--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+scheme/Hypsyst3dCurve.m	Tue Feb 07 15:47:51 2017 +0100
@@ -0,0 +1,557 @@
+classdef Hypsyst3dCurve < scheme.Scheme
+    properties
+        m % Number of points in each direction, possibly a vector
+        n %size of system
+        h % Grid spacing
+        X, Y, Z% Values of x and y for each grid point
+        Yx, Zx, Xy, Zy, Xz, Yz %Grid values for boundary surfaces
+        
+        xi,eta,zeta
+        Xi, Eta, Zeta
+        
+        Eta_xi, Zeta_xi, Xi_eta, Zeta_eta, Xi_zeta, Eta_zeta    % Metric terms
+        X_xi, X_eta, X_zeta,Y_xi,Y_eta,Y_zeta,Z_xi,Z_eta,Z_zeta % Metric terms
+        
+        order % Order accuracy for the approximation
+        
+        D % non-stabalized scheme operator
+        Aevaluated, Bevaluated, Cevaluated, Eevaluated % Numeric Coeffiecient matrices
+        Ahat, Bhat, Chat  % Symbolic Transformed Coefficient matrices
+        A, B, C, E % Symbolic coeffiecient matrices
+        
+        J, Ji % JAcobian and inverse Jacobian
+        
+        H % Discrete norm
+        % Norms in the x, y and z directions
+        Hxii,Hetai,Hzetai, Hzi % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
+        Hxi,Heta,Hzeta
+        I_xi,I_eta,I_zeta, I_N,onesN
+        e_w, e_e, e_s, e_n, e_b, e_t
+        index_w, index_e,index_s,index_n, index_b, index_t
+        params %parameters for the coeficient matrice
+    end
+    
+    
+    methods
+        function obj = Hypsyst3dCurve(m, order, A, B,C, E, params,ti,operator)
+            xilim ={0 1};
+            etalim = {0 1};
+            zetalim = {0 1};
+            
+            if length(m) == 1
+                m = [m m m];
+            end
+            m_xi = m(1);
+            m_eta = m(2);
+            m_zeta = m(3);
+            m_tot = m_xi*m_eta*m_zeta;
+            obj.params = params;
+            obj.n = length(A(obj,0,0,0));
+            
+            obj.m = m;
+            obj.order = order;
+            obj.onesN = ones(obj.n);
+            
+            switch operator
+                case 'upwind'
+                    ops_xi = sbp.D1Upwind(m_xi,xilim,order);
+                    ops_eta = sbp.D1Upwind(m_eta,etalim,order);
+                    ops_zeta = sbp.D1Upwind(m_zeta,zetalim,order);
+                case 'standard'
+                    ops_xi = sbp.D2Standard(m_xi,xilim,order);
+                    ops_eta = sbp.D2Standard(m_eta,etalim,order);
+                    ops_zeta = sbp.D2Standard(m_zeta,zetalim,order);
+                otherwise
+                    error('Operator not available')
+            end
+            
+            obj.xi = ops_xi.x;
+            obj.eta = ops_eta.x;
+            obj.zeta = ops_zeta.x;
+            
+            obj.Xi = kr(obj.xi,ones(m_eta,1),ones(m_zeta,1));
+            obj.Eta = kr(ones(m_xi,1),obj.eta,ones(m_zeta,1));
+            obj.Zeta = kr(ones(m_xi,1),ones(m_eta,1),obj.zeta);
+            
+            
+            [X,Y,Z] = ti.map(obj.Xi,obj.Eta,obj.Zeta);
+            obj.X = X;
+            obj.Y = Y;
+            obj.Z = Z;
+            
+            I_n = eye(obj.n);
+            I_xi = speye(m_xi);
+            obj.I_xi = I_xi;
+            I_eta = speye(m_eta);
+            obj.I_eta = I_eta;
+            I_zeta = speye(m_zeta);
+            obj.I_zeta = I_zeta;
+            
+            I_N=kr(I_n,I_xi,I_eta,I_zeta);
+            
+            O_xi = ones(m_xi,1);
+            O_eta = ones(m_eta,1);
+            O_zeta = ones(m_zeta,1);
+            
+            
+            obj.Hxi = ops_xi.H;
+            obj.Heta = ops_eta.H;
+            obj.Hzeta = ops_zeta.H;
+            obj.h = [ops_xi.h ops_eta.h ops_zeta.h];
+            
+            switch operator
+                case 'upwind'
+                    D1_xi = kr((ops_xi.Dp+ops_xi.Dm)/2, I_eta,I_zeta);
+                    D1_eta = kr(I_xi, (ops_eta.Dp+ops_eta.Dm)/2,I_zeta);
