Python is_independentの例

コード例 #1

ファイル: hw5.py プロジェクト: pcp135/C-CtM

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

コード例 #2

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

コード例 #3

ファイル: hw5.py プロジェクト: seeker-for-code/coding_the_matrix

def morph(S, B):
    '''
    Input:
        - S: a list of distinct Vec instances
        - B: a list of linearly independent Vec instances
        - Span S == Span B
    Output: a list of pairs of vectors to inject and eject
    Example:
        >>> #This is how our morph works.  Yours may yield different results.
        >>> S = [list2vec(v) for v in [[1,0,0],[0,1,0],[0,0,1]]]
        >>> B = [list2vec(v) for v in [[1,1,0],[0,1,1],[1,0,1]]]
        >>> morph(S, B)
        [(Vec({0, 1, 2},{0: 1, 1: 1, 2: 0}), Vec({0, 1, 2},{0: 1, 1: 0, 2: 0})), (Vec({0, 1, 2},{0: 0, 1: 1, 2: 1}), Vec({0, 1, 2},{0: 0, 1: 1, 2: 0})), (Vec({0, 1, 2},{0: 1, 1: 0, 2: 1}), Vec({0, 1, 2},{0: 0, 1: 0, 2: 1}))]

    '''
    A = []
    Sprime = S[:]
    ret = []

    while len(A) < len(B):
        for vec in B:
            A.append(vec)
            if is_independent(A):
                A.pop()
                ejected = exchange(Sprime, A, vec)
                Sprime[Sprime.index(ejected)] = vec
                ret.append((vec, ejected))
                A.append(vec)
            else:
                A.pop()
    return ret

コード例 #4

ファイル: hw5.py プロジェクト: 4DD8A19D69F5324F9D49D17EF78BBBCC/co_ding_the_m_atrix

def morph(S, B):
    '''
    Input:
        - S: a list of distinct Vec instances
        - B: a list of linearly independent Vec instances
        - Span S == Span B
    Output: a list of pairs of vectors to inject and eject
    Example:
        >>> #This is how our morph works.  Yours may yield different results.
        >>> S = [list2vec(v) for v in [[1,0,0],[0,1,0],[0,0,1]]]
        >>> B = [list2vec(v) for v in [[1,1,0],[0,1,1],[1,0,1]]]
        >>> morph(S, B)
        [(Vec({0, 1, 2},{0: 1, 1: 1, 2: 0}), Vec({0, 1, 2},{0: 1, 1: 0, 2: 0})), (Vec({0, 1, 2},{0: 0, 1: 1, 2: 1}), Vec({0, 1, 2},{0: 0, 1: 1, 2: 0})), (Vec({0, 1, 2},{0: 1, 1: 0, 2: 1}), Vec({0, 1, 2},{0: 0, 1: 0, 2: 1}))]

    '''
    A = []
    Sprime = S[:]
    ret = []

    while len(A) < len(B):
        for vec in B:
            A.append(vec)
            if is_independent(A):
                A.pop()
                ejected = exchange(Sprime, A, vec)
                Sprime[Sprime.index(ejected)] = vec
                ret.append((vec, ejected))
                A.append(vec)
            else:
                A.pop()
    return ret

コード例 #5

def is_invertible(M): 
    '''
    input: A matrix, M
    outpit: A boolean indicating if M is invertible.
    
    >>> M = Mat(({0, 1, 2, 3}, {0, 1, 2, 3}), {(0, 1): 0, (1, 2): 1, (3, 2): 0, (0, 0): 1, (3, 3): 4, (3, 0): 0, (3, 1): 0, (1, 1): 2, (2, 1): 0, (0, 2): 1, (2, 0): 0, (1, 3): 0, (2, 3): 1, (2, 2): 3, (1, 0): 0, (0, 3): 0})
    >>> is_invertible(M)
    True
    '''
    return len(M.D[0]) == len(M.D[1]) and is_independent([v for k,v in mat2coldict(M).items() ])

コード例 #6

ファイル: hw5.py プロジェクト: seeker-for-code/coding_the_matrix

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
    '''

    while not is_independent(T):
        T.pop()
    return T

コード例 #7

ファイル: hw5.py プロジェクト: 4DD8A19D69F5324F9D49D17EF78BBBCC/co_ding_the_m_atrix

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
    '''

    while not is_independent(T):
        T.pop()
    return T

コード例 #8

ファイル: hw5.py プロジェクト: johnmerm/matrix

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 in range(len(T)):
        if is_independent(S):
            return S
        S.remove(S[i])

コード例 #9

ファイル: hw5.py プロジェクト: fperezlo/matrix

def is_invertible(M): 
    '''
    input: A matrix, M
    outpit: A boolean indicating if M is invertible.
    
    >>> M = Mat(({0, 1, 2, 3}, {0, 1, 2, 3}), {(0, 1): 0, (1, 2): 1, (3, 2): 0, (0, 0): 1, (3, 3): 4, (3, 0): 0, (3, 1): 0, (1, 1): 2, (2, 1): 0, (0, 2): 1, (2, 0): 0, (1, 3): 0, (2, 3): 1, (2, 2): 3, (1, 0): 0, (0, 3): 0})
    >>> is_invertible(M)
    True
    '''
    from hw4 import is_independent
    from matutil import mat2rowdict, mat2coldict
    rowsdict = mat2rowdict(M)
    rowslist = [ rowsdict[i] for i in rowsdict.keys() ]
    
    coldict = mat2coldict(M)
    collist = [ coldict[i] for i in coldict.keys() ]
    
    if len(rowslist) == len(collist) and is_independent(collist): return True
    else: return False

コード例 #10

ファイル: hw5.py プロジェクト: fperezlo/matrix

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

コード例 #11

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
    basis = list()
    for vec in T:
        if True == is_independent(basis+[vec]):
            basis.append(vec)
    return basis

コード例 #12

ファイル: hw5.py プロジェクト: dimr/computing-the-matrix

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
    '''
    C=[]
    for i,v in enumerate(T):
        C.append(v)
        if not is_independent(C):
            C.pop()
    return C

コード例 #13

def is_invertible(M):
    '''
    input: A matrix, M
    outpit: A boolean indicating if M is invertible.
    
    >>> M = Mat(({0, 1, 2, 3}, {0, 1, 2, 3}), {(0, 1): 0, (1, 2): 1, (3, 2): 0, (0, 0): 1, (3, 3): 4, (3, 0): 0, (3, 1): 0, (1, 1): 2, (2, 1): 0, (0, 2): 1, (2, 0): 0, (1, 3): 0, (2, 3): 1, (2, 2): 3, (1, 0): 0, (0, 3): 0})
    >>> is_invertible(M)
    True
    '''
    from hw4 import is_independent
    from matutil import mat2rowdict, mat2coldict
    rowsdict = mat2rowdict(M)
    rowslist = [rowsdict[i] for i in rowsdict.keys()]

    coldict = mat2coldict(M)
    collist = [coldict[i] for i in coldict.keys()]

    if len(rowslist) == len(collist) and is_independent(collist): return True
    else: return False

コード例 #14

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

コード例 #15

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
    '''
    rank_T = rank(T)
    S = []
    for x in T:
        if(is_independent([S+[x]])):
           S.append(x)
           if rank(S) == rank_T:break
    return S

コード例 #16

ファイル: hw5.py プロジェクト: pashanitw/coding-the-matrix

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

    basis = list()
    for vec in T:
        if True == is_independent(basis + [vec]):
            basis.append(vec)
    return basis