What does the error message "input must be real and full" mean?

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When I try to compute gamma(i) I get the error message "Input must be real and full." I understand that the input is not real, but what is a full input? If I call gamma with an empty argument I get an empty output. So what is the exact meaning of this error message?

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John D'Errico
John D'Errico il 10 Feb 2024
Modificato: John D'Errico il 10 Feb 2024
The gamma function requires a real input. Although I recall that the symbolic version of gamma can handle complex input. But the gamma function for double precision arguments does not extend to the complex plane.
gamma(str2sym('1+i'))
ans =
gamma(1 + 1i)
vpa(ans)
ans =
0.4980156681183560427136911174622 - 0.15494982830181068512495513048389i
gamma(1+i)
Error using gamma
Input must be real and full.
Why does the error message include the full clause?
A = magic(3)
A = 3×3
8 1 6 3 5 7 4 9 2
On the full side of that message... As you cam see, A is a full matrix.
gamma(A)
ans = 3×3
5040 1 120 2 24 720 6 40320 1
gamma(sparse(A))
Error using gamma
Input must be real and full.
But sparse(A) is sparse, so not full.
And this explains both sides of that error message, since gamma does not apply to sparse matrices. It makes no sense for a sparse matrix, since gamma(0) is undefined. gamma(0) returns inf.

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