Function reference • rationalmatrices

Basic Classes

Different representations of rational matrix functions and special cases.

lmfd(): Constructor for Left Matrix Fraction Descriptions (LMFDs)

rmfd(): Constructor for Right Matrix Fraction Descriptions (RMFDs)

stsp(): Constructor for Statespace Realizations

polm(): Constructor for Polynomial Matrices

lpolm(): Constructor for Laurent Polynomial Matrices

pseries(): Power series Parameters

Transformation between Different Representations

as.* methods

as.lmfd(): Coerce to Left Matrix Fraction Description

as.lpolm(): Coerce to Laurent polynom object

as.polm(): Coerece to polynomial object

as.rmfd(): Coerce to Right Matrix Fraction Description

as.stsp(): Coerce to Statespace Realization

pseries2lmfd(): Construct a LMFD Representation from Impulse Response

pseries2rmfd(): Construct an RMFD Representation from Impulse Response

pseries2stsp(): Ho-Kalman Realization Algorithm

basis2nu() nu2basis() pseries2nu(): Tools related to Kronecker indices

Poles and Zeros

poles() zeroes(): Poles and Zeroes

zvalue(): Frequency Response Function

zvalues(): Frequency Response Function

is.* Methods

is.stable() is.miniphase(): Check Properties of Rational Matrices

is.polm() is.lpolm() is.lmfd() is.rmfd() is.stsp() is.pseries() is.zvalues(): Check Objects

is.coprime(): Left Prime and Left Coprime Polynomials

is.minimal(): Check the Minimality of a Statespace Realization

Helpers for creating objects for testing

test_array(): Create Test Array

test_lmfd(): Create Test Rational Matrix in LMFD Form

test_lpolm(): Create Test Laurent Polynomial Matrix

test_polm(): Create Test Polynomial Matrix

test_rmfd(): Create Test Rational Matrix in RMFD Form

test_stsp(): Create Test Rational Matrix in Statespace Form

Arithmetic (incl derivative and transpose)

`%r%`: Matrix Multiplication of Rational Matrices

Ops(<ratm>): Arithmetic Ops Group Methods for Rational Matrices

polm_div(): Division Algorithm for Polynomial Matrices

upgrade_objects(): Upgrade Objects to Common Class

derivative(): Derivative of a rational Matrix

Ht(): Hermitean Transpose

t(<polm>) t(<lpolm>) t(<lmfd>) t(<rmfd>) t(<stsp>) t(<pseries>) t(<zvalues>): Rational Matrix Transpose

Generic Functions

Standard methods for basic S3 classes and their helpers.

`[`(<polm>) `[`(<lpolm>) `[`(<lmfd>) `[`(<rmfd>) `[`(<stsp>) `[`(<pseries>) `[`(<zvalues>) `$`(<lmfd>) `$`(<rmfd>) `$`(<stsp>) `$`(<zvalues>): Extract Parts of a Rational Matrix

`[<-`(<polm>) `[<-`(<lpolm>): Replace Parts of a (Laurent) Polynomial Matrix

rbind(<ratm>) cbind(<ratm>): Combine Rational Matrices by Rows or Columns

dim(<polm>) dim(<lpolm>) dim(<lmfd>) dim(<rmfd>) dim(<stsp>) dim(<pseries>) dim(<zvalues>): Dimensions of Objects

str(<lpolm>) str(<polm>) str(<lmfd>) str(<rmfd>) str(<stsp>) str(<pseries>) str(<zvalues>): Display the Structure of Objects

print(<lpolm>) print(<polm>) print(<lmfd>) print(<rmfd>) print(<stsp>) print(<pseries>) print(<zvalues>): Print Methods

plot(<pseries>) plot(<zvalues>): Plot Methods

plot_3D(): Plot 3D Arrays

zoom_plot(): Zoom and Scroll

as_tex_matrix(): TeX Matrix

as_tex_matrixfilter(): TeX Matrix Polynomial Filters

as_tex_matrixpoly(): TeX Matrix Polynomials

as_txt_scalarfilter(): Coerce Scalar Polynomial Filters to Character Strings

as_txt_scalarpoly(): Coerce Scalar Polynomials to Character Strings

Factorisations, including Wiener-Hopf-Factorisation (WHF) specific functions

whf(): Wiener-Hopf Factorization

polm2fwd(): Transforms to Polynomial in Forward Shift

get_fwd() get_bwd(): Forward and Backward Bracket

snf(): Smith Normal Form

hnf(): Hermite Normal Form

Numeric Reduction and Factorisation (including Degree)

col_end_matrix(): Column End Matrix of a Polynomial Matrix

col_reduce(): Construct a Column Reduced Polynomial Matrix

degree(): Polynomial Degree

purge_rc(): Purge Rows or Columns of a Polynomial Matrix

prune(): Prune (Laurent) Matrix Polynomial

schur(): Schur Decomposition

ql_decomposition() lq_decomposition(): QL and LQ Decomposition

Blaschke et al.

blaschke() blaschke2(): Blaschke Factors

roots_as_list(): Polynomial Roots as List

reflect_poles(): Reflect Poles of Rational Matrices

reflect_zeroes(): Reflect Zeroes of Rational Matrices

State Space specific Functions

balance(): Balanced Realization and Balanced Truncation

companion_matrix(): Companion Matrix of a Polynomial Matrix

ctr_matrix() obs_matrix(): Controllability and Observability Matrix

grammians(): Grammians

state_trafo(): State Transformation

lyapunov(): Lyapunov Equation

Block Matrices

bdiag(): Block Diagonal Matrix

bmatrix(): Block matrices

btoeplitz(): Block Toeplitz matrix

bhankel(): Block Hankel matrix

dbind(): Bind Arrays

array2data.frame(): Coerce arrays to data frames

Other Stuff

ind2sub() sub2ind(): Transform between Linear Index and Matrix Indices

iseq(): Sequence generation

rationalmatrices: A Collection of Tools for Rational Matrices

%>%: Pipe operator