def __getitem__(self, key):
if not isinstance(key, tuple) and isinstance(key, slice):
from sympy.matrices.expressions.slice import MatrixSlice
return MatrixSlice(self, key, (0, None, 1))
if isinstance(key, tuple) and len(key) == 2:
i, j = key
if isinstance(i, slice) or isinstance(j, slice):
from sympy.matrices.expressions.slice import MatrixSlice
return MatrixSlice(self, i, j)
i, j = _sympify(i), _sympify(j)
if self.valid_index(i, j) != False:
return self._entry(i, j)
else:
raise IndexError("Invalid indices (%s, %s)" % (i, j))
elif isinstance(key, (SYMPY_INTS, Integer)):
# row-wise decomposition of matrix
rows, cols = self.shape
# allow single indexing if number of columns is known
if not isinstance(cols, Integer):
raise IndexError(filldedent('''
Single indexing is only supported when the number
of columns is known.'''))
key = _sympify(key)
i = key // cols
j = key % cols
if self.valid_index(i, j) != False:
return self._entry(i, j)
else:
raise IndexError("Invalid index %s" % key)
elif isinstance(key, (Symbol, Expr)):
raise IndexError(filldedent('''
Only integers may be used when addressing the matrix
with a single index.'''))
raise IndexError("Invalid index, wanted %s[i,j]" % self)
def __getitem__(self, key):
if not isinstance(key, tuple) and isinstance(key, slice):
from sympy.matrices.expressions.slice import MatrixSlice
return MatrixSlice(self, key, (0, None, 1))
if isinstance(key, tuple) and len(key) == 2:
i, j = key
if isinstance(i, slice) or isinstance(j, slice):
from sympy.matrices.expressions.slice import MatrixSlice
return MatrixSlice(self, i, j)
i, j = sympify(i), sympify(j)
if self.valid_index(i, j) != False:
return self._entry(i, j)
else:
raise IndexError("Invalid indices (%s, %s)" % (i, j))
elif isinstance(key, (int, Integer)):
# row-wise decomposition of matrix
rows, cols = self.shape
if not (isinstance(rows, Integer) and isinstance(cols, Integer)):
raise IndexError("Single index only supported for "
"non-symbolic matrix shapes.")
key = sympify(key)
i = key // cols
j = key % cols
if self.valid_index(i, j) != False:
return self._entry(i, j)
else:
raise IndexError("Invalid index %s" % key)
elif isinstance(key, (Symbol, Expr)):
raise IndexError("Single index only supported for "
"non-symbolic indices.")
raise IndexError("Invalid index, wanted %s[i,j]" % self)
def test_MatrixSlice():
n = Symbol('n', integer=True)
X = MatrixSymbol('X', n, n)
Y = MatrixSymbol('Y', 10, 10)
Z = MatrixSymbol('Z', 10, 10)
assert str(MatrixSlice(X, (None, None, None), (None, None, None))) == 'X[:, :]'
assert str(X[x:x + 1, y:y + 1]) == 'X[x:x + 1, y:y + 1]'
assert str(X[x:x + 1:2, y:y + 1:2]) == 'X[x:x + 1:2, y:y + 1:2]'
assert str(X[:x, y:]) == 'X[:x, y:]'
assert str(X[:x, y:]) == 'X[:x, y:]'
assert str(X[x:, :y]) == 'X[x:, :y]'
assert str(X[x:y, z:w]) == 'X[x:y, z:w]'
assert str(X[x:y:t, w:t:x]) == 'X[x:y:t, w:t:x]'
assert str(X[x::y, t::w]) == 'X[x::y, t::w]'
assert str(X[:x:y, :t:w]) == 'X[:x:y, :t:w]'
assert str(X[::x, ::y]) == 'X[::x, ::y]'
assert str(MatrixSlice(X, (0, None, None), (0, None, None))) == 'X[:, :]'
assert str(MatrixSlice(X, (None, n, None), (None, n, None))) == 'X[:, :]'
assert str(MatrixSlice(X, (0, n, None), (0, n, None))) == 'X[:, :]'
