diff --git a/fvn_sparse/UMFPACK/Demo/my_umfpack_di_demo.out b/fvn_sparse/UMFPACK/Demo/my_umfpack_di_demo.out deleted file mode 100644 index c32fe00..0000000 --- a/fvn_sparse/UMFPACK/Demo/my_umfpack_di_demo.out +++ /dev/null @@ -1,1523 +0,0 @@ - -UMFPACK V5.1 (May 31, 2007) demo: _di_ version - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - - -UMFPACK License: - - UMFPACK is available under alternate licenses, - contact T. Davis for details. - - Your use or distribution of UMFPACK or any modified version of - UMFPACK implies that you agree to this License. - - This library is free software; you can redistribute it and/or - modify it under the terms of the GNU Lesser General Public - License as published by the Free Software Foundation; either - version 2.1 of the License, or (at your option) any later version. - - This library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Lesser General Public License for more details. - - You should have received a copy of the GNU Lesser General Public - License along with this library; if not, write to the Free Software - Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 - USA - - Permission is hereby granted to use or copy this program under the - terms of the GNU LGPL, 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 this code or any modified - version of this 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. - -Availability: http://www.cise.ufl.edu/research/sparse/umfpack - -UMFPACK V5.1.0 (May 31, 2007): OK - -UMFPACK V5.1.0 (May 31, 2007), Control: - Matrix entry defined as: double - 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: Fortran BLAS. size of BLAS integer: 4 - 9: compiled for ANSI C - 10: CPU timer is POSIX times ( ) routine. - 11: compiled for normal operation (debugging disabled) - computer/operating system: Linux - size of int: 4 UF_long: 8 Int: 4 pointer: 8 double: 8 Entry: 8 (in bytes) - - -b: dense vector, n = 5. - 0 : (8) - 1 : (45) - 2 : (-3) - 3 : (3) - 4 : (19) - dense vector OK - - -A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12. - 0 : 0 0 (2) - 1 : 4 4 (1) - 2 : 1 0 (3) - 3 : 1 2 (4) - 4 : 2 1 (-1) - 5 : 2 2 (-3) - 6 : 0 1 (3) - 7 : 1 4 (6) - 8 : 2 3 (2) - 9 : 3 2 (1) - 10 : 4 1 (4) - 11 : 4 2 (2) - 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) - row 1 : (3) - - column 1: start: 2 end: 4 entries: 3 - row 0 : (3) - row 2 : (-1) - row 4 : (4) - - column 2: start: 5 end: 8 entries: 4 - row 1 : (4) - row 2 : (-3) - row 3 : (1) - row 4 : (2) - - column 3: start: 9 end: 9 entries: 1 - row 2 : (2) - - column 4: start: 10 end: 11 entries: 2 - row 1 : (6) - row 4 : (1) - 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): 80 (MBytes): 0.0 - estimated peak size (Units): 1301 (MBytes): 0.0 - estimated final size (Units): 15 (MBytes): 0.0 - symbolic factorization memory usage (Units): 151 (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)): 1.30000e+01 - initial allocation parameter used: 0.7 - frontal matrix allocation parameter used: 0.5 - final total size of Numeric object (Units): 87 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 1292 - 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: 6 - number of nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 1.42857e-01 - max abs. value on diagonal of U: 2.19231e+00 - reciprocal condition number estimate: 6.52e-02 - -Scale factors applied via multiplication -Scale factors, Rs: dense vector, n = 5. - 0 : (0.2) - 1 : (0.0769231) - 2 : (0.166667) - 3 : (1) - 4 : (0.142857) - 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 : (0.307692) - row 3 : (0.285714) - - column 2: add 1 entries. length 1. Start of Lchain. - row 4 : (0.576923) - - column 3: length 1. - row 4 : (3.23077) - - 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 : (0.571429) - - row 2: length 1. - col 4 : (0.6) - - row 1: length 0. End of Uchain. - - row 1: length 0. - - row 0: length 2. - col 1 : (-0.5) - col 4 : (-0.166667) - - -diagonal of U: dense vector, n = 5. - 0 : (0.333333) - 1 : (1) - 2 : (0.4) - 3 : (0.142857) - 4 : (-2.19231) - dense vector OK - - Numeric object: OK - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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: 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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)): 1.30000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 80 70 88% - peak size (Units) 1301 1292 99% - final size (Units) 15 13 87% - Numeric final size (Units) 92 88 96% - Numeric final size (MBytes) 0.0 0.0 96% - peak memory usage (Units) 1487 1478 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 1.43e-01 - max abs. value on diagonal of U: 2.19e+00 - estimate of reciprocal of condition number: 6.52e-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 - - solve flops: 1.19000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 1.18e-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: 1.25000e+02 - - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - -UMFPACK V5.1.0 (May 31, 2007): OK - - -x (solution of Ax=b): dense vector, n = 5. - 0 : (1) - 1 : (2) - 2 : (3) - 3 : (4) - 4 : (5) - dense vector OK - -maxnorm of residual: 1.06581e-14 - - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - -UMFPACK V5.1.0 (May 31, 2007): OK - -determinant: (1.14) * 10^(2) - -x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5. - 0 : (1) - 1 : (2) - 2 : (3) - 3 : (4) - 4 : (5) - dense vector OK - -maxnorm of residual: 1.06581e-14 - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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: 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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)): 1.30000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 80 70 88% - peak size (Units) 1301 1292 99% - final size (Units) 15 13 87% - Numeric final size (Units) 92 88 96% - Numeric final size (MBytes) 0.0 0.0 96% - peak memory usage (Units) 1487 1478 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 1.43e-01 - max abs. value on diagonal of U: 2.19e+00 - estimate of reciprocal of condition number: 6.52e-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 - - solve flops: 1.11000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 7.64e-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: 1.17000e+02 - - -x (solution of A'x=b): dense