def GF2_span(D, L):
'''
>>> from GF2 import one
>>> D = {'a', 'b', 'c'}
>>> L = [Vec(D, {'a': one, 'c': one}), Vec(D, {'b': one})]
>>> len(GF2_span(D, L))
4
>>> Vec(D, {}) in GF2_span(D, L)
True
>>> Vec(D, {'b': one}) in GF2_span(D, L)
True
>>> Vec(D, {'a':one, 'c':one}) in GF2_span(D, L)
True
>>> Vec(D, {x:one for x in D}) in GF2_span(D, L)
True
'''
l = []
multiplied =[]
for e in L:
a= scalar_mul(e, 0)
multiplied.append(a)
b = scalar_mul(e, 1)
multiplied.append(b)
for i in multiplied:
for j in multiplied:
final = add(i,j)
if final not in l:
l.append(final)
return l
def GF2_span(D, L):
'''
from GF2 import one
D = {'a', 'b', 'c'}
L = [Vec(D, {'a': one, 'c': one}), Vec(D, {'b': one})]
len(GF2_span(D, L))
4
Vec(D, {}) in GF2_span(D, L)
True
Vec(D, {'b': one}) in GF2_span(D, L)
True
Vec(D, {'a':one, 'c':one}) in GF2_span(D, L)
True
Vec(D, {x:one for x in D}) in GF2_span(D, L)
True
'''
from GF2 import one
from itertools import product
import vec
prods = [xx for xx in product([0,one], repeat=len(L))]
final_vecs = []
for prod in prods:
vecs = []
for ii, jj in enumerate(prod):
vecs.append(vec.scalar_mul(L[ii],jj))
final_vecs.append(vec_sum(vecs, D))
return final_vecs
def scale_vecs(vecdict):
'''
>>> v1 = Vec({1,2,3}, {2: 9})
>>> v2 = Vec({1,2,4}, {1: 1, 2: 2, 4: 8})
>>> scale_vecs({3: v1, 5: v2}) == [Vec({1,2,3},{2: 3.0}), Vec({1,2,4},{1: 0.2, 2: 0.4, 4: 1.6})]
True
'''
return [scalar_mul(vecdict[k], 1.0/k) for k in vecdict]
def scale_vecs(vecdict):
'''
>>> v1 = Vec({1,2,4}, {2: 9})
>>> v2 = Vec({1,2,4}, {1: 1, 2: 2, 4: 8})
>>> result = scale_vecs({3: v1, 5: v2})
>>> len(result)
2
>>> [v in [Vec({1,2,4},{2: 3.0}), Vec({1,2,4},{1: 0.2, 2: 0.4, 4: 1.6})] for v in result]
[True, True]
'''
return [ scalar_mul(v,1/k) for (k, v) in vecdict.items()]
def scale_vecs(vecdict):
'''
>>> v1 = Vec({1,2,4}, {2: 9})
>>> v2 = Vec({1,2,4}, {1: 1, 2: 2, 4: 8})
>>> result = scale_vecs({3: v1, 5: v2})
>>> len(result)
2
>>> [v in [Vec({1,2,4},{2: 3.0}), Vec({1,2,4},{1: 0.2, 2: 0.4, 4: 1.6})] for v in result]
[True, True]
'''
return [scalar_mul(vecdict[i], 1. / i) for i in vecdict.keys()]
def scale_vecs(vecdict):
'''
>>> v1 = Vec({1,2,3}, {2: 9})
>>> v2 = Vec({1,2,4}, {1: 1, 2: 2, 4: 8})
>>> scale_vecs({3: v1, 5: v2}) == [Vec({1,2,3},{2: 3.0}), Vec({1,2,4},{1: 0.2, 2: 0.4, 4: 1.6})]
True
'''
## l=[]
## for (key, value) in vecdict.items():
## x = scalar_mul(value, 1/key)
## l.append(x)
# return l
return [scalar_mul(value, 1/key) for (key,value) in vecdict.items()]
def gradient_descent_step(A, b, w, sigma):
'''
Input:
- A: feature Mat
- b: diagnoses Vec
- w: hypothesis Vec
- sigma: step size
Output:
- The vector w' resulting from 1 iteration of gradient descent
starting from w and moving sigma.
