Mercurial > octave-nkf
diff liboctave/UMFPACK/UMFPACK/Demo/umfpack_zi_demo.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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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/liboctave/UMFPACK/UMFPACK/Demo/umfpack_zi_demo.out Fri Feb 25 19:55:28 2005 +0000 @@ -0,0 +1,1542 @@ + +UMFPACK V4.4 (Jan. 28, 2005) demo: _zi_ version + +UMFPACK: Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved. + + +UMFPACK License: + + Your use or distribution of UMFPACK or any modified version of + UMFPACK implies that you agree to this License. + + THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + + Permission is hereby granted to use or copy this program, provided + that the Copyright, this License, and the Availability of the original + version is retained on all copies. User documentation of any code that + uses UMFPACK or any modified version of UMFPACK code must cite the + Copyright, this License, the Availability note, and "Used by permission." + Permission to modify the code and to distribute modified code is granted, + provided the Copyright, this License, and the Availability note are + retained, and a notice that the code was modified is included. This + software was developed with support from the National Science Foundation, + and is provided to you free of charge. + +Availability: http://www.cise.ufl.edu/research/sparse/umfpack + +UMFPACK V4.4 (Jan. 28, 2005): OK + + +UMFPACK V4.4 (Jan. 28, 2005), Control: + + Matrix entry defined as: double complex + Int (generic integer) defined as: int + + 0: print level: 5 + 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: 16 (in bytes) + + +b: dense vector, n = 5. + 0 : (8 + 1i) + 1 : (45 - 5i) + 2 : (-3 - 2i) + 3 : (3 + 0i) + 4 : (19 + 2.2i) + dense vector OK + + +A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12. + 0 : 0 0 (2 + 1i) + 1 : 4 4 (1 + 0.4i) + 2 : 1 0 (3 + 0.1i) + 3 : 1 2 (4 + 0.2i) + 4 : 2 1 (-1 - 1i) + 5 : 2 2 (-3 - 0.2i) + 6 : 0 1 (3 + 0i) + 7 : 1 4 (6 + 6i) + 8 : 2 3 (2 + 3i) + 9 : 3 2 (1 + 0i) + 10 : 4 1 (4 + 0.3i) + 11 : 4 2 (2 + 0.3i) + triplet-form matrix OK + + +A: column-form matrix, n_row 5 n_col 5, nz = 12. + + column 0: start: 0 end: 1 entries: 2 + row 0 : (2 + 1i) + row 1 : (3 + 0.1i) + + column 1: start: 2 end: 4 entries: 3 + row 0 : (3 + 0i) + row 2 : (-1 - 1i) + row 4 : (4 + 0.3i) + + column 2: start: 5 end: 8 entries: 4 + row 1 : (4 + 0.2i) + row 2 : (-3 - 0.2i) + row 3 : (1 + 0i) + row 4 : (2 + 0.3i) + + column 3: start: 9 end: 9 entries: 1 + row 2 : (2 + 3i) + + column 4: start: 10 end: 11 entries: 2 + row 1 : (6 + 6i) + row 4 : (1 + 0.4i) + column-form matrix OK + + +Symbolic factorization of A: Symbolic object: + matrix to be factorized: + n_row: 5 n_col: 5 + number of entries: 12 + block size used for dense matrix kernels: 32 + strategy used: unsymmetric + ordering used: colamd on A + + performn column etree postorder: yes + prefer diagonal pivoting (attempt P=Q): no + variable-size part of Numeric object: + minimum initial size (Units): 84 (MBytes): 0.0 + estimated peak size (Units): 2542 (MBytes): 0.0 + estimated final size (Units): 25 (MBytes): 0.0 + symbolic factorization memory usage (Units): 144 (MBytes): 0.0 + frontal matrices / supercolumns: + number of frontal chains: 1 + number of frontal matrices: 1 + largest frontal matrix row dimension: 3 + largest frontal matrix column dimension: 3 + + Frontal chain: 0. Frontal matrices 0 to 0 + Largest frontal matrix in Frontal chain: 3-by-3 + Front: 0 pivot cols: 3 (pivot columns 0 to 2) + pivot row candidates: 2 to 4 + leftmost descendant: 0 + 1st new candidate row : 2 + parent: (none) + +Initial column permutation, Q1: permutation vector, n = 5. + 0 : 3 + 1 : 2 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +Initial row permutation, P1: permutation vector, n = 5. + 0 : 2 + 1 : 3 + 2 : 0 + 3 : 1 + 4 : 4 + permutation vector OK + + Symbolic object: OK + + +Numeric factorization of A: Numeric object: + n_row: 5 n_col: 5 + relative pivot tolerance used: 0.1 + relative symmetric pivot tolerance used: 0.001 + matrix scaled: yes (divided each row by sum abs value in each row) + minimum sum (abs (rows of A)): 1.00000e+00 + maximum sum (abs (rows of A)): 1.93000e+01 + initial allocation parameter used: 0.7 + frontal matrix allocation parameter used: 0.5 + final total size of Numeric object (Units): 99 + final total size of Numeric object (MBytes): 0.0 + peak size of variable-size part (Units): 2527 + peak size of variable-size part (MBytes): 0.0 + largest actual frontal matrix size: 4 + memory defragmentations: 1 + memory reallocations: 1 + costly memory reallocations: 0 + entries in compressed pattern (L and U): 2 + number of nonzeros in L (excl diag): 4 + number of entries stored in L (excl diag): 2 + number of