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from __future__ import print_function, division
from sympy.matrices.expressions.matexpr import MatrixExpr
from sympy import Tuple, Basic
from sympy.functions.elementary.integers import floor
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) == True:
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) == True:
start += parentsize
if (stop < 0) == True:
stop += parentsize
step = step or 1
if ((stop - start) * step < 1) == True:
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)
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