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¶
When Matrix Depot is first loaded, a new directory myMatrixDepot
will be created. Matrix Depot automatically includes all Julia files
in this directory. Hence, all we need to do is to copy
the generator files to path/to/MatrixDepot/myMatrixDepot and use
the function include_generator to declare them.
-
include_generator(Stuff_To_Be_Included, Stuff, f)¶ Includes a piece of information of the function
fto Matrix Depot, whereStuff_To_Be_Includedis one of the following:FunctionName: the function name off. In this case,Stuffis a string representingf.Group: the group wherefbelongs. In this case,Stuffis the group name.
Examples¶
To get a feel of how it works, let’s see an example.
Suppose we have a file myrand.jl which contains two
matrix generator randsym and randorth:
"""
random symmetric matrix
=======================
*Input options:*
+ n: the dimension of the matrix
"""
function randsym(n)
A = zeros(n, n)
for j = 1:n
for i = j:n
A[i,j] = randn()
if i != j; A[j,i] = A[i,j] end
end
end
return A
end
"""
random Orthogonal matrix
========================
*Input options:*
+ n: the dimension of the matrix
"""
randorth(n) = qr(randn(n,n)).Q
We first need to find out where Matrix Depot is installed. This can be done by:
julia> @which matrixdepot("")
matrixdepot(p::Union{Regex,...}, args...) in MatrixDepot at
/home/.../.julia/dev/MatrixDepot/src/common.jl:508
For me, the package user data are installed at
/home/.../.julia/dev/MatrixDepot/myMatrixDepot. We can copy myrand.jl to this directory.
Now we open the file
myMatrixDepot/generator.jl and write:
include_generator(FunctionName, "randsym", randsym)
include_generator(FunctionName, "randorth", randorth)
Due to a bug we have to remove file db.data and restart julia:
rm MatrixDepot/data/db.data
This is it. We can now use them from Matrix Depot:
julia> using MatrixDepot
include group.jl for user defined matrix generators
include myrand.jl for user defined matrix generators
verify download of index files...
used remote site is https://sparse.tamu.edu/?per_page=All
populating internal database...
julia> mdinfo()
Currently loaded Matrices
–––––––––––––––––––––––––––
builtin(#)
––––––––––– ––––––––––– ––––––––––– –––––––––––– ––––––––––– ––––––––––––– ––––––––––––
1 baart 10 deriv2 19 gravity 28 kms 37 parter 46 rohess 55 ursell
2 binomial 11 dingdong 20 grcar 29 lehmer 38 pascal 47 rosser 56 vand
3 blur 12 erdrey 21 hadamard 30 lotkin 39 pei 48 sampling 57 wathen
4 cauchy 13 fiedler 22 hankel 31 magic 40 phillips 49 shaw 58 wilkinson
5 chebspec 14 forsythe 23 heat 32 minij 41 poisson 50 smallworld 59 wing
6 chow 15 foxgood 24 hilb 33 moler 42 prolate 51 spikes
7 circul 16 frank 25 invhilb 34 neumann 43 randcorr 52 toeplitz
8 clement 17 gilbert 26 invol 35 oscillate 44 rando 53 tridiag
9 companion 18 golub 27 kahan 36 parallax 45 randsvd 54 triw
user(#)
–––––––––– –––––––––
1 randorth 2 randsym
Groups
––––––– ––––– ––––– ––––––– –––––– ––––––– –––––––––––––––
all local eigen illcond posdef regprob symmetric
builtin user graph inverse random sparse test_for_paper2
Suite Sparse of
–––––––––––– ––––
2773 2833
MatrixMarket of
–––––––––––– –––
488 498
julia> mdinfo("randsym")
random symmetric matrix
≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡≡
Input options:
• n: the dimension of the matrix
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> A = matrixdepot("randorth", 5)
5x5 Array{Float64,2}:
-0.359134 0.401435 0.491005 -0.310518 0.610218
-0.524132 -0.474053 -0.53949 -0.390514 0.238764
0.627656 0.223519 -0.483424 -0.104706 0.558054
-0.171077 0.686038 -0.356957 -0.394757 -0.465654
0.416039 -0.305802 0.326723 -0.764383 -0.205834
julia> A'*A
5x5 Array{Float64,2}:
1.0 8.32667e-17 1.11022e-16 5.55112e-17 -6.93889e-17
8.32667e-17 1.0 -1.80411e-16 -2.77556e-17 -5.55112e-17
1.11022e-16 -1.80411e-16 1.0 1.94289e-16 -1.66533e-16
5.55112e-17 -2.77556e-17 1.94289e-16 1.0 1.38778e-16
-6.93889e-17 -5.55112e-17 -1.66533e-16 1.38778e-16 1.0
We can also add group information in generator.jl:
include_generator(Group, :random, randsym) include_generator(Group, :symmetric, randsym)
After re-starting julia, if we type:
julia> using MatrixDepot
include group.jl for user defined matrix generators
include myrand.jl for user defined matrix generators
verify download of index files...
used remote site is https://sparse.tamu.edu/?per_page=All
populating internal database...
julia> listnames(:symmetric)
list(22)
–––––––– –––––––– ––––––– ––––––– –––––– ––––– ––––––––– ––––––– –––––––– ––––––– –––––––––
cauchy clement fiedler hilb kms minij oscillate pei prolate randsym wathen
circul dingdong hankel invhilb lehmer moler pascal poisson randcorr tridiag wilkinson
julia> mdlist(:random)
9-element Array{ASCIIString,1}:
"golub"
"oscillate"
"randcorr"
"rando"
"randsvd"
"randsym"
"rohess"
"rosser"
"wathen"
the function randsym will be part of the groups :symmetric and :random.
It is a good idea to back up your changes. For example, we
could save it on GitHub by creating a new repository named myMatrixDepot.
(See https://help.github.com/articles/create-a-repo/ for details of creating a new repository on GitHub.)
Then we go to the directory path/to/MatrixDepot/myMatrixDepot and type:
git init
git add *.jl
git commit -m "first commit"
git remote add origin https://github.com/your-user-name/myMatrixDepot.git
git push -u origin master