Fourier transform of a non-integrable function ...
Dear all,
I am working on Fourier Transform of a non-integrable function. And I am working on the numerical implementation of the FT, using FFT.
Let's call this function F(v). One example is F(v)=-1/(5*i*v)*(1-exp(5*i*v))
The function has a 1/v term in its asymptotic expansion, which corresponds to a jump or Heaviside function in its transform.
Using FFT, I can see the jump, with some overshooting after the jump and undershooting before the jump, along with some ripples.
I want to reduce these artifacts as much as possible, because I am going to integrate this transform against other functions later. Hence obtaining a smooth function without much numerical artifacts is vital. How do I do that?

Is this thing called Interval Math? Can Maple do it?
Is this thing called Interval Math? Can Maple do it?
I am not about if this is called Interval Analysis. The thing in my mind is that I know my Monte Carlo simulation yields a result with an error tolerance of 1e-5. And I wrap that MC simulation component into a more complicated expression and form a function, I want to know the error bound of the whole function involving the MC component. Can Maple do this?
The same applies to analysis about round-off error. If I know a sub-expression has a round-off error of 1e-6, what should the error of the main expression involving this sub-expression be?

For trivial expressions, we don't need automatic code generation.
For complicated expressions, code generator creates lots of temporary variables and the performance is not far from optimal.
Once I generated a C program using codegen with 500+ temporary variables and I put that function into a numerical integral as an integrand. The result was very unstable - the integrals are often NaNs.
On the other hand, I also convert Maple expression manually into C program which has exactly the same functionality. The result was correct, no NaNs in the integrals at all.
So what's the use o

How do I programmatically save the output of "C" code generation to a "cpp" file?
I am doing all of these in Matlab via the Maple engine, which is version 10, I guess.
I cannot seem to do "writeto" redirection here, because Matlab doesn't allow that I guess.
And I like to use "fprintf" because it gives me more control of the code that is generated...
If it works, I no longer need copy and paste..
But it didn't work at all. There was no error message, but the file was empty...
Can anybody tell me why?
Thanks!
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fd:=fopen("trygenC.cpp", WRITE, TEXT)

bb:=proc(aa, n) add(add(aa[j][k], j=0 .. 5), k=0 .. n) end proc
cc:=prep2trans(bb)
dd:=C(cc, optimized)
??? Error using ==> maple at 129
Error, (in codegen/C) Unable to translate this subscript into C aa[i2][i1]
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I don't understand...