Immutable Matrices¶
The standard Matrix
class in SymPy is mutable. This is important for
performance reasons but means that standard matrices can not 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 ImmutableMatrix
class 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 Matrix-like 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.
ImmutableMatrix
[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
-
C
¶ By-element conjugation.
-
adjoint
()¶ Conjugate transpose or Hermitian conjugation.
-
as_mutable
()¶ Returns a mutable version of this matrix
Examples
>>> from sympy import ImmutableMatrix >>> X = ImmutableMatrix([[1, 2], [3, 4]]) >>> Y = X.as_mutable() >>> Y[1, 1] = 5 # Can set values in Y >>> Y Matrix([ [1, 2], [3, 5]])
-
equals
(other, failing_expression=False)¶ Applies
equals
to corresponding elements of the matrices, trying to prove that the elements are equivalent, returning True if they are, False if any pair is not, and None (or the first failing expression if failing_expression is True) if it cannot be decided if the expressions are equivalent or not. This is, in general, an expensive operation.See also
sympy.core.expr.equals
Examples
>>> from sympy.matrices import Matrix >>> from sympy.abc import x >>> from sympy import cos >>> A = Matrix([x*(x - 1), 0]) >>> B = Matrix([x**2 - x, 0]) >>> A == B False >>> A.simplify() == B.simplify() True >>> A.equals(B) True >>> A.equals(2) False
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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
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