Mercurial > octave-nkf
view liboctave/UMFPACK/UMFPACK/Demo/umf4.out @ 5164:57077d0ddc8e
[project @ 2005-02-25 19:55:24 by jwe]
| author | jwe |
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| date | Fri, 25 Feb 2005 19:55:28 +0000 |
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cc -O -DNBLAS -I../Include -I../../AMD/Include -o umf4 umf4.c ../Lib/libumfpack.a ../../AMD/Lib/libamd.a -lm f77 -O -o readhb readhb.f f77 -O -o readhb_nozeros readhb_nozeros.f f77 -O -o readhb_size readhb_size.f ./readhb_nozeros < HB/can_24.psa > tmp/A Matrix key: CAN 24 ./readhb_size < HB/can_24.psa > tmp/Asize ./umf4 =========================================================== === UMFPACK v4.4 ========================================== =========================================================== UMFPACK V4.4 (Jan. 28, 2005), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: none. UMFPACK will be slow. 9: compiled for ANSI C (uses malloc, free, realloc, and printf) 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 24 nrow 24 ncol 24 nz 160 triplet-form matrix, n_row = 24, n_col = 24 nz = 160. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 24 n_col 24, nz = 160. OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 24 number of columns in matrix A: 24 entries in matrix A: 160 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 0 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 24 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 136 nz on diagonal of matrix S: 24 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.00300e+03 est. nz in L+U (incl. diagonal): 218 est. largest front (# entries): 64 est. max nz in any column of L: 8 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 718 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 124 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 739 - - peak size (Units) 3244 - - final size (Units) 393 - - Numeric final size (Units) 591 - - Numeric final size (MBytes) 0.0 - - peak memory usage (Units) 3826 - - peak memory usage (MBytes) 0.0 - - numeric factorization flops 2.37900e+03 - - nz in L (incl diagonal) 149 - - nz in U (incl diagonal) 208 - - nz in L+U (incl diagonal) 333 - - largest front (# entries) 182 - - largest # rows in front 13 - - largest # columns in front 14 - - Symbolic object: OK Numeric object: OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 24 number of columns in matrix A: 24 entries in matrix A: 160 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 0 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 24 symmetry of nonzero pattern: 1.000000 nz in S+S' (excl. diagonal): 136 nz on diagonal of matrix S: 24 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.00300e+03 est. nz in L+U (incl. diagonal): 218 est. largest front (# entries): 64 est. max nz in any column of L: 8 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 718 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 124 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 4.00000e+00 maximum sum (abs (rows of A)): 9.00000e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 739 712 96% peak size (Units) 3244 2712 84% final size (Units) 393 179 46% Numeric final size (Units) 591 365 62% Numeric final size (MBytes) 0.0 0.0 62% peak memory usage (Units) 3826 3294 86% peak memory usage (MBytes) 0.0 0.0 86% numeric factorization flops 2.37900e+03 3.32000e+02 14% nz in L (incl diagonal) 149 78 52% nz in U (incl diagonal) 208 86 41% nz in L+U (incl diagonal) 333 140 42% largest front (# entries) 182 78 43% largest # rows in front 13 7 54% largest # columns in front 14 13 93% initial allocation ratio used: 1.2 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 10 nz in L (incl diagonal), if none dropped 78 nz in U (incl diagonal), if none dropped 86 number of small entries dropped 0 nonzeros on diagonal of U: 24 min abs. value on diagonal of U: 1.11e-01 max abs. value on diagonal of U: 2.50e-01 estimate of reciprocal of condition number: 4.44e-01 indices in compressed pattern: 92 numerical values stored in Numeric object: 140 numeric factorization defragmentations: 0 numeric factorization reallocations: 0 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 symbolic + numeric CPU time (sec): 0.00 symbolic + numeric wall clock time (sec): 0.00 solve flops: 1.13600e+03 iterative refinement steps taken: 0 iterative refinement steps attempted: 0 sparse backward error omega1: 1.22e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.46800e+03 total symbolic + numeric + solve CPU time: 0.00 total symbolic+numeric+solve wall clock time: 0.00 UMFPACK V4.4 (Jan. 28, 2005): OK dense vector, n = 24. OK relative maxnorm of residual, ||Ax-b||/||b||: 1.2919e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.1716e-15 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. amd: approximate minimum degree ordering, parameters: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes AMD ordering time: cpu 0.00 wall 0.00 amd: approximate minimum degree ordering, results: status: OK n, dimension of A: 24 nz, number of nonzeros in A: 160 symmetry of A: 1.0000 number of nonzeros on diagonal: 24 nonzeros in pattern of A+A' (excl. diagonal): 136 # dense rows/columns of A+A': 0 memory used, in bytes: 1516 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 97 nonzeros in L (including diagonal): 121 # divide operations for LDL' or LU: 97 # multiply-subtract operations for LDL': 275 # multiply-subtract operations for LU: 453 max nz. in any column of L (incl. diagonal): 8 chol flop count for real A, sqrt counted as 1 flop: 671 LDL' flop count for real A: 647 LDL' flop count for complex A: 3073 LU flop count for real A (with no pivoting): 1003 LU flop count for complex A (with no pivoting): 4497 AMD test done ./readhb_nozeros < HB/west0067.rua > tmp/A Matrix key: WEST0067 ./readhb_size < HB/west0067.