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MathGroup Archive 2001

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Re: Numerical derivative on non-uniform grid

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30275] Re: [mg30257] Numerical derivative on non-uniform grid
  • From: BobHanlon at aol.com
  • Date: Sat, 4 Aug 2001 20:02:04 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2001/8/4 1:44:15 AM, jim at freeze.org writes:

>Can Mathematica take a numerical derivative (on a list of x,y pairs)
>where the x spacing is non-uniform?
>

data = Table[ToExpression[{"x"<>ToString[k], "y"<>ToString[k]}], {k, 5}];

Rest[data-RotateRight[data]] /. {x_, y_} :> y/x

{(y2 - y1)/(x2 - x1), 
  (y3 - y2)/(x3 - x2), 
  (y4 - y3)/(x4 - x3), 
  (y5 - y4)/(x5 - x4)}

You can also use an interpolating function

data = ({#, Sin[#]}& /@ Sort[Table[2*Pi*Random[], {50}]]);

f = Interpolation[data];

Table[{x, f[x], f'[x]}, {x, Pi/8., 15Pi/8, Pi/8}]//TableForm

Plot[{f[x], f'[x]}, Evaluate[{x, f[[1, 1, 1]], f[[1, 1, 2]]}], 
    PlotStyle -> {RGBColor[0, 0, 1], RGBColor[1, 0, 0]}];


Bob Hanlon
Chantilly, VA  USA


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