R/pseudo_inverse.R

In Dahaniel/DoOR.functions: Integrating Heterogeneous Odorant Response Data into a Common Response Model: A DoOR to the Complete Olfactome

# Evaluate the pseudoinvese of a matrix
# 
# Evaluate the pseudoinvese of a matrix
# 
# The pseudoinverse of the matrix x with singular value decomposition \eqn{x=U
# D V^'} is: \eqn{x^+ = V D^+ U^'} where D^+ is the pseudoinverse of D, which
# is formed by replacing every nonzero entry by its reciprocal.
# 
# @param x a matrix
# @author Shouwen Ma <\email{shouwen.ma@@uni-konstanz.de}>
# @seealso \code{\link{LLSIestPC}}, \code{\link{svd}}
# @keywords math
# @examples
# 
# x  <- matrix(seq(1,2,length=4),nrow = 2, ncol = 2)
# PI <- pseudo_inverse(x)
# x
# x%*%PI%*%x
# 
pseudo_inverse <-
function(x) 

# part of the DoOR package: (c) 2009 C. Giovanni Galizia, Daniel Muench, Martin
# Strauch, Anja Nissler, Shouwen Ma Neurobiology, University of Konstanz,
# Germany

## Evaluate the pseudoinvese of a matrix The pseudoinverse of the matrix x with
#singular value decomposition x = U %*% D %*% V^' is: x^+ = V %*% D^+ %*% U^' 
#where D^+ is the pseudoinverse of D, which is formed by replacing every nonzero
#entry by its reciprocal.

#  x: a numeric matrix

{
  svd_x <- svd(x)
  reciprocal_D <-
    matrix(rep(0, times = length(svd_x$d) ^ 2), nrow = length(svd_x$d))
  diag(reciprocal_D) <- svd_x$d ^ -1
  return(svd_x$v %*% reciprocal_D %*%  t(svd_x$u))
}