Starting diary file "diary-2016-03-09.txt" on Wed Mar 09 2016 12:29 PM.

Dcoeff = .01; k = 100; dt = .01; t_end = 3.0;

U = mydiffusion(Dcoeff, @S, @B, @U0, k, dt, t_end, 1);
Hit space to begin simulation.

tic; U = mydiffusion(Dcoeff, @S, @B, @U0, k, dt, t_end, 0); toc
Elapsed time is 11.861771 seconds.

edit mydiffusion

edit bslashtx

edit mydiffusion % use chol() and do triangular solves inside the loop

U = mydiffusion2(Dcoeff, @S, @B, @U0, k, dt, t_end, 1);
Hit space to begin simulation.

% I left out the part where it was still slow because
% we were transposing R inside the loop every time!

tic; U = mydiffusion2(Dcoeff, @S, @B, @U0, k, dt, t_end, 0); toc
Elapsed time is 3.725698 seconds.

profile clear
profile on
tic; U = mydiffusion2(Dcoeff, @S, @B, @U0, k, dt, t_end, 0); toc
Elapsed time is 5.505217 seconds.
profile viewer

clear
clc

load choleskyexample
whos
  Name      Size            Bytes  Class     Attributes

  A         5x5               200  double              
  p         1x5                40  double              

A
A =
     4    -1     0     0    -1
    -1     4    -1    -1     0
     0    -1     4    -1     0
     0    -1    -1     4     0
    -1     0     0     0     4
nnz(A)
ans =
    15

R = chol(A)
R =
    2.0000   -0.5000         0         0   -0.5000
         0    1.9365   -0.5164   -0.5164   -0.1291
         0         0    1.9322   -0.6556   -0.0345
         0         0         0    1.8176   -0.0491
         0         0         0         0    1.9313
nnz(R)
ans =
    13

p
p =
     5     1     2     3     4

AA = A(p,p)
AA =
     4    -1     0     0     0
    -1     4    -1     0     0
     0    -1     4    -1    -1
     0     0    -1     4    -1
     0     0    -1    -1     4
nnz(AA)
ans =
    15

RR = chol(AA)
RR =
    2.0000   -0.5000         0         0         0
         0    1.9365   -0.5164         0         0
         0         0    1.9322   -0.5175   -0.5175
         0         0         0    1.9319   -0.6563
         0         0         0         0    1.8170

R
R =
    2.0000   -0.5000         0         0   -0.5000
         0    1.9365   -0.5164   -0.5164   -0.1291
         0         0    1.9322   -0.6556   -0.0345
         0         0         0    1.8176   -0.0491
         0         0         0         0    1.9313

A2 = laplacian2d_sparse2(100);
whos
  Name          Size                Bytes  Class     Attributes

  A             5x5                   200  double              
  A2        10000x10000            873608  double    sparse    
  AA            5x5                   200  double              
  R             5x5                   200  double              
  RR            5x5                   200  double              
  ans           1x1                     8  double              
  p             1x5                    40  double              

spy(A2)
nnz(A2)
ans =
       49600

R = chol(A2);
spy(R)
nnz(R)
ans =
     1000099

help amd
 AMD  Approximate minimum degree permutation.
    P = AMD(A) returns the approximate minimum degree permutation vector
    ...

p = amd(A2);
size(p)
ans =
           1       10000
p
p =
  ...
AA = A2(p,p);
nnz(AA)
ans =
       49600
nnz(A2)
ans =
       49600

spy(AA),shg

RR = chol(AA);
nnz(RR)
ans =
      206332

nnz(AA)
ans =
       49600

spy(RR),shg
figure,spy(AA),shg

clc

% now edit mydiffusion to incorporate the amd() permutation

Dcoeff = .01; k = 100; dt = .01; t_end = 3.0;

U = mydiffusion(Dcoeff, @S, @B, @U0, k, dt, t_end, 1);
Hit space to begin simulation.

tic; U = mydiffusion(Dcoeff, @S, @B, @U0, k, dt, t_end, 0); toc
Elapsed time is 1.170288 seconds.

diary off