How to Call first and last element in a Matrix of changing size in a Loop

Hello,

I have a data set that needs to be discretized with various numbers of bins. I have acheived this using the discretize() function. My goal is to recreate a Cumulative Distribution Function for a full data set with a smaller number of points.

% Normalized Distribution Data

PerVolsoft = [

17.9116652495797

35.8233304991566

35.8233304991566

53.7349957487335

71.6466609983134

71.6466609983134

71.6466609983134

107.469991497467

107.469991497467

107.469991497467

125.381656747047

143.293321996624

161.204987246201

161.204987246201

179.116652495779

197.028317745356

250.763313494090

268.674978743668

268.674978743668

304.498309242824

304.498309242824

322.409974492402

322.409974492402

322.409974492402

322.409974492402

322.409974492402

322.409974492402

322.409974492402

322.409974492402

286.586643993247

286.586643993247

286.586643993247

286.586643993247

286.586643993247

286.586643993247

286.586643993247

286.586643993247

286.586643993247

286.586643993247

304.498309242824

304.498309242824

304.498309242824

322.409974492402

358.233304991558

411.968300740292

465.703296489024

555.261622736914

644.819948984803

770.201605731850

913.494927728471

1056.78824972509

1200.08157172172

1325.46322846877

1450.84488521581

1612.04987246201

1755.34319445862

1862.81318595609

2024.01817320229

2167.31149519891

2292.69315194596

2435.98647394258

2579.27979593921

2722.57311793583

2865.86643993245

3009.15976192907

3134.54141867612

3277.83474067274

3421.12806266936

3582.33304991558

3725.62637191220

3851.00802865925

3994.30135065587

4119.68300740292

4262.97632939954

4424.18131664574

4567.47463864236

4657.03296489024

4567.47463864236

4424.18131664574

4298.79965989869

4173.41800315165

4012.21301590545

3886.83135915840

3743.53803716178

3582.33304991558

3474.86305841811

3331.56973642149

3170.36474917529

3044.98309242824

2901.68977043162

2776.30811368457

2776.30811368457

2847.95477468288

2991.24809667950

3116.62975342654

3277.83474067274

3403.21639741979

3528.59805416684

3689.80304141303

3815.18469816008

3976.38968540628

4245.06466414995

4388.35798614657

4764.50295638771

5445.14623587167

6161.61284585479

6448.19948984803

6591.49281184467

6734.78613384129

6860.16779058832

7003.46111258495

7146.75443458158

7254.22442607904

7415.42941332525

7540.81107007228

7702.01605731850

7827.39771406555

7952.77937081258

8096.07269280920

8239.36601480582

8382.65933680246

8508.04099354949

8633.42265029654

8794.62763754275

8920.00929428978

9063.30261628642

9152.86094253430

9152.86094253430

9027.47928578725

8866.27429854105

8740.89264179401

8615.51098504696

8472.21766305034

8346.83600630329

8203.54268430667

8042.33769706047

7934.86770556300

7773.66271831680

7648.28106156975

7504.98773957313

7361.69441757651

7236.31276082946

7093.01943883284

6949.72611683622

6824.34446008917

6645.22780759340

6537.75781609593

6394.46449409930

6286.99450260183

6125.78951535563

5982.49619335901

5857.11453661196

5713.82121461534

5570.52789261872

5427.23457062210

5266.02958337590

5158.55959187843

5015.26626988181

4889.88461313476

4746.59129113814

4477.91631239447

4334.62299039784

4191.32966840122

3904.74302440798

3779.36136766093

3636.06804566431

3492.77472366768

3349.48140167106

3206.18807967444

3080.80642292739

2955.42476618035

2794.21977893415

2650.92645693753

2507.63313494090

2364.33981294428

2238.95815619723

2095.66483420061

1934.45984695440

1809.07819020737

1683.69653346032

1432.93321996623

841.848266730160

698.554944733535

555.261622736914

411.968300740292

286.586643993247

143.293321996624

17.9116652495797]; %Percent Volume of Particles

PDsoft = [

1.39561666594512e-07

1.49950026858291e-07

1.62772596681806e-07

1.73104098138666e-07

1.85989210350931e-07

2.03974950973525e-07

2.19157954495947e-07

2.35471114416798e-07