assert str(MatrixSlice(X, (0, n, 2), (0, n, 2))) == 'X[::2, ::2]'
assert str(X[1:2:3, 4:5:6]) == 'X[1:2:3, 4:5:6]'
assert str(X[1:3:5, 4:6:8]) == 'X[1:3:5, 4:6:8]'
assert str(X[1:10:2]) == 'X[1:10:2, :]'
assert str(Y[:5, 1:9:2]) == 'Y[:5, 1:9:2]'
assert str(Y[:5, 1:10:2]) == 'Y[:5, 1::2]'
assert str(Y[5, :5:2]) == 'Y[5:6, :5:2]'
assert str(X[0:1, 0:1]) == 'X[:1, :1]'
assert str(X[0:1:2, 0:1:2]) == 'X[:1:2, :1:2]'
assert str((Y + Z)[2:, 2:]) == '(Y + Z)[2:, 2:]'
def test_entry():
B = MatrixSlice(X, (a, b), (c, d))
assert B[0,0] == X[a, c]
assert B[k,l] == X[a+k, c+l]
raises(IndexError, lambda : MatrixSlice(X, 1, (2, 5))[1, 0])
assert X[1::2, :][1, 3] == X[1+2, 3]
assert X[:, 1::2][3, 1] == X[3, 1+2]
def test_slicing():
assert X[1:5, 2:4] == MatrixSlice(X, (1, 5), (2, 4))
assert X[1, 2:4] == MatrixSlice(X, 1, (2, 4))
assert X[1:5, :].shape == (4, X.shape[1])
assert X[:, 1:5].shape == (X.shape[0], 4)
assert X[::2, ::2].shape == (floor(n/2), floor(m/2))
assert X[2, :] == MatrixSlice(X, 2, (0, m))
def __getitem__(self, key):
if not isinstance(key, tuple) and isinstance(key, slice):
from sympy.matrices.expressions.slice import MatrixSlice
return MatrixSlice(self, key, (0, None, 1))
if isinstance(key, tuple) and len(key) == 2:
i, j = key
if isinstance(i, slice) or isinstance(j, slice):
from sympy.matrices.expressions.slice import MatrixSlice
return MatrixSlice(self, i, j)
i, j = sympify(i), sympify(j)
if self.valid_index(i, j) is not False:
return self._entry(i, j)
else:
raise IndexError("Invalid indices (%s, %s)" % (i, j))
raise IndexError("Invalid index, wanted %s[i,j]" % self)
def __getitem__(self, key):
from sympy.matrices.expressions.slice import MatrixSlice
if not isinstance(key, tuple) and isinstance(key, slice):
return MatrixSlice(self, key, (0, None, 1))
if isinstance(key, tuple):
if len(key) == 1:
key = key[0]
elif len(key) == 2:
i, j = key
if isinstance(i, slice):
if isinstance(j, slice):
return self._entry(i, j)
else:
return self.func(self.arg[j])
# return MatrixSlice(self, i, j)
i, j = _sympify(i), _sympify(j)
if self.valid_index(i, j) != False:
return self._entry(i, j)
else:
raise IndexError("Invalid indices (%s, %s)" % (i, j))
from sympy import Integer, Symbol, Expr
if isinstance(key, (int, Integer, Symbol, Expr)):
return self._entry(key)
# # row-wise decomposition of matrix
raise IndexError("Invalid index, wanted %s[i,j]" % self)
def blockcut(expr, rowsizes, colsizes):
""" Cut a matrix expression into Blocks
>>> from sympy import ImmutableMatrix, blockcut
>>> M = ImmutableMatrix(4, 4, range(16))
>>> B = blockcut(M, (1, 3), (1, 3))
>>> type(B).__name__
'BlockMatrix'
>>> ImmutableMatrix(B.blocks[0, 1])
Matrix([[1, 2, 3]])
"""
rowbounds = bounds(rowsizes)
colbounds = bounds(colsizes)
return BlockMatrix(
[[MatrixSlice(expr, rowbound, colbound) for colbound in colbounds]
for rowbound in rowbounds])
def test_inputs():
assert MatrixSlice(X, 1, (2, 5)) == MatrixSlice(X, (1, 2), (2, 5))
assert MatrixSlice(X, 1, (2, 5)).shape == (1, 3)
def test_on_diag():
assert not MatrixSlice(X, (a, b), (c, d)).on_diag
assert MatrixSlice(X, (a, b), (a, b)).on_diag
def test_shape():
B = MatrixSlice(X, (a, b), (c, d))
assert B.shape == (b - a, d - c)