我有索引
I = [nGrid x 9] matrix % mesh on fine grid (9 point rectangle)
J = [nGrid x 4] matrix % mesh on coarse grid (4 point rectangle)
此处，nGrid是大数，具体取决于网格（例如1.e05）
然后我想做
R_ref = [4 x 9] matrix % reference restriction matrix from fine to coarse
P_ref = [9 x 4] matrix % reference prolongation matrix from coarse to fine
R = sparse(size) % n_Coarse x n_Fine
P = sparse(size) % n_Fine x n_Coarse
for k = 1 : nGrid % number of elements on coarse grid
R(I(k,:),J(k,:)) = R_ref;
P(J(k,:),I(k,:)) = P_ref;
end
size是预定的数字。
请注意，即使(I,J)中有相同的索引，我也不想累积。我只想分别在每个索引处放置模板Rref和Pref。
我知道由于稀疏的数据结构，这很慢。
通常，我使用
sparse(row,col,entry,n_row,n_col)
我可以通过I和J操纵R_ref，P_ref，bsxfun，repmat来使用此功能。
但是，由于sparse功能
（如果(i,j)存在[row(i),col(i)]==[row(j),col(j)]，那么R(row(i),row(j)) = entry(i)+entry(j)）
对于这种装配程序有什么建议吗？
%% INPUTS
% N and M could be much larger
N = 2^5+1; % number of fine grid in x direction
M = 2^5+1; % number of fine grid in y direction
% [nOx * nOy] == nGrid
nOx = floor((M)/2)+1; % number of coarse grid on x direction
nOy = floor((N)/2)+1; % number of coarse grid on y direction
Rref = [4 4 -1 4 -2 0 -1 0 0
-1 -1 -2 4 4 4 -1 4 4
-1 -1 4 -2 4 -2 4 4 -1
0 4 4 0 0 4 -1 -2 -1]/8;
Pref = [2 1 0 1 0 0 0 0 0
0 0 0 1 1 1 0 1 2
0 0 1 0 1 0 2 1 0
0 2 1 0 0 1 0 0 0]'/2;
%% INDEX GENERATION
tri_ref = reshape(bsxfun(@plus,[0,1,2]',[0,N,2*N]),[],1)';
TRI_ref = reshape(bsxfun(@plus,[0,1]',[0,nOy]),[],1)';
I = reshape(bsxfun(@plus,(1:2:N-2)',0:2*N:(M-2)*N),[],1);
J = reshape(bsxfun(@plus,(1:nOy-1)',0:nOy:(nOx-2)*nOy),[],1);
I = bsxfun(@plus,I,tri_ref);
J = bsxfun(@plus,J,TRI_ref);
%% THIS PART IS WHAT I WANT TO CHANGE
R = sparse(nOx*nOy,N*M);
P = R';
for k = 1 : size(I,1)
R(J(k,:),I(k,:)) = Rref;
P(I(k,:),J(k,:)) = Pref;
end