[Octave-bug-tracker] [bug #48085] Slow solving simultaneous equations by LU decomposition for octave 4 on windows

[Tatsuro MATSUOKA]

Follow-up Comment #7, bug #48085 (project octave):

Change a test code according to advise from Marco


% lutest\vp1.m
more off 

Num=1000; ItNum=10;
rand('seed',1); 
A=rand(Num)-0.5; 
rand('seed',2); 
B=rand(Num,ItNum)-0.5; 
[L U P]=lu(A); 
% 
disp('Simple left division'); 
tic; 
x=A\B;  
toc; 
x1=x(:,end); 
% 
disp('LU decomposition'); 
disp('c=P*B');
tic; 
c=P*B;  
toc; 
disp('y=L\c');
tic; 
y=L\c; 
toc;
disp('x=U\y');
tic; 
x=U\y; 
toc;
x2=x(:,end); 
id=1:Num; 
plot(id,x1, 'o1',id,x2, '+2'); 


I have tested on windows 10 using five versions:
3.8.2 (x86), 4.0.2(x86),  4.0.2(x64) 4.1.0+(x86) (build June 06), 4.1.0+(x64)
(Build May 28).  

3.8.2 (x86)

Simple left division
Elapsed time is 0.097065 seconds.
LU decomposition
c=P*B
Elapsed time is 0 seconds.
y=L\c
Elapsed time is 0.002002 seconds.
x=U\y
Elapsed time is 0.00200081 seconds.


4.0.2(x86)

Simple left division
Elapsed time is 0.060041 seconds.
LU decomposition
c=P*B
Elapsed time is 0 seconds.
y=L\c
Elapsed time is 0.00900602 seconds.
x=U\y
Elapsed time is 0.010006 seconds.


4.0.2(x64)

Simple left division
Elapsed time is 0.0470331 seconds.
LU decomposition
c=P*B
Elapsed time is 0 seconds.
y=L\c
Elapsed time is 0.00500488 seconds.
x=U\y
Elapsed time is 0.00400209 seconds.


4.1.0+(x86)

Simple left division
Elapsed time is 0.062043 seconds.
LU decomposition
c=P*B
Elapsed time is 0 seconds.
y=L\c
Elapsed time is 0.00800514 seconds.
x=U\y
Elapsed time is 0.00900602 seconds.


4.1.0+(x64)

Simple left division
Elapsed time is 0.212145 seconds.
LU decomposition
c=P*B
Elapsed time is 0 seconds.
y=L\c
Elapsed time is 0.011008 seconds.
x=U\y
Elapsed time is 0.0120099 seconds.


Difference which comes from x86 or x64 exists but they are minor.


The version numbers LAPACK and openblas  are the same between
octave 4.0.2 and 4.1.0+.   

Left division by triangular matrix on octave ver 4 is slower 
than that of ver. 3.

Two separate problems are considered

1. slowness of left division for triangular matrix for version 4.
2. slowness of all left division for 4.1.0+ on windows.

I will do the test on linux in the near future.  
Revised title proposed is (Marco. Please correct my poor English)  


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