R/invembeddingR6.R

In mrparker909/MGLMRiem: Multivariate Generalized Linear Models on Riemannian Manifolds

# function vnew = invembeddingR6(p, v)
# %INVEMBEDDINGR6 is the inverse of EMBEDDINGR6. This brings v in R6 to in TpM.
# %This transports v from T_{I}M to TpM.
# %
# %   This will be replaced later with the group action for n x n spd matrix and a proper vectorization. 
# %    
# %   vnew = EMBEDDINGR6(p,v)
# %
# %   p is a base point. 
# %   vnew is a tangent vector in TpM.
# %   v is a vector in R6.
# %
# %   See also INVEMBEDDINGR6_VECS, EMBEDDINGR6_VECS, EMBEDDINGR6
# 
# %   Hyunwoo J. Kim
# %   $Revision: 0.1 $  $Date: 2014/06/23 15:34:51$ 
#   
#   %    v = [Sxx Sxy Sxz Syy Syz Szz]';    
#   
#   %   step 1
#   w = [1  sqrt(2) sqrt(2)   1 sqrt(2) 1]';
#   S = vec2symmx(v./w);
#   
#   %   step 2    
#   sqrtp= sqrtm(p);
#   vnew = sqrtp*S*sqrtp;
#   end

#' @export
invembeddingR6 <- function(p, v) {
#INVEMBEDDINGR6 is the inverse of EMBEDDINGR6. This brings v in R6 to in TpM.
#This transports v from T_{I}M to TpM.
#
#   This will be replaced later with the group action for n x n spd matrix and a proper vectorization. 
#    
#   vnew = EMBEDDINGR6(p,v)
#
#   p is a base point. 
#   vnew is a tangent vector in TpM.
#   v is a vector in R6.
#
#   See also INVEMBEDDINGR6_VECS, EMBEDDINGR6_VECS, EMBEDDINGR6

#   Hyunwoo J. Kim
#   $Revision: 0.1 $  $Date: 2014/06/23 15:34:51$ 
  
#   Migrated to R by Matthew RP Parker
#   $Revision: 0.2 $  $Date: 2019/06/17 $ 

#    v = [Sxx Sxy Sxz Syy Syz Szz]';    
  
  #   step 1
  w = t(c(1,  sqrt(2), sqrt(2), 1, sqrt(2), 1))
  S = vec2symmx(v = v/w)
  
  #   step 2    
  sqrtp= Isqrtm(p)$B
  vnew = sqrtp%*%drop(S)%*%sqrtp
  
  return(vnew)
}