maotai (version 0.2.5)

sylvester: Solve Sylvester Equation

Description

The Sylvester equation is of form $$AX + XB = C$$ where \(X\) is the unknown and others are given. Though it's possible to have non-square \(A\) and \(B\) matrices, we currently support square matrices only. This is a wrapper of armadillo's sylvester function.

Usage

sylvester(A, B, C)

Value

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

Arguments

A

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

B

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

C

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)
B = matrix(rnorm(25),nrow=5)
C = A%*%X + X%*%B

#  solve using 'sylvester' function
solX = sylvester(A,B,C)
pm1 = "* Experiment with Sylvester 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=""))