From c1f8324d58811aa58260514c9cebc0696a3cbd0f Mon Sep 17 00:00:00 2001 From: hariagr Date: Tue, 11 Jul 2017 05:16:47 +0200 Subject: [PATCH 01/16] few minor changes to run example code in FAIRFEM MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 1. ‘yn’ is not defined when wc is empty. Therefore, xn should be updated by yRef. 2. Addpath for add-ons folders during FAIR startup. 3. solver is defined as a char, not string. Probably, this issue has recently arises because of structural changes in R2017a. --- FAIRstartup.m | 1 + add-ons/FAIRFEM/MLIRFEM.m | 2 +- add-ons/FAIRFEM/MLIRFEM.m~ | 251 ++++++++++++++++++++++ add-ons/FAIRFEM/examples/EFEM_SSDvsMP.mat | Bin 0 -> 1069988 bytes kernel/numerics/GaussNewton.m | 2 +- kernel/numerics/GaussNewton.m~ | 162 ++++++++++++++ 6 files changed, 416 insertions(+), 2 deletions(-) create mode 100644 add-ons/FAIRFEM/MLIRFEM.m~ create mode 100644 add-ons/FAIRFEM/examples/EFEM_SSDvsMP.mat create mode 100644 kernel/numerics/GaussNewton.m~ diff --git a/FAIRstartup.m b/FAIRstartup.m index eb4f09a..7d22e5f 100644 --- a/FAIRstartup.m +++ b/FAIRstartup.m @@ -41,6 +41,7 @@ % add subfolder containing the different parts addpath(genpath(fullfile(FAIRpath,'kernel'))); addpath(fullfile(FAIRpath,'temp')); +addpath(genpath(fullfile(FAIRpath,'add-ons'))); message({ '[new to FAIR? try the numerous examples in kernel/examples]' diff --git a/add-ons/FAIRFEM/MLIRFEM.m b/add-ons/FAIRFEM/MLIRFEM.m index a8b8fff..eb0cc19 100755 --- a/add-ons/FAIRFEM/MLIRFEM.m +++ b/add-ons/FAIRFEM/MLIRFEM.m @@ -179,7 +179,7 @@ yn = trafo(wc,xc(:)); yRef = reshape(yn,[],dim); end; - Mesh.xn = reshape(yn,[],dim); + Mesh.xn = yRef;%reshape(yn,[],dim); % compute starting guess y0 if level == minLevel, diff --git a/add-ons/FAIRFEM/MLIRFEM.m~ b/add-ons/FAIRFEM/MLIRFEM.m~ new file mode 100644 index 0000000..1b01e15 --- /dev/null +++ b/add-ons/FAIRFEM/MLIRFEM.m~ @@ -0,0 +1,251 @@ +%============================================================================== +% This code is part of the Finite Element Method app for the Matlab-based toolbox +% FAIR - Flexible Algorithms for Image Registration. +% For details see +% - https://github.com/C4IR/FAIRFEM +%============================================================================== +% +% function [yc,wc,MLhis] = MLIRFEM(ML,varargin) +% +% Multi-Level Image Registration using tetrahedral Finite Elements using +% global refinement +% +% minimizes J^h(y) = D^h(T(y),R) + S^h(y) for h=coarse:fine +% uses PIR [=@GaussNewton] and NPIR [=@GaussNewton] +% +% Input: +% ML coarse to fine representations of the data, see getMultilevel.m +% varagin optinonal parameters, see default parameter +% Output: +% yc numerical optimizer +% wc optimal parameters for PIR +% MLhis iteration history +% +% for level=minLevel:maxLevel, +% get data(level) +% if level==minLevel, get wOpt running PIR; end; +% use pre-registered Yref=trafo(wOpt,X) for regularization +% if level==minLevel +% y0 = Ystop; % use this as starting guess +% else +% get y0 by prologating Yopt from coarse to finer level +% end; +% get Yopt running NPIR using y0 as starting guess +% end%For +%============================================================================== + +function [yc,wc,MLhis] = MLIRFEM(ML,varargin) + +if nargin == 0, help(mfilename); runMinimalExample; return; end; + +%------------------------------------------------------------------------------ +% initialize some default parameter: +% 1.1 initialize output +% 1.2 determine minLevel and maxLevel from the data ML +% 1.3 flag for parametric registration (PIR) +% 2.1 regularization of of PIR objective +% 2.2 regularization of Hessian approximation, H -> H + beta*speye(size(H)) +% 2.3 setup stopping value wStop and initial value w0 +% 2.4 setup objective in PIR and optimization parameters +% 3 setup objective in NPIR and optimization parameters +% 4 setup defaults for plots +% 5 replace defaults by user input +% 6 initializes dimension, discretization, grids etc +% 7 convert optimization parameter sets for PIR and NPIR to lists +%------------------------------------------------------------------------------ +% 1.1 initialize output +yc = []; +wc = []; +MLhis = []; + +% 1.2 get minLevel and maxLevel from ML +[ML,minLevel,maxLevel] = getMultilevel(ML); + +% 1.3 flag for parametric registration (PIR) +parametric = 1; % flag: if true, run parametric pre-registration + +% 2.1 regularization of PIR objective +% J_{PIR} = D(T(Y(wc)),Rc) + S(wc) with S_{PIR} = 0.5*(wc-wRef)'*M*(wc-wRef); +wRef = []; +M = []; + +% 2.2 regularization of Hessian approximation, H -> H + beta*speye(size(H)) +beta = 0; + +% 2.3 setup stopping value wStop and initial value w0 +wStop = []; % global stopping for PIR +w0 = []; % starting guess for PIR + +% 2.4 PIR: default objective function and optimization parameter via optPara('PIR-GN') +PIRobj = @PIRobjFctn; +PIRpara = optPara('PIR-GN'); + +% 3. NPIR: default objective function and optimization parameter via optPara('NPIR-GN') +NPIRobj = @FEMobjFctn; +NPIRpara = optPara('NPIR-GN'); +NPIRpara.Plots = @FAIRplotsFEM; + + +% 4 setup defaults for plots +pause = 0; % flag for pauses +plots = 1; % flag for plots +plotIter = 0; % flag for output of iteration history each level +plotMLiter = 0; % flag for output of summarized iteration history + +% 5 replace defaults by user input +for k=1:2:length(varargin), % overwrites default parameter + eval([varargin{k},'=varargin{',int2str(k+1),'};']); +end; + +% 6 initializes dimension, discretization, grids etc +dimstr = @(m) sprintf('[%s]',sprintf(' %d',m)); +omega = ML{end}.omega; % spatial domain +dim = numel(omega)/2; +xc = []; % current grid + +% 7 convert optimization parameter sets for PIR and NPIR to lists +PO = FAIRcell2struct(PIRpara); +NO = FAIRcell2struct(NPIRpara); + +getGrid = @(m) getNodalGrid(omega,m); +if dim==2 + getMesh = @TriMesh3; +else + getMesh = @TetraMesh1; +end +% --- +FAIRmessage(sprintf('%s: MultiLevel Image Registration',mfilename),'#') +fprintf('>> %-20s : %s\n','omega',dimstr(omega)); +fprintf('>> %-20s : %s\n','IMAGE MODEL',imgModel); +fprintf('>> %-20s : %s\n','DISTANCE',distance); +fprintf('>> %-20s : %s\n','TRAFO',trafo); +fprintf('>> %-20s : %s, alpha=%s\n','REGULARIZER',... + regularizer,num2str(regularizer('get','alpha'))); +fprintf('>> %-20s : %d\n','PRE-REGISTRATION',parametric); +fprintf('>> %-20s : objective=<%s>, method = <%s>\n',... + 'PIR',func2str(PIRobj),func2str(PIRpara.scheme)); +fprintf('>> %-20s : objective=<%s>, method = <%s>\n',... + 'NPIR',func2str(NPIRobj),func2str(NPIRpara.scheme)); +fprintf('>> %-20s : minLevel=%d, maxLevel=%d\n','LEVEL',minLevel,maxLevel); +FAIRmessage('#') + +tic; +%-------------------------------------------------------------------------- +for level=minLevel:maxLevel + + FAIRmessage(sprintf('%s: level %d from %d to %d, %s',... + mfilename,level,minLevel,maxLevel,dimstr(ML{level}.m))); + + % save(old grid), update(m,grid,data coefficients) + xOld = xc; + m = ML{level}.m; + [T,R] = imgModel('coefficients',ML{level}.T,ML{level}.R,omega); + + if level == minLevel && parametric, % parametric pre-registration + % initialize plots + FAIRplots('reset','mode','PIR','fig',minLevel-1,'plots',plots); + FAIRplots('init',struct('Tc',T,'Rc',R,'omega',omega,'m',size(R))); + + % ----- call Parametric Image Registration ---------------------------- + xC = getGrid(m); + Rc = imgModel(R,omega,center(xC,m)); + + PIRfctn = @(wc) PIRobj(T,Rc,omega,m,beta,M,wRef,xC,wc); + PIRfctn([]); % report status of objective function + if isempty(w0), w0 = trafo('w0'); end; + if isempty(wStop), wStop = w0; end; + + [wc,hisPIR] = PIRpara.scheme(PIRfctn,w0,'yStop',wStop,PO{:}); + + fprintf('wc = \n'); disp(wc'); doPause(pause); + % ----- end PIR -------------------------------------- + if plotIter, + his.str{1} = 'iteration history for PIR'; + plotIterationHistory(his,'J',1:4,'fh',100+minLevel-1); + end; + elseif level == minLevel, % no pre-registration + wc = []; + end; + + % get triangulation + Mesh = getMesh(omega,m); + xc = Mesh.xn; + Rc = imgModel(R,omega,Mesh.mfPi(xc,'C')); + + % compute yRef = xc or yc = trafo(wc,xc) on the appropriate grid + if isempty(wc), % use yRef(x) = x + yRef = xc; + else % compute yn=y(wc,xNodal) and interpolate on current grid + yn = trafo(wc,xc(:)); + yRef = reshape(yn,[],dim); + end; + Mesh.xn = reshape(yn,[],dim); + + % compute starting guess y0 + if level == minLevel, + y0 = yRef; % the best known so far + else + % prolongate yc (coarse) y0 (current) + y0 = xc(:) + Mesh.mfPuNodal(yc(:) - xOld(:),m/2,'Pu'); + y0 = reshape(y0,[],dim); + end; + + % ----- call NPIR ------------------------------------- + % S(y) = 0.5*alpha*hd*norm(B*(Y-Yref))^2 + % initialize plots for NPIR + FAIRplotsFEM('reset','mode','FEM','fig',level,'plots',plots); + FAIRplotsFEM('init',struct('Tc',T,'Rc',R,'Mesh',Mesh)); + NPIRfctn = @(yc) NPIRobj(T,Rc,Mesh,yRef,yc); + if level == minLevel, NPIRfctn([]); end; % report status of objective function + yStop = yRef; + [yc,his] = NPIRpara.scheme(NPIRfctn,y0(:),'yStop',yStop(:),NO{:}); + % ----- end NPIR -------------------------------------- + + if plotIter, + his.str{1} = sprintf('iteration history for NPIR, level=%d',level); + plotIterationHistory(his,'J',1:4,'fh',100+level); + end; + + % update iteration history + if level == minLevel, + MLhis.str = his.str; + MLhis.his = his.his; + else + MLhis.his = [MLhis.his;his.his]; + end; + doPause(pause); + +%-------------------------------------------------------------------------- +end;%For level +%-------------------------------------------------------------------------- +MLhis.time = toc; +if plotMLiter, + plotMLIterationHistory(MLhis,'fh',[]); +end; +if isempty(yStop), yStop = xc; end +MLhis.reduction = NPIRfctn(yc)/NPIRfctn(yStop); +J = find(MLhis.his(:,1)==-1); +MLhis.iter(minLevel:maxLevel) = MLhis.his([J(2:end)-1;size(MLhis.his,1)],1)'; + +FAIRmessage([mfilename,' : done !']); + +function doPause(p) +if strcmp(p,'on'), + FAIRpause; +elseif p>0, + FAIRpause(p); +end; + +function runMinimalExample +setup2DhandData + +trafo('reset','trafo','affine2D'); +distance('reset','distance','SSD'); +imgModel('reset','imgModel','splineInter','regularizer','moments','theta',1e-2); +regularizer('reset','regularizer','mbHyperElasticFEM','alpha',1e2); + +NPIRpara = optPara('NPIR-GN'); +NPIRpara.Plots = @FAIRplotsFEM; +NPIRpara.lineSearch = @ArmijoDiffeomorphicFEM; +[yc,wc,his] = MLIRFEM(ML,'NPIRpara',NPIRpara,'minLevel',4); + diff --git a/add-ons/FAIRFEM/examples/EFEM_SSDvsMP.mat b/add-ons/FAIRFEM/examples/EFEM_SSDvsMP.mat new file mode 100644 index 0000000000000000000000000000000000000000..b9d1318b031a5a8d8d6cfe92548fd4c41ff90afd GIT binary patch literal 1069988 zcma&NdpOhm{|8=4tHcr|IgC^)MUpU^6-lK~DwV@3m86Uq8@5&C5Lst+hlQk4Mv~KP zPEjeNFga`(rj2dP%+9~5`~H0H@Av!rUDwa$k6m+lKVQ$o>v?!QAMZoEj~?9ZY+`G< z&E(MTqgyWoUp~LZ#Ov~z$P0+8SHP<8T=wtWvBkvY>iIK~=g*lSLcu0Sk>^bgATOI( 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FMPNvTTfP7Q literal 0 HcmV?d00001 diff --git a/kernel/numerics/GaussNewton.m b/kernel/numerics/GaussNewton.m index 86b1cbb..fcd7b2c 100644 --- a/kernel/numerics/GaussNewton.m +++ b/kernel/numerics/GaussNewton.m @@ -57,7 +57,7 @@ % -- end parameter setup ---------------------------------------------- % some output -if isstring(solver) +if ischar(solver) solverName = solver; elseif isa(solver,'function_handle') solverName = func2str(solver); diff --git a/kernel/numerics/GaussNewton.m~ b/kernel/numerics/GaussNewton.m~ new file mode 100644 index 0000000..fcd7b2c --- /dev/null +++ b/kernel/numerics/GaussNewton.m~ @@ -0,0 +1,162 @@ +%============================================================================== +% This code is part of the Matlab-based toolbox +% FAIR - Flexible Algorithms for Image Registration. +% For details see +% - https://github.com/C4IR and +% - http://www.siam.org/books/fa06/ +%============================================================================== +% +% function [yc,His] = GaussNewton(fctn,yc,varargin) +% +% Gauss-Newton scheme with variable line search for minimizing J = fctn(yc) +% +% Input: +% fctn function handle +% yc starting guess +% varargin optional parameter, see below +% +% Output: +% yc numerical optimizer (current iterate) +% his iteration history +% +% Note: the linear systems are solved using solveLinearSystem.m +%============================================================================== + +function [yc,His] = GaussNewton(fctn,yc,varargin) + +if nargin==0 + help(mfilename) + E9_Hands_NPIR + yc = 'endOfMinimalExample'; + return; +end; + +% parameter initialization ----------------------------------------------- +maxIter = 10; % maximum number of iterations +tolJ = 1e-3; % for stopping, objective function +tolY = 1e-2; % - " - , current value +tolG = 1e-2; % - " - , norm of gradient +lineSearch = @Armijo; % linesearch scheme +LSmaxIter = 10; % maximum number of line search iterations +LSreduction = 1e-4; % minimal reduction in line search +vecNorm = @norm; % norm to be used for dJ and dy +solver = []; % linear solver +yStop = []; % used for stopping in multi-level framework +Jstop = []; % +Plots = @(iter,para) []; % for plots; + +for k=1:2:length(varargin), % overwrites default parameter + eval([varargin{k},'=varargin{',int2str(k+1),'};']); +end; + +if ~isa(Plots,'function_handle') && (Plots == 0 || strcmp(Plots,'off')), + Plots = @(iter,para) []; % for plots; +end; + +if isempty(yStop), yStop = yc; end; % yStop used for stopping only +% -- end parameter setup ---------------------------------------------- + +% some output +if ischar(solver) + solverName = solver; +elseif isa(solver,'function_handle') + solverName = func2str(solver); +else + error(1); +end +FAIRmessage(sprintf('JM 2011/01/02 : %s / %s / %s',... + mfilename,func2str(lineSearch),solverName)) +fprintf('[ maxIter=%s / tolJ=%s / tolY=%s / tolG=%s / numel(yc)=%d]\n',... + num2str(maxIter),num2str(tolJ),num2str(tolY),num2str(tolG),length(yc)); + +% -- initialize --------------------------------------------------------- +STOP = zeros(5,1); + +if isempty(Jstop), + % evaluate objective function for stopping values and plots + [Jstop,para] = fctn(yStop); Jstop = abs(Jstop) + (Jstop == 0); + Plots('stop',para); +end; + +% evaluate objective function for starting values and plots +[Jc,para,dJ,H] = fctn(yc); +Plots('start',para); +iter = 0; yOld = 0*yc; Jold = Jc; y0 = yc; + +hisStr = {'iter','J','Jold-J','|\nabla J|','|dy|','LS'}; +his = zeros(maxIter+2,6); +his(1,1:3) = [-1,Jstop,Jstop-Jc]; +his(2,:) = [0,Jc,Jstop-Jc,vecNorm(dJ),vecNorm(yc-yStop),0]; + +% some output +fprintf('%4s %-12s %-12s %-12s %-12s %4s\n%s\n',... + hisStr{:},char(ones(1,64)*'-')); +dispHis = @(var) ... + fprintf('%4d %-12.4e %-12.3e %-12.3e %-12.3e %4d\n',var); +dispHis(his(1,:)); +dispHis(his(2,:)); +% -- end initialization ------------------------------------------------ + + +%-- start the iteration -------------------------------------------------- +while 1, + % check stopping rules + STOP(1) = (iter>0) && abs(Jold-Jc) <= tolJ*(1+abs(Jstop)); + STOP(2) = (iter>0) && (norm(yc-yOld) <= tolY*(1+norm(y0))); + STOP(3) = norm(dJ) <= tolG*(1+abs(Jstop)); + STOP(4) = norm(dJ) <= 1e6*eps; + STOP(5) = (iter >= maxIter); + if all(STOP(1:3)) || any(STOP(4:5)), break; end; + + iter = iter + 1; + + % solve the Gauss-Newton System + [dy,solver] = solveLinearSystem(-dJ',H,solver); + + % check descent direction + % note: descent is not granted if using an iterative solver + descent = dJ * dy; + if descent > 0, + warning('no descent direction, switch to -dy!') + dy = -dy; + end; + + % perform Armijo line-search + [t,yt,LSiter] = lineSearch(fctn,yc,dy,Jc,dJ,... + 'para',para,'LSmaxIter',LSmaxIter,'LSreduction',LSreduction); + if (t == 0), + break; + end; % break if line-search fails + + % save old values and update + yOld = yc; Jold = Jc; yc = yt; + [Jc,para,dJ,H] = fctn(yc); % evalute objective function + + % some output + his(iter+2,:) = [iter,Jc,Jold-Jc,vecNorm(dJ),vecNorm(yc-yOld),LSiter]; + dispHis(his(iter+2,:)); + para.normdY = vecNorm(yc - yOld); + Plots(iter,para); +% pause +end;%while; % end of iteration loop +%------------------------------------------------------------------------- +Plots(iter,para); + +% clean up +His.str = hisStr; +His.his = his(1:iter+2,:); +fprintf('STOPPING:\n'); +fprintf('%d[ %-10s=%16.8e <= %-25s=%16.8e]\n',STOP(1),... + '(Jold-Jc)',(Jold-Jc),'tolJ*(1+|Jstop|)',tolJ*(1+abs(Jstop))); +fprintf('%d[ %-10s=%16.8e <= %-25s=%16.8e]\n',STOP(2),... + '|yc-yOld|',norm(yc-yOld),'tolY*(1+norm(yc)) ',tolY*(1+norm(yc))); +fprintf('%d[ %-10s=%16.8e <= %-25s=%16.8e]\n',STOP(3),... + '|dJ|',norm(dJ),'tolG*(1+abs(Jstop))',tolG*(1+abs(Jstop))); +fprintf('%d[ %-10s=%16.8e <= %-25s=%16.8e]\n',STOP(4),... + 'norm(dJ)',norm(dJ),'eps',1e3*eps); +fprintf('%d[ %-10s= %-14d >= %-25s= %-14d]\n',STOP(5),... + 'iter',iter,'maxIter',maxIter); + +FAIRmessage([mfilename,' : done !'],'='); + +%============================================================================== From e889f4d64064135e39ca72ba9b7e255bb16b38fc Mon Sep 17 00:00:00 2001 From: hariagr Date: Wed, 12 Jul 2017 21:20:54 +0200 Subject: [PATCH 02/16] Matrix-free FEMAPP - SSD MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit These changes are required to use matrix-free functionality of hyper elastic regularization function in the add-on FEMAPP (Only for 2D). To verify the changes, the file “EFEM_SSD_MBvsMF.m” compares the results from MF and MB. --- add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m | 38 ++++++++++++++ add-ons/FAIRFEM/FEMobjFctn.m | 2 + add-ons/FAIRFEM/hyperElasticFEM.m | 83 +++++++++++++++++-------------- kernel/regularizers/regularizer.m | 6 +++ 4 files changed, 91 insertions(+), 38 deletions(-) create mode 100644 add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m diff --git a/add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m b/add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m new file mode 100644 index 0000000..58a5e4b --- /dev/null +++ b/add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m @@ -0,0 +1,38 @@ +% ================================================================================== +% (c) Lars Ruthotto 2012/07/26, see FAIR.2 and FAIRcopyright.m. +% http://www.mic.uni-luebeck.de/people/lars-ruthotto.html +% +% Simplified Registration of Cardiac PET +% +% data Gaussian Blobs +% +% ================================================================================== +close all; clc; clear; +setup2DGaussianData; + +distance('reset','distance','SSD'); +imgModel('reset','imgModel','splineInterMex','regularizer','moments','theta',4e-1); +regularizer('reset','regularizer','mbHyperElasticFEM','alpha',5e1); + +minLevel = 3; +maxLevel = 8; + +NPIRpara = optPara('NPIR-GN'); +NPIRpara.Plots = @FAIRplotsFEM; +NPIRpara.lineSearch = @ArmijoDiffeomorphicFEM; +NPIRpara.solver = 'mbPCG-Jacobi'; + +[ySSD_MB,~,hisSSD_MB] = MLIRFEM(ML,'parametric',0,... + 'NPIRobj',@FEMobjFctn,'NPIRpara',NPIRpara,... + 'minLevel',minLevel,'maxLevel',maxLevel); + +regularizer('reset','regularizer','mfHyperElasticFEM','alpha',5e1); +NPIRpara.solver = 'PCG-hyperElastic'; +[ySSD_MF,~,hisSSD_MF] = MLIRFEM(ML,'parametric',0,... + 'NPIRobj',@FEMobjFctn,'NPIRpara',NPIRpara,... + 'minLevel',minLevel,'maxLevel',maxLevel); + +relerr = norm(ySSD_MB-ySSD_MF)/norm(ySSD_MB) + +%% +%save('EFEM_SSDvsMP','ML','yFEMPIRE','ySSD','hisFEMPIRE','hisSSD'); \ No newline at end of file diff --git a/add-ons/FAIRFEM/FEMobjFctn.m b/add-ons/FAIRFEM/FEMobjFctn.m index ec1b23f..3f4c331 100755 --- a/add-ons/FAIRFEM/FEMobjFctn.m +++ b/add-ons/FAIRFEM/FEMobjFctn.m @@ -118,6 +118,8 @@ % d2D = P'*dr'*d2psi*dr*P % P and P' are operators matrix free H.Mesh = Mesh; + H.omega = omega; + H.m = m; H.d2D.how = 'P''*dr''*d2psi*dr*P'; H.d2D.P = P; H.d2D.dr = dr; diff --git a/add-ons/FAIRFEM/hyperElasticFEM.m b/add-ons/FAIRFEM/hyperElasticFEM.m index 7944069..8cabd30 100755 --- a/add-ons/FAIRFEM/hyperElasticFEM.m +++ b/add-ons/FAIRFEM/hyperElasticFEM.m @@ -152,7 +152,9 @@ else % matrix-free d2S.regularizer = regularizer; - d2S.alpha = alpha; + d2S.alpha = alpha; + d2S.yc = yc; + d2S.solver = 'PCG-hyperElastic';%@FEMMultiGridSolveHyper; % code only diffusion part for B d2S.By = @(u,Mesh) Mesh.mfGRAD.D(u); d2S.BTy = @(u,Mesh) Mesh.mfGRAD.Dadj(u); @@ -161,11 +163,11 @@ d2S.diagLength = @(Mesh) getDiagLength(Mesh,alphaLength); d2S.diagArea = [];%@(Mesh) getDiagArea(Mesh,alphaLength); d2S.diagVol = @(Mesh) getDiagVolume(Mesh,yc,alphaVolume); - d2S.diag = @(Mesh) d2S.diagLength(Mesh) + d2S.diagVol(Mesh); - d2S.solver = @FEMMultiGridSolveHyper; - d2S.d2S = @(uc,Mesh) ... + d2S.diag = @(yc) d2S.diagLength(Mesh) + d2S.diagVol(Mesh); + + d2S.d2S = @(uc,omega,m,yc) ... alphaLength * ... - diffusionOperator(Mesh.vol *Mesh.mfB(uc,Mesh,'By'),Mesh,'BTy') ... + d2S.BTy(repmat(Mesh.vol,[dim^2,1]).