Matrix key: QC324                         

UMFPACK V4.4 (Jan. 28, 2005), Control:

    Matrix entry defined as: double complex
    Int (generic integer) defined as: int

    0: print level: 2
    1: dense row parameter:    0.2
        "dense" rows have    > max (16, (0.2)*16*sqrt(n_col) entries)
    2: dense column parameter: 0.2
        "dense" columns have > max (16, (0.2)*16*sqrt(n_row) entries)
    3: pivot tolerance: 0.1
    4: block size for dense matrix kernels: 32
    5: strategy: 0 (auto)
    6: initial allocation ratio: 0.7
    7: max iterative refinement steps: 2
    12: 2-by-2 pivot tolerance: 0.01
    13: Q fixed during numerical factorization: 0 (auto)
    14: AMD dense row/col parameter:    10
       "dense" rows/columns have > max (16, (10)*sqrt(n)) entries
        Only used if the AMD ordering is used.
    15: diagonal pivot tolerance: 0.001
        Only used if diagonal pivoting is attempted.
    16: scaling: 1 (divide each row by sum of abs. values in each row)
    17: frontal matrix allocation ratio: 0.5
    18: drop tolerance: 0
    19: AMD and COLAMD aggressive absorption: 1 (yes)

    The following options can only be changed at compile-time:
    8: BLAS library used:  none.  UMFPACK will be slow.
    9: compiled for ANSI C (uses malloc, free, realloc, and printf)
    10: CPU timer is POSIX times ( ) routine.
    11: compiled for normal operation (debugging disabled)
    computer/operating system: Linux
    size of int: 4 long: 4 Int: 4 pointer: 4 double: 8 Entry: 16 (in bytes)

symbolic analysis:
   status:     0.
   time:      0.10E-01 (sec)
   estimates (upper bound) for numeric LU:
   size of LU:          1.17 (MB)
   memory needed:       2.40 (MB)
   flop count:      0.26E+08
   nnz (L):           24027.
   nnz (U):           39609.
numeric factorization:
   status:     0.
   time:      0.10E-01
   actual numeric LU statistics:
   size of LU:          0.72 (MB)
   memory needed:       1.14 (MB)
   flop count:      0.14E+08
   nnz (L):           23247.
   nnz (U):           23247.

UMFPACK V4.4 (Jan. 28, 2005), Info:
    matrix entry defined as:          double complex
    Int (generic integer) defined as: int
    BLAS library used:                none.  UMFPACK will be slow.
    MATLAB:                           no.
    CPU timer:                        POSIX times ( ) routine.
    number of rows in matrix A:       324
    number of columns in matrix A:    324
    entries in matrix A:              26730
    memory usage reported in:         8-byte Units
    size of int:                      4 bytes
    size of long:                     4 bytes
    size of pointer:                  4 bytes
    size of numerical entry:          16 bytes

    strategy used:                    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:                    324
        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                    324
        symmetry of nonzero pattern:               1.000000
        nz in S+S' (excl. diagonal):               26406
        nz on diagonal of matrix S:                324
        fraction of nz on diagonal:                1.000000
    AMD statistics, for strict diagonal pivoting:
        est. flops for LU factorization:           1.55342e+07
        est. nz in L+U (incl. diagonal):           47730
        est. largest front (# entries):            14641
        est. max nz in any column of L:            121
        number of "dense" rows/columns in S+S':    0
    symbolic factorization defragmentations:       0
    symbolic memory usage (Units):                 63466
    symbolic memory usage (MBytes):                0.5
    Symbolic size (Units):                         1418
    Symbolic size (MBytes):                        0
    symbolic factorization CPU time (sec):         0.01
    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)):              2.55982e-01
    maximum sum (abs (rows of A)):              1.82217e+00

    symbolic/numeric factorization:      upper bound               actual      %
    variable-sized part of Numeric object:
        initial size (Units)                   98017                97692   100%
        peak size (Units)                     307744               142557    46%
        final size (Units)                    150384                92058    61%
    Numeric final size (Units)                153181                94693    62%
    Numeric final size (MBytes)                  1.2                  0.7    62%
    peak memory usage (Units)                 314850               149663    48%
    peak memory usage (MBytes)                   2.4                  1.1    48%
    numeric factorization flops          2.56313e+07          1.43519e+07    56%
    nz in L (incl diagonal)                    24027                23247    97%
    nz in U (incl diagonal)                    39609                23247    59%
    nz in L+U (incl diagonal)                  63312                46170    73%
    largest front (# entries)                  19723                 6724    34%
    largest # rows in front                      121                   82    68%
    largest # columns in front                   163                   82    50%

    initial allocation ratio used:                 1.2
    # of forced updates due to frontal growth:     0
    number of off-diagonal pivots:                 0
    nz in L (incl diagonal), if none dropped       23247
    nz in U (incl diagonal), if none dropped       23247
    number of small entries dropped                0
    nonzeros on diagonal of U:                     324
    min abs. value on diagonal of U:               5.47e-03
    max abs. value on diagonal of U:               8.25e-01
    estimate of reciprocal of condition number:    6.63e-03
    indices in compressed pattern:                 485
    numerical values stored in Numeric object:     46170
    numeric factorization defragmentations:        0
    numeric factorization reallocations:           0
    costly numeric factorization reallocations:    0
    numeric factorization CPU time (sec):          0.01
    numeric factorization wallclock time (sec):    0.02
    numeric factorization mflops (CPU time):       1435.19
    numeric factorization mflops (wallclock):      717.60
    symbolic + numeric CPU time (sec):             0.02
    symbolic + numeric mflops (CPU time):          717.60
    symbolic + numeric wall clock time (sec):      0.02
    symbolic + numeric mflops (wall clock):        717.60

    solve flops:                                   3.70332e+05
    iterative refinement steps taken:              0
    iterative refinement steps attempted:          0
    solve CPU time (sec):                          0.00
    solve wall clock time (sec):                   0.00

    total symbolic + numeric + solve flops:        1.47223e+07
    total symbolic + numeric + solve CPU time:     0.02
    total symbolic + numeric + solve mflops (CPU): 736.11
    total symbolic+numeric+solve wall clock time:  0.02
    total symbolic+numeric+solve mflops(wallclock) 736.11

 norm (A*x-b):   2.96487174E-13