+                    D1_zeta = kr(I_xi, I_eta,(ops_zeta.Dp+ops_zeta.Dm)/2);
+                otherwise
+                    D1_xi = kr(ops_xi.D1, I_eta,I_zeta);
+                    D1_eta = kr(I_xi, ops_eta.D1,I_zeta);
+                    D1_zeta = kr(I_xi, I_eta,ops_zeta.D1);
+            end
+            
+            obj.A = A;
+            obj.B = B;
+            obj.C = C;
+            
+            obj.X_xi = D1_xi*X;
+            obj.X_eta = D1_eta*X;
+            obj.X_zeta = D1_zeta*X;
+            obj.Y_xi = D1_xi*Y;
+            obj.Y_eta = D1_eta*Y;
+            obj.Y_zeta = D1_zeta*Y;
+            obj.Z_xi = D1_xi*Z;
+            obj.Z_eta = D1_eta*Z;
+            obj.Z_zeta = D1_zeta*Z;
+            
+            obj.Ahat = @transform_coefficient_matrix;
+            obj.Bhat = @transform_coefficient_matrix;
+            obj.Chat = @transform_coefficient_matrix;
+            obj.E = @(obj,x,y,z,~,~,~,~,~,~)E(obj,x,y,z);
+            
+            obj.Aevaluated = obj.evaluateCoefficientMatrix(obj.Ahat,obj.X, obj.Y,obj.Z, obj.X_eta,obj.X_zeta,obj.Y_eta,obj.Y_zeta,obj.Z_eta,obj.Z_zeta);
+            obj.Bevaluated = obj.evaluateCoefficientMatrix(obj.Bhat,obj.X, obj.Y,obj.Z, obj.X_zeta,obj.X_xi,obj.Y_zeta,obj.Y_xi,obj.Z_zeta,obj.Z_xi);
+            obj.Cevaluated = obj.evaluateCoefficientMatrix(obj.Chat,obj.X,obj.Y,obj.Z, obj.X_xi,obj.X_eta,obj.Y_xi,obj.Y_eta,obj.Z_xi,obj.Z_eta);
+            
+            switch operator
+                case 'upwind'
+                    clear  D1_xi D1_eta D1_zeta
+                    alphaA = max(abs(eig(obj.Ahat(obj,obj.X(end), obj.Y(end),obj.Z(end), obj.X_eta(end),obj.X_zeta(end),obj.Y_eta(end),obj.Y_zeta(end),obj.Z_eta(end),obj.Z_zeta(end)))));
+                    alphaB = max(abs(eig(obj.Bhat(obj,obj.X(end), obj.Y(end),obj.Z(end), obj.X_zeta(end),obj.X_xi(end),obj.Y_zeta(end),obj.Y_xi(end),obj.Z_zeta(end),obj.Z_xi(end)))));
+                    alphaC = max(abs(eig(obj.Chat(obj,obj.X(end), obj.Y(end),obj.Z(end), obj.X_xi(end),obj.X_eta(end),obj.Y_xi(end),obj.Y_eta(end),obj.Z_xi(end),obj.Z_eta(end)))));
+                    
+                    Ap = (obj.Aevaluated+alphaA*I_N)/2;
+                    Dmxi = kr(I_n, ops_xi.Dm, I_eta,I_zeta);
+                    diffSum = -Ap*Dmxi;
+                    clear Ap Dmxi
+                    
+                    Am = (obj.Aevaluated-alphaA*I_N)/2;
+                    
+                    obj.Aevaluated = [];
+                    Dpxi = kr(I_n, ops_xi.Dp, I_eta,I_zeta);
+                    temp = Am*Dpxi;
+                    diffSum = diffSum-temp;
+                    clear Am Dpxi
+                    
+                    Bp = (obj.Bevaluated+alphaB*I_N)/2;
+                    Dmeta = kr(I_n, I_xi, ops_eta.Dm,I_zeta);
+                    temp = Bp*Dmeta;
+                    diffSum = diffSum-temp;
+                    clear Bp Dmeta
+                    
+                    Bm = (obj.Bevaluated-alphaB*I_N)/2;
+                    obj.Bevaluated = [];
+                    Dpeta = kr(I_n, I_xi, ops_eta.Dp,I_zeta);
+                    temp = Bm*Dpeta;
+                    diffSum = diffSum-temp;
+                    clear Bm Dpeta
+                    
+                    Cp = (obj.Cevaluated+alphaC*I_N)/2;
+                    Dmzeta = kr(I_n, I_xi, I_eta,ops_zeta.Dm);
+                    temp = Cp*Dmzeta;
+                    diffSum = diffSum-temp;
+                    clear Cp Dmzeta
+                    
+                    Cm = (obj.Cevaluated-alphaC*I_N)/2;
+                    clear I_N
+                    obj.Cevaluated = [];
+                    Dpzeta = kr(I_n, I_xi, I_eta,ops_zeta.Dp);
+                    temp = Cm*Dpzeta;
+                    diffSum = diffSum-temp;
+                    clear Cm Dpzeta temp
+                    
+                    obj.J = obj.X_xi.*obj.Y_eta.*obj.Z_zeta...
