# Hermite(), inc(), nonneg(), avg(), table(), stats()
#
# R. Perry, July 2018

from sympy import zeros

# create G from A,b and call lllhermite()
#
def Hermite( Dio, A, b):
  G = zeros(A.shape[1]+1, A.shape[0]+1)
  G[:-1, :-1] = A.T
  G[-1, :-1] = b.reshape(1, b.shape[0])
  G[-1, -1] = 1
  H, P, rank = Dio.lllhermite(G)
  return G, H, P, rank

# inc: add 1 to c; changes c and z in caller
# returns (count,valid) where count is number of z values tested
# and valid is 1 if no z values are negative, 0 on overflow, otherwise -1
# c[0]...c[r-1] represent digits in the range 0 to n
# pruning: skip values with sum(c) > n or which make negative z worse
#
def inc(c, r, n, z, y, R, ylen):
  count = 0
  t = sum(c)
  for i in range(r):
    valid = 1
    c[i] += 1
    t += 1
    if c[i] > n or t > n: t -= c[i]; c[i] = 0; continue
    z[0,:] = y + c*R
    count += 1
    prune = 0
    for j in range(ylen):
      if z[j] < 0:
        valid = -1
        if R[i,j] < 0: prune = 1
    if prune: t -= c[i]; c[i] = 0; continue
    return (count,valid)
  return (count,0)

# nonneg: return 1 if all vector elements are non-negative, otherwise 0
#
def nonneg( z, n):
  for i in range(n):
    if z[i] < 0: return 0
  return 1

# avg: calculate average solution
#
def avg( xTlist):
  m = len(xTlist)
  n = len(xTlist[0])
  a=[0 for i in range(n)]
  for i in range(m):
    for j in range(n):
      a[j] += xTlist[i][j]
  for j in range(n): a[j] /= m
  return a

# table: print matrix as HTML table
#
def table( a):
  (m,n) = a.shape
  print('<table class="matrix">')
  for i in range(m):
    print(' <tr>')
    space='<td>&nbsp;</td>'
    for j in range(n):
      if j == n-1: space=''
      print(' <td align=right>' + str(a[i,j]) + '</td>' + space)
    print(' </tr>')
  print('</table>')

# stats: compute mean and variance from data
# x[i] is number of occurances of vals[i]
#
def stats( x, vals):
  n = sum(x)
  m = sum(x[i]*vals[i] for i in range(len(x)))/n
  v = 0 if n < 2 else sum(x[i]*(vals[i]-m)**2 for i in range(len(x)))/(n-1)
  return m, v