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For Loop Function Iteration

I am attempting to use a for loop to run a function f(x) on a range of values. I am running into an issue when I want to recalculate my input on the next step dependent on the previous step. Below is some pseudo code that might explain my issue better and below that is the actual code I am attempting to write. The goal is to have a loop that calculates the results on one step and recalculates an input on the next step dependent on the results. IE:
for i in range(10):
H = i - 1
result_up = f(H)
H_delta = (nsolve(Eq(result_up,A(H1)),H1,1))
i += H_delta
The idea is that in the next iteration result_up = f(i += H_delta) so on and so forth.
from sympy import *
USHead = np.linspace(1,3,25)
PHeight = 1.5
WH = Symbol('WH')
for i in USHead:
if i <= PHeight:
Oh = i-1
OD = ((Cd * 0.738 * math.sqrt(2 * 32.2 * (Oh)))* 2)
i_delta = (nsolve(Eq(OD,(0.0612*(TwH1/1)+3.173)*(6-0.003)*(TwH1+.003)**(1.5)), TwH1,1))
i += i_delta
My understanding of for loops is that you have the ability to recalculate i as you continue through the iteration but am thinking the issue is because I have defined my range as a list?
The step size of the list is .083 starting at 1 and ending at 3.

You can't use a for loop if you want to update the iteration variable yourself, since it will override that with the next value from the range. Use a while loop.
i = 0
while i < 10:
H = i - 1
result_up = f(H)
H_delta = (nsolve(Eq(result_up,A(H1)),H1,1))
i += H_delta

How to tackle the Birthday Paradox Problem in Python?

I'm practicing the Birthday Paradox problem in Python. I've run it a bunch of times, with changing the random number of birthdays and **loop run number **, but the probability is either 0 or 100%, and I was unable to get other probability like 50% etc. Can someone help me look through my code and see what I did wrong? Thank you so much!!
from random import randint
from datetime import datetime, timedelta
first_day_of_year = datetime(2017, 1, 1)
num_of_ppl = 45
birthdays = []
# get 45 random birthdays list
for i in range(num_of_ppl):
new_birthday = first_day_of_year + timedelta(days = randint(0, 365))
birthdays.append(new_birthday)
# find if there's matched birthdays, run 10000 times
dups = 0
duplicates = set()
for i in range(10000):
for bday in birthdays:
if birthdays.count(bday) > 1:
duplicates.add(bday)
if len(duplicates) >= 1:
dups += 1
# calculate the probability
probability = dups/10000 * 100
print(probability)

If you generate the birthdays list each time, the probability is as expected. Also I didn't see a need to use datetime or set objects, I just replaced them with ints and bools without changing anything functionally. Also, you can use list comprehension in order to generate the birthdays list in one line:
from random import randint
num_iterations = 10000
num_people = 45
num_duplicates_overall = 0
# generate a random birthday for each person, check if there was a duplicate,
# and repeat num_iterations times
for i in range(num_iterations):
# start with a new, empty list every time.
# get a list of random birthdays, of length num_people.
birthdays = [randint(0, 365) for _ in range(num_people)]
# Keep track of whether or not there was a duplicate for this iteration
was_duplicate = False
for bday in birthdays:
if birthdays.count(bday) > 1:
# We found a duplicate for this iteration, so we can stop checking
was_duplicate = True
break
if was_duplicate:
num_duplicates_overall += 1
probability = num_duplicates_overall / num_iterations
print(f"Probability: {probability * 100}%")
Output with num_iterations = 1000000 and num_people = 23:
Probability: 50.6452%
Edit: Alternatively, there's this method to check for duplicates which is supposedly faster (but mainly I like it because it's on one line):
if len(birthdays) != len(set(birthdays)):
num_duplicates_overall += 1
So, your code could look as simple as this:
from random import randint
num_iterations = 10000
num_people = 45
num_duplicates_overall = 0
for i in range(num_iterations):
birthdays = [randint(0, 365) for _ in range(num_people)]
if len(birthdays) != len(set(birthdays)):
num_duplicates_overall += 1
probability = num_duplicates_overall / num_iterations
print(f"Probability: {probability * 100}%")

