umfpack_demo Enter the printing level for UMFPACK's output statistics: 0: none, 1: errors only, 2: statistics, 4: print some of outputs 5: print all output [default is 1]: 2 -------------------------------------------------------------- Factor and solve a small system, Ax=b, using default parameters (except for verbose printing enabled) Solving Ax=b via UMFPACK: umfpack: x = A\b UMFPACK V5.0.2 (Dec 2, 2006), Control: Matrix entry defined as: double Int (generic integer) defined as: int 1: print level: 2 2: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 3: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 4: pivot tolerance: 0.1 5: block size for dense matrix kernels: 32 6: strategy: 0 (auto) 7: initial allocation ratio: 0.7 8: max iterative refinement steps: 2 13: 2-by-2 pivot tolerance: 0.01 14: Q fixed during numerical factorization: 0 (auto) 15: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 16: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 17: scaling: 1 (divide each row by sum of abs. values in each row) 18: frontal matrix allocation ratio: 0.5 19: drop tolerance: 0 20: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 9: BLAS library used: Fortran BLAS. size of BLAS integer: 4 10: compiled for MATLAB 11: CPU timer is POSIX times ( ) routine. 12: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) UMFPACK V5.0.2 (Dec 2, 2006), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: yes. 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 UF_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): 0.00 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)): 6.59005e+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 677 42% Numeric final size (Units) 2101 1117 53% Numeric final size (MBytes) 0.0 0.0 53% peak memory usage (Units) 7462 4928 66% peak memory usage (MBytes) 0.1 0.0 66% numeric factorization flops 1.41920e+04 2.45200e+03 17% nz in L (incl diagonal) 542 322 59% nz in U (incl diagonal) 902 339 38% nz in L+U (incl diagonal) 1377 594 43% 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 322 nz in U (incl diagonal), if none dropped 339 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: 262 numerical values stored in Numeric object: 595 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 solve flops: 6.16100e+03 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 1.77e-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: 8.61300e+03 Solving Ax=b via MATLAB: Difference between UMFPACK and MATLAB solution: 0 -------------------------------------------------------------- Factorizing [L, U, P, Q, R] = umfpack2 (A) P * (R\A) * Q - L*U should be zero: norm (P*(R\A)*Q - L*U, 1) = 2.77556e-16 (exact) 1.21864e-16 (estimated) Solution to Ax=b via UMFPACK factorization: x = Q * (U \ (L \ (P * (R \ b)))) UMFPACK flop count: 2453 Factorizing [L, U, P] = lu (A (:, q)) If you are using a version of MATLAB prior to V6.0, then the following statement (q = colamd (A)) may fail. Either download colamd from http://www.cise.ufl.edu/research/sparse, upgrade to MATLAB V6.0 or later, or replace the statement with q = colmmd (A) ; Solution to Ax=b via MATLAB factorization: x = U \ (L \ (P * b)) ; x (q) = x ; Difference between UMFPACK and MATLAB solution: 4.35207e-14 MATLAB LU flop count: 3160 -------------------------------------------------------------- Solve A'x=b: Solving A'x=b via UMFPACK: umfpack: x = b/A UMFPACK V5.0.2 (Dec 2, 2006), Control: Matrix entry defined as: double Int (generic integer) defined as: int 1: print level: 2 2: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 3: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 4: pivot tolerance: 0.1 5: block size for dense matrix kernels: 32 6: strategy: 0 (auto) 7: initial allocation ratio: 0.7 8: max iterative refinement steps: 2 13: 2-by-2 pivot tolerance: 0.01 14: Q fixed during numerical factorization: 0 (auto) 15: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 16: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 17: scaling: 1 (divide each row by sum of abs. values in each row) 18: frontal matrix allocation ratio: 0.5 19: drop tolerance: 0 20: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 9: BLAS library used: Fortran BLAS. size of BLAS integer: 4 10: compiled for MATLAB 11: CPU timer is POSIX times ( ) routine. 