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LapHssTree.m
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LapHssTree.m
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classdef LapHssTree < handle
%LAPHSSTREE A handle class for storing and manipulating the HSS tree.
% Detailed explanation goes here
properties(GetAccess='public',SetAccess='public')
%... HSS decomposition factors
interp;
diag;
proxy_center_info;
skeleton_idx;
%... inverse factors
Dhat;
E;
F;
G;
invfact_tree;
%... Discretization tree
discret_tree;
perm;
%... input
nnode;
nlevel;
npanel;
nlege;
end
properties(Constant=true)
%... discret_tree constants
LEFT_CHILD=2;
RIGHT_CHILD=3;
PARENT=4;
START=5;
END=6;
DIAG_SIZE=7;
%height and width of interpolation matrix U
%(we enforce the right and left interp mat to be the same)
U_H=8;
U_W=9;
SKELETON_SIZE=10;
%... proxy_center_info constants
PROXY_X=2;
PROXY_Y=3;
PROXY_R=4;
%... invfact_tree constants
D_H=2;
D_W=3;
E_H=4;
E_W=5;
F_H=6;
F_W=7;
G_H=8;
G_W=9;
end
methods
function obj = LapHssTree(discret_tree,perm,npanel,nlege,lw)
%LAPHSSTREE Construct an instance of this class
nnode=size(discret_tree,1);
obj.nnode=nnode;
obj.nlevel=log2(nnode+1);
obj.npanel=npanel;
obj.nlege=nlege;
obj.discret_tree=discret_tree;
obj.perm=perm;
obj.proxy_center_info=-1*ones(nnode,6);
obj.proxy_center_info(:,1)=1:nnode;
obj.skeleton_idx=-1*ones(nnode,lw);
%use zeros since off diagonal blocks should be 0.
obj.diag=zeros(lw,lw,nnode);
obj.interp=-ones(lw,lw,nnode);
obj.Dhat=-ones(lw,lw,nnode);
obj.E=-ones(lw,lw,nnode);
obj.F=-ones(lw,lw,nnode);
obj.G=-ones(lw,lw,nnode);
obj.invfact_tree=-ones(nnode,10);
obj.invfact_tree(:,1)=1:nnode;
end
%... Functions for hssfact
function updateLeafDiag(obj,inode,c_coord,c_norml,c_curv,c_sqrt_whts,alpha)
%UPDATELEAFDIAG Update the D matrix of the input leaf node.
%
% What it computes is the diagonal block, which does not have
% low rank structure and cannot be compressed.
%
% Input parameters:
% inode - The index of the leaf node in discret_tree.
% c_coord - The coordinates of the Gaussian nodes on the panel.
% c_curv - 1 by nlege curvature array
% c_sqrt_whts - nlege by 1 sqrt Gaussian weight array.
obj.diag(1:obj.nlege,1:obj.nlege,inode)=...
lapintmat_dipole(c_coord,c_coord,c_norml,c_sqrt_whts,...
c_sqrt_whts,alpha,c_curv);
obj.discret_tree(inode,LapHssTree.DIAG_SIZE)=obj.nlege;
end
function [proxy_coord,proxy_norml,proxy_sqrt_whts,x0,r]=...
updateLeafProxy(obj,inode,c_coord,nproxy,lpanel)
%UPDATELEAFPROXY Update the proxy information of the leaf node.
x0=(c_coord(1,:)+c_coord(end,:))/2;
[proxy_coord,proxy_norml,r]=lapcircle_full(x0,nproxy,lpanel);
proxy_whts=2*pi*r/nproxy*ones(nproxy,1);
proxy_sqrt_whts=sqrt(proxy_whts);
%... update proxy center info
obj.proxy_center_info(inode,LapHssTree.PROXY_X:LapHssTree.PROXY_Y)=x0;
obj.proxy_center_info(inode,LapHssTree.PROXY_R)=r;
end
function [U,irows] = computeLeafSkel(obj,c_coord,c_norml,...
c_sqrt_whts,compl_bd_idx,coord,norml,sqrt_whts,ideps,...
proxy_coord,proxy_norml,proxy_sqrt_whts,x0,r)
%COMPUTELEAFSKEL Compute the skeleton of leaf panel by ID.
%
% Input parameters:
% compl_bd_idx - The index of nodes on neighboring panels.
% x0 - Coordinate of proxy circle center.
