In NumPy, there is a function for returning a logarithmically spaced range of n points between two numbers begin and end.
In Julia you could define something like this:
10 .^(range(log10(begin), log10(end), n)
but is there a built-in function like this?
I found some related questions here: https://discourse.julialang.org/t/lazy-logspace-object/70091 and https://discourse.julialang.org/t/how-to-do-logspace-in-julia-v-1-0-x/17452.
Basically, there are no built-in short hands for logspace, but you can implement a similar function using Iterators.
logspace(start, last, count) = Iterators.map(exp10, range(log10(start), log10(last), count))
Related
I write a vector in Dymola mos script in a simple manner like this:
x_axis = cell.spatialSummary.x_cell;
output: x_axis={1,2,3,4,5} // row vector
I want to do the same thing in a function.'x_cell' has 5 values which I want to store in a row vector. I use DymolaCommands.Trajectories.readTrajectory function to read x_cell values one by one in for loop (I use for loop because, readTrajectory throws an error when I try to read entire x_cell)
Real x_axis[:],axis_value[:,:];
Integer len=5;
for i in 1:len loop
axis_value:=readTrajectory(result,{"cell.spatialSummary.x_cell["+String(i)+"]"},1); //This intermediate variable returns [1,1] matrix
x_axis[i]:=scalar(axis_value);
end for;
I get an error:
Assignment failed x_axis[i] = scalar(axis_value);
what's wrong here? All I want to do is read all values of x_cell and write it into a vector. How can I do this in dymola function?
Thank you!
Solution: Initialize the vector with a certain value. In this case,
x_axis :=fill(0, len);
This solved the above problem for me.
Pre filling as in the other solution works, and is generally the best solution. However, in some cases you might have to append to the vector as follows:
x_axis=fill(0.0, 0);
for i in 1:len loop
axis_value:=readTrajectory(result,{"cell.spatialSummary.x_cell["+String(i)+"]"},1); //This intermediate variable returns [1,1] matrix
x_axis:=cat(1, x_axis, {scalar(axis_value)});
end for;
(This takes x_axis and concatenates a new element at the end. It is generally slower.)
Coming from python3 to Julia one would love to be able to write fast iterators as a function with produce/yield syntax or something like that.
Julia's macros seem to suggest that one could build a macro which transforms such a "generator" function into an julia iterator.
[It even seems like you could easily inline iterators written in function style, which is a feature the Iterators.jl package also tries to provide for its specific iterators https://github.com/JuliaCollections/Iterators.jl#the-itr-macro-for-automatic-inlining-in-for-loops ]
Just to give an example of what I have in mind:
#asiterator function myiterator(as::Array)
b = 1
for (a1, a2) in zip(as, as[2:end])
try
#produce a1[1] + a2[2] + b
catch exc
end
end
end
for i in myiterator([(1,2), (3,1), 3, 4, (1,1)])
#show i
end
where myiterator should ideally create a fast iterator with as low overhead as possible. And of course this is only one specific example. I ideally would like to have something which works with all or almost all generator functions.
The currently recommended way to transform a generator function into an iterator is via Julia's Tasks, at least to my knowledge. However they also seem to be way slower then pure iterators. For instance if you can express your function with the simple iterators like imap, chain and so on (provided by Iterators.jl package) this seems to be highly preferable.
Is it theoretically possible in julia to build a macro converting generator-style functions into flexible fast iterators?
Extra-Point-Question: If this is possible, could there be a generic macro which inlines such iterators?
Some iterators of this form can be written like this:
myiterator(as) = (a1[1] + a2[2] + 1 for (a1, a2) in zip(as, as[2:end]))
This code can (potentially) be inlined.
To fully generalize this, it is in theory possible to write a macro that converts its argument to continuation-passing style (CPS), making it possible to suspend and restart execution, giving something like an iterator. Delimited continuations are especially appropriate for this (https://en.wikipedia.org/wiki/Delimited_continuation). The result is a big nest of anonymous functions, which might be faster than Task switching, but not necessarily, since at the end of the day it needs to heap-allocate a similar amount of state.
I happen to have an example of such a transformation here (in femtolisp though, not Julia): https://github.com/JeffBezanson/femtolisp/blob/master/examples/cps.lsp
This ends with a define-generator macro that does what you describe. But I'm not sure it's worth the effort to do this for Julia.
Python-style generators – which in Julia would be closest to yielding from tasks – involve a fair amount of inherent overhead. You have to switch tasks, which is non-trivial and cannot straightforwardly be eliminated by a compiler. That's why Julia's iterators are based on functions that transform one typically immutable, simple state value, and another. Long story short: no, I do not believe that this transformation can be done automatically.
After thinking a lot how to translate python generators to Julia without loosing much performance, I implemented and tested a library of higher level functions which implement Python-like/Task-like generators in a continuation-style. https://github.com/schlichtanders/Continuables.jl
Essentially, the idea is to regard Python's yield / Julia's produce as a function which we take from the outside as an extra parameter. I called it cont for continuation. Look for instance on this reimplementation of a range
crange(n::Integer) = cont -> begin
for i in 1:n
cont(i)
end
end
You can simply sum up all integers by the following code
function sum_continuable(continuable)
a = Ref(0)
continuable() do i
a.x += i
end
a.x
end
# which simplifies with the macro Continuables.#Ref to
#Ref function sum_continuable(continuable)
a = Ref(0)
continuable() do i
a += i
end
a
end
sum_continuable(crange(4)) # 10
As you hopefully agree, you can work with continuables almost like you would have worked with generators in python or tasks in julia. Using do notation instead of for loops is kind of the one thing you have to get used to.