2.55606788076154e-07

2.80324767054815e-07

3.26946441391442e-07

3.58563188842820e-07

4.18196935782004e-07

4.44740729635290e-07

4.82771526818800e-07

5.24054424469023e-07

7.12863997280553e-07

7.81800184116777e-07

8.39993971602065e-07

9.11823777690583e-07

1.05262023625834e-06

1.14263220064314e-06

1.24034129401455e-06

1.33266687686749e-06

1.44662627012767e-06

1.55430680467442e-06

1.67000260740738e-06

1.81280835067790e-06

1.96782573973903e-06

2.13609902035778e-06

2.29510089188927e-06

2.46593816754275e-06

2.67680618134891e-06

2.90570600139896e-06

3.12199405169044e-06

3.38896290494868e-06

3.64122248622380e-06

3.99334013360134e-06

4.29058691329328e-06

4.56291902477348e-06

4.90256276678696e-06

5.32179212411611e-06

5.77687074282286e-06

6.27086417525666e-06

6.73763988672092e-06

7.23916034128975e-06

7.85819750243366e-06

8.53016994734126e-06

9.25960429322238e-06

9.74684685879053e-06

1.03654986747238e-05

1.09109336639234e-05

1.12518761785959e-05

1.17230958606127e-05

1.22140498505082e-05

1.25957118602532e-05

1.28567560393131e-05

1.33951868215624e-05

1.36727999954731e-05

1.41000447168378e-05

1.43922659615480e-05

1.48419924010910e-05

1.51495903967377e-05

1.54635633132419e-05

1.57840432698520e-05

1.61111651239670e-05

1.66146033558236e-05

1.69589384391874e-05

1.73104098138666e-05

1.76691653783942e-05

1.78513217865482e-05

1.84091360605235e-05

1.89843807952776e-05

1.95776006541100e-05

2.01893573198421e-05

2.12517260719164e-05

2.28336116429998e-05

2.45332458596066e-05

2.60904199202717e-05

2.69056877653959e-05

2.77464309252648e-05

2.86134454470491e-05

2.92064546758781e-05

2.98117539292038e-05

3.10602466235694e-05

3.20308105474619e-05

3.30317024446567e-05

3.40638699971579e-05

3.51282904999339e-05

3.62259717862563e-05

3.81321909803373e-05

4.13929618625663e-05

4.40202557345369e-05

4.58637892555499e-05

4.72969311041618e-05

4.87748554618420e-05

4.97857067931576e-05

5.02989616828277e-05

5.08175078618808e-05

5.18706928480774e-05

5.24054424469023e-05

5.40429964712156e-05

5.46001409606273e-05

5.68867517136398e-05

6.04974673389142e-05

6.43373622886160e-05

6.56707441655476e-05

6.63477623846779e-05

6.70317601755317e-05

6.84209830316993e-05

6.91263542388002e-05

6.98389973165723e-05

7.05589872327810e-05

7.20213113238556e-05

7.35139418554165e-05

7.42718178111196e-05

7.50375069237524e-05

7.65926476423511e-05

7.73822628441308e-05

7.81800184116777e-05

7.89859982663177e-05

7.98002871945455e-05

8.06229708569440e-05

8.22938694511819e-05

8.39993971602065e-05

8.75172255286644e-05

9.21224026126577e-05

9.79695952986761e-05

0.000101030928197529

0.000103124778549427

0.000106347199508683

0.000108551228760787

0.000113097268433398

0.000114263220064314

0.000115441191819362

0.000117833692654768

0.000119048473418537

0.000120275777699737

0.000121515734606842

0.000124034129401455

0.000124034129401455

0.000126604717538454

0.000126604717538454

0.000127909921270961

0.000130560834594658

0.000130560834594658

0.000131906823053425

0.000133266687686749

0.000136028619165429

0.000137430976557116

0.000138847791246584

0.000138847791246584

0.000140279212278193

0.000141725390232841

0.000143186477243811

0.000144662627012767

0.000144662627012767

0.000146153994825929

0.000149183013750700

0.000150720983505381

0.000152274808623932

0.000153844652563771

0.000155430680467442

0.000158651957266524

0.000160287545029918

0.000161939994528759

0.000163609479595435

0.000165296175854416

0.000167000260740737

0.000168721913518662

0.000168721913518662

0.000170461315300538

0.000173994099680477

0.000175787853916121

0.000177600100469975

0.000179431029984561

0.000181280835067790

0.000183149710313221

0.000185037852320535

0.000185037852320535

0.000188872733174427

0.000200860862366512

0.000202931593634451

0.000205023672654925

0.000209272756542350

0.000213609902035778

0.000220284738434044

0.000224850105548023]; % Particle Size (Diameter [m])

