Mercurial > repos > public > sbplib
changeset 296:a6ae1b104391 feature/hypsyst
Renamed class.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Mon, 26 Sep 2016 14:21:37 +0200 |
| parents | da0131655035 |
| children | cd30b22cee56 |
| files | +scheme/Hypsyst2d.m +scheme/hypsyst2d.m |
| diffstat | 2 files changed, 279 insertions(+), 279 deletions(-) [+] |
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diff -r da0131655035 -r a6ae1b104391 +scheme/Hypsyst2d.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/Hypsyst2d.m Mon Sep 26 14:21:37 2016 +0200 @@ -0,0 +1,279 @@ +classdef Hypsyst2d < scheme.Scheme + properties + m % Number of points in each direction, possibly a vector + n %size of system + h % Grid spacing + x,y % Grid + X,Y % Values of x and y for each grid point + order % Order accuracy for the approximation + + D % non-stabalized scheme operator + A, B, E + + H % Discrete norm + % Norms in the x and y directions + Hxi,Hyi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. + I_x,I_y, I_N + e_w, e_e, e_s, e_n + params %parameters for the coeficient matrices + matrices + end + + + methods + function obj = Hypsyst2d(m, lim, order, A, B, E, params) + default_arg('E', []) + xlim = lim{1}; + ylim = lim{2}; + + if length(m) == 1 + m = [m m]; + end + + m_x = m(1); + m_y = m(2); + obj.params = params; + + obj.matrices = matrices; + + ops_x = sbp.D2Standard(m_x,xlim,order); + ops_y = sbp.D2Standard(m_y,ylim,order); + + obj.x = ops_x.x; + obj.y = ops_y.x; + + obj.X = kr(obj.x,ones(m_y,1)); + obj.Y = kr(ones(m_x,1),obj.y); + + obj.A = obj.evaluateCoefficientMatrix(matrices.A, obj.X, obj.Y); + obj.B = obj.evaluateCoefficientMatrix(matrices.B, obj.X, obj.Y); + obj.E = obj.evaluateCoefficientMatrix(matrices.E, obj.X, obj.Y); + + obj.n = length(matrices.A(obj.params,0,0)); + + I_n = eye(obj.n);I_x = speye(m_x); + obj.I_x = I_x; + I_y = speye(m_y); + obj.I_y = I_y; + + + D1_x = kr(I_n, ops_x.D1, I_y); + obj.Hxi = kr(I_n, ops_x.HI, I_y); + D1_y = kr(I_n, I_x, ops_y.D1)); + obj.Hyi = kr(I_n, I_x, ops_y.HI)); + + obj.e_w = kr(I_n, ops_x.e_l, I_y); + obj.e_e = kr(I_n, ops_x.e_r, I_y); + obj.e_s = kr(I_n, I_x, ops_y.e_l); + obj.e_n = kr(I_n, I_x, ops_y.e_r); + + obj.m=m; + obj.h=[ops_x.h ops_y.h]; + obj.order=order; + + obj.D=-obj.A*D1_x-obj.B*D1_y-obj.E; + + end + + % Closure functions return the opertors applied to the own doamin to close the boundary + % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. + % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. + % type is a string specifying the type of boundary condition if there are several. + % data is a function returning the data that should be applied at the boundary. + function [closure, penalty] = boundary_condition(obj,boundary,type,L) + default_arg('type','char'); + switch type + case{'c','char'} + [closure,penalty]=boundary_condition_char(obj,boundary); + case{'general'} + [closure,penalty]=boundary_condition_general(obj,boundary,L); + otherwise + error('No such boundary condition') + end + end + + function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) + error('An interface function does not exist yet'); + end + + function N = size(obj) + N = obj.m; + end + + function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y) + params=obj.params; + + if isa(mat,'function_handle') + [rows,cols]=size(mat(params,0,0)); + matVec=mat(params,X',Y'); + matVec=sparse(matVec); + side=max(length(X),length(Y)); + else + matVec=mat; + [rows,cols]=size(matVec); + side=max(length(X),length(Y)); + cols=cols/side; + end + ret=kron(ones(rows,cols),speye(side)); + + for ii=1:rows + for jj=1:cols + ret((ii-1)*side+1:ii*side,(jj-1)*side+1:jj*side)=diag(matVec(ii,(jj-1)*side+1:jj*side)); + end + end + end + + + function [closure, penalty]=boundary_condition_char(obj,boundary) + params=obj.params; + x=obj.x; y=obj.y; + side=max(length(x),length(y)); + + switch boundary + case {'w','W','west'} + e_=obj.e_w; + mat=obj.matrices.A; + boundPos='l'; + Hi=obj.Hxi; + [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y); + case {'e','E','east'} + e_=obj.e_e; + mat=obj.matrices.A; + boundPos='r'; + Hi=obj.Hxi; + [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y); + case {'s','S','south'} + e_=obj.e_s; + mat=obj.matrices.B; + boundPos='l'; + Hi=obj.Hxi; + [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1)); + case {'n','N','north'} + e_=obj.e_n; + mat=obj.matrices.B; + boundPos='r'; + Hi=obj.Hxi; + [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end)); + end + + pos=signVec(1); zeroval=signVec(2); neg=signVec(3); + + switch boundPos + case {'l'} + tau=sparse(obj.n*side,pos*side); + Vi_plus=Vi(1:pos*side,:); + tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side)); + closure=Hi*e_*V*tau*Vi_plus*e_'; + penalty=-Hi*e_*V*tau*Vi_plus; + case {'r'} + tau=sparse(obj.n*side,neg*side); + tau((pos+zeroval)*side+1:obj.n*side,:)=-abs(D((pos+zeroval)*side+1:obj.n*side,(pos+zeroval)*side+1:obj.n*side)); + Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:); + closure=Hi*e_*V*tau*Vi_minus*e_'; + penalty=-Hi*e_*V*tau*Vi_minus; + end + end + + + function [closure,penalty]=boundary_condition_general(obj,boundary,L) + params=obj.params; + x=obj.x; y=obj.y; + side=max(length(x),length(y)); + + switch boundary + case {'w','W','west'} + e_=obj.e_w; + mat=obj.matrices.A; + boundPos='l'; + Hi=obj.Hxi; + [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y); + L=obj.evaluateCoefficientMatrix(L,x(1),y); + case {'e','E','east'} + e_=obj.e_e; + mat=obj.matrices.A; + boundPos='r'; + Hi=obj.Hxi; + [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y); + L=obj.evaluateCoefficientMatrix(L,x(end),y); + case {'s','S','south'} + e_=obj.e_s; + mat=obj.matrices.B; + boundPos='l'; + Hi=obj.Hxi; + [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1)); + L=obj.evaluateCoefficientMatrix(L,x,y(1)); + case {'n','N','north'} + e_=obj.e_n; + mat=obj.matrices.B; + boundPos='r'; + Hi=obj.Hxi; + [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end)); + L=obj.evaluateCoefficientMatrix(L,x,y(end)); + end + + pos=signVec(1); zeroval=signVec(2); neg=signVec(3); + + switch boundPos + case {'l'} + tau=sparse(obj.n*side,pos*side); + Vi_plus=Vi(1:pos*side,:); + Vi_minus=Vi(pos*side+1:obj.n*side,:); + V_plus=V(:,1:pos*side); + V_minus=V(:,(pos+zeroval)*side+1:obj.n*side); + + tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side)); + R=-inv(L*V_plus)*(L*V_minus); + closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_'; + penalty=-Hi*e_*V*tau*inv(L*V_plus)*L; + case {'r'} + tau=sparse(obj.n*side,neg*side); + tau((pos+zeroval)*side+1:obj.n*side,:)=-abs(D((pos+zeroval)*side+1:obj.n*side,(pos+zeroval)*side+1:obj.n*side)); + Vi_plus=Vi(1:pos*side,:); + Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:); + + V_plus=V(:,1:pos*side); + V_minus=V(:,(pos+zeroval)*side+1:obj.n*side); + R=-inv(L*V_minus)*(L*V_plus); + closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_'; + penalty=-Hi*e_*V*tau*inv(L*V_minus)*L; + end + end + + + function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y) + params=obj.params; + syms xs ys; + [V, D]=eig(mat(params,xs,ys)); + xs=1;ys=1; + DD=eval(diag(D)); + + poseig=find(DD>0); + zeroeig=find(DD==0); + negeig=find(DD<0); + syms xs ys + DD=diag(D); + + D=diag([DD(poseig);DD(zeroeig); DD(negeig)]); + V=[V(:,poseig) V(:,zeroeig) V(:,negeig)]; + xs=x; ys=y; + + side=max(length(x),length(y)); + Dret=zeros(obj.n,side*obj.n); + Vret=zeros(obj.n,side*obj.n); + for ii=1:obj.n + for jj=1:obj.n + Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii)); + Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii)); + end + end + + D=sparse(Dret); + V=sparse(normc(Vret)); + V=obj.evaluateCoefficientMatrix(V,x,y); + D=obj.evaluateCoefficientMatrix(D,x,y); + Vi=inv(V); + signVec=[length(poseig),length(zeroeig),length(negeig)]; + end + + end +end \ No newline at end of file