12: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) UMFPACK V5.0.2 (Dec 2, 2006), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: yes. 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 UF_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): 0.00 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)): 6.59005e+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 677 42% Numeric final size (Units) 2101 1117 53% Numeric final size (MBytes) 0.0 0.0 53% peak memory usage (Units) 7462 4928 66% peak memory usage (MBytes) 0.1 0.0 66% numeric factorization flops 1.41920e+04 2.45200e+03 17% nz in L (incl diagonal) 542 322 59% nz in U (incl diagonal) 902 339 38% nz in L+U (incl diagonal) 1377 594 43% 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 322 nz in U (incl diagonal), if none dropped 339 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: 262 numerical values stored in Numeric object: 595 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 solve flops: 6.05300e+03 iterative refinement steps taken: 1 iterative refinement steps attempted: 1 sparse backward error omega1: 1.12e-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: 8.50500e+03 Solving A'x=b via MATLAB: Difference between UMFPACK and MATLAB solution: 3.55271e-15 -------------------------------------------------------------- Compute C = A', and compute the LU factorization of C. Factorizing A' can sometimes be better than factorizing A itself (less work and memory usage). Solve C'x=b; the solution is the same as the solution to Ax=b for the original A. umfpack: numeric factorization UMFPACK V5.0.2 (Dec 2, 2006), Control: Matrix entry defined as: double Int (generic integer) defined as: int 1: print level: 2 2: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 3: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 4: pivot tolerance: 0.1 5: block size for dense matrix kernels: 32 6: strategy: 0 (auto) 7: initial allocation ratio: 0.7 8: max iterative refinement steps: 2 13: 2-by-2 pivot tolerance: 0.01 14: Q fixed during numerical factorization: 0 (auto) 15: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 16: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 17: scaling: 1 (divide each row by sum of abs. values in each row) 18: frontal matrix allocation ratio: 0.5 19: drop tolerance: 0 20: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 9: BLAS library used: Fortran BLAS. size of BLAS integer: 4 10: compiled for MATLAB 11: CPU timer is POSIX times ( ) routine. 12: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) UMFPACK V5.0.2 (Dec 2, 2006), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: yes. 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 UF_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): 1621 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 234 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-01 maximum sum (abs (rows of A)): 6.14337e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 1638 1570 96% peak size (Units) 5708 3575 63% final size (Units) 1489 656 44% Numeric final size (Units) 1962 1096 56% Numeric final size (MBytes) 0.0 0.0 56% peak memory usage (Units) 7032 4899 70% peak memory usage (MBytes) 0.1 0.0 70% numeric factorization flops 1.32810e+04 2.16900e+03 16% nz in L (incl diagonal) 548 316 58% nz in U (incl diagonal) 827 305 37% nz in L+U (incl diagonal) 1308 554 42% largest front (# entries) 380 70 18% largest # rows in front 19 10 53% largest # columns in front 20 10 50% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 316 nz in U (incl diagonal), if none dropped 305 number of small entries dropped 0 nonzeros on diagonal of U: 67 min abs. value on diagonal of U: 1.05e-01 max abs. value on diagonal of U: 1.15e+00 estimate of reciprocal of condition number: 9.07e-02 indices in compressed pattern: 277 numerical values stored in Numeric object: 557 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 P * (R\C) * Q - L*U should be zero: norm (P*(R\C)*Q - L*U, 1) = 1.17961e-16 (exact) 5.60533e-17 (estimated) Solution to Ax=b via UMFPACK, using the factors of C: x = R \ (P' * (L' \ (U' \ (Q' * b)))) ; Solution to Ax=b via MATLAB: Difference between UMFPACK and MATLAB solution: 7.99361e-15 -------------------------------------------------------------- Solve AX=B, where B is n-by-10, and sparse umfpack: numeric factorization UMFPACK V5.0.2 (Dec 2, 2006), Control: Matrix entry defined as: double Int (generic integer) defined as: int 1: print level: 2 2: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 3: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 4: pivot tolerance: 0.1 5: block size for dense matrix kernels: 32 6: strategy: 0 (auto) 7: initial allocation ratio: 0.7 8: max iterative refinement steps: 2 13: 2-by-2 pivot tolerance: 0.01 14: Q fixed during numerical factorization: 0 (auto) 15: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 16: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 17: scaling: 1 (divide each row by sum of abs. values in each row) 18: frontal matrix allocation ratio: 0.5 19: drop tolerance: 0 20: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 9: BLAS library used: Fortran BLAS. size of BLAS integer: 4 10: compiled for MATLAB 11: CPU timer is POSIX times ( ) routine. 12: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) UMFPACK V5.0.2 (Dec 2, 2006), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: yes. 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 UF_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): 0.00 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)): 6.59005e+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 677 42% Numeric final size (Units) 2101 1117 53% Numeric final size (MBytes) 0.0 0.0 53% peak memory usage (Units) 7462 4928 66% peak memory usage (MBytes) 0.1 0.0 66% numeric factorization flops 1.41920e+04 2.45200e+03 17% nz in L (incl diagonal) 542 322 59% nz in U (incl diagonal) 902 339 38% nz in L+U (incl diagonal) 1377 594 43% 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 322 nz in U (incl diagonal), if none dropped 339 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: 262 numerical values stored in Numeric object: 595 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): 0.01 numeric factorization mflops (wallclock): 0.25 Difference between UMFPACK and MATLAB solution: 3.58657e-14 -------------------------------------------------------------- Solve AX=B, where B is n-by-10, and sparse, using umfpack_btf umfpack: numeric factorization UMFPACK V5.0.2 (Dec 2, 2006), Control: Matrix entry defined as: double Int (generic integer) defined as: int 1: print level: 2 2: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 3: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 4: pivot tolerance: 0.1 5: block size for dense matrix kernels: 32 6: strategy: 0 (auto) 7: initial allocation ratio: 0.7 8: max iterative refinement steps: 2 13: 2-by-2 pivot tolerance: 0.01 14: Q fixed during numerical factorization: 0 (auto) 15: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 16: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 17: scaling: 1 (divide each row by sum of abs. values in each row) 18: frontal matrix allocation ratio: 0.5 19: drop tolerance: 0 20: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 9: BLAS library used: Fortran BLAS. size of BLAS integer: 4 10: compiled for MATLAB 11: CPU timer is POSIX times ( ) routine. 12: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) UMFPACK V5.0.2 (Dec 2, 2006), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: yes. CPU timer: POSIX times ( ) routine. number of rows in matrix A: 66 number of columns in matrix A: 66 entries in matrix A: 292 memory usage reported in: 8-byte Units size of int: 4 bytes size of UF_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: 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 66 symmetry of nonzero pattern: 0.106195 nz in S+S' (excl. diagonal): 428 nz on diagonal of matrix S: 66 fraction of nz on diagonal: 1.000000 2-by-2 pivoting to place large entries on diagonal: # of small diagonal entries of S: 0 # unmatched: 0 symmetry of P2*S: 0.106195 nz in P2*S+(P2*S)' (excl. diag.): 428 nz on diagonal of P2*S: 66 fraction of nz on diag of P2*S: 1.000000 symbolic factorization defragmentations: 2 symbolic memory usage (Units): 1616 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 249 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)): 1.45950e+00 maximum sum (abs (rows of A)): 