nonzeros in U (excl diag): 4 + number of entries stored in U (excl diag): 2 + factorization floating-point operations: 34 + number of nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 1.34629e-01 + max abs. value on diagonal of U: 1.77313e+00 + reciprocal condition number estimate: 7.59e-02 + +Scale factors applied via multiplication +Scale factors, Rs: dense vector, n = 5. + 0 : (0.166667) + 1 : (0.0518135) + 2 : (0.0980392) + 3 : (1) + 4 : (0.125) + dense vector OK + + +P: row permutation vector, n = 5. + 0 : 2 + 1 : 3 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +Q: column permutation vector, n = 5. + 0 : 3 + 1 : 2 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +L in Numeric object, in column-oriented compressed-pattern form: + Diagonal entries are all equal to 1.0 (not stored) + + column 0: length 0. + + column 1: length 2. + row 4 : (0.207254 + 0.0103627i) + row 3 : (0.25 + 0.0375i) + + column 2: add 1 entries. length 1. Start of Lchain. + row 4 : (0.379275 - 0.174093i) + + column 3: length 1. + row 4 : (3.00161 + 1.2864i) + + column 4: length 0. Start of Lchain. + + +U in Numeric object, in row-oriented compressed-pattern form: + Diagonal is stored separately. + + row 4: length 0. End of Uchain. + + row 3: length 1. End of Uchain. + col 4 : (0.5 + 0.0375i) + + row 2: length 1. + col 4 : (0.5 + 0i) + + row 1: length 0. End of Uchain. + + row 1: length 0. + + row 0: length 2. + col 1 : (-0.294118 - 0.0196078i) + col 4 : (-0.0980392 - 0.0980392i) + + +diagonal of U: dense vector, n = 5. + 0 : (0.196078 + 0.294118i) + 1 : (1 + 0i) + 2 : (0.333333 + 0.166667i) + 3 : (0.125 + 0.05i) + 4 : (-1.6422 - 0.668715i) + dense vector OK + + Numeric object: OK + + +UMFPACK V4.4 (Jan. 28, 2005), Info: + matrix entry defined as: double complex + 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: 5 + number of columns in matrix A: 5 + entries in matrix A: 12 + 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: 16 bytes + + strategy used: unsymmetric + ordering used: colamd on A + modify Q during factorization: yes + prefer diagonal pivoting: no + pivots with zero Markowitz cost: 2 + 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 3 + symmetry of nonzero pattern: 1.000000 + nz in S+S' (excl. diagonal): 4 + nz on diagonal of matrix S: 2 + fraction of nz on diagonal: 0.666667 + 2-by-2 pivoting to place large entries on diagonal: + # of small diagonal entries of S: 1 + # unmatched: 0 + symmetry of P2*S: 0.000000 + nz in P2*S+(P2*S)' (excl. diag.): 6 + nz on diagonal of P2*S: 3 + fraction of nz on diag of P2*S: 1.000000 + symbolic factorization defragmentations: 0 + symbolic memory usage (Units): 144 + symbolic memory usage (MBytes): 0.0 + Symbolic size (Units): 45 + 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)): 1.93000e+01 + + symbolic/numeric factorization: upper bound actual % + variable-sized part of Numeric object: + initial size (Units) 84 79 94% + peak size (Units) 2542 2527 99% + final size (Units) 25 21 84% + Numeric final size (Units) 106 100 94% + Numeric final size (MBytes) 0.0 0.0 94% + peak memory usage (Units) 2737 2722 99% + peak memory usage (MBytes) 0.0 0.0 99% + numeric factorization flops 6.70000e+01 3.40000e+01 51% + nz in L (incl diagonal) 10 9 90% + nz in U (incl diagonal) 10 9 90% + nz in L+U (incl diagonal) 15 13 87% + largest front (# entries) 9 4 44% + largest # rows in front 3 2 67% + largest # columns in front 3 2 67% + + initial allocation ratio used: 0.7 + # of forced updates due to frontal growth: 0 + nz in L (incl diagonal), if none dropped 9 + nz in U (incl diagonal), if none dropped 9 + number of small entries dropped 0 + nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 1.35e-01 + max abs. value on diagonal of U: 1.77e+00 + estimate of reciprocal of condition number: 7.59e-02 + indices in compressed pattern: 2 + numerical values stored in Numeric object: 9 + 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: 5.23000e+02 + iterative refinement steps taken: 0 + iterative refinement steps attempted: 0 + sparse backward error omega1: 7.87e-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: 5.57000e+02 + total symbolic + numeric + solve CPU time: 0.00 + total symbolic+numeric+solve wall clock time: 0.00 + + +UMFPACK: Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved. + +UMFPACK V4.4 (Jan. 28, 2005): OK + + +x (solution of Ax=b): dense vector, n = 5. + 0 : (0.121188 - 0.561001i) + 1 : (2.39887 + 0.666938i) + 2 : (3 + 0i) + 3 : (1.57395 - 1.52801i) + 4 : (2.3876 - 3.04245i) + dense vector OK + +maxnorm of residual: 6.21725e-15 + + +UMFPACK: Copyright (c) 2005 by Timothy A. Davis. All Rights Reserved. + +UMFPACK V4.4 (Jan. 28, 2005): OK + +determinant: (-1.7814+ (2.3784)i) * 10^(2) + +x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5. + 