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