*d2S.By(uc,Mesh),Mesh) ... + alphaVolume * ... volumeOperator(yc,Mesh,uc, Mesh.vol); @@ -174,24 +176,25 @@ Slength = .5*dSlength*uc; % volume term - dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; yc = reshape(yc,[],2); By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; det = By(:,1).*By(:,4) - By(:,3) .* By(:,2); [G,dG,d2G] = psi(det,doDerivative); Svol = alphaVolume*sum(Mesh.vol.*G); - - dDet = @(x) [ ... - dx1.Dadj(By(:,4).*x)-dx2.Dadj(By(:,3).*x);... - -dx1.Dadj(By(:,2).*x)+dx2.Dadj(By(:,1).*x)]; - dSvol = alphaVolume * transpose(dDet(dG.*Mesh.vol) ); - - Sc = Slength + Svol; - dS = dSlength + dSvol; - d2S.Dy = By; - d2S.d2G = d2G; + if doDerivative + dDet = @(x) [ ... + dx1.Dadj(By(:,4).*x)-dx2.Dadj(By(:,3).*x);... + -dx1.Dadj(By(:,2).*x)+dx2.Dadj(By(:,1).*x)]; + dSvol = alphaVolume * transpose(dDet(dG.*Mesh.vol) ); + + dS = dSlength + dSvol; + + d2S.Dy = By; + d2S.d2G = d2G; + end end @@ -233,38 +236,42 @@ if dim==2 xn = Mesh.xn; % get edges - e1 = Mesh.mfP1(xn) - Mesh.mfP3(xn); - e2 = Mesh.mfP2(xn) - Mesh.mfP3(xn); - e3 = Mesh.mfP1(xn) - Mesh.mfP2(xn); + e1 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,3); + e2 = Mesh.mfPi(xn,2) - Mesh.mfPi(xn,3); + e3 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,2); % compute gradients of basis functions - dphi1 = ([ e2(:,2) -e2(:,1)]./vol); - dphi2 = ([-e1(:,2) e1(:,1)]./vol); - dphi3 = ([ e3(:,2) -e3(:,1)]./vol); + dphi1 = ([ e2(:,2) -e2(:,1)]./[2*vol,2*vol]); + dphi2 = ([-e1(:,2) e1(:,1)]./[2*vol,2*vol]); + dphi3 = ([ e3(:,2) -e3(:,1)]./[2*vol,2*vol]); % compute diagonal of volume regularizer % MB : dDet = [sdiag(By(:,4)), sdiag(-By(:,3)) , sdiag(-By(:,2)), sdiag(By(:,1))] * B; - [dx1, dx2] = getGradientMatrixFEM(Mesh); + [dx1, dx2] = getGradientMatrixFEM(Mesh,1); yc = reshape(yc,[],2); By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; det = By(:,1).*By(:,4) - By(:,3) .* By(:,2); [~,~,d2G] = psi(det,1); % get boundaries - Dxi = @(i,j) Mesh.mfP1(d2G.*(By(:,j).*dphi1(:,i)).^2) ... - + Mesh.mfP2(d2G.*(By(:,j).*dphi2(:,i)).^2) ... - + Mesh.mfP3(d2G.*(By(:,j).*dphi3(:,i)).^2); % diagonal of Dxi'*Dxi + Dxi = @(i,j) Mesh.mfPi(vol.*d2G.*(By(:,j).*dphi1(:,i)).^2,1) ... + + Mesh.mfPi(vol.*d2G.*(By(:,j).*dphi2(:,i)).^2,2) ... + + Mesh.mfPi(vol.*d2G.*(By(:,j).*dphi3(:,i)).^2,3); % diagonal of Dxi'*Dxi + + Dxy = @(i,j,k,l) Mesh.mfPi(vol.*d2G.*(By(:,j).*dphi1(:,i)).*(By(:,l).*dphi1(:,k)),1) ... % byproduct terms for verifications + + Mesh.mfPi(vol.*d2G.*(By(:,j).*dphi2(:,i)).*(By(:,l).*dphi2(:,k)),2) ... + + Mesh.mfPi(vol.*d2G.*(By(:,j).*dphi3(:,i)).*(By(:,l).*dphi3(:,k)),3); % diagonal of Dxi'*Dxi - D = [Dxi(1,4)+ Dxi(2,3) ;Dxi(1,2)+ Dxi(2,1)]; + D = [Dxi(1,4)+ Dxi(2,3) - 2*Dxy(1,4,2,3) ;Dxi(1,2)+ Dxi(2,1) - 2*Dxy(1,2,2,1)]; else error('nyi'); end -D = alphaVolume*vol*D; +D = alphaVolume*D; % compute d2Svol*x function By = volumeOperator(yc,Mesh,x,vol) -[dx1, dx2] = getGradientMatrixFEM(Mesh); +[dx1, dx2] = getGradientMatrixFEM(Mesh,1); % volume regularization yc = reshape(yc,[],2); By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; @@ -290,24 +297,24 @@ if dim==2 xn = Mesh.xn; % get edges - e1 = Mesh.mfP1(xn) - Mesh.mfP3(xn); - e2 = Mesh.mfP2(xn) - Mesh.mfP3(xn); - e3 = Mesh.mfP1(xn) - Mesh.mfP2(xn); + e1 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,3); + e2 = Mesh.mfPi(xn,2) - Mesh.mfPi(xn,3); + e3 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,2); % compute gradients of basis functions - dphi1 = ([ e2(:,2) -e2(:,1)]./vol); - dphi2 = ([-e1(:,2) e1(:,1)]./vol); - dphi3 = ([ e3(:,2) -e3(:,1)]./vol); + dphi1 = ([ e2(:,2) -e2(:,1)]./[2*vol,2*vol]); + dphi2 = ([-e1(:,2) e1(:,1)]./[2*vol,2*vol]); + dphi3 = ([ e3(:,2) -e3(:,1)]./[2*vol,2*vol]); % get boundaries - Dxi = @(i) Mesh.mfP1(dphi1(:,i).^2) + Mesh.mfP2(dphi2(:,i).^2) + Mesh.mfP3(dphi3(:,i).^2); % diagonal of Dx1'*Dx1 - + Dxi = @(i) Mesh.mfPi(vol.*dphi1(:,i).^2,1) + Mesh.mfPi(vol.*dphi2(:,i).^2,2) + Mesh.mfPi(vol.*dphi3(:,i).^2,3); % diagonal of Dx1'*Dx1 + D = Dxi(1)+ Dxi(2); D = [D;D]; else error('nyi'); end -D = alphaLength*vol*D(:); +D = alphaLength*D(:); diff --git a/kernel/regularizers/regularizer.m b/kernel/regularizers/regularizer.m index 3809daf..034382c 100644 --- a/kernel/regularizers/regularizer.m +++ b/kernel/regularizers/regularizer.m @@ -110,6 +110,12 @@ matrixFree = 0; grid = 'FEM'; solver = 'backslash'; + + case 'mfHyperElasticFEM', + scheme = 'hyperElasticFEM'; + matrixFree = 1; + grid = 'FEM'; + solver = 'PCG-hyperElastic'; otherwise, error(mfilename) From 2827a841b7a6abb8d6bd2a5744076174db17452c Mon Sep 17 00:00:00 2001 From: hariagr Date: Thu, 13 Jul 2017 16:30:19 +0200 Subject: [PATCH 03/16] Matrixfree code - MP These are minor changes to run matrixfree functionality of FEMPIRE. But, data fidelity term is still not matrixfree. Prob, this involves little more work. Will come back to this later. Added a file to compare results from MF and MB. --- add-ons/FAIRFEM/EFEM_MP_MBvsMF.m | 38 ++++++++++++++++++++++++++++++++ add-ons/FAIRFEM/FEMPIREobjFctn.m | 17 +++++++++----- 2 files changed, 50 insertions(+), 5 deletions(-) create mode 100644 add-ons/FAIRFEM/EFEM_MP_MBvsMF.m diff --git a/add-ons/FAIRFEM/EFEM_MP_MBvsMF.m b/add-ons/FAIRFEM/EFEM_MP_MBvsMF.m new file mode 100644 index 0000000..b43088d --- /dev/null +++ b/add-ons/FAIRFEM/EFEM_MP_MBvsMF.m @@ -0,0 +1,38 @@ +% ================================================================================== +% (c) Lars Ruthotto 2012/07/26, see FAIR.2 and FAIRcopyright.m. +% http://www.mic.uni-luebeck.de/people/lars-ruthotto.html +% +% Simplified Registration of Cardiac PET +% +% data Gaussian Blobs +% +% ================================================================================== +close all; clc; clear; +setup2DGaussianData; + +distance('reset','distance','SSD'); +imgModel('reset','imgModel','splineInterMex','regularizer','moments','theta',4e-1); +regularizer('reset','regularizer','mbHyperElasticFEM','alpha',5e1); + +minLevel = 3; +maxLevel = 8; + +NPIRpara = optPara('NPIR-GN'); +NPIRpara.Plots = @FAIRplotsFEM; +NPIRpara.lineSearch = @ArmijoDiffeomorphicFEM; +NPIRpara.solver = 'mbPCG-Jacobi'; + +[yMP_MB,~,hisMP_MB] = MLIRFEM(ML,'parametric',0,... + 'NPIRobj',@FEMPIREobjFctn,'NPIRpara',NPIRpara,... + 'minLevel',minLevel,'maxLevel',maxLevel); + +regularizer('reset','regularizer','mfHyperElasticFEM','alpha',5e1); +NPIRpara.solver = 'PCG-hyperElastic'; +[yMP_MF,~,hisMP_MF] = MLIRFEM(ML,'parametric',0,... + 'NPIRobj',@FEMPIREobjFctn,'NPIRpara',NPIRpara,... + 'minLevel',minLevel,'maxLevel',maxLevel); + +relerr = norm(yMP_MB-yMP_MF)/norm(yMP_MB) + +%% +%save('EFEM_SSDvsMP','ML','yFEMPIRE','ySSD','hisFEMPIRE','hisSSD'); \ No newline at end of file diff --git a/add-ons/FAIRFEM/FEMPIREobjFctn.m b/add-ons/FAIRFEM/FEMPIREobjFctn.m index 92614c8..9d4313f 100755 --- a/add-ons/FAIRFEM/FEMPIREobjFctn.m +++ b/add-ons/FAIRFEM/FEMPIREobjFctn.m @@ -121,18 +121,25 @@ H = dr'*d2psi*dr + d2S; else % derivatives rather explicit - dr = dres*dT; - dD = dD*dT; - dJ = reshape(Mesh.mfPi(reshape(dD',[],Mesh.dim),'C'),1,[]) + dS; + %P = @(x) reshape(Mesh.mfPi(reshape(x,[],dim),'C'),[],1); + %dTcmod = P((sdiag(det)*dT)')' + sdiag(Tc)*dDet; + P = kron(speye(dim),Mesh.PC); + dTcmod = sdiag(det)*dT*P + sdiag(Tc)*dDet; + dr = dres*dTcmod; + dD = dD*dTcmod; + dJ = dD + dS; % approximation to d2D in matrix free mode % d2D = P'*dr'*d2psi*dr*P % P and P' are operators matrix free - H.Mesh = Mesh; + H.Mesh = Mesh; + H.omega = omega; + H.m = m; H.d2D.how = 'P''*dr''*d2psi*dr*P'; - H.d2D.P = @(x) Mesh.mfPi(reshape(x(:),[],Mesh.dim),'C'); + H.d2D.P = @(x) x;%reshape(Mesh.mfPi(reshape(x,[],dim),'C'),[],1); H.d2D.dr = dr; H.d2D.d2psi = d2psi; + H.solver = d2S.solver; H.d2S = d2S; end; From 4fa6cee1d723fd4465d4694aad9fca3a2f2ae446 Mon Sep 17 00:00:00 2001 From: hariagr Date: Mon, 17 Jul 2017 15:53:16 +0200 Subject: [PATCH 04/16] Delete MLIRFEM.m~ --- add-ons/FAIRFEM/MLIRFEM.m~ | 251 ------------------------------------- 1 file changed, 251 deletions(-) delete mode 100644 add-ons/FAIRFEM/MLIRFEM.m~ diff --git a/add-ons/FAIRFEM/MLIRFEM.m~ b/add-ons/FAIRFEM/MLIRFEM.m~ deleted file mode 100644 index 1b01e15..0000000 --- a/add-ons/FAIRFEM/MLIRFEM.m~ +++ /dev/null @@ -1,251 +0,0 @@ -%============================================================================== -% This code is part of the Finite Element Method app for the Matlab-based toolbox -% FAIR - Flexible Algorithms for Image Registration. -% For details see -% - https://github.com/C4IR/FAIRFEM -%============================================================================== -% -% function [yc,wc,MLhis] = MLIRFEM(ML,varargin) -% -% Multi-Level Image Registration using tetrahedral Finite Elements using -% global refinement -% -% minimizes J^h(y) = D^h(T(y),R) + S^h(y) for h=coarse:fine -% uses PIR [=@GaussNewton] and NPIR [=@GaussNewton] -% -% Input: -% ML coarse to fine representations of the data, see getMultilevel.m -% varagin optinonal parameters, see default parameter -% Output: -% yc numerical optimizer -% wc optimal parameters for PIR -% MLhis iteration history -% -% for level=minLevel:maxLevel, -% get data(level) -% if level==minLevel, get wOpt running PIR; end; -% use pre-registered Yref=trafo(wOpt,X) for regularization -% if level==minLevel -% y0 = Ystop; % use this as starting guess -% else -% get y0 by prologating Yopt from coarse to finer level -% end; -% get Yopt running NPIR using y0 as starting guess -% end%For -%============================================================================== - -function [yc,wc,MLhis] = MLIRFEM(ML,varargin) - -if nargin == 0, help(mfilename); runMinimalExample; return; end; - -%------------------------------------------------------------------------------ -% initialize some default parameter: -% 1.1 initialize output -% 1.2 determine minLevel and maxLevel from the data ML -% 1.3 flag for parametric registration (PIR) -% 2.1 regularization of of PIR objective -% 2.2 regularization of Hessian approximation, H -> H + beta*speye(size(H)) -% 2.3 setup stopping value wStop and initial value w0 -% 2.4 setup objective in PIR and optimization parameters -% 3 setup objective in NPIR and optimization parameters -% 4 setup defaults for plots -% 5 replace defaults by user input -% 6 initializes dimension, discretization, grids etc -% 7 convert optimization parameter sets for PIR and NPIR to lists -%------------------------------------------------------------------------------ -% 1.1 initialize output -yc = []; -wc = []; -MLhis = []; - -% 1.2 get minLevel and maxLevel from ML -[ML,minLevel,maxLevel] = getMultilevel(ML); - -% 1.3 flag for parametric registration (PIR) -parametric = 1; % flag: if true, run parametric pre-registration - -% 2.1 regularization of PIR objective -% J_{PIR} = D(T(Y(wc)),Rc) + S(wc) with S_{PIR} = 0.5*(wc-wRef)'*M*(wc-wRef); -wRef = []; -M = []; - -% 2.2 regularization of Hessian approximation, H -> H + beta*speye(size(H)) -beta = 0; - -% 2.3 setup stopping value wStop and initial value w0 -wStop = []; % global stopping for PIR -w0 = []; % starting guess for PIR - -% 2.4 PIR: default objective function and optimization parameter via optPara('PIR-GN') -PIRobj = @PIRobjFctn; -PIRpara = optPara('PIR-GN'); - -% 3. NPIR: default objective function and optimization parameter via optPara('NPIR-GN') -NPIRobj = @FEMobjFctn; -NPIRpara = optPara('NPIR-GN'); -NPIRpara.Plots = @FAIRplotsFEM; - - -% 4 setup defaults for plots -pause = 0; % flag for pauses -plots = 1; % flag for plots -plotIter = 0; % flag for output of iteration history each level -plotMLiter = 0; % flag for output of summarized iteration history - -% 5 replace defaults by user input -for k=1:2:length(varargin), % overwrites default parameter - eval([varargin{k},'=varargin{',int2str(k+1),'};']); -end; - -% 6 initializes dimension, discretization, grids etc -dimstr = @(m) sprintf('[%s]',sprintf(' %d',m)); -omega = ML{end}.omega; % spatial domain -dim = numel(omega)/2; -xc = []; % current grid - -% 7 convert optimization parameter sets for PIR and NPIR to lists -PO = FAIRcell2struct(PIRpara); -NO = FAIRcell2struct(NPIRpara); - -getGrid = @(m) getNodalGrid(omega,m); -if dim==2 - getMesh = @TriMesh3; -else - getMesh = @TetraMesh1; -end -% --- -FAIRmessage(sprintf('%s: MultiLevel Image Registration',mfilename),'#') -fprintf('>> %-20s : %s\n','omega',dimstr(omega)); -fprintf('>> %-20s : %s\n','IMAGE MODEL',imgModel); -fprintf('>> %-20s : %s\n','DISTANCE',distance); -fprintf('>> %-20s : %s\n','TRAFO',trafo); -fprintf('>> %-20s : %s, alpha=%s\n','REGULARIZER',... - regularizer,num2str(regularizer('get','alpha'))); -fprintf('>> %-20s : %d\n','PRE-REGISTRATION',parametric); -fprintf('>> %-20s : objective=<%s>, method = <%s>\n',... - 'PIR',func2str(PIRobj),func2str(PIRpara.scheme)); -fprintf('>> %-20s : objective=<%s>, method = <%s>\n',... - 'NPIR',func2str(NPIRobj),func2str(NPIRpara.scheme)); -fprintf('>> %-20s : minLevel=%d, maxLevel=%d\n','LEVEL',minLevel,maxLevel); -FAIRmessage('#') - -tic; -%-------------------------------------------------------------------------- -for level=minLevel:maxLevel - - FAIRmessage(sprintf('%s: level %d from %d to %d, %s',... - mfilename,level,minLevel,maxLevel,dimstr(ML{level}.m))); - - % save(old grid), update(m,grid,data coefficients) - xOld = xc; - m = ML{level}.m; - [T,R] = imgModel('coefficients',ML{level}.T,ML{level}.R,omega); - - if level == minLevel && parametric, % parametric pre-registration - % initialize plots - FAIRplots('reset','mode','PIR','fig',minLevel-1,'plots',plots); - FAIRplots('init',struct('Tc',T,'Rc',R,'omega',omega,'m',size(R))); - - % ----- call Parametric Image Registration ---------------------------- - xC = getGrid(m); - Rc = imgModel(R,omega,center(xC,m)); - - PIRfctn = @(wc) PIRobj(T,Rc,omega,m,beta,M,wRef,xC,wc); - PIRfctn([]); % report status of objective function - if isempty(w0), w0 = trafo('w0'); end; - if isempty(wStop), wStop = w0; end; - - [wc,hisPIR] = PIRpara.scheme(PIRfctn,w0,'yStop',wStop,PO{:}); - - fprintf('wc = \n'); disp(wc'); doPause(pause); - % ----- end PIR -------------------------------------- - if plotIter, - his.str{1} = 'iteration history for PIR'; - plotIterationHistory(his,'J',1:4,'fh',100+minLevel-1); - end; - elseif level == minLevel, % no pre-registration - wc = []; - end; - - % get triangulation - Mesh = getMesh(omega,m); - xc = Mesh.xn; - Rc = imgModel(R,omega,Mesh.mfPi(xc,'C')); - - % compute yRef = xc or yc = trafo(wc,xc) on the appropriate grid - if isempty(wc), % use yRef(x) = x - yRef = xc; - else % compute yn=y(wc,xNodal) and interpolate on current grid - yn = trafo(wc,xc(:)); - yRef = reshape(yn,[],dim); - end; - Mesh.xn = reshape(yn,[],dim); - - % compute starting guess y0 - if level == minLevel, - y0 = yRef; % the best known so far - else - % prolongate yc (coarse) y0 (current) - y0 = xc(:) + Mesh.mfPuNodal(yc(:) - xOld(:),m/2,'Pu'); - y0 = reshape(y0,[],dim); - end; - - % ----- call NPIR ------------------------------------- - % S(y) = 0.5*alpha*hd*norm(B*(Y-Yref))^2 - % initialize plots for NPIR - FAIRplotsFEM('reset','mode','FEM','fig',level,'plots',plots); - FAIRplotsFEM('init',struct('Tc',T,'Rc',R,'Mesh',Mesh)); - NPIRfctn = @(yc) NPIRobj(T,Rc,Mesh,yRef,yc); - if level == minLevel, NPIRfctn([]); end; % report status of objective function - yStop = yRef; - [yc,his] = NPIRpara.scheme(NPIRfctn,y0(:),'yStop',yStop(:),NO{:}); - % ----- end NPIR -------------------------------------- - - if plotIter, - his.str{1} = sprintf('iteration history for NPIR, level=%d',level); - plotIterationHistory(his,'J',1:4,'fh',100+level); - end; - - % update iteration history - if level == minLevel, - MLhis.str = his.str; - MLhis.his = his.his; - else - MLhis.his = [MLhis.his;his.his]; - end; - doPause(pause); - -%-------------------------------------------------------------------------- -end;%For