Immutable Matrices¶
The standard Matrix
class in SymPy is mutable. This is important for
performance reasons but means that standard matrices cannot interact well with
the rest of SymPy. This is because the Basic
object, from which most
SymPy classes inherit, is immutable.
The mission of the ImmutableDenseMatrix
class, which is aliased as
ImmutableMatrix
for short, is to bridge the tension
between performance/mutability and safety/immutability. Immutable matrices can
do almost everything that normal matrices can do but they inherit from
Basic
and can thus interact more naturally with the rest of SymPy.
ImmutableMatrix
also inherits from MatrixExpr
, allowing it to
interact freely with SymPy’s Matrix Expression module.
You can turn any Matrixlike object into an ImmutableMatrix
by calling
the constructor
>>> from sympy import Matrix, ImmutableMatrix
>>> M = Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
>>> M[1, 1] = 0
>>> IM = ImmutableMatrix(M)
>>> IM
Matrix([
[1, 2, 3],
[4, 0, 6],
[7, 8, 9]])
>>> IM[1, 1] = 5
Traceback (most recent call last):
...
TypeError: Can not set values in Immutable Matrix. Use Matrix instead.
ImmutableMatrix Class Reference¶

class
sympy.matrices.immutable.
ImmutableDenseMatrix
[source]¶ Create an immutable version of a matrix.
Examples
>>> from sympy import eye >>> from sympy.matrices import ImmutableMatrix >>> ImmutableMatrix(eye(3)) Matrix([ [1, 0, 0], [0, 1, 0], [0, 0, 1]]) >>> _[0, 0] = 42 Traceback (most recent call last): ... TypeError: Cannot set values of ImmutableDenseMatrix

is_zero
¶ Checks if a matrix is a zero matrix.
A matrix is zero if every element is zero. A matrix need not be square to be considered zero. The empty matrix is zero by the principle of vacuous truth. For a matrix that may or may not be zero (e.g. contains a symbol), this will be None
Examples
>>> from sympy import Matrix, zeros >>> from sympy.abc import x >>> a = Matrix([[0, 0], [0, 0]]) >>> b = zeros(3, 4) >>> c = Matrix([[0, 1], [0, 0]]) >>> d = Matrix([]) >>> e = Matrix([[x, 0], [0, 0]]) >>> a.is_zero True >>> b.is_zero True >>> c.is_zero False >>> d.is_zero True >>> e.is_zero
