| Re: Multidimensional Interpolation [message #35769] |
Tue, 22 July 2003 04:51  |
Haje Korth
Messages: 651
Registered: May 1997
|
Senior Member |
|
|
JD,
could you give me the source for your solution. Are you aware of a good
textbook on this matter?
Thanks,
Haje
"JD Smith" <jdsmith@as.arizona.edu> wrote in message
news:pan.2003.07.21.18.27.19.886736.21942@as.arizona.edu...
> On Mon, 21 Jul 2003 08:40:58 -0700, Ian Chapman wrote:
>
>> Hi,
>>
>> I have created a 5 dimensional data cube (pressure, temperature,
>> relative humidity, frequency, transmission) with a radiative transfer
>> model. I have a user that will need to get transmission data for given
>> values of the rest of the parameters, so I am currently planning to
>> interpolate the cube to the input values of the user.
>>
>> Does anyone know of any multi-dimensional interpolation routines
>> (similar to spline) that would be able to perform this task?
>>
>
>
> You could roll your own using VALUE_LOCATE to locate the point
> (p,t,h,f) within each of the 4 relevant axes (bracketed between
> i,j,k,l and i+1,j+1,k+1,l+1), and then perform quad-linear
> interpolation on the 16 nearby grid points bracketing the desired
> value. E.g., let:
>
> a=(p-p[i])/(p[i+1]-p[i])
> b=(t-t[i])/(t[j+1]-t[j])
> c=(h-h[i])/(h[k+1]-h[k])
> d=(f-f[i])/(f[l+1]-f[l])
>
> The quad-linear interpolant over you whole data cube "z" would look
> like:
>
> (1-a)(1-b)(1-c)(1-d) z[i ,j ,k ,l ] +
> (1-a)(1-b)(1-c) d z[i ,j ,k ,l+1] +
> (1-a)(1-b) c (1-d) z[i ,j ,k+1,l ] +
> (1-a)(1-b) c d z[i ,j ,k+1,l+1] +
> (1-a) b (1-c)(1-d) z[i ,j+1,k ,l ] +
> (1-a) b (1-c) d z[i ,j+1,k ,l+1] +
> (1-a) b c (1-d) z[i ,j+1,k+1,l ] +
> (1-a) b c d z[i ,j+1,k+1,l+1] +
> a (1-b)(1-c)(1-d) z[i+1,j ,k ,l ] +
> a (1-b)(1-c) d z[i+1,j ,k ,l+1] +
> a (1-b) c (1-d) z[i+1,j ,k+1,l ] +
> a (1-b) c d z[i+1,j ,k+1,l+1] +
> a b (1-c)(1-d) z[i+1,j+1,k ,l ] +
> a b (1-c) d z[i+1,j+1,k ,l+1] +
> a b c (1-d) z[i+1,j+1,k+1,l ] +
> a b c d) z[i+1,j+1,k+1,l+1]
>
> The regularity of this pattern lends one to believe a generic n-linear
> interpolation code could be written. Fancier interpolation methods
> (cubic, spline, sinc) get much harder in higher dimensions.
>
> JD
|
|
|
|
| Re: Multidimensional Interpolation [message #35771 is a reply to message #35769] |
Mon, 21 July 2003 12:46  |
R.G. Stockwell
Messages: 363
Registered: July 1999
|
Senior Member |
|
|
"Ian Chapman" <ian@terraengine.com> wrote in message
news:1b6a0bfb.0307210740.baef502@posting.google.com...
> Hi,
>
> I have created a 5 dimensional data cube (pressure, temperature,
> relative humidity, frequency, transmission) with a radiative transfer
> model. I have a user that will need to get transmission data for
> given values of the rest of the parameters, so I am currently planning
> to interpolate the cube to the input values of the user.
>
> Does anyone know of any multi-dimensional interpolation routines
> (similar to spline) that would be able to perform this task?
>
> -Ian
LOESS (local regression) interpolation is popular with some satellite
processing groups.
It is pretty straight forward (just set up your least squares fit equation
for an appropriate
function, like a quadratic, and solve with svd or cholskey).
A brief writeup is at
http://www.colorado-research.com/~stockwel/qscatsmp/qscatsmp .shtml
this may be a wee bit slow for you though.
Cheers,
bob
|
|
|
|
| Re: Multidimensional Interpolation [message #35772 is a reply to message #35771] |
Mon, 21 July 2003 11:27 |
JD Smith
Messages: 850
Registered: December 1999
|
Senior Member |
|
|
On Mon, 21 Jul 2003 08:40:58 -0700, Ian Chapman wrote:
> Hi,
>
> I have created a 5 dimensional data cube (pressure, temperature,
> relative humidity, frequency, transmission) with a radiative transfer
> model. I have a user that will need to get transmission data for given
> values of the rest of the parameters, so I am currently planning to
> interpolate the cube to the input values of the user.
>
> Does anyone know of any multi-dimensional interpolation routines
> (similar to spline) that would be able to perform this task?