level -%-------------------------------------------------------------------------- -MLhis.time = toc; -if plotMLiter, - plotMLIterationHistory(MLhis,'fh',[]); -end; -if isempty(yStop), yStop = xc; end -MLhis.reduction = NPIRfctn(yc)/NPIRfctn(yStop); -J = find(MLhis.his(:,1)==-1); -MLhis.iter(minLevel:maxLevel) = MLhis.his([J(2:end)-1;size(MLhis.his,1)],1)'; - -FAIRmessage([mfilename,' : done !']); - -function doPause(p) -if strcmp(p,'on'), - FAIRpause; -elseif p>0, - FAIRpause(p); -end; - -function runMinimalExample -setup2DhandData - -trafo('reset','trafo','affine2D'); -distance('reset','distance','SSD'); -imgModel('reset','imgModel','splineInter','regularizer','moments','theta',1e-2); -regularizer('reset','regularizer','mbHyperElasticFEM','alpha',1e2); - -NPIRpara = optPara('NPIR-GN'); -NPIRpara.Plots = @FAIRplotsFEM; -NPIRpara.lineSearch = @ArmijoDiffeomorphicFEM; -[yc,wc,his] = MLIRFEM(ML,'NPIRpara',NPIRpara,'minLevel',4); - From dab3d1f09a310477b96085ce6d81f8a16e21cae5 Mon Sep 17 00:00:00 2001 From: hariagr Date: Mon, 17 Jul 2017 15:53:58 +0200 Subject: [PATCH 05/16] Delete GaussNewton.m~ --- kernel/numerics/GaussNewton.m~ | 162 --------------------------------- 1 file changed, 162 deletions(-) delete mode 100644 kernel/numerics/GaussNewton.m~ diff --git a/kernel/numerics/GaussNewton.m~ b/kernel/numerics/GaussNewton.m~ deleted file mode 100644 index fcd7b2c..0000000 --- a/kernel/numerics/GaussNewton.m~ +++ /dev/null @@ -1,162 +0,0 @@ -%============================================================================== -% This code is part of the Matlab-based toolbox -% FAIR - Flexible Algorithms for Image Registration. -% For details see -% - https://github.com/C4IR and -% - http://www.siam.org/books/fa06/ -%============================================================================== -% -% function [yc,His] = GaussNewton(fctn,yc,varargin) -% -% Gauss-Newton scheme with variable line search for minimizing J = fctn(yc) -% -% Input: -% fctn function handle -% yc starting guess -% varargin optional parameter, see below -% -% Output: -% yc numerical optimizer (current iterate) -% his iteration history -% -% Note: the linear systems are solved using solveLinearSystem.m -%============================================================================== - -function [yc,His] = GaussNewton(fctn,yc,varargin) - -if nargin==0 - help(mfilename) - E9_Hands_NPIR - yc = 'endOfMinimalExample'; - return; -end; - -% parameter initialization ----------------------------------------------- -maxIter = 10; % maximum number of iterations -tolJ = 1e-3; % for stopping, objective function -tolY = 1e-2; % - " - , current value -tolG = 1e-2; % - " - , norm of gradient -lineSearch = @Armijo; % linesearch scheme -LSmaxIter = 10; % maximum number of line search iterations -LSreduction = 1e-4; % minimal reduction in line search -vecNorm = @norm; % norm to be used for dJ and dy -solver = []; % linear solver -yStop = []; % used for stopping in multi-level framework -Jstop = []; % -Plots = @(iter,para) []; % for plots; - -for k=1:2:length(varargin), % overwrites default parameter - eval([varargin{k},'=varargin{',int2str(k+1),'};']); -end; - -if ~isa(Plots,'function_handle') && (Plots == 0 || strcmp(Plots,'off')), - Plots = @(iter,para) []; % for plots; -end; - -if isempty(yStop), yStop = yc; end; % yStop used for stopping only -% -- end parameter setup ---------------------------------------------- - -% some output -if ischar(solver) - solverName = solver; -elseif isa(solver,'function_handle') - solverName = func2str(solver); -else - error(1); -end -FAIRmessage(sprintf('JM 2011/01/02 : %s / %s / %s',... - mfilename,func2str(lineSearch),solverName)) -fprintf('[ maxIter=%s / tolJ=%s / tolY=%s / tolG=%s / numel(yc)=%d]\n',... - num2str(maxIter),num2str(tolJ),num2str(tolY),num2str(tolG),length(yc)); - -% -- initialize --------------------------------------------------------- -STOP = zeros(5,1); - -if isempty(Jstop), - % evaluate objective function for stopping values and plots - [Jstop,para] = fctn(yStop); Jstop = abs(Jstop) + (Jstop == 0); - Plots('stop',para); -end; - -% evaluate objective function for starting values and plots -[Jc,para,dJ,H] = fctn(yc); -Plots('start',para); -iter = 0; yOld = 0*yc; Jold = Jc; y0 = yc; - -hisStr = {'iter','J','Jold-J','|\nabla J|','|dy|','LS'}; -his = zeros(maxIter+2,6); -his(1,1:3) = [-1,Jstop,Jstop-Jc]; -his(2,:) = [0,Jc,Jstop-Jc,vecNorm(dJ),vecNorm(yc-yStop),0]; - -% some output -fprintf('%4s %-12s %-12s %-12s %-12s %4s\n%s\n',... - hisStr{:},char(ones(1,64)*'-')); -dispHis = @(var) ... - fprintf('%4d %-12.4e %-12.3e %-12.3e %-12.3e %4d\n',var); -dispHis(his(1,:)); -dispHis(his(2,:)); -% -- end initialization ------------------------------------------------ - - -%-- start the iteration -------------------------------------------------- -while 1, - % check stopping rules - STOP(1) = (iter>0) && abs(Jold-Jc) <= tolJ*(1+abs(Jstop)); - STOP(2) = (iter>0) && (norm(yc-yOld) <= tolY*(1+norm(y0))); - STOP(3) = norm(dJ) <= tolG*(1+abs(Jstop)); - STOP(4) = norm(dJ) <= 1e6*eps; - STOP(5) = (iter >= maxIter); - if all(STOP(1:3)) || any(STOP(4:5)), break; end; - - iter = iter + 1; - - % solve the Gauss-Newton System - [dy,solver] = solveLinearSystem(-dJ',H,solver); - - % check descent direction - % note: descent is not granted if using an iterative solver - descent = dJ * dy; - if descent > 0, - warning('no descent direction, switch to -dy!') - dy = -dy; - end; - - % perform Armijo line-search - [t,yt,LSiter] = lineSearch(fctn,yc,dy,Jc,dJ,... - 'para',para,'LSmaxIter',LSmaxIter,'LSreduction',LSreduction); - if (t == 0), - break; - end; % break if line-search fails - - % save old values and update - yOld = yc; Jold = Jc; yc = yt; - [Jc,para,dJ,H] = fctn(yc); % evalute objective function - - % some output - his(iter+2,:) = [iter,Jc,Jold-Jc,vecNorm(dJ),vecNorm(yc-yOld),LSiter]; - dispHis(his(iter+2,:)); - para.normdY = vecNorm(yc - yOld); - Plots(iter,para); -% pause -end;%while; % end of iteration loop -%------------------------------------------------------------------------- -Plots(iter,para); - -% clean up -His.str = hisStr; -His.his = his(1:iter+2,:); -fprintf('STOPPING:\n'); -fprintf('%d[ %-10s=%16.8e <= %-25s=%16.8e]\n',STOP(1),... - '(Jold-Jc)',(Jold-Jc),'tolJ*(1+|Jstop|)',tolJ*(1+abs(Jstop))); -fprintf('%d[ %-10s=%16.8e <= %-25s=%16.8e]\n',STOP(2),... - '|yc-yOld|',norm(yc-yOld),'tolY*(1+norm(yc)) ',tolY*(1+norm(yc))); -fprintf('%d[ %-10s=%16.8e <= %-25s=%16.8e]\n',STOP(3),... - '|dJ|',norm(dJ),'tolG*(1+abs(Jstop))',tolG*(1+abs(Jstop))); -fprintf('%d[ %-10s=%16.8e <= %-25s=%16.8e]\n',STOP(4),... - 'norm(dJ)',norm(dJ),'eps',1e3*eps); -fprintf('%d[ %-10s= %-14d >= %-25s= %-14d]\n',STOP(5),... - 'iter',iter,'maxIter',maxIter); - -FAIRmessage([mfilename,' : done !'],'='); - -%============================================================================== From 6157cf39199d591b96fdfacc960041bc82199632 Mon Sep 17 00:00:00 2001 From: hariagr Date: Mon, 17 Jul 2017 15:59:46 +0200 Subject: [PATCH 06/16] *.m~ ignore --- .gitignore | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/.gitignore b/.gitignore index 11718b3..e0548dc 100644 --- a/.gitignore +++ b/.gitignore @@ -3,3 +3,7 @@ ToDo-Liste.txt kernel/matrixfree/.svn *.o temp + +*.m~ + +*.m~ From 2d156f57aac744fde99323411764e434890dd4c0 Mon Sep 17 00:00:00 2001 From: hariagr Date: Sun, 13 Aug 2017 13:59:35 +0200 Subject: [PATCH 07/16] Improvements in the MatrixFree code Matrixfree implementations of - derivative of determinants, - diagonal of hessian matrix, and - Hessian matrix --- add-ons/FAIRFEM/FEMPIREobjFctn.m | 74 +++++++++++++++++-- add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m | 60 +++++++++++++++ .../FAIRFEM/{ => examples}/EFEM_MP_MBvsMF.m | 8 +- add-ons/FAIRFEM/getDeterminant.m | 49 ++++++++---- 4 files changed, 167 insertions(+), 24 deletions(-) create mode 100644 add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m rename add-ons/FAIRFEM/{ => examples}/EFEM_MP_MBvsMF.m (85%) diff --git a/add-ons/FAIRFEM/FEMPIREobjFctn.m b/add-ons/FAIRFEM/FEMPIREobjFctn.m index 9d4313f..b297bf6 100755 --- a/add-ons/FAIRFEM/FEMPIREobjFctn.m +++ b/add-ons/FAIRFEM/FEMPIREobjFctn.m @@ -75,6 +75,7 @@ yc = reshape(yc,[],dim); yRef = reshape(yRef,[],dim); doDerivative = (nargout>2); % flag for necessity of derivatives +matrixFree = regularizer('get','matrixFree'); % do the work ------------------------------------------------------------ % define barycentric interpolation @@ -83,7 +84,7 @@ vol = Mesh.vol; % compute interpolated image and derivative -[Tc,dT] = imgModel(T,omega,Mesh.mfPi(yc,'C'),'doDerivative',doDerivative); +[Tc,dT] = imgModel(T,omega,Mesh.mfPi(yc,'C'),'doDerivative',doDerivative,'matrixFree',matrixFree); % apply intensity modulation [det,dDet] = getDeterminant(Mesh,yc,'doDerivative',doDerivative); Tcmod = Tc .* det; @@ -122,11 +123,10 @@ else % derivatives rather explicit %P = @(x) reshape(Mesh.mfPi(reshape(x,[],dim),'C'),[],1); - %dTcmod = P((sdiag(det)*dT)')' + sdiag(Tc)*dDet; - P = kron(speye(dim),Mesh.PC); - dTcmod = sdiag(det)*dT*P + sdiag(Tc)*dDet; - dr = dres*dTcmod; - dD = dD*dTcmod; + %dTcmod = P((sdiag(det)*dT)')' + sdiag(Tc)*dDet; + p = vecXmat(dD,det,dT); + dD = reshape(Mesh.mfPi(p,'C'),1,[]) + (dDet.dDetadj(dD'.*Tc))'; + dJ = dD + dS; % approximation to d2D in matrix free mode @@ -136,20 +136,78 @@ H.omega = omega; H.m = m; H.d2D.how = 'P''*dr''*d2psi*dr*P'; - H.d2D.P = @(x) x;%reshape(Mesh.mfPi(reshape(x,[],dim),'C'),[],1); - H.d2D.dr = dr; + H.d2D.P = @(x) reshape(Mesh.mfPi(x,'C'),[],1); + H.d2D.Tc = Tc; + H.d2D.dT = dT; + H.d2D.Jac = det; + H.d2D.dJac = dDet.dDet; + H.d2D.dJacadj = dDet.dDetadj; + H.d2D.diag = @(Mesh,yc) getDiag(Mesh,det,Tc,dT,yc); + H.d2D.dres = dres; H.d2D.d2psi = d2psi; H.solver = d2S.solver; H.d2S = d2S; end; +function p = vecXmat(dD,Jac,dT) +% implementation of vector' * matrix product dD * [Jac] * dT + +[len,dim] = size(dT); +p = zeros(len,dim); +for d=1:dim, + p(:,d) = dD(:).*Jac(:).*dT(:,d); +end % shortcut for sparse diagonal matrix function A = sdiag(v) A = spdiags(v(:),0,numel(v),numel(v)); +% diagonal of hessian matrix +% sum(sdiag(vol)dTcmod.^2,1) +% where dTcmod = sdiag(det)*dT*P + sdiag(Tc)*dDet; +% implemention: sum(sdiag(vol)*(sdiag(det)*dT*P(.^2 + +% sdiag(vol)*(sdiag(Tc)*dDet).^2,1) +function D = getDiag(Mesh,det,Tc,dT,yc) + +vol = Mesh.vol; + +% first term +D1 = [(Mesh.mfPi(vol.*((1/3)*det.*dT(:,1)).^2,1)) + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,1)).^2,2)) + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,1)).^2,3)) ;... + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,2)).^2,1)) + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,2)).^2,2)) + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,2)).^2,3))]; + +% second term + +xn = Mesh.xn; +% get edges +e1 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,3); +e2 = Mesh.mfPi(xn,2) - Mesh.mfPi(xn,3); +e3 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,2); + +% compute gradients of basis functions +dphi1 = ([ e2(:,2) -e2(:,1)]./[2*vol,2*vol]); +dphi2 = ([-e1(:,2) e1(:,1)]./[2*vol,2*vol]); +dphi3 = ([ e3(:,2) -e3(:,1)]./[2*vol,2*vol]); + +% compute diagonal of volume regularizer +% MB : dDet = [sdiag(By(:,4)), sdiag(-By(:,3)) , sdiag(-By(:,2)), sdiag(By(:,1))] * B; +[dx1, dx2] = getGradientMatrixFEM(Mesh,1); +yc = reshape(yc,[],2); +By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; + +% get boundaries +Dxi = @(i,j) Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi1(:,i)).^2,1) ... + + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi2(:,i)).^2,2) ... + + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi3(:,i)).^2,3); % diagonal of Dxi'*Dxi + +Dxy = @(i,j,k,l) Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi1(:,i)).*(Tc.*By(:,l).*dphi1(:,k)),1) ... % byproduct terms for verifications + + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi2(:,i)).*(Tc.*By(:,l).*dphi2(:,k)),2) ... + + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi3(:,i)).*(Tc.*By(:,l).*dphi3(:,k)),3); % diagonal of Dxi'*Dxi + +D2 = [Dxi(1,4)+ Dxi(2,3) - 2*Dxy(1,4,2,3) ;Dxi(1,2)+ Dxi(2,1) - 2*Dxy(1,2,2,1)]; + +D = D1 + D2; function runMinimalExample diff --git a/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m b/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m new file mode 100644 index 0000000..737edaa --- /dev/null +++ b/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m @@ -0,0 +1,60 @@ +%============================================================================== +% This code is part of the VAMPIRE app for the Matlab-based toolbox +% FAIR - Flexible Algorithms for Image Registration. +% For details see +% - https://github.com/C4IR/VAMPIRE.m +%============================================================================== +% PCG solver for VAMPIRE +% + +function dy = FEMPIREsolveGN_PCG(rhs, H, maxIterCG, tolCG) + +h = (H.omega(2:2:end)-H.omega(1:2:end))./H.m; +hd = prod(h); +% set pointers to simplify notation +Mesh = H.Mesh; +P = H.d2D.P; +Jac = H.d2D.Jac; +dJac = H.d2D.dJac; +dJacadj = H.d2D.dJacadj; +Tc = H.d2D.Tc; +dT = H.d2D.dT; +yc = H.d2S.yc; +dres = H.d2D.dres; +dim = Mesh.dim; + +% Tcmod(y) = T(P*y) * Jac(y) +% ==> dTcmod(y) = Jac(y) * (dT(y)*P) + T(P*y) * dJac(y) +% ==> dTcmod'(y) = (P'* dT') Jac(y) + (dJac(y))' * Tc +dTcmod = @(x) vecmatprod1(Jac,dT,H.d2D.P(reshape(x,[],dim))) + Tc .* dJac(reshape(x,[],dim)); +dTcmodadj = @(x) H.d2D.P(vecmatprod1adj(dT,Jac,x)) + dJacadj(Tc.*x); + +M = @(x) dTcmodadj(dres'*H.d2D.d2psi*(dres * dTcmod(x))); +Hoperator = @(x) M(x) + H.d2S.d2S(x,H.omega,H.m,H.d2S.yc); + +D = H.d2D.diag(Mesh,yc) + H.d2S.diag(H.d2S.yc); +Preconditioner = @(x) D.\x; % Jacobi preconditioner +[dy,flag,relres,iter] = pcg(Hoperator,rhs,tolCG,maxIterCG,Preconditioner); + + +function p= vecmatprod1(Jac,dI,x) +% We aim to compute diag(Jac) * [dI] * x +dim = size(dI,2); +n = length(Jac); + +x = reshape(x,[],dim); +p = zeros(n,1); +for d=1:dim + p = p + dI(:,d) .* x(:,d); +end +p = p.*Jac; + +function p = vecmatprod1adj(dI,Jac,x) +% We aim to compute dI' * [Jac] * x +dim = size(dI,2); +n = length(Jac); + +p = zeros(n,dim); +for d=1:dim + p(:,d) = dI(:,d) .* Jac.*x; +end diff --git a/add-ons/FAIRFEM/EFEM_MP_MBvsMF.m b/add-ons/FAIRFEM/examples/EFEM_MP_MBvsMF.m similarity index 85% rename from add-ons/FAIRFEM/EFEM_MP_MBvsMF.m rename to add-ons/FAIRFEM/examples/EFEM_MP_MBvsMF.m index b43088d..da29b44 100644 --- a/add-ons/FAIRFEM/EFEM_MP_MBvsMF.m +++ b/add-ons/FAIRFEM/examples/EFEM_MP_MBvsMF.m @@ -2,9 +2,10 @@ % (c) Lars Ruthotto 2012/07/26, see FAIR.2 and FAIRcopyright.m. % http://www.mic.uni-luebeck.de/people/lars-ruthotto.html % -% Simplified Registration of Cardiac PET +% Verification code for matrixfree implementation % -% data Gaussian Blobs +% 'relerr' shows the relative difference between matrixfree and matrix +% based implementations % % ================================================================================== close all; clc; clear; @@ -27,7 +28,8 @@ 'minLevel',minLevel,'maxLevel',maxLevel); regularizer('reset','regularizer','mfHyperElasticFEM','alpha',5e1); -NPIRpara.solver = 'PCG-hyperElastic'; +NPIRpara.solver = @FEMPIREsolveGN_PCG;%'PCG-hyperElastic'; + [yMP_MF,~,hisMP_MF] = MLIRFEM(ML,'parametric',0,... 'NPIRobj',@FEMPIREobjFctn,'NPIRpara',NPIRpara,... 'minLevel',minLevel,'maxLevel',maxLevel); diff --git a/add-ons/FAIRFEM/getDeterminant.m b/add-ons/FAIRFEM/getDeterminant.m index 5842232..80146ad 100755 --- a/add-ons/FAIRFEM/getDeterminant.m +++ b/add-ons/FAIRFEM/getDeterminant.m @@ -28,27 +28,50 @@ eval([varargin{k},'=varargin{',int2str(k+1),'};']); end; +matrixFree = regularizer('get','matrixFree'); dim = Mesh.dim; yc = reshape(yc,[],dim); switch dim case 2 - dx1 = Mesh.dx1; dx2 = Mesh.dx2; - D1y = dx1*yc; - D2y = dx2*yc; - % compute volume - det = D1y(:,1).*D2y(:,2) - D2y(:,1).*D1y(:,2); - if doDerivative, - w = [D2y(:,2), D1y(:,2), D1y(:,1), D2y(:,1)]; + if ~matrixFree + + dx1 = Mesh.dx1; dx2 = Mesh.dx2; + + D1y = dx1*yc; + D2y = dx2*yc; + % compute volume + det = D1y(:,1).*D2y(:,2) - D2y(:,1).*D1y(:,2); + + if doDerivative, + + + w = [D2y(:,2), D1y(:,2), D1y(:,1), D2y(:,1)]; + + dDet =[ + sdiag(w(:,1))*(dx1) ... + - sdiag(w(:,2))*(dx2),... + sdiag(w(:,3))*(dx2) ... + - sdiag(w(:,4))*(dx1) + ]; + + end + + else + + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; + By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; + det = By(:,1).*By(:,4) - By(:,3) .* By(:,2); + + dDet.dDet = @(x) By(:,4).*dx1.D(x(:,1)) - By(:,3).*dx2.D(x(:,1)) + By(:,1).*dx2.D(x(:,2)) - By(:,2).*dx1.D(x(:,2)); + + dDet.dDetadj = @(x) [ ... + dx1.Dadj(By(:,4).*x)-dx2.Dadj(By(:,3).*x);... + -dx1.Dadj(By(:,2).*x)+dx2.Dadj(By(:,1).*x)]; - dDet =[ - sdiag(w(:,1))*(dx1) ... - - sdiag(w(:,2))*(dx2),... - sdiag(w(:,3))*(dx2) ... - - sdiag(w(:,4))*(dx1) - ]; end + case 3 % compute derivative GRAD = Mesh.GRAD; From 4df61b1d311d33def37e58c220b01c909241ba74 Mon Sep 17 00:00:00 2001 From: hariagr Date: Mon, 14 Aug 2017 14:17:43 +0200 Subject: [PATCH 08/16] deleted files --- add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m | 38 ---------------------- add-ons/FAIRFEM/examples/EFEM_SSDvsMP.mat | Bin 1069988 -> 0 bytes 2 files changed, 38 deletions(-) delete mode 100644 add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m delete mode 100644 add-ons/FAIRFEM/examples/EFEM_SSDvsMP.mat diff --git a/add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m b/add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m deleted file mode 100644 index 58a5e4b..0000000 --- a/add-ons/FAIRFEM/EFEM_SSD_MBvsMF.m +++ /dev/null @@ -1,38 +0,0 @@ -% ================================================================================== -% (c) Lars Ruthotto 2012/07/26, see FAIR.2 and FAIRcopyright.m. -% http://www.mic.uni-luebeck.de/people/lars-ruthotto.html -% -% Simplified Registration of Cardiac PET -% -% data Gaussian Blobs -% -% ================================================================================== -close all; clc; clear; -setup2DGaussianData; - -distance('reset','distance','SSD'); -imgModel('reset','imgModel','splineInterMex','regularizer','moments','theta',4e-1); -regularizer('reset','regularizer','mbHyperElasticFEM','alpha',5e1); - -minLevel = 3; -maxLevel = 8; - -NPIRpara = optPara('NPIR-GN'); -NPIRpara.Plots = @FAIRplotsFEM; -NPIRpara.lineSearch = @ArmijoDiffeomorphicFEM; -NPIRpara.solver = 'mbPCG-Jacobi'; - -[ySSD_MB,~,hisSSD_MB] = MLIRFEM(ML,'parametric',0,... - 'NPIRobj',@FEMobjFctn,'NPIRpara',NPIRpara,... - 'minLevel',minLevel,'maxLevel',maxLevel); - -regularizer('reset','regularizer','mfHyperElasticFEM','alpha',5e1); -NPIRpara.solver = 'PCG-hyperElastic'; -[ySSD_MF,~,hisSSD_MF] = MLIRFEM(ML,'parametric',0,... - 'NPIRobj',@FEMobjFctn,'NPIRpara',NPIRpara,... - 'minLevel',minLevel,'maxLevel',maxLevel); - -relerr = norm(ySSD_MB-ySSD_MF)/norm(ySSD_MB) - -%% -%save('EFEM_SSDvsMP','ML','yFEMPIRE','ySSD','hisFEMPIRE','hisSSD'); \ No newline at end of file diff --git a/add-ons/FAIRFEM/examples/EFEM_SSDvsMP.mat b/add-ons/FAIRFEM/examples/EFEM_SSDvsMP.mat deleted file mode 100644 index b9d1318b031a5a8d8d6cfe92548fd4c41ff90afd..