Esempio n. 1
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def regular_completion(matrix):
    m,n = matrix.shape
    r = matrix.rank()
    
    #~ IPS()
    assert m!=n, "There is no regular completion of a square matrix."

    if m<n:
        assert r==m, "Matrix does not have full row rank."
        A, B, V_pi = reshape_matrix_columns(matrix)
        zeros = sp.zeros(n-m,m)
        ones = sp.eye(n-m)
        S = st.col_stack(zeros,ones)
        completion = S*V_pi.T
        
        regular_matrix = st.row_stack(matrix,completion)
        assert st.rnd_number_rank(regular_matrix)==n, "Regular completion seems to be wrong."

    elif n<m:
        assert r==n, "Matrix does not have full column rank."
        A, B, V_pi = reshape_matrix_columns(matrix.T)
        zeros = sp.zeros(m-n,n)
        ones = sp.eye(m-n)
        S = st.col_stack(zeros,ones)
        completion = V_pi*S.T
        
        regular_matrix = st.col_stack(completion,matrix)
        assert st.rnd_number_rank(regular_matrix)==m, "Regular completion seems to be wrong."

    return completion
Esempio n. 2
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def regular_completion(matrix):
    m, n = matrix.shape
    r = matrix.rank()

    #~ IPS()
    assert m != n, "There is no regular completion of a square matrix."

    if m < n:
        assert r == m, "Matrix does not have full row rank."
        A, B, V_pi = reshape_matrix_columns(matrix)
        zeros = sp.zeros(n - m, m)
        ones = sp.eye(n - m)
        S = st.col_stack(zeros, ones)
        completion = S * V_pi.T

        regular_matrix = st.row_stack(matrix, completion)
        assert st.rnd_number_rank(
            regular_matrix) == n, "Regular completion seems to be wrong."

    elif n < m:
        assert r == n, "Matrix does not have full column rank."
        A, B, V_pi = reshape_matrix_columns(matrix.T)
        zeros = sp.zeros(m - n, n)
        ones = sp.eye(m - n)
        S = st.col_stack(zeros, ones)
        completion = V_pi * S.T

        regular_matrix = st.col_stack(completion, matrix)
        assert st.rnd_number_rank(
            regular_matrix) == m, "Regular completion seems to be wrong."

    return completion
Esempio n. 3
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def is_linearly_independent(matrix, column_vector):
    m, n = matrix.shape

    rank1 = st.rnd_number_rank(matrix)
    tmp = st.concat_cols(matrix, column_vector)
    rank2 = st.rnd_number_rank(tmp)
    
    assert rank2 >= rank1
        
    return rank2 > rank1
Esempio n. 4
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def is_linearly_independent(matrix, column_vector):
    m, n = matrix.shape

    rank1 = st.rnd_number_rank(matrix)
    tmp = st.concat_cols(matrix, column_vector)
    rank2 = st.rnd_number_rank(tmp)

    assert rank2 >= rank1

    return rank2 > rank1
Esempio n. 5
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def left_pseudo_inverse(matrix):
    m, n = matrix.shape
    r = st.rnd_number_rank(matrix)
    #assert r==n, "Matrix does not have full column rank!"
    assert not is_zero_matrix(matrix), "Matrix is zero matrix!"

    transposed_rpinv = right_pseudo_inverse(matrix.T)
    matrix_lpinv = transposed_rpinv.T

    assert is_unit_matrix(matrix_lpinv*matrix), "Leftpseudoinverse is not correct."

    return matrix_lpinv
Esempio n. 6
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def left_pseudo_inverse(matrix):
    m, n = matrix.shape
    r = st.rnd_number_rank(matrix)
    #assert r==n, "Matrix does not have full column rank!"
    assert not is_zero_matrix(matrix), "Matrix is zero matrix!"

    transposed_rpinv = right_pseudo_inverse(matrix.T)
    matrix_lpinv = transposed_rpinv.T

    assert is_unit_matrix(matrix_lpinv *
                          matrix), "Leftpseudoinverse is not correct."

