interp1 function not working properly

When I have signal of 1:130 and I interpolate it over 1:115/130:115 it returns array of only 129 values.

[Les Beckham]

Why would you expect more than that?

size(1:115/130:115)

ans = 1×2

1 129

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[Stephen23]

"interp1 function not working properly"

No, INTERP1 is working correctly.

However you did not check the data you are using, and so provided INTERP1 with exactly 129 values:

numel(1:115/130:115)

ans = 129

The cause is mathematics. Lets check the values by going two steps further:

V = 1:115/130:116;
X = (-4:0)+numel(V) % last five indices

X = 1×5

127 128 129 130 131

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V(X) % last five values

ans = 1×5

112.4615 113.3462 114.2308 115.1154 116.0000

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Note how element 129 has a value less than 115.

Note how element 130 has a value greater than 115.

So your step never actually reaches the value 115 (even within binary floating point precision). There is certainly no reason to expect to get 130 elements from that operation, and the mistake has absolutely nothing to do with INTERP1.

Solution: use LINSPACE.

[Dominik Stolfa]

Thank you.

[Dominik Stolfa]

Alright. I went briefly through the links but I still don’t know how to fix it.

[Stephen23]

" I went briefly through the links but I still don’t know how to fix it."

V = linspace(1,115,130)

V = 1×130

1.0000 1.8837 2.7674 3.6512 4.5349 5.4186 6.3023 7.1860 8.0698 8.9535 9.8372 10.7209 11.6047 12.4884 13.3721 14.2558 15.1395 16.0233 16.9070 17.7907 18.6744 19.5581 20.4419 21.3256 22.2093 23.0930 23.9767 24.8605 25.7442 26.6279

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V(130)

ans = 115

Or if you really want to obfuscate your code:

V = interp1([1,130],[1,115],1:130)

V = 1×130

1.0000 1.8837 2.7674 3.6512 4.5349 5.4186 6.3023 7.1860 8.0698 8.9535 9.8372 10.7209 11.6047 12.4884 13.3721 14.2558 15.1395 16.0233 16.9070 17.7907 18.6744 19.5581 20.4419 21.3256 22.2093 23.0930 23.9767 24.8605 25.7442 26.6279

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V(130)

ans = 115

V = rescale(1:130,1,115)

V = 1×130

1.0000 1.8837 2.7674 3.6512 4.5349 5.4186 6.3023 7.1860 8.0698 8.9535 9.8372 10.7209 11.6047 12.4884 13.3721 14.2558 15.1395 16.0233 16.9070 17.7907 18.6744 19.5581 20.4419 21.3256 22.2093 23.0930 23.9767 24.8605 25.7442 26.6279

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V(130)

ans = 115

V = 1+114.*(0:129)./129

V = 1×130

1.0000 1.8837 2.7674 3.6512 4.5349 5.4186 6.3023 7.1860 8.0698 8.9535 9.8372 10.7209 11.6047 12.4884 13.3721 14.2558 15.1395 16.0233 16.9070 17.7907 18.6744 19.5581 20.4419 21.3256 22.2093 23.0930 23.9767 24.8605 25.7442 26.6279

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V(130)

ans = 115

See also: https://en.wikipedia.org/wiki/Off-by-one_error#Fencepost_error

[Dominik Stolfa]

But you din’t interpolate anything did you? I need to do this: interp1=(1:115,x(1:115),1:115/130:115)

and 115/130 is the problem

Edit: I basically want to turn 115 values into 130 values. But I am getting only 129.

[Dominik Stolfa]

Alright, I see. Unfortunately I don’t think I can use linspace for my case and interp1 is not working properly. What can I do?

[Voss]

interp1(1:115,x(1:115),linspace(1,115,130))

[Dominik Stolfa]

Thank you very much. Sometimes I can be pretty dense.

[Image Analyst]

You should have already learned about quantization and truncation error when you took your college math course on linear algebra or numerical analysis. Hopefully this FAQ entry will supply your missing knowledge:

https://matlab.fandom.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_(or_similar)_not_equal_to_zero?

Answer 1

[Subhajyoti]

Hi @Dominik Stolfa,

When you are creating the new range '1:115/130:115', it might not include the last point 115 due to floating-point arithmetic precision, leading to only 129 interpolated values instead of 130.

