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#!/usr/bin/python
from Numeric import *
from LinearAlgebra import *
pascals_triangle = []
rows_done = 0
def choose(n, k):
r = 1
for i in range(1,k+1):
r *= n-k+i
r /= i
return r
# http://www.research.att.com/~njas/sequences/A109954
def T(n, k):
return ((-1)**(n+k))*choose(n+k+2, 2*k+2)
def inver(q):
result = zeros((q+2,q+2))
q2 = q/2+1
for i in range(q2):
for j in range(i+1):
val = T(i,j)
result[q/2-j][q/2-i] = val
result[q/2+j+2][q/2+i+2] = val
result[q/2+j+2][q/2-i-1] = -val
if q/2+i+3 < q+2:
result[q/2-j][q/2+i+3] = -val
for i in range(q+2):
result[q2][i] = [1,-1][(i-q2)%2]
return result
def simple(q):
result = zeros((q+2,q+2))
for i in range(q/2+1):
for j in range(q+1):
result[j][i] = choose(q-2*i, j-i)
result[j+1][q-i+1] = choose(q-2*i, j-i)
result[q/2+1][q/2+1] = 1
return result
print "The aim of the game is to work out the correct indexing to make the two matrices match :)"
s = simple(4)
si = floor(inverse(s)+0.5)
print si.astype(Int)
print inver(4)
exit(0)
print "<html><head><title></title></head><body>"
def arrayhtml(a):
s = "<table>"
r,c = a.shape
for i in range(r):
s += "<tr>";
for j in range(c):
s += "<td>%g</td>" % a[i,j]
s += "</tr>"
s += "</table>"
return s
for i in [21]:#range(1,13,2):
s = simple(i)
print "<h1>T<sup>-1</sup> = </h1>"
print arrayhtml(s)
print "<h1>T = </h1>"
print arrayhtml(floor(inverse(s)+0.5))
print "</body></html>"
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