Unique ordered ratio of integers

I have two ordered lists of consecutive integers m=0, 1, ... M and n=0, 1, 2, ... N. Each value of m has a probability pm, and each value of n has a probability pn. I am trying to find the ordered list of unique values r=n/m and their probabilities pr. I am aware that r is infinite if n=0 and can even be undefined if m=n=0.
In practice, I would like to run for M and N each be of the order of 2E4, meaning up to 4E8 values of r - which would mean 3 GB of floats (assuming 8 Bytes/float).
For this calculation, I have written the python code below.
The idea is to iterate over m and n, and for each new m/n, insert it in the right place with its probability if it isn't there yet, otherwise add its probability to the existing number. My assumption is that it is easier to sort things on the way instead of waiting until the end.
The cases related to 0 are added at the end of the loop.
I am using the Fraction class since we are dealing with fractions.
The code also tracks the multiplicity of each unique value of m/n.
I have tested up to M=N=100, and things are quite slow. Are there better approaches to the question, or more efficient ways to tackle the code?
Timing:
M=N=30: 1 s
M=N=50: 6 s
M=N=80: 30 s
M=N=100: 82 s
import numpy as np
from fractions import Fraction
import time # For timiing
start_time = time.time() # Timing
M, N = 6, 4
mList, nList = np.arange(1, M+1), np.arange(1, N+1) # From 1 to M inclusive, deal with 0 later
mProbList, nProbList = [1/(M+1)]*(M), [1/(N+1)]*(N) # Probabilities, here assumed equal (not general case)
# Deal with mn=0 later
pmZero, pnZero = 1/(M+1), 1/(N+1) # P(m=0) and P(n=0)
pNaN = pmZero * pnZero # P(0/0) = P(m=0)P(n=0)
pZero = pmZero * (1 - pnZero) # P(0) = P(m=0)P(n!=0)
pInf = pnZero * (1 - pmZero) # P(inf) = P(m!=0)P(n=0)
# Main list of r=m/n, P(r) and mult(r)
# Start with first line, m=1
rList = [Fraction(mList[0], n) for n in nList[::-1]] # Smallest first
rProbList = [mProbList[0] * nP for nP in nProbList[::-1]] # Start with first line
rMultList = [1] * len(rList) # Multiplicity of each element
# Main loop
for m, mP in zip(mList[1:], mProbList[1:]):
for n, nP in zip(nList[::-1], nProbList[::-1]): # Pick an n value
r, rP, rMult = Fraction(m, n), mP*nP, 1
for i in range(len(rList)-1): # See where it fits in existing list
if r < rList[i]:
rList.insert(i, r)
rProbList.insert(i, rP)
rMultList.insert(i, 1)
break
elif r == rList[i]:
rProbList[i] += rP
rMultList[i] += 1
break
elif r < rList[i+1]:
rList.insert(i+1, r)
rProbList.insert(i+1, rP)
rMultList.insert(i+1, 1)
break
elif r == rList[i+1]:
rProbList[i+1] += rP
rMultList[i+1] += 1
break
if r > rList[-1]:
rList.append(r)
rProbList.append(rP)
rMultList.append(1)
break
# Deal with 0
rList.insert(0, Fraction(0, 1))
rProbList.insert(0, pZero)
rMultList.insert(0, N)
# Deal with infty
rList.append(np.Inf)
rProbList.append(pInf)
rMultList.append(M)
# Deal with undefined case
rList.append(np.NAN)
rProbList.append(pNaN)
rMultList.append(1)
print(".... done in %s seconds." % round(time.time() - start_time, 2))
print("************** Final list\nr", 'Prob', 'Mult')
for r, rP, rM in zip(rList, rProbList, rMultList): print(r, rP, rM)
print("************** Checks")
print("mList", mList, 'nList', nList)
print("Sum of proba = ", np.sum(rProbList))
print("Sum of multi = ", np.sum(rMultList), "\t(M+1)*(N+1) = ", (M+1)*(N+1))

