In lingxuko/pack: Function used to solve Sylvester equation AX + XB = C

knitr::opts_chunk$set(
  echo = TRUE,
  collapse = TRUE,
  comment = "#>"
)
library(SolSyl)
library(Matrix)
library(knitr)

#A B are square Matrices and dimension of A is larger
A <- matrix(c(1,0,-1,2,1,0,0,0,-1),3,3,byrow = TRUE) #3x3 Matrix
B <- matrix(c(2,1,0,0),2,2,byrow = TRUE) #2x2 Matrix
C <- matrix(c(2,2,1,1,1,1),3,2) #3x2 Matrix
SolveSylvester(A,B,C)

#A B are square Matrices and dimensions of A and B are the same
A <- matrix(c(1,0,-1,2,1,0,0,0,-1),3,3,byrow = TRUE) #3x3 Matrix
B <- matrix(c(2,1,0,0,1,3,4,5,0),3,3,byrow = TRUE) #3x3 Matrix
C <- matrix(c(2,2,1,1,1,1,3,2,4),3,3) #3x3 Matrix
SolveSylvester(A,B,C)

#A B are square Matrices and dimension of B is larger
A <- matrix(c(1,0,-1,2),2,2,byrow = TRUE) #2x2 Matrix
B <- matrix(c(2,1,0,0,1,3,4,5,0),3,3,byrow = TRUE) #3x3 Matrix
C <- matrix(c(2,2,1,3,2,4),2,3) #2x3 Matrix
SolveSylvester(A,B,C)

#A B are square Matrices and dimension of B is larger
A <- matrix(c(1,0,-1,2),2,2,byrow = TRUE) #2x2 Matrix
B <- matrix(c(2,1,0,0,1,3,4,5,0),3,3,byrow = TRUE) #3x3 Matrix
C <- matrix(c(2,2,1,3,2,4),2,3) #2x3 Matrix
X <- SolveSylvester(A,B,C)

#A B are square Matrices and dimension of B is larger
A <- matrix(c(1,0,-1,2),2,2,byrow = TRUE) #2x2 Matrix
B <- 2 #number
C <- matrix(c(2,2,1,3),2,2) #2x2 Matrix
SolveSylvester(A,B,C)

#A B are square Matrices and dimension of B is larger
A <- 2 #number
B <- matrix(c(1,0,-1,2),2,2,byrow = TRUE) #2x2 Matrix
C <- matrix(c(2,2,1,3),2,2) #2x2 Matrix
SolveSylvester(A,B,C)

set.seed(123)
A <- matrix(rnorm(9,0,1),3,3)
B <- 0
C <- matrix(rnorm(9,0,1),3,3)
all.equal.numeric(as.vector(solve(A,C)),as.vector(SolveSylvester(A,B,C)))
microbenchmark(solve(A,C),SolveSylvester(A,B,C))
#C++ sloves matrix equations faster than R