bandwidth reduction for a sparse matrix
[iperm,mrepi,prof,ierr] = bandwr(sp,[iopt]) [iperm,mrepi,prof,ierr] = bandwr(lp,ls,n,[iopt])
sparse matrix
integer row vector
integer row vector
integer
integer
integer row vector
integer row vector
integer row vector
integer
bandwr
solves the problem of bandwidth reduction for a sparse
matrix: the matrix is supposed to be upper triangular with a full
diagonal (it is easy to complete a non symmetric matrix, and then
discards the added terms).
In the first calling sequence, sp
denotes a
sparse matrix; the optional argument iopt
is 0 or 1: 1 if
reducing the profile of the matrix is more important than reducing
the bandwidth and 0 if bandwidth reduction is most important.
The second calling sequence corresponds to the description of a graph:
lp
is a row vector, pointer array of the adjacency lists
description of a graph (its size is the number of nodes of the graph + 1);
ls
is a row vector, node array of the adjacency lists
description (its size is the number of edges of the graph i.e. the
number of non-zero terms of the corresponding sparse matrix).
n
is the number of nodes (dimension of sp
).
iperm
is the permutation vector for reordering the rows
and columns
which reduces the bandwidth and/or profile (new numbering of the nodes
of the graph);
mrepi
is the inverse permutation (mrepi(iperm) is the identity).
prof
is the array giving the profile of the sparse matrix
after the bandwidth reduction if iopt
is 1. If iopt
is 0
this array is zero except for the first term giving the bandwidth.
The simple command max(prof(2:$)-prof(1:($-1)))
returns
the bandwidth of the matrix.
ierr
is an integer indicating an error if its value is not zero.
//Build the initial graph ta=[2 1 3 2 2 4 4 5 6 7 8 8 9 10 10 10 10 11 12 13 13 14 15 16 16 17 17]; he=[1 10 2 5 7 3 2 4 5 8 6 9 7 7 11 13 15 12 13 9 14 11 16 1 17 14 15]; g=make_graph('foo',0,17,ta,he); g.nodes.graphics.x=[283 163 63 57 164 164 273 271 339 384 504 513 439 623 631 757 642]; g.nodes.graphics.y=[59 133 223 318 227 319 221 324 432 141 209 319 428 443 187 151 301]; //Initial Display g.nodes.graphics.name=string(1:17); g.nodes.graphics.display='name'; show_graph(g); a=graph_2_mat(g,'node-node'); ww=tril(a)'+eye(); ww1=full(ww); scf(1); hist3d((ww1+tril(ww1',-1)+tril(ww1,-1)'),52,85); // BANDWIDTH REDUCTION FOR THE MATRIX [iperm,mrepi,prof,ierr]=bandwr(ww); disp(max(prof(2:$)-prof(1:($-1)))); // GRAPH WITH THE NEW NUMBERING g2=g; g2.nodes.graphics.name=string(iperm); show_graph(g2,'new') // NEW MATRIX n=g.nodes.number; yy=ww1(mrepi,mrepi); scf(3) hist3d((yy+tril(yy',-1)+tril(yy,-1)'),52,85); // STARTING WITH THE SAME MATRIX [ij,v,mn]=spget(ww); g1=make_graph('foo',0,n,ij(:,1)',ij(:,2)'); g1.nodes.graphics.x=g.nodes.graphics.x;g1.nodes.graphics.y=g.nodes.graphics.y; // GRAPH //show_graph(g1,'rep'); [lp,la,ls] = adj_lists(1,n,g1.edges.tail,g1.edges.head); [iperm,mrepi,prof,ierr]=bandwr(lp,ls,n,0); g2=g;g2.nodes.graphics.name=string(iperm); show_graph(g2,'new'); | ![]() | ![]() |