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59 lines
2.0 KiB
Plaintext
59 lines
2.0 KiB
Plaintext
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step 1.1: preparation
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step 1.1: read matrix market format
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GPU Device 0: "Hopper" with compute capability 9.0
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Using default input file [../../../../Samples/4_CUDA_Libraries/cuSolverRf/lap2D_5pt_n100.mtx]
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WARNING: cusolverRf only works for base-0
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sparse matrix A is 10000 x 10000 with 49600 nonzeros, base=0
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step 1.2: set right hand side vector (b) to 1
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step 2: reorder the matrix to reduce zero fill-in
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Q = symrcm(A) or Q = symamd(A)
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step 3: B = Q*A*Q^T
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step 4: solve A*x = b by LU(B) in cusolverSp
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step 4.1: create opaque info structure
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step 4.2: analyze LU(B) to know structure of Q and R, and upper bound for nnz(L+U)
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step 4.3: workspace for LU(B)
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step 4.4: compute Ppivot*B = L*U
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step 4.5: check if the matrix is singular
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step 4.6: solve A*x = b
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i.e. solve B*(Qx) = Q*b
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step 4.7: evaluate residual r = b - A*x (result on CPU)
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(CPU) |b - A*x| = 4.547474E-12
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(CPU) |A| = 8.000000E+00
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(CPU) |x| = 7.513384E+02
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(CPU) |b - A*x|/(|A|*|x|) = 7.565621E-16
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step 5: extract P, Q, L and U from P*B*Q^T = L*U
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L has implicit unit diagonal
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nnzL = 671550, nnzU = 681550
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step 6: form P*A*Q^T = L*U
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step 6.1: P = Plu*Qreroder
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step 6.2: Q = Qlu*Qreorder
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step 7: create cusolverRf handle
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step 8: set parameters for cusolverRf
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step 9: assemble P*A*Q = L*U
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step 10: analyze to extract parallelism
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step 11: import A to cusolverRf
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step 12: refactorization
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step 13: solve A*x = b
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step 14: evaluate residual r = b - A*x (result on GPU)
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(GPU) |b - A*x| = 4.320100E-12
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(GPU) |A| = 8.000000E+00
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(GPU) |x| = 7.513384E+02
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(GPU) |b - A*x|/(|A|*|x|) = 7.187340E-16
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===== statistics
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nnz(A) = 49600, nnz(L+U) = 1353100, zero fill-in ratio = 27.280242
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===== timing profile
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reorder A : 0.003304 sec
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B = Q*A*Q^T : 0.000761 sec
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cusolverSp LU analysis: 0.000188 sec
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cusolverSp LU factor : 0.069354 sec
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cusolverSp LU solve : 0.001780 sec
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cusolverSp LU extract : 0.005654 sec
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cusolverRf assemble : 0.002426 sec
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cusolverRf reset : 0.000021 sec
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cusolverRf refactor : 0.097122 sec
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cusolverRf solve : 0.123813 sec
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