I don't know if this feature exists or if symbolic is the right name for it.
I want to be able to have a variable, say f, for a (math) function with certain properties. I want to be able to use this variable in expressions. But I don't actually want to define what the function f does.
For example, I might want to say "define f to be a function in one variable that is differentiable on the real numbers". Then I want to be able to use f(x) in expressions. I might want to define another function g(x) in terms of f(x) and be able to differentiate g(x) and get an expression from sage. So I want to issue the following commands
f is defined as before
define g(x)=(f(x))^2
differentiate g
output: g'(x)=2f(x)f'(x)
Does this feature exist?
How about this:
sage: f = function('f')
sage: g(x) = f(x)**2
sage: g.derivative()
x |--> 2*f(x)*diff(f(x), x)
Related
I have some code that runs fine and does what I want, although there may be a simpler more elegant solution, this works :
round(Int16, floor(rand(TruncatedNormal(150,20,50,250))))
However when I try to execute it multiple times, using map, it throws an error saying it doesn't like the Int16 specification, so this:
map(round(Int16, floor(rand(TruncatedNormal(150,20,50,250)))), 1:2)
throws this error
ERROR: MethodError: objects of type Int16 are not callable
I just want to run it twice (in this case) and sum the results. Why is it unhappy? Thx. J
The first argument to map is a function. So, with your code, Julia is trying to make a function call:
round(Int16, floor(rand(TruncatedNormal(150,20,50,250))))()
But the output of round(Int16, ...) isn't a function, it's a number, so you cannot call it. That's why the error says "objects of type Int16 are not callable." You could fix this by using an anonymous function:
map(() -> round(Int16, floor(rand(TruncatedNormal(150,20,50,250)))), 1:2)
But the "Julian" way to do this is to use a comprehension:
[round(Int16, floor(rand(TruncatedNormal(150,20,50,250)))) for _ in 1:2]
EDIT:
If you are going to sum the results, then you can use something that looks like a comprehension but is called a generator expression. This is basically everything above with the [ ] around the expression. A generator expression can be used directly in functions like sum or mean, etc.
sum(round(Int16, floor(rand(TruncatedNormal(150,20,50,250)))) for _ in 1:2)
The advantage to generator expressions is that they don't allocate the memory for the full array. So, if you did this 100 times and used the sum approach above, you wouldn't need to allocate space for 100 numbers.
This goes beyond the original question, but OP wanted to use the sum expression where the 2 in 1:2 is a 1-element vector. Of course, if the input is always a 1-element vector, then I recommend first(x) like the comments. But this is a nice opportunity to show the importance of breaking things down into functions frequently in Julia. For example, you could take the entire sum expression and define a function
generatenumbers(n::Integer) = sum(... for _ in 1:n)
where n is a scalar. Then if you have some odd array expression for n (1-element vector, many such ns in a multi-dim array, etc.), you can just do:
generatenumbers.(ns)
# will apply to each element and return same shape as ns
If the de-sugaring logic is more complex than applying element-wise, you can even define:
generatenumbers(ns::AbstractArray) = # ... something more complex
The point is to define an "atomic" function that expresses the statement or task you want clearly, then use dispatch to apply it to more complicated data-structures that appear in practical code. This is a common design pattern in Julia (not the only option, but an effective one).
Adding on the answer from #darsnack.
If you want to run it multiple times in order to keep the results (it wasn't clear from the question). Then you could also ask rand to produce a vector by doing the following (and also making the type conversion through the floor call).
Moving from:
map(round(Int16, floor(rand(TruncatedNormal(150,20,50,250)))), 1:2)
to:
floor.(Int16, rand(TruncatedNormal(150,20,50,250), 2))
The documentation is here.
Is there a simpler way to do apply a function in Julia to nested array than defining a new function? - e.g. for this simple example:
a = collect(1:10)
b = [ a*i for i in 100:100:400]
arraylog(x) = log.(x) ## Need to define an extra function to do the inner array?
arraylog.(b)
I would use a comprehension just like you used it to define b: [log.(x) for x in b].
The benefit of this approach is that such code should be easy to read later.
EDIT
Referring to the answer by Tasos actually a comprehension implicitly defines an anonymous function that is passed to Base.Generator. In this use case a comprehension and map should be largely equivalent.
I assumed that MR_MPI-BGC wanted to avoid defining an anonymous function.
If it were allowed one could also use a double broadcast like this:
(x->log.(x)).(b)
which is even shorer but I thought that it would not be very readable in comparison to a comprehension.
You could define it as a lambda instead.
Obviously the distinction may be moot, depending on how you're using this later in your code, but if all you want is to not waste a line in your code for the sake of conciseness, you could easily dump this inside a map statement, for instance:
map( x->log.(x), b )
or, if you prefer do syntax:
map(b) do x
log.(x)
end
PS. I'm not familiar with a syntax which allows the broadcasted version of a function to be plugged directly into map, but if one exists it would be even cleaner than a lambda here ... but alas 'map( log., b )' is not valid syntax.
I'm looking for a way to call Precursor on another feature. The context is that I redefine a routine calling another heir's feature that calls mine, and I'd like to call it explicitly. Is there a way to do something such as in java Precursor.feature_a.
