TODO: Should be #define
    //	//int TILE_SIZE = blockDim.x;
    //
    //	__shared__ FT sh_b[TILE_SIZE][TILE_SIZE+1];
    //	__shared__ FT sh_x[TILE_SIZE][TILE_SIZE+1];
    //
    //	int TILES = m / TILE_SIZE;
    //
    //	int tid_l =  threadIdx.x;
    //	int bid   =  blockIdx.x;
    //	int tid   =  blockIdx.x * blockDim.x + threadIdx.x;
    //
    //	// Basis of an adress used to read dat from global memory to tiles in shared memory
    //	// - this is rused multiple times
    //	//int base_addr = tid_l + m*m*TILE_SIZE*(bid%TILE_SIZE) + (bid/TILE_SIZE)*m;
    //	int base_addr = tid_l +
    //					(tid / m) * m +
    //				    (m*m) * TILE_SIZE *  ( bid % (m / TILE_SIZE));
    //			//    + tile * TILE_SIZE
    //			//    + i*m*m
    //
    //    // **************************************************************************************************************
    //    // *** Forward substitution ************************************************************************************
    //
    //	// Read input data to fill the first tile in shared memoru
    //	#pragma unroll
    //	for (int i = 0; i < TILE_SIZE; i++) {
    //		int a = base_addr +  m*m*i;
    //		sh_b[tid_l][i] = b[a];
    //		//printf("tid = %d - SM a = [%d,%d] - g a = %d ; val = %f \n", tid, tid_l, i, a, b[ a ] );
    //	}
    //
    //	// Calculate first element of the forward substitution
    //    FT work_buffer_reg = sh_b[0][tid_l] * alpha_23 / (FT(2) + alpha);
    //    sh_x[0][tid_l] = work_buffer_reg;
    //    //printf("A tid = %d - work_buffer_reg = %f ; in_val = %f \n", tid, work_buffer_reg, sh_b[0][tid_l]);
    //
    //    // Calculate the rest of the forward substitution for the first tile
    //    #pragma unroll
    //    for (int i = 1; i < TILE_SIZE; ++i) {
    //        int ca = i - 1;
    //    	work_buffer_reg  = (sh_b[i][tid_l] * alpha_23 + work_buffer_reg) / (FT(2) + alpha + dev_c_prime[ca]);
    //        sh_x[i][tid_l] = work_buffer_reg;
    //        //printf("X tid = %d - work_buffer_reg = %f - prim a = %d \n", tid, work_buffer_reg, ca);
    //    }
    //
    //    // Save results of for the first tile to the global memory
    //	#pragma unroll
    //	for (int i = 0; i < TILE_SIZE; i++) {
    //		int a = base_addr +  m*m*i;
    //		x[a] = sh_x[tid_l][i];
    //		//printf("tid = %d - SM a = [%d,%d] - g a = %d \n", tid, tid_l, i, a );
    //	}
    //
    //	// Processing of the remaining tiles
    //    for (int tile = 1; tile < TILES; tile++) {
    //
    //    	// Read data from global memory to tile in shared memory
    //    	#pragma unroll
    //		for (int i = 0; i < TILE_SIZE; i++) {
    //			int a = base_addr + m*m*i + (tile * TILE_SIZE);
    //			sh_b[tid_l][i] = b[a];
    //			//printf("tid = %d - SM a = [%d,%d] - g a = %d \n", tid, tid_l, i, a );
    //		}
    //
    //		// Calculate forward substitution for the current tile
    //    	#pragma unroll
    //		for (int i = 0; i < TILE_SIZE; i++) {
    //			int ca = (tile * TILE_SIZE) + i - 1;
    //            work_buffer_reg  = (sh_b[i][tid_l] * alpha_23 + work_buffer_reg) / (FT(2) + alpha + dev_c_prime[ca]);
    //            sh_x[i][tid_l] = work_buffer_reg;
    //            //printf("Z tid = %d - work_buffer_reg = %f - prim a = %d \n", tid, work_buffer_reg, ca);
    //		}
    //
    //		// Save the results of the forward substitution of the current tile to a global memory - this does not have to be done fot the last tile
    //		#pragma unroll
    //		for (int i = 0; i < TILE_SIZE; i++) {
    //			int a = base_addr + m*m*i + (tile * TILE_SIZE);
    //			x[a] = sh_x[tid_l][i];
    //			//printf("tid = %d - SM a = [%d,%d] - g a = %d \n", tid, tid_l, i, a );
    //		}
    //
    //
    //    }
