R help - Aug 2010 - Surface generated as product of two curves

I have the following data table:

     [,1] [,2] [,3] [,4] [,5]
[1,] 2575 1927 1754  581  354
[2,] 1156  810  730  541  237
[3,]  417  297  199  125  110
[4,]  281  132  132   47   58
[5,]  152   84   87   54   19

Each column represents a time interval expressed in nano-seconds
Each row represents an energy interval expressed m=n MeV
Each table value represents the average gamma rays intensity measured during the
time interval identified by the column and
the energy range identified by the row.
The Energy marginal has been fitted through a Gamma curve with parameters (alpha
= 1.85342, beta = 348.18)
The Time  marginal has been fitted through a Weibull curve with parameters
(alpha = 0.334489, beta = 9.14066)

The scaling factor = 1403.88. 

My goal is:
1. to generate and plot the 2D surface which is generated by the product of the
two curves (like Bezier surfaces)
2. to generate a 3D stairsplot of the above table
3. *ideally* to draw the generated product surface *and* the 3D stairplot in the
same plot

I had a look at graphic functions (persp, plot3D, sctterplot3d) but I feel
intimidated. I have to sample somehow the two curves
to generate the product surface ... maybe using tensors ?
Please, help.
Thank you.
Maura 
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Essentially, you just want to fit a "smooth" surface over your grid of
x,y values. Lots of ways to do this, but check out ?loess for a simple
base R approach. The mgcv package does tensor product splines. Also
search on "thin plate splines", "2d spatial" and the like
for other
approaches. There are probably a dozen R packages that offer various
approaches.

As for the plotting, that will be tricky. The rgl package may be of
use here I believe, but I have never used it. I prefer contour plots
to perspective plots for a variety of reasons that I won't bother you
about here (not as pretty but much more informative imho).

--
Bert Gunter
Genentech Nonclinical Statistics

On Fri, Aug 20, 2010 at 8:23 AM, mauede at alice.it <mauede at alice.it>
wrote:
> ?I have the following data table:
>
> ? ? [,1] [,2] [,3] [,4] [,5]
> [1,] 2575 1927 1754 ?581 ?354
> [2,] 1156 ?810 ?730 ?541 ?237
> [3,] ?417 ?297 ?199 ?125 ?110
> [4,] ?281 ?132 ?132 ? 47 ? 58
> [5,] ?152 ? 84 ? 87 ? 54 ? 19
>
> Each column represents a time interval expressed in nano-seconds
> Each row represents an energy interval expressed m=n MeV
> Each table value represents the average gamma rays intensity measured
during the time interval identified by the column and
> the energy range identified by the row.
> The Energy marginal has been fitted through a Gamma curve with parameters
(alpha = 1.85342, beta = 348.18)
> The Time ?marginal has been fitted through a Weibull curve with parameters
(alpha = 0.334489, beta = 9.14066)
>
> The scaling factor = 1403.88.
>
> My goal is:
> 1. to generate and plot the 2D surface which is generated by the product of
the two curves (like Bezier surfaces)
> 2. to generate a 3D stairsplot of the above table
> 3. *ideally* to draw the generated product surface *and* the 3D stairplot
in the same plot
>
> I had a look at graphic functions (persp, plot3D, sctterplot3d) but I feel
intimidated. I have to sample somehow the two curves
> to generate the product surface ... maybe using tensors ?
> Please, help.
> Thank you.
> Maura
> ? ? ? ? ? ? ? ?Alice ? ? ? ? ? ? ? ? ? ? ? ? ? body {margin:0;padding:0;} ?
? ? ? ? ? ? ? ? ? ? ? ? ? ?#footer { height:13px; font-size:11px;
font-family:Arial, FreeSans, sans-serif; color:#ADADAD; margin:0; padding:7px
12px; text-align:right; border-top:1px solid #dcdcdc; } ? ? ? ? ? ?#footer a {
text-decoration:none; color:#ADADAD; } ? ? ? ? ? ? ?#footer a:hover {
color:#848484; } ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?Inviato dalla nuova Alice mail
> ? ? ? ?[[alternative HTML version deleted]]
>
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