step 1.1: preparation
step 1.1: read matrix market format
GPU Device 0: "Hopper" with compute capability 9.0

Using default input file [../../../../Samples/4_CUDA_Libraries/cuSolverRf/lap2D_5pt_n100.mtx]
WARNING: cusolverRf only works for base-0 
sparse matrix A is 10000 x 10000 with 49600 nonzeros, base=0
step 1.2: set right hand side vector (b) to 1
step 2: reorder the matrix to reduce zero fill-in
        Q = symrcm(A) or Q = symamd(A) 
step 3: B = Q*A*Q^T
step 4: solve A*x = b by LU(B) in cusolverSp
step 4.1: create opaque info structure
step 4.2: analyze LU(B) to know structure of Q and R, and upper bound for nnz(L+U)
step 4.3: workspace for LU(B)
step 4.4: compute Ppivot*B = L*U 
step 4.5: check if the matrix is singular 
step 4.6: solve A*x = b 
    i.e.  solve B*(Qx) = Q*b 
step 4.7: evaluate residual r = b - A*x (result on CPU)
(CPU) |b - A*x| = 4.547474E-12 
(CPU) |A| = 8.000000E+00 
(CPU) |x| = 7.513384E+02 
(CPU) |b - A*x|/(|A|*|x|) = 7.565621E-16 
step 5: extract P, Q, L and U from P*B*Q^T = L*U 
        L has implicit unit diagonal
nnzL = 671550, nnzU = 681550
step 6: form P*A*Q^T = L*U
step 6.1: P = Plu*Qreroder
step 6.2: Q = Qlu*Qreorder 
step 7: create cusolverRf handle
step 8: set parameters for cusolverRf 
step 9: assemble P*A*Q = L*U 
step 10: analyze to extract parallelism 
step 11: import A to cusolverRf 
step 12: refactorization 
step 13: solve A*x = b 
step 14: evaluate residual r = b - A*x (result on GPU)
(GPU) |b - A*x| = 4.320100E-12 
(GPU) |A| = 8.000000E+00 
(GPU) |x| = 7.513384E+02 
(GPU) |b - A*x|/(|A|*|x|) = 7.187340E-16 
===== statistics 
 nnz(A) = 49600, nnz(L+U) = 1353100, zero fill-in ratio = 27.280242

===== timing profile 
 reorder A   : 0.003304 sec
 B = Q*A*Q^T : 0.000761 sec

 cusolverSp LU analysis: 0.000188 sec
 cusolverSp LU factor  : 0.069354 sec
 cusolverSp LU solve   : 0.001780 sec
 cusolverSp LU extract : 0.005654 sec

 cusolverRf assemble : 0.002426 sec
 cusolverRf reset    : 0.000021 sec
 cusolverRf refactor : 0.097122 sec
 cusolverRf solve    : 0.123813 sec