    //    // *** END - Forward substitution ************************************************************************************
    //    // **************************************************************************************************************
    //
    //    __syncthreads();
    //
    //    // **************************************************************************************************************
    //    // *** Backward substitution ************************************************************************************
    //
    //    // Backward substitution - last TILE - compute backward substitution using data already stored in tile in shared memory
    //	#pragma unroll
    //    for (int i = TILE_SIZE-2; i >= 0; --i) {
    //    	int ca = (TILES-1) * TILE_SIZE + i;
    //    	work_buffer_reg = sh_x[i][tid_l] - dev_c_prime[ ca ] * work_buffer_reg;
    //        sh_x[i][tid_l] = work_buffer_reg;
    //        //printf("B0 - tid = %d - work_buffer_reg = %f - prim a = %d \n", tid, work_buffer_reg, m - TILE_SIZE + i);
    //
    //    }
    //
    //    // Backward substitution - last TILE - store results from tile in shared memory to global memory
    //	#pragma unroll
    //	for (int i = 0; i < TILE_SIZE; i++) {
    //		int a = base_addr +  m*m*i + (TILES-1) * TILE_SIZE;   //m - TILE_SIZE;
    //		x[ a ] = sh_x[tid_l][i];
    //		//printf("Sav0 - tid = %d - SM a = [%d,%d] - g a = %d \n", tid, tid_l, i, a );
    //	}
    //
    //    // Backward substitution - remainig tiles
    //    for (int tile = TILES - 2; tile >= 0; tile--) {
    //
    //    	// Load new tile from global memory to tile in shared memory
    //    	#pragma unroll
    //		for (int i = 0; i < TILE_SIZE; i++) {
    //			//sh_b[tid_l][i] = b[ start + m * m * ( tile * TILE_SIZE + i ) ];
    //			int a = base_addr + m*m*i + tile * TILE_SIZE;
    //			sh_b[tid_l][i] = x[ a ];
    //			//printf("Lod1 - tid = %d - SM a = [%d,%d] - g a = %d \n", tid, tid_l, i, a );
    //		}
    //
    //		// compute backward substitution - use date stored in tile in shared memory
    //		#pragma unroll
    //		for (int i = TILE_SIZE-1; i >= 0; --i) {
    //			int ca = tile * TILE_SIZE + i;
    //			work_buffer_reg = sh_b[i][tid_l] - dev_c_prime[ca] * work_buffer_reg;
    //			sh_x[i][tid_l] = work_buffer_reg;
    //            //printf("B1 - tid = %d - work_buffer_reg = %f - prim a = %d \n", tid, work_buffer_reg, ca);
    //		}
    //
    //		// Store current tile from shared memory to global memory
    //		#pragma unroll
    //		for (int i = 0; i < TILE_SIZE; i++) {
    //			//sh_b[tid_l][i] = b[ start + m * m * ( tile * TILE_SIZE + i ) ];
    //			int a = base_addr + m*m*i + tile * TILE_SIZE;
    //			x[a] = sh_x[tid_l][i];
    //			//printf("tid = %d - SM a = [%d,%d] - g a = %d \n", tid, tid_l, i, a );
    //		}
    //
    //    }
    //    // *** Backward substitution - END ******************************************************************************
    //    // **************************************************************************************************************
    //
    //	return;
    //
    //
    //
    //}
    //
    //
    //
    //
    //template<class FT>
    //__global__ void thomas_kernel3DT(int const m, int n, FT const alpha, FT const alpha_23, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x, FT * const __restrict__ tmp_g) {
    //
    //#define T 		W
    ////#define THREADS 	4
    ////#define BLOCKS		4
    //
    //	__shared__ FT SM [THREADS/T][T][T];
    //
    //	int tid	 	= blockIdx.x * blockDim.x + threadIdx.x;
    //	int tmt	    = threadIdx.x % T;
    //	int tdt		= threadIdx.x / T;
    //
    //	FT x_reg;
    //
    //	if (tid >= n) {
    //		return;
    //	}
    //
