Re: Setting parts of matrices

*Subject*: [mg2980] Re: Setting parts of matrices*From*: crstover at aol.com (CRStover)*Date*: 18 Jan 1996 05:01:41 -0600*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: America Online, Inc. (1-800-827-6364)*Sender*: mj at wri.com

> Can somebody tell me how to set a submatrix of a larger matrix? > Assume a is a larger matrix than b. I would like to do something > like > > a[[Range[i1,i2],Range[j1,j2]]]=b; > > ... > > Jens Olav Nygaard Dear Mr. Nygaard, Here is one solution to your problem. Evaluating setSubmatrix[a, b, {i1, j1}] will reset the appropriate submatrix of a with upper left corner {i1, j1} to b, where the function setSubmatrix is defined as follows: SetAttributes[setSubmatrix, HoldFirst]; setSubmatrix[mat_?MatrixQ, newSubmat_?MatrixQ, {imin_Integer, jmin_Integer}] := ReleaseHold[ Hold[Set][ Table[ Hold[mat[[##]] ]&[i, j], {i, imin, -1 + imin + Dimensions[newSubmat][[1]] }, {j, jmin, -1 + jmin + Dimensions[newSubmat][[2]] } ], Hold[newSubmat] ] ]; For example, if you enter a = {{1, 2, 3}, {4, 5, 6}}; setSubmatrix[a, {{"P"}, {"Q"}}, {1, 2}] then the new value of a is {{1, "P", 3}, {4, "Q", 6}}. What the function setSubmatrix does in this case is to form and execute the expression {{a[[2, 1]]}, {a[[2, 2]]}} = {{"P"}, {"Q"}} Mathematica knows how interpret a statement like a[[2, 1]] = "P" as a request to change part 2, 1 of the value of a; and also how, in effect, to thread Set commands over Lists, in a way that is more efficient than a user-written loop. Another way to solve your problem would be to use Join, Take, Drop and Transpose statements to write a function replaceSubmatrix that *returns* the result of replacing the appropriate submatrix of a with b. You could then type a = replaceSubmatrix[a, b, {i1, j1}] to change the value of a. Sincerely, Chris Stover crstover at aol.com