Why is my cod not working?

I wrote an interpolation code to get parameter called "landa" by just having two input parameters called "Alpha" and "Mu" respectively. Plese find attached the graph for which I am doing such interpolation. First, I fitted 6 degree polynomial to each alpha curve(please note that the number shown on each curve is Alpha). The coefficients of all curves are saved in "Coefficient " matrix (this also has been attached here). I am wondering why the cod is not working for some cases(e.g. suppose that we have Alpha=2, and Mu=2. In this case the code does not enter to the defined if condition!). can anyone help me with this regard?

clear
close all
clc
load("Coefficient.mat")
Alpha=2;
Mu=2;
%%%%%% calculating landa based on the coefficient matrix
Alpha_vector=Coefficient(:,2)+Coefficient(:,3)*Mu+Coefficient(:,4)*(Mu^2)+Coefficient(:,5)*(Mu^3)+Coefficient(:,6)*(Mu^4)...
    +Coefficient(:,7)*(Mu^5)+Coefficient(:,8)*(Mu^6);
%%%%%%% if Alpha is exactly equall to one of graph values. 
if Alpha==Coefficient(1,1)
    landa=Alpha_vector(1);
elseif Alpha==Coefficient(2,1)
    landa=Alpha_vector(2);
elseif Alpha==Coefficient(3,1)
    landa=Alpha_vector(3);
elseif Alpha==Coefficient(4,1)
    landa=Alpha_vector(4);
elseif Alpha==Coefficient(5,1)
    landa=Alpha_vector(5);
elseif Alpha==Coefficient(6,1)
    landa=Alpha_vector(6);
elseif Alpha==Coefficient(7,1)
    landa=Alpha_vector(7);
elseif Alpha==Coefficient(8,1)
    landa=Alpha_vector(8);
elseif Alpha==Coefficient(9,1)
    landa=Alpha_vector(9);
elseif Alpha==Coefficient(10,1)
    landa=Alpha_vector(10);
elseif Alpha==Coefficient(11,1)
    landa=Alpha_vector(11);
elseif Alpha==Coefficient(12,1)
    landa=Alpha_vector(12);
elseif Alpha==Coefficient(13,1)
    landa=Alpha_vector(13);
elseif Alpha==Coefficient(14,1)
    landa=Alpha_vector(14);
elseif Alpha==Coefficient(15,1)
    landa=Alpha_vector(15);
elseif Alpha==Coefficient(16,1)
    landa=Alpha_vector(16);
elseif Alpha==Coefficient(17,1)
    landa=Alpha_vector(17);
elseif Alpha==Coefficient(18,1)
    landa=Alpha_vector(18);
elseif Alpha==Coefficient(19,1)
    landa=Alpha_vector(19);
elseif Alpha==Coefficient(20,1)
    landa=Alpha_vector(20);
elseif Alpha==Coefficient(21,1)
    landa=Alpha_vector(21);
elseif Alpha==Coefficient(22,1)
    landa=Alpha_vector(22);
elseif Alpha==Coefficient(23,1)
    landa=Alpha_vector(23);
elseif Alpha==Coefficient(24,1)
    landa=Alpha_vector(24);
elseif Alpha==Coefficient(25,1)
    landa=Alpha_vector(25);
elseif Alpha==Coefficient(26,1)
    landa=Alpha_vector(26);
    
%%%%%% if Alpha are not something we see on the graph
elseif Alpha>0 && Alpha<0.1
    landa=Alpha_vector(1)-((Alpha-0)*(Alpha_vector(1)-Alpha_vector(2))/0.1);
elseif Alpha>0.1 && Alpha<0.2
    landa=Alpha_vector(2)-((Alpha-0.1)*(Alpha_vector(2)-Alpha_vector(3))/0.1);
elseif Alpha>0.2 && Alpha<0.3
    landa=Alpha_vector(3)-((Alpha-.2)*(Alpha_vector(3)-Alpha_vector(4))/0.1);
elseif Alpha>0.3 && Alpha<0.4
    landa=Alpha_vector(4)-((Alpha-.3)*(Alpha_vector(4)-Alpha_vector(5))/0.1);
elseif Alpha>0.4 && Alpha<0.5
    landa=Alpha_vector(5)-((Alpha-.4)*(Alpha_vector(5)-Alpha_vector(6))/0.1);    
elseif Alpha>0.5 && Alpha<0.6
    landa=Alpha_vector(6)-((Alpha-.5)*(Alpha_vector(6)-Alpha_vector(7))/0.1);
elseif Alpha>0.6 && Alpha<0.7
    landa=Alpha_vector(7)-((Alpha-.6)*(Alpha_vector(7)-Alpha_vector(8))/0.1);
elseif Alpha>0.7 && Alpha<0.8
    landa=Alpha_vector(8)-((Alpha-.7)*(Alpha_vector(8)-Alpha_vector(9))/0.1);
elseif Alpha>0.8 && Alpha<0.9
    landa=Alpha_vector(9)-((Alpha-.8)*(Alpha_vector(9)-Alpha_vector(10))/0.1);
elseif Alpha>0.9 && Alpha<1
    landa=Alpha_vector(10)-((Alpha-.9)*(Alpha_vector(10)-Alpha_vector(11))/0.1);
elseif Alpha>1 && Alpha<1.2
    landa=Alpha_vector(11)-((Alpha-1)*(Alpha_vector(11)-Alpha_vector(12))/0.1);
elseif Alpha>1.2 && Alpha<1.4
    landa=Alpha_vector(12)-((Alpha-1.2)*(Alpha_vector(12)-Alpha_vector(13))/0.1);
elseif Alpha>1.4 && Alpha<1.6
    landa=Alpha_vector(13)-((Alpha-1.4)*(Alpha_vector(13)-Alpha_vector(14))/0.1);
elseif Alpha>1.6 && Alpha<1.8
    landa=Alpha_vector(14)-((Alpha-1.6)*(Alpha_vector(14)-Alpha_vector(15))/0.1);
elseif Alpha>1.8 && Alpha<2
    landa=Alpha_vector(15)-((Alpha-1.8)*(Alpha_vector(15)-Alpha_vector(16))/0.1);
elseif Alpha>2 && Alpha<2.5
    landa=Alpha_vector(16)-((Alpha-2)*(Alpha_vector(16)-Alpha_vector(17))/0.1);
elseif Alpha>2.5 && Alpha<3
    landa=Alpha_vector(17)-((Alpha-2.5)*(Alpha_vector(17)-Alpha_vector(18))/0.1);
elseif Alpha>3 && Alpha<3.5
    landa=Alpha_vector(18)-((Alpha-3)*(Alpha_vector(18)-Alpha_vector(19))/0.1);
elseif Alpha>3.5 && Alpha<4
    landa=Alpha_vector(19)-((Alpha-3.5)*(Alpha_vector(19)-Alpha_vector(20))/0.1);
elseif Alpha>4 && Alpha<4.5
    landa=Alpha_vector(20)-((Alpha-4)*(Alpha_vector(20)-Alpha_vector(21))/0.1);
elseif Alpha>4.5 && Alpha<5
    landa=Alpha_vector(21)-((Alpha-4.5)*(Alpha_vector(21)-Alpha_vector(22))/0.1);
elseif Alpha>5 && Alpha<5.5
    landa=Alpha_vector(22)-((Alpha-5)*(Alpha_vector(22)-Alpha_vector(23))/0.1);
elseif Alpha>5.5 && Alpha<6
    landa=Alpha_vector(23)-((Alpha-5.5)*(Alpha_vector(23)-Alpha_vector(24))/0.1);
elseif Alpha>6 && Alpha<7
    landa=Alpha_vector(24)-((Alpha-6)*(Alpha_vector(24)-Alpha_vector(25))/0.1);
elseif Alpha>7 && Alpha<8
    landa=Alpha_vector(25)-((Alpha-7)*(Alpha_vector(25)-Alpha_vector(26))/0.1);
end

