Solving Ax=b for large sparse matrix(1e+6 X 1e+5) and cholinc failure
- From: "Alessio Rucci" <alessio.rucci@xxxxxxxxx>
- Date: Thu, 8 Nov 2007 10:57:51 +0000 (UTC)
I have to solve Ax=b where A is a large sparse matrix (1e+6
x 1e+5) with about
7e+6 non-zero elements.
I tried to solve A'Ax=A'b using pcg, but the new matrix
(A'A) is very bad conditioned. I tried to use cholinc to
precondition the system, but A’A has about 1e+7 non-zero
elements, and Matlab gives me out of memory error.
I tried also to solve the system using:
x=(A’A)\(A’b)
but here it is what I get:
sp\: bandwidth = 5864+1+5864.
sp\: is A diagonal? no.
sp\: is band density (0.01) > bandden (0.50) to try banded
solver? no.
sp\: is A triangular? no.
sp\: is A morally triangular? no.
sp\: is A a candidate for Cholesky (symmetric, real positive
diagonal)? yes.
sp\: is CHOLMOD's symbolic Cholesky factorization (with
automatic reordering) successful? yes.
sp\: is CHOLMOD's numeric Cholesky factorization successful? no.
CHOLMOD version 1.1.0, May 5, 2006: : status: ERROR, out of
memory
Architecture: Linux
sizeof(int): 4
sizeof(UF_long): 4
sizeof(void *): 4
sizeof(double): 8
sizeof(Int): 4 (CHOLMOD's basic integer)
sizeof(BLAS_INT): 4 (integer used in the BLAS)
Results from most recent analysis:
Cholesky flop count: 8.0627e+11
Nonzeros in L: 1.9098e+08
memory blocks in use: 11
memory in use (MB): 8.8
peak memory usage (MB): 1961.0
maxrank: update/downdate rank: 8
supernodal control: 1 40 (supernodal if flops/lnz >= 40)
nmethods=0: default strategy: Try user permutation if
given. Try AMD.
Select best ordering tried.
method 0: user permutation (if given)
method 1: AMD (or COLAMD if factorizing AA')
prune_dense: for pruning dense nodes: 10
a dense node has degree >= max(16,(10)*sqrt(n))
flop count: 8.0627e+11
nnz(L): 1.9098e+08
final_asis: TRUE, leave as is
dbound: LDL' diagonal threshold: 0
Entries with abs. value less than dbound are replaced
with +/- dbound.
grow0: memory reallocation: 1.2
grow1: memory reallocation: 1.2
grow2: memory reallocation: 5
nrelax, zrelax: supernodal amalgamation rule:
s = # columns in two adjacent supernodes
z = % of zeros in new supernode if they are merged.
Two supernodes are merged if (s <= 4) or (no new zero
entries) or
(s <= 16 and z < 80%) or (s <= 48 and z < 10%) or (z < 5%)
OK
sp\: But A is real symmetric; try MA57.
MA57 Control Parameters
Ordering used: AMD ordering using MC47.
Block Size for Level 3 BLAS: 16
Merge assembly tree nodes if number of eliminations
is less than: 16
Matrix is scaled using symmetrized version of HSL code MC64.
Maximum iterative refinement steps: 10
Pivot Threshold: 1.000000e-02
Zero Pivot Tolerance: 1.000000e-20
sp\: is MA57's symbolic analysis successful? yes.
Forecast number of Real entries in factors: 191653054
Forecast number of Integer entries in factors: 1466442
Forecast maximum frontal size: 8071
Number of nodes in Assembly tree: 5001
Forecast length of FACT array (real)
without numerical pivot: 288897514
Forecast length of ifact array (integer)
without numerical pivot 15335967
Length of fact required for a successful
completion of the numerical phase allowing
data compression (without numerical pivoting) 284102031
Length of ifact required for a successful
completion of the numerical phase allowing
data compression (without numerical pivoting) 15335967
Number of data compresses 0
Forecast number of floating point additions
for the assembly processes 6.036817e+08
Forecast number of floating point operations
to perform the elimination operations
counting multiply-add pair as two operations 7.745417e+11
*** Return code from MA57AD: 1
??? Error using ==> mldivide
Out of memory. Type HELP MEMORY for your options.
Can anyone suggest me a solution or a different strategy to
solve the original problem Ax=b?
Thank you
.
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