%... compute near field info
npoint=obj.nlege*obj.npanel;
nmaxnearpoint=obj.nlege*2;
near_coord=zeros(nmaxnearpoint,2);
near_norml=zeros(nmaxnearpoint,2);
near_sqrt_whts=zeros(nmaxnearpoint,1);
istack=1;
compl_bd_coord=LapHssTree.getper_ran(coord,compl_bd_idx,npoint);
compl_bd_norml=LapHssTree.getper_ran(norml,compl_bd_idx,npoint);
compl_bd_sqrt_whts=LapHssTree.getper_ran(sqrt_whts,compl_bd_idx,npoint);
for k=1:size(compl_bd_coord,1)
if LapHssTree.is_in_circle(compl_bd_coord(k,:),x0,r)
near_coord(istack,:)=compl_bd_coord(k,:);
near_norml(istack,:)=compl_bd_norml(k,:);
near_sqrt_whts(istack)=compl_bd_sqrt_whts(k);
istack=istack+1;
end
end
nnear=istack-1;
near_coord=near_coord(1:nnear,:);
near_norml=near_norml(1:nnear,:);
near_sqrt_whts=near_sqrt_whts(1:nnear);
%... compute int mats
intmat=LapHssTree.compute_intmat(c_coord,c_norml,near_coord,...
near_norml,proxy_coord,proxy_norml,c_sqrt_whts,...
near_sqrt_whts,proxy_sqrt_whts);
%... ID
[irows,~,~,~,U,~,~,~]=rskeleton(intmat,ideps,'silent'); %assert U*concat_blocks(irows,:)=concat_blocks
end
function updateLevelProxy(obj,inode_list,nproxy,lpanel)
%UPDATELEVELPROXY Create the proxy information for the whole parent level.
%
% Input parameters:
% inode_list - A list of node indices.
% lpanel - arclength of the each node on the corresponding
% parent level.
for inode=inode_list
lchild=obj.discret_tree(inode,LapHssTree.LEFT_CHILD);
rchild=obj.discret_tree(inode,LapHssTree.RIGHT_CHILD);
%... new proxy setup
[lproxy_x,lproxy_y,~]=...
LapHssTree.get_proxy_info(lchild,obj.proxy_center_info);
[rproxy_x,rproxy_y,~]=...
LapHssTree.get_proxy_info(rchild,obj.proxy_center_info);
x0=[(lproxy_x+rproxy_x)/2 (lproxy_y+rproxy_y)/2];
obj.proxy_center_info(inode,LapHssTree.PROXY_X:LapHssTree.PROXY_Y)=x0;
cur_npanel=obj.discret_tree(inode,LapHssTree.END)-...
obj.discret_tree(inode,LapHssTree.START)+1;
cur_lpanel=cur_npanel*lpanel;
[~,~,r]=lapcircle_full(x0,nproxy,cur_lpanel);
obj.proxy_center_info(inode,LapHssTree.PROXY_R)=r;
end
end
function proxyidx2incircle = computeNearPointTable(obj,inode_list,coord)
%COMPUTENEARPOINTTABLE Compute points in the near field for each parent node on the given level.
proxy_centers=...
obj.proxy_center_info(inode_list,LapHssTree.PROXY_X:LapHssTree.PROXY_Y);
proxy_radius=...
obj.proxy_center_info(inode_list,LapHssTree.PROXY_R);
proxyidx2incircle=false(length(inode_list),size(coord,1));
for j=1:size(coord,1)
cur_pt=coord(j,:);
cur_in=LapHssTree.is_in_circle(cur_pt,proxy_centers,proxy_radius);
proxyidx2incircle(cur_in,j)=true;
end
end
function [iskel,c_coord,c_norml,c_sqrt_whts,lskel_coord,lskel_norml,...
lskel_sqrt_whts,rskel_coord,rskel_norml,rskel_sqrt_whts,...
proxy_coord,proxy_norml,proxy_sqrt_whts] = ...
