caracas (version 2.0.0)

linalg: Do linear algebra operation

Description

Performs various linear algebra operations like finding the inverse, the QR decomposition, the eigenvectors and the eigenvalues.

Usage

columnspace(x)
nullspace(x)
rowspace(x)
singular_values(x)
inv(x, method = c("lu", "gauss", "cf", "yac"))
inv2fl(x)
eigenval(x)
eigenvec(x)
GramSchmidt(x)
pinv(x)
rref(x)
QRdecomposition(x)
det(x, ...)

Value

Returns the requested property of a matrix.

Arguments

x

A matrix for which a property is requested

method

The default works by $LU$ decomposition. The alternatives are Gaussian elimination (gauss), the cofactor method (cf), and Ryacas (yac).

...

Auxillary arguments

See Also

do_la()

Examples

if (has_sympy()) {
  A <- matrix(c("a", "0", "0", "1"), 2, 2) %>% as_sym()
  
  QRdecomposition(A)
  eigenval(A)
  eigenvec(A)
  inv(A)
  inv2fl(A)
  det(A)
  
  ## Matrix inversion:
  d <- 3
  m <- matrix_sym(d, d)
  print(system.time(inv(m)))       ## Gauss elimination
  print(system.time(inv(m, method="cf")))     ## Cofactor 
  print(system.time(inv(m, method="lu")))     ## LU decomposition
  if (requireNamespace("Ryacas")){
    print(system.time(inv(m, method="yac")))  ## Use Ryacas
  }

  A <- matrix(c("a", "b", "c", "d"), 2, 2) %>% as_sym()
  evec <- eigenvec(A)
  evec
  evec1 <- evec[[1]]$eigvec
  evec1
  simplify(evec1)
  
  lapply(evec, function(l) simplify(l$eigvec))

  A <- as_sym("[[1, 2, 3], [4, 5, 6]]")
  pinv(A)


}