[Walter Roberson]

I suggest you replace the whole

if Alpha==Coefficient(1,1)

chain with

[wasfound, idx] = ismember(Alpha, Coefficient(1:26,1));
if wasfound
    landa = Alpha_vector(idx);
else
    the other stuff
end

[Walter Roberson]

Your other code looks like it could be done with

interp1([0:0.1:1, 1.2:0.2:2, 2.5:0.5:6, 7, 8], Alpha_vector, Alpha)

or something similar.

Answer 1

[Walter Roberson]

elseif Alpha>1.4 && Alpha<1.6
    landa=Alpha_vector(13)-((Alpha-1.4)*(Alpha_vector(13)-Alpha_vector(14))/0.1);

The division should not be by 0.1 each time; it should be by the difference between the endpoints of the interval.

I suspect you could do the whole thing with an interp1() call, all of the branches of both cases.

[Behrooz Daneshian]

Thank you very much for your reply and so sorry to ask silly question since I am almost new to Matlab.

The function "interp1" worked.However, I still have another problem. For each alpha curve in the attached Figure, fusion(Mu) parameter should be in a specific range so that we can determine landa factor from figure and interpolation. if you take Mu something which is not in that range, you would get weird answers for landa(relatively large value,however we know from the chart that landa must lies between 0.3 and 1). I want landa to be 0.3 if such condition happens. Do you have any idea for that?

[Behrooz Daneshian]

I figured out what to do regarding my previous question. Now I am wondering why Matlab does not accept that alpha(1) is not equal to Coefficient(11,1) which is 1.0000. Can you guide me in this regard?

[Walter Roberson]

Observe:

format long g
load Coefficient

Coefficient(1:10,1)

ans = 10×1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Coefficient(1:10,1) - (0:.1:.9).'

ans = 10×1

1.0e+00 * 0 0 0 0 0 0 0 0 -1.11022302462516e-16 -1.11022302462516e-16

(Coefficient(1:10,1) * 10 - (0:9).')/10

ans = 10×1

1.0e+00 * 0 0 0 4.44089209850063e-17 0 0 0 0 -8.88178419700125e-17 0

Coefficient(1:10,1) - (0:9).'/10

ans = 10×1

1.0e+00 * 0 0 0 5.55111512312578e-17 0 0 0 0 -1.11022302462516e-16 -1.11022302462516e-16

Different ways of calculating the 0, 0.1, 0.2, ... give different exact results -- and none of them match exactly what you have in your file.

num2hex(Coefficient([4,5,9,10],1))

ans = 4×16 char array
    '3fd3333333333334'
    '3fd999999999999a'
    '3fe9999999999999'
    '3feccccccccccccc'

num2hex([0.3;0.4;0.8;0.9])

ans = 4×16 char array
    '3fd3333333333333'
    '3fd999999999999a'
    '3fe999999999999a'
    '3feccccccccccccd'

lin = (0:9)/10;
num2hex(lin([4,5,9,10]))

ans = 4×16 char array
    '3fd3333333333333'
    '3fd999999999999a'
    '3fe999999999999a'
    '3feccccccccccccd'

incr = (0:.1:.9).';
num2hex(incr([4,5,9,10]))

ans = 4×16 char array
    '3fd3333333333334'
    '3fd999999999999a'
    '3fe999999999999a'
    '3feccccccccccccd'