Skip to contents

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