0 : (0.121188 - 0.561001i) + 1 : (2.39887 + 0.666938i) + 2 : (3 + 0i) + 3 : (1.57395 - 1.52801i) + 4 : (2.3876 - 3.04245i) + dense vector OK + +maxnorm of residual: 6.21725e-15 + + +UMFPACK V4.4 (Jan. 28, 2005), Info: + matrix entry defined as: double complex + 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: 5 + number of columns in matrix A: 5 + entries in matrix A: 12 + 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: 16 bytes + + strategy used: unsymmetric + ordering used: colamd on A + modify Q during factorization: yes + prefer diagonal pivoting: no + pivots with zero Markowitz cost: 2 + 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 3 + symmetry of nonzero pattern: 1.000000 + nz in S+S' (excl. diagonal): 4 + nz on diagonal of matrix S: 2 + fraction of nz on diagonal: 0.666667 + 2-by-2 pivoting to place large entries on diagonal: + # of small diagonal entries of S: 1 + # unmatched: 0 + symmetry of P2*S: 0.000000 + nz in P2*S+(P2*S)' (excl. diag.): 6 + nz on diagonal of P2*S: 3 + fraction of nz on diag of P2*S: 1.000000 + symbolic factorization defragmentations: 0 + symbolic memory usage (Units): 144 + symbolic memory usage (MBytes): 0.0 + Symbolic size (Units): 45 + 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)): 1.93000e+01 + + symbolic/numeric factorization: upper bound actual % + variable-sized part of Numeric object: + initial size (Units) 84 79 94% + peak size (Units) 2542 2527 99% + final size (Units) 25 21 84% + Numeric final size (Units) 106 100 94% + Numeric final size (MBytes) 0.0 0.0 94% + peak memory usage (Units) 2737 2722 99% + peak memory usage (MBytes) 0.0 0.0 99% + numeric factorization flops 6.70000e+01 3.40000e+01 51% + nz in L (incl diagonal) 10 9 90% + nz in U (incl diagonal) 10 9 90% + nz in L+U (incl diagonal) 15 13 87% + largest front (# entries) 9 4 44% + largest # rows in front 3 2 67% + largest # columns in front 3 2 67% + + initial allocation ratio used: 0.7 + # of forced updates due to frontal growth: 0 + nz in L (incl diagonal), if none dropped 9 + nz in U (incl diagonal), if none dropped 9 + number of small entries dropped 0 + nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 1.35e-01 + max abs. value on diagonal of U: 1.77e+00 + estimate of reciprocal of condition number: 7.59e-02 + indices in compressed pattern: 2 + numerical values stored in Numeric object: 9 + 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: 4.80000e+02 + iterative refinement steps taken: 0 + iterative refinement steps attempted: 0 + sparse backward error omega1: 6.06e-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: 5.14000e+02 + total symbolic + numeric + solve CPU time: 0.00 + total symbolic+numeric+solve wall clock time: 0.00 + + +x (solution of A'x=b): dense vector, n = 5. + 0 : (3.39246 + 0.13257i) + 1 : (0.31463 + 1.38626i) + 2 : (0.461538 + 0.692308i) + 3 : (-20.9089 - 1.55801i) + 4 : (9.04015 - 0.613724i) + dense vector OK + +maxnorm of residual: 7.68703e-15 + + +changing A (1,4) to zero + +modified A: column-form matrix, n_row 5 n_col 5, nz = 12. + + column 0: start: 0 end: 1 entries: 2 + row 0 : (2 + 1i) + row 1 : (3 + 0.1i) + + column 1: start: 2 end: 4 entries: 3 + row 0 : (3 + 0i) + row 2 : (-1 - 1i) + row 4 : (4 + 0.3i) + + column 2: start: 5 end: 8 entries: 4 + row 1 : (4 + 0.2i) + row 2 : (-3 - 0.2i) + row 3 : (1 + 0i) + row 4 : (2 + 0.3i) + + column 3: start: 9 end: 9 entries: 1 + row 2 : (2 + 3i) + + column 4: start: 10 end: 11 entries: 2 + row 1 : (0 + 0i) + row 4 : (1 + 0.4i) + column-form matrix OK + + +Numeric factorization of modified A: Numeric object: + n_row: 5 n_col: 5 + relative pivot tolerance used: 0.1 + relative symmetric pivot tolerance used: 0.001 + matrix scaled: yes (divided each row by sum abs value in each row) + minimum sum (abs (rows of A)): 1.00000e+00 + maximum sum (abs (rows of A)): 1.02000e+01 + initial allocation parameter used: 0.7 + frontal matrix allocation parameter used: 0.5 + final total size of Numeric object (Units): 97 + final total size of Numeric object (MBytes): 0.0 + peak size of variable-size part (Units): 2527 + peak size of variable-size part (MBytes): 0.0 + largest actual frontal matrix size: 4 + memory defragmentations: 1 + memory reallocations: 1 + costly memory reallocations: 0 + entries in compressed pattern (L and U): 2 + number of nonzeros in L (excl diag): 3 + number of entries stored in L (excl diag): 1 + number of nonzeros in U (excl diag): 4 + number of entries stored in U (excl diag): 2 + factorization floating-point operations: 17 + number of nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 1.34629e-01 + max abs. value on diagonal of U: 1.00000e+00 + reciprocal condition number estimate: 1.35e-01 + +Scale factors applied via multiplication +Scale factors, Rs: dense vector, n = 5. + 0 : (0.166667) + 1 : (0.136986) + 2 : (0.0980392) + 3 : (1) + 4 : (0.125) + dense vector OK + + +P: row permutation vector, n = 5. + 0 : 2 + 1 : 3 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +Q: column permutation vector, n = 5. + 0 : 3 + 1 : 2 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +L in Numeric object, in column-oriented compressed-pattern form: + Diagonal entries are all equal to 1.0 (not stored) + + column 0: length 0. + + column 1: length 2. + row 4 : (0.547945 + 0.0273973i) + row 3 : (0.25 + 0.0375i) + + column 2: add 1 entries. length 1. Start of Lchain. + row 4 : (1.00274 - 0.460274i) + + column 3: length 0. Start of Lchain. + + column 4: length 0. Start of Lchain. + + +U in Numeric object, in row-oriented compressed-pattern form: + Diagonal is stored separately. + + row 4: length 0. End of Uchain. + + row 3: length 1. End of Uchain. + col 4 : (0.5 + 0.0375i) + + row 2: length 1. + col 4 : (0.5 + 0i) + + row 1: length 0. End of Uchain. + + row 1: length 0. + + row 0: length 2. + col 1 : (-0.294118 - 0.0196078i) + col 4 : (-0.0980392 - 0.0980392i) + + +diagonal of U: dense vector, n = 5. + 0 : (0.196078 + 0.294118i) + 1 : (1 + 0i) + 2 : (0.333333 + 0.166667i) + 3 : (0.125 + 0.05i) + 4 : (-0.50137 + 0.230137i) + dense vector OK + + Numeric object: OK + + +UMFPACK V4.4 (Jan. 28, 2005), Info: + matrix entry defined as: double complex + 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: 5 + number of columns in matrix A: 5 + entries in matrix A: 12 + 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: 16 bytes + + strategy used: unsymmetric + ordering used: colamd on A + modify Q during factorization: yes + prefer diagonal pivoting: no + pivots with zero Markowitz cost: 2 + 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 3 + symmetry of nonzero pattern: 1.000000 + nz in S+S' (excl. diagonal): 4 + nz on diagonal of matrix S: 2 + fraction of nz on diagonal: 0.666667 + 2-by-2 pivoting to place large entries on diagonal: + # of small diagonal entries of S: 1 + # unmatched: 0 + symmetry of P2*S: 0.000000 + nz in P2*S+(P2*S)' (excl. diag.): 6 + nz on diagonal of P2*S: 3 + fraction of nz on diag of P2*S: 1.000000 + symbolic factorization defragmentations: 0 + symbolic memory usage (Units): 144 + symbolic memory usage (MBytes): 0.0 + Symbolic size (Units): 45 + 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)): 1.02000e+01 + + symbolic/numeric factorization: upper bound actual % + variable-sized part of Numeric object: + initial size (Units) 84 79 94% + peak size (Units) 2542 2527 99% + final size (Units) 25 19 76% + Numeric final size (Units) 106 98 92% + Numeric final size (MBytes) 0.0 0.0 92% + peak memory usage (Units) 2737 2722 99% + peak memory usage (MBytes) 0.0 0.0 99% + numeric factorization flops 6.70000e+01 1.70000e+01 25% + nz in L (incl diagonal) 10 8 80% + nz in U (incl diagonal) 10 9 90% + nz in L+U (incl diagonal) 15 12 80% + largest front (# entries) 9 4 44% + largest # rows in front 3 2 67% + largest # columns in front 3 2 67% + + initial allocation ratio used: 0.7 + # of forced updates due to frontal growth: 0 + nz in L (incl diagonal), if none dropped 8 + nz in U (incl diagonal), if none dropped 9 + number of small entries dropped 0 + nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 1.35e-01 + max abs. value on diagonal of U: 1.00e+00 + estimate of reciprocal of condition number: 1.35e-01 + indices in compressed pattern: 2 + numerical values stored in Numeric object: 8 + 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: 5.15000e+02 + iterative refinement steps taken: 0 + iterative refinement steps attempted: 0 + sparse backward error omega1: 7.33e-17 + sparse backward error omega2: 0.00e+00 + solve CPU time (sec): 0.00 + solve wall clock time (sec): 0.01 + solve mflops (wall clock time): 0.05 + + total symbolic + numeric + solve flops: 5.32000e+02 + total symbolic + numeric + solve CPU time: 0.00 + total symbolic+numeric+solve wall clock time: 0.00 + + +x (with modified A): dense vector, n = 5. + 0 : (10.9256 - 2.23085i) + 1 : (-5.36071 - 1.82131i) + 2 : (3 + 0i) + 3 : (-1.60191 - 1.88814i) + 4 : (32.7361 - 2.90097i) + dense vector OK + +maxnorm of residual: 3.9968e-15 + +changing real part of A (0,0) from 2 to 2 +changing real part of A (1,0) from 3 to 2 +changing real part of A (0,1) from 3 to 13 +changing real part of A (2,1) from -1 to 7 +changing real part of A (4,1) from 4 to 10 +changing real part of A (1,2) from 4 to 23 +changing real part of A (2,2) from -3 to 15 +changing real part of A (3,2) from 1 to 18 +changing real part of A (4,2) from 2 to 18 +changing real part of A (2,3) from 2 to 30 +changing real part of A (1,4) from 0 to 39 +changing real part of A (4,4) from 1 to 37 + +completely modified A (same pattern): column-form