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A test on few matrices between umfpack V3 and Sparse 1.3
via their Scilab interface. The test consists in loading
some Harwell-Boeing sparse matrices and solve a linear
system with a random rhs via umfpack and sparse 1.3 :
t1 = 0
for i = 1:nb_rep
hrtimer(); x = umfpack(A,"\",b); t1 = t1 + hrtimer();
end
t1 = t1 / nb_rep
t2 = 0
for i = 1:nb_rep
hrtimer(); x = A\b; t2 = t2 + hrtimer();
end
t2 = t2 / nb_rep
then display t1 and t2 and also the norm 2 residual ; i have
used nb_rep = 10.
The computer is a 933 M Hz Pentium III / 1 Go Memory / 256 Mo cache
running Gnu-Linux and the ATLAS BLAS is used.
n : order of the matrix
nnz : number of non zeros elements
t1 : mean time for solving Ax=b with umfpack
t2 : mean time for solving Ax=b with Sparse 1.3 (current
package to solve sparse systems in scilab)
The matrices come from the Florida University Sparse Collection
(www.cise.ufl.edu/research/sparse/matrices) maintained by Tim
Davis the author of UMFPACK
The hrtimer is a scilab extension package from Christoph L. Spiel
& Lydia E. van Dijk (www.hammersmith-consulting.com).
-----------------------------------------------------------------
arc130.rua : n = 130 , nnz = 1037
mean time umfpack V3 : t1 = 0.002783 , ||Ax-b|| = 6.538563e-11
mean time sparse 1.3 : t2 = 0.015559 , ||Ax-b|| = 1.026040e-10
speed up : t2/t1 = 5.591677
-----------------------------------------------------------------
bcsstk24.rsa : n = 3562 , nnz = 159910
mean time umfpack V3 : t1 = 1.540691 , ||Ax-b|| = 1.298751e-07
mean time sparse 1.3 : t2 = 52.546995 , ||Ax-b|| = 1.299314e-07
speed up : t2/t1 = 34.106113
-----------------------------------------------------------------
bcsstk34.rsa : n = 588 , nnz = 21418
mean time umfpack V3 : t1 = 0.068137 , ||Ax-b|| = 2.921253e-14
mean time sparse 1.3 : t2 = 4.162029 , ||Ax-b|| = 6.665581e-14
speed up : t2/t1 = 61.083241
-----------------------------------------------------------------
bcsstk38.rsa : n = 8032 , nnz = 355460
mean time umfpack V3 : t1 = 4.671143 , ||Ax-b|| = 1.465322e-09
mean time sparse 1.3 : t2 = 295.272744 , ||Ax-b|| = 5.456355e-09
speed up : t2/t1 = 63.212092
-----------------------------------------------------------------
cavity16.rua : n = 4562 , nnz = 137887
mean time umfpack V3 : t1 = 0.915590 , ||Ax-b|| = 3.816630e-11
mean time sparse 1.3 : t2 = 21.034642 , ||Ax-b|| = 1.278231e-10
speed up : t2/t1 = 22.973871
-----------------------------------------------------------------
epb2.rua : n = 25228 , nnz = 175027
mean time umfpack V3 : t1 = 5.606093 , ||Ax-b|| = 1.141705e-12
mean time sparse 1.3 : t2 = 951.516539 , ||Ax-b|| = 5.832767e-12
speed up : t2/t1 = 169.729009
-----------------------------------------------------------------
ex14.rua : n = 3251 , nnz = 65875
mean time umfpack V3 : t1 = 1.014328 , ||Ax-b|| = 7.475711e-07
mean time sparse 1.3 : t2 = 159.702604 , ||Ax-b|| = 2.502100e-06
speed up : t2/t1 = 157.446646
-----------------------------------------------------------------
utm5940.rua : n = 5940 , nnz = 83842
mean time umfpack V3 : t1 = 1.037315 , ||Ax-b|| = 7.392123e-08
mean time sparse 1.3 : t2 = 288.563648 , ||Ax-b|| = 1.583351e-07
speed up : t2/t1 = 278.183294
-----------------------------------------------------------------
wang1.rua : n = 2903 , nnz = 19093
mean time umfpack V3 : t1 = 0.654956 , ||Ax-b|| = 1.286372e-12
mean time sparse 1.3 : t2 = 29.773115 , ||Ax-b|| = 6.243728e-12
speed up : t2/t1 = 45.458204
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