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1069988 zcma&NdpOhm{|8=4tHcr|IgC^)MUpU^6-lK~DwV@3m86Uq8@5&C5Lst+hlQk4Mv~KP zPEjeNFga`(rj2dP%+9~5`~H0H@Av!rUDwa$k6m+lKVQ$o>v?!QAMZoEj~?9ZY+`G< 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FMPNvTTfP7Q From 4ce857af4fe6aa4231775c5d9b3e1629de0bc35c Mon Sep 17 00:00:00 2001 From: "Ruthotto, Lars" Date: Thu, 31 Aug 2017 10:54:19 -0400 Subject: [PATCH 09/16] two minor changes --- add-ons/FAIRFEM/FEMPIREobjFctn.m | 11 +---------- add-ons/FAIRFEM/getDeterminant.m | 21 ++++----------------- 2 files changed, 5 insertions(+), 27 deletions(-) diff --git a/add-ons/FAIRFEM/FEMPIREobjFctn.m b/add-ons/FAIRFEM/FEMPIREobjFctn.m index b297bf6..20b17f2 100755 --- a/add-ons/FAIRFEM/FEMPIREobjFctn.m +++ b/add-ons/FAIRFEM/FEMPIREobjFctn.m @@ -124,7 +124,7 @@ % derivatives rather explicit %P = @(x) reshape(Mesh.mfPi(reshape(x,[],dim),'C'),[],1); %dTcmod = P((sdiag(det)*dT)')' + sdiag(Tc)*dDet; - p = vecXmat(dD,det,dT); + p = (dD(:).*det).*dT; dD = reshape(Mesh.mfPi(p,'C'),1,[]) + (dDet.dDetadj(dD'.*Tc))'; dJ = dD + dS; @@ -150,15 +150,6 @@ H.d2S = d2S; end; -function p = vecXmat(dD,Jac,dT) -% implementation of vector' * matrix product dD * [Jac] * dT - -[len,dim] = size(dT); -p = zeros(len,dim); -for d=1:dim, - p(:,d) = dD(:).*Jac(:).*dT(:,d); -end - % shortcut for sparse diagonal matrix function A = sdiag(v) diff --git a/add-ons/FAIRFEM/getDeterminant.m b/add-ons/FAIRFEM/getDeterminant.m index 80146ad..7a82905 100755 --- a/add-ons/FAIRFEM/getDeterminant.m +++ b/add-ons/FAIRFEM/getDeterminant.m @@ -24,7 +24,7 @@ if nargin==0, help(mfilename); runMinimalExample; return; end; doDerivative = (nargout>1); -for k=1:2:length(varargin), % overwrites default parameter +for k=1:2:length(varargin) % overwrites default parameter eval([varargin{k},'=varargin{',int2str(k+1),'};']); end; @@ -34,9 +34,7 @@ switch dim case 2 - if ~matrixFree - dx1 = Mesh.dx1; dx2 = Mesh.dx2; D1y = dx1*yc; @@ -44,22 +42,13 @@ % compute volume det = D1y(:,1).*D2y(:,2) - D2y(:,1).*D1y(:,2); - if doDerivative, - - + if doDerivative w = [D2y(:,2), D1y(:,2), D1y(:,1), D2y(:,1)]; - dDet =[ - sdiag(w(:,1))*(dx1) ... - - sdiag(w(:,2))*(dx2),... - sdiag(w(:,3))*(dx2) ... - - sdiag(w(:,4))*(dx1) - ]; - + sdiag(w(:,1))*(dx1)-sdiag(w(:,2))*(dx2),... + sdiag(w(:,3))*(dx2)-sdiag(w(:,4))*(dx1)]; end - else - dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; det = By(:,1).*By(:,4) - By(:,3) .* By(:,2); @@ -69,9 +58,7 @@ dDet.dDetadj = @(x) [ ... dx1.Dadj(By(:,4).*x)-dx2.Dadj(By(:,3).*x);... -dx1.Dadj(By(:,2).*x)+dx2.Dadj(By(:,1).*x)]; - end - case 3 % compute derivative GRAD = Mesh.GRAD; From 5d236e9e8f0bd9e76131d301d744043178737772 Mon Sep 17 00:00:00 2001 From: "Ruthotto, Lars" Date: Thu, 31 Aug 2017 11:06:34 -0400 Subject: [PATCH 10/16] another minor edit --- add-ons/FAIRFEM/FEMPIREobjFctn.m | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/add-ons/FAIRFEM/FEMPIREobjFctn.m b/add-ons/FAIRFEM/FEMPIREobjFctn.m index 20b17f2..f799796 100755 --- a/add-ons/FAIRFEM/FEMPIREobjFctn.m +++ b/add-ons/FAIRFEM/FEMPIREobjFctn.m @@ -165,8 +165,7 @@ vol = Mesh.vol; % first term -D1 = [(Mesh.mfPi(vol.*((1/3)*det.*dT(:,1)).^2,1)) + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,1)).^2,2)) + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,1)).^2,3)) ;... - (Mesh.mfPi(vol.*((1/3)*det.*dT(:,2)).^2,1)) + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,2)).^2,2)) + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,2)).^2,3))]; +D1 = Mesh.mfPi(vol.*(det.*dT).^2,'C'); % second term From 6952a8b5729b43320749f880788890d7287315a0 Mon Sep 17 00:00:00 2001 From: Hari Om Aggraval Date: Sun, 3 Sep 2017 22:54:20 +0200 Subject: [PATCH 11/16] 3D - Matrixfree code ... in progress MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Implement matrix free code to evaluate determinant. Added a script “verifyMF_getdeterminant” to verify results --- add-ons/FAIRFEM/FEMPIREobjFctn.m | 1 + .../FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m | 9 +- .../examples/verifyMF_getdeterminant.m | 29 +++++++ add-ons/FAIRFEM/getDeterminant.m | 86 +++++++++++++------ add-ons/FAIRFEM/hyperElasticFEM.m | 4 +- 5 files changed, 101 insertions(+), 28 deletions(-) create mode 100644 add-ons/FAIRFEM/examples/verifyMF_getdeterminant.m diff --git a/add-ons/FAIRFEM/FEMPIREobjFctn.m b/add-ons/FAIRFEM/FEMPIREobjFctn.m index f799796..9530e5e 100755 --- a/add-ons/FAIRFEM/FEMPIREobjFctn.m +++ b/add-ons/FAIRFEM/FEMPIREobjFctn.m @@ -166,6 +166,7 @@ % first term D1 = Mesh.mfPi(vol.*(det.*dT).^2,'C'); +D1 = D1(:)./3; % second term diff --git a/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m b/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m index 87ec57a..127b6e5 100755 --- a/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m +++ b/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m @@ -6,7 +6,10 @@ % % ================================================================================== close all; clc; clear; -setup3DmiceData; level = 4; +%setup3DmiceData; +setup3DmouseData; + +level = 3; omega = ML{level}.omega; m = ML{level}.m; viewImage('reset','viewImage','imgmontage','colormap','gray'); @@ -24,6 +27,6 @@ FAIRplotsFEM('reset','mode','FEM','fig',level,'plots',1); FAIRplotsFEM('init',struct('Tc',T,'Rc',R,'Mesh',Mesh)); -yc = GaussNewton(fctn,xc(:),'Plots',@FAIRplotsFEM,'solver','pcg'); +yc = GaussNewton(fctn,xc(:),'Plots',@FAIRplotsFEM,'solver','mbPCG-Jacobi'); -showResults(ML,yc,'level',level); +%showResults(ML,yc,'level',level); diff --git a/add-ons/FAIRFEM/examples/verifyMF_getdeterminant.m b/add-ons/FAIRFEM/examples/verifyMF_getdeterminant.m new file mode 100644 index 0000000..b4165f3 --- /dev/null +++ b/add-ons/FAIRFEM/examples/verifyMF_getdeterminant.m @@ -0,0 +1,29 @@ +% verify getdeterminant matrix free implementation + +%omega = [0 3 0 5]; m = [2 4]; +%Mesh = TriMesh1(omega,m); +omega = [0 3 0 5 0 2]; m = [2 4 3]; +Mesh = TetraMesh1(omega,m); +xc = Mesh.xn; +% rotate x-y plane by 45 degree +yc(:,1) = (1/sqrt(2))*(xc(:,1) - xc(:,2)); +yc(:,2) = (1/sqrt(2))*(xc(:,1) + xc(:,2)); +yc(:,3) = xc(:,3); +xc = yc; + +[det,dD] = getDeterminant(Mesh,xc,'matrixFree',0); + +[detMF,dDMF] = getDeterminant(Mesh,xc,'matrixFree',1); + +% error in determinant value +err_det = norm(det-detMF); + +% error in dDet +x = rand(size(xc)); +err_dD = norm(dD*x(:) - dDMF.dDet(x)); + +% error in adjoint of dDet +z = rand(Mesh.ntri,1); +err_dDT = norm(dD'*z - dDMF.dDetadj(z)); + + diff --git a/add-ons/FAIRFEM/getDeterminant.m b/add-ons/FAIRFEM/getDeterminant.m index 7a82905..e6f0323 100755 --- a/add-ons/FAIRFEM/getDeterminant.m +++ b/add-ons/FAIRFEM/getDeterminant.m @@ -23,15 +23,15 @@ dDet = []; if nargin==0, help(mfilename); runMinimalExample; return; end; +matrixFree = regularizer('get','matrixFree'); +dim = Mesh.dim; +yc = reshape(yc,[],dim); + doDerivative = (nargout>1); for k=1:2:length(varargin) % overwrites default parameter eval([varargin{k},'=varargin{',int2str(k+1),'};']); end; -matrixFree = regularizer('get','matrixFree'); -dim = Mesh.dim; -yc = reshape(yc,[],dim); - switch dim case 2 if ~matrixFree @@ -60,30 +60,68 @@ -dx1.Dadj(By(:,2).*x)+dx2.Dadj(By(:,1).*x)]; end case 3 - % compute derivative - GRAD = Mesh.GRAD; - By = reshape(GRAD*reshape(yc,[],3),[],9); - D = @(i,j) By(:,(i-1)*3+j); - cof = [ - D(2,2).*D(3,3)-D(2,3).*D(3,2),... - D(2,1).*D(3,3)-D(2,3).*D(3,2),... - D(2,1).*D(3,2)-D(2,2).*D(3,1),... - ]; - - det = sum(By(:,1:3).*cof(:,1:3),2); - if doDerivative, + + if ~matrixFree + % compute derivative + GRAD = Mesh.GRAD; + By = reshape(GRAD*reshape(yc,[],3),[],9); + D = @(i,j) By(:,(j-1)*3+i); % gets partial_i y^j + cof = [ + D(2,2).*D(3,3)-D(3,2).*D(2,3),...%C(1,1) + -D(1,2).*D(3,3)+D(3,2).*D(1,3),...%C(1,2) + D(1,2).*D(2,3)-D(2,2).*D(1,3),...%C(1,3) + -D(2,1).*D(3,3)+D(3,1).*D(2,3),...%C(2,1) + D(1,1).*D(3,3)-D(3,1).*D(1,3),...%C(2,2) + -D(1,1).*D(2,3)+D(2,1).*D(1,3),...%C(2,3) + D(2,1).*D(3,2)-D(3,1).*D(2,2),...%C(3,1) + -D(1,1).*D(3,2)+D(3,1).*D(1,2),...%C(3,2) + D(1,1).*D(2,2)-D(2,1).*D(1,2)... %C(3,3) + ]; + + det = sum(By(:,1:3).*cof(:,1:3),2); + if doDerivative + + D1 = Mesh.dx1; D2 = Mesh.dx2; D3 = Mesh.dx3; + + dDet = [sdiag(cof(:,1))*D1 + sdiag(cof(:,2))*D2 + sdiag(cof(:,3))*D3,... + sdiag(cof(:,4))*D1 + sdiag(cof(:,5))*D2 + sdiag(cof(:,6))*D3,... + sdiag(cof(:,7))*D1 + sdiag(cof(:,8))*D2 + sdiag(cof(:,9))*D3]; + + end + + else - D1 = Mesh.dx1; D2 = Mesh.dx2; D3 = Mesh.dx3; - Z = sparse(size(D1,1), size(D2,2)); - D = @(i,j) sdiag(By(:,(i-1)*3+j)); + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; - dCof{1} = [ Z , D(3,3)*D2-D(3,2)*D3, D(2,2)*D3-D(2,3)*D2]; - dCof{2} = [ Z , D(3,3)*D1-D(3,2)*D3, D(2,1)*D3-D(2,3)*D2]; - dCof{3} = [ Z , D(3,2)*D1-D(3,1)*D2, D(2,1)*D2-D(2,2)*D1]; + cof11 = @(yc) dx2.D(yc(:,2)).*dx3.D(yc(:,3)) - dx3.D(yc(:,2)).*dx2.D(yc(:,3)); + cof12 = @(yc) -dx1.D(yc(:,2)).*dx3.D(yc(:,3)) + dx3.D(yc(:,2)).*dx1.D(yc(:,3)); + cof13 = @(yc) dx1.D(yc(:,2)).*dx2.D(yc(:,3)) - dx2.D(yc(:,2)).*dx1.D(yc(:,3)); + cof21 = @(yc) -dx2.D(yc(:,1)).*dx3.D(yc(:,3)) + dx3.D(yc(:,1)).*dx2.D(yc(:,3)); + cof22 = @(yc) dx1.D(yc(:,1)).*dx3.D(yc(:,3)) - dx3.D(yc(:,1)).*dx1.D(yc(:,3)); + cof23 = @(yc) -dx1.D(yc(:,1)).*dx2.D(yc(:,3)) + dx2.D(yc(:,1)).*dx1.D(yc(:,3)); + cof31 = @(yc) dx2.D(yc(:,1)).*dx3.D(yc(:,2)) - dx3.D(yc(:,1)).*dx2.D(yc(:,2)); + cof32 = @(yc) -dx1.D(yc(:,1)).*dx3.D(yc(:,2)) + dx3.D(yc(:,1)).*dx1.D(yc(:,2)); + cof33 = @(yc) dx1.D(yc(:,1)).*dx2.D(yc(:,2)) - dx2.D(yc(:,1)).*dx1.D(yc(:,2)); + + det = dx1.D(yc(:,1)).*cof11(yc) + dx2.D(yc(:,1)).*cof12(yc) + dx3.D(yc(:,1)).*cof13(yc); + if doDerivative + + dDet.dDet = @(x) cof11(yc).*dx1.D(x(:,1)) + cof12(yc).*dx2.D(x(:,1)) + cof13(yc).*dx3.D(x(:,1)) +... + cof21(yc).*dx1.D(x(:,2)) + cof22(yc).*dx2.D(x(:,2)) + cof23(yc).*dx3.D(x(:,2)) +... + cof31(yc).*dx1.D(x(:,3)) + cof32(yc).*dx2.D(x(:,3)) + cof33(yc).*dx3.D(x(:,3)); + + dDet.dDetadj = @(x) [ ... + dx1.Dadj(cof11(yc).*x) + dx2.Dadj(cof12(yc).*x) + dx3.Dadj(cof13(yc).*x);... + dx1.Dadj(cof21(yc).*x) + dx2.Dadj(cof22(yc).*x) + dx3.Dadj(cof23(yc).*x);... + dx1.Dadj(cof31(yc).*x) + dx2.Dadj(cof32(yc).*x) + dx3.Dadj(cof33(yc).*x) + ]; + + + end - dDet = [sdiag(cof(:,1))*D1 + sdiag(cof(:,2))*D2 + sdiag(cof(:,3))*D3,Z,Z]... - + sdiag(By(:,1))*dCof{1} + sdiag(By(:,2))*dCof{2} + sdiag(By(:,3))*dCof{3}; end + + otherwise error('only dim=2,3.'); end diff --git a/add-ons/FAIRFEM/hyperElasticFEM.m b/add-ons/FAIRFEM/hyperElasticFEM.m index 8cabd30..f6e0ed8 100755 --- a/add-ons/FAIRFEM/hyperElasticFEM.m +++ b/add-ons/FAIRFEM/hyperElasticFEM.m @@ -155,15 +155,17 @@ d2S.alpha = alpha; d2S.yc = yc; d2S.solver = 'PCG-hyperElastic';%@FEMMultiGridSolveHyper; + % code only diffusion part for B d2S.By = @(u,Mesh) Mesh.mfGRAD.D(u); d2S.BTy = @(u,Mesh) Mesh.mfGRAD.Dadj(u); d2S.B = @(Mesh) Mesh.GRAD; + % give seperate handles for diagonals of length, area and volume d2S.diagLength = @(Mesh) getDiagLength(Mesh,alphaLength); d2S.diagArea = [];%@(Mesh) getDiagArea(Mesh,alphaLength); d2S.diagVol = @(Mesh) getDiagVolume(Mesh,yc,alphaVolume); - d2S.diag = @(yc) d2S.diagLength(Mesh) + d2S.diagVol(Mesh); + d2S.diag = @(yc) d2S.diagLength(Mesh) + d2S.diagVol(Mesh); d2S.d2S = @(uc,omega,m,yc) ... alphaLength * ... From f3e9d3ffc7db6122a8ac221e5845771eeb2d7065 Mon Sep 17 00:00:00 2001 From: Hari Om Aggraval Date: Fri, 8 Sep 2017 20:47:57 +0200 Subject: [PATCH 12/16] MatrixFree code for 3D... in progress Modified HyperElasticFEM function. Work to do: MatrixFree code for diagonal elements of Hessian matrix. --- add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m | 3 +- add-ons/FAIRFEM/hyperElasticFEM.m | 238 +++++++++++++++++++++------ 2 files changed, 189 insertions(+), 52 deletions(-) diff --git a/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m b/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m index 737edaa..a267c7d 100644 --- a/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m +++ b/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m @@ -30,7 +30,8 @@ dTcmodadj = @(x) H.d2D.P(vecmatprod1adj(dT,Jac,x)) + dJacadj(Tc.*x); M = @(x) dTcmodadj(dres'*H.d2D.d2psi*(dres * dTcmod(x))); -Hoperator = @(x) M(x) + H.d2S.d2S(x,H.omega,H.m,H.d2S.yc); +%Hoperator = @(x) M(x) + H.d2S.d2S(x,H.omega,H.m,H.d2S.yc); +Hoperator = @(x) M(x) + H.d2S.d2S(x); D = H.d2D.diag(Mesh,yc) + H.d2S.diag(H.d2S.yc); Preconditioner = @(x) D.\x; % Jacobi preconditioner diff --git a/add-ons/FAIRFEM/hyperElasticFEM.m b/add-ons/FAIRFEM/hyperElasticFEM.m index f6e0ed8..4a11a0f 100755 --- a/add-ons/FAIRFEM/hyperElasticFEM.m +++ b/add-ons/FAIRFEM/hyperElasticFEM.m @@ -79,7 +79,7 @@ % ===================================================================== % area regularization if dim==3, - [cof, dCof] = cofactor3D(By,Mesh,doDerivative); + [cof, dCof] = cofactor3D(By,Mesh,doDerivative,matrixFree); % compute areas area = [ sum(cof(:,[1 4 7]).^2,2); @@ -167,71 +167,202 @@ d2S.diagVol = @(Mesh) getDiagVolume(Mesh,yc,alphaVolume); d2S.diag = @(yc) d2S.diagLength(Mesh) + d2S.diagVol(Mesh); - d2S.d2S = @(uc,omega,m,yc) ... - alphaLength * ... - d2S.BTy(repmat(Mesh.vol,[dim^2,1]).*d2S.By(uc,Mesh),Mesh) ... - + alphaVolume * ... - volumeOperator(yc,Mesh,uc, Mesh.vol); - % length regularizer dSlength = transpose( alphaLength* d2S.BTy(repmat(Mesh.vol,[dim^2,1]).*d2S.By(uc,Mesh),Mesh) ); Slength = .5*dSlength*uc; - % volume term - dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; - yc = reshape(yc,[],2); - By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; - det = By(:,1).*By(:,4) - By(:,3) .* By(:,2); - [G,dG,d2G] = psi(det,doDerivative); - Svol = alphaVolume*sum(Mesh.vol.*G); - Sc = Slength + Svol; + if doDerivative + d2Slength = @(uc) alphaLength * d2S.BTy(repmat(Mesh.vol,[dim^2,1]).*d2S.By(uc,Mesh),Mesh); + end + + % area regularizer + if dim==3 + yc = reshape(yc,[],dim); + [cof, dCof] = cofactor3D([],Mesh,doDerivative,matrixFree); + % compute areas + area = [ + cof{1}(yc).^2+cof{4}(yc).^2+cof{7}(yc).^2; + cof{2}(yc).^2+cof{5}(yc).^2+cof{8}(yc).^2; + cof{3}(yc).^2+cof{6}(yc).^2+cof{9}(yc).^2; + ]; + % compute penalty + [H,dH,d2H] = phiDW(area,doDerivative); + % compute area regularizer + Sarea = alphaArea * repmat(vol,[3 1])'*H; + + if doDerivative + dH = reshape(dH,[],3); + d2H = reshape(d2H,[],3); + dAadj = @(x,i) 2*(dCof.dCofadj{i}(x.*cof{i}(yc),yc) + dCof.dCofadj{i+3}(x.*cof{i+3}(yc),yc) + dCof.dCofadj{i+6}(x.*cof{i+6}(yc),yc)); + dSarea = zeros(1,Mesh.nnodes*dim); + for i=1:3 + dSarea = dSarea + alphaArea*dAadj(vol.*dH(:,i),i)'; + end + + dA = @(x,i) 2*(cof{i}(yc).*dCof.dCof{i}(x,yc) + cof{i+3}(yc).*dCof.dCof{i+3}(x,yc) + cof{i+6}(yc).*dCof.dCof{i+6}(x,yc)); + d2Sarea = @(x) dAadj(alphaArea*vol.*d2H(:,1).*dA(reshape(x,[],3),1),1) + dAadj(alphaArea*vol.*d2H(:,2).*dA(reshape(x,[],3),2),2) + dAadj(alphaArea*vol.*d2H(:,3).*dA(reshape(x,[],3),3),3); + + end + + else + Sarea = 0; + dSarea = 0; + d2Sarea = 0; + end + + % volume regularizer + if dim==2 + % volume term + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; + yc = reshape(yc,[],2); + By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; + det = By(:,1).*By(:,4) - By(:,3) .* By(:,2); + [G,dG,d2G] = psi(det,doDerivative); + Svolume = alphaVolume*sum(Mesh.vol.*G); + + if doDerivative + + dDet = @(x) By(:,4).*dx1.D(x(:,1))- By(:,3).*dx2.D(x(:,1))... + -By(:,2).*dx1.D(x(:,2))+By(:,1).*dx2.D(x(:,2)); + + dDetadj = @(x) [ ... + dx1.Dadj(By(:,4).*x)-dx2.Dadj(By(:,3).*x);... + -dx1.Dadj(By(:,2).*x)+dx2.Dadj(By(:,1).*x)]; + + dSvolume = alphaVolume * transpose(dDetadj(dG.*Mesh.vol)); + + d2Svolume = @(x) dDetadj(vol.*d2G.*dDet(reshape(x,[],2))); + + end + + else + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; + det = dx1.D(yc(:,1)).*cof{1}(yc) + dx2.D(yc(:,1)).*cof{2}(yc) + dx3.D(yc(:,1)).*cof{3}(yc); + [G,dG,d2G] = psi(det,doDerivative); + Svolume = alphaVolume*sum(Mesh.vol.*G); + + if doDerivative + + dDet = @(x) cof{1}(yc).*dx1.D(x(:,1)) + cof{2}(yc).*dx2.D(x(:,1)) + cof{3}(yc).*dx3.D(x(:,1)) +... + cof{4}(yc).*dx1.D(x(:,2)) + cof{5}(yc).*dx2.D(x(:,2)) + cof{6}(yc).*dx3.D(x(:,2)) +... + cof{7}(yc).*dx1.D(x(:,3)) + cof{8}(yc).*dx2.D(x(:,3)) + cof{9}(yc).*dx3.D(x(:,3)); + + dDetadj = @(x) [ ... + dx1.Dadj(cof{1}(yc).*x) + dx2.Dadj(cof{2}(yc).*x) + dx3.Dadj(cof{3}(yc).*x);... + dx1.Dadj(cof{4}(yc).*x) + dx2.Dadj(cof{5}(yc).*x) + dx3.Dadj(cof{6}(yc).*x);... + dx1.Dadj(cof{7}(yc).*x) + dx2.Dadj(cof{8}(yc).*x) + dx3.Dadj(cof{9}(yc).*x) + ]; + + dSvolume = alphaVolume * transpose(dDetadj(dG.*Mesh.vol)); + + d2Svolume = @(x) alphaVolume * dDetadj(vol.*d2G.*dDet(reshape(x,[],3))); + + end + + end + Sc = Slength +Sarea + Svolume; if doDerivative - dDet = @(x) [ ... - dx1.Dadj(By(:,4).*x)-dx2.Dadj(By(:,3).*x);... - -dx1.Dadj(By(:,2).*x)+dx2.Dadj(By(:,1).*x)]; - dSvol = alphaVolume * transpose(dDet(dG.*Mesh.vol) ); + if dim==3 + dS = dSlength + dSarea + dSvolume; + d2S.d2S = @(x) d2Slength(x) + d2Sarea(x) + d2Svolume(x); + elseif dim==2 + dS = dSlength + dSvolume; + d2S.d2S = @(x) d2Slength(x) + d2Svolume(x); + end + end + + +end - dS = dSlength + dSvol; +function [cof,dCof] = cofactor3D(By,Mesh,doDerivative,matrixFree) + +if ~matrixFree + + dCof = []; + D = @(i,j) By(:,(j-1)*3+i); % gets partial_i y^j + cof = [ + D(2,2).*D(3,3)-D(3,2).*D(2,3),...%ok + -D(1,2).*D(3,3)+D(3,2).*D(1,3),...%trouble + D(1,2).*D(2,3)-D(2,2).*D(1,3),...%ok + -D(2,1).*D(3,3)+D(3,1).*D(2,3),...%ok + D(1,1).*D(3,3)-D(3,1).*D(1,3),...%ok + -D(1,1).*D(2,3)+D(2,1).*D(1,3),...%ok + D(2,1).*D(3,2)-D(3,1).*D(2,2),...%ok + -D(1,1).*D(3,2)+D(3,1).*D(1,2),...%ok + D(1,1).