getParentInfo(obj,inode,coord,norml,sqrt_whts,lpanel,nproxy)
lchild=obj.discret_tree(inode,LapHssTree.LEFT_CHILD);
rchild=obj.discret_tree(inode,LapHssTree.RIGHT_CHILD);
%... Init of skeleton points info
nlskel=obj.discret_tree(lchild,LapHssTree.SKELETON_SIZE);
nrskel=obj.discret_tree(rchild,LapHssTree.SKELETON_SIZE);
ilskel=obj.skeleton_idx(lchild,1:nlskel);
irskel=obj.skeleton_idx(rchild,1:nrskel);
iskel=[ilskel irskel];
c_coord=coord(iskel,:); %locations of all points in the current panel
c_norml=norml(iskel,:);
c_sqrt_whts=sqrt_whts(iskel);
lskel_coord=coord(ilskel,:);
lskel_norml=norml(ilskel,:);
lskel_sqrt_whts=sqrt_whts(ilskel);
rskel_coord=coord(irskel,:);
rskel_norml=norml(irskel,:);
rskel_sqrt_whts=sqrt_whts(irskel);
%... when proxy info is not needed (first level)
if nargin~=5
[x,y,r]=obj.get_proxy_info(inode,obj.proxy_center_info);
x0=[x y];
proxy_whts=2*pi*r/nproxy*ones(nproxy,1);
proxy_sqrt_whts=sqrt(proxy_whts);
cur_npanel=obj.discret_tree(inode,LapHssTree.END)-...
obj.discret_tree(inode,LapHssTree.START)+1;
cur_lpanel=cur_npanel*lpanel;
[proxy_coord,proxy_norml,~]=lapcircle_full(x0,nproxy,cur_lpanel);
end
end
function updateParentDiag(obj,inode,lskel_coord,lskel_norml,...
lskel_sqrt_whts,rskel_coord,rskel_norml,rskel_sqrt_whts)
%UPDATEPARENTDIAG Update the B matrix of the input parent node.
%
% What it computes is the diagonal block, which does not have
% low rank structure and cannot be compressed.
nlskel=size(lskel_coord,1);
nrskel=size(rskel_coord,1);
obj.diag(1:nlskel,nlskel+1:nlskel+nrskel,inode)=...
lapintmat_dipole(lskel_coord,rskel_coord,rskel_norml,...
lskel_sqrt_whts,rskel_sqrt_whts);
obj.diag(nlskel+1:nlskel+nrskel,1:nlskel,inode)=...
lapintmat_dipole(rskel_coord,lskel_coord,lskel_norml,...
rskel_sqrt_whts,lskel_sqrt_whts);
obj.discret_tree(inode,LapHssTree.DIAG_SIZE)=nlskel+nrskel;
end
function [U,irows] = computeParentSkel(obj,c_coord,c_norml,...
c_sqrt_whts,coord,norml,sqrt_whts,ideps,proxy_coord,...
proxy_norml,proxy_sqrt_whts,j,proxyidx2incircle,inode)
%COMPUTELEAFSKEL Compute the skeleton of parent panel by ID.
%... compute near field points
compl_bd_idx=true(1,size(coord,1));
compl_bd_idx(LapHssTree.get_panelpts_idx(...
obj.discret_tree(inode,LapHssTree.START),...
obj.discret_tree(inode,LapHssTree.END),...
obj.nlege)...
)=false;
inear=compl_bd_idx&proxyidx2incircle(j,:);
near_coord=coord(inear,:);
near_norml=norml(inear,:);
near_sqrt_whts=sqrt_whts(inear);
%... compute int mats
intmat=LapHssTree.compute_intmat(c_coord,c_norml,near_coord,...
near_norml,proxy_coord,proxy_norml,c_sqrt_whts,...
near_sqrt_whts,proxy_sqrt_whts);
%... ID
[irows,~,~,~,U,~,~,errout]=rskeleton(intmat,ideps,'silent'); %assert U*concat_blocks(irows,:)=concat_blocks
end
function updateInterpSkel(obj,inode,U,irows,bd_idx)
%UPDATEINTERPSKEL Update the interpolative skeleton for the given node.
obj.interp(1:size(U,1),1:size(U,2),inode)=U;
obj.discret_tree(inode,LapHssTree.U_H)=size(U,1);
obj.discret_tree(inode,LapHssTree.U_W)=size(U,2);
obj.skeleton_idx(inode,1:length(irows))=bd_idx(irows);
obj.discret_tree(inode,LapHssTree.SKELETON_SIZE)=length(irows);
end
%... Functions for hssinv
function Dtilde = getDtilde(obj,inode)
%GETDTILDE Get the Dtilde matrix given an inode.
if inode>obj.nnode-obj.npanel
%... Is a leaf.
Dtilde=...
LapHssTree.extract_mat(inode,obj.diag,obj.discret_tree,...
[LapHssTree.DIAG_SIZE LapHssTree.DIAG_SIZE]);
else
%... Is a parent.
lchild=obj.discret_tree(inode,LapHssTree.LEFT_CHILD);
rchild=obj.discret_tree(inode,LapHssTree.RIGHT_CHILD);
[lDhat,lDhat_h,lDhat_w]=...
