Neglecting difference between two values if it is very small so that value1= value2

I am working on a dataset. After some eigendecompostion process. I realise the difference between my values are as small as 1.8097e-14 which is my further implementation process.

Example

data1(1:10) = 0 0.1502 0.2970 0.4371 0.5673 0.6845 0.7863 0.8702 0.9343 0.9773

data2(1:10) = -0.0000 0.1502 0.2970 0.4371 0.5673 0.6845 0.7863 0.8702 0.9343 0.9773

C= data1(1:10)-data2(1:10)

C =

1.0e-12 *

0.0862 0.1227 0.1545 0.0772 0.1019 0.1178 -0.0174 0.0048 0.0170 0.0181

How do I code that the these difference be neglected so that values in data1 & data2 will be equal since the difference is very small

Answer 1

[Fangjun Jiang]

To compare element by element, abs(C) < Tolerance

To compare the two vectors as a whole, all(abs(C) < Tolerance)

or use

ismembertol(C,0,Tolerance)

[Cutie]

@Fangjun Jiang.

Thank you for your answer but Can you please explain the 'tolerance' how I can define it. I can't find it as inbuilt function in MATLAB.

[Stephen23]

abs(C) < 1e-10

[Fangjun Jiang]

It is a small number like the one @Stephen Cobeldick gave. It is the difference that can be neglected based on the meaning of your data.

[Cutie]

Thank you @Fangjun Jiangand @Stephen Cobeldick

Hmmm....I am not clear yet.

Let me simply put it that if I have two data.

Data1=2.0000000001

Data2 = 2.0

Data1-Data2 = 1e-10 (which is very small).

How do I write my code to neglect this difference in such as way that Data1-Data2 will output 0 (i.e Data1-Data2 = 0) instead of 1e-10

[Fangjun Jiang]

You goal is to compare if Data1 and Data2 are equal,

instead of using "if Data1==Data2 (or Data1-Data2==0)" which are problematic,

you use "if abs(Data1-Data2)<1e-6"

[Cutie]

@Fangjun Jiang will it look like

if abs(Data1-Data2)<1e-6

Data1=Data2

end

[Fangjun Jiang]

I guess you could to that. The solution is clear, do whatever to get the result you need.