from sympy.matrices.expressions.matexpr  import MatrixExpr
from sympy import Tuple, Basic
from sympy.functions.elementary.integers import floor
from sympy.assumptions import Q, ask

def normalize(i, parentsize):
    if isinstance(i, slice):
        i = (i.start, i.stop, i.step)
    if not isinstance(i, (tuple, list, Tuple)):
        if i < 0:
            i += parentsize
        i = (i, i+1, 1)
    i = list(i)
    if len(i) == 2:
        i.append(1)
    start, stop, step = i
    start = start or 0
    if stop == None:
        stop = parentsize
    if start < 0:
        start += parentsize
    if stop < 0:
        stop += parentsize
    step = step or 1

    if (stop - start) * step < 1:
        raise IndexError()

    return (start, stop, step)

class MatrixSlice(MatrixExpr):
    """ A MatrixSlice of a Matrix Expression

    Examples

    >>> from sympy import MatrixSlice, ImmutableMatrix
    >>> M = ImmutableMatrix(4, 4, range(16))
    >>> print M
    Matrix([
    [ 0,  1,  2,  3],
    [ 4,  5,  6,  7],
    [ 8,  9, 10, 11],
    [12, 13, 14, 15]])

    >>> B = MatrixSlice(M, (0, 2), (2, 4))
    >>> print ImmutableMatrix(B)
    Matrix([
    [2, 3],
    [6, 7]])
    """
    parent = property(lambda self: self.args[0])
    rowslice = property(lambda self: self.args[1])
    colslice = property(lambda self: self.args[2])

    def __new__(cls, parent, rowslice, colslice):
        rowslice = normalize(rowslice, parent.shape[0])
        colslice = normalize(colslice, parent.shape[1])
        if not (len(rowslice) == len(colslice) == 3):
            raise IndexError()
        if ((0 > rowslice[0]) == True or
            (parent.shape[0] < rowslice[1]) == True or
            (0 > colslice[0]) == True or
            (parent.shape[1] < colslice[1]) == True):
            raise IndexError()
        if isinstance(parent, MatrixSlice):
            return mat_slice_of_slice(parent, rowslice, colslice)
        return Basic.__new__(cls, parent, Tuple(*rowslice), Tuple(*colslice))

    @property
    def shape(self):
        rows = self.rowslice[1] - self.rowslice[0]
        rows = rows if self.rowslice[2] == 1 else floor(rows/self.rowslice[2])
        cols = self.colslice[1] - self.colslice[0]
        cols = cols if self.colslice[2] == 1 else floor(cols/self.colslice[2])
        return rows, cols

    def _entry(self, i, j):
        return self.parent._entry(i*self.rowslice[2] + self.rowslice[0],
                                  j*self.colslice[2] + self.colslice[0])

    @property
    def on_diag(self):
        return self.rowslice == self.colslice


def slice_of_slice(s, t):
    start1, stop1, step1 = s
    start2, stop2, step2 = t

    start = start1 + start2*step1
    step = step1 * step2
    stop = start1 + step1*stop2

    if stop > stop1:
        raise IndexError()

    return start, stop, step


def mat_slice_of_slice(parent, rowslice, colslice):
    """ Collapse nested matrix slices

    >>> from sympy import MatrixSymbol
    >>> X = MatrixSymbol('X', 10, 10)
    >>> X[:, 1:5][5:8, :]
    X[5:8, 1:5]
    >>> X[1:9:2, 2:6][1:3, 2]
    X[3:7:2, 4]
    """
    row = slice_of_slice(parent.rowslice, rowslice)
    col = slice_of_slice(parent.colslice, colslice)
    return MatrixSlice(parent.parent, row, col)
