2
$\begingroup$

I have a InterpolatingFunction from a list of complex data $j(x,y)$ in two variables $x$ and $y$.

I need to evaluate this equation $( x ∂j/∂y - y ∂j/∂x )$.

x = {0.01, 0.02, 0.03, 0.04, 0.01, 0.02, 0.03, 0.04, 0.01, 0.02, 0.03,
0.04, 0.01, 0.02, 0.03, 0.04};
y = {0.05, 0.05, 0.05, 0.05, 0.06, 0.06, 0.06, 0.06, 0.07, 0.07, 0.07,
0.07, 0.08, 0.08, 0.08, 0.08};

j = {0.010561397860905564` + 0.0015976985131723536` I, 
  0.014020635474832743` + 0.0025977169091002837` I, 
   0.017487513072750305` + 0.003602592422820732` I, 
   0.020961981006940338` + 
   0.0046123543767775275` I, -0.01371285709417238` - 
    0.0049735813378507425` I, -0.010312644229723354` - 
    0.004004629742597602` I, -0.00690445946081937` - 
    0.0030310857543026193` I, -0.003488357390773193` - 
     0.002052913771772308` I, -0.00006438567799935371` - 
    0.001070077781411395` I, 
    0.0033674092402317087` - 0.00008254401950370003` I, 
    0.006806973184737428` + 0.0009097221180533224` I, 
    0.010254263771322686` + 0.0019067570422475653` I, 
    0.01370921819568967` + 0.0029085892815736082` I, 
    0.017171802982761625` + 0.003915256260194262` I, 
    0.020641953493563608` + 
   0.004926787666825977` I, -0.013998626378818357` - 
    0.0046779948653150735` I};

I used the interpolation:

    jj = Interpolation[Transpose[{x, y, j}]]

I tried to do the derivative as following:

     dd[a_, b_, d_, i_] :=  
    Evaluate[a[[i]]*D[0, 1][jj[[i]]][a[[i]], b[[i]]] - 
    b[[i]]*D[1, 0][jj[[i]]][a[[i]], b[[i]]]]


    m = Table[dd[x, y, jj, i], {i, Length[x]}]

I am a new in Mathematica, and I tried the similar questions here, but I couldn't find a solution. Please can anyone help me to calculate this derivative.

Thank you

$\endgroup$
2
$\begingroup$
jj = Interpolation[Transpose[{x, y, j}]];
der[xx_,yy_] := xx Derivative[1, 0][jj][xx, yy] - yy Derivative[0, 1][jj][xx, yy]

der[0.015, 0.055]
(* 0.12972 + 0.0351906 I *)

Plot3D[
 Evaluate[
  ReIm[der[xx, yy]]
  ]
 , {xx, 0.01, 0.04}, {yy, 0.05, 0.08}
 , PlotStyle -> Opacity[0.5]
 ]

Mathematica graphics

$\endgroup$
0
$\begingroup$
z[u_, v_] := {-v, u}.Grad[jj[a, b], {a, b}] /. Thread[{a, b} -> {u, v}]

Plot3D[Evaluate[ReIm[z[u, v]]], {u,##& @@ MinMax[x]}, {v, ##& @@ MinMax[y]}, 
 PlotStyle -> Opacity[0.5], PlotLegends -> {HoldForm @ Re[z[u, v]], HoldForm@Im[z[u, v]]}]

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.