diff -r da0131655035 -r a6ae1b104391 +scheme/hypsyst2d.m --- a/+scheme/hypsyst2d.m Mon Sep 26 14:19:34 2016 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,279 +0,0 @@ -classdef Hypsyst2d < scheme.Scheme - properties - m % Number of points in each direction, possibly a vector - n %size of system - h % Grid spacing - x,y % Grid - X,Y % Values of x and y for each grid point - order % Order accuracy for the approximation - - D % non-stabalized scheme operator - A, B, E - - H % Discrete norm - % Norms in the x and y directions - Hxi,Hyi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir. - I_x,I_y, I_N - e_w, e_e, e_s, e_n - params %parameters for the coeficient matrices - matrices - end - - - methods - function obj = Hypsyst2d(m, lim, order, A, B, E, params) - default_arg('E', []) - xlim = lim{1}; - ylim = lim{2}; - - if length(m) == 1 - m = [m m]; - end - - m_x = m(1); - m_y = m(2); - obj.params = params; - - obj.matrices = matrices; - - ops_x = sbp.D2Standard(m_x,xlim,order); - ops_y = sbp.D2Standard(m_y,ylim,order); - - obj.x = ops_x.x; - obj.y = ops_y.x; - - obj.X = kr(obj.x,ones(m_y,1)); - obj.Y = kr(ones(m_x,1),obj.y); - - obj.A = obj.evaluateCoefficientMatrix(matrices.A, obj.X, obj.Y); - obj.B = obj.evaluateCoefficientMatrix(matrices.B, obj.X, obj.Y); - obj.E = obj.evaluateCoefficientMatrix(matrices.E, obj.X, obj.Y); - - obj.n = length(matrices.A(obj.params,0,0)); - - I_n = eye(obj.n);I_x = speye(m_x); - obj.I_x = I_x; - I_y = speye(m_y); - obj.I_y = I_y; - - - D1_x = kr(I_n, ops_x.D1, I_y); - obj.Hxi = kr(I_n, ops_x.HI, I_y); - D1_y = kr(I_n, I_x, ops_y.D1)); - obj.Hyi = kr(I_n, I_x, ops_y.HI)); - - obj.e_w = kr(I_n, ops_x.e_l, I_y); - obj.e_e = kr(I_n, ops_x.e_r, I_y); - obj.e_s = kr(I_n, I_x, ops_y.e_l); - obj.e_n = kr(I_n, I_x, ops_y.e_r); - - obj.m=m; - obj.h=[ops_x.h ops_y.h]; - obj.order=order; - - obj.D=-obj.A*D1_x-obj.B*D1_y-obj.E; - - end - - % Closure functions return the opertors applied to the own doamin to close the boundary - % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. - % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. - % type is a string specifying the type of boundary condition if there are several. - % data is a function returning the data that should be applied at the boundary. - function [closure, penalty] = boundary_condition(obj,boundary,type,L) - default_arg('type','char'); - switch type - case{'c','char'} - [closure,penalty]=boundary_condition_char(obj,boundary); - case{'general'} - [closure,penalty]=boundary_condition_general(obj,boundary,L); - otherwise - error('No such boundary condition') - end - end - - function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) - error('An interface function does not exist yet'); - end - - function N = size(obj) - N = obj.m; - end - - function [ret] = evaluateCoefficientMatrix(obj, mat, X, Y) - params=obj.params; - - if isa(mat,'function_handle') - [rows,cols]=size(mat(params,0,0)); - matVec=mat(params,X',Y'); - matVec=sparse(matVec); - side=max(length(X),length(Y)); - else - matVec=mat; - [rows,cols]=size(matVec); - side=max(length(X),length(Y)); - cols=cols/side; - end - ret=kron(ones(rows,cols),speye(side)); - - for ii=1:rows - for jj=1:cols - ret((ii-1)*side+1:ii*side,(jj-1)*side+1:jj*side)=diag(matVec(ii,(jj-1)*side+1:jj*side)); - end - end - end - - - function [closure, penalty]=boundary_condition_char(obj,boundary) - params=obj.params; - x=obj.x; y=obj.y; - side=max(length(x),length(y)); - - switch boundary - case {'w','W','west'} - e_=obj.e_w; - mat=obj.matrices.A; - boundPos='l'; - Hi=obj.Hxi; - [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y); - case {'e','E','east'} - e_=obj.e_e; - mat=obj.matrices.A; - boundPos='r'; - Hi=obj.Hxi; - [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y); - case {'s','S','south'} - e_=obj.e_s; - mat=obj.matrices.B; - boundPos='l'; - Hi=obj.Hxi; - [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1)); - case {'n','N','north'} - e_=obj.e_n; - mat=obj.matrices.B; - boundPos='r'; - Hi=obj.Hxi; - [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end)); - end - - pos=signVec(1); zeroval=signVec(2); neg=signVec(3); - - switch boundPos - case {'l'} - tau=sparse(obj.n*side,pos*side); - Vi_plus=Vi(1:pos*side,:); - tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side)); - closure=Hi*e_*V*tau*Vi_plus*e_'; - penalty=-Hi*e_*V*tau*Vi_plus; - case {'r'} - tau=sparse(obj.n*side,neg*side); - tau((pos+zeroval)*side+1:obj.n*side,:)=-abs(D((pos+zeroval)*side+1:obj.n*side,(pos+zeroval)*side+1:obj.n*side)); - Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:); - closure=Hi*e_*V*tau*Vi_minus*e_'; - penalty=-Hi*e_*V*tau*Vi_minus; - end - end - - - function [closure,penalty]=boundary_condition_general(obj,boundary,L) - params=obj.params; - x=obj.x; y=obj.y; - side=max(length(x),length(y)); - - switch boundary - case {'w','W','west'} - e_=obj.e_w; - mat=obj.matrices.A; - boundPos='l'; - Hi=obj.Hxi; - [V,Vi,D,signVec]=obj.matrixDiag(mat,x(1),y); - L=obj.evaluateCoefficientMatrix(L,x(1),y); - case {'e','E','east'} - e_=obj.e_e; - mat=obj.matrices.A; - boundPos='r'; - Hi=obj.Hxi; - [V,Vi,D,signVec]=obj.matrixDiag(mat,x(end),y); - L=obj.evaluateCoefficientMatrix(L,x(end),y); - case {'s','S','south'} - e_=obj.e_s; - mat=obj.matrices.B; - boundPos='l'; - Hi=obj.Hxi; - [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(1)); - L=obj.evaluateCoefficientMatrix(L,x,y(1)); - case {'n','N','north'} - e_=obj.e_n; - mat=obj.matrices.B; - boundPos='r'; - Hi=obj.Hxi; - [V,Vi,D,signVec]=obj.matrixDiag(mat,x,y(end)); - L=obj.evaluateCoefficientMatrix(L,x,y(end)); - end - - pos=signVec(1); zeroval=signVec(2); neg=signVec(3); - - switch boundPos - case {'l'} - tau=sparse(obj.n*side,pos*side); - Vi_plus=Vi(1:pos*side,:); - Vi_minus=Vi(pos*side+1:obj.n*side,:); - V_plus=V(:,1:pos*side); - V_minus=V(:,(pos+zeroval)*side+1:obj.n*side); - - tau(1:pos*side,:)=-abs(D(1:pos*side,1:pos*side)); - R=-inv(L*V_plus)*(L*V_minus); - closure=Hi*e_*V*tau*(Vi_plus-R*Vi_minus)*e_'; - penalty=-Hi*e_*V*tau*inv(L*V_plus)*L; - case {'r'} - tau=sparse(obj.n*side,neg*side); - tau((pos+zeroval)*side+1:obj.n*side,:)=-abs(D((pos+zeroval)*side+1:obj.n*side,(pos+zeroval)*side+1:obj.n*side)); - Vi_plus=Vi(1:pos*side,:); - Vi_minus=Vi((pos+zeroval)*side+1:obj.n*side,:); - - V_plus=V(:,1:pos*side); - V_minus=V(:,(pos+zeroval)*side+1:obj.n*side); - R=-inv(L*V_minus)*(L*V_plus); - closure=Hi*e_*V*tau*(Vi_minus-R*Vi_plus)*e_'; - penalty=-Hi*e_*V*tau*inv(L*V_minus)*L; - end - end - - - function [V,Vi, D,signVec]=matrixDiag(obj,mat,x,y) - params=obj.params; - syms xs ys; - [V, D]=eig(mat(params,xs,ys)); - xs=1;ys=1; - DD=eval(diag(D)); - - poseig=find(DD>0); - zeroeig=find(DD==0); - negeig=find(DD<0); - syms xs ys - DD=diag(D); - - D=diag([DD(poseig);DD(zeroeig); DD(negeig)]); - V=[V(:,poseig) V(:,zeroeig) V(:,negeig)]; - xs=x; ys=y; - - side=max(length(x),length(y)); - Dret=zeros(obj.n,side*obj.n); - Vret=zeros(obj.n,side*obj.n); - for ii=1:obj.n - for jj=1:obj.n - Dret(jj,(ii-1)*side+1:side*ii)=eval(D(jj,ii)); - Vret(jj,(ii-1)*side+1:side*ii)=eval(V(jj,ii)); - end - end - - D=sparse(Dret); - V=sparse(normc(Vret)); - V=obj.evaluateCoefficientMatrix(V,x,y); - D=obj.evaluateCoefficientMatrix(D,x,y); - Vi=inv(V); - signVec=[length(poseig),length(zeroeig),length(negeig)]; - end - - end -end \ No newline at end of file