matutil.py

# Copyright 2013 Philip N. Klein
from vec import Vec
from mat import Mat

def efficient_rowdict2mat(rowdict):
    col_labels = value(rowdict).D
    M = Mat((set(keys(rowdict)), col_labels), {})
    for r in rowdict:
        for c in rowdict[r].f:
            M[r,c] = rowdict[r][c]
    return M

def identity(D, one):
    """Given a set D and the field's one, returns the DxD identity matrix
    e.g.:

    >>> identity({0,1,2}, 1)
    Mat(({0, 1, 2}, {0, 1, 2}), {(0, 0): 1, (1, 1): 1, (2, 2): 1})
    """
    return Mat((D,D), {(d,d):one for d in D})

def keys(d):
    """Given a dict, returns something that generates the keys; given a list,
       returns something that generates the indices.  Intended for coldict2mat and rowdict2mat.
    """
    return d.keys() if isinstance(d, dict) else range(len(d))

def value(d):
    """Given either a dict or a list, returns one of the values.
       Intended for coldict2mat and rowdict2mat.
    """
    return next(iter(d.values())) if isinstance(d, dict) else d[0]

def mat2rowdict(A):
    """Given a matrix, return a dictionary mapping row labels of A to rows of A
           e.g.:

       >>> M = Mat(({0, 1, 2}, {0, 1}), {(0, 1): 1, (2, 0): 8, (1, 0): 4, (0, 0): 3, (2, 1): -2})
           >>> mat2rowdict(M)
           {0: Vec({0, 1},{0: 3, 1: 1}), 1: Vec({0, 1},{0: 4, 1: 0}), 2: Vec({0, 1},{0: 8, 1: -2})}
           >>> mat2rowdict(Mat(({0,1},{0,1}),{}))
           {0: Vec({0, 1},{0: 0, 1: 0}), 1: Vec({0, 1},{0: 0, 1: 0})}
           """
    return {row:Vec(A.D[1], {col:A[row,col] for col in A.D[1]}) for row in A.D[0]}

def mat2coldict(A):
    """Given a matrix, return a dictionary mapping column labels of A to columns of A
           e.g.:
           >>> M = Mat(({0, 1, 2}, {0, 1}), {(0, 1): 1, (2, 0): 8, (1, 0): 4, (0, 0): 3, (2, 1): -2})
           >>> mat2coldict(M)
           {0: Vec({0, 1, 2},{0: 3, 1: 4, 2: 8}), 1: Vec({0, 1, 2},{0: 1, 1: 0, 2: -2})}
           >>> mat2coldict(Mat(({0,1},{0,1}),{}))
           {0: Vec({0, 1},{0: 0, 1: 0}), 1: Vec({0, 1},{0: 0, 1: 0})}
    """
    return {col:Vec(A.D[0], {row:A[row,col] for row in A.D[0]}) for col in A.D[1]}

def coldict2mat(coldict):
    """
    Given a dictionary or list whose values are Vecs, returns the Mat having these
    Vecs as its columns.  This is the inverse of mat2coldict.
    Assumes all the Vecs have the same label-set.
    Assumes coldict is nonempty.
    If coldict is a dictionary then its keys will be the column-labels of the Mat.
    If coldict is a list then {0...len(coldict)-1} will be the column-labels of the Mat.
    e.g.:

    >>> A = {0:Vec({0,1},{0:1,1:2}),1:Vec({0,1},{0:3,1:4})}
    >>> B = [Vec({0,1},{0:1,1:2}),Vec({0,1},{0:3,1:4})]
    >>> mat2coldict(coldict2mat(A)) == A
    True
    >>> coldict2mat(A)
    Mat(({0, 1}, {0, 1}), {(0, 1): 3, (1, 0): 2, (0, 0): 1, (1, 1): 4})
    >>> coldict2mat(A) == coldict2mat(B)
    True
    """
    row_labels = value(coldict).D
    return Mat((row_labels, set(keys(coldict))), {(r,c):coldict[c][r] for c in keys(coldict) for r in row_labels})

def rowdict2mat(rowdict):
    """
    Given a dictionary or list whose values are Vecs, returns the Mat having these
    Vecs as its rows.  This is the inverse of mat2rowdict.
    Assumes all the Vecs have the same label-set.
    Assumes row_dict is nonempty.
    If rowdict is a dictionary then its keys will be the row-labels of the Mat.
    If rowdict is a list then {0...len(rowdict)-1} will be the row-labels of the Mat.
    e.g.:

    >>> A = {0:Vec({0,1},{0:1,1:2}),1:Vec({0,1},{0:3,1:4})}
    >>> B = [Vec({0,1},{0:1,1:2}),Vec({0,1},{0:3,1:4})]
    >>> mat2rowdict(rowdict2mat(A)) == A
    True
    >>> rowdict2mat(A)
    Mat(({0, 1}, {0, 1}), {(0, 1): 2, (1, 0): 3, (0, 0): 1, (1, 1): 4})
    >>> rowdict2mat(A) == rowdict2mat(B)
    True
    """
    col_labels = value(rowdict).D
    return Mat((set(keys(rowdict)), col_labels), {(r,c):rowdict[r][c] for r in keys(rowdict) for c in col_labels})

def listlist2mat(L):
    """Given a list of lists of field elements, return a matrix whose ith row consists
    of the elements of the ith list.  The row-labels are {0...len(L)}, and the
    column-labels are {0...len(L[0])}
    >>> A=listlist2mat([[10,20,30,40],[50,60,70,80]])
    >>> print(A)
    <BLANKLINE>
            0  1  2  3
         -------------
     0  |  10 20 30 40
     1  |  50 60 70 80
    <BLANKLINE>
  """
    m,n = len(L), len(L[0])
    return Mat((set(range(m)),set(range(n))), {(r,c):L[r][c] for r in range(m) for c in range(n)})

def submatrix(M, rows, cols):
    return Mat((M.D[0]&rows, M.D[1]&cols), {(r,c):val for (r,c),val in M.f.items() if r in rows and c in cols})