matrix, n_row 5 n_col 5, nz = 12. + + column 0: start: 0 end: 1 entries: 2 + row 0 : (2 + 1i) + row 1 : (2 + 0.1i) + + column 1: start: 2 end: 4 entries: 3 + row 0 : (13 + 0i) + row 2 : (7 - 1i) + row 4 : (10 + 0.3i) + + column 2: start: 5 end: 8 entries: 4 + row 1 : (23 + 0.2i) + row 2 : (15 - 0.2i) + row 3 : (18 + 0i) + row 4 : (18 + 0.3i) + + column 3: start: 9 end: 9 entries: 1 + row 2 : (30 + 3i) + + column 4: start: 10 end: 11 entries: 2 + row 1 : (39 + 0i) + row 4 : (37 + 0.4i) + column-form matrix OK + + +Saving symbolic object: + +Freeing symbolic object: + +Loading symbolic object: + +Done loading symbolic object + +Numeric factorization of completely modified A: Numeric object: + n_row: 5 n_col: 5 + relative pivot tolerance used: 0.1 + relative symmetric pivot tolerance used: 0.001 + matrix scaled: yes (divided each row by sum abs value in each row) + minimum sum (abs (rows of A)): 1.60000e+01 + maximum sum (abs (rows of A)): 6.60000e+01 + initial allocation parameter used: 0.7 + frontal matrix allocation parameter used: 0.5 + final total size of Numeric object (Units): 99 + final total size of Numeric object (MBytes): 0.0 + peak size of variable-size part (Units): 2527 + peak size of variable-size part (MBytes): 0.0 + largest actual frontal matrix size: 4 + memory defragmentations: 1 + memory reallocations: 1 + costly memory reallocations: 0 + entries in compressed pattern (L and U): 2 + number of nonzeros in L (excl diag): 4 + number of entries stored in L (excl diag): 2 + number of nonzeros in U (excl diag): 4 + number of entries stored in U (excl diag): 2 + factorization floating-point operations: 34 + number of nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 1.39754e-01 + max abs. value on diagonal of U: 1.00000e+00 + reciprocal condition number estimate: 1.40e-01 + +Scale factors applied via multiplication +Scale factors, Rs: dense vector, n = 5. + 0 : (0.0625) + 1 : (0.0155521) + 2 : (0.0177936) + 3 : (0.0555556) + 4 : (0.0151515) + dense vector OK + + +P: row permutation vector, n = 5. + 0 : 2 + 1 : 3 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +Q: column permutation vector, n = 5. + 0 : 3 + 1 : 2 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +L in Numeric object, in column-oriented compressed-pattern form: + Diagonal entries are all equal to 1.0 (not stored) + + column 0: length 0. + + column 1: length 2. + row 4 : (0.357698 + 0.00311042i) + row 3 : (0.272727 + 0.00454545i) + + column 2: add 1 entries. length 1. Start of Lchain. + row 4 : (0.204044 - 0.0895801i) + + column 3: length 1. + row 4 : (1.0818 - 0.0116951i) + + column 4: length 0. Start of Lchain. + + +U in Numeric object, in row-oriented compressed-pattern form: + Diagonal is stored separately. + + row 4: length 0. End of Uchain. + + row 3: length 1. End of Uchain. + col 4 : (0.151515 + 0.00454545i) + + row 2: length 1. + col 4 : (0.8125 + 0i) + + row 1: length 0. End of Uchain. + + row 1: length 0. + + row 0: length 2. + col 1 : (0.266904 - 0.00355872i) + col 4 : (0.124555 - 0.0177936i) + + +diagonal of U: dense vector, n = 5. + 0 : (0.533808 + 0.0533808i) + 1 : (1 + 0i) + 2 : (0.125 + 0.0625i) + 3 : (0.560606 + 0.00606061i) + 4 : (-0.329747 + 0.0696386i) + dense vector OK + + Numeric object: OK + + +UMFPACK V4.4 (Jan. 28, 2005), Info: + matrix entry defined as: double complex + 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: 5 + number of columns in matrix A: 5 + entries in matrix A: 12 + 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: 16 bytes + + strategy used: unsymmetric + ordering used: colamd on A + modify Q during factorization: yes + prefer diagonal pivoting: no + pivots with zero Markowitz cost: 2 + 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 3 + symmetry of nonzero pattern: 1.000000 + nz in S+S' (excl. diagonal): 4 + nz on diagonal of matrix S: 2 + fraction of nz on diagonal: 0.666667 + 2-by-2 pivoting to place large entries on diagonal: + # of small diagonal entries of S: 1 + # unmatched: 0 + symmetry of P2*S: 0.000000 + nz in P2*S+(P2*S)' (excl. diag.): 6 + nz on diagonal of P2*S: 3 + fraction of nz on diag of P2*S: 1.000000 + symbolic factorization defragmentations: 0 + symbolic memory usage (Units): 144 + symbolic memory usage (MBytes): 0.0 + Symbolic size (Units): 45 + 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)): 1.60000e+01 + maximum sum (abs (rows of A)): 6.60000e+01 + + symbolic/numeric factorization: upper bound actual % + variable-sized part of Numeric object: + initial size (Units) 84 79 94% + peak size (Units) 2542 2527 99% + final size (Units) 25 21 84% + Numeric final size (Units) 106 100 94% + Numeric final size (MBytes) 0.0 0.0 94% + peak memory usage (Units) 2737 2722 99% + peak memory usage (MBytes) 0.0 0.0 99% + numeric factorization flops 