%pylab inline

n = 6
pre_t = rand(n, n)
print pre_t

col_sums = sum(pre_t, axis=0)
print col_sums

t = pre_t / col_sums
print t

sum(t, axis=0), t.min(), t.max()

v = zeros(n)
v[0] = 1
print t.dot(v)

def ndot(m, n, v):
    for i in range(n):
        v = m.dot(v)
    return v

print ndot(t, 1, v)

print ndot(t, 2, v)

print ndot(t, 10, v)

print array([ndot(t, k, v) for k in (0, 1, 10, 20, 100, 101, 102)])

sum(ndot(t, 100, v))

print ndot(t, 100, t)

vals, vecs = linalg.eig(t)
print vals; print vecs

eig0 = vecs[:,0]
print eig0; print eig0/sum(eig0)

pt = array([[0, 1],
            [1, 0]])
print array([ndot(pt, k, [1, 0]) for k in range(8)])

bpt = array([[0, .1,  0,.9],
             [.1, 0, .9, 0],
             [0, .9,  0,.1],
             [.9, 0, .1, 0]])
print array([ndot(bpt, k, [1, 0, 0, 0]) for k in range(8) + [100, 101]])

bt = array([[0, .1,  0,  .9],
            [.1, 0, .9, 0],
            [0, .9,  0, 0.0999],
            [.9, 0, .1, 0.0001]])
print array([ndot(bt, k, [1, 0, 0, 0])
             for k in range(8)
             + [100, 101, 100000, 100001]])

vals2, vecs2 = linalg.eig(bt)
print vals2; print vecs2

vals2, vecs2= linalg.eig([[0.1, 0.1, 0.1, 0.7],
                          [0.7, 0.1, 0.1, 0.1],
                          [0.1, 0.7, 0.1, 0.1],
                          [0.1, 0.1, 0.7, 0.1]])
print vals2; print vecs2

print vecs2[:,0]

st_denorm = array([[ 1,  1, -1],
                   [ 1,  1,  0],
                   [-1, -1,  1.]])

def normcols(m):
    return m / (m**2).sum(axis=0)**0.5

st = normcols(st_denorm)
print st

print array([ndot(st, k, [1, 0, 0]) for k in range(10)])

print array([ndot(st, k, [0, 0, 1]) for k in range(10)])

def ndotn(m, n, v):
    for i in range(n):
        v = m.dot(v)
        v /= v.T.dot(v)
    return v

print array([ndotn(m, k, [0, 0, 1])
             for m in st, st_denorm
             for k in range(10) + [100, 101, 102, 1001, 10000]])

svals, svecs = linalg.eig(st)
print svals; print svecs

st_n = st / svals.max()
print st_n

minority_report = array([ndot(st_n, k, [0, 0, 1]) for k in range(8) + [100, 101]])
print minority_report

first_eigenvector = svecs[:,0]
minority_report[-1] / first_eigenvector

print array([ndot(st_n, k, [1, 0, 0]) for k in range(8) + [100, 101]])

ndot(st_n, 100, [1, 0, 0]) / first_eigenvector

print array([ndot(st_n, k, [0, 1, 1]) for k in range(8) + [100, 101]])

print ndot(st_n, 100, [0, .785, 1])

tl = array([[1, 1, 1],
            [1, 1, 0],
            [-1, -1, 1]])
tlvals, tlvecs = linalg.eig(tl)
tl_n = tl / tlvals.max()
print tl_n

print tlvals; print tlvecs