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v4.4 ========================================== =========================================================== UMFPACK V4.4 (Jan. 28, 2005), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: none. UMFPACK will be slow. 9: compiled for ANSI C (uses malloc, free, realloc, and printf) 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 67 nrow 67 ncol 67 nz 294 triplet-form matrix, n_row = 67, n_col = 67 nz = 294. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 67 n_col 67, nz = 294. OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 67 number of columns in matrix A: 67 entries in matrix A: 294 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 1 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S not square or diagonal not preserved symbolic factorization defragmentations: 1 symbolic memory usage (Units): 1632 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 245 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.01 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 1643 - - peak size (Units) 6115 - - final size (Units) 1628 - - Numeric final size (Units) 2101 - - Numeric final size (MBytes) 0.0 - - peak memory usage (Units) 7462 - - peak memory usage (MBytes) 0.1 - - numeric factorization flops 1.41920e+04 - - nz in L (incl diagonal) 542 - - nz in U (incl diagonal) 902 - - nz in L+U (incl diagonal) 1377 - - largest front (# entries) 483 - - largest # rows in front 21 - - largest # columns in front 23 - - Symbolic object: OK Numeric object: OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 67 number of columns in matrix A: 67 entries in matrix A: 294 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: unsymmetric ordering used: colamd on A modify Q during factorization: yes prefer diagonal pivoting: no pivots with zero Markowitz cost: 1 submatrix S after removing zero-cost pivots: number of "dense" rows: 0 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S not square or diagonal not preserved symbolic factorization defragmentations: 1 symbolic memory usage (Units): 1632 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 245 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.01 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.00000e+00 maximum sum (abs (rows of A)): 6.59006e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 1643 1574 96% peak size (Units) 6115 3581 59% final size (Units) 1628 685 42% Numeric final size (Units) 2101 1125 54% Numeric final size (MBytes) 0.0 0.0 54% peak memory usage (Units) 7462 4928 66% peak memory usage (MBytes) 0.1 0.0 66% numeric factorization flops 1.41920e+04 2.58700e+03 18% nz in L (incl diagonal) 542 329 61% nz in U (incl diagonal) 902 340 38% nz in L+U (incl diagonal) 1377 602 44% largest front (# entries) 483 80 17% largest # rows in front 21 10 48% largest # columns in front 23 11 48% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 329 nz in U (incl diagonal), if none dropped 340 number of small entries dropped 0 nonzeros on diagonal of U: 67 min abs. value on diagonal of U: 2.74e-02 max abs. value on diagonal of U: 2.28e+00 estimate of reciprocal of condition number: 1.20e-02 indices in compressed pattern: 256 numerical values stored in Numeric object: 605 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 symbolic + numeric CPU time (sec): 0.00 symbolic + numeric wall clock time (sec): 0.01 symbolic + numeric mflops (wall clock): 0.26 solve flops: 6.19300e+03 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 9.49e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 8.78000e+03 total symbolic + numeric + solve CPU time: 0.00 total symbolic+numeric+solve wall clock time: 0.01 total symbolic+numeric+solve mflops(wallclock) 0.88 UMFPACK V4.4 (Jan. 28, 2005): OK dense vector, n = 67. OK relative maxnorm of residual, ||Ax-b||/||b||: 1.83101e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 2.47921e-15 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. amd: approximate minimum degree ordering, parameters: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes AMD ordering time: cpu 0.00 wall 0.00 amd: approximate minimum degree ordering, results: status: OK n, dimension of A: 67 nz, number of nonzeros in A: 294 symmetry of A: 0.0342 number of nonzeros on diagonal: 2 nonzeros in pattern of A+A' (excl. diagonal): 574 # dense rows/columns of A+A': 0 memory used, in bytes: 5164 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 930 nonzeros in L (including diagonal): 997 # divide operations for LDL' or LU: 930 # multiply-subtract operations for LDL': 9170 # multiply-subtract operations for LU: 17410 max nz. in any column of L (incl. diagonal): 33 chol flop count for real A, sqrt counted as 1 flop: 19337 LDL' flop count for real A: 19270 LDL' flop count for complex A: 81730 LU flop count for real A (with no pivoting): 35750 LU flop count for complex A (with no pivoting): 147650 AMD test done ./readhb_nozeros < HB/fs_183_6.rua > tmp/A Matrix key: FS 183 6 ./readhb_size < HB/fs_183_6.