Re: Using implicit information about row indices

*To*: mathgroup at smc.vnet.net*Subject*: [mg68331] Re: Using implicit information about row indices*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Tue, 1 Aug 2006 07:00:03 -0400 (EDT)*Organization*: The University of Western Australia*References*: <eakcj6$qce$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <eakcj6$qce$1 at smc.vnet.net>, "Diamond, Mark" <dot at dot.dot> wrote: > I am wanting to fill a square matrix M (say, r by r) using information from > a list, L. > The list L is also of length r, but is not a square matrix. It contains > lists of ordered pairs {col, num} > It typically looks something like this; I have arranged it into rows so that > it is more obvious > { > {{1, a}, {2, b}}, > > {{1, c}, {2, d}, {3, e}, {4, f}}, > > {{2, g}, {3, h}, {4, i}}, > > {{3, k}, {4, l}, {5,m}}, > > {{4, n}, {5, p}} > > } > > Now what I am trying to do is, for example, set M[[1,1]]=a, M[[1,2]]=b, > M[[2,1]]=c, M[[2.2]]=d, M[[2,3]]=e and so forth, and leave (or set) all the > other entries in M to zero. Then SparseArray is your friend. > The row information for M is implicit in the > structure of the list L; additionally, the column indices as they appear > within sublist of L are guraranteed to be sequential. It seems with all this > info, there should be an easy way to fill M correctly, but I have struggled > without success to do anything other than an iterative process with Do[]. I > would appreciate any guidance you might have. Here is one solution. For mat = { {{1, a}, {2, b}}, {{1, c}, {2, d}, {3, e}, {4, f}}, {{2, g}, {3, h}, {4, i}}, {{3, k}, {4, l}, {5,m}}, {{4, n}, {5, p}} }; use MapIndexed and SparseArray: Flatten[MapIndexed[{First[#2],First[#1]} -> Last[#1]&, mat, {2}], 1] // SparseArray // Normal {{a, b, 0, 0}, {c, d, e, f}, {g, h, i, 0}, {k, l, m, 0}, {n, p, 0, 0}} Cheers, Paul _______________________________________________________________________ Paul Abbott Phone: 61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul