How to divide an array into separate arrays when the division concerns a proportion of the cell?

Hello,

I have a flow passing through a trough of 24.5 mm. The trough is divided into nb = 10 number of virtual streams (so the length of each virtual stream is Lb = 2.45 mm). The flowrate within each virtual stream is also known. The flow at the end of the trough is divided into n number of flows by n-1 number of cutters. n might vary in different applications. The cutters position x across the trough might also vary. I need to simulate the cutters actions by calculating the proportion of the flow directing to each separate flow. The below figure shows the concept. The below array is the trough of 10 virtual streams and the digits in each cell shows the flowrate. The red sections show the width of the separated flows at the end of the trough. For instance, the first left flow contains the first plus ¾ of the second virtual streams and so on.

I tried to write the below code to calculate each separate flow and it works, but I am searching a more intelligent generic code. I was wondering if you could help me improve it.

clc;
clear;
close all;
D = [1.1 1.2 1.4 1.7 2.0 2.3 2.7 3.1 3.6 4.2];
nb = 10;
Lb = 2.45;
x = [0;4;7;11;16;24.5];
L = x(2:end)-x(1:end-1);
n = floor(L ./ Lb); % Number of virtual streams that report completely to a separate flow
p = (L(1:end-1) - n(1:end-1) .* Lb) ./ Lb; % Proportion of the virtual stream that PARTIALLY reports to a separate flow
z(1,:) = [ones(1,n(1)), p(1), zeros(1,nb-n(1)-1)];
z(2,:) = [zeros(1,n(1)) 1-p(1) ones(1,n(2)), p(2), zeros(1,nb-n(1)-n(2)-2)];
z(3,:) = [zeros(1,n(1)+n(2)+ceil(p(1)+p(2))) 1-p(2) ones(1,n(3)), p(3), zeros(1,nb-n(1)-n(2)-n(3)-3)];
z(4,:) = [zeros(1,n(1)+n(2)+n(3)+ceil(p(1)+p(2)+p(3))) 1-p(3) ones(1,n(4)), p(4), zeros(1,nb-n(1)-n(2)-n(3)-n(4)-4)];
f = z .* repmat(D,length (L(1:end-1)),1);
f(5,:) = D - sum(f);
F = sum(f,2);

[Stephen23]

Your code appears to allocate the cutter-locations incorrectly. For example, given ten streams with eleven edges:

>> linspace(0,24.5,nb+1) % 11 edges for 10 streams
ans =
    0.00000    2.45000    4.90000    7.35000    9.80000   12.25000   14.70000   17.15000   19.60000   22.05000   24.50000
%      |  str 1   |  str 2   |  str 3   |  str 4   |  str 5   |  str 6   |  str 7   |  str 8   |  str 9   |  str 10   |

and your cutter positions:

x = [0;4;7;11;16;24.5]

it is clear that the cutters at positions 4 & 7 fall within streams two and three respectively (stream edges 2.45, 4.9, 7.35). But your scaling matrix z shows these cutters over three streams (not two), as shown on the second row of z:

>> z
z =
   1.00000   0.63265   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.36735   1.00000   0.22449   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.77551   1.00000   0.63265   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000   0.00000   0.36735   1.00000   1.00000   0.04082   0.00000
%   str 1  |  str 2  |  str 3  |  str 4  |  str 5  |  str 6  |  str 7  |  str 8  |  str 9  |  str 10

The cutter at position 7 clearly is not within the fourth stream, which only starts at position 7.35, so based on your explanation it would be erroneous to include any of the fourth stream to be in the flow between cutters 2 and 3. But according to your z matrix, you count part of the fourth stream in the 2nd flow.

Another indication that something is not quite right is in matrix f:

>> f
f =
   1.10000   0.75918   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.44082   1.40000   0.38163   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   1.31837   2.00000   1.45510   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000   0.00000   0.84490   2.70000   3.10000   0.14694   0.00000
   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   3.45306   4.20000
%   str 1  |  str 2  |  str 3  |  str 4  |  str 5  |  str 6  |  str 7  |  str 8  |  str 9  |  str 10

The last row is for the fifth flow, i.e. between the cutters at 16 & 24.5. But the cutter at position 16 falls within the seventh stream, not the ninth stream as your matrix indicates (the seventh stream goes from 14.7 to 17.15, which clearly includes the position of the cutter at position 16).

Answer 1

[Stephen23]

% data:
D  = [1.1,1.2,1.4,1.7,2.0,2.3,2.7,3.1,3.6,4.2];
nb = 10;
Lb = 2.45;
x  = [0;4;7;11;16;24.5];
% code:
Lw = linspace(0,24.5,nb+1) % stream edges
ida = x(1:end-1)<=Lw(2:end) & x(2:end)>=Lw(1:end-1) % any
idl = x(1:end-1)>Lw(1:end-1) & x(1:end-1)<Lw(2:end) % left
idr = x(2:end)>Lw(1:end-1) & x(2:end)<Lw(2:end)     % right
K2 = ida + idr.*(x(2:end)-Lw(2:end))./Lb + idl.*(Lw(1:end-1)-x(1:end-1))./Lb % scale
F2 = sum(D.*K2,2)

Giving:

F2 =
    1.8592
    1.6408
    2.8796
    4.7531
   12.1673

This code requires MATLAB >=R2016b, for earlier versions use bsxfun where required.

[Maryam S]

Hi Stephen,

Thanks a lot for your code. It works! :) I see my code's error too.

Maryam S.