Re: Matrix Manipulation
- To: mathgroup at smc.vnet.net
- Subject: [mg16472] Re: [mg16389] Matrix Manipulation
- From: BobHanlon at aol.com
- Date: Sat, 13 Mar 1999 02:22:07 -0500
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 3/11/99 4:27:22 PM, bernhard at eng.umd.edu writes:
>I am trying to modify the elements of a submatrix in a matrix, without
>having to replace each element explicitly
>
>for example:
>mm = { {1,2,3}, {4,5,6}, {7,8,9} }
>msub = { {21,22}, {23,24} }
>I now wish to add the sub matrix: to positions (1,1),(1,3),(3,1),(3,3)
>
>I have tried using ReplacePart but it does not recognize the
>multidimensional replacement, I have also tried
>mm[ {{1,3} , {1,3}} ] = mm[ {{1,3} , {1,3}}] + msub
>
>but this crashes horribly
>
Andy,
mm =Array[m, {3,3}];
msub =Array[s, {2,2}];
For such small matrices, the easiest approach is just to pad msub with
zeroes and then add to mm.
msub0 = {{s[1, 1], 0, s[1, 2]}, {0,0,0},
{s[2, 1], 0, s[2, 2]}};
mm+msub0
{{m[1, 1] + s[1, 1], m[1, 2], m[1, 3] + s[1, 2]},
{m[2, 1], m[2, 2], m[2, 3]},
{m[3, 1] + s[2, 1], m[3, 2], m[3, 3] + s[2, 2]}}
However, for larger matrices
pos = {{1,1}, {1,3}, {3,1}, {3,3}};
msubPos = Transpose[{Flatten[msub], pos}]
{{s[1, 1], {1, 1}}, {s[1, 2], {1, 3}}, {s[2, 1], {3, 1}},
{s[2, 2], {3, 3}}}
Fold[ReplacePart[#1, #1[[Sequence @@ #2[[2]]]]+#2[[1]], #2[[2]]]&, mm,
msubPos]
{{m[1, 1] + s[1, 1], m[1, 2], m[1, 3] + s[1, 2]},
{m[2, 1], m[2, 2], m[2, 3]},
{m[3, 1] + s[2, 1], m[3, 2], m[3, 3] + s[2, 2]}}
I'm not sure whether this meets the intent of what you meant by your
criteria "without having to replace each element explicitly" since this
uses Fold to step through each replacement.
Bob Hanlon