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v4.4 ========================================== =========================================================== UMFPACK V4.4 (Jan. 28, 2005), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: none. UMFPACK will be slow. 9: compiled for ANSI C (uses malloc, free, realloc, and printf) 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 183 nrow 183 ncol 183 nz 1000 triplet-form matrix, n_row = 183, n_col = 183 nz = 1000. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 183 n_col 183, nz = 1000. OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 183 number of columns in matrix A: 183 entries in matrix A: 1000 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric 2-by-2 ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 36 submatrix S after removing zero-cost pivots: number of "dense" rows: 4 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 147 symmetry of nonzero pattern: 0.490515 nz in S+S' (excl. diagonal): 1114 nz on diagonal of matrix S: 147 fraction of nz on diagonal: 1.000000 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 7 # unmatched: 7 symmetry of P2*S: 0.490515 nz in P2*S+(P2*S)' (excl. diag.): 1114 nz on diagonal of P2*S: 147 fraction of nz on diag of P2*S: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.02930e+04 est. nz in L+U (incl. diagonal): 1625 est. largest front (# entries): 196 est. max nz in any column of L: 14 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4839 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 756 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4274 - - peak size (Units) 26277 - - final size (Units) 15717 - - Numeric final size (Units) 16944 - - Numeric final size (MBytes) 0.1 - - peak memory usage (Units) 29673 - - peak memory usage (MBytes) 0.2 - - numeric factorization flops 2.67903e+05 - - nz in L (incl diagonal) 2122 - - nz in U (incl diagonal) 9931 - - nz in L+U (incl diagonal) 11870 - - largest front (# entries) 2337 - - largest # rows in front 21 - - largest # columns in front 136 - - Symbolic object: OK Numeric object: OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 183 number of columns in matrix A: 183 entries in matrix A: 1000 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric 2-by-2 ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 36 submatrix S after removing zero-cost pivots: number of "dense" rows: 4 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 147 symmetry of nonzero pattern: 0.490515 nz in S+S' (excl. diagonal): 1114 nz on diagonal of matrix S: 147 fraction of nz on diagonal: 1.000000 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 7 # unmatched: 7 symmetry of P2*S: 0.490515 nz in P2*S+(P2*S)' (excl. diag.): 1114 nz on diagonal of P2*S: 147 fraction of nz on diag of P2*S: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.02930e+04 est. nz in L+U (incl. diagonal): 1625 est. largest front (# entries): 196 est. max nz in any column of L: 14 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4839 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 756 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.84689e-01 maximum sum (abs (rows of A)): 8.73139e+08 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4274 4089 96% peak size (Units) 26277 8291 32% final size (Units) 15717 1658 11% Numeric final size (Units) 16944 2794 16% Numeric final size (MBytes) 0.1 0.0 16% peak memory usage (Units) 29673 11687 39% peak memory usage (MBytes) 0.2 0.1 39% numeric factorization flops 2.67903e+05 7.82700e+03 3% nz in L (incl diagonal) 2122 838 39% nz in U (incl diagonal) 9931 804 8% nz in L+U (incl diagonal) 11870 1459 12% largest front (# entries) 2337 420 18% largest # rows in front 21 14 67% largest # columns in front 136 36 26% initial allocation ratio used: 0.265 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 3 nz in L (incl diagonal), if none dropped 838 nz in U (incl diagonal), if none dropped 804 number of small entries dropped 0 nonzeros on diagonal of U: 183 min abs. value on diagonal of U: 2.30e-09 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 2.30e-09 indices in compressed pattern: 550 numerical values stored in Numeric object: 1396 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 symbolic + numeric CPU time (sec): 0.00 symbolic + numeric wall clock time (sec): 0.00 solve flops: 1.79470e+04 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 1.51e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 2.57740e+04 total symbolic + numeric + solve CPU time: 0.00 total symbolic+numeric+solve wall clock time: 0.00 UMFPACK V4.4 (Jan. 28, 2005): OK dense vector, n = 183. OK relative maxnorm of residual, ||Ax-b||/||b||: 1.55669e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.08984e-06 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. amd: approximate minimum degree ordering, parameters: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes AMD ordering time: cpu 0.00 wall 0.00 amd: approximate minimum degree ordering, results: status: OK n, dimension of A: 183 nz, number of nonzeros in A: 1000 symmetry of A: 0.4431 number of nonzeros on diagonal: 183 nonzeros in pattern of A+A' (excl. diagonal): 1272 # dense rows/columns of A+A': 0 memory used, in bytes: 12692 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 882 nonzeros in L (including diagonal): 1065 # divide operations for LDL' or LU: 882 # multiply-subtract operations for LDL': 3378 # multiply-subtract operations for LU: 5874 max nz. in any column of L (incl. diagonal): 15 chol flop count for real A, sqrt counted as 1 flop: 7821 LDL' flop count for real A: 7638 LDL' flop count for complex A: 34962 LU flop count for real A (with no pivoting): 12630 LU flop count for complex A (with no pivoting): 54930 AMD test done ./readhb < HB/fs_183_6.rua > tmp/A Matrix key: FS 183 6 ./readhb_size < HB/fs_183_6.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v4.4 ========================================== =========================================================== UMFPACK V4.4 (Jan. 28, 2005), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: none. UMFPACK will be slow. 9: compiled for ANSI C (uses malloc, free, realloc, and printf) 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 183 nrow 183 ncol 183 nz 1069 triplet-form matrix, n_row = 183, n_col = 183 nz = 1069. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 183 n_col 183, nz = 1069. OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 183 number of columns in matrix A: 183 entries in matrix A: 1069 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric 2-by-2 ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 29 submatrix S after removing zero-cost pivots: number of "dense" rows: 4 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 154 symmetry of nonzero pattern: 0.446860 nz in S+S' (excl. diagonal): 1286 nz on diagonal of matrix S: 154 fraction of nz on diagonal: 1.000000 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 7 # unmatched: 7 symmetry of P2*S: 0.446860 nz in P2*S+(P2*S)' (excl. diag.): 1286 nz on diagonal of P2*S: 154 fraction of nz on diag of P2*S: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.78450e+04 est. nz in L+U (incl. diagonal): 2080 est. largest front (# entries): 400 est. max nz in any column of L: 20 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4959 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 766 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4558 - - peak size (Units) 26357 - - final size (Units) 17822 - - Numeric final size (Units) 19049 - - Numeric final size (MBytes) 0.1 - - peak memory usage (Units) 29795 - - peak memory usage (MBytes) 0.2 - - numeric factorization flops 3.51312e+05 - - nz in L (incl diagonal) 2633 - - nz in U (incl diagonal) 10968 - - nz in L+U (incl diagonal) 13418 - - largest front (# entries) 3220 - - largest # rows in front 25 - - largest # columns in front 140 - - Symbolic object: OK Numeric object: OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 183 number of columns in matrix A: 183 entries in matrix A: 1069 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric 2-by-2 ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 29 submatrix S after removing zero-cost pivots: number of "dense" rows: 4 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 154 symmetry of nonzero pattern: 0.446860 nz in S+S' (excl. diagonal): 1286 nz on diagonal of matrix S: 154 fraction of nz on diagonal: 1.000000 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 7 # unmatched: 7 symmetry of P2*S: 0.446860 nz in P2*S+(P2*S)' (excl. diag.): 1286 nz on diagonal of P2*S: 154 fraction of nz on diag of P2*S: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 1.78450e+04 est. nz in L+U (incl. diagonal): 2080 est. largest front (# entries): 400 est. max nz in any column of L: 20 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4959 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 766 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 1.84689e-01 maximum sum (abs (rows of A)): 8.73139e+08 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4558 4376 96% peak size (Units) 26357 11140 42% final size (Units) 17822 2107 12% Numeric final size (Units) 19049 3243 17% Numeric final size (MBytes) 0.1 0.0 17% peak memory usage (Units) 29795 14578 49% peak memory usage (MBytes) 0.2 0.1 49% numeric factorization flops 3.51312e+05 1.19670e+04 3% nz in L (incl diagonal) 2633 1136 43% nz in U (incl diagonal) 10968 870 8% nz in L+U (incl diagonal) 13418 1823 14% largest front (# entries) 3220 728 23% largest # rows in front 25 20 80% largest # columns in