Closures and random numbers in F# - random

For fun, I am trying to write a simple simulation of the
Monty Hall problem
problem using F#.
I have created a function getShow which returns an array of three booleans (representing doors), one of which is randomly true (it has a car behind it) and the other two false.
let getShow =
let doorWithCar = System.Random().Next(3)+1
[|for door in 1..3 -> door = doorWithCar|]
Now when I try to get a sequence of shows using yield to call the getShow function, I keep getting the first random show repeated (I am guessing because of the way closures work in F#).
let shows =
seq { for i in 1 .. 10 do yield getShow} // Keeps generating the same show over and over
What is the correct way to call the getShow function using yield so that it actually calls the function and gets a new random array?

getShow is a value and not a function, so it's calculated once and you keep yielding the same value. To turn it into a function you have to add (). Also, you keep creating a new Random instance, which is probably initialized with the same time seed, not giving you what you want. Try this instead:
let random = System.Random()
let getShow() =
let doorWithCar = random.Next(3)+1
[|for door in 1..3 -> door = doorWithCar|]
let shows =
seq { for i in 1 .. 10 do yield getShow()}

Related

Python: Printing vertically

The final code will print the distance between states. I'm trying to print the menu with the names of the states numbered and vertically. I really struggle to find my mistakes.
This code doesn't raise any error, it just prints nothing, empty.
state_data = """
LA 34.0522°N 118.2437°W
Florida 27.6648°N 81.5158°W
NY 40.7128°N 74.0060°W"""
states = []
import re
state_data1 = re.sub("[°N#°E]", "", state_data)
def process_states(string):
states_temp = string.split()
states = [(states_temp[x], float(states_temp[x + 1]), float(states_temp[x + 2])) for x in
range(0, len(states_temp), 3)]
return states
def menu():
for state_data in range(state_data1):
print(f'{state_data + 1} {name[number]}')
My first guess is, your code does not print anything without errors because you never actually execute process_airports() nor menu().
You have to call them like this at the end of your script:
something = process_airports(airport_data1)
menu()
This will now raise some errors though. So let's address them.
The menu() function will raise an error because neither name nor number are defined and because you are trying to apply the range function over a string (airport_data1) instead of an integer.
First fixing the range error: you mixed two ideas in your for-loop: iterating over the elements in your list airport_data1 and iterating over the indexes of the elements in the list.
You have to choose one (we'll see later that you can do both at once), in this example, I choose to iterate over the indexes of the list.
Then, since neither name nor number exists anywhere they will raise an error. You always need to declare variables somewhere, however, in this case they are not needed at all so let's just remove them:
def menu(data):
for i in range(len(data)):
print(f'{i + 1} {data[i]}')
processed_airports = process_airports(airport_data1)
menu(processed_airports)
Considering data is the output of process_airports()
Now for some general advices and improvements.
First, global variables.
Notice how you can access airport_data1 within the menu() function just fine, while it works this is not something recommended, it's usually better to explicitly pass variables as arguments.
Notice how in the function I proposed above, every single variable is declared in the function itself, there is no information coming from a higher scope. Again, this is not mandatory but makes the code way easier to work with and understand.
airport_data = """
Alexandroupoli 40.855869°N 25.956264°E
Athens 37.936389°N 23.947222°E
Chania 35.531667°N 24.149722°E
Chios 38.343056°N 26.140556°E
Corfu 39.601944°N 19.911667°E"""
airports = []
import re
airport_data1 = re.sub("[°N#°E]", "", airport_data)
def process_airports(string):
airports_temp = string.split()
airports = [(airports_temp[x], float(airports_temp[x + 1]), float(airports_temp[x + 2])) for x in
range(0, len(airports_temp), 3)]
return airports
def menu(data):
for i in range(len(data)):
print(f'{i + 1} {data[i]}')
# I'm adding the call to the functions for clarity
data = process_airports(airport_data1)
menu(data)
The printed menu now looks like that:
1 ('Alexandroupoli', 40.855869, 25.956264)
2 ('Athens', 37.936389, 23.947222)
3 ('Chania', 35.531667, 24.149722)
4 ('Chios', 38.343056, 26.140556)
5 ('Corfu', 39.601944, 19.911667)
Second and this is mostly fyi, but you can access both the index of a iterable and the element itself by looping over enumerate() meaning, the following function will print the exact same thing as the one with range(len(data)). This is handy if you need to work with both the element itself and it's index.
def menu(data):
for the_index, the_element in enumerate(data):
print(f'{the_index + 1} {the_element}')

Is there a way to use range with Z3ints in z3py?