vector, n = 5. - 0 : (1.81579) - 1 : (1.45614) - 2 : (1.5) - 3 : (-24.8509) - 4 : (10.2632) - dense vector OK - -maxnorm of residual: 7.10543e-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) - row 1 : (3) - - column 1: start: 2 end: 4 entries: 3 - row 0 : (3) - row 2 : (-1) - row 4 : (4) - - column 2: start: 5 end: 8 entries: 4 - row 1 : (4) - row 2 : (-3) - row 3 : (1) - row 4 : (2) - - column 3: start: 9 end: 9 entries: 1 - row 2 : (2) - - column 4: start: 10 end: 11 entries: 2 - row 1 : (0) - row 4 : (1) - 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)): 7.00000e+00 - initial allocation parameter used: 0.7 - frontal matrix allocation parameter used: 0.5 - final total size of Numeric object (Units): 86 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 1292 - 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): 3 - number of entries stored in U (excl diag): 1 - factorization floating-point operations: 4 - number of nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 1.50000e-01 - max abs. value on diagonal of U: 1.00000e+00 - reciprocal condition number estimate: 1.50e-01 - -Scale factors applied via multiplication -Scale factors, Rs: dense vector, n = 5. - 0 : (0.2) - 1 : (0.142857) - 2 : (0.166667) - 3 : (1) - 4 : (0.142857) - dense vector OK - - -P: row permutation vector, n = 5. - 0 : 2 - 1 : 3 - 2 : 1 - 3 : 4 - 4 : 0 - permutation vector OK - - -Q: column permutation vector, n = 5. - 0 : 3 - 1 : 2 - 2 : 0 - 3 : 1 - 4 : 4 - 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 2 : (0.571429) - row 3 : (0.285714) - - column 2: add 1 entries. length 1. Start of Lchain. - row 4 : (0.933333) - - column 3: length 1. - row 4 : (1.05) - - 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 : (0.142857) - - row 2: length 0. End of Uchain. - - row 1: length 0. End of Uchain. - - row 1: length 0. - - row 0: length 2. - col 1 : (-0.5) - col 3 : (-0.166667) - - -diagonal of U: dense vector, n = 5. - 0 : (0.333333) - 1 : (1) - 2 : (0.428571) - 3 : (0.571429) - 4 : (-0.15) - dense vector OK - - Numeric object: OK - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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: 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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)): 7.00000e+00 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 80 70 88% - peak size (Units) 1301 1292 99% - final size (Units) 15 12 80% - Numeric final size (Units) 92 87 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 1487 1478 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 4.00000e+00 31% - nz in L (incl diagonal) 10 9 90% - nz in U (incl diagonal) 10 8 80% - 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 9 - nz in U (incl diagonal), if none dropped 8 - number of small entries dropped 0 - nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 1.50e-01 - max abs. value on diagonal of U: 1.00e+00 - estimate of reciprocal of condition number: 1.50e-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 - - solve flops: 1.17000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 7.89e-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: 1.21000e+02 - - -x (with modified A): dense vector, n = 5. - 0 : (11) - 1 : (-4.66667) - 2 : (3) - 3 : (0.666667) - 4 : (31.6667) - dense vector OK - -maxnorm of residual: 7.10543e-15 - -changing A (0,0) from 2 to 2 -changing A (1,0) from 3 to 2 -changing A (0,1) from 3 to 13 -changing A (2,1) from -1 to 7 -changing A (4,1) from 4 to 10 -changing A (1,2) from 4 to 23 -changing A (2,2) from -3 to 15 -changing A (3,2) from 1 to 18 -changing A (4,2) from 2 to 18 -changing A (2,3) from 2 to 30 -changing A (1,4) from 0 to 39 -changing 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) - row 1 : (2) - - column 1: start: 2 end: 4 entries: 3 - row 0 : (13) - row 2 : (7) - row 4 : (10) - - column 2: start: 5 end: 8 entries: 4 - row 1 : (23) - row 2 : (15) - row 3 : (18) - row 4 : (18) - - column 3: start: 9 end: 9 entries: 1 - row 2 : (30) - - column 4: start: 10 end: 11 entries: 2 - row 1 : (39) - row 4 : (37) - 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)): 1.50000e+01 - maximum sum (abs (rows of A)): 6.50000e+01 - initial allocation parameter used: 0.7 - frontal matrix allocation parameter used: 0.5 - final total size of Numeric object (Units): 87 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 1292 - 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: 6 - number of nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 1.33333e-01 - max abs. value on diagonal of U: 1.00000e+00 - reciprocal condition number estimate: 1.33e-01 - -Scale factors applied via multiplication -Scale factors, Rs: dense vector, n = 5. - 0 : (0.0666667) - 1 : (0.015625) - 2 : (0.0192308) - 3 : (0.0555556) - 4 : (0.0153846) - 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 : (0.359375) - row 3 : (0.276923) - - column 2: add 1 entries. length 1. Start of Lchain. - row 4 : (0.234375) - - column 3: length 1. - row 4 : (1.07052) - - 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 : (0.153846) - - row 2: length 1. - col 4 : (0.866667) - - row 1: length 0. End of Uchain. - - row 1: length 0. - - row 0: length 2. - col 1 : (0.288462) - col 4 : (0.134615) - - -diagonal of U: dense vector, n = 5. - 0 : (0.576923) - 1 : (1) - 2 : (0.133333) - 3 : (0.569231) - 4 : (-0.367821) - dense vector OK - - Numeric object: OK - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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: 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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)): 1.50000e+01 - maximum sum (abs (rows of A)): 6.50000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 80 70 88% - peak size (Units) 1301 1292 99% - final size (Units) 15 13 87% - Numeric final size (Units) 92 88 96% - Numeric final size (MBytes) 0.0 0.0 96% - peak memory usage (Units) 1487 1478 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 1.33e-01 - max abs. value on diagonal of U: 1.00e+00 - estimate of reciprocal of condition number: 1.33e-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 - - solve flops: 1.19000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 1.04e-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: 1.25000e+02 - - -x (with completely modified A): dense