6.70000e+01 3.40000e+01 51% + nz in L (incl diagonal) 10 9 90% + nz in U (incl diagonal) 10 9 90% + nz in L+U (incl diagonal) 15 13 87% + largest front (# entries) 9 4 44% + largest # rows in front 3 2 67% + largest # columns in front 3 2 67% + + initial allocation ratio used: 0.7 + # of forced updates due to frontal growth: 0 + nz in L (incl diagonal), if none dropped 9 + nz in U (incl diagonal), if none dropped 9 + number of small entries dropped 0 + nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 1.40e-01 + max abs. value on diagonal of U: 1.00e+00 + estimate of reciprocal of condition number: 1.40e-01 + indices in compressed pattern: 2 + numerical values stored in Numeric object: 9 + 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: 5.23000e+02 + iterative refinement steps taken: 0 + iterative refinement steps attempted: 0 + sparse backward error omega1: 4.75e-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: 5.57000e+02 + total symbolic + numeric + solve CPU time: 0.00 + total symbolic+numeric+solve wall clock time: 0.00 + + +x (with completely modified A): dense vector, n = 5. + 0 : (7.56307 - 3.68974i) + 1 : (-0.831991 + 0.0627998i) + 2 : (0.166667 + 0i) + 3 : (-0.00206892 - 0.107735i) + 4 : (0.658245 + 0.0407649i) + dense vector OK + +maxnorm of residual: 5.92582e-15 + + +C (transpose of A): column-form matrix, n_row 5 n_col 5, nz = 12. + + column 0: start: 0 end: 1 entries: 2 + row 0 : (2 - 1i) + row 1 : (13 + 0i) + + column 1: start: 2 end: 4 entries: 3 + row 0 : (2 - 0.1i) + row 2 : (23 - 0.2i) + row 4 : (39 + 0i) + + column 2: start: 5 end: 7 entries: 3 + row 1 : (7 + 1i) + row 2 : (15 + 0.2i) + row 3 : (30 - 3i) + + column 3: start: 8 end: 8 entries: 1 + row 2 : (18 + 0i) + + column 4: start: 9 end: 11 entries: 3 + row 1 : (10 - 0.3i) + row 2 : (18 - 0.3i) + row 4 : (37 - 0.4i) + column-form matrix OK + + +Symbolic factorization of C: Symbolic object: + matrix to be factorized: + n_row: 5 n_col: 5 + number of entries: 12 + block size used for dense matrix kernels: 32 + strategy used: unsymmetric + ordering used: colamd on A + + performn column etree postorder: yes + prefer diagonal pivoting (attempt P=Q): no + variable-size part of Numeric object: + minimum initial size (Units): 85 (MBytes): 0.0 + estimated peak size (Units): 2543 (MBytes): 0.0 + estimated final size (Units): 26 (MBytes): 0.0 + symbolic factorization memory usage (Units): 144 (MBytes): 0.0 + frontal matrices / supercolumns: + number of frontal chains: 1 + number of frontal matrices: 1 + largest frontal matrix row dimension: 3 + largest frontal matrix column dimension: 3 + + Frontal chain: 0. Frontal matrices 0 to 0 + Largest frontal matrix in Frontal chain: 3-by-3 + Front: 0 pivot cols: 3 (pivot columns 0 to 2) + pivot row candidates: 2 to 4 + leftmost descendant: 0 + 1st new candidate row : 2 + parent: (none) + +Initial column permutation, Q1: permutation vector, n = 5. + 0 : 3 + 1 : 2 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +Initial row permutation, P1: permutation vector, n = 5. + 0 : 2 + 1 : 3 + 2 : 0 + 3 : 1 + 4 : 4 + permutation vector OK + + Symbolic object: OK + + +Get the contents of the Symbolic object for C: +(compare with umfpack_zi_report_symbolic output, above) +From the Symbolic object, C is of dimension 5-by-5 + with nz = 12, number of fronts = 1, + number of frontal matrix chains = 1 + +Pivot columns in each front, and parent of each front: + Front 0: parent front: -1 number of pivot cols: 3 + 0-th pivot column is column 3 in original matrix + 1-th pivot column is column 2 in original matrix + 2-th pivot column is column 0 in original matrix + +Note that the column ordering, above, will be refined +in the numeric factorization below. The assignment of pivot +columns to frontal matrices will always remain unchanged. + +Total number of pivot columns in frontal matrices: 3 + +Frontal matrix chains: + Frontal matrices 0 to 0 are factorized in a single + working array of size 3-by-3 + +Numeric factorization of C: Numeric object: + n_row: 5 n_col: 5 + relative pivot tolerance used: 0.1 + relative symmetric pivot tolerance used: 0.001 + matrix scaled: yes (divided each row by sum abs value in each row) + minimum sum (abs (rows of A)): 5.10000e+00 + maximum sum (abs (rows of A)): 7.64000e+01 + initial allocation parameter used: 0.7 + frontal matrix allocation parameter used: 0.5 + final total size of Numeric object (Units): 100 + final total size of Numeric object (MBytes): 0.0 + peak size of variable-size part (Units): 2528 + peak size of variable-size part (MBytes): 0.0 + largest actual frontal matrix size: 4 + memory defragmentations: 1 + memory reallocations: 1 + costly memory reallocations: 0 + entries in compressed pattern (L and U): 2 + number of nonzeros in L (excl diag): 3 + number