*D(2,2)-D(2,1).*D(1,2)... %ok + ]; - d2S.Dy = By; - d2S.d2G = d2G; + if doDerivative + D1 = Mesh.dx1; D2 = Mesh.dx2; D3 = Mesh.dx3; + Z = sparse(size(D1,1), size(D2,2)); + D = @(i,j) sdiag(By(:,(j-1)*3+i)); + + dCof{1} = [ Z , D(3,3)*D2-D(2,3)*D3, D(2,2)*D3-D(3,2)*D2]; + dCof{2} = [ Z , D(1,3)*D3-D(3,3)*D1, D(3,2)*D1-D(1,2)*D3]; + dCof{3} = [ Z , D(2,3)*D1-D(1,3)*D2, D(1,2)*D2-D(2,2)*D1]; + dCof{4} = [ D(2,3)*D3-D(3,3)*D2, Z , D(3,1)*D2-D(2,1)*D3]; + dCof{5} = [ D(3,3)*D1-D(1,3)*D3, Z , D(1,1)*D3-D(3,1)*D1]; + dCof{6} = [ D(1,3)*D2-D(2,3)*D1, Z , D(2,1)*D1-D(1,1)*D2]; + dCof{7} = [ D(3,2)*D2-D(2,2)*D3 , D(2,1)*D3-D(3,1)*D2, Z]; + dCof{8} = [ D(1,2)*D3-D(3,2)*D1 , D(3,1)*D1-D(1,1)*D3, Z]; + dCof{9} = [ D(2,2)*D1-D(1,2)*D2 , D(1,1)*D2-D(2,1)*D1, Z]; end + +else + + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; + + cof{1} = @(yc) dx2.D(yc(:,2)).*dx3.D(yc(:,3)) - dx3.D(yc(:,2)).*dx2.D(yc(:,3)); + cof{2} = @(yc) -dx1.D(yc(:,2)).*dx3.D(yc(:,3)) + dx3.D(yc(:,2)).*dx1.D(yc(:,3)); + cof{3} = @(yc) dx1.D(yc(:,2)).*dx2.D(yc(:,3)) - dx2.D(yc(:,2)).*dx1.D(yc(:,3)); + cof{4} = @(yc) -dx2.D(yc(:,1)).*dx3.D(yc(:,3)) + dx3.D(yc(:,1)).*dx2.D(yc(:,3)); + cof{5} = @(yc) dx1.D(yc(:,1)).*dx3.D(yc(:,3)) - dx3.D(yc(:,1)).*dx1.D(yc(:,3)); + cof{6} = @(yc) -dx1.D(yc(:,1)).*dx2.D(yc(:,3)) + dx2.D(yc(:,1)).*dx1.D(yc(:,3)); + cof{7} = @(yc) dx2.D(yc(:,1)).*dx3.D(yc(:,2)) - dx3.D(yc(:,1)).*dx2.D(yc(:,2)); + cof{8} = @(yc) -dx1.D(yc(:,1)).*dx3.D(yc(:,2)) + dx3.D(yc(:,1)).*dx1.D(yc(:,2)); + cof{9} = @(yc) dx1.D(yc(:,1)).*dx2.D(yc(:,2)) - dx2.D(yc(:,1)).*dx1.D(yc(:,2)); -end + if doDerivative - function [cof,dCof] = cofactor3D(By,Mesh,doDerivative) -dCof = []; -D = @(i,j) By(:,(j-1)*3+i); % gets partial_i y^j -cof = [ - D(2,2).*D(3,3)-D(3,2).*D(2,3),...%ok - -D(1,2).*D(3,3)+D(3,2).*D(1,3),...%trouble - D(1,2).*D(2,3)-D(2,2).*D(1,3),...%ok - -D(2,1).*D(3,3)+D(3,1).*D(2,3),...%ok - D(1,1).*D(3,3)-D(3,1).*D(1,3),...%ok - -D(1,1).*D(2,3)+D(2,1).*D(1,3),...%ok - D(2,1).*D(3,2)-D(3,1).*D(2,2),...%ok - -D(1,1).*D(3,2)+D(3,1).*D(1,2),...%ok - D(1,1).*D(2,2)-D(2,1).*D(1,2)... %ok - ]; + dx{1}.D = Mesh.mfdx1.D; dx{1}.Dadj = Mesh.mfdx1.Dadj; + dx{2}.D = Mesh.mfdx2.D; dx{2}.Dadj = Mesh.mfdx2.Dadj; + dx{3}.D = Mesh.mfdx3.D; dx{3}.Dadj = Mesh.mfdx3.Dadj; + + % adjoint/transpose of an element of dCof matrix + dCofadjele = @(i,j,k,x,yc) dx{i}.Dadj(dx{j}.D(yc(:,k)).*x); + + dCof.dCofadj{1} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(2,3,3,x,yc)-dCofadjele(3,2,3,x,yc); dCofadjele(3,2,2,x,yc)-dCofadjele(2,3,2,x,yc)]; + dCof.dCofadj{2} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(3,1,3,x,yc)-dCofadjele(1,3,3,x,yc); dCofadjele(1,3,2,x,yc)-dCofadjele(3,1,2,x,yc)]; + dCof.dCofadj{3} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(1,2,3,x,yc)-dCofadjele(2,1,3,x,yc); dCofadjele(2,1,2,x,yc)-dCofadjele(1,2,2,x,yc)]; + + dCof.dCofadj{4} = @(x,yc) [dCofadjele(3,2,3,x,yc)-dCofadjele(2,3,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(2,3,1,x,yc)-dCofadjele(3,2,1,x,yc)]; + dCof.dCofadj{5} = @(x,yc) [dCofadjele(1,3,3,x,yc)-dCofadjele(3,1,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(3,1,1,x,yc)-dCofadjele(1,3,1,x,yc)]; + dCof.dCofadj{6} = @(x,yc) [dCofadjele(2,1,3,x,yc)-dCofadjele(1,2,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(1,2,1,x,yc)-dCofadjele(2,1,1,x,yc)]; + + dCof.dCofadj{7} = @(x,yc) [dCofadjele(2,3,2,x,yc)-dCofadjele(3,2,2,x,yc); dCofadjele(3,2,1,x,yc)-dCofadjele(2,3,1,x,yc); zeros(Mesh.nnodes,1)]; + dCof.dCofadj{8} = @(x,yc) [dCofadjele(3,1,2,x,yc)-dCofadjele(1,3,2,x,yc); dCofadjele(1,3,1,x,yc)-dCofadjele(3,1,1,x,yc); zeros(Mesh.nnodes,1)]; + dCof.dCofadj{9} = @(x,yc) [dCofadjele(1,2,2,x,yc)-dCofadjele(2,1,2,x,yc); dCofadjele(2,1,1,x,yc)-dCofadjele(1,2,1,x,yc); zeros(Mesh.nnodes,1)]; + + % element of dCof matrix + dCofele = @(i,j,k,l,x,yc) dx{i}.D(yc(:,j)).*dx{k}.D(x(:,l)); -if doDerivative - D1 = Mesh.dx1; D2 = Mesh.dx2; D3 = Mesh.dx3; - Z = sparse(size(D1,1), size(D2,2)); - D = @(i,j) sdiag(By(:,(j-1)*3+i)); + dCof.dCof{1} = @(x,yc) dCofele(3,3,2,2,x,yc)-dCofele(2,3,3,2,x,yc) + dCofele(2,2,3,3,x,yc) - dCofele(3,2,2,3,x,yc); + dCof.dCof{2} = @(x,yc) dCofele(1,3,3,2,x,yc)-dCofele(3,3,1,2,x,yc) + dCofele(3,2,1,3,x,yc) - dCofele(1,2,3,3,x,yc); + dCof.dCof{3} = @(x,yc) dCofele(2,3,1,2,x,yc)-dCofele(1,3,2,2,x,yc) + dCofele(1,2,2,3,x,yc) - dCofele(2,2,1,3,x,yc); + + dCof.dCof{4} = @(x,yc) dCofele(2,3,3,1,x,yc)-dCofele(3,3,2,1,x,yc) + dCofele(3,1,2,3,x,yc) - dCofele(2,1,3,3,x,yc); + dCof.dCof{5} = @(x,yc) dCofele(3,3,1,1,x,yc)-dCofele(1,3,3,1,x,yc) + dCofele(1,1,3,3,x,yc) - dCofele(3,1,1,3,x,yc); + dCof.dCof{6} = @(x,yc) dCofele(1,3,2,1,x,yc)-dCofele(2,3,1,1,x,yc) + dCofele(2,1,1,3,x,yc) - dCofele(1,1,2,3,x,yc); + + dCof.dCof{7} = @(x,yc) dCofele(3,2,2,1,x,yc)-dCofele(2,2,3,1,x,yc) + dCofele(2,1,3,2,x,yc) - dCofele(3,1,2,2,x,yc); + dCof.dCof{8} = @(x,yc) dCofele(1,2,3,1,x,yc)-dCofele(3,2,1,1,x,yc) + dCofele(3,1,1,2,x,yc) - dCofele(1,1,3,2,x,yc); + dCof.dCof{9} = @(x,yc) dCofele(2,2,1,1,x,yc)-dCofele(1,2,2,1,x,yc) + dCofele(1,1,2,2,x,yc) - dCofele(2,1,1,2,x,yc); + + end - dCof{1} = [ Z , D(3,3)*D2-D(2,3)*D3, D(2,2)*D3-D(3,2)*D2]; - dCof{2} = [ Z , D(1,3)*D3-D(3,3)*D1, D(3,2)*D1-D(1,2)*D3]; - dCof{3} = [ Z , D(2,3)*D1-D(1,3)*D2, D(1,2)*D2-D(2,2)*D1]; - dCof{4} = [ D(2,3)*D3-D(3,3)*D2, Z , D(3,1)*D2-D(2,1)*D3]; - dCof{5} = [ D(3,3)*D1-D(1,3)*D3, Z , D(1,1)*D3-D(3,1)*D1]; - dCof{6} = [ D(1,3)*D2-D(2,3)*D1, Z , D(2,1)*D1-D(1,1)*D2]; - dCof{7} = [ D(3,2)*D2-D(2,2)*D3 , D(2,1)*D3-D(3,1)*D2, Z]; - dCof{8} = [ D(1,2)*D3-D(3,2)*D1 , D(3,1)*D1-D(1,1)*D3, Z]; - dCof{9} = [ D(2,2)*D1-D(1,2)*D2 , D(1,1)*D2-D(2,1)*D1, Z]; end - function D = getDiagVolume(Mesh,yc,alphaVolume) dim = Mesh.dim; vol = Mesh.vol; @@ -411,3 +542,8 @@ fctn = @(y) feval(mfilename,y-xn(:),xn(:),Mesh,regOptn{:},'matrixFree',0); [Sc, dS, d2S] = fctn(yn(:)); checkDerivative(fctn,yn(:)); + +fctn = @(y) feval(mfilename,y-xn(:),xn(:),Mesh,regOptn{:},'matrixFree',1); +[ScMF, dSMF, d2SMF] = fctn(yn(:)); + + From 5a48a754f8513fefab6b3e38ffb401684c7635b8 Mon Sep 17 00:00:00 2001 From: Hari Om Aggraval Date: Fri, 15 Sep 2017 17:19:50 +0200 Subject: [PATCH 13/16] MatrixFree 3D - diag of hessian MatrixFree code for diagonal of Hessian matrix is implemented. We may have an issue in the implementation. - if we set only alphaVolume parameter to check the accuracy of Matrixfree code with MB code, there is a slight error in the calculation. You can run hyperelastic.m to see the error norm. It appears that the differences are high only for few nodes. These nodes varies with different yc/yn values. Generally, d2Svolume has very high values. Small numerical errors in least decimal points are probably showing up. These are few quick observations. --- add-ons/FAIRFEM/hyperElasticFEM.m | 207 +++++++++++++++++++++++++++--- 1 file changed, 192 insertions(+), 15 deletions(-) diff --git a/add-ons/FAIRFEM/hyperElasticFEM.m b/add-ons/FAIRFEM/hyperElasticFEM.m index 4a11a0f..d3a6eb4 100755 --- a/add-ons/FAIRFEM/hyperElasticFEM.m +++ b/add-ons/FAIRFEM/hyperElasticFEM.m @@ -103,7 +103,6 @@ d2Sarea = d2Sarea + dA'*sdiag(alphaArea*vol.*d2H(:,i))*dA; end clear dA dH d2H -% dCof{4:9} = []; end else @@ -127,10 +126,15 @@ det = By(:,1).*cof(:,1)+By(:,2).*cof(:,2)+By(:,3).*cof(:,3); if doDerivative, - Z = sparse(size(D1,1),size(D1,2)); + %Z = sparse(size(D1,1),size(D1,2)); % simple product rule - dDet = [sdiag(cof(:,1))*D1 + sdiag(cof(:,2))*D2 + sdiag(cof(:,3))*D3,Z,Z]... - + sdiag(By(:,1))*dCof{1} + sdiag(By(:,2))*dCof{2} + sdiag(By(:,3))*dCof{3}; + %dDet = [sdiag(cof(:,1))*D1 + sdiag(cof(:,2))*D2 + sdiag(cof(:,3))*D3,Z,Z]... + % + sdiag(By(:,1))*dCof{1} + sdiag(By(:,2))*dCof{2} + sdiag(By(:,3))*dCof{3}; + + dDet = [sdiag(cof(:,1))*D1 + sdiag(cof(:,2))*D2 + sdiag(cof(:,3))*D3,... + sdiag(cof(:,4))*D1 + sdiag(cof(:,5))*D2 + sdiag(cof(:,6))*D3,... + sdiag(cof(:,7))*D1 + sdiag(cof(:,8))*D2 + sdiag(cof(:,9))*D3]; + end end [G,dG,d2G] = psi(det,doDerivative); @@ -163,9 +167,8 @@ % give seperate handles for diagonals of length, area and volume d2S.diagLength = @(Mesh) getDiagLength(Mesh,alphaLength); - d2S.diagArea = [];%@(Mesh) getDiagArea(Mesh,alphaLength); + d2S.diagArea = @(Mesh) getDiagArea(Mesh,yc,alphaArea); d2S.diagVol = @(Mesh) getDiagVolume(Mesh,yc,alphaVolume); - d2S.diag = @(yc) d2S.diagLength(Mesh) + d2S.diagVol(Mesh); % length regularizer dSlength = transpose( alphaLength* d2S.BTy(repmat(Mesh.vol,[dim^2,1]).*d2S.By(uc,Mesh),Mesh) ); @@ -244,8 +247,8 @@ if doDerivative dDet = @(x) cof{1}(yc).*dx1.D(x(:,1)) + cof{2}(yc).*dx2.D(x(:,1)) + cof{3}(yc).*dx3.D(x(:,1)) +... - cof{4}(yc).*dx1.D(x(:,2)) + cof{5}(yc).*dx2.D(x(:,2)) + cof{6}(yc).*dx3.D(x(:,2)) +... - cof{7}(yc).*dx1.D(x(:,3)) + cof{8}(yc).*dx2.D(x(:,3)) + cof{9}(yc).*dx3.D(x(:,3)); + cof{4}(yc).*dx1.D(x(:,2)) + cof{5}(yc).*dx2.D(x(:,2)) + cof{6}(yc).*dx3.D(x(:,2)) +... + cof{7}(yc).*dx1.D(x(:,3)) + cof{8}(yc).*dx2.D(x(:,3)) + cof{9}(yc).*dx3.D(x(:,3)); dDetadj = @(x) [ ... dx1.Dadj(cof{1}(yc).*x) + dx2.Dadj(cof{2}(yc).*x) + dx3.Dadj(cof{3}(yc).*x);... @@ -266,9 +269,11 @@ if dim==3 dS = dSlength + dSarea + dSvolume; d2S.d2S = @(x) d2Slength(x) + d2Sarea(x) + d2Svolume(x); + d2S.diag = @(yc) d2S.diagLength(Mesh) + d2S.diagArea(Mesh) + d2S.diagVol(Mesh); elseif dim==2 dS = dSlength + dSvolume; d2S.d2S = @(x) d2Slength(x) + d2Svolume(x); + d2S.diag = @(yc) d2S.diagLength(Mesh) + d2S.diagVol(Mesh); end end @@ -304,13 +309,14 @@ dCof{4} = [ D(2,3)*D3-D(3,3)*D2, Z , D(3,1)*D2-D(2,1)*D3]; dCof{5} = [ D(3,3)*D1-D(1,3)*D3, Z , D(1,1)*D3-D(3,1)*D1]; dCof{6} = [ D(1,3)*D2-D(2,3)*D1, Z , D(2,1)*D1-D(1,1)*D2]; - dCof{7} = [ D(3,2)*D2-D(2,2)*D3 , D(2,1)*D3-D(3,1)*D2, Z]; - dCof{8} = [ D(1,2)*D3-D(3,2)*D1 , D(3,1)*D1-D(1,1)*D3, Z]; - dCof{9} = [ D(2,2)*D1-D(1,2)*D2 , D(1,1)*D2-D(2,1)*D1, Z]; + dCof{7} = [ D(3,2)*D2-D(2,2)*D3, D(2,1)*D3-D(3,1)*D2, Z]; + dCof{8} = [ D(1,2)*D3-D(3,2)*D1, D(3,1)*D1-D(1,1)*D3, Z]; + dCof{9} = [ D(2,2)*D1-D(1,2)*D2, D(1,1)*D2-D(2,1)*D1, Z]; end else - + + dCof = []; dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; cof{1} = @(yc) dx2.D(yc(:,2)).*dx3.D(yc(:,3)) - dx3.D(yc(:,2)).*dx2.D(yc(:,3)); @@ -396,12 +402,111 @@ + Mesh.mfPi(vol.*d2G.*(By(:,j).*dphi3(:,i)).*(By(:,l).*dphi3(:,k)),3); % diagonal of Dxi'*Dxi D = [Dxi(1,4)+ Dxi(2,3) - 2*Dxy(1,4,2,3) ;Dxi(1,2)+ Dxi(2,1) - 2*Dxy(1,2,2,1)]; + else - error('nyi'); + dphi = getBasisGradient(Mesh); + dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; dphi4 = dphi{4}; + + [cof, dCof] = cofactor3D([],Mesh,0,1); + yc = reshape(yc,[],3); + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; + det = dx1.D(yc(:,1)).*cof{1}(yc) + dx2.D(yc(:,1)).*cof{2}(yc) + dx3.D(yc(:,1)).*cof{3}(yc); + [~,~,d2G] = psi(det,1); + + % get boundaries + Dxi = @(i,j) Mesh.mfPi(vol.*d2G.*(cof{j}(yc).*dphi1(:,i)).^2,1) ... + + Mesh.mfPi(vol.*d2G.*(cof{j}(yc).*dphi2(:,i)).^2,2) ... + + Mesh.mfPi(vol.*d2G.*(cof{j}(yc).*dphi3(:,i)).^2,3) ... + + Mesh.mfPi(vol.*d2G.*(cof{j}(yc).*dphi4(:,i)).^2,4); % diagonal of Dxi'*Dxi + + Dxy = @(i,j,k,l) Mesh.mfPi(vol.*d2G.*(cof{j}(yc).*dphi1(:,i)).*(cof{l}(yc).*dphi1(:,k)),1) ... % byproduct terms for verifications + + Mesh.mfPi(vol.*d2G.*(cof{j}(yc).*dphi2(:,i)).*(cof{l}(yc).*dphi2(:,k)),2) ... + + Mesh.mfPi(vol.*d2G.*(cof{j}(yc).*dphi3(:,i)).*(cof{l}(yc).*dphi3(:,k)),3) ... + + Mesh.mfPi(vol.*d2G.*(cof{j}(yc).*dphi4(:,i)).*(cof{l}(yc).*dphi4(:,k)),4); % diagonal of Dxi'*Dxi + + D1 = Dxi(1,1)+ Dxi(2,2) + Dxi(3,3) + 2*Dxy(1,1,2,2) + 2*Dxy(1,1,3,3) + 2*Dxy(2,2,3,3); + D2 = Dxi(1,4)+ Dxi(2,5) + Dxi(3,6) + 2*Dxy(1,4,2,5) + 2*Dxy(1,4,3,6) + 2*Dxy(2,5,3,6); + D3 = Dxi(1,7)+ Dxi(2,8) + Dxi(3,9) + 2*Dxy(1,7,2,8) + 2*Dxy(1,7,3,9) + 2*Dxy(2,8,3,9); + + D = [D1;D2;D3]; + end D = alphaVolume*D; +function D = getDiagArea(Mesh,yc,alphaArea) +%dim = Mesh.dim; +vol = Mesh.vol; + +dphi = getBasisGradient(Mesh); +%dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; dphi4 = dphi{4}; + +[cof, ~] = cofactor3D([],Mesh,0,1); +yc = reshape(yc,[],3); +% compute areas +area = [ + cof{1}(yc).^2+cof{4}(yc).^2+cof{7}(yc).^2; + cof{2}(yc).^2+cof{5}(yc).^2+cof{8}(yc).^2; + cof{3}(yc).^2+cof{6}(yc).^2+cof{9}(yc).^2; + ]; +% compute penalty +[~,~,d2H] = phiDW(area,1); +d2H = reshape(d2H,[],3); + +dx{1}.D = Mesh.mfdx1.D; dx{1}.Dadj = Mesh.mfdx1.Dadj; +dx{2}.D = Mesh.mfdx2.D; dx{2}.Dadj = Mesh.mfdx2.Dadj; +dx{3}.D = Mesh.mfdx3.D; dx{3}.Dadj = Mesh.mfdx3.Dadj; + +D = @(i,j) dx{i}.D(yc(:,j)); +%dA = 2*(cof{i}(yc)*dCof{i}+sdiag(cof(:,i+3))*dCof{i+3}+sdiag(cof(:,i+6))*dCof{i+6}); +%vol.*d2H(:,i))*dA; + +% dCof{1} = [ Z , D(3,3)*D2-D(2,3)*D3, D(2,2)*D3-D(3,2)*D2]; +% dCof{2} = [ Z , D(1,3)*D3-D(3,3)*D1, D(3,2)*D1-D(1,2)*D3]; +% dCof{3} = [ Z , D(2,3)*D1-D(1,3)*D2, D(1,2)*D2-D(2,2)*D1]; +% dCof{4} = [ D(2,3)*D3-D(3,3)*D2, Z , D(3,1)*D2-D(2,1)*D3]; +% dCof{5} = [ D(3,3)*D1-D(1,3)*D3, Z , D(1,1)*D3-D(3,1)*D1]; +% dCof{6} = [ D(1,3)*D2-D(2,3)*D1, Z , D(2,1)*D1-D(1,1)*D2]; +% dCof{7} = [ D(3,2)*D2-D(2,2)*D3, D(2,1)*D3-D(3,1)*D2, Z]; +% dCof{8} = [ D(1,2)*D3-D(3,2)*D1, D(3,1)*D1-D(1,1)*D3, Z]; +% dCof{9} = [ D(2,2)*D1-D(1,2)*D2, D(1,1)*D2-D(2,1)*D1, Z]; +Z = zeros(Mesh.ntri,1); +dCof{1} = @(j) [ Z , D(3,3).*dphi{j}(:,2)-D(2,3).*dphi{j}(:,3), D(2,2).*dphi{j}(:,3)-D(3,2).*dphi{j}(:,2)]; +dCof{2} = @(j) [ Z , D(1,3).*dphi{j}(:,3)-D(3,3).*dphi{j}(:,1), D(3,2).*dphi{j}(:,1)-D(1,2).*dphi{j}(:,3)]; +dCof{3} = @(j) [ Z , D(2,3).*dphi{j}(:,1)-D(1,3).*dphi{j}(:,2), D(1,2).*dphi{j}(:,2)-D(2,2).*dphi{j}(:,1)]; +dCof{4} = @(j) [ D(2,3).*dphi{j}(:,3)-D(3,3).*dphi{j}(:,2) , Z , D(3,1).*dphi{j}(:,2)-D(2,1).*dphi{j}(:,3)]; +dCof{5} = @(j) [ D(3,3).*dphi{j}(:,1)-D(1,3).*dphi{j}(:,3) , Z , D(1,1).*dphi{j}(:,3)-D(3,1).*dphi{j}(:,1)]; +dCof{6} = @(j) [ D(1,3).*dphi{j}(:,2)-D(2,3).*dphi{j}(:,1) , Z , D(2,1).*dphi{j}(:,1)-D(1,1).*dphi{j}(:,2)]; +dCof{7} = @(j) [ D(3,2).*dphi{j}(:,2)-D(2,2).*dphi{j}(:,3) , D(2,1).*dphi{j}(:,3)-D(3,1).*dphi{j}(:,2), Z]; +dCof{8} = @(j) [ D(1,2).*dphi{j}(:,3)-D(3,2).*dphi{j}(:,1) , D(3,1).*dphi{j}(:,1)-D(1,1).*dphi{j}(:,3), Z]; +dCof{9} = @(j) [ D(2,2).*dphi{j}(:,1)-D(1,2).*dphi{j}(:,2) , D(1,1).*dphi{j}(:,2)-D(2,1).*dphi{j}(:,1), Z]; + +% vol.*d2H(:,i))*2*cof{i}(yc)*dCof{i} + +coeff = @(i,j) 4.*vol.*d2H(:,i).*cof{j}(yc).^2; + +Dxi = @(i,j) Mesh.mfPi(coeff(i,j).*dCof{j}(1).^2,1) ... + + Mesh.mfPi(coeff(i,j).*dCof{j}(2).^2,2) ... + + Mesh.mfPi(coeff(i,j).*dCof{j}(3).^2,3) ... + + Mesh.mfPi(coeff(i,j).*dCof{j}(4).^2,4); % diagonal of Dxi'*Dxi + +coeff2 = @(i,j,k) 4.*vol.*d2H(:,i).*cof{j}(yc).*cof{k}(yc); + +Dxy = @(i,j,k) Mesh.mfPi(coeff2(i,j,k).*dCof{j}(1).*dCof{k}(1),1) ... + + Mesh.mfPi(coeff2(i,j,k).*dCof{j}(2).*dCof{k}(2),2) ... + + Mesh.mfPi(coeff2(i,j,k).*dCof{j}(3).*dCof{k}(3),3) ... + + Mesh.mfPi(coeff2(i,j,k).*dCof{j}(4).*dCof{k}(4),4); % diagonal of Dxi'*Dxi + +D = zeros(Mesh.nnodes,3); +for i=1:3 + D = D + Dxi(i,i) + Dxi(i,i+3) + Dxi(i,i+6) + 2*Dxy(i,i,i+3) + 2*Dxy(i,i,i+6) + 2*Dxy(i,i+3,i+6); +end + +D = alphaArea*D(:); + + + + % compute d2Svol*x function By = volumeOperator(yc,Mesh,x,vol) [dx1, dx2] = getGradientMatrixFEM(Mesh,1); @@ -445,11 +550,70 @@ D = Dxi(1)+ Dxi(2); D = [D;D]; else - error('nyi'); + dphi = getBasisGradient(Mesh); + dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; dphi4 = dphi{4}; + + % get boundaries + Dxi = @(i) Mesh.mfPi(vol.*dphi1(:,i).^2,1) + ... + Mesh.mfPi(vol.*dphi2(:,i).^2,2) + ... + Mesh.mfPi(vol.*dphi3(:,i).^2,3) + ... + Mesh.mfPi(vol.*dphi4(:,i).^2,4); % diagonal of Dx1'*Dx1 + + D = Dxi(1)+ Dxi(2) + Dxi(3); + D = [D;D;D]; + end D = alphaLength*D(:); +function [dphi] = getBasisGradient(Mesh) +xn = Mesh.xn; +vol = Mesh.vol; +if Mesh.dim == 3 +% compute edges + v1 = Mesh.mfPi(xn,1); + v2 = Mesh.mfPi(xn,2); + v3 = Mesh.mfPi(xn,3); + v4 = Mesh.mfPi(xn,4); + e1 = v1 - v4; + e2 = v2 - v4; + e3 = v3 - v4; + % compute inverse transformation to reference element + cofA = [ + e2(:,2).*e3(:,3)-e2(:,3).*e3(:,2), ... + -(e1(:,2).*e3(:,3)-e1(:,3).*e3(:,2)), ... + e1(:,2).*e2(:,3)-e1(:,3).*e2(:,2), ... + -(e2(:,1).*e3(:,3)-e2(:,3).*e3(:,1)), ... + e1(:,1).*e3(:,3)-e1(:,3).*e3(:,1), ... + -(e1(:,1).*e2(:,3)-e1(:,3).*e2(:,1)), ... + e2(:,1).*e3(:,2)-e2(:,2).*e3(:,1), ... + -(e1(:,1).*e3(:,2)-e1(:,2).*e3(:,1)), ... + e1(:,1).*e2(:,2)-e1(:,2).*e2(:,1), ... + ]; + detA = e1(:,1).*cofA(:,1) + e2(:,1).*cofA(:,2)+ e3(:,1).*cofA(:,3); + + + % compute gradients of basis functions + dphi{1} = cofA(:,[1 4 7])./repmat(detA,[1 3]); + dphi{2} = cofA(:,[2 5 8])./repmat(detA,[1 3]); + dphi{3} = cofA(:,[3 6 9])./repmat(detA,[1 3]); + dphi{4} = -dphi{1} - dphi{2} - dphi{3}; + +else + + % compute edges + x1 = Mesh.mfPi(xn,1); + x2 = Mesh.mfPi(xn,2); + x3 = Mesh.mfPi(xn,3); + e1 = x1 - x3; + e2 = x2 - x3; + + % compute gradients of basis functions + dphi{1} = [ e2(:,2) -e2(:,1)]./[2*vol,2*vol]; + dphi{2} = [-e1(:,2) e1(:,1)]./[2*vol,2*vol]; + dphi{3} = -dphi{1} - dphi{2}; + +end function [G dG d2G] = psi(x,doDerivative) % @@ -533,11 +697,12 @@ %========== 3D omega = [0,10,0,8,0 4]; m = [5,6,8]; type = 1; +%omega = [0,5,0,5,0 5]; m = [5,5,5]; type = 1; Mesh = TetraMesh1(omega,m); xn = Mesh.xn; yn = xn + 1e-1* randn(size(xn)); -regOptn = {'alpha',1,'alphaLength',0,'alphaArea',1,'alphaVolume',0}; +regOptn = {'alpha',1,'alphaLength',0,'alphaArea',0,'alphaVolume',1}; fctn = @(y) feval(mfilename,y-xn(:),xn(:),Mesh,regOptn{:},'matrixFree',0); [Sc, dS, d2S] = fctn(yn(:)); @@ -546,4 +711,16 @@ fctn = @(y) feval(mfilename,y-xn(:),xn(:),Mesh,regOptn{:},'matrixFree',1); [ScMF, dSMF, d2SMF] = fctn(yn(:)); +% error MB - MF +errdS = norm(dS - dSMF) + +z = rand(3*Mesh.nnodes,1); +errd2S = norm(d2S*z - d2SMF.d2S(z)) + +errDiag = norm(diag(d2S) - d2SMF.diag(yn)) + +ans + + + From 5c14fcfa390f084996c8d6aeaf3c02e46db22d2e Mon Sep 17 00:00:00 2001 From: Hari Om Aggraval Date: Fri, 15 Sep 2017 18:47:32 +0200 Subject: [PATCH 14/16] MatrixFree Code .. Running! Most of the pieces required for MatrixFree code are completed now. Run EFEM_FEMPIRE_Mice3D.m. I have not done rigorous testing so far. Specially for 3D code, few of the calculations are being done multiple times. May be we can restructure the code little bit to reduce computational time. --- add-ons/FAIRFEM/FEMPIREobjFctn.m | 269 +++++++++++++++--- .../FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m | 4 + 2 files changed, 241 insertions(+), 32 deletions(-) diff --git a/add-ons/FAIRFEM/FEMPIREobjFctn.m b/add-ons/FAIRFEM/FEMPIREobjFctn.m index 9530e5e..14ba390 100755 --- a/add-ons/FAIRFEM/FEMPIREobjFctn.m +++ b/add-ons/FAIRFEM/FEMPIREobjFctn.m @@ -163,42 +163,247 @@ function D = getDiag(Mesh,det,Tc,dT,yc) vol = Mesh.vol; +dim = Mesh.dim; -% first term -D1 = Mesh.mfPi(vol.