    //	int start = tid;
    //
    //	FT work_buffer_reg = b[start] * alpha_23 / (FT(2) + alpha);
    //
    //	tmp_g[start] = work_buffer_reg;
    //	for (int i = 1; i < m; ++i) {
    //		int        j   = start + i*n;
    //		double input   = b[j];
    //		double c_prime = dev_c_prime[i-1];
    //
    //		work_buffer_reg  = (input * alpha_23 + work_buffer_reg) / (double(2) + alpha + c_prime);
    //		tmp_g[j] = work_buffer_reg;
    //	}
    //
    //	x_reg = tmp_g[start + (m-1)*n];
    //	SM[tdt][tmt][0] = x_reg;
    //
    //	for (int i = 1; i < T; i++) {
    //		int j = start + (m-1-i)*n;
    //		x_reg = tmp_g[j] - dev_c_prime[ (m-1-i) ] * x_reg;
    //		SM[tdt][tmt][i] = x_reg;
    //	}
    //
    //
    //	int addr1	 = T * tdt;
    //	int addr2	 = blockIdx.x;
    //	int addr3 	 = m - 1 - tmt;
    //	int addr4;
    //
    //	int addr	 = (addr2 * m * m) + addr3;
    //
    //	for (int i = 0; i < T; i++) {
    //		x[ addr + (addr1 + i) * m ] = SM[tdt][i][tmt];
    //	}
    //
    //	for (int T_loop = 1; T_loop < m/T; T_loop++) {
    //
    //		int T_offset 	= T * T_loop;
    //		addr4 	= m - 1 - T_offset;
    //		addr3   = addr4 - tmt;
    //		addr    = (addr2 * m * m) + addr3;
    //
    //		for (int i = 0; i < T; i++) {
    //			int g_addr = addr4 - i;
    //			int j 	   = start + n * g_addr;
    //
    //			x_reg           = tmp_g[j] - dev_c_prime[ g_addr ] * x_reg;
    //			SM[tdt][tmt][i] = x_reg;
    //		}
    //
    //		for (int i = 0; i < T; i++) {
    //			x[ addr + (addr1 + i) * m ] = SM[tdt][i][tmt];
    //		}
    //
    //
    //	}
    //
    //
    //
    //	//	int addr3D(int s, int r, int c, int m){ //[system, row, col_in_system = coallesced]
    //	//	  return s*m + r*m*m + c;
    //	//	}
    //
    //
    //}
    //
    //
    //
    //// Thomas algorithm with storing intermediate results in shared memory - saves one global memory read and global memory write into x - compare with previous Thomas kernel
    //template<class FT>
    //__global__ void thomas_kernel3D2(int const m, int n, FT const alpha, FT const alpha_23, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x) {
    //
    //	extern __shared__ FT xs[];
    //
    //	int tid   = blockIdx.x * blockDim.x + threadIdx.x;
    //	int tid_l = threadIdx.x;
    //	int block_size = m;
    //
    //        if (tid >= n) {
    //          return;
    //        }
    //
    //        int start = tid;
    //
    //        FT work_buffer_reg = b[start] * alpha_23 / (FT(2) + alpha);
    //
    //        //x[start] = work_buffer_reg;
    //        xs[tid_l * block_size + 0 + tid_l] = work_buffer_reg;
    //	for (int i = 1; i < m; ++i) {
    //                int j = start + i*n;
    //                work_buffer_reg  = (b[j] * alpha_23 + work_buffer_reg) / (FT(2) + alpha + dev_c_prime[i-1]);
    //                //x[j] = work_buffer_reg;
    //		xs[ tid_l * block_size + i + tid_l ] = work_buffer_reg;
    //        }
    //
    //        FT x_reg = work_buffer_reg; //x[start + (m-1)*n];
    //        x[start + (m-1)*n] = x_reg;
    //        for (int i = m-2; i >= 0; --i) {
    //                int j = start + i*n;
    //                //x_reg = x[j] - dev_c_prime[i] * x_reg;
    //                x_reg = xs[tid_l * block_size + i + tid_l] - dev_c_prime[i] * x_reg;
    //		x[j] = x_reg;
    //        }
    //
    //}
    //
    //
    //
    //template<class FT>
    //__global__ void thomas_kernel3D3(int const m, int n, FT const alpha, FT const alpha_23, FT const * const __restrict__ dev_c_prime,  FT const * const __restrict__ b, FT * const __restrict__ x) {
    //
    //
    //}
    //
    //
    ///*
    // *      Preconditioner for the 3D problem. Uses the thomas algorithm to invert M.