vector, n = 5. - 0 : (8.50124) - 1 : (-0.692499) - 2 : (0.166667) - 3 : (-0.0217502) - 4 : (0.619594) - dense vector OK - -maxnorm of residual: 3.55271e-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) - row 1 : (13) - - column 1: start: 2 end: 4 entries: 3 - row 0 : (2) - row 2 : (23) - row 4 : (39) - - column 2: start: 5 end: 7 entries: 3 - row 1 : (7) - row 2 : (15) - row 3 : (30) - - column 3: start: 8 end: 8 entries: 1 - row 2 : (18) - - column 4: start: 9 end: 11 entries: 3 - row 1 : (10) - row 2 : (18) - row 4 : (37) - 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): 81 (MBytes): 0.0 - estimated peak size (Units): 1302 (MBytes): 0.0 - estimated final size (Units): 16 (MBytes): 0.0 - symbolic factorization memory usage (Units): 151 (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_di_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)): 4.00000e+00 - maximum sum (abs (rows of A)): 7.60000e+01 - initial allocation parameter used: 0.7 - frontal matrix allocation parameter used: 0.5 - final total size of Numeric object (Units): 88 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 1293 - 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: 6 - number of nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 2.43243e-01 - max abs. value on diagonal of U: 1.00000e+00 - reciprocal condition number estimate: 2.43e-01 - -Scale factors applied via multiplication -Scale factors, Rs: dense vector, n = 5. - 0 : (0.25) - 1 : (0.0333333) - 2 : (0.0135135) - 3 : (0.0333333) - 4 : (0.0131579) - 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 : (0.233333) - - column 2: add 1 entries. length 1. Start of Lchain. - row 4 : (0.866667) - - column 3: length 1. - row 4 : (0.684685) - - 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 : (0.513158) - - row 2: length 1. - col 4 : (0.5) - - row 1: length 0. End of Uchain. - - row 1: length 0. - - row 0: length 3. - col 1 : (0.202703) - col 3 : (0.243243) - col 4 : (0.310811) - - -diagonal of U: dense vector, n = 5. - 0 : (0.243243) - 1 : (1) - 2 : (0.5) - 3 : (0.486842) - 4 : (-0.784685) - 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) - - row 1: start: 1 end: 1 entries: 1 - column 1 : (1) - - row 2: start: 2 end: 2 entries: 1 - column 2 : (1) - - row 3: start: 3 end: 3 entries: 1 - column 3 : (1) - - row 4: start: 4 end: 7 entries: 4 - column 1 : (0.233333) - column 2 : (0.866667) - column 3 : (0.684685) - column 4 : (1) - 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 : (0.243243) - - column 1: start: 1 end: 2 entries: 2 - row 0 : (0.202703) - row 1 : (1) - - column 2: start: 3 end: 3 entries: 1 - row 2 : (0.5) - - column 3: start: 4 end: 5 entries: 2 - row 0 : (0.243243) - row 3 : (0.486842) - - column 4: start: 6 end: 9 entries: 4 - row 0 : (0.310811) - row 2 : (0.5) - row 3 : (0.513158) - row 4 : (-0.784685) - 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: 0.25 -1: 0.0333333 -2: 0.0135135 -3: 0.0333333 -4: 0.0131579 - -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) - 1 : 1 1 (1) - 2 : 2 2 (1) - 3 : 3 3 (1) - 4 : 4 1 (0.233333) - 5 : 4 2 (0.866667) - 6 : 4 3 (0.684685) - 7 : 4 4 (1) - triplet-form matrix OK - - -Saving numeric object: - -Freeing numeric object: - -Loading numeric object: - -Done loading numeric object -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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: 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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)): 7.60000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 81 71 88% - peak size (Units) 1302 1293 99% - final size (Units) 16 14 88% - Numeric final size (Units) 93 89 96% - Numeric final size (MBytes) 0.0 0.0 96% - peak memory usage (Units) 1488 1479 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 2.43e-01 - max abs. value on diagonal of U: 1.00e+00 - estimate of reciprocal of condition number: 2.43e-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 - - solve flops: 1.11000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 8.07e-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: 1.17000e+02 - - -x (solution of C'x=b): dense vector, n = 5. - 0 : (8.50124) - 1 : (-0.692499) - 2 : (0.166667) - 3 : (-0.0217502) - 4 : (0.619594) - dense vector OK - -maxnorm of residual: 3.55271e-15 - - -Solving C'x=b again, using umfpack_di_wsolve instead: -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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: 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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)): 7.60000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 81 71 88% - peak size (Units) 1302 1293 99% - final size (Units) 16 14 88% - Numeric final size (Units) 93 89 96% - Numeric final size (MBytes) 0.0 0.0 96% - peak memory usage (Units) 1488 1479 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 2.43e-01 - max abs. value on diagonal of U: 1.00e+00 - estimate of reciprocal of condition number: 2.43e-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 - - solve flops: 1.11000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 8.07e-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: 1.17000e+02 - - -x (solution of C'x=b): dense vector, n = 5. - 0 : (8.50124) - 1 : (-0.692499) - 2 : (0.166667) - 3 : (-0.0217502) - 4 : (0.619594) - dense vector OK - -maxnorm of residual: 3.55271e-15 - - -umfpack_di_demo complete. -Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time) diff --git a/fvn_sparse/UMFPACK/Demo/my_umfpack_dl_demo.out b/fvn_sparse/UMFPACK/Demo/my_umfpack_dl_demo.out deleted file mode 100644 index 07803ca..0000000 --- a/fvn_sparse/UMFPACK/Demo/my_umfpack_dl_demo.out +++ /dev/null @@ -1,1523 +0,0 @@ - -UMFPACK V5.1 (May 31, 2007) demo: _dl_ version - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - - -UMFPACK License: - - UMFPACK is available under alternate licenses, - contact T. Davis for details. - - Your use or distribution of UMFPACK or any modified version of - UMFPACK implies that you agree to this License. - - This library is free software; you can redistribute it and/or - modify it under the terms of the GNU Lesser General Public - License as published by the Free Software Foundation; either - version 2.1 of the License, or (at your option) any later version. - - This