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MathGroup Archive 2001

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Re: Special Matrix

  • To: mathgroup at smc.vnet.net
  • Subject: [mg28327] Re: Special Matrix
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Wed, 11 Apr 2001 02:01:06 -0400 (EDT)
  • References: <9ah5nq$ps0@smc.vnet.net> <9ajmap$s9e@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

There is a problem with the code:

CreateMatrix[n_]:=Block[{r,c,m},Needs["LinearAlgebra`MatrixManipulation`"];
    r=ZeroMatrix[1,n];m=Table[1,{n-2},{n-2}];
    c=ZeroMatrix[n-2,1];
    BlockMatrix[{{r},{c,m,c},{r}}]]

As shown below

CreateMatrix[5]

BlockMatrix::shdw: Symbol BlockMatrix appears in multiple contexts \
{LinearAlgebra`MatrixManipulation`,Global`}; definitions in context \
LinearAlgebra`MatrixManipulation` may shadow or be shadowed by other \
definitions.

ZeroMatrix::shdw: Symbol ZeroMatrix appears in multiple contexts \
{LinearAlgebra`MatrixManipulation`,Global`}; definitions in context \
LinearAlgebra`MatrixManipulation` may shadow or be shadowed by other \
definitions.

BlockMatrix[{{ZeroMatrix[1,5]},{ZeroMatrix[3,1],{{1,1,1},{1,1,1},{1,1,1}},
      ZeroMatrix[3,1]},{ZeroMatrix[1,5]}}]

This is because the context of the symbols ZeroMatrix and BlockMatrix are
prepended when the definion is enterered : they become
          Global`ZeroMatrix
          Global`BlockMatrix

When CreateMatrix[5] is evaluated the package
LinearAlgebra`MatrixManipulation` is loaded and creates the symbols
          LinearAlgebra`MatrixManipulation`ZeroMatrix
          LinearAlgebra`MatrixManipulation`BlockMatrix
with their definitions.

Unfortunately  Global`ZeroMatrix , Global`BlockMatrix do not pick up these
definitions.

Here are two ways of avoiding this problem


1) Load the package before loading defining CreateMatrix

Needs["LinearAlgebra`MatrixManipulation`"];
CreateMatrix[n_]:=
  Block[{r,c,m},
    r=ZeroMatrix[1,n];m=Table[1,{n-2},{n-2}];
    c=ZeroMatrix[n-2,1];
    BlockMatrix[{{r},{c,m,c},{r}}]]

2) Give ZeroMatrix and BlockMatrix the long names that loading the package
will make.

Needs["LinearAlgebra`MatrixManipulation`"];
CreateMatrix[n_]:=
  Block[{r,c,m},
    r=
      LinearAlgebra`MatrixManipulation`ZeroMatrix[1,n];
    m=Table[1,{n-2},{n-2}];
    c=LinearAlgebra`MatrixManipulation`ZeroMatrix[n-2,1];
    LinearAlgebra`MatrixManipulation`BlockMatrix[{{r},{c,m,c},{r}}]]

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"Souvik Banerjee" <s-banerjee at nwu.edu> wrote in message
news:9ajmap$s9e at smc.vnet.net...
> Not sure if the shortest but it works:
>
> CreateMatrix[n_] :=
>   Block[{r,c,m},
>     Needs["LinearAlgebra`MatrixManipulation`"];
>     r = ZeroMatrix[1, n]; m = Table[1, {n - 2}, {n - 2}];
>     c = ZeroMatrix[n - 2, 1];
>     BlockMatrix[{{r}, {c, m, c}, {r}}]
>     ]
>
> The bottleneck seems to be the Table[] operations. If there is a built in
> function to create a matrix with a constant element then it will speed
this
> up.
>
> -Souvik
>
>
> Yoram Pollack <syftech at saad.org.il> wrote in message
> news:9ah5nq$ps0 at smc.vnet.net...
> > Hello
> > I am trying to create a "n x n" matrix with "1" in every position exept
in
> > first and last row, and first and last coulumn, where "0" is needed. In
> > other words: sqare matrix full of  "1" sorounded by "0".
> > What will be the fastest and shortest way to do it?
> >
> > Thanks
> > Yoram
> >
> >
> >
>
>
>




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