Negative Value when using Trapz

Question

Jana Stucke 2019-10-3

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评论： Star Strider 2021-3-24

Hi guys,

I try to calculate the area under this curve using trapz. However, it returns a negative value. Can someone tell me as to why this is the case when my x and y-values are positive?

x=[1	0.938524445788592	0.928012855054005	0.869986463167799	0.866618294101049	0.851905469533143	0.816509718296436	0.804756601303802	0.773481908667312	0.743487036373908	0.721555011244502	0.692238382577883	0.660395319804889	0.622278234454403	0.600185408288678	0.582390124224061	0.534500435615996	0.496551977223480	0.460628844607043	0.403312845618717	0.396635208896749	0.369880255480953	0.330164761722580	0.320181673106196	0.266016313621435	0.232051898082808	0.207117082563950	0.160899350279211	0.149854984446954	0.0908664503933046	0.0762867242364327	0.00582165604699889	0];
y=[0.4503 0.9715 1.0442 1.1506 1.1598 1.2079 1.3224 1.3278 1.3576 1.2198 1.0836 0.8967 0.6814 0.5081 0.4139 0.3949 0.3297 0.3276 0.3335 0.3500 0.3516 0.3560 0.3627 0.3634 0.3651 0.3640 0.3629 0.3594 0.3587 0.3522 0.3511 0.3488 0.3486]
a= trapz(x,y)

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Star Strider 2019-10-3

‘Can someone tell me as to why this is the case when my x and y-values are positive?’

Not without your code and data.

Jana Stucke 2019-10-3

edited

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Answer 1

Star Strider 2019-10-3

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The problem is easiest to see with:

dx = diff(x)

All the ‘dx’ results are negative because ‘x’ is goinmg from highest-to-lowest.

To get a positive result:

a = trapz(fliplr(x),fliplr(y))

produces:

a =
      0.60535

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Andrea Mira 2021-3-24

Excuse me @Star StriderStar Strider, could I ask you a doubt about your comment?

In case the "function" has a part where dx decreases and another where dx increases. Could fliplr be used?

Or would it be necessary to calculate the area in two parts? The part where dx decreases applying fliplr and the part where dx increases without fliplr?

(I'm interested in calculating the red area between the "scatter function" and the blue horizontal line)

Thanks in advance

Star Strider 2021-3-24

Andrea Mira — If I understand correctly what you want to do, I would simply calculate (integrate) those two red areas separately and then add their absolute values if you want to get the total area. Otherwise, they would subtract from each other, producing an area that would be essentially (within calculation error) 0.

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Answer 2

Guillaume 2019-10-3

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Can someone tell me as to why this is the case

Because your x vector is decreasing, so

is negative for each trapeze

a = trapz(fliplr(x), fliplr(y))

to use increasing x and matching y.

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Answer 3

Steven Lord 2019-10-3

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编辑：Steven Lord 2019-10-3

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Your x vector is sorted descending.

>> issorted(x, 'ascend')
ans =
  logical
   0
>> issorted(x, 'descend')
ans =
  logical
   1

In essence, you're integrating the function represented by the y data from x = 1 to x = 0, not from x = 0 to x = 1. If you flip your x vector so you're integrating from x = 0 to x = 1 (essentially swapping the limits of integration) the area will be positive.

>> trapz(flip(x), flip(y))

[edited: I had forgotten to flip y until I saw Guillaume's answer.]