I'm relatively new to Z3 and experimenting with it in python. I've coded a program which returns the order in which different actions is performed, represented with a number. Z3 returns an integer representing the second the action starts.
Now I want to look at the model and see if there is an instance of time where nothing happens. To do this I made a list with only 0's and I want to change the index at the times where each action is being executed, to 1. For instance, if an action start at the 5th second and takes 8 seconds to be executed, the index 5 to 12 would be set to 1. Doing this with all the actions and then look for 0's in the list would hopefully give me the instances where nothing happens.
The problem is: I would like to write something like this for coding the problem
list_for_check = [0]*total_time
m = s.model()
for action in actions:
for index in range(m.evaluate(action.number) , m.evaluate(action.number) + action.time_it_takes):
list_for_check[index] = 1
But I get the error:
'IntNumRef' object cannot be interpreted as an integer
I've understood that Z3 isn't returning normal ints or bools in their models, but writing
if m.evaluate(action.boolean):
works, so I'm assuming the if is overwritten in a way, but this doesn't seem to be the case with range. So my question is: Is there a way to use range with Z3 ints? Or is there another way to do this?
The problem might also be that action.time_it_takes is an integer and adding a Z3int with a "normal" int doesn't work. (Done in the second part of the range).
I've also tried using int(m.evaluate(action.number)), but it doesn't work.
Thanks in advance :)
When you call evaluate it returns an IntNumRef, which is an internal z3 representation of an integer number inside z3. You need to call as_long() method of it to convert it to a Python number. Here's an example:
from z3 import *
s = Solver()
a = Int('a')
s.add(a > 4);
s.add(a < 7);
if s.check() == sat:
m = s.model()
print("a is %s" % m.evaluate(a))
print("Iterating from a to a+5:")
av = m.evaluate(a).as_long()
for index in range(av, av + 5):
print(index)
When I run this, I get:
a is 5
Iterating from a to a+5:
5
6
7
8
9
which is exactly what you're trying to achieve.
The method as_long() is defined here. Note that there are similar conversion functions from bit-vectors and rationals as well. You can search the z3py api using the interface at: https://z3prover.github.io/api/html/namespacez3py.html

Sorting a list of objects by property in Matlab, and then deleting the smallest one

I'm trying to use Matlab to implement the MDO algorithm, which requires me to sort an array of objects of a custom-defined mdoVertex class by their degree, and then delete the one with the smallest degree value. My first attempt was this:
for i = 1:m
if graph(i).degree < minDegree
minDegree = graph(i).degree;
elimObject = graph(i);
end
end
Matlab is complaining that elimObject, or the object to be eliminated after the loop executes, is an undefined function or variable. How, then, can I keep track of not only the current smallest degree the loop has encountered, but also which object it corresponded to? 'graph' is the name of the array holding all of my vertex objects.
I suspect that you're somehow trying to call clear on the object returned from your function. Or is it just a few lines of code in a script? I'm guessing here. In any event, calling clear won't work. As you've noticed, clear expects to be given a variable name.
But in this case, you're not trying to delete a variable, you're trying to remove an element from an array. For that, you do arrayname(indextodelete) = [];
So I think that you want...
minDegree = inf; % See what I did there? I defined the variable, and I did it in such a way that I KNOW that the first vertex will satisfy the condition.
for i = 1:length(graph) % Properly loop over the entire graph
if graph(i).degree < minDegree % The first vertex will definitely satisfy this. Maybe another one (or more) will later!
minDegree = graph(i).degree;
minDegreeIndex = i; % Don't record the value, just remember WHERE it is in the array.
end
end
graph(minDegreeIndex) = []; % Now, remove the element that you identified from the array!
(By the way, you never showed us how you tried to eliminate elimObject. I assume that you called clear (the object that you identified)? You shouldn't make us guess; show us.)

