def subset_basis(T):
'''
input: A list, T, of Vecs
output: A list, S, containing Vecs from T, that is a basis for the
space spanned by T.
>>> a0 = Vec({'a','b','c','d'}, {'a':1})
>>> a1 = Vec({'a','b','c','d'}, {'b':1})
>>> a2 = Vec({'a','b','c','d'}, {'c':1})
>>> a3 = Vec({'a','b','c','d'}, {'a':1,'c':3})
>>> subset_basis([a0,a1,a2,a3]) == [Vec({'c', 'b', 'a', 'd'},{'a': 1}), Vec({'c', 'b', 'a', 'd'},{'b': 1}), Vec({'c', 'b', 'a', 'd'},{'c': 1})]
True
'''
# Subset basis is not unique. Depends on where one starts.
# For example the above problems also has a basis given by
# >>> subset_basis([a0,a1,a2,a3]) == [Vec({'c', 'b', 'a', 'd'},{'b': 1}), Vec({'c', 'b', 'a', 'd'},{'c': 1}), Vec({'c', 'b', 'a', 'd'},{'a':1, 'c': 3})]
inT = T[:]
for i in range(len(list(inT))):
if is_superfluous (inT, i):
del(inT[i])
break
return inT
def findbasis(V): while not hw4.is_independent(V): for i in range(len(V)): if hw4.is_superfluous(V,i): V.remove(V[i]) break return V
def findbasis(V):
while not hw4.is_independent(V):
for i in range(len(V)):
if hw4.is_superfluous(V, i):
V.remove(V[i])
break
return V
def rec_shrink_basis(S, i):
if i == len(S):
return S
if is_superfluous(S,i):
S.pop(i)
else:
i=i+1
return rec_shrink_basis(S,i)
def subset_basis(T):
'''
input: A list, T, of Vecs
output: A list, S, containing Vecs from T, that is a basis for the
space spanned by T.
>>> a0 = Vec({'a','b','c','d'}, {'a':1})
>>> a1 = Vec({'a','b','c','d'}, {'b':1})
>>> a2 = Vec({'a','b','c','d'}, {'c':1})
>>> a3 = Vec({'a','b','c','d'}, {'a':1,'c':3})
>>> subset_basis([a0,a1,a2,a3]) == [Vec({'c', 'b', 'a', 'd'},{'a': 1}), Vec({'c', 'b', 'a', 'd'},{'b': 1}), Vec({'c', 'b', 'a', 'd'},{'c': 1})]
True
'''
S = list(T)
for i, v in enumerate(S):
if is_superfluous(S, i):
S.remove(v)
return S
def subset_basis(T):
'''
input: A list, T, of Vecs
output: A list, S, containing Vecs from T, that is a basis for the
space spanned by T.
>>> a0 = Vec({'a','b','c','d'}, {'a':1})
>>> a1 = Vec({'a','b','c','d'}, {'b':1})
>>> a2 = Vec({'a','b','c','d'}, {'c':1})
>>> a3 = Vec({'a','b','c','d'}, {'a':1,'c':3})
>>> subset_basis([a0,a1,a2,a3]) == [Vec({'c', 'b', 'a', 'd'},{'a': 1}), Vec({'c', 'b', 'a', 'd'},{'b': 1}), Vec({'c', 'b', 'a', 'd'},{'c': 1})]
True
'''
S = list(T)
for i,v in enumerate(S):
if is_superfluous(S, i):
S.remove(v)
return S
def subset_basis(T):
'''
input: A list, T, of Vecs
output: A list, S, containing Vecs from T, that is a basis for the
space spanned by T.
