#!/usr/bin/env python
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 1997-2016 California Institute of Technology.
# Copyright (c) 2016-2021 The Uncertainty Quantification Foundation.
# License: 3-clause BSD.  The full license text is available at:
#  - https://github.com/uqfoundation/mystic/blob/master/LICENSE
"""
tools for generating points on a grid
"""

def gridpts(q, dist=None):
    """
takes a list of lists of arbitrary length q = [[1,2],[3,4]]
and produces a list of gridpoints g = [[1,3],[1,4],[2,3],[2,4]]

Notes:
    if a mystic.math.Distribution is provided, use it to inject randomness
    """
    w = [[] for i in range(len(q[-1]))]
    for j in range(len(q)-1,-1,-1):
      for k in range(len(q[j])):
        for l in range(k*len(w)//len(q[j]), (k+1)*len(w)//len(q[j])):
          w[l].append(q[j][k])
      if j: w += [i[:] for i in w[:]*(len(q[j-1])-1)]
    pts = [list(reversed(w[i])) for i in range(len(w))]
    # inject some randomness
    if dist is None: return pts
    if not len(pts): return pts
    pts += dist((len(pts),len(pts[0])))
    return pts.tolist()


def samplepts(lb,ub,npts,dist=None):
    """
takes lower and upper bounds (e.g. lb = [0,3], ub = [2,4])
produces a list of sample points s = [[1,3],[1,4],[2,3],[2,4]]

Inputs:
    lb  --  a list of the lower bounds
    ub  --  a list of the upper bounds
    npts  --  number of sample points
    dist  --  a mystic.math.Distribution instance
    """
    from mystic.math.samples import random_samples
    q = random_samples(lb,ub,npts,dist)
    return q.T.tolist()
   #q = [list(i) for i in q]
   #q = zip(*q)
   #return [list(i) for i in q]


def fillpts(lb,ub,npts,data=None,rtol=None,dist=None):
    """
takes lower and upper bounds (e.g. lb = [0,3], ub = [2,4])
finds npts that are at least rtol away from legacy data
produces a list of sample points s = [[1,3],[1,4],[2,3],[2,4]]

Inputs:
    lb  --  a list of the lower bounds
    ub  --  a list of the upper bounds
    npts  --  number of sample points
    data  --  a list of legacy sample points
    rtol  --  target radial distance from each point
    dist  --  a mystic.math.Distribution instance

Notes: if rtol is None, use max rtol; if rtol < 0, use quick-n-dirty method
    """
    bounds = list(zip(lb,ub))
    from mystic.math.distance import euclidean as metric
    #XXX: expose solver settings to user? #XXX: better npop,ftol? faster?
    ###if rtol is None or type(rtol) in (int, float):
    from mystic.solvers import diffev as solver
    kwds = dict(npop=20, ftol=1e-4, gtol=None, disp=0, full_output=0)
    ###initial = lambda : bounds
    ###else: # assume it's a string
    #   from mystic.solvers import fmin_powell as solver
    #   kwds = dict(xtol=1e-8, ftol=1e-8, gtol=2, disp=0, full_output=0)
    #   if rtol == 'None': rtol = None
    #   else: rtol = float(rtol)
    #   import random as rd
    #   initial = lambda : [rd.randrange(l,u)+rd.random() for (l,u) in bounds]
    #from numpy import round
    #kwds['constraints'] = lambda x: round(x, 3)
    # copy the legacy data points (e.g. monitor.x) #XXX: more efficient method?
    pts = [] if data is None else list(data)
    # 'min', 'np.sum()', 'np.min()' are also a choice of distance metric
    if rtol and rtol < 0: # neg radius uses quick-n-dirty method
        def holes(x):
            return (metric(pts,x,axis=0).min(axis=0) < -rtol).sum()
    elif rtol is None: # no radius finds max distance away
        def holes(x):
            res =  metric(pts,x,axis=0).min()
            return -res
    else: # all points should be at least rtol away
        def holes(x):
            res =  metric(pts,x,axis=0).min()
            return -res if res < rtol else 0.0
    # iteratively find a point away from all other points
    for pt in range(npts):
        res = solver(holes, x0=bounds, bounds=bounds, **kwds)
        #res,cost = res[0],res[1]
        pts.append(res.ravel().tolist())
    pts = pts[-npts:]
    # inject some randomness #XXX: what are alternatives? some sampling?
    if dist is None: return pts
    if not len(pts): return pts
    pts += dist((len(pts),len(pts[0])))
    return pts.tolist()


def randomly_bin(N, ndim=None, ones=True, exact=True):
    """
generate N bins randomly gridded across ndim dimensions

Inputs:
    N  --  integer number of bins, where N = prod(bins)
    ndim  --  integer length of bins, thus ndim = len(bins)
    ones  --  if False, prevent bins from containing "1s", wherever possible
    exact  --  if False, find N-1 bins for prime numbers
    """
    if ndim == 0: return []
    if N == 0: return [0] if ndim else [0]*ndim
    from itertools import chain
    from mystic.tools import random_state
    try:
        xrange
    except NameError:
        xrange = range
    random = random_state().random
    def factors(n):
        result = list()
        for i in chain([2],xrange(3,n+1,2)):
            s = 0
            while n%i == 0:
                n //= i
                s += 1
            result.extend([i]*s)
            if n == 1:
                return result
    result = factors(N)
    dim = nfact = len(result)
    prime = nfact == 1
    if ndim: result += [1] * (ndim - (nfact // ndim));  dim = ndim
    elif ones: result += [1] # add some 'randomness' by adding a "1"
    # if ones, mix in the 1s; otherwise, only use 1s when ndim < len(result)
    if ones: result = sorted(result, key=lambda v: random())
    else: result[:nfact] = sorted(result[:nfact], key=lambda v: random())
    from numpy import product
    result = [product(result[i::dim]) for i in range(dim)]
    # if not ones, now needs a full sort to sort in the 1s
    if not ones: result = sorted(result, key=lambda v: random())
    elif not ndim and 1 in result: result.remove(1) # remove the added "1"
    # if it's a prime, then do N-1 if exact=False
    if not exact and N > 3 and prime:
        result = randomly_bin(N-1, ndim, ones)
    return result


#######################################################################
if __name__ == '__main__':

  nbins = 2
  lower = [0, 3, 6]
  upper = [2, 5, 8]

  # generate arrays of points defining a grid in parameter space
  grid_dimensions = len(lower)
  bins = []
  for i in range(grid_dimensions):  #XXX: different nbins for each direction?
    step = abs(upper[i] - lower[i])//nbins  #XXX: // or / ?
    bins.append( [lower[i] + (j+0.5)*step for j in range(nbins)] )

  # build a grid of starting points
  initial_values = gridpts(bins)
  print("grid: %s" % initial_values)

  npts = 10
  lower = [0.0, 3.0, 6.0]
  upper = [2.0, 5.0, 8.0]

  # generate a set of random starting points
  initial_values = samplepts(lower,upper,npts)
  print("scatter: %s" % initial_values)

  npts = 8
  lower = [0.0, 0.0, 0.0] 
  upper = [6.0, 6.0, 6.0]

  # generate a set of space-filling points
  initial_values = fillpts(lower,upper,npts,[[3,3,3]])
  print("filled: %s" % initial_values)


# EOF
