Subtracting two values that are very small

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Muhammad Choudhury 2022-2-11

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https://ww2.mathworks.cn/matlabcentral/answers/1647990-subtracting-two-values-that-are-very-small

评论： Image Analyst 2022-2-12

I'm subtracting two variables (R1 and R2) that are around a magnitude of e-3. I work out a difference between them (Diff = R2 - R1) but my Diff variable outputs as 0 for the whole matrix. I am trying to plot Diff on a plot. How can I make Diff not output as all 0's? Thank you.

R1 = [0.00212278260869565	0.00212931740869565	0.00213585398260870	0.00214239233043478	0.00214893245217391	0.00215547434782609	0.00216201801739130	0.00216856346086957	0.00217511067826087	0.00218165966956522	0.00218821043478261	0.00219476297391304	0.00220131728695652	0.00220787337391304	0.00221443123478261	0.00222099086956522	0.00222755227826087	0.00223411546086957	0.00224068041739130	0.00224724714782609	0.00225381565217391]
R1 = 1×21
    0.0021    0.0021    0.0021    0.0021    0.0021    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0023
R2 = [0.00212278260869565	0.00212931740869565	0.00213585398260870	0.00214239233043478	0.00214893245217391	0.00215547434782609	0.00216201801739130	0.00216856346086957	0.00217511067826087	0.00218165966956522	0.00218821043478261	0.00219476297391304	0.00220131728695652	0.00220787337391304	0.00221443123478261	0.00222099086956522	0.00222755227826087	0.00223411546086957	0.00224068041739130	0.00224724714782609	0.00225381565217391]
R2 = 1×21
    0.0021    0.0021    0.0021    0.0021    0.0021    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0022    0.0023
Diff = R2 - R1
Diff = 1×21
     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0

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Muhammad Choudhury 2022-2-11

编辑：Muhammad Choudhury 2022-2-11

that is very true i didn't even realise, sorry about that, if my question still held, how would go about working it out?

William Rose 2022-2-11

在 MATLAB Online 中打开

@Muhammad Choudhury, if they were different then the vecotr

R2mR1=R2-R1;

wil have the correct difference.

I would not use

diff=R2-R1;

because there is a built-in function called diff() that computes the successive differences of a vector or array.

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Answer 1

Voss 2022-2-11

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1647990-subtracting-two-values-that-are-very-small#answer_894120

在 MATLAB Online 中打开

R1 and R2 are equal, so their difference is in fact 0 everywhere.

R1 = [0.00212278260869565	0.00212931740869565	0.00213585398260870	0.00214239233043478	0.00214893245217391	0.00215547434782609	0.00216201801739130	0.00216856346086957	0.00217511067826087	0.00218165966956522	0.00218821043478261	0.00219476297391304	0.00220131728695652	0.00220787337391304	0.00221443123478261	0.00222099086956522	0.00222755227826087	0.00223411546086957	0.00224068041739130	0.00224724714782609	0.00225381565217391];
R2 = [0.00212278260869565	0.00212931740869565	0.00213585398260870	0.00214239233043478	0.00214893245217391	0.00215547434782609	0.00216201801739130	0.00216856346086957	0.00217511067826087	0.00218165966956522	0.00218821043478261	0.00219476297391304	0.00220131728695652	0.00220787337391304	0.00221443123478261	0.00222099086956522	0.00222755227826087	0.00223411546086957	0.00224068041739130	0.00224724714782609	0.00225381565217391];
Diff = R2 - R1
Diff = 1×21
     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0     0
isequal(R2,R1)
ans = logical
   1

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Voss 2022-2-11

在 MATLAB Online 中打开

If they were different then the output from diff() would be non-zero somewhere. You can plot the difference the same way regardless:

R1 = [0.00212278260869565 0.00212931740869565 0.00213585398260870 0.00214239233043478 0.00214893245217391 0.00215547434782609 0.00216201801739130 0.00216856346086957 0.00217511067826087 0.00218165966956522 0.00218821043478261 0.00219476297391304 0.00220131728695652 0.00220787337391304 0.00221443123478261 0.00222099086956522 0.00222755227826087 0.00223411546086957 0.00224068041739130 0.00224724714782609 0.00225381565217391];

% increased R2(1) by 1e-17:

R2 = [0.00212278260869566 0.00212931740869565 0.00213585398260870 0.00214239233043478 0.00214893245217391 0.00215547434782609 0.00216201801739130 0.00216856346086957 0.00217511067826087 0.00218165966956522 0.00218821043478261 0.00219476297391304 0.00220131728695652 0.00220787337391304 0.00221443123478261 0.00222099086956522 0.00222755227826087 0.00223411546086957 0.00224068041739130 0.00224724714782609 0.00225381565217391];

Diff = R2 - R1

Diff = 1×21

1.0e+-17 * 0.9975 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

plot(Diff);

Image Analyst 2022-2-12

@Muhammad Choudhury I presume you had two vectors that were definitely different and you plotted Diff and got all zeros, or think you did. It should look something like Benjamin's plot above. Did it not?

If not then you either had all zeros, and a very long vector, and the only-non-zero Diff element was the first one or last one so it essentially overlapped with the y axis so you didn't notice it.

OR you just looked at the command window and saw only zeros and though they were all zeros because the command window by default only prints the first 4 decimal places.

OR they actually were all zeros despite what you thought.

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