*(det.*dT).^2,'C'); -D1 = D1(:)./3; +if dim == 2 -% second term + % first term + D1 = Mesh.mfPi(vol.*(det.*dT).^2,'C'); + D1 = D1(:)./3; + + % second term + xn = Mesh.xn; + % get edges + e1 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,3); + e2 = Mesh.mfPi(xn,2) - Mesh.mfPi(xn,3); + e3 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,2); + + % compute gradients of basis functions + dphi1 = ([ e2(:,2) -e2(:,1)]./[2*vol,2*vol]); + dphi2 = ([-e1(:,2) e1(:,1)]./[2*vol,2*vol]); + dphi3 = ([ e3(:,2) -e3(:,1)]./[2*vol,2*vol]); + + % compute diagonal of volume regularizer + % MB : dDet = [sdiag(By(:,4)), sdiag(-By(:,3)) , sdiag(-By(:,2)), sdiag(By(:,1))] * B; + [dx1, dx2] = getGradientMatrixFEM(Mesh,1); + yc = reshape(yc,[],2); + By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; + + % get boundaries + Dxi = @(i,j) Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi1(:,i)).^2,1) ... + + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi2(:,i)).^2,2) ... + + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi3(:,i)).^2,3); % diagonal of Dxi'*Dxi + + Dxy = @(i,j,k,l) Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi1(:,i)).*(Tc.*By(:,l).*dphi1(:,k)),1) ... % byproduct terms for verifications + + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi2(:,i)).*(Tc.*By(:,l).*dphi2(:,k)),2) ... + + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi3(:,i)).*(Tc.*By(:,l).*dphi3(:,k)),3); % diagonal of Dxi'*Dxi + + D2 = [Dxi(1,4)+ Dxi(2,3) - 2*Dxy(1,4,2,3) ;Dxi(1,2)+ Dxi(2,1) - 2*Dxy(1,2,2,1)]; + + % third byproduct term + D3 = [(Mesh.mfPi(vol.*((1/3)*det.*dT(:,1)).*Tc.*(By(:,4).*dphi1(:,1) - By(:,3).*dphi1(:,2)),1)) + ... + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,1)).*Tc.*(By(:,4).*dphi2(:,1) - By(:,3).*dphi2(:,2)),2)) + ... + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,1)).*Tc.*(By(:,4).*dphi3(:,1) - By(:,3).*dphi3(:,2)),3)) ;... + + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,2)).*Tc.*(By(:,1).*dphi1(:,2) - By(:,2).*dphi1(:,1)),1)) + ... + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,2)).*Tc.*(By(:,1).*dphi2(:,2) - By(:,2).*dphi2(:,1)),2)) + ... + (Mesh.mfPi(vol.*((1/3)*det.*dT(:,2)).*Tc.*(By(:,1).*dphi3(:,2) - By(:,2).*dphi3(:,1)),3))]; + + D = D1 + D2 + 2*D3; + +else + + % first term + D1 = Mesh.mfPi(vol.*(det.*dT).^2,'C'); + D1 = D1(:)./4; + + + dphi = getBasisGradient(Mesh); + dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; dphi4 = dphi{4}; + + [cof, dCof] = cofactor3D([],Mesh,0,1); + yc = reshape(yc,[],3); + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; + %det = dx1.D(yc(:,1)).*cof{1}(yc) + dx2.D(yc(:,1)).*cof{2}(yc) + dx3.D(yc(:,1)).*cof{3}(yc); + + % get boundaries + Dxi = @(i,j) Mesh.mfPi(vol.*(Tc.*cof{j}(yc).*dphi1(:,i)).^2,1) ... + + Mesh.mfPi(vol.*(Tc.*cof{j}(yc).*dphi2(:,i)).^2,2) ... + + Mesh.mfPi(vol.*(Tc.*cof{j}(yc).*dphi3(:,i)).^2,3) ... + + Mesh.mfPi(vol.*(Tc.*cof{j}(yc).*dphi4(:,i)).^2,4); % diagonal of Dxi'*Dxi + + Dxy = @(i,j,k,l) Mesh.mfPi(vol.*(Tc.*cof{j}(yc).*dphi1(:,i)).*(Tc.*cof{l}(yc).*dphi1(:,k)),1) ... % byproduct terms for verifications + + Mesh.mfPi(vol.*(Tc.*cof{j}(yc).*dphi2(:,i)).*(Tc.*cof{l}(yc).*dphi2(:,k)),2) ... + + Mesh.mfPi(vol.*(Tc.*cof{j}(yc).*dphi3(:,i)).*(Tc.*cof{l}(yc).*dphi3(:,k)),3) ... + + Mesh.mfPi(vol.*(Tc.*cof{j}(yc).*dphi4(:,i)).*(Tc.*cof{l}(yc).*dphi4(:,k)),4); % diagonal of Dxi'*Dxi + + D21 = Dxi(1,1)+ Dxi(2,2) + Dxi(3,3) + 2*Dxy(1,1,2,2) + 2*Dxy(1,1,3,3) + 2*Dxy(2,2,3,3); + D22 = Dxi(1,4)+ Dxi(2,5) + Dxi(3,6) + 2*Dxy(1,4,2,5) + 2*Dxy(1,4,3,6) + 2*Dxy(2,5,3,6); + D23 = Dxi(1,7)+ Dxi(2,8) + Dxi(3,9) + 2*Dxy(1,7,2,8) + 2*Dxy(1,7,3,9) + 2*Dxy(2,8,3,9); + + D2 = [D21;D22;D23]; + + % third term + D3 = [(Mesh.mfPi(vol.*((1/4)*det.*dT(:,1)).*Tc.*(cof{1}(yc).*dphi1(:,1) + cof{2}(yc).*dphi1(:,2) + cof{3}(yc).*dphi1(:,3)),1)) + ... + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,1)).*Tc.*(cof{1}(yc).*dphi2(:,1) + cof{2}(yc).*dphi2(:,2) + cof{3}(yc).*dphi2(:,3)),2)) + ... + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,1)).*Tc.*(cof{1}(yc).*dphi3(:,1) + cof{2}(yc).*dphi3(:,2) + cof{3}(yc).*dphi3(:,3)),3)) + ... + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,1)).*Tc.*(cof{1}(yc).*dphi4(:,1) + cof{2}(yc).*dphi4(:,2) + cof{3}(yc).*dphi4(:,3)),4));... + + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,2)).*Tc.*(cof{4}(yc).*dphi1(:,1) + cof{5}(yc).*dphi1(:,2) + cof{6}(yc).*dphi1(:,3)),1)) + ... + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,2)).*Tc.*(cof{4}(yc).*dphi2(:,1) + cof{5}(yc).*dphi2(:,2) + cof{6}(yc).*dphi2(:,3)),2)) + ... + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,2)).*Tc.*(cof{4}(yc).*dphi3(:,1) + cof{5}(yc).*dphi3(:,2) + cof{6}(yc).*dphi3(:,3)),3)) + ... + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,2)).*Tc.*(cof{4}(yc).*dphi4(:,1) + cof{5}(yc).*dphi4(:,2) + cof{6}(yc).*dphi4(:,3)),4));... + + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,3)).*Tc.*(cof{7}(yc).*dphi1(:,1) + cof{8}(yc).*dphi1(:,2) + cof{9}(yc).*dphi1(:,3)),1)) + ... + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,3)).*Tc.*(cof{7}(yc).*dphi2(:,1) + cof{8}(yc).*dphi2(:,2) + cof{9}(yc).*dphi2(:,3)),2)) + ... + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,3)).*Tc.*(cof{7}(yc).*dphi3(:,1) + cof{8}(yc).*dphi3(:,2) + cof{9}(yc).*dphi3(:,3)),3)) + ... + (Mesh.mfPi(vol.*((1/4)*det.*dT(:,3)).*Tc.*(cof{7}(yc).*dphi4(:,1) + cof{8}(yc).*dphi4(:,2) + cof{9}(yc).*dphi4(:,3)),4))]; + + D = D1 + D2 + 2*D3; +end + + +function [dphi] = getBasisGradient(Mesh) xn = Mesh.xn; -% get edges -e1 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,3); -e2 = Mesh.mfPi(xn,2) - Mesh.mfPi(xn,3); -e3 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,2); - -% compute gradients of basis functions -dphi1 = ([ e2(:,2) -e2(:,1)]./[2*vol,2*vol]); -dphi2 = ([-e1(:,2) e1(:,1)]./[2*vol,2*vol]); -dphi3 = ([ e3(:,2) -e3(:,1)]./[2*vol,2*vol]); - -% compute diagonal of volume regularizer -% MB : dDet = [sdiag(By(:,4)), sdiag(-By(:,3)) , sdiag(-By(:,2)), sdiag(By(:,1))] * B; -[dx1, dx2] = getGradientMatrixFEM(Mesh,1); -yc = reshape(yc,[],2); -By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; - -% get boundaries -Dxi = @(i,j) Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi1(:,i)).^2,1) ... - + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi2(:,i)).^2,2) ... - + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi3(:,i)).^2,3); % diagonal of Dxi'*Dxi - -Dxy = @(i,j,k,l) Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi1(:,i)).*(Tc.*By(:,l).*dphi1(:,k)),1) ... % byproduct terms for verifications - + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi2(:,i)).*(Tc.*By(:,l).*dphi2(:,k)),2) ... - + Mesh.mfPi(vol.*(Tc.*By(:,j).*dphi3(:,i)).*(Tc.*By(:,l).*dphi3(:,k)),3); % diagonal of Dxi'*Dxi - -D2 = [Dxi(1,4)+ Dxi(2,3) - 2*Dxy(1,4,2,3) ;Dxi(1,2)+ Dxi(2,1) - 2*Dxy(1,2,2,1)]; - -D = D1 + D2; +vol = Mesh.vol; +if Mesh.dim == 3 +% compute edges + v1 = Mesh.mfPi(xn,1); + v2 = Mesh.mfPi(xn,2); + v3 = Mesh.mfPi(xn,3); + v4 = Mesh.mfPi(xn,4); + e1 = v1 - v4; + e2 = v2 - v4; + e3 = v3 - v4; + % compute inverse transformation to reference element + cofA = [ + e2(:,2).*e3(:,3)-e2(:,3).*e3(:,2), ... + -(e1(:,2).*e3(:,3)-e1(:,3).*e3(:,2)), ... + e1(:,2).*e2(:,3)-e1(:,3).*e2(:,2), ... + -(e2(:,1).*e3(:,3)-e2(:,3).*e3(:,1)), ... + e1(:,1).*e3(:,3)-e1(:,3).*e3(:,1), ... + -(e1(:,1).*e2(:,3)-e1(:,3).*e2(:,1)), ... + e2(:,1).*e3(:,2)-e2(:,2).*e3(:,1), ... + -(e1(:,1).*e3(:,2)-e1(:,2).*e3(:,1)), ... + e1(:,1).*e2(:,2)-e1(:,2).*e2(:,1), ... + ]; + detA = e1(:,1).*cofA(:,1) + e2(:,1).*cofA(:,2)+ e3(:,1).*cofA(:,3); + + + % compute gradients of basis functions + dphi{1} = cofA(:,[1 4 7])./repmat(detA,[1 3]); + dphi{2} = cofA(:,[2 5 8])./repmat(detA,[1 3]); + dphi{3} = cofA(:,[3 6 9])./repmat(detA,[1 3]); + dphi{4} = -dphi{1} - dphi{2} - dphi{3}; + +else + + % compute edges + x1 = Mesh.mfPi(xn,1); + x2 = Mesh.mfPi(xn,2); + x3 = Mesh.mfPi(xn,3); + e1 = x1 - x3; + e2 = x2 - x3; + + % compute gradients of basis functions + dphi{1} = [ e2(:,2) -e2(:,1)]./[2*vol,2*vol]; + dphi{2} = [-e1(:,2) e1(:,1)]./[2*vol,2*vol]; + dphi{3} = -dphi{1} - dphi{2}; + +end + + +function [cof,dCof] = cofactor3D(By,Mesh,doDerivative,matrixFree) + +if ~matrixFree + + dCof = []; + D = @(i,j) By(:,(j-1)*3+i); % gets partial_i y^j + cof = [ + D(2,2).*D(3,3)-D(3,2).*D(2,3),...%ok + -D(1,2).*D(3,3)+D(3,2).*D(1,3),...%trouble + D(1,2).*D(2,3)-D(2,2).*D(1,3),...%ok + -D(2,1).*D(3,3)+D(3,1).*D(2,3),...%ok + D(1,1).*D(3,3)-D(3,1).*D(1,3),...%ok + -D(1,1).*D(2,3)+D(2,1).*D(1,3),...%ok + D(2,1).*D(3,2)-D(3,1).*D(2,2),...%ok + -D(1,1).*D(3,2)+D(3,1).*D(1,2),...%ok + D(1,1).*D(2,2)-D(2,1).*D(1,2)... %ok + ]; + + if doDerivative + D1 = Mesh.dx1; D2 = Mesh.dx2; D3 = Mesh.dx3; + Z = sparse(size(D1,1), size(D2,2)); + D = @(i,j) sdiag(By(:,(j-1)*3+i)); + + dCof{1} = [ Z , D(3,3)*D2-D(2,3)*D3, D(2,2)*D3-D(3,2)*D2]; + dCof{2} = [ Z , D(1,3)*D3-D(3,3)*D1, D(3,2)*D1-D(1,2)*D3]; + dCof{3} = [ Z , D(2,3)*D1-D(1,3)*D2, D(1,2)*D2-D(2,2)*D1]; + dCof{4} = [ D(2,3)*D3-D(3,3)*D2, Z , D(3,1)*D2-D(2,1)*D3]; + dCof{5} = [ D(3,3)*D1-D(1,3)*D3, Z , D(1,1)*D3-D(3,1)*D1]; + dCof{6} = [ D(1,3)*D2-D(2,3)*D1, Z , D(2,1)*D1-D(1,1)*D2]; + dCof{7} = [ D(3,2)*D2-D(2,2)*D3, D(2,1)*D3-D(3,1)*D2, Z]; + dCof{8} = [ D(1,2)*D3-D(3,2)*D1, D(3,1)*D1-D(1,1)*D3, Z]; + dCof{9} = [ D(2,2)*D1-D(1,2)*D2, D(1,1)*D2-D(2,1)*D1, Z]; + end + +else + + dCof = []; + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; + + cof{1} = @(yc) dx2.D(yc(:,2)).*dx3.D(yc(:,3)) - dx3.D(yc(:,2)).*dx2.D(yc(:,3)); + cof{2} = @(yc) -dx1.D(yc(:,2)).*dx3.D(yc(:,3)) + dx3.D(yc(:,2)).*dx1.D(yc(:,3)); + cof{3} = @(yc) dx1.D(yc(:,2)).*dx2.D(yc(:,3)) - dx2.D(yc(:,2)).*dx1.D(yc(:,3)); + cof{4} = @(yc) -dx2.D(yc(:,1)).*dx3.D(yc(:,3)) + dx3.D(yc(:,1)).*dx2.D(yc(:,3)); + cof{5} = @(yc) dx1.D(yc(:,1)).*dx3.D(yc(:,3)) - dx3.D(yc(:,1)).*dx1.D(yc(:,3)); + cof{6} = @(yc) -dx1.D(yc(:,1)).*dx2.D(yc(:,3)) + dx2.D(yc(:,1)).*dx1.D(yc(:,3)); + cof{7} = @(yc) dx2.D(yc(:,1)).*dx3.D(yc(:,2)) - dx3.D(yc(:,1)).*dx2.D(yc(:,2)); + cof{8} = @(yc) -dx1.D(yc(:,1)).*dx3.D(yc(:,2)) + dx3.D(yc(:,1)).*dx1.D(yc(:,2)); + cof{9} = @(yc) dx1.D(yc(:,1)).*dx2.D(yc(:,2)) - dx2.D(yc(:,1)).*dx1.D(yc(:,2)); + + if doDerivative + + dx{1}.D = Mesh.mfdx1.D; dx{1}.Dadj = Mesh.mfdx1.Dadj; + dx{2}.D = Mesh.mfdx2.D; dx{2}.Dadj = Mesh.mfdx2.Dadj; + dx{3}.D = Mesh.mfdx3.D; dx{3}.Dadj = Mesh.mfdx3.Dadj; + + % adjoint/transpose of an element of dCof matrix + dCofadjele = @(i,j,k,x,yc) dx{i}.Dadj(dx{j}.D(yc(:,k)).*x); + + dCof.dCofadj{1} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(2,3,3,x,yc)-dCofadjele(3,2,3,x,yc); dCofadjele(3,2,2,x,yc)-dCofadjele(2,3,2,x,yc)]; + dCof.dCofadj{2} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(3,1,3,x,yc)-dCofadjele(1,3,3,x,yc); dCofadjele(1,3,2,x,yc)-dCofadjele(3,1,2,x,yc)]; + dCof.dCofadj{3} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(1,2,3,x,yc)-dCofadjele(2,1,3,x,yc); dCofadjele(2,1,2,x,yc)-dCofadjele(1,2,2,x,yc)]; + + dCof.dCofadj{4} = @(x,yc) [dCofadjele(3,2,3,x,yc)-dCofadjele(2,3,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(2,3,1,x,yc)-dCofadjele(3,2,1,x,yc)]; + dCof.dCofadj{5} = @(x,yc) [dCofadjele(1,3,3,x,yc)-dCofadjele(3,1,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(3,1,1,x,yc)-dCofadjele(1,3,1,x,yc)]; + dCof.dCofadj{6} = @(x,yc) [dCofadjele(2,1,3,x,yc)-dCofadjele(1,2,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(1,2,1,x,yc)-dCofadjele(2,1,1,x,yc)]; + + dCof.dCofadj{7} = @(x,yc) [dCofadjele(2,3,2,x,yc)-dCofadjele(3,2,2,x,yc); dCofadjele(3,2,1,x,yc)-dCofadjele(2,3,1,x,yc); zeros(Mesh.nnodes,1)]; + dCof.dCofadj{8} = @(x,yc) [dCofadjele(3,1,2,x,yc)-dCofadjele(1,3,2,x,yc); dCofadjele(1,3,1,x,yc)-dCofadjele(3,1,1,x,yc); zeros(Mesh.nnodes,1)]; + dCof.dCofadj{9} = @(x,yc) [dCofadjele(1,2,2,x,yc)-dCofadjele(2,1,2,x,yc); dCofadjele(2,1,1,x,yc)-dCofadjele(1,2,1,x,yc); zeros(Mesh.nnodes,1)]; + + % element of dCof matrix + dCofele = @(i,j,k,l,x,yc) dx{i}.D(yc(:,j)).*dx{k}.D(x(:,l)); + + dCof.dCof{1} = @(x,yc) dCofele(3,3,2,2,x,yc)-dCofele(2,3,3,2,x,yc) + dCofele(2,2,3,3,x,yc) - dCofele(3,2,2,3,x,yc); + dCof.dCof{2} = @(x,yc) dCofele(1,3,3,2,x,yc)-dCofele(3,3,1,2,x,yc) + dCofele(3,2,1,3,x,yc) - dCofele(1,2,3,3,x,yc); + dCof.dCof{3} = @(x,yc) dCofele(2,3,1,2,x,yc)-dCofele(1,3,2,2,x,yc) + dCofele(1,2,2,3,x,yc) - dCofele(2,2,1,3,x,yc); + + dCof.dCof{4} = @(x,yc) dCofele(2,3,3,1,x,yc)-dCofele(3,3,2,1,x,yc) + dCofele(3,1,2,3,x,yc) - dCofele(2,1,3,3,x,yc); + dCof.dCof{5} = @(x,yc) dCofele(3,3,1,1,x,yc)-dCofele(1,3,3,1,x,yc) + dCofele(1,1,3,3,x,yc) - dCofele(3,1,1,3,x,yc); + dCof.dCof{6} = @(x,yc) dCofele(1,3,2,1,x,yc)-dCofele(2,3,1,1,x,yc) + dCofele(2,1,1,3,x,yc) - dCofele(1,1,2,3,x,yc); + + dCof.dCof{7} = @(x,yc) dCofele(3,2,2,1,x,yc)-dCofele(2,2,3,1,x,yc) + dCofele(2,1,3,2,x,yc) - dCofele(3,1,2,2,x,yc); + dCof.dCof{8} = @(x,yc) dCofele(1,2,3,1,x,yc)-dCofele(3,2,1,1,x,yc) + dCofele(3,1,1,2,x,yc) - dCofele(1,1,3,2,x,yc); + dCof.dCof{9} = @(x,yc) dCofele(2,2,1,1,x,yc)-dCofele(1,2,2,1,x,yc) + dCofele(1,1,2,2,x,yc) - dCofele(2,1,1,2,x,yc); + + end + +end + + function runMinimalExample diff --git a/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m b/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m index 127b6e5..6fe1689 100755 --- a/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m +++ b/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m @@ -29,4 +29,8 @@ yc = GaussNewton(fctn,xc(:),'Plots',@FAIRplotsFEM,'solver','mbPCG-Jacobi'); +% matrixfree version +regularizer('reset','regularizer','mfHyperElasticFEM','alpha',1e1); +ycMF = GaussNewton(fctn,xc(:),'Plots',@FAIRplotsFEM,'solver',@FEMPIREsolveGN_PCG); + %showResults(ML,yc,'level',level); From a5f5cc38864e1d90b2004dc22eeae3adb2c1eecf Mon Sep 17 00:00:00 2001 From: Hari Om Aggraval Date: Wed, 27 Sep 2017 14:00:56 +0200 Subject: [PATCH 15/16] Basic changes to improve efficiency Moved getBasisGradient and Cofactor3D functions in a separate script file. Gradient of basis functions are now computed only once in the entire function call, by moving these calculations to MESH structure main file. NOTE: There is a slight difference between estimates coming out from MatrixFree and Non-MatrixFree code, in the 3D case. --- add-ons/FAIRFEM/FEMPIREobjFctn.m | 160 +------------- add-ons/FAIRFEM/cofactor3D.m | 107 ++++++++++ .../FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m | 2 +- add-ons/FAIRFEM/getBasisGradient.m | 67 ++++++ add-ons/FAIRFEM/hyperElasticFEM.m | 201 +++--------------- add-ons/FAIRFEM/meshes/TetraMesh1.m | 12 ++ add-ons/FAIRFEM/meshes/TriMesh1.m | 13 ++ add-ons/FAIRFEM/meshes/TriMesh2.m | 12 ++ add-ons/FAIRFEM/meshes/TriMesh3.m | 14 ++ 9 files changed, 255 insertions(+), 333 deletions(-) create mode 100644 add-ons/FAIRFEM/cofactor3D.m create mode 100644 add-ons/FAIRFEM/getBasisGradient.m diff --git a/add-ons/FAIRFEM/FEMPIREobjFctn.m b/add-ons/FAIRFEM/FEMPIREobjFctn.m index 14ba390..83f8ad4 100755 --- a/add-ons/FAIRFEM/FEMPIREobjFctn.m +++ b/add-ons/FAIRFEM/FEMPIREobjFctn.m @@ -172,17 +172,9 @@ D1 = D1(:)./3; % second term - xn = Mesh.xn; - % get edges - e1 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,3); - e2 = Mesh.mfPi(xn,2) - Mesh.mfPi(xn,3); - e3 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,2); - - % compute gradients of basis functions - dphi1 = ([ e2(:,2) -e2(:,1)]./[2*vol,2*vol]); - dphi2 = ([-e1(:,2) e1(:,1)]./[2*vol,2*vol]); - dphi3 = ([ e3(:,2) -e3(:,1)]./[2*vol,2*vol]); - + dphi = Mesh.dphi; + dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; + % compute diagonal of volume regularizer % MB : dDet = [sdiag(By(:,4)), sdiag(-By(:,3)) , sdiag(-By(:,2)), sdiag(By(:,1))] * B; [dx1, dx2] = getGradientMatrixFEM(Mesh,1); @@ -216,9 +208,8 @@ % first term D1 = Mesh.mfPi(vol.*(det.*dT).^2,'C'); D1 = D1(:)./4; - - dphi = getBasisGradient(Mesh); + dphi = Mesh.dphi; dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; dphi4 = dphi{4}; [cof, dCof] = cofactor3D([],Mesh,0,1); @@ -263,149 +254,6 @@ end -function [dphi] = getBasisGradient(Mesh) - -xn = Mesh.xn; -vol = Mesh.vol; -if Mesh.dim == 3 -% compute edges - v1 = Mesh.mfPi(xn,1); - v2 = Mesh.mfPi(xn,2); - v3 = Mesh.mfPi(xn,3); - v4 = Mesh.mfPi(xn,4); - e1 = v1 - v4; - e2 = v2 - v4; - e3 = v3 - v4; - % compute inverse transformation to reference element - cofA = [ - e2(:,2).*e3(:,3)-e2(:,3).*e3(:,2), ... - -(e1(:,2).*e3(:,3)-e1(:,3).*e3(:,2)), ... - e1(:,2).*e2(:,3)-e1(:,3).*e2(:,2), ... - -(e2(:,1).*e3(:,3)-e2(:,3).*e3(:,1)), ... - e1(:,1).*e3(:,3)-e1(:,3).*e3(:,1), ... - -(e1(:,1).*e2(:,3)-e1(:,3).*e2(:,1)), ... - e2(:,1).*e3(:,2)-e2(:,2).*e3(:,1), ... - -(e1(:,1).*e3(:,2)-e1(:,2).*e3(:,1)), ... - e1(:,1).*e2(:,2)-e1(:,2).*e2(:,1), ... - ]; - detA = e1(:,1).*cofA(:,1) + e2(:,1).*cofA(:,2)+ e3(:,1).*cofA(:,3); - - - % compute gradients of basis functions - dphi{1} = cofA(:,[1 4 7])./repmat(detA,[1 3]); - dphi{2} = cofA(:,[2 5 8])./repmat(detA,[1 3]); - dphi{3} = cofA(:,[3 6 9])./repmat(detA,[1 3]); - dphi{4} = -dphi{1} - dphi{2} - dphi{3}; - -else - - % compute edges - x1 = Mesh.mfPi(xn,1); - x2 = Mesh.mfPi(xn,2); - x3 = Mesh.mfPi(xn,3); - e1 = x1 - x3; - e2 = x2 - x3; - - % compute gradients of basis functions - dphi{1} = [ e2(:,2) -e2(:,1)]./[2*vol,2*vol]; - dphi{2} = [-e1(:,2) e1(:,1)]./[2*vol,2*vol]; - dphi{3} = -dphi{1} - dphi{2}; - -end - - -function [cof,dCof] = cofactor3D(By,Mesh,doDerivative,matrixFree) - -if ~matrixFree - - dCof = []; - D = @(i,j) By(:,(j-1)*3+i); % gets partial_i y^j - cof = [ - D(2,2).*D(3,3)-D(3,2).*D(2,3),...%ok - -D(1,2).*D(3,3)+D(3,2).*D(1,3),...%trouble - D(1,2).*D(2,3)-D(2,2).*D(1,3),...%ok - -D(2,1).*D(3,3)+D(3,1).*D(2,3),...%ok - D(1,1).*D(3,3)-D(3,1).*D(1,3),...%ok - -D(1,1).*D(2,3)+D(2,1).*D(1,3),...%ok - D(2,1).*D(3,2)-D(3,1).*D(2,2),...%ok - -D(1,1).*D(3,2)+D(3,1).*D(1,2),...%ok - D(1,1).*D(2,2)-D(2,1).