I wanted to ask how can I can write this in MATLAB.
I want to integrate fp(z) with z(0,x). I tried this :
fpz=#(z) f1x(z) ./ quadl(f1x(z),0,1);
sol=int(fpz,0,x) --> i also tried sol=quadl(fpz,0,x)
y=solve('y=sol',x)
xf=# (y) y ; -->this is the function i want
where f1x=# (x) 1 ./(x.^2+1) and fpx = #(x) f1x(x) ./ quadl(f1x,0,1);
but it doesn't work.
Hello,thanks for helping.
The problem is that i want an analytically solution and i can't get one.
I want f1x to give me " 1/x^2+1" , fpx "4/pi*(1+x^2) and fpz "4ArcTan(x)/pi", instead of giving me "f1x=# 1./(x^2+1)"..
With the code you send me ,still the same problem.
I managed to come into this :
f1x=# (x) 1 ./(x.^2+1)
fpx = #(x) f1x(x) ./ quadl(f1x,0,1)
f2z=# (z) 1 ./(z.^2+1);
fpz=#(z) fpx(z) ./ quadl(f2z,0,1)
sol=int(fpz(z),z,0,x)
y=solve(subs('y=sol'),x)
xf=# (y) y
The "sol" and "y=" gives me analytically answer but it is wrong because i assume f1x and fpx,fpz doesn't return into analytically expressions.
0 Your definition of fpz doesn't make any sense; as Marcin already said, you're trying to integrate something that isn't a function. This shouldn't be a problem for your alternative version with f2z. I think the code in the original question should have had just f1x rather than f1x(z) in the first line.
1 Your revised version with f2z has a different problem: now in fpz you aren't actually providing the function with an argument.
The following code seems to be the kind of thing you had in mind, and works fine for me (in MATLAB R2008a, as it happens, but none of this should be different in other versions):
f1x = #(x) 1 ./ (x.^2+1);
fpx = #(x) f1x(x) ./ quadl(f1x,0,1);
fpz = #(z) fpx(z) ./ quadl(fpx,0,1);
Now evaluating fpz(3), for instance, spins for about half a second (on my old slow laptop computer) and returns 0.1273.
So I think the problems you've been having with integration of anonymous functions are just a matter of not being quite careful enough to distinguish between the function itself and a particular value of the function.
You have some further questions about the "solve" and "int" functions in the Symbolic Math Toolbox. You should take the following with a pinch of salt because I don't have that toolbox and am relying on the online documentation for it.
3 You're feeding the names of functions you've defined in MATLAB to the Symbolic Math Toolbox functions. I don't think that is supposed to work; "int" and "solve" expect explicit algebraic expressions, not MATLAB functions. (And, further, your functions all use numerical integration -- quad, quadl, etc. -- and there's no possible way that the symbolic functions can do anything useful with that.)
Finally: When you're asking questions of this sort, it's helpful if rather than "it doesn't work" you say how it doesn't work. For instance, your most recent comment is much more useful ("it gives me ..." followed by the actual output you get from MATLAB).
Related
It seems that, as w/ Inductive and Fixpoint, you can mutually define Function's w/ with. Can you give the syntax and/or an example of this? I couldn't find anything anywhere. I suppose it's the same as for Fixpoint
(found nothing on this either). A non-working (but half-compiling -- the 2 last lines highlight in red) example:
Variable ARG:Type.
Variable phy inf phyinf: ARG.
Function Phy (x:ARG): ARG := match x with Inf x => phyinf | _ => phy end
with Inf (x:ARG): ARG := match x with Phy x => phyinf | _ => inf end. (*Error: Unknown constructor: Inf.*)
Alright, I think I finally understood your question.
There is indeed a way to mutually define several Fixpoint. It is (lightly) documented in the variant section here.
Similarly, there is a way to mutually define several Inductive types (documented here).