library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Lesser General Public License for more details. - - You should have received a copy of the GNU Lesser General Public - License along with this library; if not, write to the Free Software - Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 - USA - - Permission is hereby granted to use or copy this program under the - terms of the GNU LGPL, 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 this code or any modified - version of this 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. - -Availability: http://www.cise.ufl.edu/research/sparse/umfpack - -UMFPACK V5.1.0 (May 31, 2007): OK - -UMFPACK V5.1.0 (May 31, 2007), Control: - Matrix entry defined as: double - Int (generic integer) defined as: UF_long - - 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: Fortran BLAS. size of BLAS integer: 4 - 9: compiled for ANSI C - 10: CPU timer is POSIX times ( ) routine. - 11: compiled for normal operation (debugging disabled) - computer/operating system: Linux - size of int: 4 UF_long: 8 Int: 8 pointer: 8 double: 8 Entry: 8 (in bytes) - - -b: dense vector, n = 5. - 0 : (8) - 1 : (45) - 2 : (-3) - 3 : (3) - 4 : (19) - dense vector OK - - -A: triplet-form matrix, n_row = 5, n_col = 5 nz = 12. - 0 : 0 0 (2) - 1 : 4 4 (1) - 2 : 1 0 (3) - 3 : 1 2 (4) - 4 : 2 1 (-1) - 5 : 2 2 (-3) - 6 : 0 1 (3) - 7 : 1 4 (6) - 8 : 2 3 (2) - 9 : 3 2 (1) - 10 : 4 1 (4) - 11 : 4 2 (2) - 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) - row 1 : (3) - - column 1: start: 2 end: 4 entries: 3 - row 0 : (3) - row 2 : (-1) - row 4 : (4) - - column 2: start: 5 end: 8 entries: 4 - row 1 : (4) - row 2 : (-3) - row 3 : (1) - row 4 : (2) - - column 3: start: 9 end: 9 entries: 1 - row 2 : (2) - - column 4: start: 10 end: 11 entries: 2 - row 1 : (6) - row 4 : (1) - 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): 69 (MBytes): 0.0 - estimated peak size (Units): 681 (MBytes): 0.0 - estimated final size (Units): 10 (MBytes): 0.0 - symbolic factorization memory usage (Units): 138 (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)): 1.30000e+01 - initial allocation parameter used: 0.7 - frontal matrix allocation parameter used: 0.5 - final total size of Numeric object (Units): 67 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 675 - 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: 6 - number of nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 1.42857e-01 - max abs. value on diagonal of U: 2.19231e+00 - reciprocal condition number estimate: 6.52e-02 - -Scale factors applied via multiplication -Scale factors, Rs: dense vector, n = 5. - 0 : (0.2) - 1 : (0.0769231) - 2 : (0.166667) - 3 : (1) - 4 : (0.142857) - 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 : (0.307692) - row 3 : (0.285714) - - column 2: add 1 entries. length 1. Start of Lchain. - row 4 : (0.576923) - - column 3: length 1. - row 4 : (3.23077) - - 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 : (0.571429) - - row 2: length 1. - col 4 : (0.6) - - row 1: length 0. End of Uchain. - - row 1: length 0. - - row 0: length 2. - col 1 : (-0.5) - col 4 : (-0.166667) - - -diagonal of U: dense vector, n = 5. - 0 : (0.333333) - 1 : (1) - 2 : (0.4) - 3 : (0.142857) - 4 : (-2.19231) - dense vector OK - - Numeric object: OK - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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: 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 1.30000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 69 64 93% - peak size (Units) 681 675 99% - final size (Units) 10 11 110% - Numeric final size (Units) 69 68 99% - Numeric final size (MBytes) 0.0 0.0 99% - peak memory usage (Units) 832 826 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 1.43e-01 - max abs. value on diagonal of U: 2.19e+00 - estimate of reciprocal of condition number: 6.52e-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 - - solve flops: 1.19000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 1.18e-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: 1.25000e+02 - - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - -UMFPACK V5.1.0 (May 31, 2007): OK - - -x (solution of Ax=b): dense vector, n = 5. - 0 : (1) - 1 : (2) - 2 : (3) - 3 : (4) - 4 : (5) - dense vector OK - -maxnorm of residual: 1.06581e-14 - - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - -UMFPACK V5.1.0 (May 31, 2007): OK - -determinant: (1.14) * 10^(2) - -x (solution of Ax=b, solve is split into 3 steps): dense vector, n = 5. - 0 : (1) - 1 : (2) - 2 : (3) - 3 : (4) - 4 : (5) - dense vector OK - -maxnorm of residual: 1.06581e-14 - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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: 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 1.30000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 69 64 93% - peak size (Units) 681 675 99% - final size (Units) 10 11 110% - Numeric final size (Units) 69 68 99% - Numeric final size (MBytes) 0.0 0.0 99% - peak memory usage (Units) 832 826 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 1.43e-01 - max abs. value on diagonal of U: 2.19e+00 - estimate of reciprocal of condition number: 6.52e-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 - - solve flops: 1.11000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 7.64e-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: 1.17000e+02 - - -x (solution of A'x=b): dense vector, n = 5. - 0 : (1.81579) - 1 : (1.45614) - 2 : (1.5) - 3 : (-24.8509) - 4 : (10.2632) - dense vector OK - -maxnorm of residual: 7.10543e-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) - row 1 : (3) - - column 1: start: 2 end: 4 entries: 3 - row 0 : (3) - row 2 : (-1) - row 4 : (4) - - column 2: start: 5 end: 8 entries: 4 - row 1 : (4) - row 2 : (-3) - row 3 : (1) - row 4 : (2) - - column 3: start: 9 end: 9 entries: 1 - row 2 : (2) - - column 4: start: 10 end: 11 entries: 2 - row 1 : (0) - row 4 : (1) - 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)): 7.00000e+00 - initial allocation parameter used: 0.7 - frontal matrix allocation parameter used: 0.5 - final total size of Numeric object (Units): 66 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 675 - 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): 3 - number of entries stored in U (excl diag): 1 - factorization