+                        +obj.X_zeta.*obj.Y_xi.*obj.Z_eta...
+                        +obj.X_eta.*obj.Y_zeta.*obj.Z_xi...
+                        -obj.X_xi.*obj.Y_zeta.*obj.Z_eta...
+                        -obj.X_eta.*obj.Y_xi.*obj.Z_zeta...
+                        -obj.X_zeta.*obj.Y_eta.*obj.Z_xi;
+                    
+                    obj.Ji = kr(I_n,spdiags(1./obj.J,0,m_tot,m_tot));
+                    obj.Eevaluated = obj.evaluateCoefficientMatrix(obj.E, obj.X, obj.Y,obj.Z,[],[],[],[],[],[]);
+                    
+                    obj.D = obj.Ji*diffSum-obj.Eevaluated;
+                    
+                case 'standard'
+                    D1_xi = kr(I_n,D1_xi);
+                    D1_eta = kr(I_n,D1_eta);
+                    D1_zeta = kr(I_n,D1_zeta);
+                    
+                    obj.J = obj.X_xi.*obj.Y_eta.*obj.Z_zeta...
+                        +obj.X_zeta.*obj.Y_xi.*obj.Z_eta...
+                        +obj.X_eta.*obj.Y_zeta.*obj.Z_xi...
+                        -obj.X_xi.*obj.Y_zeta.*obj.Z_eta...
+                        -obj.X_eta.*obj.Y_xi.*obj.Z_zeta...
+                        -obj.X_zeta.*obj.Y_eta.*obj.Z_xi;
+                    
+                    obj.Ji = kr(I_n,spdiags(1./obj.J,0,m_tot,m_tot));
+                    obj.Eevaluated = obj.evaluateCoefficientMatrix(obj.E, obj.X, obj.Y,obj.Z,[],[],[],[],[],[]);
+                    
+                    obj.D = obj.Ji*(-obj.Aevaluated*D1_xi-obj.Bevaluated*D1_eta -obj.Cevaluated*D1_zeta)-obj.Eevaluated;
+                otherwise
+                    error('Operator not supported')
+            end
+            
+            obj.Hxii = kr(I_n, ops_xi.HI, I_eta,I_zeta);
+            obj.Hetai = kr(I_n, I_xi, ops_eta.HI,I_zeta);
+            obj.Hzetai = kr(I_n, I_xi,I_eta, ops_zeta.HI);
+            
+            obj.index_w = (kr(ops_xi.e_l, O_eta,O_zeta)==1);
+            obj.index_e = (kr(ops_xi.e_r, O_eta,O_zeta)==1);
+            obj.index_s = (kr(O_xi, ops_eta.e_l,O_zeta)==1);
+            obj.index_n = (kr(O_xi, ops_eta.e_r,O_zeta)==1);
+            obj.index_b = (kr(O_xi, O_eta, ops_zeta.e_l)==1);
+            obj.index_t = (kr(O_xi, O_eta, ops_zeta.e_r)==1);
+            
+            obj.e_w = kr(I_n, ops_xi.e_l, I_eta,I_zeta);
+            obj.e_e = kr(I_n, ops_xi.e_r, I_eta,I_zeta);
+            obj.e_s = kr(I_n, I_xi, ops_eta.e_l,I_zeta);
+            obj.e_n = kr(I_n, I_xi, ops_eta.e_r,I_zeta);
+            obj.e_b = kr(I_n, I_xi, I_eta, ops_zeta.e_l);
+            obj.e_t = kr(I_n, I_xi, I_eta, ops_zeta.e_r);
+            
+            obj.Eta_xi = kr(obj.eta,ones(m_xi,1));
+            obj.Zeta_xi = kr(ones(m_eta,1),obj.zeta);
+            obj.Xi_eta = kr(obj.xi,ones(m_zeta,1));
+            obj.Zeta_eta = kr(ones(m_xi,1),obj.zeta);
+            obj.Xi_zeta = kr(obj.xi,ones(m_eta,1));
+            obj.Eta_zeta = kr(ones(m_zeta,1),obj.eta);           
+        end
+        
+        function [ret] = transform_coefficient_matrix(obj,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2)
+            ret = obj.A(obj,x,y,z).*(y_1.*z_2-z_1.*y_2);
+            ret = ret+obj.B(obj,x,y,z).*(x_2.*z_1-x_1.*z_2);
+            ret = ret+obj.C(obj,x,y,z).*(x_1.*y_2-x_2.*y_1);
+        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');
+            BM = boundary_matrices(obj,boundary);
+            
+            switch type
+                case{'c','char'}
+                    [closure,penalty] = boundary_condition_char(obj,BM);
+                case{'general'}
+                    [closure,penalty] = boundary_condition_general(obj,BM,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