front 140 58 41% initial allocation ratio used: 0.282 # of forced updates due to frontal growth: 2 number of off-diagonal pivots: 3 nz in L (incl diagonal), if none dropped 1136 nz in U (incl diagonal), if none dropped 870 number of small entries dropped 0 nonzeros on diagonal of U: 183 min abs. value on diagonal of U: 2.30e-09 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 2.30e-09 indices in compressed pattern: 741 numerical values stored in Numeric object: 1781 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 1 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 symbolic + numeric CPU time (sec): 0.00 symbolic + numeric wall clock time (sec): 0.00 solve flops: 2.00240e+04 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 2.21e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 3.19910e+04 total symbolic + numeric + solve CPU time: 0.00 total symbolic+numeric+solve wall clock time: 0.00 UMFPACK V4.4 (Jan. 28, 2005): OK dense vector, n = 183. OK relative maxnorm of residual, ||Ax-b||/||b||: 1.94586e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.22537e-06 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. amd: approximate minimum degree ordering, parameters: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes AMD ordering time: cpu 0.01 wall 0.00 amd: approximate minimum degree ordering, results: status: OK n, dimension of A: 183 nz, number of nonzeros in A: 1069 symmetry of A: 0.4176 number of nonzeros on diagonal: 183 nonzeros in pattern of A+A' (excl. diagonal): 1402 # dense rows/columns of A+A': 0 memory used, in bytes: 13316 # of memory compactions: 1 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 1072 nonzeros in L (including diagonal): 1255 # divide operations for LDL' or LU: 1072 # multiply-subtract operations for LDL': 5320 # multiply-subtract operations for LU: 9568 max nz. in any column of L (incl. diagonal): 21 chol flop count for real A, sqrt counted as 1 flop: 11895 LDL' flop count for real A: 11712 LDL' flop count for complex A: 52208 LU flop count for real A (with no pivoting): 20208 LU flop count for complex A (with no pivoting): 86192 AMD test done ./readhb < HB/arc130.rua > tmp/A Matrix key: ARC130 ./readhb_size < HB/arc130.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v4.4 ========================================== =========================================================== UMFPACK V4.4 (Jan. 28, 2005), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: none. UMFPACK will be slow. 9: compiled for ANSI C (uses malloc, free, realloc, and printf) 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 130 nrow 130 ncol 130 nz 1282 triplet-form matrix, n_row = 130, n_col = 130 nz = 1282. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 130 n_col 130, nz = 1282. OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1282 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 6 submatrix S after removing zero-cost pivots: number of "dense" rows: 7 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 124 symmetry of nonzero pattern: 0.841193 nz in S+S' (excl. diagonal): 1204 nz on diagonal of matrix S: 124 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 8.27000e+03 est. nz in L+U (incl. diagonal): 1336 est. largest front (# entries): 324 est. max nz in any column of L: 18 number of "dense" rows/columns in S+S': 2 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4759 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 637 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4599 - - peak size (Units) 25036 - - final size (Units) 12837 - - Numeric final size (Units) 13724 - - Numeric final size (MBytes) 0.1 - - peak memory usage (Units) 27681 - - peak memory usage (MBytes) 0.2 - - numeric factorization flops 9.41610e+04 - - nz in L (incl diagonal) 1009 - - nz in U (incl diagonal) 7849 - - nz in L+U (incl diagonal) 8728 - - largest front (# entries) 2337 - - largest # rows in front 19 - - largest # columns in front 123 - - Symbolic object: OK Numeric object: OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1282 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 6 submatrix S after removing zero-cost pivots: number of "dense" rows: 7 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 124 symmetry of nonzero pattern: 0.841193 nz in S+S' (excl. diagonal): 1204 nz on diagonal of matrix S: 124 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 8.27000e+03 est. nz in L+U (incl. diagonal): 1336 est. largest front (# entries): 324 est. max nz in any column of L: 18 number of "dense" rows/columns in S+S': 2 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4759 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 637 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 7.94859e-01 maximum sum (abs (rows of A)): 1.08460e+06 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 4599 4452 97% peak size (Units) 25036 6478 26% final size (Units) 12837 1054 8% Numeric final size (Units) 13724 1876 14% Numeric final size (MBytes) 0.1 0.0 14% peak memory usage (Units) 27681 9123 33% peak memory usage (MBytes) 0.2 0.1 33% numeric factorization flops 9.41610e+04 