Adding New Matrix Generators

Matrix Depot provides a diverse collection of test matrices, including parametrized matrices and real-life matrices. But occasionally, you may want to define your own matrix generators and be able to use them from Matrix Depot.

Declaring Generators

All we need to do is to code the generators in path/to/MatrixDepot/user/generator.jl and use include_generator to declare them.

include_generator(Stuff To Be Included, Stuff, f)

Includes a piece of information of the function f to Matrix Depot, where Stuff To Be Included is one of the following:

• FunctionName: the function name of f. In this case, Stuff is a string representing f.
• Help: the helper lines of f. In this case, Stuff is the helper lines of f.
• Group: the group where f belongs. In this case, Stuff is the group name.

Examples

To get a feel of how it works, let’s see an example. Suppose we want to include a random symmetric matrix randsym in Matrix Depot:

function randsym{T}(::Type{T}, n)
  A = zeros(T, n, n)
  for j = 1:n
      for i = j:n
          A[i,j] = randn()
      end
  end
  A = A + tril(A, -1)'
  return A
end

Note

To be consistent with Matrix Depot’s matrix generators, the first argument of the function must be the element type of matrix.

We first need to find out where Matrix Depot is installed. This can be done by:

julia> Pkg.dir("MatrixDepot")
"/home/weijian/.julia/v0.4/MatrixDepot"

For me, the package is installed at /home/weijian/.julia/v0.4/MatrixDepot. Now we open the file user/generator.jl. It looks like this:

##########################################
# Please put your matrix generators here #
##########################################

We can copy and paste the function randsym anywhere below the comments and use the function include_generator to declare it:

##########################################
# Please put your matrix generators here #
##########################################

function randsym{T}(::Type{T}, n)
 A = zeros(T, n, n)
  for j = 1:n
      for i = j:n
          A[i,j] = randn()
      end
  end
  A = A + tril(A, -1)'
  return A
end
include_generator(FunctionName, "randsym", randsym)

This is it. We can now use it from Matrix Depot:

julia> matrixdepot()

Matrices:
  1) baart            2) binomial         3) blur             4) cauchy
  5) chebspec         6) chow             7) circul           8) clement
  9) deriv2          10) dingdong        11) fiedler         12) forsythe
 13) foxgood         14) frank           15) golub           16) gravity
 17) grcar           18) hadamard        19) hankel          20) heat
 21) hilb            22) invhilb         23) invol           24) kahan
 25) kms             26) lehmer          27) lotkin          28) magic
 29) minij           30) moler           31) neumann         32) oscillate
 33) parter          34) pascal          35) pei             36) phillips
 37) poisson         38) prolate         39) randcorr        40) rando
 41) randsvd         42) randsym         43) rohess          44) rosser
 45) sampling        46) shaw            47) spikes          48) toeplitz
 49) tridiag         50) triw            51) vand            52) wathen
 53) wilkinson       54) wing
Groups:
  all           data          eigen         ill-cond
  inverse       pos-def       random        regprob
  sparse        symmetric

julia> matrixdepot("randsym", 5)
5x5 Array{Float64,2}:
 1.57579    0.474591  0.0261732  -0.536217  -0.0900839
 0.474591   0.388406  0.77178     0.239696   0.302637
 0.0261732  0.77178   1.7336      1.72549    0.127008
-0.536217   0.239696  1.72549     0.304016   1.5854
-0.0900839  0.302637  0.127008    1.5854    -0.656608

julia> matrixdepot("randsym", Float32, 5)
5x5 Array{Float32,2}:
-0.633797  -0.154157   0.972601  0.554571  -0.692858
-0.154157  -0.319152  -0.710942  2.81623    1.2637
 0.972601  -0.710942  -0.165526  1.16547   -0.705227
 0.554571   2.81623    1.16547   0.351268   0.410586
-0.692858   1.2637    -0.705227  0.410586  -0.786438

To make it more useful, we can declare the helper strings and group information:

function randsym{T}(::Type{T}, n)
 A = zeros(T, n, n)
  for j = 1:n
      for i = j:n
          A[i,j] = randn()
      end
  end
  A = A + tril(A, -1)'
  return A
end
include_generator(FunctionName, "randsym", randsym)
helplines = "random symmetric matrix:
          \n Input options: [type, n]: the dimension of the matrix is n."
include_generator(Help, helplines, randsym)
include_generator(Group, "random", randsym)
include_generator(Group, "symmetric", randsym)

Now we can do:

julia> matrixdepot("randsym")
random symmetric matrix:

Input options: [type, n]: the dimension of the matrix is n.

julia> matrixdepot("random")
9-element Array{ASCIIString,1}:
"golub"
"oscillate"
"randcorr"
"rando"
"randsvd"
"randsym"
"rohess"
"rosser"
"wathen"

julia> matrixdepot("symmetric")
22-element Array{ASCIIString,1}:
"cauchy"
"circul"
"clement"
"dingdong"
"fiedler"
"hankel"
"hilb"
"invhilb"
"kms"
"lehmer"
⋮
"pascal"
"pei"
"poisson"
"prolate"
"randcorr"
"randsym"
"tridiag"
"wathen"
"wilkinson"

Notice randsym is now part of the group symmetric and random.