*D(1,2)... %ok - ]; - - if doDerivative - D1 = Mesh.dx1; D2 = Mesh.dx2; D3 = Mesh.dx3; - Z = sparse(size(D1,1), size(D2,2)); - D = @(i,j) sdiag(By(:,(j-1)*3+i)); - - dCof{1} = [ Z , D(3,3)*D2-D(2,3)*D3, D(2,2)*D3-D(3,2)*D2]; - dCof{2} = [ Z , D(1,3)*D3-D(3,3)*D1, D(3,2)*D1-D(1,2)*D3]; - dCof{3} = [ Z , D(2,3)*D1-D(1,3)*D2, D(1,2)*D2-D(2,2)*D1]; - dCof{4} = [ D(2,3)*D3-D(3,3)*D2, Z , D(3,1)*D2-D(2,1)*D3]; - dCof{5} = [ D(3,3)*D1-D(1,3)*D3, Z , D(1,1)*D3-D(3,1)*D1]; - dCof{6} = [ D(1,3)*D2-D(2,3)*D1, Z , D(2,1)*D1-D(1,1)*D2]; - dCof{7} = [ D(3,2)*D2-D(2,2)*D3, D(2,1)*D3-D(3,1)*D2, Z]; - dCof{8} = [ D(1,2)*D3-D(3,2)*D1, D(3,1)*D1-D(1,1)*D3, Z]; - dCof{9} = [ D(2,2)*D1-D(1,2)*D2, D(1,1)*D2-D(2,1)*D1, Z]; - end - -else - - dCof = []; - dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; - - cof{1} = @(yc) dx2.D(yc(:,2)).*dx3.D(yc(:,3)) - dx3.D(yc(:,2)).*dx2.D(yc(:,3)); - cof{2} = @(yc) -dx1.D(yc(:,2)).*dx3.D(yc(:,3)) + dx3.D(yc(:,2)).*dx1.D(yc(:,3)); - cof{3} = @(yc) dx1.D(yc(:,2)).*dx2.D(yc(:,3)) - dx2.D(yc(:,2)).*dx1.D(yc(:,3)); - cof{4} = @(yc) -dx2.D(yc(:,1)).*dx3.D(yc(:,3)) + dx3.D(yc(:,1)).*dx2.D(yc(:,3)); - cof{5} = @(yc) dx1.D(yc(:,1)).*dx3.D(yc(:,3)) - dx3.D(yc(:,1)).*dx1.D(yc(:,3)); - cof{6} = @(yc) -dx1.D(yc(:,1)).*dx2.D(yc(:,3)) + dx2.D(yc(:,1)).*dx1.D(yc(:,3)); - cof{7} = @(yc) dx2.D(yc(:,1)).*dx3.D(yc(:,2)) - dx3.D(yc(:,1)).*dx2.D(yc(:,2)); - cof{8} = @(yc) -dx1.D(yc(:,1)).*dx3.D(yc(:,2)) + dx3.D(yc(:,1)).*dx1.D(yc(:,2)); - cof{9} = @(yc) dx1.D(yc(:,1)).*dx2.D(yc(:,2)) - dx2.D(yc(:,1)).*dx1.D(yc(:,2)); - - if doDerivative - - dx{1}.D = Mesh.mfdx1.D; dx{1}.Dadj = Mesh.mfdx1.Dadj; - dx{2}.D = Mesh.mfdx2.D; dx{2}.Dadj = Mesh.mfdx2.Dadj; - dx{3}.D = Mesh.mfdx3.D; dx{3}.Dadj = Mesh.mfdx3.Dadj; - - % adjoint/transpose of an element of dCof matrix - dCofadjele = @(i,j,k,x,yc) dx{i}.Dadj(dx{j}.D(yc(:,k)).*x); - - dCof.dCofadj{1} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(2,3,3,x,yc)-dCofadjele(3,2,3,x,yc); dCofadjele(3,2,2,x,yc)-dCofadjele(2,3,2,x,yc)]; - dCof.dCofadj{2} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(3,1,3,x,yc)-dCofadjele(1,3,3,x,yc); dCofadjele(1,3,2,x,yc)-dCofadjele(3,1,2,x,yc)]; - dCof.dCofadj{3} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(1,2,3,x,yc)-dCofadjele(2,1,3,x,yc); dCofadjele(2,1,2,x,yc)-dCofadjele(1,2,2,x,yc)]; - - dCof.dCofadj{4} = @(x,yc) [dCofadjele(3,2,3,x,yc)-dCofadjele(2,3,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(2,3,1,x,yc)-dCofadjele(3,2,1,x,yc)]; - dCof.dCofadj{5} = @(x,yc) [dCofadjele(1,3,3,x,yc)-dCofadjele(3,1,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(3,1,1,x,yc)-dCofadjele(1,3,1,x,yc)]; - dCof.dCofadj{6} = @(x,yc) [dCofadjele(2,1,3,x,yc)-dCofadjele(1,2,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(1,2,1,x,yc)-dCofadjele(2,1,1,x,yc)]; - - dCof.dCofadj{7} = @(x,yc) [dCofadjele(2,3,2,x,yc)-dCofadjele(3,2,2,x,yc); dCofadjele(3,2,1,x,yc)-dCofadjele(2,3,1,x,yc); zeros(Mesh.nnodes,1)]; - dCof.dCofadj{8} = @(x,yc) [dCofadjele(3,1,2,x,yc)-dCofadjele(1,3,2,x,yc); dCofadjele(1,3,1,x,yc)-dCofadjele(3,1,1,x,yc); zeros(Mesh.nnodes,1)]; - dCof.dCofadj{9} = @(x,yc) [dCofadjele(1,2,2,x,yc)-dCofadjele(2,1,2,x,yc); dCofadjele(2,1,1,x,yc)-dCofadjele(1,2,1,x,yc); zeros(Mesh.nnodes,1)]; - - % element of dCof matrix - dCofele = @(i,j,k,l,x,yc) dx{i}.D(yc(:,j)).*dx{k}.D(x(:,l)); - - dCof.dCof{1} = @(x,yc) dCofele(3,3,2,2,x,yc)-dCofele(2,3,3,2,x,yc) + dCofele(2,2,3,3,x,yc) - dCofele(3,2,2,3,x,yc); - dCof.dCof{2} = @(x,yc) dCofele(1,3,3,2,x,yc)-dCofele(3,3,1,2,x,yc) + dCofele(3,2,1,3,x,yc) - dCofele(1,2,3,3,x,yc); - dCof.dCof{3} = @(x,yc) dCofele(2,3,1,2,x,yc)-dCofele(1,3,2,2,x,yc) + dCofele(1,2,2,3,x,yc) - dCofele(2,2,1,3,x,yc); - - dCof.dCof{4} = @(x,yc) dCofele(2,3,3,1,x,yc)-dCofele(3,3,2,1,x,yc) + dCofele(3,1,2,3,x,yc) - dCofele(2,1,3,3,x,yc); - dCof.dCof{5} = @(x,yc) dCofele(3,3,1,1,x,yc)-dCofele(1,3,3,1,x,yc) + dCofele(1,1,3,3,x,yc) - dCofele(3,1,1,3,x,yc); - dCof.dCof{6} = @(x,yc) dCofele(1,3,2,1,x,yc)-dCofele(2,3,1,1,x,yc) + dCofele(2,1,1,3,x,yc) - dCofele(1,1,2,3,x,yc); - - dCof.dCof{7} = @(x,yc) dCofele(3,2,2,1,x,yc)-dCofele(2,2,3,1,x,yc) + dCofele(2,1,3,2,x,yc) - dCofele(3,1,2,2,x,yc); - dCof.dCof{8} = @(x,yc) dCofele(1,2,3,1,x,yc)-dCofele(3,2,1,1,x,yc) + dCofele(3,1,1,2,x,yc) - dCofele(1,1,3,2,x,yc); - dCof.dCof{9} = @(x,yc) dCofele(2,2,1,1,x,yc)-dCofele(1,2,2,1,x,yc) + dCofele(1,1,2,2,x,yc) - dCofele(2,1,1,2,x,yc); - - end - -end - - - - function runMinimalExample setup2DGaussianData diff --git a/add-ons/FAIRFEM/cofactor3D.m b/add-ons/FAIRFEM/cofactor3D.m new file mode 100644 index 0000000..e44f7cb --- /dev/null +++ b/add-ons/FAIRFEM/cofactor3D.m @@ -0,0 +1,107 @@ +% For details see +% - https://github.com/C4IR/FAIRFEM +%============================================================================== +% +% function [cof,dCof] = cofactor3D(By,Mesh,doDerivative,matrixFree) +% +% cofactor matrix, and derivative +% +% Input: +% +% By - partial derivative of y wrt x +% Mesh - description of mesh, struct +% +% Output: +% +% [cof, dcof] - cofactor and partial derivative operators +% +%============================================================================== + +function [cof,dCof] = cofactor3D(By,Mesh,doDerivative,matrixFree) + +if ~matrixFree + + dCof = []; + D = @(i,j) By(:,(j-1)*3+i); % gets partial_i y^j + cof = [ + D(2,2).*D(3,3)-D(3,2).*D(2,3),...%ok + -D(1,2).*D(3,3)+D(3,2).*D(1,3),...%trouble + D(1,2).*D(2,3)-D(2,2).*D(1,3),...%ok + -D(2,1).*D(3,3)+D(3,1).*D(2,3),...%ok + D(1,1).*D(3,3)-D(3,1).*D(1,3),...%ok + -D(1,1).*D(2,3)+D(2,1).*D(1,3),...%ok + D(2,1).*D(3,2)-D(3,1).*D(2,2),...%ok + -D(1,1).*D(3,2)+D(3,1).*D(1,2),...%ok + D(1,1).*D(2,2)-D(2,1).*D(1,2)... %ok + ]; + + if doDerivative + D1 = Mesh.dx1; D2 = Mesh.dx2; D3 = Mesh.dx3; + Z = sparse(size(D1,1), size(D2,2)); + D = @(i,j) sdiag(By(:,(j-1)*3+i)); + + dCof{1} = [ Z , D(3,3)*D2-D(2,3)*D3, D(2,2)*D3-D(3,2)*D2]; + dCof{2} = [ Z , D(1,3)*D3-D(3,3)*D1, D(3,2)*D1-D(1,2)*D3]; + dCof{3} = [ Z , D(2,3)*D1-D(1,3)*D2, D(1,2)*D2-D(2,2)*D1]; + dCof{4} = [ D(2,3)*D3-D(3,3)*D2, Z , D(3,1)*D2-D(2,1)*D3]; + dCof{5} = [ D(3,3)*D1-D(1,3)*D3, Z , D(1,1)*D3-D(3,1)*D1]; + dCof{6} = [ D(1,3)*D2-D(2,3)*D1, Z , D(2,1)*D1-D(1,1)*D2]; + dCof{7} = [ D(3,2)*D2-D(2,2)*D3, D(2,1)*D3-D(3,1)*D2, Z]; + dCof{8} = [ D(1,2)*D3-D(3,2)*D1, D(3,1)*D1-D(1,1)*D3, Z]; + dCof{9} = [ D(2,2)*D1-D(1,2)*D2, D(1,1)*D2-D(2,1)*D1, Z]; + end + +else + + dCof = []; + dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; + + cof{1} = @(yc) dx2.D(yc(:,2)).*dx3.D(yc(:,3)) - dx3.D(yc(:,2)).*dx2.D(yc(:,3)); + cof{2} = @(yc) -dx1.D(yc(:,2)).*dx3.D(yc(:,3)) + dx3.D(yc(:,2)).*dx1.D(yc(:,3)); + cof{3} = @(yc) dx1.D(yc(:,2)).*dx2.D(yc(:,3)) - dx2.D(yc(:,2)).*dx1.D(yc(:,3)); + cof{4} = @(yc) -dx2.D(yc(:,1)).*dx3.D(yc(:,3)) + dx3.D(yc(:,1)).*dx2.D(yc(:,3)); + cof{5} = @(yc) dx1.D(yc(:,1)).*dx3.D(yc(:,3)) - dx3.D(yc(:,1)).*dx1.D(yc(:,3)); + cof{6} = @(yc) -dx1.D(yc(:,1)).*dx2.D(yc(:,3)) + dx2.D(yc(:,1)).*dx1.D(yc(:,3)); + cof{7} = @(yc) dx2.D(yc(:,1)).*dx3.D(yc(:,2)) - dx3.D(yc(:,1)).*dx2.D(yc(:,2)); + cof{8} = @(yc) -dx1.D(yc(:,1)).*dx3.D(yc(:,2)) + dx3.D(yc(:,1)).*dx1.D(yc(:,2)); + cof{9} = @(yc) dx1.D(yc(:,1)).*dx2.D(yc(:,2)) - dx2.D(yc(:,1)).*dx1.D(yc(:,2)); + + if doDerivative + + dx{1}.D = Mesh.mfdx1.D; dx{1}.Dadj = Mesh.mfdx1.Dadj; + dx{2}.D = Mesh.mfdx2.D; dx{2}.Dadj = Mesh.mfdx2.Dadj; + dx{3}.D = Mesh.mfdx3.D; dx{3}.Dadj = Mesh.mfdx3.Dadj; + + % adjoint/transpose of an element of dCof matrix + dCofadjele = @(i,j,k,x,yc) dx{i}.Dadj(dx{j}.D(yc(:,k)).*x); + + dCof.dCofadj{1} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(2,3,3,x,yc)-dCofadjele(3,2,3,x,yc); dCofadjele(3,2,2,x,yc)-dCofadjele(2,3,2,x,yc)]; + dCof.dCofadj{2} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(3,1,3,x,yc)-dCofadjele(1,3,3,x,yc); dCofadjele(1,3,2,x,yc)-dCofadjele(3,1,2,x,yc)]; + dCof.dCofadj{3} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(1,2,3,x,yc)-dCofadjele(2,1,3,x,yc); dCofadjele(2,1,2,x,yc)-dCofadjele(1,2,2,x,yc)]; + + dCof.dCofadj{4} = @(x,yc) [dCofadjele(3,2,3,x,yc)-dCofadjele(2,3,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(2,3,1,x,yc)-dCofadjele(3,2,1,x,yc)]; + dCof.dCofadj{5} = @(x,yc) [dCofadjele(1,3,3,x,yc)-dCofadjele(3,1,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(3,1,1,x,yc)-dCofadjele(1,3,1,x,yc)]; + dCof.dCofadj{6} = @(x,yc) [dCofadjele(2,1,3,x,yc)-dCofadjele(1,2,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(1,2,1,x,yc)-dCofadjele(2,1,1,x,yc)]; + + dCof.dCofadj{7} = @(x,yc) [dCofadjele(2,3,2,x,yc)-dCofadjele(3,2,2,x,yc); dCofadjele(3,2,1,x,yc)-dCofadjele(2,3,1,x,yc); zeros(Mesh.nnodes,1)]; + dCof.dCofadj{8} = @(x,yc) [dCofadjele(3,1,2,x,yc)-dCofadjele(1,3,2,x,yc); dCofadjele(1,3,1,x,yc)-dCofadjele(3,1,1,x,yc); zeros(Mesh.nnodes,1)]; + dCof.dCofadj{9} = @(x,yc) [dCofadjele(1,2,2,x,yc)-dCofadjele(2,1,2,x,yc); dCofadjele(2,1,1,x,yc)-dCofadjele(1,2,1,x,yc); zeros(Mesh.nnodes,1)]; + + % element of dCof matrix + dCofele = @(i,j,k,l,x,yc) dx{i}.D(yc(:,j)).*dx{k}.D(x(:,l)); + + dCof.dCof{1} = @(x,yc) dCofele(3,3,2,2,x,yc)-dCofele(2,3,3,2,x,yc) + dCofele(2,2,3,3,x,yc) - dCofele(3,2,2,3,x,yc); + dCof.dCof{2} = @(x,yc) dCofele(1,3,3,2,x,yc)-dCofele(3,3,1,2,x,yc) + dCofele(3,2,1,3,x,yc) - dCofele(1,2,3,3,x,yc); + dCof.dCof{3} = @(x,yc) dCofele(2,3,1,2,x,yc)-dCofele(1,3,2,2,x,yc) + dCofele(1,2,2,3,x,yc) - dCofele(2,2,1,3,x,yc); + + dCof.dCof{4} = @(x,yc) dCofele(2,3,3,1,x,yc)-dCofele(3,3,2,1,x,yc) + dCofele(3,1,2,3,x,yc) - dCofele(2,1,3,3,x,yc); + dCof.dCof{5} = @(x,yc) dCofele(3,3,1,1,x,yc)-dCofele(1,3,3,1,x,yc) + dCofele(1,1,3,3,x,yc) - dCofele(3,1,1,3,x,yc); + dCof.dCof{6} = @(x,yc) dCofele(1,3,2,1,x,yc)-dCofele(2,3,1,1,x,yc) + dCofele(2,1,1,3,x,yc) - dCofele(1,1,2,3,x,yc); + + dCof.dCof{7} = @(x,yc) dCofele(3,2,2,1,x,yc)-dCofele(2,2,3,1,x,yc) + dCofele(2,1,3,2,x,yc) - dCofele(3,1,2,2,x,yc); + dCof.dCof{8} = @(x,yc) dCofele(1,2,3,1,x,yc)-dCofele(3,2,1,1,x,yc) + dCofele(3,1,1,2,x,yc) - dCofele(1,1,3,2,x,yc); + dCof.dCof{9} = @(x,yc) dCofele(2,2,1,1,x,yc)-dCofele(1,2,2,1,x,yc) + dCofele(1,1,2,2,x,yc) - dCofele(2,1,1,2,x,yc); + + end + +end \ No newline at end of file diff --git a/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m b/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m index 6fe1689..fb719ad 100755 --- a/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m +++ b/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m @@ -30,7 +30,7 @@ yc = GaussNewton(fctn,xc(:),'Plots',@FAIRplotsFEM,'solver','mbPCG-Jacobi'); % matrixfree version -regularizer('reset','regularizer','mfHyperElasticFEM','alpha',1e1); +regularizer('reset','regularizer','mfHyperElasticFEM','alpha',1e2); ycMF = GaussNewton(fctn,xc(:),'Plots',@FAIRplotsFEM,'solver',@FEMPIREsolveGN_PCG); %showResults(ML,yc,'level',level); diff --git a/add-ons/FAIRFEM/getBasisGradient.m b/add-ons/FAIRFEM/getBasisGradient.m new file mode 100644 index 0000000..8c0c999 --- /dev/null +++ b/add-ons/FAIRFEM/getBasisGradient.m @@ -0,0 +1,67 @@ +% For details see +% - https://github.com/C4IR/FAIRFEM +%============================================================================== +% +% function [dphi] = getBasisGradient(Mesh) +% +% builds gradient operator for piecewise linear basis functions +% +% Input: +% +% Mesh - description of mesh, struct +% +% Output: +% +% [dphi] - discrete partial derivative operators +% +%============================================================================== + +function [dphi] = getBasisGradient(Mesh) + +xn = Mesh.xn; +vol = Mesh.vol; +if Mesh.dim == 3 +% compute edges + v1 = Mesh.mfPi(xn,1); + v2 = Mesh.mfPi(xn,2); + v3 = Mesh.mfPi(xn,3); + v4 = Mesh.mfPi(xn,4); + e1 = v1 - v4; + e2 = v2 - v4; + e3 = v3 - v4; + % compute inverse transformation to reference element + cofA = [ + e2(:,2).*e3(:,3)-e2(:,3).*e3(:,2), ... + -(e1(:,2).*e3(:,3)-e1(:,3).*e3(:,2)), ... + e1(:,2).*e2(:,3)-e1(:,3).*e2(:,2), ... + -(e2(:,1).*e3(:,3)-e2(:,3).*e3(:,1)), ... + e1(:,1).*e3(:,3)-e1(:,3).*e3(:,1), ... + -(e1(:,1).*e2(:,3)-e1(:,3).*e2(:,1)), ... + e2(:,1).*e3(:,2)-e2(:,2).*e3(:,1), ... + -(e1(:,1).*e3(:,2)-e1(:,2).*e3(:,1)), ... + e1(:,1).*e2(:,2)-e1(:,2).*e2(:,1), ... + ]; + detA = e1(:,1).*cofA(:,1) + e2(:,1).*cofA(:,2)+ e3(:,1).*cofA(:,3); + + + % compute gradients of basis functions + dphi{1} = cofA(:,[1 4 7])./repmat(detA,[1 3]); + dphi{2} = cofA(:,[2 5 8])./repmat(detA,[1 3]); + dphi{3} = cofA(:,[3 6 9])./repmat(detA,[1 3]); + dphi{4} = -dphi{1} - dphi{2} - dphi{3}; + +else + + % compute edges + x1 = Mesh.mfPi(xn,1); + x2 = Mesh.mfPi(xn,2); + x3 = Mesh.mfPi(xn,3); + e1 = x1 - x3; + e2 = x2 - x3; + + % compute gradients of basis functions + dphi{1} = [ e2(:,2) -e2(:,1)]./[2*vol,2*vol]; + dphi{2} = [-e1(:,2) e1(:,1)]./[2*vol,2*vol]; + dphi{3} = -dphi{1} - dphi{2}; + +end \ No newline at end of file diff --git a/add-ons/FAIRFEM/hyperElasticFEM.m b/add-ons/FAIRFEM/hyperElasticFEM.m index d3a6eb4..4450e58 100755 --- a/add-ons/FAIRFEM/hyperElasticFEM.m +++ b/add-ons/FAIRFEM/hyperElasticFEM.m @@ -280,109 +280,14 @@ end -function [cof,dCof] = cofactor3D(By,Mesh,doDerivative,matrixFree) - -if ~matrixFree - - dCof = []; - D = @(i,j) By(:,(j-1)*3+i); % gets partial_i y^j - cof = [ - D(2,2).*D(3,3)-D(3,2).*D(2,3),...%ok - -D(1,2).*D(3,3)+D(3,2).*D(1,3),...%trouble - D(1,2).*D(2,3)-D(2,2).*D(1,3),...%ok - -D(2,1).*D(3,3)+D(3,1).*D(2,3),...%ok - D(1,1).*D(3,3)-D(3,1).*D(1,3),...%ok - -D(1,1).*D(2,3)+D(2,1).*D(1,3),...%ok - D(2,1).*D(3,2)-D(3,1).*D(2,2),...%ok - -D(1,1).*D(3,2)+D(3,1).*D(1,2),...%ok - D(1,1).*D(2,2)-D(2,1).*D(1,2)... %ok - ]; - - if doDerivative - D1 = Mesh.dx1; D2 = Mesh.dx2; D3 = Mesh.dx3; - Z = sparse(size(D1,1), size(D2,2)); - D = @(i,j) sdiag(By(:,(j-1)*3+i)); - - dCof{1} = [ Z , D(3,3)*D2-D(2,3)*D3, D(2,2)*D3-D(3,2)*D2]; - dCof{2} = [ Z , D(1,3)*D3-D(3,3)*D1, D(3,2)*D1-D(1,2)*D3]; - dCof{3} = [ Z , D(2,3)*D1-D(1,3)*D2, D(1,2)*D2-D(2,2)*D1]; - dCof{4} = [ D(2,3)*D3-D(3,3)*D2, Z , D(3,1)*D2-D(2,1)*D3]; - dCof{5} = [ D(3,3)*D1-D(1,3)*D3, Z , D(1,1)*D3-D(3,1)*D1]; - dCof{6} = [ D(1,3)*D2-D(2,3)*D1, Z , D(2,1)*D1-D(1,1)*D2]; - dCof{7} = [ D(3,2)*D2-D(2,2)*D3, D(2,1)*D3-D(3,1)*D2, Z]; - dCof{8} = [ D(1,2)*D3-D(3,2)*D1, D(3,1)*D1-D(1,1)*D3, Z]; - dCof{9} = [ D(2,2)*D1-D(1,2)*D2, D(1,1)*D2-D(2,1)*D1, Z]; - end - -else - - dCof = []; - dx1 = Mesh.mfdx1; dx2 = Mesh.mfdx2; dx3 = Mesh.mfdx3; - - cof{1} = @(yc) dx2.D(yc(:,2)).*dx3.D(yc(:,3)) - dx3.D(yc(:,2)).*dx2.D(yc(:,3)); - cof{2} = @(yc) -dx1.D(yc(:,2)).*dx3.D(yc(:,3)) + dx3.D(yc(:,2)).*dx1.D(yc(:,3)); - cof{3} = @(yc) dx1.D(yc(:,2)).*dx2.D(yc(:,3)) - dx2.D(yc(:,2)).*dx1.D(yc(:,3)); - cof{4} = @(yc) -dx2.D(yc(:,1)).*dx3.D(yc(:,3)) + dx3.D(yc(:,1)).*dx2.D(yc(:,3)); - cof{5} = @(yc) dx1.D(yc(:,1)).*dx3.D(yc(:,3)) - dx3.D(yc(:,1)).*dx1.D(yc(:,3)); - cof{6} = @(yc) -dx1.D(yc(:,1)).*dx2.D(yc(:,3)) + dx2.D(yc(:,1)).*dx1.D(yc(:,3)); - cof{7} = @(yc) dx2.D(yc(:,1)).*dx3.D(yc(:,2)) - dx3.D(yc(:,1)).*dx2.D(yc(:,2)); - cof{8} = @(yc) -dx1.D(yc(:,1)).*dx3.D(yc(:,2)) + dx3.D(yc(:,1)).*dx1.D(yc(:,2)); - cof{9} = @(yc) dx1.D(yc(:,1)).*dx2.D(yc(:,2)) - dx2.D(yc(:,1)).*dx1.D(yc(:,2)); - - if doDerivative - - dx{1}.D = Mesh.mfdx1.D; dx{1}.Dadj = Mesh.mfdx1.Dadj; - dx{2}.D = Mesh.mfdx2.D; dx{2}.Dadj = Mesh.mfdx2.Dadj; - dx{3}.D = Mesh.mfdx3.D; dx{3}.Dadj = Mesh.mfdx3.Dadj; - - % adjoint/transpose of an element of dCof matrix - dCofadjele = @(i,j,k,x,yc) dx{i}.Dadj(dx{j}.D(yc(:,k)).*x); - - dCof.dCofadj{1} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(2,3,3,x,yc)-dCofadjele(3,2,3,x,yc); dCofadjele(3,2,2,x,yc)-dCofadjele(2,3,2,x,yc)]; - dCof.dCofadj{2} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(3,1,3,x,yc)-dCofadjele(1,3,3,x,yc); dCofadjele(1,3,2,x,yc)-dCofadjele(3,1,2,x,yc)]; - dCof.dCofadj{3} = @(x,yc) [zeros(Mesh.nnodes,1); dCofadjele(1,2,3,x,yc)-dCofadjele(2,1,3,x,yc); dCofadjele(2,1,2,x,yc)-dCofadjele(1,2,2,x,yc)]; - - dCof.dCofadj{4} = @(x,yc) [dCofadjele(3,2,3,x,yc)-dCofadjele(2,3,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(2,3,1,x,yc)-dCofadjele(3,2,1,x,yc)]; - dCof.dCofadj{5} = @(x,yc) [dCofadjele(1,3,3,x,yc)-dCofadjele(3,1,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(3,1,1,x,yc)-dCofadjele(1,3,1,x,yc)]; - dCof.dCofadj{6} = @(x,yc) [dCofadjele(2,1,3,x,yc)-dCofadjele(1,2,3,x,yc); zeros(Mesh.nnodes,1); dCofadjele(1,2,1,x,yc)-dCofadjele(2,1,1,x,yc)]; - - dCof.dCofadj{7} = @(x,yc) [dCofadjele(2,3,2,x,yc)-dCofadjele(3,2,2,x,yc); dCofadjele(3,2,1,x,yc)-dCofadjele(2,3,1,x,yc); zeros(Mesh.nnodes,1)]; - dCof.dCofadj{8} = @(x,yc) [dCofadjele(3,1,2,x,yc)-dCofadjele(1,3,2,x,yc); dCofadjele(1,3,1,x,yc)-dCofadjele(3,1,1,x,yc); zeros(Mesh.nnodes,1)]; - dCof.dCofadj{9} = @(x,yc) [dCofadjele(1,2,2,x,yc)-dCofadjele(2,1,2,x,yc); dCofadjele(2,1,1,x,yc)-dCofadjele(1,2,1,x,yc); zeros(Mesh.nnodes,1)]; - - % element of dCof matrix - dCofele = @(i,j,k,l,x,yc) dx{i}.D(yc(:,j)).*dx{k}.D(x(:,l)); - - dCof.dCof{1} = @(x,yc) dCofele(3,3,2,2,x,yc)-dCofele(2,3,3,2,x,yc) + dCofele(2,2,3,3,x,yc) - dCofele(3,2,2,3,x,yc); - dCof.dCof{2} = @(x,yc) dCofele(1,3,3,2,x,yc)-dCofele(3,3,1,2,x,yc) + dCofele(3,2,1,3,x,yc) - dCofele(1,2,3,3,x,yc); - dCof.dCof{3} = @(x,yc) dCofele(2,3,1,2,x,yc)-dCofele(1,3,2,2,x,yc) + dCofele(1,2,2,3,x,yc) - dCofele(2,2,1,3,x,yc); - - dCof.dCof{4} = @(x,yc) dCofele(2,3,3,1,x,yc)-dCofele(3,3,2,1,x,yc) + dCofele(3,1,2,3,x,yc) - dCofele(2,1,3,3,x,yc); - dCof.dCof{5} = @(x,yc) dCofele(3,3,1,1,x,yc)-dCofele(1,3,3,1,x,yc) + dCofele(1,1,3,3,x,yc) - dCofele(3,1,1,3,x,yc); - dCof.dCof{6} = @(x,yc) dCofele(1,3,2,1,x,yc)-dCofele(2,3,1,1,x,yc) + dCofele(2,1,1,3,x,yc) - dCofele(1,1,2,3,x,yc); - - dCof.dCof{7} = @(x,yc) dCofele(3,2,2,1,x,yc)-dCofele(2,2,3,1,x,yc) + dCofele(2,1,3,2,x,yc) - dCofele(3,1,2,2,x,yc); - dCof.dCof{8} = @(x,yc) dCofele(1,2,3,1,x,yc)-dCofele(3,2,1,1,x,yc) + dCofele(3,1,1,2,x,yc) - dCofele(1,1,3,2,x,yc); - dCof.dCof{9} = @(x,yc) dCofele(2,2,1,1,x,yc)-dCofele(1,2,2,1,x,yc) + dCofele(1,1,2,2,x,yc) - dCofele(2,1,1,2,x,yc); - - end - -end function D = getDiagVolume(Mesh,yc,alphaVolume) dim = Mesh.dim; vol = Mesh.vol; if dim==2 - xn = Mesh.xn; - % get edges - e1 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,3); - e2 = Mesh.mfPi(xn,2) - Mesh.mfPi(xn,3); - e3 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,2); - % compute gradients of basis functions - dphi1 = ([ e2(:,2) -e2(:,1)]./[2*vol,2*vol]); - dphi2 = ([-e1(:,2) e1(:,1)]./[2*vol,2*vol]); - dphi3 = ([ e3(:,2) -e3(:,1)]./[2*vol,2*vol]); + dphi = Mesh.dphi; + dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; % compute diagonal of volume regularizer % MB : dDet = [sdiag(By(:,4)), sdiag(-By(:,3)) , sdiag(-By(:,2)), sdiag(By(:,1))] * B; @@ -404,7 +309,7 @@ D = [Dxi(1,4)+ Dxi(2,3) - 2*Dxy(1,4,2,3) ;Dxi(1,2)+ Dxi(2,1) - 2*Dxy(1,2,2,1)]; else - dphi = getBasisGradient(Mesh); + dphi = Mesh.dphi; dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; dphi4 = dphi{4}; [cof, dCof] = cofactor3D([],Mesh,0,1); @@ -438,7 +343,7 @@ %dim = Mesh.dim; vol = Mesh.vol; -dphi = getBasisGradient(Mesh); +dphi = Mesh.dphi; %dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; dphi4 = dphi{4}; [cof, ~] = cofactor3D([],Mesh,0,1); @@ -508,24 +413,24 @@ % compute d2Svol*x -function By = volumeOperator(yc,Mesh,x,vol) -[dx1, dx2] = getGradientMatrixFEM(Mesh,1); -% volume regularization -yc = reshape(yc,[],2); -By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; -det = By(:,1).