4.20900e+03 4% nz in L (incl diagonal) 1009 417 41% nz in U (incl diagonal) 7849 787 10% nz in L+U (incl diagonal) 8728 1074 12% largest front (# entries) 2337 270 12% largest # rows in front 19 18 95% largest # columns in front 123 15 12% initial allocation ratio used: 0.36 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 0 nz in L (incl diagonal), if none dropped 417 nz in U (incl diagonal), if none dropped 796 number of small entries dropped 9 nonzeros on diagonal of U: 130 min abs. value on diagonal of U: 9.22e-07 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 9.22e-07 indices in compressed pattern: 79 numerical values stored in Numeric object: 977 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 symbolic + numeric CPU time (sec): 0.00 symbolic + numeric wall clock time (sec): 0.00 solve flops: 1.80440e+04 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 8.47e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 2.22530e+04 total symbolic + numeric + solve CPU time: 0.00 total symbolic+numeric+solve wall clock time: 0.00 UMFPACK V4.4 (Jan. 28, 2005): OK dense vector, n = 130. OK relative maxnorm of residual, ||Ax-b||/||b||: 1.37368e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.74277e-10 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. amd: approximate minimum degree ordering, parameters: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes AMD ordering time: cpu 0.00 wall 0.00 amd: approximate minimum degree ordering, results: status: OK n, dimension of A: 130 nz, number of nonzeros in A: 1282 symmetry of A: 0.7587 number of nonzeros on diagonal: 130 nonzeros in pattern of A+A' (excl. diagonal): 1430 # dense rows/columns of A+A': 2 memory used, in bytes: 11544 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 756 nonzeros in L (including diagonal): 886 # divide operations for LDL' or LU: 756 # multiply-subtract operations for LDL': 2959 # multiply-subtract operations for LU: 5162 max nz. in any column of L (incl. diagonal): 18 chol flop count for real A, sqrt counted as 1 flop: 6804 LDL' flop count for real A: 6674 LDL' flop count for complex A: 30476 LU flop count for real A (with no pivoting): 11080 LU flop count for complex A (with no pivoting): 48100 AMD test done ./readhb_nozeros < HB/arc130.rua > tmp/A Matrix key: ARC130 ./readhb_size < HB/arc130.rua > tmp/Asize ./umf4 =========================================================== === UMFPACK v4.4 ========================================== =========================================================== UMFPACK V4.4 (Jan. 28, 2005), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 0 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: none. UMFPACK will be slow. 9: compiled for ANSI C (uses malloc, free, realloc, and printf) 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 130 nrow 130 ncol 130 nz 1037 triplet-form matrix, n_row = 130, n_col = 130 nz = 1037. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 130 n_col 130, nz = 1037. OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1037 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 54 submatrix S after removing zero-cost pivots: number of "dense" rows: 5 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 76 symmetry of nonzero pattern: 0.733224 nz in S+S' (excl. diagonal): 774 nz on diagonal of matrix S: 76 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 5.81700e+03 est. nz in L+U (incl. diagonal): 858 est. largest front (# entries): 289 est. max nz in any column of L: 17 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4111 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 527 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 3196 - - peak size (Units) 9801 - - final size (Units) 4259 - - Numeric final size (Units) 5146 - - Numeric final size (MBytes) 0.0 - - peak memory usage (Units) 12135 - - peak memory usage (MBytes) 0.1 - - numeric factorization flops 2.47640e+04 - - nz in L (incl diagonal) 606 - - nz in U (incl diagonal) 2537 - - nz in L+U (incl diagonal) 3013 - - largest front (# entries) 459 - - largest # rows in front 17 - - largest # columns in front 48 - - Symbolic object: OK Numeric object: OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1037 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 54 submatrix S after removing zero-cost pivots: number of "dense" rows: 5 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 76 symmetry of nonzero pattern: 0.733224 nz in S+S' (excl. diagonal): 774 nz on diagonal of matrix S: 76 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 5.81700e+03 est. nz in L+U (incl. diagonal): 858 est. largest front (# entries): 289 est. max nz in any column of L: 17 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4111 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 527 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 7.94859e-01 maximum sum (abs (rows of A)): 1.08460e+06 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 3196 3062 96% peak size (Units) 9801 6376 65% final size (Units) 4259 1141 27% Numeric final size (Units) 5146 1963 38% Numeric final size (MBytes) 0.0 0.0 38% peak