Package: polyMatrix 0.9.11
polyMatrix: Infrastructure for Manipulation Polynomial Matrices
Implementation of class "polyMatrix" for storing a matrix of polynomials and implements basic matrix operations; including a determinant and characteristic polynomial. It is based on the package 'polynom' and uses a lot of its methods to implement matrix operations. This package includes 3 methods of triangularization of polynomial matrices: Extended Euclidean algorithm which is most classical but numerically unstable; Sylvester algorithm based on LQ decomposition; Interpolation algorithm is based on LQ decomposition and Newton interpolation. Both methods are described in D. Henrion & M. Sebek, Reliable numerical methods for polynomial matrix triangularization, IEEE Transactions on Automatic Control (Volume 44, Issue 3, Mar 1999, Pages 497-508) <doi:10.1109/9.751344> and in Salah Labhalla, Henri Lombardi & Roger Marlin, Algorithmes de calcule de la reduction de Hermite d'une matrice a coefficients polynomeaux, Theoretical Computer Science (Volume 161, Issue 1-2, July 1996, Pages 69-92) <doi:10.1016/0304-3975(95)00090-9>.
Authors:
polyMatrix_0.9.11.tar.gz
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polyMatrix.pdf |polyMatrix.html✨
polyMatrix/json (API)
| # Install 'polyMatrix' in R: |
| install.packages('polyMatrix', repos = c('https://namezys.r-universe.dev', 'https://cloud.r-project.org')) |
Bug tracker:https://github.com/namezys/polymatrix/issues
Last updated 3 years agofrom:abdde48012. Checks:OK: 1 WARNING: 6. Indexed: yes.
| Target | Result | Date |
|---|---|---|
| Doc / Vignettes | OK | Aug 31 2024 |
| R-4.5-win | WARNING | Aug 31 2024 |
| R-4.5-linux | WARNING | Aug 31 2024 |
| R-4.4-win | WARNING | Aug 31 2024 |
| R-4.4-mac | WARNING | Aug 31 2024 |
| R-4.3-win | WARNING | Aug 31 2024 |
| R-4.3-mac | WARNING | Aug 31 2024 |
Exports:adjointcbindcharpolynomcofactordegreedetdiagGCDinvis.column.properis.polyMatrixis.properis.row.properis.zeroLCMmatrix.degreeminorncolnrowparse.polyMatrixparse.polynomialpolyMatrixpolyMatrix.applypredictrbindshowttrtriang_Sylvesterzero.round
Readme and manuals
Help Manual
| Help page | Topics |
|---|---|
| Adjugate or classical adjoint of a square matrix | adjoint adjoint,polyMatrix-method |
| Combine polynial matrices by rows or coluns | cbind rbind |
| Characteristic polynomial of matrix | charpolynom charpolynom,matrix-method charpolynom,polyMatrix-method charpolynom,polynomial-method degree,polyMatrixCharPolynomial-method predict,polyMatrixCharPolynomial-method show,polyMatrixCharPolynomial-method [[,polyMatrixCharPolynomial,ANY-method |
| Cofactor of matrix | cofactor |
| Gets maximum degree of polynomial objects | degree degree,matrix-method degree,numeric-method degree,polyMatrix-method degree,polynomial-method |
| Polynomial matrix Diagonals Extract or construct a diagonal polynomial matrix. | diag diag,polyMatrix-method diag,polynomial-method |
| GCD for polynomial matrices | GCD GCD,polyMatrix-method |
| Inverse polynomial matrix | inv |
| Check if object is polyMatrix | is.polyMatrix |
| Proper polynomial matrices | is.column.proper is.proper is.row.proper |
| Test if something is zero | is.zero is.zero,polyMatrix-method is.zero,polynomial-method |
| LCM for polynomial matrices | LCM LCM,polyMatrix-method |
| Degree of each item of matrix | matrix.degree matrix.degree,matrix-method matrix.degree,polyMatrix-method matrix.degree,polynomial-method |
| Minor of matrix item | minor |
| Build matrix of polynimal decomposition using Newton interpolation in Newton bais: (x-x_0), (x - x_0) * (x x_1) | newton |
| Parse polynomial matrix from strings | parse.polyMatrix |
| Parse polynomial from string | parse.polynomial |
| Create polyMatrix object | polyMatrix |
| A class to represent matrix of polinomials | !=,ANY,polyMatrix-method !=,polyMatrix,ANY-method %*%,matrix,polyMatrix-method %*%,polyMatrix,matrix-method %*%,polyMatrix,polyMatrix-method *,ANY,polyMatrix-method *,polyMatrix,numeric-method *,polyMatrix,polyMatrix-method *,polyMatrix,polynomial-method +,ANY,polyMatrix-method +,polyMatrix,matrix-method +,polyMatrix,missing-method +,polyMatrix,numeric-method +,polyMatrix,polyMatrix-method +,polyMatrix,polynomial-method -,ANY,polyMatrix-method -,polyMatrix,ANY-method -,polyMatrix,polyMatrix-method ==,ANY,polyMatrix-method ==,polyMatrix,matrix-method ==,polyMatrix,numeric-method ==,polyMatrix,polyMatrix-method ==,polyMatrix,polynomial-method det,polyMatrix-method dim,polyMatrix-method ncol,polyMatrix-method ncol,polynomial-method nrow,polyMatrix-method nrow,polynomial-method polyMatrix-class polyMatrixClass predict,polyMatrix-method round,polyMatrix-method show,polyMatrix-method [,polyMatrix,ANY,missing,missing-method [,polyMatrix,logical,logical,missing-method [,polyMatrix,logical,numeric,missing-method [,polyMatrix,missing,ANY,missing-method [,polyMatrix,missing,missing,missing-method [,polyMatrix,numeric,logical,missing-method [,polyMatrix,numeric,numeric,missing-method [<-,polyMatrix,ANY,missing,ANY-method [<-,polyMatrix,missing,ANY,ANY-method [<-,polyMatrix,missing,missing,ANY-method [<-,polyMatrix,numeric,numeric,matrix-method [<-,polyMatrix,numeric,numeric,numeric-method [<-,polyMatrix,numeric,numeric,polyMatrix-method [<-,polyMatrix,numeric,numeric,polynomial-method [[,polyMatrix,numeric-method |
| Apply for polynomial matrix | polyMatrix.apply |
| Polynomial matrix transpose | t,polyMatrix-method |
| Trace of a 'matrix' or 'polyMatrix' class matrix | tr |
| Triangularization of a polynomial matrix by interpolation method | triang_Interpolation |
| Triangularization of a polynomial matrix by Sylvester method | triang_Sylvester |
| Get zero lead hyper rows of size sub_nrow of matrix M | zero_lead_hyp_rows |
| Get zero lead rows of matrix M | zero_lead_rows |
| Rounds object to zero if it's too small | zero.round zero.round,polyMatrix-method zero.round,polynomial-method |
