示例#1
0
def direct_sum_decompose(U_basis, V_basis, w):
    '''
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    '''
    uv_basis = U_basis + V_basis #basis of space U+V
    x = vec2rep(uv_basis,w) #x is the coordination representation in space U+V : uv_basis*x = w
    #then split the coordinations : the first len(U_basis) are coordinates in U, the rest are coordinates in V

    # coordinates in U
    uc = list2vec([x[i] for i in range(len(U_basis))])
    # coordinates in V
    uv = list2vec([x[i] for i in range(len(U_basis),len(uv_basis))])

    u = coldict2mat(U_basis)*uc 
    v = coldict2mat(V_basis)*uv

    return (u,v)
示例#2
0
def direct_sum_decompose(U_basis, V_basis, w):
    '''
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.

    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    '''
    #W_basis = U_basis + V_basis
    #rep_w = vec2rep(W_basis, w)

    #U = set(range(len(U_basis)))
    #rep_u = Vec(U,{u:rep_w[u] for u in U})
    #u = coldict2mat(U_basis)*rep_u

    #V = set(range(len(U_basis), len(rep_w.D)))
    #rep_v = Vec(V,{v:rep_w[v] for v in V})
    #v = coldict2mat(V_basis)*rep_v
    T  = U_basis + V_basis
    x  = vec2rep(T, w)
    rep= list(x.f.values())
    u1 = list2vec(rep[0:len(U_basis)])
    v1 = list2vec(rep[len(U_basis):len(T)])
    u  = rep2vec(u1,U_basis)
    v  = rep2vec(v1,V_basis)
    return (u,v)
示例#3
0
def direct_sum_decompose(U_basis, V_basis, w):
    '''
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    '''
    joined_list = U_basis + V_basis
    u_vec = Vec(U_basis[0].D,{})
    v_vec = Vec(V_basis[0].D,{})
    from hw4 import vec2rep
    rep = vec2rep(joined_list, w)
    for key in rep.f.keys():
        if (joined_list[key] in U_basis):
            u_vec = u_vec + rep.f[key]*joined_list[key]
        elif (joined_list[key] in V_basis):
            v_vec = v_vec + rep.f[key]*joined_list[key]
    return (u_vec,v_vec)
示例#4
0
def direct_sum_decompose(U_basis, V_basis, w):
    '''
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    '''
    from hw4 import vec2rep
    u_dim = len(U_basis)
    v_dim = len(V_basis)

    w_rep = vec2rep(U_basis + V_basis, w)

    u = w_rep[0] * U_basis[0]
    for i in range(1, u_dim):
        u = u + w_rep[i] * U_basis[i]

    v = w_rep[u_dim] * V_basis[0]
    for i in range(1, v_dim):
        v = v + w_rep[u_dim + i] * V_basis[i]

    return (u, v)
示例#5
0
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}))]

    '''
    
    pairs = []                                                # Initialize to empty set of (inject, eject) pairs
    scpy = S[:]
    for inject in B:                                          # Inject one vector at a time from B into S.
        scpy = scpy + [inject]
        for i in range(len(scpy)):                            # Take one vector at a time in bigger set
            if scpy[i] == inject: continue                    # We don no want to test the vector we injected
            u = vec2rep (scpy[:i]+scpy[i+1:], scpy[i])        # See if it can be written as a linear combination of the remaining vectors
            if u is not None:                                 # If it can be expressed a linear combination , then it can be ejected 
                pairs.append((inject, scpy[i]))
                del(scpy[i])
                break                                         # Move on to the next vector to inject
    return pairs
示例#6
0
文件: hw5.py 项目: fperezlo/matrix
def direct_sum_decompose(U_basis, V_basis, w):
    '''
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    '''
    from hw4 import vec2rep
    U = coldict2mat(U_basis)
    V = coldict2mat(V_basis)
    sum = U_basis + V_basis
    sol_w = vec2rep(sum,w)
    lenU = len(U_basis)
    wu = list2vec ([ v for i, v in sol_w.f.items () if i <  lenU ])
    wv = list2vec ([ v for i, v in sol_w.f.items () if i >= lenU ])
    u = U*wu
    v = V*wv
    return (u,v)
示例#7
0
def direct_sum_decompose(U_basis, V_basis, w):
    """
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    """
    joined_list = U_basis + V_basis
    u_vec = Vec(U_basis[0].D, {})
    v_vec = Vec(V_basis[0].D, {})
    from hw4 import vec2rep

    rep = vec2rep(joined_list, w)
    for key in rep.f.keys():
        if joined_list[key] in U_basis:
            u_vec = u_vec + rep.f[key] * joined_list[key]
        elif joined_list[key] in V_basis:
            v_vec = v_vec + rep.f[key] * joined_list[key]
    return (u_vec, v_vec)
示例#8
0
def direct_sum_decompose(U_basis, V_basis, w):
    '''
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    '''
    from hw4 import vec2rep
    U = coldict2mat(U_basis)
    V = coldict2mat(V_basis)
    sum = U_basis + V_basis
    sol_w = vec2rep(sum, w)
    lenU = len(U_basis)
    wu = list2vec([v for i, v in sol_w.f.items() if i < lenU])
    wv = list2vec([v for i, v in sol_w.f.items() if i >= lenU])
    u = U * wu
    v = V * wv
    return (u, v)
示例#9
0
文件: hw5.py 项目: qluo1/codingMatrix
def direct_sum_decompose(U_basis, V_basis, w):
    """
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    """
    w_rep = vec2rep(U_basis + V_basis, w)