LapHssTree.extract_mat(lchild,obj.Dhat,obj.invfact_tree,...
[LapHssTree.D_H LapHssTree.D_W]);
[rDhat,rDhat_h,rDhat_w]=...
LapHssTree.extract_mat(rchild,obj.Dhat,obj.invfact_tree,...
[LapHssTree.D_H LapHssTree.D_W]);
Dtilde=...
LapHssTree.extract_mat(inode,obj.diag,obj.discret_tree,...
[LapHssTree.DIAG_SIZE LapHssTree.DIAG_SIZE]);
Dtilde(1:lDhat_h,1:lDhat_w)=lDhat;
Dtilde(end-rDhat_h+1:end,end-rDhat_w+1:end)=rDhat;
end
end
function updateInvFactors(obj,inode,Dtilde)
%UPDATEINVFACTORS Update the inverse factors given an inode and its corresponding Dtilde.
%
% Reference: Martinsson paper's algo3. Note that his assignment for G is wrong.
U=LapHssTree.extract_mat(inode,obj.interp,obj.discret_tree,...
[LapHssTree.U_H,LapHssTree.U_W]);
invDtilde=inv(Dtilde);
tmpDhat=inv(U'*invDtilde*U);
tmpE=invDtilde*U*tmpDhat;
tmpF=tmpDhat*U'*invDtilde;
tmpG=invDtilde-invDtilde*U*tmpDhat*U'*invDtilde;
%... Store the inverse factors
obj.invfact_tree(inode,[LapHssTree.D_H LapHssTree.D_W])=size(tmpDhat);
obj.Dhat(1:size(tmpDhat,1),1:size(tmpDhat,2),inode)=tmpDhat;
obj.invfact_tree(inode,[LapHssTree.E_H LapHssTree.E_W])=size(tmpE);
obj.E(1:size(tmpE,1),1:size(tmpE,2),inode)=tmpE;
obj.invfact_tree(inode,[LapHssTree.F_H LapHssTree.F_W])=size(tmpF);
obj.F(1:size(tmpF,1),1:size(tmpF,2),inode)=tmpF;
obj.invfact_tree(inode,[LapHssTree.G_H LapHssTree.G_W])=size(tmpG);
obj.G(1:size(tmpG,1),1:size(tmpG,2),inode)=tmpG;
end
end
methods(Static=true,Access=private)
function [x,y,r] = get_proxy_info(inode,proxy_center_info)
x=proxy_center_info(inode,LapHssTree.PROXY_X);
y=proxy_center_info(inode,LapHssTree.PROXY_Y);
r=proxy_center_info(inode,LapHssTree.PROXY_R);
end
function idx = get_panelpts_idx(istart,iend,nlege)
idx=1+nlege*(istart-1):nlege*iend;
end
function pts = getper_ran(car,range,npoint)
% for discontinuous range (unlike getper_se)
idx1=range<1;
range(idx1)=range(idx1)+npoint;
idx2=range>npoint;
range(idx2)=range(idx2)-npoint;
pts=car(range,:);
end
function in = is_in_circle(pt,car_center,radius)
n=size(car_center,1);
assert(n==size(radius,1),'size(car_center,1)~=size(radius,1)');
d=sqrt(sum((pt-car_center).^2,2));
in=d<radius-(1e-15);
end
function intmat = compute_intmat(c_coord,c_norml,near_coord,...
near_norml,proxy_coord,proxy_norml,c_sqrt_whts,...
near_sqrt_whts,proxy_sqrt_whts)
intmat_n2t=...
lapintmat_dipole(c_coord,near_coord,near_norml,c_sqrt_whts,near_sqrt_whts);
intmat_p2t=...
lapintmat_dipole(c_coord,proxy_coord,proxy_norml,c_sqrt_whts,proxy_sqrt_whts);
intmat_t2n=...
lapintmat_dipole(near_coord,c_coord,c_norml,near_sqrt_whts,c_sqrt_whts);
intmat_t2p=...
lapintmat_dipole(proxy_coord,c_coord,c_norml,proxy_sqrt_whts,c_sqrt_whts);
intmat=[intmat_p2t intmat_n2t intmat_t2p' intmat_t2n'];
end
function [mat,h,w] = extract_mat(inode,mat_table,tree,field)
h=tree(inode,field(1));
w=tree(inode,field(2));
mat=mat_table(1:h,1:w,inode);
end
end
end