This idea takes you really really far. The only standard method which is not purely implementable using this idea is zip. All the other standard higher-level tools work just like you would hope.
The performance is unbelievably faster than Tasks and even faster than Iterators in some cases (notably the naive implementation of Continuables.cmap is orders of magnitude faster than Iterators.imap). Check out the Readme.md of the github repository https://github.com/schlichtanders/Continuables.jl for more details.
EDIT: To answer my own question more directly, there is no need for a macro #asiterator, just use continuation style directly.
mycontinuable(as::Array) = cont -> begin
b = 1
for (a1, a2) in zip(as, as[2:end])
try
cont(a1[1] + a2[2] + b)
catch exc
end
end
end
mycontinuable([(1,2), (3,1), 3, 4, (1,1)]) do i
#show i
end
I am making my first steps in julia, and I would like to reproduce something I achieved with numpy.
I would like to write a new array-like type which is essentially an vector of elements of arbitrary type, and, to keep the example simple, an scalar attribute such as the sampling frequency fs.
I started with something like
type TimeSeries{T} <: DenseVector{T,}
data::Vector{T}
fs::Float64
end
Ideally, I would like:
1) all methods that take a Vector{T} as argument to take on TimeSeries{T}.
e.g.:
ts = TimeSeries([1,2,3,1,543,1,24,5], 12.01)
median(ts)
2) that indexing a TimeSeries always returns a TimeSeries:
ts[1:3]
3) built-in functions that return a Vector to return a TimeSeries:
ts * 2
ts + [1,2,3,1,543,1,24,5]
I have started by implementing size, getindex and so on, but I definitely do not see how it could be possible to match points 2 and 3.
numpy has a quite comprehensive way to doing this: http://docs.scipy.org/doc/numpy/user/basics.subclassing.html. R also seems to allow linking attributes attr()<- to arrays.
Do you have any idea about the best strategy to implement this sort of "array with attributes".
Maybe I'm not understanding, why is for say point 3 it not sufficient to do
(*)(ts::TimeSeries, n) = TimeSeries(ts.data*n, ts.fs)
(+)(ts::TimeSeries, n) = TimeSeries(ts.data+n, ts.fs)
As for point 2
Base.getindex(ts::TimeSeries, r::Range) = TimeSeries(ts.data[r], ts.fs)
Or are you asking for some easier way where you delegate all these operations to the internal vector? You can clever things like
for op in (:(+), :(*))
#eval $(op)(ts::TimeSeries, x) = TimeSeries($(op)(ts.data,x), ts.fs)
end
According to the GMP documentation here:
Function: unsigned long int mpz_remove
(mpz_t rop, mpz_t op, mpz_t f)
Remove all occurrences of the factor f
from op and store the result in rop.
The return value is how many such
occurrences were removed.
So the mpz_remove function should be able to be used to answer the titled question. At the moment my code looks like this:
mpz_set_ui(temp2,2);
mpz_remove(temp,K0,temp2);
which works fine, but the result I want is K0 divided by temp (and not temp itself) [which I could get by adding a subsequent division operation, but that seems wasteful].
How should I actually get K0/temp?
You might try the combination of mpz_scan1() and mpz_tdiv_q_2exp().
mpz_tdiv_q_2exp(result,K0,mpz_scan1(K0,0))
I am trying to use a Taylor polynomial programmatically in Maple, but the following does not seem to work...
T[6]:=taylor(sin(x),x=Pi/4,6);convert(T[6], polynom, x);
f:=proc(x)
convert(T[6], polynom, x);
end proc;
f(1);
All of the following also do not work:
f:=convert(T[6], polynom);
f:=convert(T[6], polynom, x);
f:=x->convert(T[6], polynom);
f:=x->convert(T[6], polynom, x);.
Is there a way of doing this without copying and pasting the output of convert into the definition of f?
If I understood you correctly, this accomplishes what you want:
f := proc(z)
local p :: polynom;
p := convert(T[6], polynom);
return subs(x = z, p)
end proc
Several earlier answers involving procedures and subs will do the entire taylor series derivation, as well as the conversion to polynom, for each and every input. That is highly inefficient.
You only need to produce the taylor result, and convert to polynom, once. With that result in hand you can then create an operator (with which to act on as many inputs as you wish, merely by evaluating the polynomial at the point but without having to recompute the whole taylor answer).
Below is a way to create a procedure f with which to evaluate at any given point for the argument x. It computes the (truncated) taylor series and converts to polynom just once.
> f:=unapply(convert(taylor(sin(x),x=Pi/4,6),polynom),x):
It might also be natural to define T as a function.
T:=y->subs(x=y,convert(taylor(sin(x),x=Pi/4,6),polynom));
T(1);