*By(:,4) - By(:,3) .* By(:,2); -[~,~,d2G] = psi(det,1); - -% MB : dDet = [sdiag(By(:,4)), sdiag(-By(:,3)) , sdiag(-By(:,2)), sdiag(By(:,1))] * B; - -dDet = @(x) By(:,4).*dx1.D(x(:,1))- By(:,3).*dx2.D(x(:,1))... - -By(:,2).*dx1.D(x(:,2))+By(:,1).*dx2.D(x(:,2)); - -dDetAdj = @(x) [ ... - dx1.Dadj(By(:,4).*x)-dx2.Dadj(By(:,3).*x);... - -dx1.Dadj(By(:,2).*x)+dx2.Dadj(By(:,1).*x) - ]; -By = dDetAdj(vol.*d2G.*dDet(reshape(x,[],2))); +% function By = volumeOperator(yc,Mesh,x,vol) +% [dx1, dx2] = getGradientMatrixFEM(Mesh,1); +% % volume regularization +% yc = reshape(yc,[],2); +% By = [dx1.D(yc(:,1)) dx2.D(yc(:,1)) dx1.D(yc(:,2)) dx2.D(yc(:,2))]; +% det = By(:,1).*By(:,4) - By(:,3) .* By(:,2); +% [~,~,d2G] = psi(det,1); +% +% % MB : dDet = [sdiag(By(:,4)), sdiag(-By(:,3)) , sdiag(-By(:,2)), sdiag(By(:,1))] * B; +% +% dDet = @(x) By(:,4).*dx1.D(x(:,1))- By(:,3).*dx2.D(x(:,1))... +% -By(:,2).*dx1.D(x(:,2))+By(:,1).*dx2.D(x(:,2)); +% +% dDetAdj = @(x) [ ... +% dx1.Dadj(By(:,4).*x)-dx2.Dadj(By(:,3).*x);... +% -dx1.Dadj(By(:,2).*x)+dx2.Dadj(By(:,1).*x) +% ]; +% By = dDetAdj(vol.*d2G.*dDet(reshape(x,[],2))); @@ -533,16 +438,9 @@ dim = Mesh.dim; vol = Mesh.vol; if dim==2 - xn = Mesh.xn; - % get edges - e1 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,3); - e2 = Mesh.mfPi(xn,2) - Mesh.mfPi(xn,3); - e3 = Mesh.mfPi(xn,1) - Mesh.mfPi(xn,2); - % compute gradients of basis functions - dphi1 = ([ e2(:,2) -e2(:,1)]./[2*vol,2*vol]); - dphi2 = ([-e1(:,2) e1(:,1)]./[2*vol,2*vol]); - dphi3 = ([ e3(:,2) -e3(:,1)]./[2*vol,2*vol]); + dphi = Mesh.dphi; + dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; % get boundaries Dxi = @(i) Mesh.mfPi(vol.*dphi1(:,i).^2,1) + Mesh.mfPi(vol.*dphi2(:,i).^2,2) + Mesh.mfPi(vol.*dphi3(:,i).^2,3); % diagonal of Dx1'*Dx1 @@ -550,7 +448,7 @@ D = Dxi(1)+ Dxi(2); D = [D;D]; else - dphi = getBasisGradient(Mesh); + dphi = Mesh.dphi; dphi1 = dphi{1}; dphi2 = dphi{2}; dphi3 = dphi{3}; dphi4 = dphi{4}; % get boundaries @@ -565,55 +463,6 @@ end D = alphaLength*D(:); -function [dphi] = getBasisGradient(Mesh) - -xn = Mesh.xn; -vol = Mesh.vol; -if Mesh.dim == 3 -% compute edges - v1 = Mesh.mfPi(xn,1); - v2 = Mesh.mfPi(xn,2); - v3 = Mesh.mfPi(xn,3); - v4 = Mesh.mfPi(xn,4); - e1 = v1 - v4; - e2 = v2 - v4; - e3 = v3 - v4; - % compute inverse transformation to reference element - cofA = [ - e2(:,2).*e3(:,3)-e2(:,3).*e3(:,2), ... - -(e1(:,2).*e3(:,3)-e1(:,3).*e3(:,2)), ... - e1(:,2).*e2(:,3)-e1(:,3).*e2(:,2), ... - -(e2(:,1).*e3(:,3)-e2(:,3).*e3(:,1)), ... - e1(:,1).*e3(:,3)-e1(:,3).*e3(:,1), ... - -(e1(:,1).*e2(:,3)-e1(:,3).*e2(:,1)), ... - e2(:,1).*e3(:,2)-e2(:,2).*e3(:,1), ... - -(e1(:,1).*e3(:,2)-e1(:,2).*e3(:,1)), ... - e1(:,1).*e2(:,2)-e1(:,2).*e2(:,1), ... - ]; - detA = e1(:,1).*cofA(:,1) + e2(:,1).*cofA(:,2)+ e3(:,1).*cofA(:,3); - - - % compute gradients of basis functions - dphi{1} = cofA(:,[1 4 7])./repmat(detA,[1 3]); - dphi{2} = cofA(:,[2 5 8])./repmat(detA,[1 3]); - dphi{3} = cofA(:,[3 6 9])./repmat(detA,[1 3]); - dphi{4} = -dphi{1} - dphi{2} - dphi{3}; - -else - - % compute edges - x1 = Mesh.mfPi(xn,1); - x2 = Mesh.mfPi(xn,2); - x3 = Mesh.mfPi(xn,3); - e1 = x1 - x3; - e2 = x2 - x3; - - % compute gradients of basis functions - dphi{1} = [ e2(:,2) -e2(:,1)]./[2*vol,2*vol]; - dphi{2} = [-e1(:,2) e1(:,1)]./[2*vol,2*vol]; - dphi{3} = -dphi{1} - dphi{2}; - -end function [G dG d2G] = psi(x,doDerivative) % diff --git a/add-ons/FAIRFEM/meshes/TetraMesh1.m b/add-ons/FAIRFEM/meshes/TetraMesh1.m index a2a117b..8400498 100755 --- a/add-ons/FAIRFEM/meshes/TetraMesh1.m +++ b/add-ons/FAIRFEM/meshes/TetraMesh1.m @@ -171,6 +171,10 @@ mfdx2 mfdx3 mfGRAD + % =================================== + % Partial derivatives of Basis functions + % =================================== + dphi end properties (Access = private) @@ -193,6 +197,7 @@ mfGRAD_ boundaryIdx_ boundaryProj_ + dphi_ end methods @@ -764,6 +769,13 @@ function runMinimalExample(~) mfGRAD = this.mfGRAD_; end + function dphi = get.dphi(this) + if isempty(this.dphi_), + [this.dphi_] = getBasisGradient(this); + end + dphi = this.dphi_; + end + function idx = get.boundaryIdx(this) if isempty(this.boundaryIdx_), mkvc = @(v) v(:); diff --git a/add-ons/FAIRFEM/meshes/TriMesh1.m b/add-ons/FAIRFEM/meshes/TriMesh1.m index 7b5c935..8185556 100755 --- a/add-ons/FAIRFEM/meshes/TriMesh1.m +++ b/add-ons/FAIRFEM/meshes/TriMesh1.m @@ -172,6 +172,10 @@ mfdx1 mfdx2 mfGRAD + % =================================== + % Partial derivatives of Basis functions + % =================================== + dphi end properties (Access = private) @@ -191,6 +195,7 @@ mfGRAD_ boundaryIdx_ boundaryProj_ + dphi_ end methods @@ -439,6 +444,14 @@ function runMinimalExample(~) end mfGRAD = this.mfGRAD_; end + + function dphi = get.dphi(this) + if isempty(this.dphi_), + [this.dphi_] = getBasisGradient(this); + end + dphi = this.dphi_; + end + function idx = get.boundaryIdx(this) if isempty(this.boundaryIdx_), id = reshape(1:prod(this.m+1),this.m+1); diff --git a/add-ons/FAIRFEM/meshes/TriMesh2.m b/add-ons/FAIRFEM/meshes/TriMesh2.m index 25ee2d7..f913583 100755 --- a/add-ons/FAIRFEM/meshes/TriMesh2.m +++ b/add-ons/FAIRFEM/meshes/TriMesh2.m @@ -172,6 +172,10 @@ mfdx1 mfdx2 mfGRAD + % =================================== + % Partial derivatives of Basis functions + % =================================== + dphi end properties (Access = private) @@ -191,6 +195,7 @@ mfGRAD_ boundaryIdx_ boundaryProj_ + dphi_ end methods @@ -446,6 +451,13 @@ function runMinimalExample(~) mfGRAD = this.mfGRAD_; end + function dphi = get.dphi(this) + if isempty(this.dphi_), + [this.dphi_] = getBasisGradient(this); + end + dphi = this.dphi_; + end + function idx = get.boundaryIdx(this) if isempty(this.boundaryIdx_), id = reshape(1:prod(this.m+1),this.m+1); diff --git a/add-ons/FAIRFEM/meshes/TriMesh3.m b/add-ons/FAIRFEM/meshes/TriMesh3.m index f5bc136..6355be3 100755 --- a/add-ons/FAIRFEM/meshes/TriMesh3.m +++ b/add-ons/FAIRFEM/meshes/TriMesh3.m @@ -176,6 +176,10 @@ mfdx1 mfdx2 mfGRAD + % =================================== + % Partial derivatives of Basis functions + % =================================== + dphi end properties (Access = private) @@ -196,6 +200,7 @@ boundaryIdx_ boundaryProj_ AvN_ + dphi_ end @@ -535,6 +540,15 @@ function runMinimalExample(~) end mfGRAD = this.mfGRAD_; end + + function dphi = get.dphi(this) + if isempty(this.dphi_), + [this.dphi_] = getBasisGradient(this); + end + dphi = this.dphi_; + end + + function idx = get.boundaryIdx(this) if isempty(this.boundaryIdx_), id = reshape(1:prod(this.m+1),this.m+1); From 925f7782cc3c992d1056dd25e5af771490043bbf Mon Sep 17 00:00:00 2001 From: Hari Om Aggraval Date: Thu, 5 Oct 2017 11:03:45 +0200 Subject: [PATCH 16/16] MatrixFree Functionality for non-mass preserving case Minor changes in FEMobjFctn.m for MatrixFree functionality and added a PCG solver function. --- add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m | 2 +- add-ons/FAIRFEM/FEMSSDsolveGN_PCG.m | 44 +++++++++++++ add-ons/FAIRFEM/FEMobjFctn.m | 65 +++++++++++++------ .../FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m | 5 +- add-ons/FAIRFEM/examples/EFEM_FEMSSD_Mice3D.m | 37 +++++++++++ add-ons/FAIRFEM/examples/EFEM_MBvsMF.m | 39 +++++++++++ add-ons/FAIRFEM/examples/EFEM_MP_MBvsMF.m | 4 +- add-ons/FAIRFEM/examples/EFEM_SSDvsMP.m | 1 + kernel/numerics/solveLinearSystem.m | 4 +- 9 files changed, 175 insertions(+), 26 deletions(-) create mode 100644 add-ons/FAIRFEM/FEMSSDsolveGN_PCG.m create mode 100644 add-ons/FAIRFEM/examples/EFEM_FEMSSD_Mice3D.m create mode 100644 add-ons/FAIRFEM/examples/EFEM_MBvsMF.m diff --git a/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m b/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m index a267c7d..c72ba79 100644 --- a/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m +++ b/add-ons/FAIRFEM/FEMPIREsolveGN_PCG.m @@ -4,7 +4,7 @@ % For details see % - https://github.com/C4IR/VAMPIRE.m %============================================================================== -% PCG solver for VAMPIRE +% PCG solver for FEMPIRE % function dy = FEMPIREsolveGN_PCG(rhs, H, maxIterCG, tolCG) diff --git a/add-ons/FAIRFEM/FEMSSDsolveGN_PCG.m b/add-ons/FAIRFEM/FEMSSDsolveGN_PCG.m new file mode 100644 index 0000000..7720d5f --- /dev/null +++ b/add-ons/FAIRFEM/FEMSSDsolveGN_PCG.m @@ -0,0 +1,44 @@ +%============================================================================== +% This code is part of the VAMPIRE app for the Matlab-based toolbox +% FAIR - Flexible Algorithms for Image Registration. +% For details see +% - https://github.com/C4IR/VAMPIRE.m +%============================================================================== +% PCG solver for FEMSSD +% + +function dy = FEMSSDsolveGN_PCG(rhs, H, maxIterCG, tolCG) + +% set pointers to simplify notation +Mesh = H.Mesh; +P = H.d2D.P; +Tc = H.d2D.Tc; +dT = H.d2D.dT; +yc = H.d2S.yc; +dres = H.d2D.dres; +dim = Mesh.dim; + +% Tcmod(y) = T(P*y) +% ==> dTcmod(y) = (dT(y)*P) +% ==> dTcmod'(y) = (P'* dT')(y) +%dTcmod = @(x) vecmatprod1(dT,H.d2D.P(reshape(x,[],dim))); +%dTcmodadj = @(x) H.d2D.P(vecmatprod1adj(dT,x)); + +dTcmod = @(x) vecmatprod1(dT,H.d2D.P(reshape(x,[],dim))); +dTcmodadj = @(x) H.d2D.P(dT.*x); + +M = @(x) dTcmodadj(dres'*H.d2D.d2psi*(dres * dTcmod(x))); +Hoperator = @(x) M(x) + H.d2S.d2S(x); + +D = H.d2D.diag() + H.d2S.diag(H.d2S.yc); +Preconditioner = @(x) D.\x; % Jacobi preconditioner +[dy,flag,relres,iter] = pcg(Hoperator,rhs,tolCG,maxIterCG,Preconditioner); + + +function p= vecmatprod1(dI,x) +% We aim to compute [dI] * x +dim = size(dI,2); + +x = reshape(x,[],dim); +p = sum(dI.*x,2); + diff --git a/add-ons/FAIRFEM/FEMobjFctn.m b/add-ons/FAIRFEM/FEMobjFctn.m index 3f4c331..feaa822 100755 --- a/add-ons/FAIRFEM/FEMobjFctn.m +++ b/add-ons/FAIRFEM/FEMobjFctn.m @@ -68,6 +68,7 @@ yc = reshape(yc,[],dim); yRef = reshape(yRef,[],dim); doDerivative = (nargout>2); % flag for necessity of derivatives +matrixFree = regularizer('get','matrixFree'); % do the work ------------------------------------------------------------ @@ -75,7 +76,7 @@ vol = Mesh.vol; % compute interpolated image and derivative -[Tc,dT] = imgModel(T,omega,Mesh.mfPi(yc,'C'),'doDerivative',doDerivative); +[Tc,dT] = imgModel(T,omega,Mesh.mfPi(yc,'C'),'doDerivative',doDerivative,'matrixFree',matrixFree); % compute SSD distance rc = Tc-Rc; % the residual @@ -109,24 +110,28 @@ H = dr'*d2psi*dr + d2S; else % derivatives rather explicit - P = @(x) reshape(Mesh.mfPi(reshape(x,[],dim),'C'),[],1); - dr = dres*dT; - dD = dD*dT; - dJ = P(dD')' + dS; - - % approximation to d2D in matrix free mode - % d2D = P'*dr'*d2psi*dr*P - % P and P' are operators matrix free - H.Mesh = Mesh; - H.omega = omega; - H.m = m; - H.d2D.how = 'P''*dr''*d2psi*dr*P'; - H.d2D.P = P; - H.d2D.dr = dr; - H.d2D.d2psi = d2psi; - H.solver = d2S.solver; - - H.d2S = d2S; + p = dD(:).*dT; + dD = reshape(Mesh.mfPi(p,'C'),1,[]); + + dJ = dD + dS; + + % approximation to d2D in matrix free mode + % d2D = P'*dr'*d2psi*dr*P + % P and P' are operators matrix free + H.Mesh = Mesh; + H.omega = omega; + H.m = m; + H.d2D.how = 'P''*dr''*d2psi*dr*P'; + H.d2D.P = @(x) reshape(Mesh.mfPi(x,'C'),[],1); + H.d2D.Tc = Tc; + H.d2D.dT = dT; + H.d2D.diag = @() getDiag(Mesh,dT); + H.d2D.dres = dres; + H.d2D.d2psi = d2psi; + H.solver = d2S.solver; + + H.d2S = d2S; + end; @@ -136,6 +141,28 @@ A = spdiags(v(:),0,numel(v),numel(v)); +% diagonal of hessian matrix +% sum(sdiag(vol)dTcmod.^2,1) +% where dTcmod = dT*P; +function D = getDiag(Mesh,dT) + +vol = Mesh.vol; +dim = Mesh.dim; + +if dim == 2 + + % first term + D = Mesh.mfPi(vol.*(dT).^2,'C'); + D = D(:)./3; + +else + + % first term + D = Mesh.mfPi(vol.*(dT).^2,'C'); + D = D(:)./4; + +end + function runMinimalExample setup2DhandData diff --git a/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m b/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m index fb719ad..02f86fd 100755 --- a/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m +++ b/add-ons/FAIRFEM/examples/EFEM_FEMPIRE_Mice3D.m @@ -9,12 +9,12 @@ %setup3DmiceData; setup3DmouseData; -level = 3; +level = 4; omega = ML{level}.omega; m = ML{level}.m; viewImage('reset','viewImage','imgmontage','colormap','gray'); imgModel('reset','imgModel','splineInterMex','regularizer','moments','theta',1e-1); -regularizer('reset','regularizer','mbHyperElasticFEM','alpha',1e1); +regularizer('reset','regularizer','mbHyperElasticFEM','alpha',1e2); [T,R] = imgModel('coefficients',ML{level}.T,ML{level}.R,omega,'out',0); Mesh = TetraMesh1(omega,m); @@ -33,4 +33,5 @@ regularizer('reset','regularizer','mfHyperElasticFEM','alpha',1e2); ycMF = GaussNewton(fctn,xc(:),'Plots',@FAIRplotsFEM,'solver',@FEMPIREsolveGN_PCG); +relerr = norm(yc-ycMF)/norm(yc) %showResults(ML,yc,'level',level); diff --git a/add-ons/FAIRFEM/examples/EFEM_FEMSSD_Mice3D.m b/add-ons/FAIRFEM/examples/EFEM_FEMSSD_Mice3D.m new file mode 100644 index 0000000..08a3891 --- /dev/null +++ b/add-ons/FAIRFEM/examples/EFEM_FEMSSD_Mice3D.m @@ -0,0 +1,37 @@ +% ================================================================================== +% (c) Lars Ruthotto 2012/07/26, see FAIR.2 and FAIRcopyright.m. +% http://www.mic.uni-luebeck.de/people/lars-ruthotto.html +% +% Registration of 3D PET of a mice heart using FEM +% +% ================================================================================== +close all; clc; clear; +%setup3DmiceData; +setup3DmouseData; + +level = 4; +omega = ML{level}.omega; m = ML{level}.m; + +viewImage('reset','viewImage','imgmontage','colormap','gray'); +imgModel('reset','imgModel','splineInterMex','regularizer','moments','theta',1e-1); +regularizer('reset','regularizer','mbHyperElasticFEM','alpha',1e2); +[T,R] = imgModel('coefficients',ML{level}.T,ML{level}.R,omega,'out',0); + +Mesh = TetraMesh1(omega,m); +xc = Mesh.xn; +Rc = imgModel(R,omega,Mesh.mfPi(xc,'C')); +Tc = imgModel(T,omega,Mesh.mfPi(xc,'C')); +fctn = @(yc) FEMobjFctn(T,Rc,Mesh,xc,yc(:)); +fctn([]); + +FAIRplotsFEM('reset','mode','FEM','fig',level,'plots',1); +FAIRplotsFEM('init',struct('Tc',T,'Rc',R,'Mesh',Mesh)); + +yc = GaussNewton(fctn,xc(:),'Plots',@FAIRplotsFEM,'solver','mbPCG-Jacobi'); + +% matrixfree version +regularizer('reset','regularizer','mfHyperElasticFEM','alpha',1e2); +ycMF = GaussNewton(fctn,xc(:),'Plots',@FAIRplotsFEM,'solver',@FEMSSDsolveGN_PCG); + +relerr = norm(yc-ycMF)/norm(yc) +%showResults(ML,yc,'level',level); diff --git a/add-ons/FAIRFEM/examples/EFEM_MBvsMF.m b/add-ons/FAIRFEM/examples/EFEM_MBvsMF.m new file mode 100644 index 0000000..eec07de --- /dev/null +++ b/add-ons/FAIRFEM/examples/EFEM_MBvsMF.m @@ -0,0 +1,39 @@ +% ================================================================================== +% (c) Lars Ruthotto 2012/07/26, see FAIR.2 and FAIRcopyright.m. +% http://www.mic.uni-luebeck.de/people/lars-ruthotto.html +% +% Simplified Registration of Cardiac PET +% +% data Gaussian Blobs +% +% ================================================================================== +close all; clc; clear; +setup2DGaussianData; + +distance('reset','distance','SSD'); +imgModel('reset','imgModel','splineInterMex','regularizer','moments','theta',4e-1); +regularizer('reset','regularizer','mbHyperElasticFEM','alpha',1e2); + +minLevel = 3; +maxLevel = 3; + +NPIRpara = optPara('NPIR-GN'); +NPIRpara.Plots = @FAIRplotsFEM; +NPIRpara.lineSearch = @ArmijoDiffeomorphicFEM; +NPIRpara.solver = 'mbPCG-Jacobi'; + +[ySSD_MB,~,hisSSD_MB] = MLIRFEM(ML,'parametric',0,... + 'NPIRobj',@FEMobjFctn,'NPIRpara',NPIRpara,... + 'minLevel',minLevel,'maxLevel',maxLevel); + +regularizer('reset','regularizer','mfHyperElasticFEM','alpha',5e1); +NPIRpara.solver = @FEMSSDsolveGN_PCG; + +[ySSD_MF,~,hisSSD_MF] = MLIRFEM(ML,'parametric',0,... + 'NPIRobj',@FEMobjFctn,'NPIRpara',NPIRpara,... + 'minLevel',minLevel,'maxLevel',maxLevel); + +relerr = norm(ySSD_MB-ySSD_MF)/norm(ySSD_MB) + +%% +%save('EFEM_SSDvsMP','ML','yFEMPIRE','ySSD','hisFEMPIRE','hisSSD'); \ No newline at end of file diff --git a/add-ons/FAIRFEM/examples/EFEM_MP_MBvsMF.m b/add-ons/FAIRFEM/examples/EFEM_MP_MBvsMF.m index da29b44..7820ab0 100644 --- a/add-ons/FAIRFEM/examples/EFEM_MP_MBvsMF.m +++ b/add-ons/FAIRFEM/examples/EFEM_MP_MBvsMF.m @@ -15,8 +15,8 @@ imgModel('reset','imgModel','splineInterMex','regularizer','moments','theta',4e-1); regularizer('reset','regularizer','mbHyperElasticFEM','alpha',5e1); -minLevel = 3; -maxLevel = 8; +minLevel = 5; +maxLevel = 5; NPIRpara = optPara('NPIR-GN'); NPIRpara.Plots = @FAIRplotsFEM; diff --git a/add-ons/FAIRFEM/examples/EFEM_SSDvsMP.m b/add-ons/FAIRFEM/examples/EFEM_SSDvsMP.m index 842347d..bd108a3 100755 --- a/add-ons/FAIRFEM/examples/EFEM_SSDvsMP.m +++ b/add-ons/FAIRFEM/examples/EFEM_SSDvsMP.m @@ -30,5 +30,6 @@ [ySSD,~,hisSSD] = MLIRFEM(ML,'parametric',0,... 'NPIRobj',@FEMobjFctn,'NPIRpara',NPIRpara,... 'minLevel',minLevel,'maxLevel',maxLevel); + %% save('EFEM_SSDvsMP','ML','yFEMPIRE','ySSD','hisFEMPIRE','hisSSD'); \ No newline at end of file diff --git a/kernel/numerics/solveLinearSystem.m b/kernel/numerics/solveLinearSystem.m index a08cbcc..4da85ff 100644 --- a/kernel/numerics/solveLinearSystem.m +++ b/kernel/numerics/solveLinearSystem.m @@ -158,14 +158,14 @@ [dy,flag,relres,iter] = pcg(H,rhs,tolCG,maxIterCG); end - case {'PCG-hyperElastic'} + case {'PCG-hyperElastic'} M = @(x) H.d2D.P((H.d2D.dr'*H.d2D.d2psi*H.d2D.dr)*H.d2D.P(x)); Hoperator = @(x) M(x) + H.d2S.d2S(x,H.omega,H.m,H.d2S.yc); Ddiag = diag(H.d2D.dr'*H.d2D.d2psi*H.d2D.dr); D = H.d2D.P(full(Ddiag)) + H.d2S.diag(H.d2S.yc); Preconditioner = @(x) D.\x; % Jacobi preconditioner [dy,flag,relres,iter] = pcg(Hoperator,rhs,tolCG,maxIterCG,Preconditioner); - + otherwise, keyboard error(1)

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