    return (vec2rep(U_basis, w), vec2rep(V_basis, w))
示例#10
0
文件: hw5.py 项目: qluo1/codingMatrix
def swap(S, A, v):
    """ 
        S - list of vector
        A - protected set 
        v - inject vec
        out: (T,w)
    """
    for i in range(len(S)):
        T = copy.copy(S)
        o, T[i] = T[i], v
        u = vec2rep(T, o)
        e = coldict2mat(T) * u - o
        if e * e < 10e-14:
            if o in A:
                continue
            return (T, o)
    return []
示例#11
0
def direct_sum_decompose(U_basis, V_basis, w):
    '''
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    '''
    dsum_basis = U_basis + V_basis                              # Basis of the direct sum is the union of the bases of the sub spaces
    sol = vec2rep (dsum_basis, w)                               # get the linear solution that multiplies with dsum_basis that gives w
    com = list (sol.f.values())                                 # break the U and V parts of the solution
    uvals = list2vec (com[:len(U_basis)])                            
    vvals = list2vec (com[len(U_basis):])     
    u = rep2vec(uvals, U_basis)
    v = rep2vec(vvals, V_basis)
    return u, v                       
示例#12
0
文件: hw5.py 项目: srikanth235/Matrix
def direct_sum_decompose(U_basis, V_basis, w):
    '''
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    '''
    result = vec2rep(U_basis+V_basis, w)
    u = Vec(U_basis[0].D,{})
    v = Vec(V_basis[0].D,{})
    for k,a in result.f.items():
        if k < len(U_basis):
            u = u + a*U_basis[k]
        else:
            v = v + a*V_basis[k-len(U_basis)]
    return (u, v)
示例#13
0
def direct_sum_decompose(U_basis, V_basis, w):
    '''
    input:  A list of Vecs, U_basis, containing a basis for a vector space, U.
    A list of Vecs, V_basis, containing a basis for a vector space, V.
    A Vec, w, that belongs to the direct sum of these spaces.
    output: A pair, (u, v), such that u+v=w and u is an element of U and
    v is an element of V.
    
    >>> U_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 1, 2: 0, 3: 0, 4: 6, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 11, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0}), Vec({0, 1, 2, 3, 4, 5},{0: 3, 1: 1.5, 2: 0, 3: 0, 4: 7.5, 5: 0})]
    >>> V_basis = [Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 7, 3: 0, 4: 0, 5: 1}), Vec({0, 1, 2, 3, 4, 5},{0: 0, 1: 0, 2: 15, 3: 0, 4: 0, 5: 2})]
    >>> w = Vec({0, 1, 2, 3, 4, 5},{0: 2, 1: 5, 2: 0, 3: 0, 4: 1, 5: 0})
    >>> direct_sum_decompose(U_basis, V_basis, w) == (Vec({0, 1, 2, 3, 4, 5},{0: 2.0, 1: 4.999999999999972, 2: 0.0, 3: 0.0, 4: 1.0, 5: 0.0}), Vec({0, 1, 2, 3, 4, 5},{0: 0.0, 1: 0.0, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0}))
    True
    '''
    coeffvec = vec2rep(U_basis+V_basis, w)
    u=list2vec([0,0,0,0,0,0])
    v=list2vec([0,0,0,0,0,0])

    for i in range(len(U_basis)):
        u=u+coeffvec[i]*U_basis[i]
    for j in range(len(V_basis)):
        v=v+coeffvec[j+len(U_basis)]*V_basis[j]
    return (u,v)
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}))]

    '''
    T = list(S)
    retList = list()
    for z in B:
        for k, v in vec2rep(T, z).f.items():
            if v != 0 and T[k] not in B:
                retList.append((z, T[k]))
                T[k] = z
                break
    return retList
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}))]

    '''
    T = list(S)
    retList = list()
    for z in B:
        for k,v in vec2rep(T, z).f.items():
            if v!=0 and T[k] not in B:
                retList.append((z, T[k]))
                T[k] = z
                break
    return retList
## week4 video 9  Perspective_rendering

from vecutil import list2vec
from hw4 import vec2rep
from plotting import plot
from matutil import coldict2mat

a1 = list2vec([1/100, 0, 0])
a2 = list2vec([0, 1/100, 0])
a3 = list2vec([-1/2, -1/2, 1])
camera_basis = [a1, a2, a3]

pt = list2vec([1, 1, 8])
coordinate_representation = vec2rep(camera_basis, pt)
print(coordinate_representation)

print(coordinate_representation/coordinate_representation[2])

i, j = 62.5, 62.5
plot([(i,j)], 80)

def line_segment(pt1, pt2, samples=100):
    return [(i/samples)*pt1 + (1-i/samples)*pt2 for i in range(samples+1)]

corners = [list2vec([1,1,8])+list2vec(v) for v in [[0,0,0],[1,0,0],[0,1,0],[1,1,0],[0,0,1],[1,0,1],[0,1,1],[1,1,1]]]
line_segments = [line_segment(corners[i], corners[j]) for i,j in [(0,1),(2,3),(0,2),(1,3),(4,5),(6,7),(4,6),(5,7),(0,4),(1,5),(2,6),(3,7)]]
pts = sum(line_segments, [])
reps = [vec2rep(camera_basis, v) for v in pts]

def scale_down(u): return list2vec([u[0]/u[2], u[1]/u[2], 1])
in_camera_plane = [scale_down(u) for u in reps]