6.59005e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 1641 1571 96% peak size (Units) 5974 3518 59% final size (Units) 1593 730 46% Numeric final size (Units) 2064 1168 57% Numeric final size (MBytes) 0.0 0.0 57% peak memory usage (Units) 7318 4862 66% peak memory usage (MBytes) 0.1 0.0 66% numeric factorization flops 1.33160e+04 3.04900e+03 23% nz in L (incl diagonal) 532 349 66% nz in U (incl diagonal) 869 364 42% nz in L+U (incl diagonal) 1335 647 48% largest front (# entries) 441 108 24% largest # rows in front 21 10 48% largest # columns in front 21 12 57% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 349 nz in U (incl diagonal), if none dropped 364 number of small entries dropped 0 nonzeros on diagonal of U: 66 min abs. value on diagonal of U: 2.64e-02 max abs. value on diagonal of U: 9.72e+00 estimate of reciprocal of condition number: 2.71e-03 indices in compressed pattern: 249 numerical values stored in Numeric object: 656 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 Difference between UMFPACK and MATLAB solution: 7.30935e-14 -------------------------------------------------------------- Solve A'X=B, where B is n-by-10, and sparse umfpack: numeric factorization UMFPACK V5.0.2 (Dec 2, 2006), Control: Matrix entry defined as: double Int (generic integer) defined as: int 1: print level: 2 2: dense row parameter: 0.2 "dense" rows have > max (16, (0.2)*16*sqrt(n_col) entries) 3: dense column parameter: 0.2 "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries) 4: pivot tolerance: 0.1 5: block size for dense matrix kernels: 32 6: strategy: 0 (auto) 7: initial allocation ratio: 0.7 8: max iterative refinement steps: 2 13: 2-by-2 pivot tolerance: 0.01 14: Q fixed during numerical factorization: 0 (auto) 15: AMD dense row/col parameter: 10 "dense" rows/columns have > max (16, (10)*sqrt(n)) entries Only used if the AMD ordering is used. 16: diagonal pivot tolerance: 0.001 Only used if diagonal pivoting is attempted. 17: scaling: 1 (divide each row by sum of abs. values in each row) 18: frontal matrix allocation ratio: 0.5 19: drop tolerance: 0 20: AMD and COLAMD aggressive absorption: 1 (yes) The following options can only be changed at compile-time: 9: BLAS library used: Fortran BLAS. size of BLAS integer: 4 10: compiled for MATLAB 11: CPU timer is POSIX times ( ) routine. 12: compiled for normal operation (debugging disabled) computer/operating system: Linux size of int: 4 UF_long: 4 Int: 4 pointer: 4 double: 8 Entry: 8 (in bytes) UMFPACK V5.0.2 (Dec 2, 2006), Info: matrix entry defined as: double Int (generic integer) defined as: int BLAS library used: Fortran BLAS. size of BLAS integer: 4 MATLAB: yes. 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 UF_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): 1621 symbolic memory usage (MBytes): 0.0 Symbolic size (Units): 234 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-01 maximum sum (abs (rows of A)): 6.14337e+00 symbolic/numeric factorization: upper bound actual % variable-sized part of Numeric object: initial size (Units) 1638 1570 96% peak size (Units) 5708 3575 63% final size (Units) 1489 656 44% Numeric final size (Units) 1962 1096 56% Numeric final size (MBytes) 0.0 0.0 56% peak memory usage (Units) 7032 4899 70% peak memory usage (MBytes) 0.1 0.0 70% numeric factorization flops 1.32810e+04 2.16900e+03 16% nz in L (incl diagonal) 548 316 58% nz in U (incl diagonal) 827 305 37% nz in L+U (incl diagonal) 1308 554 42% largest front (# entries) 380 70 18% largest # rows in front 19 10 53% largest # columns in front 20 10 50% initial allocation ratio used: 0.7 # of forced updates due to frontal growth: 0 nz in L (incl diagonal), if none dropped 316 nz in U (incl diagonal), if none dropped 305 number of small entries dropped 0 nonzeros on diagonal of U: 67 min abs. value on diagonal of U: 1.05e-01 max abs. value on diagonal of U: 1.15e+00 estimate of reciprocal of condition number: 9.07e-02 indices in compressed pattern: 277 numerical values stored in Numeric object: 557 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 Difference between UMFPACK and MATLAB solution: 1.48414e-13 -------------------------------------------------------------- det(A): -4.07453e-05 UMFPACK determinant: -4.07453e-05 diary off