And there is a way to mutually define several Function. Note however the remark that the manual makes about this feature:
The Function construction enjoys also the with extension to define mutually recursive definitions. However, this feature does not work for non structural recursive functions.
The error that you are getting in your half-working example is not about syntax though, neither is it related to the Function ... with feature. The error is that you can only use pattern-matching on inductive types and branches must start with a constructor. In your example, ARG is not an inductive type and Inf is not a constructor. I can't really "correct" your example as I don't really see what you were trying to express. Was this example made just for this question? In this case, you stripped it down to too little.
PS: I wonder if somehow, you were trying to do induction-recursion (definining at the same time a recursive function and an inductive type). If this were the case, then no luck: Coq does not have this feature yet.
So I'm doing some hobby-related stuff which involves taking Fourier transforms of large real arrays which barely fit in memory, and was curious to see if there was an in-place version of rfft and irfft that saved RAM, since RAM consumption is important to me. These transforms are possible despite the input-vs-output-type mismatch, and require an extra row of padding.
In Implement in-place rfft! and irfft!, Tim Holy said he was working on an in-place rfft! and irfft! that made use of a buffer-containing RCpair object, but then Steven Johnson said that he was implementing something equivalent using A_mul_B!(y, plan, x), which he elaborated on here.
Things get a little weird from then on. In the documentation for both 0.3.0 and 0.4.0 there is no mention of A_mul_B!, although A_mul_B is listed. But when I try entering them into Julia, I get
A_mul_B!
A_mul_B! (generic function with 28 methods)
A_mul_B
ERROR: A_mul_B not defined
which suggests that the situation is actually the opposite of what the documentation currently describes.
So since A_mul_B! seems to exist, but isn't documented anywhere, I tried to guess how to test it in-place as follows:
A = rand(Float32, 10, 10);
p = plan_rfft(A);
A_mul_B!(A,p,A)
which resulted in
ERROR: `A_mul_B!` has no method matching A_mul_B!(::Array{Float32,2}, ::Function, ::Array{Float32,2})
So...
Are in-place real FFTs still a work in progress? Or am I using A_mul_B! wrong?
Is there a mismatch between the 0.3.0 documentation and 0.3.0's function library?
That pull request from Steven Johnson is listed as open, not merged; that means the work hasn't been finished yet. The one from me is closed, but if you want the code you can grab it by clicking on the commits.
The docs indeed omit mention of A_mul_B!. A_mul_B is equivalent to A*B, and so isn't exported independently now. A_mul_B! would be used like this: instead of C = A*B, you could say A_mul_B!(C, A, B).
Can you please edit the docs to fix these issues? (You can edit files here in your webbrowser.)
I'm trying to build a program in Pascal to differentiate mathematical functions. It's working very well (calculate min/max, symmetry, drawing the graph, etc.) but I have to put the functions (i.e. x^3+3x+2) into the source code like this:
function f(x : real): real;
begin
f := x * x * x + 3 * x + 2;
end;
Though, I want the user to define the function to differentiate. Obviosly the readln function does not help.
Somebody told me the only solution would be a specific parser. But it's very difficult, and I don't know how to do it.
My idea would be to extract the function into a *.txt file for example so that it could be changed easily. Is that possible?
Can somebody show me a parser which could solve this problem or have anybody some other great solution?
I would really appreciate your help!
Thanks in advance ;)
Free Pascal ships with the symbolic package, which has both a parser and evaluator for mathematical expressions. You can probably use this as a starting point. See the documentation for usage.
There are also a number of parsers/evalutaors on SWAG:
EQUATE.PAS (short, clean evaluator)
PARSMATH.PAS (very short example code)
Math Parsing Unit (undocumented, kind of messy)
Math Evaluations (Somewhat cryptic.)
Nice Expression Parser (Small, seems well done.)
Expression Evaluator (Messier, includes trig functions.)