    // *
    // *      @param FT Field Type - Either float or double
    // *
    // */
    //template<class FT>
    //class ThomasPreconditioner3D : public Preconditioner<FT> {
    //private:
    //        FT *c_prime;
    //        int m;
    //        cublasHandle_t cublas_handle;
    //        FT *b_trans;
    //        FT alpha, alpha_23;
    //
    //        int thomas_kernel_block_size;
    //public:
    //        virtual void init(int const m, FT const alpha, cublasHandle_t cublas_handle, cusparseHandle_t cusparse_handle) {
    //                this->m = m;
    //                this->alpha = alpha;
    //                this-> cublas_handle = cublas_handle;
    //
    //                FT *host_c_prime = new FT[m];
    //
    //                alpha_23 = pow(alpha, FT(2)/FT(3));
    //
    //                host_c_prime[0] = FT(-1) / (alpha + FT(2));
    //                for (int i = 1; i < m; ++i) {
    //                        host_c_prime[i] = FT(-1) / (host_c_prime[i-1] + FT(2) + alpha);
    //                }
    //
    //                cudaMalloc((void **) &c_prime, m*sizeof(FT));
    //                cudaMemcpy(c_prime, host_c_prime, m*sizeof(FT), cudaMemcpyHostToDevice);
    //
    //                delete[] host_c_prime;
    //
    //                cudaMalloc((void **) &b_trans, m*m*m*sizeof(FT));
    //
    //                int minGridSize;
    //                cudaOccupancyMaxPotentialBlockSize(&minGridSize, &thomas_kernel_block_size, thomas_kernel3D<FT>, 0, m*m);
    //
    //
    //
    //
    //        }
    //
    //        virtual void run(FT const * const b, FT * const x) {
    //        	FT block_count       = m; //divide_and_round_up(m*m, thomas_kernel_block_size);
    //        	FT threads_per_block = m; //thomas_kernel_block_size;
    //
    //        	std::cout << "Blocks            = " << block_count << std::endl;
    //        	std::cout << "threads_per_block = " << threads_per_block << std::endl;
    //
    //        	//int n = m*m*m;
    //
    //        	// delete --------------
    //
    //        	FT *h_x;
    //        	h_x  = (FT * ) malloc ( (m*m*m)*sizeof(FT) );
    //        	FT *h_x2;
    //        	h_x2 = (FT * ) malloc ( (m*m*m)*sizeof(FT) );
    //
    //        	cudaMemcpy( h_x, b, (m*m*m)*sizeof(FT) , cudaMemcpyDeviceToHost );
    //        	for (int i = 0; i < m*m*m; i++) {
    //        		if (m <= 8)
    //        			if (i % (m*m) == 0)
    //        				std::cout << std::endl;
    //        		if (m <= 8) std::cout << h_x[i] << "\t";
    //        	}
    //        	if (m <= 8) std::cout << std::endl;
    //
    //        	FT *xx = x;
    //
    //        	FT *bb;
    //        	cudaMalloc((void **) &bb, m*m*m*sizeof(FT));
    //        	FT *bbb;
    //        	cudaMalloc((void **) &bbb, m*m*m*sizeof(FT));
    //        	FT *bbbb;
    //        	cudaMalloc((void **) &bbbb, m*m*m*sizeof(FT));
    //
    //
    //        	// Ker 1 *************
    //
    //        	device_memset<FT>(xx, FT(0), m*m*m);
    //        	thomas_kernel3D_X1<FT><<<block_count, threads_per_block>>>(m, alpha, alpha_23, c_prime, b, xx); //bb);
    //
    //        	FT sum = 0.0;
    //        	cudaMemcpy( h_x, xx, (m*m*m)*sizeof(FT) , cudaMemcpyDeviceToHost );
    //        	for (int i = 0; i < m*m*m; i++) {
    //        		if (m <= 8)
    //        			if (i % (m*m) == 0)
    //        				std::cout << std::endl;
    //        		//std::cout << h_x[i] << "\t";
    //        		if (m <= 8) printf("%4.1f\t",h_x[i]);
    //
    //        		sum+=h_x[i];
    //        	}
    //        	if (m <= 8) std::cout << std::endl;
    //        	std::cout << sum << std::endl;
    //
    //        	// Ker 2 *****************
    //
    //        	cublas_transpose2(cublas_handle, m, m*m, b, bb);
    //        	device_memset<FT>(xx, FT(0), m*m*m);
    //        	cudaMemcpy( h_x, bb, (m*m*m)*sizeof(FT) , cudaMemcpyDeviceToHost );
    //
    //        	for (int i = 0; i < m*m*m; i++) {
    //        		if (m <= 8)
    //        			if (i % (m*m) == 0)
    //        				std::cout << std::endl;
    //        		if (m <= 8) std::cout << h_x[i] << "\t";