Returning multiple ints and passing them as multiple arguements in Lua

I have a function that takes a variable amount of ints as arguments.
thisFunction(1,1,1,2,2,2,2,3,4,4,7,4,2)
this function was given in a framework and I'd rather not change the code of the function or the .lua it is from. So I want a function that repeats a number for me a certain amount of times so this is less repetitive. Something that could work like this and achieve what was done above
thisFunction(repeatNum(1,3),repeatNum(2,4),3,repeatNum(4,2),7,4,2)
is this possible in Lua? I'm even comfortable with something like this:
thisFunction(repeatNum(1,3,2,4,3,1,4,2,7,1,4,1,2,1))
I think you're stuck with something along the lines of your second proposed solution, i.e.
thisFunction(repeatNum(1,3,2,4,3,1,4,2,7,1,4,1,2,1))
because if you use a function that returns multiple values in the middle of a list, it's adjusted so that it only returns one value. However, at the end of a list, the function does not have its return values adjusted.
You can code repeatNum as follows. It's not optimized and there's no error-checking. This works in Lua 5.1. If you're using 5.2, you'll need to make adjustments.
function repeatNum(...)
local results = {}
local n = #{...}
for i = 1,n,2 do
local val = select(i, ...)
local reps = select(i+1, ...)
for j = 1,reps do
table.insert(results, val)
end
end
return unpack(results)
end
I don't have 5.2 installed on this computer, but I believe the only change you need is to replace unpack with table.unpack.
I realise this question has been answered, but I wondered from a readability point of view if using tables to mark the repeats would be clearer, of course it's probably far less efficient.
function repeatnum(...)
local i = 0
local t = {...}
local tblO = {}
for j,v in ipairs(t) do
if type(v) == 'table' then
for k = 1,v[2] do
i = i + 1
tblO[i] = v[1]
end
else
i = i + 1
tblO[i] = v
end
end
return unpack(tblO)
end
print(repeatnum({1,3},{2,4},3,{4,2},7,4,2))