    return matrix_lpinv
Esempio n. 7
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def has_left_ortho_complement(matrix):
    r = st.rnd_number_rank(matrix)
    m, n = matrix.shape
    if(n>=m):
        return True if (r<m) else False
    return True
Esempio n. 8
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def is_regular_matrix(matrix):
    assert is_square_matrix(matrix), "Matrix is not a square matrix."
    m, n = matrix.shape
    r = st.rnd_number_rank(matrix)
    return True if (r == m) else False
Esempio n. 9
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def has_full_row_rank(matrix):
    m, n = matrix.shape
    r = st.rnd_number_rank(matrix)
    return True if (m==r) else False
Esempio n. 10
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def reshape_matrix_columns(P):
    m0, n0 = P.shape

    # pick m0 of the simplest lin. independent columns of P:
    P_new = remove_zero_columns(P)
    m1, n1 = P_new.shape

    list_of_cols = matrix_to_vectorlist(P_new)

    # sort by "complexity"
    if pinv_optimization == "free_symbols":
        cols_sorted_by_atoms = sorted(list_of_cols,
                                      key=lambda x: x.free_symbols,
                                      reverse=False)
    elif pinv_optimization == "count_ops":
        cols_sorted_by_atoms = sorted(list_of_cols,
                                      key=lambda x: nr_of_ops(x),
                                      reverse=False)
    elif pinv_optimization == "none":
        cols_sorted_by_atoms = list_of_cols

    # sort by number of zero entries
    colvecs_sorted = sorted(cols_sorted_by_atoms,
                            key=lambda x: count_zero_entries(x),
                            reverse=True)

    # pick m suitable column vectors and add to new matrix A: ----------
    A = colvecs_sorted[0]
    for j in range(len(colvecs_sorted) - 1):
        column = colvecs_sorted[j + 1]
        if is_linearly_independent(A, column):
            A = st.concat_cols(A, column)

        if st.rnd_number_rank(A) == m1:
            break

    assert A.is_square

    # calculate transformation matrix R: -------------------------------
    #R_tilde = sp.Matrix([])
    used_cols = []
    R = sp.Matrix([])
    for k in range(m1):
        new_column_index = k
        old_column_index = get_column_index_of_matrix(P, A.col(k))
        used_cols.append(old_column_index)
        tmp = sp.zeros(n0, 1)
        tmp[old_column_index] = 1

        #R_tilde = st.concat_cols(R_tilde,tmp)
        R = st.concat_cols(R, tmp)
    #R=R_tilde

    # remainder columns of R matrix
    #m2,n2 = R_tilde.shape
    m2, n2 = R.shape
    for l in range(n0):
        if l not in used_cols:
            R_col = sp.zeros(n0, 1)
            R_col[l] = 1
            R = st.concat_cols(R, R_col)

    m3, n3 = A.shape
    r2 = st.rnd_number_rank(A)
    assert m3 == r2, "A problem occured in reshaping the matrix."

    # calculate B matrix: ----------------------------------------------
    B = sp.Matrix([])
    tmp = P * R
    for i in range(n0 - m0):
        B = st.concat_cols(B, tmp.col(m0 + i))

    assert is_zero_matrix(
        (P * R) -
        st.concat_cols(A, B)), "A problem occured in reshaping the matrix."

    return A, B, R
Esempio n. 11
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def reshape_matrix_columns(P):
    m0, n0 = P.shape

    # pick m0 of the simplest lin. independent columns of P:
    P_new = remove_zero_columns(P)
    m1, n1 = P_new.shape

    list_of_cols = matrix_to_vectorlist(P_new)

