# Last edited on 2021-08-01 20:46:53 by jstolfi

import rn

def basis_sampled_project(f, C, w):
  # Assumes {f} is a vector of some size {ns}. Assumes {C} is a list of
  # {nb} orthonormal vectors of the same size. Projects the vector {f}
  # orthogonally onto the space {<C>}. If {w} is not {None}, uses the
  # weighted dot product {rn.wdot} instead of plain {rn.dot}.
  #
  # Returns the coefficient vector {cf[0..nb-1]} of the component
  # {fp[0..ns-1]}  of {f} that is in the space {<C>}, that component {fp},
  # and the residual vector {fr[0..ns-1] = f - fp}.
  
  ns = len(f)
  nb = len(C)
  
  cf = []
  fp = [0]*ns
  for Cj in C:
   cfj = rn.wdot(fr, Cj, w)
   cf.append(cfj)
   fp = rn.mix(1, fp, cfj, Cj)
  fr = rn.sub(f, fp)
  return cf, fp, fr
  # ----------------------------------------------------------------------