memory usage (Units) 12135 8710 72% peak memory usage (MBytes) 0.1 0.1 72% numeric factorization flops 2.47640e+04 4.10700e+03 17% nz in L (incl diagonal) 606 409 67% nz in U (incl diagonal) 2537 792 31% nz in L+U (incl diagonal) 3013 1071 36% largest front (# entries) 459 240 52% largest # rows in front 17 16 94% largest # columns in front 48 15 31% initial allocation ratio used: 0.755 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 0 nz in L (incl diagonal), if none dropped 409 nz in U (incl diagonal), if none dropped 792 number of small entries dropped 0 nonzeros on diagonal of U: 130 min abs. value on diagonal of U: 9.22e-07 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 9.22e-07 indices in compressed pattern: 70 numerical values stored in Numeric object: 782 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 symbolic + numeric CPU time (sec): 0.00 symbolic + numeric wall clock time (sec): 0.00 solve flops: 1.58270e+04 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 7.18e-17 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 1.99340e+04 total symbolic + numeric + solve CPU time: 0.00 total symbolic+numeric+solve wall clock time: 0.00 UMFPACK V4.4 (Jan. 28, 2005): OK dense vector, n = 130. OK relative maxnorm of residual, ||Ax-b||/||b||: 1.37368e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.74255e-10 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. amd: approximate minimum degree ordering, parameters: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes AMD ordering time: cpu 0.00 wall 0.00 amd: approximate minimum degree ordering, results: status: OK n, dimension of A: 130 nz, number of nonzeros in A: 1037 symmetry of A: 0.4939 number of nonzeros on diagonal: 130 nonzeros in pattern of A+A' (excl. diagonal): 1366 # dense rows/columns of A+A': 2 memory used, in bytes: 11236 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 725 nonzeros in L (including diagonal): 855 # divide operations for LDL' or LU: 725 # multiply-subtract operations for LDL': 2742 # multiply-subtract operations for LU: 4759 max nz. in any column of L (incl. diagonal): 18 chol flop count for real A, sqrt counted as 1 flop: 6339 LDL' flop count for real A: 6209 LDL' flop count for complex A: 28461 LU flop count for real A (with no pivoting): 10243 LU flop count for complex A (with no pivoting): 44597 AMD test done ./readhb_nozeros < HB/arc130.rua > tmp/A Matrix key: ARC130 ./readhb_size < HB/arc130.rua > tmp/Asize ./umf4 a 1e-6 =========================================================== === UMFPACK v4.4 ========================================== =========================================================== droptol 1e-06 UMFPACK V4.4 (Jan. 28, 2005), Control: Matrix entry defined as: double Int (generic integer) defined as: int 0: print level: 3 1: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 2: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 3: pivot tolerance: 0.1 4: block size for dense matrix kernels: 32 5: strategy: 0 (auto) 6: initial allocation ratio: 0.7 7: max iterative refinement steps: 2 12: 2-by-2 pivot tolerance: 0.01 13: Q fixed during numerical factorization: 0 (auto) 14: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 15: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 16: scaling: 1 (divide each row by sum of abs. values in each row) 17: frontal matrix allocation ratio: 0.5 18: drop tolerance: 1e-06 19: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 8: BLAS library used: none. UMFPACK will be slow. 9: compiled for ANSI C (uses malloc, free, realloc, and printf) 10: CPU timer is POSIX times ( ) routine. 11: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) File: tmp/A File: tmp/Asize n 130 nrow 130 ncol 130 nz 1037 triplet-form matrix, n_row = 130, n_col = 130 nz = 1037. OK triplet-to-col time: wall 0 cpu 0 column-form matrix, n_row 130 n_col 130, nz = 1037. OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1037 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 54 submatrix S after removing zero-cost pivots: number of "dense" rows: 5 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 76 symmetry of nonzero pattern: 0.733224 nz in S+S' (excl. diagonal): 774 nz on diagonal of matrix S: 76 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 5.81700e+03 est. nz in L+U (incl. diagonal): 858 est. largest front (# entries): 289 est. max nz in any column of L: 17 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4111 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 527 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 3196 - - peak size (Units) 9801 - - final size (Units) 4259 - - Numeric final size (Units) 5146 - - Numeric final size (MBytes) 0.0 - - peak memory usage (Units) 12135 - - peak memory usage (MBytes) 0.1 - - numeric factorization flops 2.47640e+04 - - nz in L (incl diagonal) 606 - - nz in U (incl diagonal) 2537 - - nz in L+U (incl diagonal) 3013 - - largest front (# entries) 459 - - largest # rows in front 17 - - largest # columns in front 48 - - Symbolic object: OK Numeric object: OK UMFPACK V4.4 (Jan. 28, 2005), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: none. UMFPACK will be slow. MATLAB: no. