polyMatrix: pMgen.a – R documentation

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pMgen.a

Generate a polyMatrix class polynomial matrix with storage method 'array', 'broad-matrix', 'list of cells' or 'double list'

Description

A primitive tool to generate a polynomial matrix in 'polyMatrix' form. The 'polyMatrix' objects independently on the storage method has three invariant element: the $dim, $degree and $symb. The $dim is the size of the matrix. The $degree is a matrix of non-negetive numbers, the degree of the polynomial elements of the polynomial matrix. The $symb the symbol to print and identify the reference to the algebraic set over which the polynom defined – sorry, this option not fully works.

Usage

polyMgen.a(nrow=2, ncol=3, rawData=1:(nrow * ncol * (max(degree) + 1)),
           symb="x", rand=FALSE, degree=2, byrow=FALSE)
polyMgen.b(nrow=2, ncol=3, rawData=1:(nrow * ncol * (degree + 1)),
           symb="x", rand=FALSE, degree=2, byrow=FALSE)
polyMgen.c(nrow=2, ncol=3, rawData=1:(nrow * ncol * (max(degree) + 1)),
           symb="x", rand=FALSE, degree=2, byrow=FALSE)
polyMgen.d(nrow=2, ncol=3, rawData=NULL,
           symb="x", rand=NULL, degree=NULL, byrow=FALSE)
polyMgen.varma(nrow=3, ncol=3, rawData=list(polynomial(1:3)),
               symb="x", rand=FALSE, degree=c(1,1), byrow=FALSE)

Arguments

`nrow`	the desired number of rows.
`ncol`	the desired number of columns.
`degree`	the desired degrees of polynomials when it is random filled.
`rawData`	material to fill the polynomial matrix. In case of `polyMgen.a`, `polyMgen.b` and `polyMgen.c` a vector of the required coefficients of the polynomials. The case of `polyMgen.d` is different: here the `rawData` is a list of `polynomial` class objects.
`symb`	the desired polynom symbol.
`rand`	the name of wanted random generator to generate the coefficients of a random polynomial matrix.
`byrow`	logical. If `FALSE` (the default) the matrix is filled by columns, if `TRUE` the matrix is filled by rows.

Details

A polynomial matrix from the given material rawData or (the default) or random values the four possible storage methods are:

'array', when the coefficient matrices of the polinomial matrix stored in two independent element of the list of the polyMatrix: the constant matrix in $const, and the coefficients of the first, second... degree of the polynomial in the first, second,... element of the $array. In this case the extra class of the generated polyMatrix object is polyMarray.
'broad-matrix', when the coefficients are stored in one broad matrix in the $broad element of the polyMatrix object. The size of this broad matrix is: nx(m*(k+1)), when the degree of the nxm size polynomial matrix is d. In this case the extra class of the generated polyMatrix object is polyMbroad.
'list of cells', when the nxm size coefficient matrices are stored in d+1 element of the $cells list element of the polyMatrix object. In this case the extra class of the generated polyMatrix object is polyMcells.
'double list', when the elements of the polynomial matrix are stored in the form of polynomial class objects in a nxm element double list. In this case the extra class of the generated polyMatrix object is polyMdlist.

Value

A polyMatrix class object with a extra class polyMarray, polyMbroad, polyMcells or polyMdlist, which signs the storage method.

Examples

polyMgen.a() # default size & coefficients & rank

# given coefficients & default rank
polyMgen.a(2, 3, 1:6)
# given coefficients & rank
polyMgen.a(2, 3, 1:6, degree=1)
# given coefficients & ranks
polyMgen.a(2, 3, 1:36, degree=matrix(0:5, 2, 3))
# given coefficients & ranks
polyMgen.a(2, 3, 1:12, degree=matrix(2:0, 2, 3))

polyMgen.a(rand=TRUE) # normally distributed coefficients

polyMgen.a(rand=rexp) # exponentially distributed coefficients

pois.vg.fv <- function(x) rpois(x,1)
polyMgen.a(rand=pois.vg.fv) # Poisson(1) distributed coefficients

# clean up
# rm(pois.vg.fv)

polyMgen.b() # class="polyMbroad", broad matrix form
polyMgen.c() # class="polyMcells", list of coefficient matrices
polyMgen.d() # class="polyMdlist", dubble list

polyMgen.d(2,2, rawData=list(
  polynom::polynomial(1), polynom::polynomial(c(0,0,1)),
  polynom::polynomial(c(0,1)), polynom::polynomial(0)
))

px <- polyMgen.d(3, 3, rawData=ch2pn(
    c("-3 + z^2", "2 + 4*z", "-z^2", "1", "2", "3 + z", "2*z", "0", "2 - 3*z"), "z"
  )
)
class(px) # "polyMdlist" "polyMatrix"
px

px <- polyMgen.d(3, 3, rawData=ch2pn(
    c("-3 + z^2", "2 + 4*z", "-z^2", "1", "2", "3 + z", "2*z", "0", "2 - 3*z"), "z"
  ),
  byrow=TRUE
)
class(px) # "polyMdlist" "polyMatrix"
px

# clean up
# rm(px)

polyMatrix

Infrastructure for Manipulation Polynomial Matrices

v0.3.1

MIT + file LICENSE

Authors

Tamas Prohle [aut], Peter Prohle [aut], Nikolai Ryzhkov [aut, cre], Ildiko Laszlo [aut] (<https://orcid.org/0000-0003-2324-8183>), Ulas Onat Alakent [ctb]

Initial release