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I want to distribute n rectangles from a dataframe with different heights and lengths so that the aspect ratio (r_expected) of the total length (L) and total height (H) is roughly L/H = 0.33. A sketch of the rectangle distribution logic below:

To find the most optimal length, I start with a guessed length (L_guess). From that I can calculate the total height (H) (note: I'm omitting a detailed description of how this is done since it is secondary) and therefore the ratio r, as seen here:

import pandas as pd
import numpy as np

H = 0
L_guess = 18

l_cum = [2.5, 6.1, 9.9, 13.8, 18.1, 20.0] #cumulative length of rects
h = [3.5, 4.5, 6.7, 4.8, 6.8, 3.1] # height of rects
df = pd.DataFrame(list(zip(l_cum,h)), columns = ["l_cum", "h"])

tolerance = 0.01 #error tolerance for calculated ratio
r_expected = 0.33 #expected target ratio L/H


rowlist = [np.floor(i/L_guess) for i in df["l_cum"]] #check how many rects fit in L_guess by assigning a row index

for k in range(int(max(rowlist))): #check with rect has the largest height
        vals = [j for j,i in enumerate(rowlist) if i == k]
        H += max(df['h'][vals]) #add largest height to get total height

r = L_guess/H #calculated ratio out of L_guess and calculated h

I then update the L_guess if the calculated ratio r is not within a given tolerance to the expected ratio of 0.33. NOW HERE'S MY PROBLEM: Currently, I arbitrarily increase or decrease L_guess by 15% until the calculated ratio is within the given tolerance and L_guess is returned:

if abs(r_expected - r) <= tolerance: #if ratio difference is <= tolerance
     return L_guess #stop iterating and return length that works best

elif r < r_expected: #if L_guess too small
    L_guess += L_guess * 0.15 #increase
    findbestL(df,L_guess) #try again

else: #If L_guess too big
     L_guess -= L_guess * 0.15 #decrease
     findbestL(df,L_guess)

Is there a way to find the suitable increment without guessing and therefore speed up the calculation time? I have read about the gradient descent that aims at minimizing some function that seems somewhat similar?

emily
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  • I find unclear what you are trying to do. Could you perhaps include some toy input / output in a minimal reproducible example? Also I am not sure how the `gradient-descent` and `nonlinear-optimization` apply here. – norok2 May 25 '20 at 14:17
  • I added more explanation and a reproducible example. Basically, I am trying to optimize a length under consideration of a specific aspect ratio. Hope this helps. – emily May 25 '20 at 15:01
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    Perhaps it is me, but I do not have a better understanding. What do you mean by "distribute n rectangles": if I have n rectangles their total width/height is given and so is their ratio. If you say distribute, I assume you start from a group and end up with two or more groups. But then what would "total" refer to? Are you "rotating" the rectangles? Also, the code you posted does not run (beyond the missing `import`s...). Perhaps try reading [ask?](/help/how-to-ask), [mwe](/help/mcve) and [XY-prob](https://en.wikipedia.org/wiki/XY_problem). – norok2 May 25 '20 at 16:04
  • Same problem here, I can't understand your problem. – m.raynal May 26 '20 at 11:49
  • I included a sketch of the rectangle distribution logic and updated the code. To clarify, the total width is not given. I start with a random guess (L_guess) – emily May 26 '20 at 13:51

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