You can use 'linspace' function in MATLAB to generate linearly spaced vector. Here, in the following code snippet, I have used it to create 130 uniformly-spaced values between 1 and 115.

linspace(1, 115, 130)

ans = 1×130

1.0000 1.8837 2.7674 3.6512 4.5349 5.4186 6.3023 7.1860 8.0698 8.9535 9.8372 10.7209 11.6047 12.4884 13.3721 14.2558 15.1395 16.0233 16.9070 17.7907 18.6744 19.5581 20.4419 21.3256 22.2093 23.0930 23.9767 24.8605 25.7442 26.6279

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Refer to the following MathWorks Documentation to know more about 'linspace':

https://www.mathworks.com/help/matlab/ref/double.linspace.html

[Dominik Stolfa]

Thank you. I will try that.

[Dominik Stolfa]

Can I somehow force interp1 to include also the last number though? I tried using double here and there but it didn’t help.

[Stephen23]

"Can I somehow force interp1 to include also the last number though?"

The problem has nothing to do with INTERP1. Nothing you do with INTERP1 will make any difference to how many sample points you provide it with. Solution: use LINSPACE.

"I tried using double here and there but it didn’t help."

Correct.

[Dominik Stolfa]

Linspace doesn’t seem to work for my case: interp1=(1:115,x(1:115),1:115/130:115) I think.

Answer 2

[Image Analyst]

Like @Subhajyoti said, linspace would be the preferred way to get exactly the number of elements you want and to get it to end exactly in the number you want.

However, you said you want the last number to be 115 so there are two ways: either assign/overwrite the final number to 115, OR concatenate the 115 onto the existing vector.

v1 = linspace(1, 115, 130) % Best way.
% Using colon operator (less preferred than linspace():
v2 = 1 : (115/130) : 115 % 1 through 114.230769230769
% If you want the last value to be 
% 115 instead of 114.230769230769 you can do this
v2(end) = 115;
% Or you can do this
v2 = 1 : (115/130) : 115 % 1 through 114.230769230769
v2 = [v2, 115] % Last two numbers are 114.230769230769 and 115.

[Stephen23]

"...either assign/overwrite the final number to 115"

Note that this does not change the number of elements in the vector.

"... OR concatenate the 115 onto the existing vector."

Note that in general this returns unequal spacing of the last value:

V = [1:115/130:115,115];
D = diff(V);
plot(D,'-*')

Solution: use LINSPACE.

[Dominik Stolfa]

I see, but linspace doesn’t seem to work with variable array.

[Dominik Stolfa]

I actually need solution for this: interp1=(1:115,x(1:115),1:115/130:115)

[Walter Roberson]

v = sym(1):sym(115)/sym(130):sym(115); disp(char(v))

[1, 49/26, 36/13, 95/26, 59/13, 141/26, 82/13, 187/26, 105/13, 233/26, 128/13, 279/26, 151/13, 25/2, 174/13, 371/26, 197/13, 417/26, 220/13, 463/26, 243/13, 509/26, 266/13, 555/26, 289/13, 601/26, 24, 647/26, 335/13, 693/26, 358/13, 739/26, 381/13, 785/26, 404/13, 831/26, 427/13, 877/26, 450/13, 71/2, 473/13, 969/26, 496/13, 1015/26, 519/13, 1061/26, 542/13, 1107/26, 565/13, 1153/26, 588/13, 1199/26, 47, 1245/26, 634/13, 1291/26, 657/13, 1337/26, 680/13, 1383/26, 703/13, 1429/26, 726/13, 1475/26, 749/13, 117/2, 772/13, 1567/26, 795/13, 1613/26, 818/13, 1659/26, 841/13, 1705/26, 864/13, 1751/26, 887/13, 1797/26, 70, 1843/26, 933/13, 1889/26, 956/13, 1935/26, 979/13, 1981/26, 1002/13, 2027/26, 1025/13, 2073/26, 1048/13, 163/2, 1071/13, 2165/26, 1094/13, 2211/26, 1117/13, 2257/26, 1140/13, 2303/26, 1163/13, 2349/26, 1186/13, 2395/26, 93, 2441/26, 1232/13, 2487/26, 1255/13, 2533/26, 1278/13, 2579/26, 1301/13, 2625/26, 1324/13, 2671/26, 1347/13, 209/2, 1370/13, 2763/26, 1393/13, 2809/26, 1416/13, 2855/26, 1439/13, 2901/26, 1462/13, 2947/26, 1485/13]

