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| Re: How to calculate the curve area? [message #44519 is a reply to message #44516] |
Tue, 21 June 2005 13:30  |
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Paul Van Delst[1]
Messages: 1157
Registered: April 2002
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Senior Member |
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Julio wrote:
> Hi Benjamin.
>
> The total command returns me returns the sum of the elements of an
> array. However, I need to find the area of the curve.
>
> I found the TSUM.PRO routine (see below), it calculates the integrated
> area of a curve. I think it is what I need,
> Thanks at any rate,
> Julio
>
> http://idlastro.gsfc.nasa.gov/ftp/pro/math/tsum.pro
>
You could use the INT_TABULATED IDL function.
Or use Simpson's rule. I have a integral.pro routine that does this. From the header:
; CALLING SEQUENCE:
; result = integral( x, y )
;
; INPUTS:
; x: Vector of abscissa points. Elements must be unique and monotonically
; increasing.
;
; y: Vector of corresponding ordinate points.
;
; EXAMPLE:
; Define 11 x-values on the closed interval [0.0 , 0.8].
;
; IDL> x = [ 0.0, .12, .22, .32, .36, .40, .44, .54, .64, .70, .80 ]
;
; Define 11 f-values corresponding to x(i).
;
; IDL> f = [ 0.200000, 1.30973, 1.30524, 1.74339, 2.07490, 2.45600, $
; IDL> 2.84299, 3.50730, 3.18194, 2.36302, 0.231964 ]
;
; Compute the integral:
;
; IDL> result = integral( x, f )
; IDL> HELP, result
; RESULT DOUBLE = 1.6274544
;
; In this example, the f-values are generated from a known function,
; (f = .2 + 25*x - 200*x^2 + 675*x^3 - 900*x^4 + 400*x^5)
;
; The Multiple Application Trapezoid Method yields; result = 1.5648
; The Multiple Application Simpson's Method yields; result = 1.6036
; IDL User Library INT_TABULATED.PRO yields; result = 1.6232
; INTEGRAL.PRO yields; result = 1.6274
; The Exact Solution (4 decimal accuracy) yields; result = 1.6405
paulv
--
Paul van Delst
CIMSS @ NOAA/NCEP/EMC
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| Re: How to calculate the curve area? [message #44520 is a reply to message #44519] |
Tue, 21 June 2005 13:19 |
Benjamin Hornberger
Messages: 258
Registered: March 2004
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Senior Member |
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Julio wrote:
> Hi Benjamin.
>
> The total command returns me returns the sum of the elements of an
> array. However, I need to find the area of the curve.
>
Well, as long as the dataset is equally spaced on the X axis, the result
from TOTAL is proportional to the area under the curve. If it's not
equally spaced, you could interpolate. It's just a question of the units
on each axis. Or am I missing something?
Benjamin
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| Re: How to calculate the curve area? [message #44524 is a reply to message #44522] |
Tue, 21 June 2005 12:49 |
Benjamin Hornberger
Messages: 258
Registered: March 2004
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Senior Member |
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Julio wrote:
> Hello!
>
> Although my question is very simple, I haven't got it.
> I'm using PLOT command to plot curve from a 2D matrix. My problem is I
> need to calculate the area bellow the curve.
>
How about using TOTAL() on the dataset (if it is equally spaced)?
Benjamin
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