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MathGroup Archive 2007

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Re: How to calculate gradient and laplace of a list

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72902] Re: How to calculate gradient and laplace of a list
  • From: dh <dh at metrohm.ch>
  • Date: Wed, 24 Jan 2007 17:37:36 -0500 (EST)
  • References: <ep4kd5$rat$1@smc.vnet.net>

Hi,
you can do this using ListCorrelate or ListConvolve. For ListCorelate 
the Kernel would be:
x component of Gradient: ker={{0,0,0},{-1,0,1},{0,0,0}}/2
y component of Gradient: ker={{0,1,0},{0,0,0},{0,-1,0}}/2
Laplacian: ker={{0,1,0},{1,-4,1},{0,1,0}}/4
you would then write:
ListCorrelate[ker,matrix]
To plot you can use: ListPlotVectorField from: Graphics`PlotField`. But 
you first have to prepare the data. Assume that gradx and grady are 
matrixes with the corresponding components, then the gradient matrix is:
grad=Transpose[{gradx, grady}, {3, 1, 2}]
and we get a Plot by:
<<Graphics`PlotField`
ListPlotVectorField[grad]
Daniel


leoshen wrote:
> Hi, guys
> I have a matrix of n*m read from a file. mathematica has built in function 
> to do discrete fourier transform of the list.
> Can I calculate the gradient and the laplace of the matrix?
> I can use the listcontourplot to plot the matrix, Is there any way to plot 
> the gradient plot of it?
> 
> 
> 
> 


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