maotai (version 0.2.5)

lyapunov: Solve Lyapunov Equation

Description

The Lyapunov equation is of form $$AX + XA^\top = Q$$ where \(A\) and \(Q\) are square matrices of same size. Above form is also known as continuous form. This is a wrapper of armadillo's sylvester function.

Usage

lyapunov(A, Q)

Value

a solution matrix \(X\) of size \((p\times p)\).

Arguments

A

a \((p\times p)\) matrix as above.

Q

a \((p\times p)\) matrix as above.

References

sanderson_armadillo_2016maotai

eddelbuettel_rcpparmadillo_2014maotai

Examples

## simulated example
#  generate square matrices
A = matrix(rnorm(25),nrow=5)
X = matrix(rnorm(25),nrow=5)
Q = A%*%X + X%*%t(A)

#  solve using 'lyapunov' function
solX = lyapunov(A,Q)
if (FALSE) {
pm1 = "* Experiment with Lyapunov Solver"
pm2 = paste("* Absolute Error  : ",norm(solX-X,"f"),sep="")
pm3 = paste("* Relative Error  : ",norm(solX-X,"f")/norm(X,"f"),sep="")
cat(paste(pm1,"\n",pm2,"\n",pm3,sep=""))
}