of entries stored in L (excl diag): 2 + number of nonzeros in U (excl diag): 5 + number of entries stored in U (excl diag): 2 + factorization floating-point operations: 34 + number of nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 2.40964e-01 + max abs. value on diagonal of U: 9.13625e-01 + reciprocal condition number estimate: 2.64e-01 + +Scale factors applied via multiplication +Scale factors, Rs: dense vector, n = 5. + 0 : (0.196078) + 1 : (0.0319489) + 2 : (0.0133869) + 3 : (0.030303) + 4 : (0.013089) + dense vector OK + + +P: row permutation vector, n = 5. + 0 : 2 + 1 : 3 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +Q: column permutation vector, n = 5. + 0 : 3 + 1 : 2 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +L in Numeric object, in column-oriented compressed-pattern form: + Diagonal entries are all equal to 1.0 (not stored) + + column 0: length 0. + + column 1: length 1. + row 4 : (0.240091 + 0.0591529i) + + column 2: add 1 entries. length 1. Start of Lchain. + row 4 : (0.847284 + 0.423642i) + + column 3: length 1. + row 4 : (0.659838 - 0.0126577i) + + column 4: length 0. Start of Lchain. + + +U in Numeric object, in row-oriented compressed-pattern form: + Diagonal is stored separately. + + row 4: length 0. End of Uchain. + + row 3: length 1. End of Uchain. + col 4 : (0.510471 + 0i) + + row 2: length 1. + col 4 : (0.392157 - 0.0196078i) + + row 1: length 0. End of Uchain. + + row 1: length 0. + + row 0: length 3. + col 1 : (0.200803 + 0.00267738i) + col 3 : (0.240964 - 0.00401606i) + col 4 : (0.307898 - 0.00267738i) + + +diagonal of U: dense vector, n = 5. + 0 : (0.240964 + 0i) + 1 : (0.909091 - 0.0909091i) + 2 : (0.392157 - 0.196078i) + 3 : (0.484293 - 0.0052356i) + 4 : (-0.677403 - 0.143059i) + dense vector OK + + Numeric object: OK + + +L (lower triangular factor of C): row-form matrix, n_row 5 n_col 5, nz = 8. + + row 0: start: 0 end: 0 entries: 1 + column 0 : (1 + 0i) + + row 1: start: 1 end: 1 entries: 1 + column 1 : (1 + 0i) + + row 2: start: 2 end: 2 entries: 1 + column 2 : (1 + 0i) + + row 3: start: 3 end: 3 entries: 1 + column 3 : (1 + 0i) + + row 4: start: 4 end: 7 entries: 4 + column 1 : (0.240091 + 0.0591529i) + column 2 : (0.847284 + 0.423642i) + column 3 : (0.659838 - 0.0126577i) + column 4 : (1 + 0i) + row-form matrix OK + + +U (upper triangular factor of C): column-form matrix, n_row 5 n_col 5, nz = 10. + + column 0: start: 0 end: 0 entries: 1 + row 0 : (0.240964 + 0i) + + column 1: start: 1 end: 2 entries: 2 + row 0 : (0.200803 + 0.00267738i) + row 1 : (0.909091 - 0.0909091i) + + column 2: start: 3 end: 3 entries: 1 + row 2 : (0.392157 - 0.196078i) + + column 3: start: 4 end: 5 entries: 2 + row 0 : (0.240964 - 0.00401606i) + row 3 : (0.484293 - 0.0052356i) + + column 4: start: 6 end: 9 entries: 4 + row 0 : (0.307898 - 0.00267738i) + row 2 : (0.392157 - 0.0196078i) + row 3 : (0.510471 + 0i) + row 4 : (-0.677403 - 0.143059i) + column-form matrix OK + + +P: permutation vector, n = 5. + 0 : 2 + 1 : 3 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +Q: permutation vector, n = 5. + 0 : 3 + 1 : 2 + 2 : 0 + 3 : 4 + 4 : 1 + permutation vector OK + + +Scale factors: row i of A is to be multiplied by the ith scale factor +0: 0.196078 +1: 0.0319489 +2: 0.0133869 +3: 0.030303 +4: 0.013089 + +Converting L to triplet form, and printing it: + +L, in triplet form: triplet-form matrix, n_row = 5, n_col = 5 nz = 8. + 0 : 0 0 (1 + 0i) + 1 : 1 1 (1 + 0i) + 2 : 2 2 (1 + 0i) + 3 : 3 3 (1 + 0i) + 4 : 4 1 (0.240091 + 0.0591529i) + 5 : 4 2 (0.847284 + 0.423642i) + 6 : 4 3 (0.659838 - 0.0126577i) + 7 : 4 4 (1 + 0i) + triplet-form matrix OK + + +Saving numeric object: + +Freeing numeric object: + +Loading numeric object: + +Done loading numeric object + +UMFPACK V4.4 (Jan. 28, 2005), Info: + matrix entry defined as: double complex + 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: 5 + number of columns in matrix A: 5 + entries in matrix A: 12 + 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: 16 bytes + + strategy used: unsymmetric + ordering used: colamd on A + modify Q during factorization: yes + prefer diagonal pivoting: no + pivots with zero Markowitz cost: 2 + 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 3 + symmetry of nonzero pattern: 1.000000 + nz in S+S' (excl. diagonal): 4 + nz on diagonal of matrix S: 2 + fraction of nz on diagonal: 0.666667 + 2-by-2 pivoting to place large entries on diagonal: + # of small diagonal entries of S: 1 + # unmatched: 0 + symmetry of P2*S: 0.000000 + nz in P2*S+(P2*S)' (excl. diag.): 6 + nz on diagonal of P2*S: 3 + fraction of nz on diag of P2*S: 1.000000 + symbolic factorization defragmentations: 0 + symbolic memory usage (Units): 144 + symbolic memory usage (MBytes): 0.0 + Symbolic size (Units): 45 + 