[SciPy-User] GIS Raster Calculation: Combination of NumPy Arrays and SciPy Density function

Johannes Radinger JRadinger at gmx.at
Thu Jan 6 09:59:08 EST 2011 

Hello...

I am working mostly in ArcGIS but as it's Raster Calculator resp. Map Algebra is limited I want to use NumPy Arrays and perform calcultations in SciPy.

I can get my Rasterfiles in ArcGIS quite easily transformed/exported into a NumPy Array with the function:

newArray = arcpy.RasterToNumPyArray(inRaster)

This Raster/Array contains distance values (ranging from around -20000 to + 20000 float).

Some time before you helped with some distance-density functions which I want to apply now. New Values should be assigned to the cells/elements in the array by following function:

DensityRaster = p * stats.norm.pdf(x, loc=m, scale=s)

where p = 0.3, m=0 and s=200, the x-value is the distance value from the single cells in newArray. Can I just define x=newArray ? and use an array as input variable?

thank you
/j


-------- Original-Nachricht --------
> Datum: Thu, 6 Jan 2011 07:10:58 -0500
> Von: josef.pktd at gmail.com
> An: SciPy Users List <scipy-user at scipy.org>
> Betreff: Re: [SciPy-User] solving integration, density function

> On Thu, Jan 6, 2011 at 7:01 AM, Johannes Radinger <JRadinger at gmx.at>
> wrote:
> > Thank you for the simplification of the formula,
> > but I still get a different result in the case
> > when x<s1 (eg. x=2, s1=3).
> >
> > here a code to try:
> >
> > ********************
> > import math
> > from scipy import stats
> >
> > s1 = 3
> > m = 0
> > p = 1
> > x = 2
> >
> > func = stats.norm.pdf(x, loc=m, scale=(s1))
> > func2 = (1/(s1*math.sqrt(2*math.pi)) * math.exp(-0.5*((x-m)/s1)**2))
> >
> > print func
> > print func2
> > ********************************
> 
> use floats, I think you just run into integer division
> 
> (x-m)/s1
> 
> Josef
> 
> >
> > /j
> >
> > -------- Original-Nachricht --------
> >> Datum: Thu, 6 Jan 2011 05:48:25 -0600
> >> Von: Warren Weckesser <warren.weckesser at enthought.com>
> >> An: SciPy Users List <scipy-user at scipy.org>
> >> Betreff: Re: [SciPy-User] solving integration, density function
> >
> >> On Thu, Jan 6, 2011 at 5:27 AM, Johannes Radinger <JRadinger at gmx.at>
> >> wrote:
> >>
> >> > Hey
> >> >
> >> > Last time you helped me a lot with my normal
> >> > probabilty density function. My problem now is
> >> > quite simple, I think it's just a problem with
> >> > the syntax (brackets):
> >> >
> >> > There are two ways to calculate the pdf, with the
> >> > stats-function and with pure mathematically, but
> >> > the give different results and I can't find the
> >> > where I make the mistake:
> >> >
> >> >
> >> > func1 = stats.norm.pdf(x, loc=m, scale=(s1))
> >> > func2 =
> >> > 1/((s1)*(math.sqrt(2*math.pi))))*(math.exp(((-0.5)*((x-m)/(s1)))**2)
> >> >
> >> > Where is the problem
> >> >
> >>
> >>
> >> func2 = 1/(s1*math.sqrt(2*math.pi)) * math.exp(-0.5*((x-m)/s1)**2)
> >>
> >>
> >> Warren
> >>
> >>
> >>
> >> > thank you...
> >> >
> >> > /j
> >> >
> >> > -------- Original-Nachricht --------
> >> > > Datum: Tue, 21 Dec 2010 09:18:15 -0500
> >> > > Von: Skipper Seabold <jsseabold at gmail.com>
> >> > > An: SciPy Users List <scipy-user at scipy.org>
> >> > > Betreff: Re: [SciPy-User] solving integration, density function
> >> >
> >> > > On Tue, Dec 21, 2010 at 7:48 AM, Johannes Radinger
> <JRadinger at gmx.at>
> >> > > wrote:
> >> > > >
> >> > > > -------- Original-Nachricht --------
> >> > > >> Datum: Tue, 21 Dec 2010 13:20:47 +0100
> >> > > >> Von: Gregor Thalhammer <Gregor.Thalhammer at gmail.com>
> >> > > >> An: SciPy Users List <scipy-user at scipy.org>