Based on the suggestion of #Prune, and on this thread about merging lists of tuples, I have modified the code as below. It's a lot easier to read, and runs about an order of magnitude faster for N=M=80 (I have omitted dealing with 0 - would be done same way as in original post). I assume there may be ways to tweak the merge and conversion back to lists further yet.
# Do calculations
data = [(Fraction(m, n), mProb(m) * nProb(n)) for n in range(1, N+1) for m in range(1, M+1)]
data.sort()
# Merge duplicates using a dictionary
d = {}
for r, p in data:
if not (r in d): d[r] = [0, 0]
d[r][0] += p
d[r][1] += 1
# Convert back to lists
rList, rProbList, rMultList = [], [], []
for k in d:
rList.append(k)
rProbList.append(d[k][0])
rMultList.append(d[k][1])

I expect that "things are quite slow" because you've chosen a known inefficient sort. A single list insertion is O(K) (later list elements have to be bumped over, and there is added storage allocation on a regular basis). Thus a full-list insertion sort is O(K^2). For your notation, that is O((M*N)^2).
If you want any sort of reasonable performance, research and use the best-know methods. The most straightforward way to do this is to make your non-exception results as a simple list comprehension, and use the built-in sort for your penultimate list. Simply append your n=0 cases, and you're done in O(K log K) time.
I the expression below, I've assumed functions for m and n probabilities.
This is a notational convenience; you know how to directly compute them, and can substitute those expressions if you wish.
data = [ (mProb(m) * nProb(n), Fraction(m, n))
for n in range(1, N+1)
for m in range(0, M+1) ]
data.sort()
data.extend([ # generate your "zero" cases here ])

How to append randomized float values into array within loop

I have a set of randomized float values that are to be arranged into an array at the end of each loop that produces 67 of them, however, there are 64 total loops.
As an example, if I had 4 values per loop and 3 total loops of integers, I would like it to be like this:
values = [[0, 4, 5, 1],[6, 6, 5, 3],[0,0,0,7]]
such that I could identify them as separate arrays, however, I am unsure of the best way to append the values after they are created, but am aware of how to return them. Forgive me as I am unskilled with the logic.
import math
import random
funcs = []
coord = []
pi = math.pi
funcAmt = 0
coordAmt = 0
repeatAmt = 0
coordPass = 0
while funcAmt < 64:
while coordAmt < 67:
coordAmt += 1
uniform = round(random.uniform(-pi, pi), 2)
print("Coord [",coordAmt,"] {",uniform,"} Func:", funcAmt + 1)
if uniform in coord:
repeatAmt += 1
print("Repeat Found!")
coordAmt -= 1
print("Repeat [",repeatAmt,"] Resolved")
pass
else:
coordPass += 1
coord.append(uniform)
#<<<Append Here>>>
funcAmt += 1
coord.clear()
coordAmt = 0
In my given code above, it would be similar to:
func = [
[<67 items>],
...63 more times
]

Your "append here" logic should append the coordinate list and then clear that list for the next iteration of the outer loop:
funcs.append(coord[:]) # The slice notation makes a copy of the list
coord.clear() # or simply coord = []
You should learn to use a for loop. This will simplify your looping: you don't have to maintain the counts yourself. For instance:
for funcAmt in range(64):
for coordAmt in range(67):
...
You might also look up how to make a "list comprehension", which can reduce your process to a single line of code -- a long, involved line, but readable with proper white space.
Does that get you moving?