>>> a0 = Vec({'a','b','c','d'}, {'a':1})
>>> a1 = Vec({'a','b','c','d'}, {'b':1})
>>> a2 = Vec({'a','b','c','d'}, {'c':1})
>>> a3 = Vec({'a','b','c','d'}, {'a':1,'c':3})
>>> subset_basis([a0,a1,a2,a3]) == [Vec({'c', 'b', 'a', 'd'},{'a': 1}), Vec({'c', 'b', 'a', 'd'},{'b': 1}), Vec({'c', 'b', 'a', 'd'},{'c': 1})]
True
'''
from hw4 import is_independent,is_superfluous
T_temp = list(T)
if not is_independent(T):
for i in range(len(T)-1,-1,-1):
if is_superfluous(T_temp,i): T_temp.remove(T[i])
return T_temp
def subset_basis(T):
'''
input: A list, T, of Vecs
output: A list, S, containing Vecs from T, that is a basis for the
space spanned by T.
>>> a0 = Vec({'a','b','c','d'}, {'a':1})
>>> a1 = Vec({'a','b','c','d'}, {'b':1})
>>> a2 = Vec({'a','b','c','d'}, {'c':1})
>>> a3 = Vec({'a','b','c','d'}, {'a':1,'c':3})
>>> subset_basis([a0,a1,a2,a3]) == [Vec({'c', 'b', 'a', 'd'},{'a': 1}), Vec({'c', 'b', 'a', 'd'},{'b': 1}), Vec({'c', 'b', 'a', 'd'},{'c': 1})]
True
'''
from hw4 import is_independent, is_superfluous
T_temp = list(T)
if not is_independent(T):
for i in range(len(T) - 1, -1, -1):
if is_superfluous(T_temp, i): T_temp.remove(T[i])
return T_temp
def subset_basis(T):
'''
input: A list, T, of Vecs
output: A list, S, containing Vecs from T, that is a basis for the
space spanned by T.
>>> a0 = Vec({'a','b','c','d'}, {'a':1})
>>> a1 = Vec({'a','b','c','d'}, {'b':1})
>>> a2 = Vec({'a','b','c','d'}, {'c':1})
>>> a3 = Vec({'a','b','c','d'}, {'a':1,'c':3})
>>> subset_basis([a0,a1,a2,a3]) == [Vec({'c', 'b', 'a', 'd'},{'a': 1}), Vec({'c', 'b', 'a', 'd'},{'b': 1}), Vec({'c', 'b', 'a', 'd'},{'c': 1})]
True
'''
S = []
for i, l in enumerate(T):
S.append(l)
if hw4.is_superfluous(S, len(S)-1):
S.remove(l)
return S
def subset_basis(T):
'''
input: A list, T, of Vecs
output: A list, S, containing Vecs from T, that is a basis for the
space spanned by T.
>>> a0 = Vec({'a','b','c','d'}, {'a':1})
>>> a1 = Vec({'a','b','c','d'}, {'b':1})
>>> a2 = Vec({'a','b','c','d'}, {'c':1})
>>> a3 = Vec({'a','b','c','d'}, {'a':1,'c':3})
>>> subset_basis([a0,a1,a2,a3]) == [Vec({'c', 'b', 'a', 'd'},{'a': 1}), Vec({'c', 'b', 'a', 'd'},{'b': 1}), Vec({'c', 'b', 'a', 'd'},{'c': 1})]
True
'''
S = []
for i, l in enumerate(T):
S.append(l)
if hw4.is_superfluous(S, len(S) - 1):
S.remove(l)
return S
def subset_basis(T):
'''
input: A list, T, of Vecs
output: A list, S, containing Vecs from T, that is a basis for the
space spanned by T.
>>> a0 = Vec({'a','b','c','d'}, {'a':1})
>>> a1 = Vec({'a','b','c','d'}, {'b':1})
>>> a2 = Vec({'a','b','c','d'}, {'c':1})
>>> a3 = Vec({'a','b','c','d'}, {'a':1,'c':3})
>>> subset_basis([a0,a1,a2,a3]) == [Vec({'c', 'b', 'a', 'd'},{'a': 1}), Vec({'c', 'b', 'a', 'd'},{'b': 1}), Vec({'c', 'b', 'a', 'd'},{'c': 1})]
True
'''
from hw4 import is_superfluous
i = 0 # initializing index for list T
S = T.copy() # creating copy of T
while i < len(S):
if is_superfluous(S, i):
S = S[:i] + S[i + 1:] #remove entry i
else:
i += 1
return S
