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Re: Converting set of equations to matrix
*To*: mathgroup at smc.vnet.net
*Subject*: [mg26740] Re: [mg26709] Converting set of equations to matrix
*From*: Daniel Lichtblau <danl at wolfram.com>
*Date*: Fri, 19 Jan 2001 02:14:16 -0500 (EST)
*References*: <200101180557.AAA16610@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Helge Kreutzmann wrote:
>
> Hello !
> I have a set of equations I create following some rules, like
>
> 3 a[0,0] + 2 a[0,2] + 4 a[2,0] = 0
> -1 a[0,0] + 0.3 a[2,0] = 0
> 4 a[0,2] - 1 a[0,2] = 0
>
> The numbers of coefficients (the a[i,j]) is different in each run
> but fixed. For further calculations I would like to transform the
> above equations into the matrix
> {{3,2,4 },{-1,0,0.3},{0,4,-1}}
>
> Currently I have a list (called coeffli) where I can get the equations
> from. The existing coefficients are stored in a second list (klist).
> I also have a list where the values i,j are stored (cplist).
>
> The above list I would create by
> For[i = 1, i <= Length[kflist], i++,
> Print[Collect[coeffli[[cplist[[i]][[1]]]][[cplist[[i]][[2]]]], klist]]]
>
> I can create a list of the equations but I do not know how to tear
> apart the sum into matrix elements.
>
> Thanks
>
> Helge
There is a built in utility for this sort of thing in the
MatrixManipulation standard add-on package.
eqns = {3*a[0,0] + 2*a[0,2] + 4*a[2,0] == 0,
-a[0,0] + 0.3*a[2,0] == 0,
4*a[0,2] - a[0,2] == 0};
vars = Variables[Map[#[[1]]-#[[2]]&,eqns]];
<<LinearAlgebra`MatrixManipulation`
In[111]:= LinearEquationsToMatrices[eqns, vars]
Out[111]= {{{3., 2., 4.}, {-1., 0., 0.3}, {0., 3., 0.}}, {0., 0., 0.}}
Daniel Lichtblau
Wolfram Research
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