    # sort by "complexity"
    if pinv_optimization=="free_symbols":
        cols_sorted_by_atoms = sorted( list_of_cols, key=lambda x: x.free_symbols, reverse=False)
    elif pinv_optimization=="count_ops":
        cols_sorted_by_atoms = sorted( list_of_cols, key=lambda x: nr_of_ops(x), reverse=False)
    elif pinv_optimization=="none":
        cols_sorted_by_atoms = list_of_cols

    # sort by number of zero entries
    colvecs_sorted = sorted( cols_sorted_by_atoms, key=lambda x: count_zero_entries(x), reverse=True)

    # pick m suitable column vectors and add to new matrix A: ----------
    A = colvecs_sorted[0]
    for j in xrange(len(colvecs_sorted)-1):
        column = colvecs_sorted[j+1]
        if is_linearly_independent(A,column):
            A = st.concat_cols(A,column)

        if st.rnd_number_rank(A)==m1:
            break

    assert A.is_square
            
    # calculate transformation matrix R: -------------------------------
    #R_tilde = sp.Matrix([])
    used_cols = []
    R = sp.Matrix([])
    for k in xrange(m1):
        new_column_index = k
        old_column_index = get_column_index_of_matrix(P,A.col(k))
        used_cols.append(old_column_index)
        tmp = sp.zeros(n0,1)
        tmp[old_column_index] = 1

        #R_tilde = st.concat_cols(R_tilde,tmp)
        R = st.concat_cols(R,tmp)
    #R=R_tilde

    # remainder columns of R matrix
    #m2,n2 = R_tilde.shape
    m2,n2 = R.shape
    for l in xrange(n0):
        if l not in used_cols:
            R_col = sp.zeros(n0,1)
            R_col[l] = 1
            R = st.concat_cols(R,R_col)

    m3, n3 = A.shape
    r2 = st.rnd_number_rank(A)
    assert m3==r2, "A problem occured in reshaping the matrix."

    # calculate B matrix: ----------------------------------------------
    B = sp.Matrix([])
    tmp = P*R
    for i in xrange(n0-m0):
        B = st.concat_cols(B,tmp.col(m0+i))

    
    assert is_zero_matrix( (P*R) - st.concat_cols(A,B)), "A problem occured in reshaping the matrix."

    return A, B, R
Esempio n. 12
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def is_special_case(Bi):
    """ Checks for special case
    """
    n, p = Bi.shape
    return True if (st.rnd_number_rank(Bi) < p) else False
Esempio n. 13
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def is_regular_matrix(matrix):
    assert is_square_matrix(matrix), "Matrix is not a square matrix."
    m, n = matrix.shape
    r = st.rnd_number_rank(matrix)
    return True if (r == m) else False
Esempio n. 14
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def is_special_case(Bi):
    """ Checks for special case
    """
    n, p = Bi.shape
    return True if (st.rnd_number_rank(Bi) < p) else False
Esempio n. 15
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def has_right_ortho_complement(matrix):
    r = st.rnd_number_rank(matrix)
    m, n = matrix.shape
    if(m>=n):
        return True if (r<n) else False
    return True
Esempio n. 16
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def has_right_ortho_complement(matrix):
    r = st.rnd_number_rank(matrix)
    m, n = matrix.shape
    if (m >= n):
        return True if (r < n) else False
    return True
Esempio n. 17
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def has_left_ortho_complement(matrix):
    r = st.rnd_number_rank(matrix)
    m, n = matrix.shape
    if (n >= m):
        return True if (r < m) else False
    return True
Esempio n. 18
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def has_full_row_rank(matrix):
    m, n = matrix.shape
    r = st.rnd_number_rank(matrix)
    return True if (m == r) else False
Esempio n. 19
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def end_condition(Bi):
    """ The algorithm ends if Bi has full row rank.
    """
    n, p = Bi.shape
    return True if (n == st.rnd_number_rank(Bi)) else False
Esempio n. 20
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def end_condition(Bi):
    """ The algorithm ends if Bi has full row rank.
    """
    n, p = Bi.shape
    return True if (n == st.rnd_number_rank(Bi)) else False