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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), 0.01 seconds (wallclock time)
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