% Matlab diary for CS 240A Wednesday, May 4, 2011
%
% Routines and matrix files are from the meshpart toolbox:
%   http://www.cerfacs.fr/algor/Softs/MESHPART/
% or from the CS 240A matlab directory:
%   http://www.cs.ucsb.edu/~gilbert/cs240aSpr2011/matlab/
%
% Some output lines are omitted.

>> G = grid5(100);
>> size(G)
ans =
       10000       10000
>> spy(G)
>> [G,xy] = grid5(100);
>> size(xy)
ans =
       10000           2
>> xy
>> gplotg(G,xy),shg
>> load CGmats
>> whos
  Name                  Size                Bytes  Class     Attributes

  A                 10000x10000            873608  double    sparse    
  Airfoil            4253x4253             563376  double    sparse    
  Airfoil2           4720x4720             552392  double    sparse    
  Airfoil2info          1x51                  102  char                
  Axy                4253x2                 68048  double              
  Axy2               4720x2                 75520  double              
  BCSSTK08           1074x1074             215976  double    sparse    
  BCSSTK08info          1x1                216670  struct              
  Eppstein            547x547               63248  double    sparse    
  Exy                 547x2                  8752  double              
  G                 10000x10000            873608  double    sparse    
  Grid                225x225               18848  double    sparse    
  Gxy                 225x2                  3600  double              
  Smallmesh           136x136               14600  double    sparse    
  Sxy                 136x2                  2176  double              
  Tapir              1024x1024             115656  double    sparse    
  Txy                1024x2                 16384  double              
  ans                   1x2                    16  double              
  xy                10000x2                160000  double              

>> size(Airfoil)
ans =
        4253        4253
>> gplotg(Airfoil,Axy)

>> size(A)
ans =
       10000       10000
>> nnz(A)
ans =
       49600
>> A = A-diag(diag(A)); A=A|A';
>> nnz(A)
ans =
       39600
>> ne = nnz(A)/2
ne =
       19800
>> nv = length(A)
nv =
       10000
>> sum(A)
>> hist(sum(A))
>> clc

>> what
>> load coAuthorsDBLP
>> Problem
Problem = 
      name: 'DIMACS10/coAuthorsDBLP'
     title: [1x36 char]
         A: [299067x299067 double]
        id: 2462
      date: '2008'
    author: [1x42 char]
        ed: 'H. Meyerhenke'
      kind: 'undirected graph'
     notes: [113x72 char]
>> Co = Problem.A;
>> length(Co)
ans =
      299067
>> nnz(Co)
ans =
     1955352
>> nnz(diag(Co))
ans =
     0
>> max(max(Co))
ans =
   (1,1)        1
>> nnz( Co - Co')
ans =
     0
>> spy(Co)
>> nnz(Co)/2 / length(Co)
ans =
    3.2691
>> hist(sum(Co))
>> dhist(Co)

>> load circuit_3
>> Problem
Problem = 
     title: [1x62 char]
         A: [12127x12127 double]
         b: [12127x1 double]
         x: [12127x1 double]
      name: 'Bomhof/circuit_3'
        id: 372
      date: '2000'
    author: 'W. Bomhof'
        ed: 'T. Davis'
      kind: [1x26 char]
>> Ci = Problem.A;
>> length(Ci)
ans =
       12127
>> nnz(Ci)
ans =
       48137
>> nnz(diag(Ci))
ans =
       11917
>> Ci = Ci - diag(diag(Ci));
>> Ci = Ci | Ci';
>> nnz(Ci)
ans =
       44548
>> length(Ci)
ans =
       12127
>> dhist(Ci)

>> help bfslevels
>> bfslevels(Co)

Graph has 299067 vertices and 977676 edges
 Level   Size
   0       1
   1      27
   2      94
   3     504
   4    3064
   5   23215
   6   92647
   7  111268
   8   49423
   9   14079
  10    3629
  11     813
  12     178
  13      87
  14      27
  15      10
  16       1
Reached 299067 vertices in search

>> nv = length(Co)
>> sqrt(nv)
ans =
  546.8702
>> A = grid5(546);
>> length(A)
ans =
      298116
>> A = A-diag(diag(A)); A=A|A';
>> nnz(A)
ans =
     1190280
>> nnz(Co)
ans =
     1955352

>> bfslevels(A)

Graph has 298116 vertices and 595140 edges
 Level   Size
   0       1
   1       4
   2       8
   3      12
   4      16
   5      20
   6      24
   7      28
   8      32
   9      35
  10      37
 100     217
 200     319
 300     419
 400     519
 500     546
 600     421
 700     273
 800     173
 900      73
 950      23
 970       3
 971       2
 972       1
Reached 298116 vertices in search

>> yCo = bfslevels(Co);
>> yCo
>> yA = bfslevels(A);
>> yA
>> close all
>> loglog(yCo)
>> title('collaboration')
>> figure
>> loglog(yA)
>> title('grid')

>> yAir = bfslevels(Airfoil);
>> length(yAir)
ans =
    38     
>> yAir
>> figure
>> loglog(yAir)
>> title('airfoil')

>> R = rmat(18);
>> size(R)
ans =
      262144      262144
>> R = R-diag(diag(R)); R = R|R';
>> nnz(R)
ans =
     3901934
>> nnz(Co)
ans =
     1955352
>> spy(R)
>> dhist(R)
>> bfslevels(R)
Graph has 262144 vertices and 1950967 edges
 Level   Size
   0       1
Reached 1 vertices in search

>> bfslevels(R)
Graph has 262144 vertices and 1950967 edges
 Level   Size
   0       1
   1       1
   2      12
   3    1534
   4   69594
   5   91351
   6   10574
   7     478
   8      26
   9       1
Reached 173572 vertices in search

>> ccoeff(Co)
coeff =
    0.3176
>> ccoeff(Ci)
coeff =
    0.0023
>> ccoeff(Airfoil)
coeff =
    0.4031
>> ccoeff(grid5(100))
coeff =
     0
>> ccoeff(grid9(100))
coeff =
    0.4311
>> ccoeff(R)
coeff =
    0.0454
>> ccoeff(Co)
coeff =
    0.3176