If not, the only alternative I find is to write a feature_a_implementation and call it from redefined feature. Is there a particular reason not to have this mechanism? The consequences of doing that would be to define 2 times the contract of feature_a into feature_a and feature_a_implementation
Feature replication can be used for that:
class A feature
f do print ("A") end
end
class B inherit
A redefine f select f end
A rename f as g end
feature
f do print ("B") end
h do g end
end
Feature f of class A appears in class B twice: under name f (the redefined and selected version) and under name g (the original version). The feature h calls g and prints A as expected.
Is there a built-in lagged operator function in julia? I.e., a function of the form:
lagop(op,array,offset)
that returns something like
[array[i + offset] (op) array[i] for i in 1:length(array)-offset]
For successive differences, there is the diff function. For sums either of the following works:
x = collect(1:10)
x[1:end-1]+x[2:end]
[x[i]+x[i+1] for i in 1:length(x)-1]
Is there a general function to accomplish tasks like this?
You mention the zoo library in R, which is for time series. If that's your use case, you will find lag implemented in TimeSeries.jl: http://timeseriesjl.readthedocs.io/en/latest/apply.html#lag It may not be exactly what you want, though.
This is a sort of followup to my previous question about nested registered C functions found here:
Trying to call a function in Lua with nested tables
The previous question gave me the answer to adding a nested function like this:
dog.beagle.fetch()
I also would like to have variables at that level like:
dog.beagle.name
dog.beagle.microchipID
I want this string and number to be allocated in C and accessible by Lua. So, in C code, the variables might be defined as:
int microchipIDNumber;
char dogname[500];
The C variables need to be updated by assignments in Lua and its value needs to be retrieved by Lua when it is on the right of the equal sign. I have tried the __index and __newindex metamethod concept but everything I try seems to break down when I have 2 dots in the Lua path to the variable. I know I am probably making it more complicated with the 2 dots, but it makes the organization much easier to read in the Lua code. I also need to get an event for the assignment because I need to spin up some hardware when the microchipIDNumber value changes. I assume I can do this through the __newindex while I am setting the value.
Any ideas on how you would code the metatables and methods to accomplish the nesting? Could it be because my previous function declarations are confusing Lua?
The colon operator (:) in Lua is used only for functions. Consider the following example:
meta = {}
meta["__index"] = function(n,m) print(n) print(m) return m end
object = {}
setmetatable(object,meta)
print(object.foo)
The index function will simply print the two arguments it is passed and return the second one (which we will also print, because just doing object.foo is a syntax error). The output is going to be table: 0x153e6d0 foo foo with new lines. So __index gets the object in which we're looking up the variable and it's name. Now, if we replace object.foo with object:foo we get this:
input:5: function arguments expected near ')'
This is the because : in object:foo is syntactic sugar for object.foo(object), so Lua expects that you will provide arguments for a function call. If we did provide arguments (object:foo("bar")) we get this:
table: 0x222b3b0
foo
input:5: attempt to call method 'foo' (a string value)
So our __index function still gets called, but it is not passed the argument - Lua simply attemps to call the return value. So don't use : for members.
With that out of the way, let's look at how you can sync variables between Lua and C. This is actually quite involved and there are different ways to do it. One solution would be to use a combination of __index and __newindex. If you have a beagle structure in C, I'd recommend making these C functions and pushing them into the metatable of a Lua table as C-closures with a pointer to your C struct as an upvalue. Look at this for some info on lua_pushcclosure and this on closures in Lua in general.
If you don't have a single structure you can reference, it gets a lot more complicated, since you'll have to somehow store pairs variableName-variableLocation on the C side and know what type each is. You could maintain such a list in the actual Lua table, so dog.beagle would be a map of variable name to one or two something's. There a couple of options for this 'something'. First - one light user data (ie - a C pointer), but then you'll have the issue of figuring out what that is pointing to, so that you know what Lua type to push in for __index and what to pop out for __newindex . The other option is to push two functions/closures. You can make a C function for each type you'll have to handle (number, string, table, etc) and push the appropriate one for each variable, or make a uber-closure that takes a parameter what type it's being given and then just vary the up-values you push it with. In this case the __index and __newindex functions will simply lookup the appropriate function for a given variable name and call it, so it would be probably easiest to implement it in Lua.
In the case of two functions your dog.beagle might look something like this (not actual Lua syntax):
dog.beagle = {
__metatable = {
__index = function(table,key)
local getFunc = rawget(table,key).get
return getFunc(table,key)
end
__newindex = function(table,key,value)
local setFunc = rawget(table,key).set
setFunc(table,key,value)
end
}
"color" = {
"set" = *C function for setting color or closure with an upvalue to tell it's given a color*,
"get" = *C function for getting color or closure with an upvalue to tell it to return a color*
}
}
Notes about the above: 1.Don't set an object's __metatable field directly - it's used to hide the real metatable. Use setmetatable(object,metatable). 2. Notice the usage of rawget. We need it because otherwise trying to get a field of the object from within __index would be an infinite recursion. 3. You'll have to do a bit more error checking in the event rawget(table,key) returns nil, or if what it returns does not have get/set members.