D and InterpolatingFunction again

• To: mathgroup at yoda.physics.unc.edu
• Subject: D and InterpolatingFunction again
• From: Pekka.Janhunen at fmi.fi
• Date: Wed, 23 Jun 1993 08:50:53 -0800

```I asked,

> How does D handle interpolating functions? This would be
> extremely useful, but I haven't been able to find out how.

and Jerry Keiper replied:

>In[2]:= f = Interpolation[Table[{x, Sin[x]}, {x, 0., 5., .1}]]
>
>Out[2]= InterpolatingFunction[{0., 5.}, <>]
>
>In[3]:= D[f[x], x]
>
>Out[3]= InterpolatingFunction[{0., 5.}, <>][x]

That's nice, but actually I need that feature for 2D datasets... how about
that. At least the same recipe doesn't seem to work:

In[1]:=  data = Flatten[Table[{x,y,Sin[x]Cos[y]},{x,0.,5.,1.},{y,0.,5.,1.}],1];

In[2]:= ff=Interpolation[data]

Out[2]= InterpolatingFunction[{{0., 5.}, {0., 5.}}, <>]

In[3]:= ff[2,3]

Out[3]= -0.900198

In[4]:= D[ff[x,y],x]

Out[4]= D[InterpolatingFunction[{{0., 5.}, {0., 5.}}, <>][x, y], x]

In[5]:= Derivative[1,0][ff][2,3]

(1,0)
Out[5]= (InterpolatingFunction[{{0., 5.}, {0., 5.}}, <>])     [2, 3]

Pekka

```

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