Math Expression Evaluator (not well documented)
Equation Parser (converts equations to arrays of coefficients)
Text Formula Parser (fairly complete parser/evaluator unit)
I bolded the ones I thought were the most useful. I don't think any of them are as complete as the symbolic package in my other answer, but they might be worth reading if you need help.
(All of this is fairly old code. Unless otherwise stated, the rule with SWAG is to treat this stuff as having a new-style BSD license)
Sometimes I accidentally declare variables that have the name of a function.
Here is a constructed example:
max(4:5) % 5
max(1:10)=10*ones(10,1); % oops, should be == instead of =
max(4:5) % [10 10]
At the moment I always find this out the hard way and it especially happens with function names that I don't use frequently.
Is there any way to let matlab give a warning about this? It would be ideal to see this on the right hand side of the screen with the other warnings, but I am open to other suggestions.
Since Matlab allows you to overload built-in functionality, you will not receive any warnings when using existing names.
There are, however, a few tricks to minimize the risk of overloading existing functions:
Use explicitFunctionNames. It is much less likely that there is a function maxIndex instead of max.
Use the "Tab"-key often. Matlab will auto-complete functions on the path (as well as variables that you've declared previously). Thus, if the variable auto-completes, it already exists. In case you don't remember whether it's also a function, hit "F1" to see whether there exists a help page for it.
Use functions rather than scripts, so that "mis-"assigned variables in the workspace won't mess up your code.
I'm pretty sure mlint can also check for that.
Generally I would wrap code into functions as much as possible. That way the range of such an override is limited to the scope of the function - so no lasting problems, besides the accidental assumption of course.
When in doubt, check:
exist max
ans =
5
Looking at help exist, you can see that "max" is a function, and shouldn't be assigned as a variable.
>> help exist
exist Check if variables or functions are defined.
exist('A') returns:
0 if A does not exist
1 if A is a variable in the workspace
2 if A is an M-file on MATLAB's search path. It also returns 2 when
A is the full pathname to a file or when A is the name of an
ordinary file on MATLAB's search path
3 if A is a MEX-file on MATLAB's search path
4 if A is a MDL-file on MATLAB's search path
5 if A is a built-in MATLAB function
6 if A is a P-file on MATLAB's search path
7 if A is a directory
8 if A is a class (exist returns 0 for Java classes if you
start MATLAB with the -nojvm option.)
I am defining a function that takes as input a function and I want to specify it in the input type i.e. Operat[_?FunctionQ]:=...
But there is no functionQ as of yet in mathematica. How do I get aroud this except not specifying any type at all.
Any ideas?
Oh!
This: Test if an expression is a Function?
may be the answer i am looking for. I am reading further
Is the solution proposed there robust?, i.e.:
FunctionQ[_Function | _InterpolatingFunction | _CompiledFunction] = True;
FunctionQ[f_Symbol] := Or[
DownValues[f] =!= {},
MemberQ[ Attributes[f], NumericFunction ]]
FunctionQ[_] = False;
The exhibited definition has great utility. The question is: what exactly constitutes a function in Mathematica? Pure functions and the like are easily to classify as functions, but what about definitions that involve pattern-matching? Consider:
h[g[x_]] ^:= x + 1
Is h to be considered a function? If so, it will be hard to identify as it will entail examining the up-values of every symbol in the system to make that determination. Is g a function? It has an up-value, but g[x] is an inert expression.
What about head composition:
f[x_][y_][z_] := x + y + z
Is f a function? How about f[1] or f[1][2]?
And then there are the various capabilities like JLink and NETLink:
Needs["JLink`"]
obj = JavaNew["java.util.Date"]
obj#toString[]
Is obj#toString a function?
I hate to bring up these problems without offering solutions -- but I want to emphasize that the question as to what constitutes a function in the Mathematica context is a tricky one. It is tricky from both the theoretical and practical standpoints.
I think that the answer to whether the exhibited function test is complete really depends upon the types of expressions that you will be feeding it in your specific application.