+        
+        % Evaluates the symbolic Coeffiecient matrix mat
+        function [ret] = evaluateCoefficientMatrix(obj,mat, X, Y, Z , x_1 , x_2 , y_1 , y_2 , z_1 , z_2)
+            params = obj.params;
+            side = max(length(X),length(Y));
+            if isa(mat,'function_handle')
+                [rows,cols] = size(mat(obj,0,0,0,0,0,0,0,0,0));
+                x_1 = kr(obj.onesN,x_1);
+                x_2 = kr(obj.onesN,x_2);
+                y_1 = kr(obj.onesN,y_1);
+                y_2 = kr(obj.onesN,y_2);
+                z_1 = kr(obj.onesN,z_1);
+                z_2 = kr(obj.onesN,z_2);
+                matVec = mat(obj,X',Y',Z',x_1',x_2',y_1',y_2',z_1',z_2');
+                matVec = sparse(matVec);
+            else
+                matVec = mat;
+                [rows,cols] = size(matVec);
+                side = max(length(X),length(Y));
+                cols = cols/side;
+            end
+            matVec(abs(matVec)<10^(-10)) = 0;
+            ret = cell(rows,cols);
+            
+            for ii = 1:rows
+                for jj = 1:cols
+                    ret{ii,jj} = diag(matVec(ii,(jj-1)*side+1:jj*side));
+                end
+            end
+            ret = cell2mat(ret);
+        end
+        
+        function [BM] = boundary_matrices(obj,boundary)
+            params = obj.params;
+            BM.boundary = boundary;
+            switch boundary
+                case {'w','W','west'}
+                    BM.e_ = obj.e_w;
+                    mat = obj.Ahat;
+                    BM.boundpos = 'l';
+                    BM.Hi = obj.Hxii;
+                    BM.index = obj.index_w;
+                    BM.x_1 = obj.X_eta(BM.index);
+                    BM.x_2 = obj.X_zeta(BM.index);
+                    BM.y_1 = obj.Y_eta(BM.index);
+                    BM.y_2 = obj.Y_zeta(BM.index);
+                    BM.z_1 = obj.Z_eta(BM.index);
+                    BM.z_2 = obj.Z_zeta(BM.index);
+                case {'e','E','east'}
+                    BM.e_ = obj.e_e;
+                    mat = obj.Ahat;
+                    BM.boundpos = 'r';
+                    BM.Hi = obj.Hxii;
+                    BM.index = obj.index_e;
+                    BM.x_1 = obj.X_eta(BM.index);
+                    BM.x_2 = obj.X_zeta(BM.index);
+                    BM.y_1 = obj.Y_eta(BM.index);
+                    BM.y_2 = obj.Y_zeta(BM.index);
+                    BM.z_1 = obj.Z_eta(BM.index);
+                    BM.z_2 = obj.Z_zeta(BM.index);
+                case {'s','S','south'}
+                    BM.e_ = obj.e_s;
+                    mat = obj.Bhat;
+                    BM.boundpos = 'l';
+                    BM.Hi = obj.Hetai;
+                    BM.index = obj.index_s;
+                    BM.x_1 = obj.X_zeta(BM.index);
+                    BM.x_2 = obj.X_xi(BM.index);
+                    BM.y_1 = obj.Y_zeta(BM.index);
+                    BM.y_2 = obj.Y_xi(BM.index);
+                    BM.z_1 = obj.Z_zeta(BM.index);
+                    BM.z_2 = obj.Z_xi(BM.index);
+                case {'n','N','north'}
+                    BM.e_ = obj.e_n;
+                    mat = obj.Bhat;
+                    BM.boundpos = 'r';
+                    BM.Hi = obj.Hetai;
+                    BM.index = obj.index_n;
+                    BM.x_1 = obj.X_zeta(BM.index);
+                    BM.x_2 = obj.X_xi(BM.index);
+                    BM.y_1 = obj.Y_zeta(BM.index);
+                    BM.y_2 = obj.Y_xi(BM.index);
+                    BM.z_1 = obj.Z_zeta(BM.index);
+                    BM.z_2 = obj.Z_xi(BM.index);
+                case{'b','B','Bottom'}
+                    BM.e_ = obj.e_b;