floating-point operations: 4 - number of nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 1.50000e-01 - max abs. value on diagonal of U: 1.00000e+00 - reciprocal condition number estimate: 1.50e-01 - -Scale factors applied via multiplication -Scale factors, Rs: dense vector, n = 5. - 0 : (0.2) - 1 : (0.142857) - 2 : (0.166667) - 3 : (1) - 4 : (0.142857) - dense vector OK - - -P: row permutation vector, n = 5. - 0 : 2 - 1 : 3 - 2 : 1 - 3 : 4 - 4 : 0 - permutation vector OK - - -Q: column permutation vector, n = 5. - 0 : 3 - 1 : 2 - 2 : 0 - 3 : 1 - 4 : 4 - 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 2 : (0.571429) - row 3 : (0.285714) - - column 2: add 1 entries. length 1. Start of Lchain. - row 4 : (0.933333) - - column 3: length 1. - row 4 : (1.05) - - 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 : (0.142857) - - row 2: length 0. End of Uchain. - - row 1: length 0. End of Uchain. - - row 1: length 0. - - row 0: length 2. - col 1 : (-0.5) - col 3 : (-0.166667) - - -diagonal of U: dense vector, n = 5. - 0 : (0.333333) - 1 : (1) - 2 : (0.428571) - 3 : (0.571429) - 4 : (-0.15) - dense vector OK - - Numeric object: OK - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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: 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 7.00000e+00 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 69 64 93% - peak size (Units) 681 675 99% - final size (Units) 10 10 100% - Numeric final size (Units) 69 67 97% - Numeric final size (MBytes) 0.0 0.0 97% - peak memory usage (Units) 832 826 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 4.00000e+00 31% - nz in L (incl diagonal) 10 9 90% - nz in U (incl diagonal) 10 8 80% - 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 9 - nz in U (incl diagonal), if none dropped 8 - number of small entries dropped 0 - nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 1.50e-01 - max abs. value on diagonal of U: 1.00e+00 - estimate of reciprocal of condition number: 1.50e-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 - - solve flops: 1.17000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 7.89e-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: 1.21000e+02 - - -x (with modified A): dense vector, n = 5. - 0 : (11) - 1 : (-4.66667) - 2 : (3) - 3 : (0.666667) - 4 : (31.6667) - dense vector OK - -maxnorm of residual: 7.10543e-15 - -changing A (0,0) from 2 to 2 -changing A (1,0) from 3 to 2 -changing A (0,1) from 3 to 13 -changing A (2,1) from -1 to 7 -changing A (4,1) from 4 to 10 -changing A (1,2) from 4 to 23 -changing A (2,2) from -3 to 15 -changing A (3,2) from 1 to 18 -changing A (4,2) from 2 to 18 -changing A (2,3) from 2 to 30 -changing A (1,4) from 0 to 39 -changing 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) - row 1 : (2) - - column 1: start: 2 end: 4 entries: 3 - row 0 : (13) - row 2 : (7) - row 4 : (10) - - column 2: start: 5 end: 8 entries: 4 - row 1 : (23) - row 2 : (15) - row 3 : (18) - row 4 : (18) - - column 3: start: 9 end: 9 entries: 1 - row 2 : (30) - - column 4: start: 10 end: 11 entries: 2 - row 1 : (39) - row 4 : (37) - 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)): 1.50000e+01 - maximum sum (abs (rows of A)): 6.50000e+01 - initial allocation parameter used: 0.7 - frontal matrix allocation parameter used: 0.5 - final total size of Numeric object (Units): 67 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 675 - 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: 6 - number of nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 1.33333e-01 - max abs. value on diagonal of U: 1.00000e+00 - reciprocal condition number estimate: 1.33e-01 - -Scale factors applied via multiplication -Scale factors, Rs: dense vector, n = 5. - 0 : (0.0666667) - 1 : (0.015625) - 2 : (0.0192308) - 3 : (0.0555556) - 4 : (0.0153846) - 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 : (0.359375) - row 3 : (0.276923) - - column 2: add 1 entries. length 1. Start of Lchain. - row 4 : (0.234375) - - column 3: length 1. - row 4 : (1.07052) - - 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 : (0.153846) - - row 2: length 1. - col 4 : (0.866667) - - row 1: length 0. End of Uchain. - - row 1: length 0. - - row 0: length 2. - col 1 : (0.288462) - col 4 : (0.134615) - - -diagonal of U: dense vector, n = 5. - 0 : (0.576923) - 1 : (1) - 2 : (0.133333) - 3 : (0.569231) - 4 : (-0.367821) - dense vector OK - - Numeric object: OK - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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: 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 1.50000e+01 - maximum sum (abs (rows of A)): 6.50000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 69 64 93% - peak size (Units) 681 675 99% - final size (Units) 10 11 110% - Numeric final size (Units) 69 68 99% - Numeric final size (MBytes) 0.0 0.0 99% - peak memory usage (Units) 832 826 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 1.33e-01 - max abs. value on diagonal of U: 1.00e+00 - estimate of reciprocal of condition number: 1.33e-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 - - solve flops: 1.19000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 1.04e-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: 1.25000e+02 - - -x (with completely modified A): dense vector, n = 5. - 0 : (8.50124) - 1 : (-0.692499) - 2 : (0.166667) - 3 : (-0.0217502) - 4 : (0.619594) - dense vector OK - -maxnorm of residual: 3.55271e-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) - row 1 : (13) - - column 1: start: 2 end: 4 entries: 3 - row 0 : (2) - row 2 : (23) - row 4 : (39) - - column 2: start: 5 end: 7 entries: 3 - row 1 : (7) - row 2 : (15) - row 3 : (30) - - column 3: start: 8 end: 8 entries: 1 - row 2 : (18) - - column 4: start: 9 end: 11 entries: 3 - row 1 : (10) - row 2 : (18) - row 4 : (37) - 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): 71 (MBytes): 0.0 - estimated peak size (Units): 683 (MBytes): 0.0 - estimated final size (Units): 12 (MBytes): 0.0 - symbolic factorization memory usage (Units): 138 (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_dl_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)): 4.00000e+00 - maximum sum (abs (rows of A)): 7.60000e+01 - initial allocation parameter used: 0.7 - frontal matrix allocation parameter used: 