# Last edited on 2021-07-31 15:39:40 by jstolfi

from ixdiff import ixdiff

def basis_sampled_write(wr, s, B, w, grid):
  # Assumes that {s} is a list of {ns} sampling points in {d}-space ({d}-tuples of floats)
  # and {B} is a list of {nb} vectors (lists) of {ns} floats, which are the 
  # values of {nb} basis functions at those sampling points.  Writes that data
  # to {wr}. 
  # 
  # The parameter {w}, if not {None}, is a vector of {ns} non-negative floats
  # that specify the weight of each sampling point.  If {None}, all
  # weights are assumed to be 1.
  #
  # Each line has the format 
  #
  #   "{k} {w[k]} {s[k][0]} ... {s[k][d-1]} {B[0][k]} ... {B[nb-1][k]}"
  #
  # for {k} in {0..ns-1}.
  #
  # If {grid} is true, the procedure assumes that the samples come from
  # a regular grid and are sorted in lex or reverse lex order. Then
  # blank lines are inserted between slices of the grid. THus, if {d} is
  # 2, the file can be used with {gnumplot}'s {splot} command.
  #
  nb = len(B)
  assert nb > 0, "empty basis"
  ns = len(s)
  sprev = None
  for ks in range(ns):
    sk = s[ks]
    if grid:
      for j in range(ixdiff(sprev, sk) - 1): wr.write("\n");
    wr.write("%5d" % ks)
    ws = 1 if w == None else w[ks]
    wr.write("  %12.10f " % ws)
    for skj in sk:
      wr.write(" %12.8f" % skj)
    wr.write(" ")
    for kb in range(nb):
      wr.write(" %+16.10f" % B[kb][ks])
    wr.write("\n")
    sprev = s[ks]
  wr.flush()
  return
  # ----------------------------------------------------------------------