+                    mat = obj.Chat;
+                    BM.boundpos = 'l';
+                    BM.Hi = obj.Hzetai;
+                    BM.index = obj.index_b;
+                    BM.x_1 = obj.X_xi(BM.index);
+                    BM.x_2 = obj.X_eta(BM.index);
+                    BM.y_1 = obj.Y_xi(BM.index);
+                    BM.y_2 = obj.Y_eta(BM.index);
+                    BM.z_1 = obj.Z_xi(BM.index);
+                    BM.z_2 = obj.Z_eta(BM.index);
+                case{'t','T','Top'}
+                    BM.e_ = obj.e_t;
+                    mat = obj.Chat;
+                    BM.boundpos = 'r';
+                    BM.Hi = obj.Hzetai;
+                    BM.index = obj.index_t;
+                    BM.x_1 = obj.X_xi(BM.index);
+                    BM.x_2 = obj.X_eta(BM.index);
+                    BM.y_1 = obj.Y_xi(BM.index);
+                    BM.y_2 = obj.Y_eta(BM.index);
+                    BM.z_1 = obj.Z_xi(BM.index);
+                    BM.z_2 = obj.Z_eta(BM.index);
+            end
+            [BM.V,BM.Vi,BM.D,signVec] = obj.matrixDiag(mat,obj.X(BM.index),obj.Y(BM.index),obj.Z(BM.index),...
+                BM.x_1,BM.x_2,BM.y_1,BM.y_2,BM.z_1,BM.z_2);
+            BM.side = sum(BM.index);
+            BM.pos = signVec(1); BM.zeroval=signVec(2); BM.neg=signVec(3);
+        end
+        
+        % Characteristic boundary condition
+        function [closure, penalty] = boundary_condition_char(obj,BM)
+            side = BM.side;
+            pos = BM.pos;
+            neg = BM.neg;
+            zeroval = BM.zeroval;
+            V = BM.V;
+            Vi = BM.Vi;
+            Hi = BM.Hi;
+            D = BM.D;
+            e_ = BM.e_;
+            
+            switch BM.boundpos
+                case {'l'}
+                    tau = sparse(obj.n*side,pos);
+                    Vi_plus = Vi(1:pos,:);
+                    tau(1:pos,:) = -abs(D(1:pos,1:pos));
+                    closure = Hi*e_*V*tau*Vi_plus*e_';
+                    penalty = -Hi*e_*V*tau*Vi_plus;
+                case {'r'}
+                    tau = sparse(obj.n*side,neg);
+                    tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side));
+                    Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:);
+                    closure = Hi*e_*V*tau*Vi_minus*e_';
+                    penalty = -Hi*e_*V*tau*Vi_minus;
+            end
+        end
+        
+        % General boundary condition in the form Lu=g(x)
+        function [closure,penalty] = boundary_condition_general(obj,BM,boundary,L)
+            side = BM.side;
+            pos = BM.pos;
+            neg = BM.neg;
+            zeroval = BM.zeroval;
+            V = BM.V;
+            Vi = BM.Vi;
+            Hi = BM.Hi;
+            D = BM.D;
+            e_ = BM.e_;
+            index = BM.index;
+            
+            switch BM.boundary
+                case{'b','B','bottom'}
+                    Ji_vec = diag(obj.Ji);
+                    Ji = diag(Ji_vec(index));
+                    Zeta_x = Ji*(obj.Y_xi(index).*obj.Z_eta(index)-obj.Z_xi(index).*obj.Y_eta(index));
+                    Zeta_y = Ji*(obj.X_eta(index).*obj.Z_xi(index)-obj.X_xi(index).*obj.Z_eta(index));
+                    Zeta_z = Ji*(obj.X_xi(index).*obj.Y_eta(index)-obj.Y_xi(index).*obj.X_eta(index));
+                    
+                    L = obj.evaluateCoefficientMatrix(L,Zeta_x,Zeta_y,Zeta_z,[],[],[],[],[],[]);
+            end
+            
+            switch BM.boundpos
+                case {'l'}
+                    tau = sparse(obj.n*side,pos);
+                    Vi_plus = Vi(1:pos,:);
