Using symbolic matrix operations correctly?
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I am new to symbolic computations in MATLAB and am trying out matrix differentiations.
If we take derivative of trace(X*A) w.r.t. X, we should get A^T.
But MATLAB tells me
>> syms X A;
>> diff(trace(X*A), X)
ans =
A
Where am I wrong?
采纳的回答
John D'Errico
2016-7-27
As you have defined them, X and A are SCALAR symbolic objects, not general matrices. So the trace operation is a no-op, essentially ignored as the trace of a scalar, and the differentiation does not see them as matrices, since A and X are indeed scalars.
However, if A and X are symbolic matrices, it appears that diff does not allow differentiation with respect to a symbolic matrix. So:
>> A = sym('A',[2,2])
A =
[ A1_1, A1_2]
[ A2_1, A2_2]
>> X = sym('X',[2,2])
X =
[ X1_1, X1_2]
[ X2_1, X2_2]
>> diff(trace(A*X),X)
Error using sym/diff (line 69)
The second argument must be a variable or a nonnegative integer specifying the number of differentiations.
So as you can see, this produces an error as you wish to do the operation. Yet, if you compute the derivatives wrt the scalar elements of X, we see the proper elements of the transpose of A are indeed produced.
>> diff(trace(A*X),X(1,2))
ans =
A2_1
>> diff(trace(A*X),X(2,1))
ans =
A1_2
更多回答（2 个）
Andrei Bobrov
2016-7-27
reshape(jacobian(trace(A.*X),X(:)),size(A))
Azzi Abdelmalek
2016-7-27
A is not defined as a symbolic matrix.
A=sym('a',5)
syms x
diff(trace(x*A),x)
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