> >> > > >> Betreff: Re: [SciPy-User] solving integration, density function
> >> > > >
> >> > > >>
> >> > > >> Am 21.12.2010 um 12:06 schrieb Johannes Radinger:
> >> > > >>
> >> > > >> > Hello,
> >> > > >> >
> >> > > >> > I am really new to python and Scipy.
> >> > > >> > I want to solve a integrated function with a python script
> >> > > >> > and I think Scipy should do that :)
> >> > > >> >
> >> > > >> > My task:
> >> > > >> >
> >> > > >> > I do have some variables (s, m, K,) which are now absolutely
> set,
> >> > but
> >> > > in
> >> > > >> future I'll get the values via another process of pyhton.
> >> > > >> >
> >> > > >> > s = 400
> >> > > >> > m = 0
> >> > > >> > K = 1
> >> > > >> >
> >> > > >> > And have have following function:
> >> > > >> > (1/((s*K)*sqrt(2*pi)))*exp((-1/2*(((x-m)/s*K))^2) which is the
> >> > > density
> >> > > >> function of the normal distribution a symetrical curve with the
> >> mean
> >> > > (m) of
> >> > > >> 0.
> >> > > >> >
> >> > > >> > The total area under the curve is 1 (100%) which is for an
> >> > > integration
> >> > > >> from -inf to +inf.
> >> > > >> > I want to know x in the case of 99%: meaning that the integral
> >> (-x
> >> > to
> >> > > >> +x) of the function is 0.99. Due to the symetry of the curve you
> >> can
> >> > > also set
> >> > > >> the integral from 0 to +x equal to (0.99/2):
> >> > > >> >
> >> > > >> > 0.99 =
> >> integral((1/((s*K)*sqrt(2*pi)))*exp((-1/2*(((x-m)/s*K))^2)),
> >> > > -x,
> >> > > >> x)
> >> > > >> > resp.
> >> > > >> > (0.99/2) =
> >> > > integral((1/((s*K)*sqrt(2*pi)))*exp((-1/2*(((x-m)/s*K))^2)),
> >> > > >> 0, x)
> >> > > >> >
> >> > > >> > How can I solve that question in Scipy/python
> >> > > >> > so that I get x in the end. I don't know how to write
> >> > > >> > the code...
> >> > > >>
> >> > > >>
> >> > > >> --->
> >> > > >> erf(x[, out])
> >> > > >>
> >> > > >>     y=erf(z) returns the error function of complex argument
> defined
> >> > > as
> >> > > >>     as 2/sqrt(pi)*integral(exp(-t**2),t=0..z)
> >> > > >> ---
> >> > > >>
> >> > > >> from scipy.special import erf, erfinv
> >> > > >> erfinv(0.99)*sqrt(2)
> >> > > >>
> >> > > >>
> >> > > >> Gregor
> >> > > >>
> >> > > >
> >> > > >
> >> > > > Thank you Gregor,
> >> > > > I only understand a part of your answer... I know that the
> integral
> >> of
> >> > > the density function is a error function and I know that the
> argument
> >> > "from
> >> > > scipy.special import erf, erfinv" is to load the module.
> >> > > >
> >> > > > But how do I write the code including my orignial function so
> that I
> >> > can
> >> > > modify it (I have also another function I want to integrate). how
> do i
> >> > > start? I want to save the whole code to a python-script I can then
> >> load
> >> > e.g.
> >> > > into ArcGIS where I want to use the value of x for further
> >> calculations.
> >> > > >
> >> > >
> >> > > Are you always integrating densities?  If so, you don't want to
> use
> >> > > integrals probably, but you could use scipy.stats
> >> > >
> >> > > erfinv(.99)*np.sqrt(2)
> >> > > 2.5758293035489004
> >> > >
> >> > > from scipy import stats
> >> > >
> >> > > stats.norm.ppf(.995)
> >> > > 2.5758293035489004
> >> > >
> >> > > Skipper
> >> > > _______________________________________________
> >> > > SciPy-User mailing list
> >> > > SciPy-User at scipy.org
> >> > > http://mail.scipy.org/mailman/listinfo/scipy-user
> >> >
> >> > --
> >> > NEU: FreePhone - kostenlos mobil telefonieren und surfen!
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> >> >
> >
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