| partial differential equation [message #93980] |
Tue, 13 December 2016 00:49  |
Ali Gamal
Messages: 98
Registered: June 2013
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Member |
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Hi,
If
lm=[623.2,624.5,665.3,778.2]
S=ss[0:300,0:400,0:18,0] ;;; an image
compute
x=∑[(∂^2 (s))/(∂(lm)^2)] ;;; image
How can I do it using IDL?
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| Re: partial differential equation [message #93982 is a reply to message #93980] |
Tue, 13 December 2016 07:24  |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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On Tuesday, December 13, 2016 at 3:49:42 AM UTC-5, AGW wrote:
> Hi,
>
> If
> lm=[623.2,624.5,665.3,778.2]
> S=ss[0:300,0:400,0:18,0] ;;; an image
> compute
>
> x=∑[(∂^2 (s))/(∂(lm)^2)] ;;; image
>
> How can I do it using IDL?
So S has 19 slices but lm only has 4 elements? How is that supposed to work? You can check out Wikipedia's article on finite differences.
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| Re: partial differential equation [message #93985 is a reply to message #93980] |
Tue, 13 December 2016 09:18 |
Ali Gamal
Messages: 98
Registered: June 2013
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Member |
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On Tuesday, December 13, 2016 at 10:49:42 AM UTC+2, AGW wrote:
> Hi,
>
> If
> lm=[623.2,624.5,665.3,778.2]
> S=ss[0:300,0:400,0:18,0] ;;; an image
> compute
>
> x=∑[(∂^2 (s))/(∂(lm)^2)] ;;; image
>
> How can I do it using IDL?
lm have 19 value, but I did not write all values, suppose
lm=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]
else
x=∑_i[(∂^2(s))/(∂ lm^2 )]]_i
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| Re: partial differential equation [message #93987 is a reply to message #93985] |
Tue, 13 December 2016 09:35 |
Craig Markwardt
Messages: 1869
Registered: November 1996
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Senior Member |
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On Tuesday, December 13, 2016 at 12:18:32 PM UTC-5, AGW wrote:
> On Tuesday, December 13, 2016 at 10:49:42 AM UTC+2, AGW wrote:
>> Hi,
>>
>> If
>> lm=[623.2,624.5,665.3,778.2]
>> S=ss[0:300,0:400,0:18,0] ;;; an image
>> compute
>>
>> x=∑[(∂^2 (s))/(∂(lm)^2)] ;;; image
>>
>> How can I do it using IDL?
>
> lm have 19 value, but I did not write all values, suppose
> lm=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]
>
> else
> x=∑_i[(∂^2(s))/(∂ lm^2 )]]_i
Well, it's easy and it's hard. If you read the Wikipedia article about finite differences, it's easy. The expression for finite differences is,
∂^2(s))/(∂ lm^2) = ( s(lm+h) - 2 s(lm) + s(lm-h) ) /h^2
That's easy to express in IDL,
d2s_dlm2 = s*0 ;; Initialize to blank array
for i = 1, 17 do begin
h2 = (lm[i]-lm[i-1])*(lm[i+1]-lm[i]) ;; compute h^2 term
d2s_dlm2[*,*,i] = (s[*,*,i+1]-2*s[*,*,i]+s[i-1]) / h2
endfor
Note that it's not possible to compute the finite difference second derivative at the first and last LM position because there's not enough data to estimate it.
Now you want to sum it. That's easy too,
x = total(d2s_dlm2,3)
But the problem is that the sum of a second derivative is more or less equivalent to the integral of a second derivative, i.e. just a single derivative. It's really equivalent to computing the mean slope of S. You don't have to do any of the second derivative stuff to do this. You should basically get the same answer by doing,
x = (s(*,*,18) - s(*,*,0))/(lm(18)-lm(0))
This is not quite true if LM is unevenly spaced.
So you really have to decide if this is what you want.
Did you mean to take an absolute value? Or square the second derivative before summing it?
CM
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| Re: partial differential equation [message #93988 is a reply to message #93980] |
Tue, 13 December 2016 09:50 |
Ali Gamal
Messages: 98
Registered: June 2013
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Member |
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On Tuesday, December 13, 2016 at 10:49:42 AM UTC+2, AGW wrote:
> Hi,
>
> If
> lm=[623.2,624.5,665.3,778.2]
> S=ss[0:300,0:400,0:18,0] ;;; an image
> compute
>
> x=∑[(∂^2 (s))/(∂(lm)^2)] ;;; image
>
> How can I do it using IDL?
Thanks
Of course I want absolute value of [(∂^2 (s))/(∂(lm)^2)]
.....
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