Re: multi-dimensional SVDFIT

["R.G.S." <rgs1967(at)hotmail.com>]

Ingo Wardinski <ingo@gfz-potsdam.de> wrote in message
ynlelryc66q.fsf@mt35.gfz-potsdam.de">news:ynlelryc66q.fsf@mt35.gfz-potsdam.de...
> Hi,
> does anyone know, if it is possible to make a multi-dimensional SDVFIT
> to a certain dataset? I'm looking for a SDVFIT of y=f(x1,x2), but
> AFAIK the standard idl SDVFIT routine works only for 1-d.
> thanks in advance
> ingo
> --
> ingo wardinski                                  ingo@gfz-potsdam.de
>  GeoForschungsZentrum Potsdam, Telegrafenberg F456, 14473 Potsdam
>
> "Ich war ganz allein in der Maschine und habe dem Piloten gesagt..."
>       (Helmut Kohl in "Am Ende des Jahrhunderts")



Hello,
the SVD solution to a least squares fit (Ax=b) to higher dimensions is
trivial.
Merely add on the other dimensions as columns of A, since there is no
difference
in principal between "x^2" and "xy", since to the SVD, the matrix A is
merely a collection
of numbers.

Cheers,
bob stockwell
stocwkell at co-ra dot com



For instance, here is a smallpiece of code that will compute a fit to
f(x,y,z)  = a0+a1*x+a2*y+a3*z+a4x*y+a5x*z+a6y*z+a7= x^2+a8y^2+a9z^2

(i.e. 10 parameters second order term polynomial  in 3D)



; Here zon = data(x,y,z)
m = 10 ; number of terms in equation
n = n_elements(zon) ; n = number of data points


; create matrix colum by colum
a = dblarr(m,n)
a(0,*) = 1
a(1,*) = x
a(2,*) = y
a(3,*) = z
a(4,*) = x*y
a(5,*) = x*z
a(6,*) = y*z
a(7,*) = x^2
a(8,*) = y^2
a(9,*) = z^2




; Decompose A:
tic = systime(1)
SVDC, A, W, U, V,/double
toc = systime(1)

; Compute the solution and print the result:
result1 = SVSOL(U, W, V, zon,/double)
toc2 = systime(1)
print,result1