+                    Vi_minus = Vi(pos+zeroval+1:obj.n*side,:);
+                    V_plus = V(:,1:pos);
+                    V_minus = V(:,(pos+zeroval)+1:obj.n*side);
+                    
+                    tau(1:pos,:) = -abs(D(1:pos,1:pos));
+                    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);
+                    tau((pos+zeroval)+1:obj.n*side,:) = -abs(D((pos+zeroval)+1:obj.n*side,(pos+zeroval)+1:obj.n*side));
+                    Vi_plus = Vi(1:pos,:);
+                    Vi_minus = Vi((pos+zeroval)+1:obj.n*side,:);
+                    
+                    V_plus = V(:,1:pos);
+                    V_minus = V(:,(pos+zeroval)+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 that diagonalizes a symbolic matrix A as A=V*D*Vi
+        % D         is a diagonal matrix with the eigenvalues on A on the diagonal sorted by their sign
+        %                                    [d+       ]
+        %                               D =  [   d0    ]
+        %                                    [       d-]
+        % signVec   is a vector specifying the number of possitive, zero and negative eigenvalues of D
+        function [V,Vi, D,signVec] = matrixDiag(obj,mat,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2)
+            params = obj.params;
+            eps = 10^(-10);
+            if(sum(abs(x_1))>eps)
+                syms x_1s
+            else
+                x_1s = 0;
+            end
+            
+            if(sum(abs(x_2))>eps)
+                syms x_2s;
+            else
+                x_2s = 0;
+            end
+            
+            
+            if(sum(abs(y_1))>eps)
+                syms y_1s
+            else
+                y_1s = 0;
+            end
+            
+            if(sum(abs(y_2))>eps)
+                syms y_2s;
+            else
+                y_2s = 0;
+            end
+            
+            if(sum(abs(z_1))>eps)
+                syms z_1s
+            else
+                z_1s = 0;
+            end
+            
+            if(sum(abs(z_2))>eps)
+                syms z_2s;
+            else
+                z_2s = 0;
+            end
+            
+            syms xs ys zs
+            [V, D] = eig(mat(obj,xs,ys,zs,x_1s,x_2s,y_1s,y_2s,z_1s,z_2s));
+            Vi = inv(V);
+            xs = x;
+            ys = y;
+            zs = z;
+            x_1s = x_1;
+            x_2s = x_2;
+            y_1s = y_1;
+            y_2s = y_2;
+            z_1s = z_1;
+            z_2s = z_2;
+            
+            side = max(length(x),length(y));
+            Dret = zeros(obj.n,side*obj.n);
+            Vret = zeros(obj.n,side*obj.n);
+            Viret = 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));
+                    Viret(jj,(ii-1)*side+1:side*ii) = eval(Vi(jj,ii));
+                end
+            end
+            
+            D = sparse(Dret);
+            V = sparse(Vret);
+            Vi = sparse(Viret);
+            V = obj.evaluateCoefficientMatrix(V,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2);
+            D = obj.evaluateCoefficientMatrix(D,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2);
+            Vi = obj.evaluateCoefficientMatrix(Vi,x,y,z,x_1,x_2,y_1,y_2,z_1,z_2);
+            DD = diag(D);
+            
+            poseig = (DD>0);
+            zeroeig = (DD==0);
+            negeig = (DD<0);
+            
+            D = diag([DD(poseig); DD(zeroeig); DD(negeig)]);
+            V = [V(:,poseig) V(:,zeroeig) V(:,negeig)];
+            Vi = [Vi(poseig,:); Vi(zeroeig,:); Vi(negeig,:)];
+            signVec = [sum(poseig),sum(zeroeig),sum(negeig)];
+        end
+    end
+end