Removing a "row" from a structure array

This is similar to a question I asked before, but is slightly different:
So I have a very large structure array in matlab. Suppose, for argument's sake, to simplify the situation, suppose I have something like:
structure(1).name, structure(2).name, structure(3).name structure(1).returns, structure(2).returns, structure(3).returns (in my real program I have 647 structures)
Suppose further that structure(i).returns is a vector (very large vector, approximately 2,000,000 entries) and that a condition comes along where I want to delete the jth entry from structure(i).returns for all i. How do you do this? or rather, how do you do this reasonably fast? I have tried some things, but they are all insanely slow (I will show them in a second) so I was wondering if the community knew of faster ways to do this.
I have parsed my data two different ways; the first way had everything saved as cell arrays, but because things hadn't been working well for me I parsed the data again and placed everything as vectors.
What I'm actually doing is trying to delete NaN data, as well as all data in the same corresponding row of my data file, and then doing the very same thing after applying the Hampel filter. The relevant part of my code in this attempt is:
for i=numStock+1:-1:1
for j=length(stock(i).return):-1:1
if(isnan(stock(i).return(j)))
for k=numStock+1:-1:1
stock(k).return(j) = [];
end
end
end
stock(i).return = sort(stock(i).return);
stock(i).returnLength = length(stock(i).return);
stock(i).medianReturn = median(stock(i).return);
stock(i).madReturn = mad(stock(i).return,1);
end;
for i=numStock:-1:1
for j = length(stock(i+1).volume):-1:1
if(isnan(stock(i+1).volume(j)))
for k=numStock:-1:1
stock(k+1).volume(j) = [];
end
end
end
stock(i+1).volume = sort(stock(i+1).volume);
stock(i+1).volumeLength = length(stock(i+1).volume);
stock(i+1).medianVolume = median(stock(i+1).volume);
stock(i+1).madVolume = mad(stock(i+1).volume,1);
end;
for i=numStock+1:-1:1
for j=stock(i).returnLength:-1:1
if (abs(stock(i).return(j) - stock(i).medianReturn) > 3*stock(i).madReturn)
for k=numStock+1:-1:1
stock(k).return(j) = [];
end
end;
end;
end;
for i=numStock:-1:1
for j=stock(i+1).volumeLength:-1:1
if (abs(stock(i+1).volume(j) - stock(i+1).medianVolume) > 3*stock(i+1).madVolume)
for k=numStock:-1:1
stock(k+1).volume(j) = [];
end
end;
end;
end;
However, this returns an error:
"Matrix index is out of range for deletion.
Error in Failure (line 110)
stock(k).return(j) = [];"
So instead I tried by parsing everything in as vectors. Then I decided to try and delete the appropriate entries in the vectors prior to building the structure array. This isn't returning an error, but it is very slow:
%% Delete bad data, Hampel Filter
% Delete bad entries
id=strcmp(returns,'');
returns(id)=[];
volume(id)=[];
date(id)=[];
ticker(id)=[];
name(id)=[];
permno(id)=[];
sp500(id) = [];
id=strcmp(returns,'C');
returns(id)=[];
volume(id)=[];
date(id)=[];
ticker(id)=[];
name(id)=[];
permno(id)=[];
sp500(id) = [];
% Convert returns from string to double
returns=cellfun(#str2double,returns);
sp500=cellfun(#str2double,sp500);
% Delete all data for which a return is not a number
nanid=isnan(returns);
returns(nanid)=[];
volume(nanid)=[];
date(nanid)=[];
ticker(nanid)=[];
name(nanid)=[];
permno(nanid)=[];
% Delete all data for which a volume is not a number
nanid=isnan(volume);
returns(nanid)=[];
volume(nanid)=[];
date(nanid)=[];
ticker(nanid)=[];
name(nanid)=[];
permno(nanid)=[];
% Apply the Hampel filter, and delete all data corresponding to
% observations deleted by the filter.
medianReturn = median(returns);
madReturn = mad(returns,1);
for i=length(returns):-1:1
if (abs(returns(i) - medianReturn) > 3*madReturn)
returns(i) = [];
volume(i)=[];
date(i)=[];
ticker(i)=[];
name(i)=[];
permno(i)=[];
end;
end
medianVolume = median(volume);
madVolume = mad(volume,1);
for i=length(volume):-1:1
if (abs(volume(i) - medianVolume) > 3*madVolume)
returns(i) = [];
volume(i)=[];
date(i)=[];
ticker(i)=[];
name(i)=[];
permno(i)=[];
end;
end
As I said, this is very slow, probably because I'm using a for loop on a very large data set; however, I'm not sure how else one would do this. Sorry for the gigantic post, but does anyone have a suggestion as to how I might go about doing what I'm asking in a reasonable way?
EDIT: I should add that getting the vector method to work is probably preferable, since my aim is to put all of the return vectors into a matrix and get all of the volume vectors into a matrix and perform PCA on them, and I'm not sure how I would do that using cell arrays (or even if princomp would work on cell arrays).
EDIT2: I have altered the code to match your suggestion (although I did decide to give up speed and keep with the for-loops to keep with the structure array, since reparsing this data will be way worse time-wise). The new code snipet is:
stock_return = zeros(numStock+1,length(stock(1).return));
for i=1:numStock+1
for j=1:length(stock(i).return)
stock_return(i,j) = stock(i).return(j);
end
end
stock_return = stock_return(~any(isnan(stock_return)), : );
This returns an Index exceeds matrix dimensions error, and I'm not sure why. Any suggestions?
I could not find a convenient way to handle structures, therefore I would restructure the code so that instead of structures it uses just arrays.
For example instead of stock(i).return(j) I would do stock_returns(i,j).
I show you on a part of your code how to get rid of for-loops.
Say we deal with this code:
for j=length(stock(i).return):-1:1
if(isnan(stock(i).return(j)))
for k=numStock+1:-1:1
stock(k).return(j) = [];
end
end
end
Now, the deletion of columns with any NaN data goes like this:
stock_return = stock_return(:, ~any(isnan(stock_return)) );
As for the absolute difference from medianVolume, you can write a similar code:
% stock_return_length is a scalar
% stock_median_return is a column vector (eg. [1;2;3])
% stock_mad_return is also a column vector.
median_return = repmat(stock_median_return, stock_return_length, 1);
is_bad = abs(stock_return - median_return) > 3.* stock_mad_return;
stock_return = stock_return(:, ~any(is_bad));
Using a scalar for stock_return_length means of course that the return lengths are the same, but you implicitly assume it in your original code anyway.
The important point in my answer is using any. Logical indexing is not sufficient in itself, since in your original code you delete all the values if any of them is bad.
Reference to any: http://www.mathworks.co.uk/help/matlab/ref/any.html.
If you want to preserve the original structure, so you stick to stock(i).return, you can speed-up your code using essentially the same scheme but you can only get rid of one less for-loop, meaning that your program will be substantially slower.

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