0.5 - final total size of Numeric object (Units): 69 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 677 - 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: 6 - number of nonzeros on diagonal of U: 5 - min abs. value on diagonal of U: 2.43243e-01 - max abs. value on diagonal of U: 1.00000e+00 - reciprocal condition number estimate: 2.43e-01 - -Scale factors applied via multiplication -Scale factors, Rs: dense vector, n = 5. - 0 : (0.25) - 1 : (0.0333333) - 2 : (0.0135135) - 3 : (0.0333333) - 4 : (0.0131579) - 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 : (0.233333) - - column 2: add 1 entries. length 1. Start of Lchain. - row 4 : (0.866667) - - column 3: length 1. - row 4 : (0.684685) - - 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 : (0.513158) - - row 2: length 1. - col 4 : (0.5) - - row 1: length 0. End of Uchain. - - row 1: length 0. - - row 0: length 3. - col 1 : (0.202703) - col 3 : (0.243243) - col 4 : (0.310811) - - -diagonal of U: dense vector, n = 5. - 0 : (0.243243) - 1 : (1) - 2 : (0.5) - 3 : (0.486842) - 4 : (-0.784685) - 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) - - row 1: start: 1 end: 1 entries: 1 - column 1 : (1) - - row 2: start: 2 end: 2 entries: 1 - column 2 : (1) - - row 3: start: 3 end: 3 entries: 1 - column 3 : (1) - - row 4: start: 4 end: 7 entries: 4 - column 1 : (0.233333) - column 2 : (0.866667) - column 3 : (0.684685) - column 4 : (1) - 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 : (0.243243) - - column 1: start: 1 end: 2 entries: 2 - row 0 : (0.202703) - row 1 : (1) - - column 2: start: 3 end: 3 entries: 1 - row 2 : (0.5) - - column 3: start: 4 end: 5 entries: 2 - row 0 : (0.243243) - row 3 : (0.486842) - - column 4: start: 6 end: 9 entries: 4 - row 0 : (0.310811) - row 2 : (0.5) - row 3 : (0.513158) - row 4 : (-0.784685) - 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: 0.25 -1: 0.0333333 -2: 0.0135135 -3: 0.0333333 -4: 0.0131579 - -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) - 1 : 1 1 (1) - 2 : 2 2 (1) - 3 : 3 3 (1) - 4 : 4 1 (0.233333) - 5 : 4 2 (0.866667) - 6 : 4 3 (0.684685) - 7 : 4 4 (1) - triplet-form matrix OK - - -Saving numeric object: - -Freeing numeric object: - -Loading numeric object: - -Done loading numeric object -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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: 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 7.60000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 71 66 93% - peak size (Units) 683 677 99% - final size (Units) 12 13 108% - Numeric final size (Units) 71 70 99% - Numeric final size (MBytes) 0.0 0.0 99% - peak memory usage (Units) 834 828 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 2.43e-01 - max abs. value on diagonal of U: 1.00e+00 - estimate of reciprocal of condition number: 2.43e-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 - - solve flops: 1.11000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 8.07e-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: 1.17000e+02 - - -x (solution of C'x=b): dense vector, n = 5. - 0 : (8.50124) - 1 : (-0.692499) - 2 : (0.166667) - 3 : (-0.0217502) - 4 : (0.619594) - dense vector OK - -maxnorm of residual: 3.55271e-15 - - -Solving C'x=b again, using umfpack_dl_wsolve instead: -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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: 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 7.60000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 71 66 93% - peak size (Units) 683 677 99% - final size (Units) 12 13 108% - Numeric final size (Units) 71 70 99% - Numeric final size (MBytes) 0.0 0.0 99% - peak memory usage (Units) 834 828 99% - peak memory usage (MBytes) 0.0 0.0 99% - numeric factorization flops 1.30000e+01 6.00000e+00 46% - 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: 2.43e-01 - max abs. value on diagonal of U: 1.00e+00 - estimate of reciprocal of condition number: 2.43e-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 - - solve flops: 1.11000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 8.07e-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: 1.17000e+02 - - -x (solution of C'x=b): dense vector, n = 5. - 0 : (8.50124) - 1 : (-0.692499) - 2 : (0.166667) - 3 : (-0.0217502) - 4 : (0.619594) - dense vector OK - -maxnorm of residual: 3.55271e-15 - - -umfpack_dl_demo complete. -Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time) diff --git a/fvn_sparse/UMFPACK/Demo/my_umfpack_zi_demo.out b/fvn_sparse/UMFPACK/Demo/my_umfpack_zi_demo.out deleted file mode 100644 index f74d49b..0000000 --- a/fvn_sparse/UMFPACK/Demo/my_umfpack_zi_demo.out +++ /dev/null @@ -1,1523 +0,0 @@ - -UMFPACK V5.1 (May 31, 2007) demo: _zi_ version - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - - -UMFPACK License: - - UMFPACK is available under alternate licenses, - contact T. Davis for details. - - Your use or distribution of UMFPACK or any modified version of - UMFPACK implies that you agree to this License. - - This library is free software; you can redistribute it and/or - modify it under the terms of the GNU Lesser General Public - License as published by the Free Software Foundation; either - version 2.1 of the License, or (at your option) any later version. - - This library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Lesser General Public License for more details. - - You should have received a copy of the GNU Lesser General Public - License along with this library; if not, write to the Free Software - Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 - USA - - Permission is hereby granted to use or copy this program under the - terms of the GNU LGPL, 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 this code or any modified - version of this 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. - -Availability: http://www.cise.ufl.edu/research/sparse/umfpack - -UMFPACK V5.1.0 (May 31, 2007): OK - -UMFPACK V5.1.0 (May 31, 2007), 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: Fortran BLAS. size of BLAS integer: 4 - 9: compiled for ANSI C - 10: CPU timer is POSIX times ( ) routine. - 11: compiled for normal operation (debugging disabled) - computer/operating system: Linux - size of int: 4 UF_long: 8 Int: 4 pointer: 8 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): 