>
You could roll your own using VALUE_LOCATE to locate the point
(p,t,h,f) within each of the 4 relevant axes (bracketed between
i,j,k,l and i+1,j+1,k+1,l+1), and then perform quad-linear
interpolation on the 16 nearby grid points bracketing the desired
value. E.g., let:
a=(p-p[i])/(p[i+1]-p[i])
b=(t-t[i])/(t[j+1]-t[j])
c=(h-h[i])/(h[k+1]-h[k])
d=(f-f[i])/(f[l+1]-f[l])
The quad-linear interpolant over you whole data cube "z" would look
like:
(1-a)(1-b)(1-c)(1-d) z[i ,j ,k ,l ] +
(1-a)(1-b)(1-c) d z[i ,j ,k ,l+1] +
(1-a)(1-b) c (1-d) z[i ,j ,k+1,l ] +
(1-a)(1-b) c d z[i ,j ,k+1,l+1] +
(1-a) b (1-c)(1-d) z[i ,j+1,k ,l ] +
(1-a) b (1-c) d z[i ,j+1,k ,l+1] +
(1-a) b c (1-d) z[i ,j+1,k+1,l ] +
(1-a) b c d z[i ,j+1,k+1,l+1] +
a (1-b)(1-c)(1-d) z[i+1,j ,k ,l ] +
a (1-b)(1-c) d z[i+1,j ,k ,l+1] +
a (1-b) c (1-d) z[i+1,j ,k+1,l ] +
a (1-b) c d z[i+1,j ,k+1,l+1] +
a b (1-c)(1-d) z[i+1,j+1,k ,l ] +
a b (1-c) d z[i+1,j+1,k ,l+1] +
a b c (1-d) z[i+1,j+1,k+1,l ] +
a b c d) z[i+1,j+1,k+1,l+1]
The regularity of this pattern lends one to believe a generic n-linear
interpolation code could be written. Fancier interpolation methods
(cubic, spline, sinc) get much harder in higher dimensions.
JD
|
|
|
|
| Re: Multidimensional Interpolation [message #35918 is a reply to message #35769] |
Tue, 22 July 2003 05:39 |
Paul Van Delst[1]
Messages: 1157
Registered: April 2002
|
Senior Member |
|
|
Haje Korth wrote:
>
> JD,
> could you give me the source for your solution. Are you aware of a good
> textbook on this matter?
I would be interested also. I want to do some 2-D (or is it 3-D?) interpolation
but using bicubic interpolation. My (feeble) initial attempts to figure out how
have led me to my NR book, but the method of deriving the coefficients to do the
interpolation is brazenly swept under the rug.
paulv
>
> Thanks,
> Haje
>
> "JD Smith" <jdsmith@as.arizona.edu> wrote in message
> news:pan.2003.07.21.18.27.19.886736.21942@as.arizona.edu...
>> On Mon, 21 Jul 2003 08:40:58 -0700, Ian Chapman wrote:
>>
>>> Hi,
>>>
>>> I have created a 5 dimensional data cube (pressure, temperature,
>>> relative humidity, frequency, transmission) with a radiative transfer
>>> model. I have a user that will need to get transmission data for given
>>> values of the rest of the parameters, so I am currently planning to
>>> interpolate the cube to the input values of the user.
>>>
>>> Does anyone know of any multi-dimensional interpolation routines
>>> (similar to spline) that would be able to perform this task?
>>>
>>
>>
>> You could roll your own using VALUE_LOCATE to locate the point
>> (p,t,h,f) within each of the 4 relevant axes (bracketed between
>> i,j,k,l and i+1,j+1,k+1,l+1), and then perform quad-linear
>> interpolation on the 16 nearby grid points bracketing the desired
>> value. E.g., let:
>>
>> a=(p-p[i])/(p[i+1]-p[i])
>> b=(t-t[i])/(t[j+1]-t[j])
>> c=(h-h[i])/(h[k+1]-h[k])
>> d=(f-f[i])/(f[l+1]-f[l])
>>
>> The quad-linear interpolant over you whole data cube "z" would look
>> like:
>>
>> (1-a)(1-b)(1-c)(1-d) z[i ,j ,k ,l ] +
>> (1-a)(1-b)(1-c) d z[i ,j ,k ,l+1] +
>> (1-a)(1-b) c (1-d) z[i ,j ,k+1,l ] +
>> (1-a)(1-b) c d z[i ,j ,k+1,l+1] +
>> (1-a) b (1-c)(1-d) z[i ,j+1,k ,l ] +
>> (1-a) b (1-c) d z[i ,j+1,k ,l+1] +
>> (1-a) b c (1-d) z[i ,j+1,k+1,l ] +
>> (1-a) b c d z[i ,j+1,k+1,l+1] +
>> a (1-b)(1-c)(1-d) z[i+1,j ,k ,l ] +
>> a (1-b)(1-c) d z[i+1,j ,k ,l+1] +
>> a (1-b) c (1-d) z[i+1,j ,k+1,l ] +
>> a (1-b) c d z[i+1,j ,k+1,l+1] +
>> a b (1-c)(1-d) z[i+1,j+1,k ,l ] +
>> a b (1-c) d z[i+1,j+1,k ,l+1] +
>> a b c (1-d) z[i+1,j+1,k+1,l ] +
>> a b c d) z[i+1,j+1,k+1,l+1]
>>
>> The regularity of this pattern lends one to believe a generic n-linear
>> interpolation code could be written. Fancier interpolation methods
>> (cubic, spline, sinc) get much harder in higher dimensions.
>>
>> JD
--
Paul van Delst
CIMSS @ NOAA/NCEP/EMC
Ph: (301)763-8000 x7748
Fax:(301)763-8545
|
|
|
|
comp.lang.idl-pvwave archive
Members
Search
Help
Login
Home