Your algorithm for generating 130 values is faulty.

w = sym(0):sym(115)/sym(130):sym(115); disp(char(w))

[0, 23/26, 23/13, 69/26, 46/13, 115/26, 69/13, 161/26, 92/13, 207/26, 115/13, 253/26, 138/13, 23/2, 161/13, 345/26, 184/13, 391/26, 207/13, 437/26, 230/13, 483/26, 253/13, 529/26, 276/13, 575/26, 23, 621/26, 322/13, 667/26, 345/13, 713/26, 368/13, 759/26, 391/13, 805/26, 414/13, 851/26, 437/13, 69/2, 460/13, 943/26, 483/13, 989/26, 506/13, 1035/26, 529/13, 1081/26, 552/13, 1127/26, 575/13, 1173/26, 46, 1219/26, 621/13, 1265/26, 644/13, 1311/26, 667/13, 1357/26, 690/13, 1403/26, 713/13, 1449/26, 736/13, 115/2, 759/13, 1541/26, 782/13, 1587/26, 805/13, 1633/26, 828/13, 1679/26, 851/13, 1725/26, 874/13, 1771/26, 69, 1817/26, 920/13, 1863/26, 943/13, 1909/26, 966/13, 1955/26, 989/13, 2001/26, 1012/13, 2047/26, 1035/13, 161/2, 1058/13, 2139/26, 1081/13, 2185/26, 1104/13, 2231/26, 1127/13, 2277/26, 1150/13, 2323/26, 1173/13, 2369/26, 92, 2415/26, 1219/13, 2461/26, 1242/13, 2507/26, 1265/13, 2553/26, 1288/13, 2599/26, 1311/13, 2645/26, 1334/13, 207/2, 1357/13, 2737/26, 1380/13, 2783/26, 1403/13, 2829/26, 1426/13, 2875/26, 1449/13, 2921/26, 1472/13, 2967/26, 115]

Whereas starting from zero gives you something that ends exactly at 115 (at least when carried out to indefinite precision.)

whos v w

  Name      Size             Bytes  Class    Attributes

  v         1x129                8  sym                
  w         1x131                8  sym                

w has 131 values, not 130. It starts with 0, and the second element is less than 1, so if you were to discard the entries less than 1 then you would end up with only 129 values.

x = linspace(sym(1), sym(115), 130);
w1 = x(2)-x(1)
w2 = double(w1)

w2 = 0.8837

y1 = 1:w1:115
y2 = 1:w2:115

y2 = 1×130

1.0000 1.8837 2.7674 3.6512 4.5349 5.4186 6.3023 7.1860 8.0698 8.9535 9.8372 10.7209 11.6047 12.4884 13.3721 14.2558 15.1395 16.0233 16.9070 17.7907 18.6744 19.5581 20.4419 21.3256 22.2093 23.0930 23.9767 24.8605 25.7442 26.6279

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whos y1 y2

  Name      Size             Bytes  Class     Attributes

  y1        1x130                8  sym                 
  y2        1x130             1040  double              

So if you want to use the colon operator, you need to use an increment of 38/43. Which is exactly (115-1)/(130-1)

[Dominik Stolfa]

It is hard to understand for me what you did but @Voss already helped me get the missing pieces. I am still thankful for your replay though.

[Walter Roberson]

Short summary:

In order to use 1:INCREMENT:115 and end up with 130 results, you need the increment to be (115-1)/(130-1)

[Dominik Stolfa]

Interesting approach. I imagine this helps with the floating point error. This wil likely work only with large fractions right?

[Walter Roberson]

@Dominik Stolfa

I don't know what you mean by "large fractions".

It works fine for 7/5

A = 1:(7-1)/(5-1):115;
A(end)

ans = 115

whos A

  Name      Size            Bytes  Class     Attributes

  A         1x77              616  double              

B = linspace(1,115,77);
[~,idx] = max(abs(A-B));
A(idx), B(idx), A(idx)-B(idx)

ans = 1

ans = 1

ans = 0

[Dominik Stolfa]

I will try to use the extreme case. If I wanted to increment every 1/2 and I could not because of rounding error and therefore used step (1-1)/2-1), the results won’t be same anymore.