90 (MBytes): 0.0 - estimated peak size (Units): 2542 (MBytes): 0.0 - estimated final size (Units): 25 (MBytes): 0.0 - symbolic factorization memory usage (Units): 151 (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): 106 - 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 V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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) 90 80 89% - peak size (Units) 2542 2527 99% - final size (Units) 25 21 84% - Numeric final size (Units) 113 107 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 2751 2736 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 - - solve flops: 1.02800e+03 - iterative refinement steps taken: 1 - iterative refinement steps attempted: 1 - sparse backward error omega1: 5.28e-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: 1.06200e+03 - - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - -UMFPACK V5.1.0 (May 31, 2007): 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: 1.77636e-15 - - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - -UMFPACK V5.1.0 (May 31, 2007): 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: 1.77636e-14 - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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) 90 80 89% - peak size (Units) 2542 2527 99% - final size (Units) 25 21 84% - Numeric final size (Units) 113 107 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 2751 2736 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 - - solve flops: 4.80000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 7.82e-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 - - -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: 4.52416e-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): 104 - 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 V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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) 90 80 89% - peak size (Units) 2542 2527 99% - final size (Units) 25 19 76% - Numeric final size (Units) 113 105 93% - Numeric final size (MBytes) 0.0 0.0 93% - peak memory usage (Units) 2751 2736 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 - - solve flops: 5.15000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 6.01e-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: 5.32000e+02 - - -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: 4.66294e-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): 106 - 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 V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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) 90 80 89% - peak size (Units) 2542 2527 99% - final size (Units) 25 21 84% - Numeric final size (Units) 113 107 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 2751 2736 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 - - solve flops: 5.23000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 8.05e-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 - - -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: 9.10383e-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): 91 (MBytes): 0.0 - estimated peak size (Units): 2543 (MBytes): 0.0 - estimated final size (Units): 26 (MBytes): 0.0 - symbolic factorization memory usage (Units): 151 (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): 107 - 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 V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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) 91 81 89% - peak size (Units) 2543 2528 99% - final size (Units) 26 22 85% - Numeric final size (Units) 114 108 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 2752 2737 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 - - solve flops: 4.80000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 9.42e-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 - - -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: 4.88498e-15 - - -Solving C'x=b again, using umfpack_zi_wsolve instead: -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: int - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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 UF_long: 8 bytes - size of pointer: 8 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): 151 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 52 - 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) 91 81 89% - peak size (Units) 2543 2528 99% - final size (Units) 26 22 85% - Numeric final size (Units) 114 108 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 2752 2737 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 - - solve flops: 4.80000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 9.42e-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 - - -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: 4.88498e-15 - - -umfpack_zi_demo complete. -Total time: 0.00 seconds (CPU time), 0.00 seconds (wallclock time) diff --git a/fvn_sparse/UMFPACK/Demo/my_umfpack_zl_demo.out b/fvn_sparse/UMFPACK/Demo/my_umfpack_zl_demo.out deleted file mode 100644 index 4dd1e55..0000000 --- a/fvn_sparse/UMFPACK/Demo/my_umfpack_zl_demo.out +++ /dev/null @@ -1,1523 +0,0 @@ - -UMFPACK V5.1 (May 31, 2007) demo: _zl_ version - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - - -UMFPACK License: - - UMFPACK is available under alternate licenses, - contact T. Davis for details. - - Your use or distribution of UMFPACK or any modified version of - UMFPACK implies that you agree to this License. - - This library is free software; you can redistribute it and/or - modify it under the terms of the GNU Lesser General Public - License as published by the Free Software Foundation; either - version 2.1 of the License, or (at your option) any later version. - - This library is distributed in the hope that it will be useful, - but WITHOUT ANY WARRANTY; without even the implied warranty of - MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU - Lesser General Public License for more details. - - You should have received a copy of the GNU Lesser General Public - License along with this library; if not, write to the Free Software - Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 - USA - - Permission is hereby granted to use or copy this program under the - terms of the GNU LGPL, 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 