とっても大きな SDP その７

以前に掲載した巨大 SDP だが、多分これは現時点で高精度な最適解を得ることができた世界最大の SDP であると思われる。low rank など特殊な構造を持っていたり、あるいは精度が悪くても良いのであれば、さらに大きな SDP を解くことは可能であるが、それ以外の場合では巨大な SDP を解くことは難しい。

問題名：C2.1Sigmag+.VDZ.pqgt1t2p.dat-s
76554 (= mDIM)
22 (= nBLOCK)
18 18 18 18 153 153 324 153 153 324 648 324 324 816 2754 2754 816 8604 8604 2754 2754 -694 (= bLOCKsTRUCT)

phase.value = pdOPT
Iteration = 48
mu = +3.7701550392400866e-11
relative gap = +0.0000000000000000e+00
gap = +0.0000000000000000e+00
digits = +inf
objValPrimal = -9.0977516315119601e+01
objValDual = -9.0977516315119601e+01
p.feas.error = +6.3903804436704646e-09
d.feas.error = +2.9498643527858803e-09

Time(sec) Ratio(% : MainLoop)
Predictor time = 1533602.778546, 98.646569
Corrector time = 12479.556376, 0.802728
Make bMat time = 1513766.862287, 97.370655
Make bDia time = 0.119716, 0.000008
Make bF1 time = 0.000000, 0.000000
Make bF2 time = 0.000000, 0.000000
Make bF3 time = 1495391.534023, 96.188692
Make bPRE time = 0.000000, 0.000000
Make rMat time = 5937.965214, 0.381950
Make gVec Mul = 2882.918933, 0.185439
Make gVec time = 2907.332203, 0.187010
copy gVec time = 0.000061, 0.000000
copy bMat time = 355.684425, 0.022879
symm bMat time = 0.001933, 0.000000
Cholesky bMat = 10299.300986, 0.662486
Ste Pre time = 0.010811, 0.000001
Ste Cor time = 2456.153895, 0.157988
solve = 302.752659, 0.019474
copy DyVec = 1.129476, 0.000073
sumDz = 366.806799, 0.023594
makedX = 11467.240929, 0.737612
symmetriseDx = 525.256194, 0.033786
makedXdZ = 12359.304259, 0.794993
xMatTime = 2147.063343, 0.138106
zMatTime = 3624.994260, 0.233172
invzMatTime = 0.000000, 0.000000
xMatzMatTime = 0.000000, 0.000000
EigxMatTime = 1157.500556, 0.074454
EigzMatTime = 1136.709648, 0.073117
EigxMatzMatTime = 0.000000, 0.000000
updateRes = 284.279656, 0.018286
EigTime = 2294.210204, 0.147571
sub_total_bMat = 40876.941835, 2.629345
Main Loop = 1554643.804122, 100.000000
File Check = 0.000000, 0.000000
File Change = 0.031656, 0.000002
File Read = 31.315174, 0.002014
File Trans = 493.991695, 0.031775
Total = 1554675.150952, 100.002016

○ SDPA クラスタ
16 Nodes, 32 CPUs, 128 CPU cores;
CPU : Intel Xeon 5460 3.16GHz (quad cores) x 2 / node
Memory : 48GB / node
NIC : GbE x 2 and Myrinet-10G x 1 / node
OS : CentOS 5.4 for x86_64