Every matrix in the collection is represented by a string
"matrix_name", for example, the Cauchy matrix is represented by
"cauchy" and the Hilbert matrix is represented by "hilb".
The matrix groups are noted as symbols.
For example, the class of the symmetric
matrices is symbolized by :symmetric.
.. function:: mdinfo()
Return a list of all the matrices in the collection::
julia> mdinfo()
Matrices:
1) baart 2) binomial 3) blur 4) cauchy
5) chebspec 6) chow 7) circul 8) clement
9) companion 10) deriv2 11) dingdong 12) fiedler
13) forsythe 14) foxgood 15) frank 16) golub
17) gravity 18) grcar 19) hadamard 20) hankel
21) heat 22) hilb 23) invhilb 24) invol
25) kahan 26) kms 27) lehmer 28) lotkin
29) magic 30) minij 31) moler 32) neumann
33) oscillate 34) parter 35) pascal 36) pei
37) phillips 38) poisson 39) prolate 40) randcorr
41) rando 42) randsvd 43) rohess 44) rosser
45) sampling 46) shaw 47) spikes 48) toeplitz
49) tridiag 50) triw 51) ursell 52) vand
53) wathen 54) wilkinson 55) wing
Groups:
all data eigen illcond
inverse posdef random regprob
sparse symmetric
.. function:: matrixdepot(matrix_name, p1, p2, ...)
Return a matrix specified by the query string ``matrix_name``.
The string must be a matrix name or a query pattern which matches exactly one matrix.
``p1, p2, ...`` are input parameters depending on ``matrix_name``.
For example::
julia> matrixdepot("hilb", 5, 4)
5x4 Array{Float64,2}:
1.0 0.5 0.333333 0.25
0.5 0.333333 0.25 0.2
0.333333 0.25 0.2 0.166667
0.25 0.2 0.166667 0.142857
0.2 0.166667 0.142857 0.125
.. function:: mdinfo(matrix_name)
Return the documentation of ``matrix_name``, including input options,
groups and reference. For example::
julia> mdinfo("moler")
Moler Matrix
≡≡≡≡≡≡≡≡≡≡≡≡≡≡
The Moler matrix is a symmetric positive definite matrix. It has one small
eigenvalue.
Input options:
• [type,] dim, alpha: dim is the dimension of the matrix, alpha is a
scalar;
• [type,] dim: alpha = -1.
Groups: ["inverse", "ill-cond", "symmetric", "pos-def"]
References:
J.C. Nash, Compact Numerical Methods for Computers: Linear Algebra and
Function Minimisation, second edition, Adam Hilger, Bristol, 1990
(Appendix 1).
.. function:: mdlist(group_name)
Return a list of matrices which belong to group ``group_name`` (symbol) as an array.
For example::
julia> mdlist(:posdef)
11-element Array{ASCIIString,1}:
"hilb"
"cauchy"
"circul"
"invhilb"
"moler"
"pascal"
"pei"
"minij"
"tridiag"
"lehmer"
"poisson"
.. function:: listnames(group1 & group2 & ...) Return a iformatted list of matrices which belong to ``group1`` and ``group2``, etc. For example:: julia> listnames(:symmetric & :inverse & :illcond & :posdef) list(8) ––––––– –––– ––––––– ––– ––––– –––––– ––– ––––––– cauchy hilb invhilb kms moler pascal pei tridiag
.. function:: mdlist({builtin\user\sp\mm}(num))
Access matrix by number. For example::
julia> mdlist(builtin(3))
"chebspec"
.. function:: mdlist(builtin(num1:num2, ...))
Access matrix by range and combinations. For example::
julia> mdlist(builtin(1:4, 6, 10:15))
11-element Array{String,1}:
"baart"
"binomial"
"blur"
"cauchy"
"chow"
"deriv2"
"dingdong"
"erdrey"
"fiedler"
"forsythe"
"foxgood"
We can define our own groups using the macro @addgroup and
remove a defined group using @rmgroup.
.. function:: @addgroup group_name = ["matrix1", "matrix2", "matrix3"] Create a new group ``"group_name"`` such that it has members ``"matrix1"``, ``"matrix2"`` and ``"matrix3"``.
.. function:: @rmgroup group_name Delete a created group ``group_name``.