There are a couple of ways around this. Instead of using while lists and counters, you could just use for loops. Or at least do that for the outer loop, since it looks like you still want to check for repeats. Here's an example using your original dimensions of 3 and 4:
from math import pi
import random
coord_sets = 3
coords = 4
biglist = []
for i in range(coord_sets):
coords_set = []
non_repeating_coords = 0
while non_repeating_coords < coords:
new_coord = round(random.uniform(-1.0*pi, pi), 2)
if new_coord not in coords_set:
coords_set.append(new_coord)
non_repeating_coords += 1
biglist.append(coords_set)
print(biglist)

You can use sets because they don't allow duplicate values:
from math import pi
import random
funcs = []
funcAmt = 0
while funcAmt < 64: # This is the number of loops
myset = set()
while len(myset) < 67: # This is the length of each set
uniform = round(random.uniform(-pi, pi), 2)
myset.add(uniform)
funcs.append(list(myset)) # Append randomly generated set as a list
funcAmt += 1
print(funcs)

maybe you can benefit from arrays in numpy:
import numpy as np
funcs = np.random.uniform(-np.pi, np.pi, [63, 67])
This creates an array of shape (63, 67) from uniform random between -pi to pi.

For cycle gets stuck in Python

My code below is getting stuck on a random point:
import functions
from itertools import product
from random import randrange
values = {}
tables = {}
letters = "abcdefghi"
nums = "123456789"
for x in product(letters, nums): #unnecessary
values[x[0] + x[1]] = 0
for x in product(nums, letters): #unnecessary
tables[x[0] + x[1]] = 0
for line_cnt in range(1,10):
for column_cnt in range(1,10):
num = randrange(1,10)
table_cnt = functions.which_table(line_cnt, column_cnt) #Returns a number identifying the table considered
#gets the values already in the line and column and table considered
line = [y for x,y in values.items() if x.startswith(letters[line_cnt-1])]
column = [y for x,y in values.items() if x.endswith(nums[column_cnt-1])]
table = [x for x,y in tables.items() if x.startswith(str(table_cnt))]
#if num is not contained in any of these then it's acceptable, otherwise find another number
while num in line or num in column or num in table:
num = randrange(1,10)
values[letters[line_cnt-1] + nums[column_cnt-1]] = num #Assign the number to the values dictionary
print(line_cnt) #debug
print(sorted(values)) #debug
As you can see it's a program that generates random sudoku schemes using 2 dictionaries : values that contains the complete scheme and tables that contains the values for each table.
Example :
5th square on the first line = 3
|
v
values["a5"] = 3
tables["2b"] = 3
So what is the problem? Am I missing something?

import functions
...
table_cnt = functions.which_table(line_cnt, column_cnt) #Returns a number identifying the table considered
It's nice when we can execute the code right ahead on our own computer to test it. In other words, it would have been nice to replace "table_cnt" with a fixed value for the example (here, a simple string would have sufficed).
for x in product(letters, nums):
values[x[0] + x[1]] = 0
Not that important, but this is more elegant:
values = {x+y: 0 for x, y in product(letters, nums)}
And now, the core of the problem:
while num in line or num in column or num in table:
num = randrange(1,10)
This is where you loop forever. So, you are trying to generate a random sudoku. From your code, this is how you would generate a random list:
nums = []
for _ in range(9):
num = randrange(1, 10)
while num in nums:
num = randrange(1, 10)
nums.append(num)
The problem with this approach is that you have no idea how long the program will take to finish. It could take one second, or one year (although, that is unlikely). This is because there is no guarantee the program will not keep picking a number already taken, over and over.
Still, in practice it should still take a relatively short time to finish (this approach is not efficient but the list is very short). However, in the case of the sudoku, you can end up in an impossible setting. For example:
line = [6, 9, 1, 2, 3, 4, 5, 8, 0]
column = [0, 0, 0, 0, 7, 0, 0, 0, 0]
Where those are the first line (or any line actually) and the last column. When the algorithm will try to find a value for line[8], it will always fail since 7 is blocked by column.
If you want to keep it this way (aka brute force), you should detect such a situation and start over. Again, this is very unefficient and you should look at how to generate sudokus properly (my naive approach would be to start with a solved one and swap lines and columns randomly but I know this is not a good way).