    //        	}
    //        	if (m <= 8) std::cout << std::endl;
    //
    //        	thomas_kernel3D_X2<FT><<<block_count, threads_per_block>>>(m, alpha, alpha_23, c_prime, bb, xx); //bb);
    //        	cublas_transpose2(cublas_handle, m*m, m, xx, bbb);
    //
    //
    //        	cudaMemcpy( h_x, bbb, (m*m*m)*sizeof(FT) , cudaMemcpyDeviceToHost );
    //        	sum = 0.0;
    //        	for (int i = 0; i < m*m*m; i++) {
    //        		if (m <= 8)
    //        			if (i % (m*m) == 0)
    //        				std::cout << std::endl;
    //        		//std::cout << h_x[i] << "\t";
    //        		if (m <= 8) printf("%4.1f\t",h_x[i]);
    //        		sum+=h_x[i];
    //        		h_x2[i] = h_x[i];
    //        	}
    //        	if (m <= 8) std::cout << std::endl;
    //        	std::cout << sum <<std::endl;
    //
    //
    //        	// Ker 3 *****************
    //
    //        	cublas_transpose2(cublas_handle, m, m*m, b, bb);
    //        	cublas_transpose2(cublas_handle, m, m*m, bb, bbb);
    //
    //        	device_memset<FT>(xx, FT(0), m*m*m);
    //        	cudaMemcpy( h_x, bbb, (m*m*m)*sizeof(FT) , cudaMemcpyDeviceToHost );
    //
    //        	for (int i = 0; i < m*m*m; i++) {
    //        		if (m <= 8)
    //        			if (i % (m*m) == 0)
    //        				std::cout << std::endl;
    //        		if (m <= 8) std::cout << h_x[i] << "\t";
    //        	}
    //        	if (m <= 8) std::cout << std::endl;
    //
    //        	int blocks  = m*m / TILE_SIZE;
    //        	int threads = TILE_SIZE;
    //        	//blocks = 1;
    //        	//threads = 2;
    //        	std::cout << "\nThomas 3D Tiled kernel - Blocks: " << blocks << " Threads = " << threads << "\n";
    //
    //        	thomas_kernel3D_XT<FT><<<blocks, threads>>>(m, alpha, alpha_23, c_prime, bbb, xx); //bb);
    //
    //        	cublas_transpose2(cublas_handle, m*m, m, xx, bbb);
    //        	cublas_transpose2(cublas_handle, m*m, m, bbb, xx);
    //
    //        	cudaMemcpy( h_x, xx, (m*m*m)*sizeof(FT) , cudaMemcpyDeviceToHost );
    //        	sum = 0.0;
    //        	for (int i = 0; i < m*m*m; i++) {
    //        		if (m <= 8)
    //        			if (i % (m*m) == 0)
    //        				std::cout << std::endl;
    //        		//std::cout << h_x[i] << "\t";
    //        		if (m <= 8)
    //        			printf("%4.1f\t",h_x[i]);
    //        		sum+=h_x[i];
    //        	}
    //        	if (m <= 8) std::cout << std::endl;
    //        	std::cout << sum <<std::endl;
    //
    //
    //        	sum = 0.0;
    //        	for (int i = 0; i < m*m*m; i++) {
    //        		if (m <= 8)
    //        			if (i % (m*m) == 0)
    //        				std::cout << std::endl;
    //        		//std::cout << h_x[i] << "\t";
    //        		if (m <= 8)
    //        			printf("%4.1f\t",h_x2[i] - h_x[i]);
    //
    //        		sum+=h_x[i];
    //        	}
    //        	if (m <= 8) std::cout << std::endl;
    //        	std::cout << sum <<std::endl;
    //
    //
    //        	cudaFree(bb);
    //        	cudaFree(bbb);
    //        	cudaFree(bbbb);
    //
    //
    //        	//device_memset<FT>(x, FT(0), m*m);
    //
    //        	// delete --------------
    //
    //        	return;
    //
    //        	FT *y = x;
    //        	thomas_kernel3D<FT><<<block_count, threads_per_block>>>(m,  m*m, alpha, alpha_23, c_prime, b, y);
    //
    //        	FT *y_trans = b_trans;
    //        	cublas_transpose2(cublas_handle, m*m, m, y, y_trans);
    //
    //        	FT *z_trans = y;
    //        	thomas_kernel3D<FT><<<block_count, threads_per_block>>>(m,  m*m, alpha, alpha_23, c_prime, y_trans, z_trans);
    //
    //        	FT *z_trans2 = y_trans;
    //        	cublas_transpose2(cublas_handle, m*m, m, z_trans, z_trans2);
    //        	FT *x_trans2 = z_trans;
    //
    //        	thomas_kernel3D<FT><<<block_count, threads_per_block>>>(m,  m*m, alpha, alpha_23, c_prime, z_trans2, x_trans2);
    //        	FT *x_trans = z_trans2;
    //        	cublas_transpose2(cublas_handle, m, m*m, x_trans2, x_trans);
    //
    //        	cublas_transpose2(cublas_handle, m, m*m, x_trans, x);
    //        }