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 130 number of columns in matrix A: 130 entries in matrix A: 1037 memory usage reported in: 8-byte Units size of int: 4 bytes size of long: 4 bytes size of pointer: 4 bytes size of numerical entry: 8 bytes strategy used: symmetric ordering used: amd on A+A' modify Q during factorization: no prefer diagonal pivoting: yes pivots with zero Markowitz cost: 54 submatrix S after removing zero-cost pivots: number of "dense" rows: 5 number of "dense" columns: 0 number of empty rows: 0 number of empty columns 0 submatrix S square and diagonal preserved pattern of square submatrix S: number rows and columns 76 symmetry of nonzero pattern: 0.733224 nz in S+S' (excl. diagonal): 774 nz on diagonal of matrix S: 76 fraction of nz on diagonal: 1.000000 AMD statistics, for strict diagonal pivoting: est. flops for LU factorization: 5.81700e+03 est. nz in L+U (incl. diagonal): 858 est. largest front (# entries): 289 est. max nz in any column of L: 17 number of "dense" rows/columns in S+S': 0 symbolic factorization defragmentations: 0 symbolic memory usage (Units): 4111 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 527 Symbolic size (MBytes): 0 symbolic factorization CPU time (sec): 0.00 symbolic factorization wallclock time(sec): 0.00 matrix scaled: yes (divided each row by sum of abs values in each row) minimum sum (abs (rows of A)): 7.94859e-01 maximum sum (abs (rows of A)): 1.08460e+06 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 3196 2762 86% peak size (Units) 9801 5323 54% final size (Units) 4259 457 11% Numeric final size (Units) 5146 1279 25% Numeric final size (MBytes) 0.0 0.0 25% peak memory usage (Units) 12135 7657 63% peak memory usage (MBytes) 0.1 0.1 63% numeric factorization flops 2.47640e+04 4.10700e+03 17% nz in L (incl diagonal) 606 318 52% nz in U (incl diagonal) 2537 285 11% nz in L+U (incl diagonal) 3013 473 16% largest front (# entries) 459 240 52% largest # rows in front 17 16 94% largest # columns in front 48 15 31% initial allocation ratio used: 0.755 # of forced updates due to frontal growth: 0 number of off-diagonal pivots: 0 nz in L (incl diagonal), if none dropped 409 nz in U (incl diagonal), if none dropped 792 number of small entries dropped 598 nonzeros on diagonal of U: 130 min abs. value on diagonal of U: 9.22e-07 max abs. value on diagonal of U: 1.00e+00 estimate of reciprocal of condition number: 9.22e-07 indices in compressed pattern: 82 numerical values stored in Numeric object: 386 numeric factorization defragmentations: 1 numeric factorization reallocations: 1 costly numeric factorization reallocations: 0 numeric factorization CPU time (sec): 0.00 numeric factorization wallclock time (sec): 0.00 symbolic + numeric CPU time (sec): 0.00 symbolic + numeric wall clock time (sec): 0.00 solve flops: 2.06060e+04 iterative refinement steps taken: 2 iterative refinement steps attempted: 2 sparse backward error omega1: 1.30e-16 sparse backward error omega2: 0.00e+00 solve CPU time (sec): 0.00 solve wall clock time (sec): 0.00 total symbolic + numeric + solve flops: 2.47130e+04 total symbolic + numeric + solve CPU time: 0.00 total symbolic+numeric+solve wall clock time: 0.00 UMFPACK V4.4 (Jan. 28, 2005): OK dense vector, n = 130. OK relative maxnorm of residual, ||Ax-b||/||b||: 1.37368e-16 relative maxnorm of error, ||x-xtrue||/||xtrue||: 1.94084e-10 Writing tmp/x Writing tmp/info.umf4 umf4 done, strategy: 0 =========================================================== === AMD =================================================== =========================================================== ------- Now trying the AMD ordering. This not part of the UMFPACK analysis or factorization, above, but a separate test of just the AMD ordering routine. amd: approximate minimum degree ordering, parameters: dense row parameter: 10 (rows with more than max (10 * sqrt (n), 16) entries are considered "dense", and placed last in output permutation) aggressive absorption: yes AMD ordering time: cpu 0.00 wall 0.00 amd: approximate minimum degree ordering, results: status: OK n, dimension of A: 130 nz, number of nonzeros in A: 1037 symmetry of A: 0.4939 number of nonzeros on diagonal: 130 nonzeros in pattern of A+A' (excl. diagonal): 1366 # dense rows/columns of A+A': 2 memory used, in bytes: 11236 # of memory compactions: 0 The following approximate statistics are for a subsequent factorization of A(P,P) + A(P,P)'. They are slight upper bounds if there are no dense rows/columns in A+A', and become looser if dense rows/columns exist. nonzeros in L (excluding diagonal): 725 nonzeros in L (including diagonal): 855 # divide operations for LDL' or LU: 725 # multiply-subtract operations for LDL': 2742 # multiply-subtract operations for LU: 4759 max nz. in any column of L (incl. diagonal): 18 chol flop count for real A, sqrt counted as 1 flop: 6339 LDL' flop count for real A: 6209 LDL' flop count for complex A: 28461 LU flop count for real A (with no pivoting): 10243 LU flop count for complex A (with no pivoting): 44597 AMD test done