this code or any modified - version of this 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. - -Availability: http://www.cise.ufl.edu/research/sparse/umfpack - -UMFPACK V5.1.0 (May 31, 2007): OK - -UMFPACK V5.1.0 (May 31, 2007), Control: - Matrix entry defined as: double complex - Int (generic integer) defined as: UF_long - - 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: Fortran BLAS. size of BLAS integer: 4 - 9: compiled for ANSI C - 10: CPU timer is POSIX times ( ) routine. - 11: compiled for normal operation (debugging disabled) - computer/operating system: Linux - size of int: 4 UF_long: 8 Int: 8 pointer: 8 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): 74 (MBytes): 0.0 - estimated peak size (Units): 1301 (MBytes): 0.0 - estimated final size (Units): 15 (MBytes): 0.0 - symbolic factorization memory usage (Units): 138 (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): 74 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 1292 - 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 V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 1.93000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 74 69 93% - peak size (Units) 1301 1292 99% - final size (Units) 15 13 87% - Numeric final size (Units) 79 75 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 1463 1454 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 - - solve flops: 1.02800e+03 - iterative refinement steps taken: 1 - iterative refinement steps attempted: 1 - sparse backward error omega1: 5.28e-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: 1.06200e+03 - - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - -UMFPACK V5.1.0 (May 31, 2007): 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: 1.77636e-15 - - -UMFPACK: Copyright (c) 2005-2006 by Timothy A. Davis. All Rights Reserved. - -UMFPACK V5.1.0 (May 31, 2007): 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: 1.77636e-14 - -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 1.93000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 74 69 93% - peak size (Units) 1301 1292 99% - final size (Units) 15 13 87% - Numeric final size (Units) 79 75 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 1463 1454 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 - - solve flops: 4.80000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 7.82e-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 - - -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: 4.52416e-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): 73 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 1292 - 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 V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 1.02000e+01 - - symbolic/numeric factorization: upper bound actual % - variable-sized part of Numeric object: - initial size (Units) 74 69 93% - peak size (Units) 1301 1292 99% - final size (Units) 15 12 80% - Numeric final size (Units) 79 74 94% - Numeric final size (MBytes) 0.0 0.0 94% - peak memory usage (Units) 1463 1454 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 - - solve flops: 5.15000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 6.01e-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: 5.32000e+02 - - -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: 4.66294e-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): 74 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 1292 - 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 V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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)): 1.60000e+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) 74 69 93% - peak size (Units) 1301 1292 99% - final size (Units) 15 13 87% - Numeric final size (Units) 79 75 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 1463 1454 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 - - solve flops: 5.23000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 8.05e-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 - - -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: 9.10383e-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): 75 (MBytes): 0.0 - estimated peak size (Units): 1302 (MBytes): 0.0 - estimated final size (Units): 16 (MBytes): 0.0 - symbolic factorization memory usage (Units): 138 (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_zl_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): 75 - final total size of Numeric object (MBytes): 0.0 - peak size of variable-size part (Units): 1293 - 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 V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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) 75 70 93% - peak size (Units) 1302 1293 99% - final size (Units) 16 14 88% - Numeric final size (Units) 80 76 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 1464 1455 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 - - solve flops: 4.80000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 9.42e-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 - - -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: 4.88498e-15 - - -Solving C'x=b again, using umfpack_zl_wsolve instead: -UMFPACK V5.1.0 (May 31, 2007), Info: - matrix entry defined as: double complex - Int (generic integer) defined as: UF_long - BLAS library used: Fortran BLAS. size of BLAS integer: 4 - 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: 16-byte Units - size of int: 4 bytes - size of UF_long: 8 bytes - size of pointer: 8 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): 138 - symbolic memory usage (MBytes): 0.0 - Symbolic size (Units): 41 - 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) 75 70 93% - peak size (Units) 1302 1293 99% - final size (Units) 16 14 88% - Numeric final size (Units) 80 76 95% - Numeric final size (MBytes) 0.0 0.0 95% - peak memory usage (Units) 1464 1455 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 - - solve flops: 4.80000e+02 - iterative refinement steps taken: 0 - iterative refinement steps attempted: 0 - sparse backward error omega1: 9.42e-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 - - -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: 4.88498e-15 - - -umfpack_zl_demo complete. -Total time: 0.00 seconds (CPU time), 0.01 seconds (wallclock time)