Nb = 25; %Number of Bins

alpha = 0.001; %Volume Fraction of Inlet

aa = cumtrapz(PDsoft,PerVolsoft); % Cumulative Integral

aa = aa.*alpha;

figrue

semilogx(PDsoft,aa), hold on

grid on

[Y,PDedges] = discretize(aa,Nb);

for j = 1:Nb

for i = 1:length(aa)

if Y(i) == j

I(i,1) = aa(i);

end

end

a(j,1) = I(length(I))-I(j);

end

semilogx(PDedges(1:end-1),a)

grid on

Y() is the bin number that each element of aa falls into after being discretized. This code does work, however, I don't recover the same curve.

The problem i see is that matrix I() changes size each iteration of j. What i need to be doing is, for each iteration of the j loop, call the first element of aa() and the last element of aa() that are in each bin. Then calculate the difference between the two. I want to call the values of aa() rather than use the PDedges that come out of the discretize() function because they are actual data points within the set.

For example if the number of bins Nb = 25, then the number of elements that belong in the First bin is 76. I want to call aa(76) and aa(1) without knowing exactly the element number becasue their location changes.

If I change the code to:

Nb = 25; %Number of Bins

alpha = 0.001; %Volume Fraction of Inlet

aa = cumtrapz(PDsoft,PerVolsoft); % Cumulative Integral

aa = aa.*alpha;

figrue

semilogx(PDsoft,aa), hold on

grid on

[Y,PDedges] = discretize(aa,Nb);

for j = 1:Nb

for i = 1:length(aa)

if Y(i) == j

I(i,j) = aa(i);

end

end

a(j,1) = I(length(I))-I(j);

end

semilogx(PDedges(1:end-1),a)

grid on

I() returns as the matrix with the columns of the bin values at their location in aa() with zeros before and after the bin values.

Thank you for your help!

Best,

Keegan

Answer 1

[Siraj]

Hi! It is my understanding that after grouping the data into different bins using “discretize” function, you want to find which elements of “aa” belong to which bin so that we can find the first and last element of each bin and take their difference to calculate the actual bin width.

Based on my understanding, it seems that the issue with the provided code is that the matrix "I" does not accurately indicate which elements of the variable "aa" are present in each bin. Upon analyzing the matrix "I," I noticed that starting from column 2, all columns have their initial values set to 0.

To address this problem, an alternative approach is to create a cell array with 25 cells (representing the number of bins). Each cell will contain an array that identifies the elements belonging to the corresponding bin.

To determine the bin width, we can retrieve the list of elements belonging to each bin from the cell array. By obtaining this list, we can extract the first and last element of the bin, calculate the difference between them, and store it.

Refer to the following code for better understanding.

%% creating a cell array where each cell represents a bin and the cell itself contains values of "aa" that belong to the corresponding bin 
bin_cell = cell(Nb,1); 
for j = 1:Nb 
    for i = 1 : length(aa) 
        if Y(i) == j % means aa(i) belongs to the jth bin. 
            current_element_in_bin = bin_cell{j}; 
            new_elements_in_bin = [current_element_in_bin aa(i)]; %appending this element to the array 
            bin_cell{j} = new_elements_in_bin; 
        end 
    end 
end 


for j = 1: Nb
    %get the jth bin
    elements_in_bin = bin_cell{j};
    if(numel(elements_in_bin) == 0)
        continue;
    end
    % get the first element of aa() that belongs to the jth bin
    first = elements_in_bin(1);
    % get the last element of aa() that belongs to the jth bin
    last = elements_in_bin(end); 

    a(j,1) = first - last;
end

To gain a deeper understanding of cell arrays and how they can be utilized in the context mentioned here refer to the link below.

https://www.mathworks.com/help/matlab/matlab_prog/create-a-cell-array.html

Hope this helps.