Matlab diary from CS 290H, Wednesday, April 09, 2014

This is /Users/gilbert/Documents/CS290hSpring2014/Matlab/startup.m
Starting diary file diary-09-Apr-2014.txt

> help grid5
  GRID5 : Generate 5-point finite difference mesh.
 
  [A,xy] = GRID5(k) returns a k^2-by-k^2 symmetric positive definite 
         matrix A with the structure of the k-by-k 5-point grid,
         and an array xy of coordinates for the grid points.
 
> k = 40;
> [A,xy ] = grid5(k);
> whos
  Name         Size               Bytes  Class     Attributes

  A         1600x1600            138248  double    sparse    
  xy        1600x2                25600  double              

> L = laplacian(A);
> spy(L)
> gplotg(L,xy)
> nnz(L)
ans = 7840

> n = k^2
n = 1600

> v = [ones(n/2,1) ; -ones(n/2,1)];
> size(v)
ans =
        1600           1

v' * L * v / (v'*v)
ans =
    0.1000

> ans * sqrt(n)
ans =
     4
> x = (k-1 : -2 : -(k-1))
x =
  Columns 1 through 8
    39    37    35    33    31    29    27    25
  Columns 9 through 16
    23    21    19    17    15    13    11     9
  Columns 17 through 24
     7     5     3     1    -1    -3    -5    -7
  Columns 25 through 32
    -9   -11   -13   -15   -17   -19   -21   -23
  Columns 33 through 40
   -25   -27   -29   -31   -33   -35   -37   -39

> size(x)
ans =
     1    40
> x=x'
x =
    39
    37
    35
    ...
   -37
   -39

> y = ones(1,k)
y =
  Columns 1 through 8
     1     1     1     1     1     1     1     1
  Columns 9 through 16
     1     1     1     1     1     1     1     1
  Columns 17 through 24
     1     1     1     1     1     1     1     1
  Columns 25 through 32
     1     1     1     1     1     1     1     1
  Columns 33 through 40
     1     1     1     1     1     1     1     1

> V = x * y
V =
  Columns 1 through 8
    39    39    39    39    39    39    39    39
    37    37    37    37    37    37    37    37
    35    35    35    35    35    35    35    35
    33    33    33    33    33    33    33    33
    31    31    31    31    31    31    31    31
    29    29    29    29    29    29    29    29
    27    27    27    27    27    27    27    27
    25    25    25    25    25    25    25    25
    23    23    23    23    23    23    23    23
    21    21    21    21    21    21    21    21
    19    19    19    19    19    19    19    19
    17    17    17    17    17    17    17    17
    15    15    15    15    15    15    15    15
    13    13    13    13    13    13    13    13
    11    11    11    11    11    11    11    11
     9     9     9     9     9     9     9     9
     7     7     7     7     7     7     7     7
     5     5     5     5     5     5     5     5
     3     3     3     3     3     3     3     3
     1     1     1     1     1     1     1     1
    -1    -1    -1    -1    -1    -1    -1    -1
    -3    -3    -3    -3    -3    -3    -3    -3
    -5    -5    -5    -5    -5    -5    -5    -5
    -7    -7    -7    -7    -7    -7    -7    -7
    -9    -9    -9    -9    -9    -9    -9    -9
   -11   -11   -11   -11   -11   -11   -11   -11
   -13   -13   -13   -13   -13   -13   -13   -13
   -15   -15   -15   -15   -15   -15   -15   -15
   -17   -17   -17   -17   -17   -17   -17   -17
   -19   -19   -19   -19   -19   -19   -19   -19
   -21   -21   -21   -21   -21   -21   -21   -21
   -23   -23   -23   -23   -23   -23   -23   -23
   -25   -25   -25   -25   -25   -25   -25   -25
   -27   -27   -27   -27   -27   -27   -27   -27
   -29   -29   -29   -29   -29   -29   -29   -29
   -31   -31   -31   -31   -31   -31   -31   -31
   -33   -33   -33   -33   -33   -33   -33   -33
   -35   -35   -35   -35   -35   -35   -35   -35
   -37   -37   -37   -37   -37   -37   -37   -37
   -39   -39   -39   -39   -39   -39   -39   -39
  Columns 9 through 16
    ...
  Columns 33 through 40
    ...

> v = V(:)
v =
    39
    37
    35
    ...
   -37
   -39

> size(v)
ans =
        1600           1

> v' * L * v / (v'*v)
ans = 0.0073

> x = [ones(n/2,1) ; -ones(n/2,1)];
> x'*L*x / (x'*x)
ans = 0.1000

> v' * L * v / (v'*v)
ans =
    0.0073

> ans * n
ans =
   11.7073

> [a,b] = fiedler(L);
> b
b =
    0.0062

> diary off