'''
hypothesis_vec = find_grad(A,b,w)
x = scalar_mul(hypothesis_vec,sigma)
next_w = w - x
return next_w
def scale_vecs(vecdict):
'''
>>> v1 = Vec({1,2,4}, {2: 9})
>>> v2 = Vec({1,2,4}, {1: 1, 2: 2, 4: 8})
>>> result = scale_vecs({3: v1, 5: v2})
>>> len(result)
2
>>> [v in [Vec({1,2,4},{2: 3.0}), Vec({1,2,4},{1: 0.2, 2: 0.4, 4: 1.6})] for v in result]
[True, True]
'''
retveclist = list()
from vec import scalar_mul
for k in vecdict.keys():
v = vecdict[k]
retveclist.append(scalar_mul(v, (1/k)))
#domain = v.D
#for d in domain:
# if d in v.f and k != 0:
# v.f[d] /= k
#retveclist.append(v)
return retveclist
def scale_vecs(vecdict):
return [scalar_mul(vecdict[k], 1.0/k) for k in vecdict]
from vec import Vec
from vec import scalar_mul
from GF2 import one
v1 = Vec([0, 1, 2, 3, 4],{0:one, 1:one, 3:one, 4:one})
v2 = Vec([0, 1, 2, 3, 4],{2: one})
v3 = Vec([0, 1, 2, 3, 4],{2:one, 3:one, 4:one})
v4 = Vec([0, 1, 2, 3, 4],{0: one, 2:one, 3:one, 4:one})
v5 = Vec([0, 1, 2, 3, 4],{0: one, 1:one, 2:one, 3:one, 4:one})
for x1 in (0, one):
for x2 in (0, one):
for x3 in (0, one):
for x4 in (0, one):
for x5 in (0, one):
if (scalar_mul(v1,x1)+scalar_mul(v2,x2)+scalar_mul(v3,x3)+scalar_mul(v4,x4)+scalar_mul(v5,x5)) == Vec([0, 1, 2, 3, 4],{}):
print(x1, ", ", x2, ", ", x3, ", ", x4, ", ", x5)
from vec import Vec
from vec import scalar_mul
from GF2 import one
v1 = Vec([0, 1, 2, 3, 4, 5, 6, 7],{0: one, 1: one})
v2 = Vec([0, 1, 2, 3, 4, 5, 6, 7],{1: one, 2: one})
v3 = Vec([0, 1, 2, 3, 4, 5, 6, 7],{0: one, 3: one})
v4 = Vec([0, 1, 2, 3, 4, 5, 6, 7],{1: one, 4: one})
v5 = Vec([0, 1, 2, 3, 4, 5, 6, 7],{2: one, 4: one})
v6 = Vec([0, 1, 2, 3, 4, 5, 6, 7],{3: one, 4: one})
v7 = Vec([0, 1, 2, 3, 4, 5, 6, 7],{5: one, 7: one})
v8 = Vec([0, 1, 2, 3, 4, 5, 6, 7],{6: one, 7: one})
for x1 in (0, one):
for x2 in (0, one):
for x3 in (0, one):
for x4 in (0, one):
for x5 in (0, one):
for x6 in (0, one):
for x7 in (0, one):
for x8 in (0, one):
if (scalar_mul(v1,x1)+scalar_mul(v2,x2)+scalar_mul(v3,x3)+scalar_mul(v4,x4)+scalar_mul(v5,x5)+scalar_mul(v6,x6)+scalar_mul(v7,x7)+scalar_mul(v8,x8)) == Vec([0, 1, 2, 3, 4, 5, 6, 7],{1: one, 3: one}):
print(x1, ", ", x2, ", ", x3, ", ", x4, ", ", x5, ", ", x6, ", ", x7, ", ", x8)
def rep2vec(u, veclist):
return sum([scalar_mul(veclist[i], u[i]) for i in range(len(veclist))])
def lin_comb(vlist, clist):
return sum([scalar_mul(v, a) for (v, a) in zip(vlist, clist)])