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)): 5.10000e+00 + maximum sum (abs (rows of A)): 7.64000e+01 + + symbolic/numeric factorization: upper bound actual % + variable-sized part of Numeric object: + initial size (Units) 85 80 94% + peak size (Units) 2543 2528 99% + final size (Units) 26 22 85% + Numeric final size (Units) 107 101 94% + Numeric final size (MBytes) 0.0 0.0 94% + peak memory usage (Units) 2738 2723 99% + peak memory usage (MBytes) 0.0 0.0 99% + numeric factorization flops 6.70000e+01 3.40000e+01 51% + nz in L (incl diagonal) 9 8 89% + nz in U (incl diagonal) 11 10 91% + nz in L+U (incl diagonal) 15 13 87% + largest front (# entries) 9 4 44% + largest # rows in front 3 2 67% + largest # columns in front 3 2 67% + + initial allocation ratio used: 0.7 + # of forced updates due to frontal growth: 0 + nz in L (incl diagonal), if none dropped 8 + nz in U (incl diagonal), if none dropped 10 + number of small entries dropped 0 + nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 2.41e-01 + max abs. value on diagonal of U: 9.14e-01 + estimate of reciprocal of condition number: 2.64e-01 + indices in compressed pattern: 2 + numerical values stored in Numeric object: 9 + 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: 4.80000e+02 + iterative refinement steps taken: 0 + iterative refinement steps attempted: 0 + sparse backward error omega1: 8.89e-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: 5.14000e+02 + total symbolic + numeric + solve CPU time: 0.00 + total symbolic+numeric+solve wall clock time: 0.00 + + +x (solution of C'x=b): dense vector, n = 5. + 0 : (7.56307 - 3.68974i) + 1 : (-0.831991 + 0.0627998i) + 2 : (0.166667 + 0i) + 3 : (-0.00206892 - 0.107735i) + 4 : (0.658245 + 0.0407649i) + dense vector OK + +maxnorm of residual: 5.6552e-15 + + +Solving C'x=b again, using umfpack_zi_wsolve instead: + +UMFPACK V4.4 (Jan. 28, 2005), Info: + matrix entry defined as: double complex + 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: 5 + number of columns in matrix A: 5 + entries in matrix A: 12 + 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: 16 bytes + + strategy used: unsymmetric + ordering used: colamd on A + modify Q during factorization: yes + prefer diagonal pivoting: no + pivots with zero Markowitz cost: 2 + 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 3 + symmetry of nonzero pattern: 1.000000 + nz in S+S' (excl. diagonal): 4 + nz on diagonal of matrix S: 2 + fraction of nz on diagonal: 0.666667 + 2-by-2 pivoting to place large entries on diagonal: + # of small diagonal entries of S: 1 + # unmatched: 0 + symmetry of P2*S: 0.000000 + nz in P2*S+(P2*S)' (excl. diag.): 6 + nz on diagonal of P2*S: 3 + fraction of nz on diag of P2*S: 1.000000 + symbolic factorization defragmentations: 0 + symbolic memory usage (Units): 144 + symbolic memory usage (MBytes): 0.0 + Symbolic size (Units): 45 + 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)): 5.10000e+00 + maximum sum (abs (rows of A)): 7.64000e+01 + + symbolic/numeric factorization: upper bound actual % + variable-sized part of Numeric object: + initial size (Units) 85 80 94% + peak size (Units) 2543 2528 99% + final size (Units) 26 22 85% + Numeric final size (Units) 107 101 94% + Numeric final size (MBytes) 0.0 0.0 94% + peak memory usage (Units) 2738 2723 99% + peak memory usage (MBytes) 0.0 0.0 99% + numeric factorization flops 6.70000e+01 3.40000e+01 51% + nz in L (incl diagonal) 9 8 89% + nz in U (incl diagonal) 11 10 91% + nz in L+U (incl diagonal) 15 13 87% + largest front (# entries) 9 4 44% + largest # rows in front 3 2 67% + largest # columns in front 3 2 67% + + initial allocation ratio used: 0.7 + # of forced updates due to frontal growth: 0 + nz in L (incl diagonal), if none dropped 8 + nz in U (incl diagonal), if none dropped 10 + number of small entries dropped 0 + nonzeros on diagonal of U: 5 + min abs. value on diagonal of U: 2.41e-01 + max abs. value on diagonal of U: 9.14e-01 + estimate of reciprocal of condition number: 2.64e-01 + indices in compressed pattern: 2 + numerical values stored in Numeric object: 9 + 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: 4.80000e+02 + iterative refinement steps taken: 0 + iterative refinement steps attempted: 0 + sparse backward error omega1: 8.89e-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: 5.14000e+02 + total symbolic + numeric + solve CPU time: 0.00 + total symbolic+numeric+solve wall clock time: 0.00 + + +x (solution of C'x=b): dense vector, n = 5. + 0 : (7.56307 - 3.68974i) + 1 : (-0.831991 + 0.0627998i) + 2 : (0.166667 + 0i) + 3 : (-0.00206892 - 0.107735i) + 4 : (0.658245 + 0.0407649i) + dense vector OK + +maxnorm of residual: 5.6552e-15 + + +umfpack_zi_demo complete. +Total time: 0.00 seconds (CPU time), 0.01 seconds (wallclock time)