Matlab diary from CS 290H, Wednesday, May 07, 2014

This is /Users/gilbert/Documents/CS290hSpring2014/Matlab/startup.m
Starting diary file diary-07-May-2014.txt

> A = grid5(10);
> whos
  Name        Size             Bytes  Class     Attributes

  A         100x100             8168  double    sparse    

> spy(A)
> A
A =
   (1,1)        4
   (2,1)       -1
  (11,1)       -1
   (1,2)       -1
   (2,2)        4
   (3,2)       -1
  (12,2)       -1
   (2,3)       -1
   (3,3)        4
   (4,3)       -1
  ...
 (100,100)      4

> condest(A)
ans =
   69.8634
> e = eigs(A,5,'SM')
e =
    0.7713
    0.6350
    0.3985
    0.3985
    0.1620

> f = eigs(A,5,'LM')
f =
    7.8380
    7.6015
    7.6015
    7.3650
    7.2287

> n = length(A)
n =
   100
> b = rand(n,1);
> x = A \ b;
> norm(A*x-b)
ans =
   2.0146e-14

help pcg
 PCG   Preconditioned Conjugate Gradients Method.
    X = PCG(A,B) attempts to solve the system of linear equations A*X=B for
    X. The N-by-N coefficient matrix A must be symmetric and positive
    definite and the right hand side column vector B must have length N.
    ...
    X = PCG(A,B,TOL) specifies the tolerance of the method. If TOL is []
    then PCG uses the default, 1e-6.
 
    X = PCG(A,B,TOL,MAXIT) specifies the maximum number of iterations. If
    MAXIT is [] then PCG uses the default, min(N,20).
 
    X = PCG(A,B,TOL,MAXIT,M) and X = PCG(A,B,TOL,MAXIT,M1,M2) use symmetric
    positive definite preconditioner M or M=M1*M2 and effectively solve the
    system inv(M)*A*X = inv(M)*B for X. If M is [] then a preconditioner
    is not applied. M may be a function handle MFUN returning M\X.
    ...
    [X,FLAG,RELRES,ITER,RESVEC] = PCG(A,B,...) also returns a vector of the
    estimated residual norms at each iteration including NORM(B-A*X0).
    ...

> [x, flag, relres, iter, resvec] = pcg(A,b,1e-8,n);
> iter
iter =
    32
> norm(A*x-b)
ans =
   3.5636e-08
> semilogy(resvec / resvec(1)),hold on, shg
> what

M-files in the current directory /Users/gilbert/Documents/CS290hSpring2014/Matlab/graphs

bfslevels    eigsvdgui    plotccd      
btermatch    gploth       plotdegs     
ccoeff       matstats     rmat         
clustereg    misluby      rmatstats    
dhist        misseq       

MAT-files in the current directory /Users/gilbert/Documents/CS290hSpring2014/Matlab/graphs

G3_circuit         fourvtx            
PGPgiantcompo      graphs             
bcsstk08           matlab             
circuit_3          meshes             
clusters           samplegraphs       
coAuthorsDBLP      
dodec              

> clear
> load bcsstk08
> whos
  Name             Size               Bytes  Class     Attributes

  BCSSTK08      1074x1074            215976  double    sparse    
  M                1x1               216670  struct              

> A = BCSSTK08;
> n = length(A)
n =
        1074
> b = rand(n,1);
> [x, flag, relres, iter, resvec] = pcg(A,b,1e-8,n);
> semilogy(resvec / resvec(1)),shg
> [x, flag, relres, iter, resvec] = pcg(A,b,1e-8,10*n);
> semilogy(resvec / resvec(1)),shg
> condest(A)
ans =
   4.7262e+07

> clear
> load PGPgiantcompo
> whos
  Name         Size              Bytes  Class     Attributes

  Problem      1x1             1037746  struct              

> A = Problem.A;
> whos
  Name             Size                 Bytes  Class     Attributes

  A            10680x10680             863560  double    sparse    
  Problem          1x1                1037746  struct              

> A = laplacian(A);
> max(sum(A))
ans =
   All zero sparse: 1-by-1
> nnz(A-A')
ans =
     0
> max(components(A))
ans =
     1
> n = length(A)
n =
       10680
> b = rand(n,1);
> b = b - mean(b);
> sum(b)
ans =
  -6.9657e-12
> [x, flag, relres, iter, resvec] = pcg(A,b,1e-8,n);
> iter
iter =
   832
> semilogy(resvec / resvec(1)),shg
> norm(A*x-b)
ans =
   2.9539e-07
> sum(x)
ans =
  -5.3072e-09
> sum(b)
ans =
  -6.9657e-12

> clear
> load bcsstk08
> A = BCSSTK08;
> n = length(A)
n =
        1074
> b = rand(n,1);
> [x, flag, relres, iter, resvec] = pcg(A,b,1e-8,n);
> semilogy(resvec / resvec(1)),hold on, shg

> R = cholinc(A,'0');
> [x, flag, relres, iter, resvec] = pcg(A,b,1e-8,n,R',R);
> semilogy(resvec / resvec(1),'r');shg

> diary off