EIDORS 3D Matlab based package Version 2.0 Matlab 6.1 is required for some of the plotting functions. ------------------------------------------------------------------------- [1] function [E,D,Ela,pp] = fem_master_full(vtx,simp,mat,gnd_ind,elec,zc,perm_sym); Builds up the system matrix based on the complete electrode model. E is not yet permuted. To permute E -> E(pp,pp) as in fwd_solver. -------------------------------------------------------------------------- [2] function [Ef,D,Ela] = bld_master_full(vtx,simp,mat,elec,zc); System matrix assembling based on the complete electrode model. This function is called within fem_master_full. -------------------------------------------------------------------------- [3] function [Ef,D,Ela] = bld_master(vtx,simp,mat_ref); Builds up the main compartment (GAP-SHUNT) of the system matrix for the complete electrode model. It is called within the function fem_master_full -------------------------------------------------------------------------- [4] function [Er] = ref_master(E,vtx,gnd_ind,sch); Applys reference conditions to the system. Modifying the system matrix to preserve the uniqueness of the forward solution. -------------------------------------------------------------------------- [5] function [I,Ib] = set_3d_currents(protocol,elec,vtx,gnd_ind,no_pl); This function sets current patterns in a system with (no_pl) planes of equal number of electrodes according to "opposite" or "adjacent" protocols, or their 3D similar. -------------------------------------------------------------------------- [6] function [I,Ib] = set_multi_currents(protocol,elec,vtx,gnd_ind,no_pl); This functions applies opposite or adjacent current patterns to each of the planes of the system simultaneously. -------------------------------------------------------------------------- [7] function [V] = forward_solver(E,I,tol,pp,V); This function solves the forward problem using the Cholesky or LU method or conjugate gradients. -------------------------------------------------------------------------- [8] function [voltageH,voltageV,indH,indV,df] = get_3d_meas(elec,vtx,V,Ib,no_pl); This function extracts multi-plane voltage measurements from a calculated 3D nodal potential distribution V inside a tank with (no_pl) electrode planes. Each plane holds the same number of electrodes. Only the non-current caring electrodes at the time are involved in the measurements. -------------------------------------------------------------------------- [9] function [voltage,ind,df] = get_multi_meas(protocol,elec,V,I,vtx,no_pl); The function can be used in the occasions where plane current patterns (adjacent or polar) are adopted for systems with more planes, i.e. set by set_multi_currents function. Only non-current carrying electrodes are involved in the measurements. -------------------------------------------------------------------------- [10] [v_f] = m_3d_fields(vtx,el_no,m_ind,E,tol,gnd_ind,v_f); This function calculates the measurement fields using preconditioned conjugate gradients. These are used in the calculation of the Jacobian. -------------------------------------------------------------------------- [11] function [fc] = figaro3d(srf,vtx,simp,fc,BB,h); This function plots the solution as a 3D object crossed at the plane z=h within the 3D boundaries of the volume. -------------------------------------------------------------------------- [12] function [fc] = slicer_plot(h,BB,vtx,simp,fc); This function plots a 2D slice of the 3D solution vector BB at z=h. The function plots a smooth approximation to the calculated solution. -------------------------------------------------------------------------- [13] function [fc] = slicer_plot_n(h,BB,vtx,simp,fc); This function plots a 2D slice of the 3D solution vector BB at z=h. -------------------------------------------------------------------------- [14] function [CC] = solution_ext(BB,vtx,simp); Auxiliary function that extracts a secondary NODE-wise solution CC based on the calculated ELEMENT-wise solution BB. This function is called from slicer_plot function. -------------------------------------------------------------------------- [15] function [J] = jacobian_3d(I,elec,vtx,simp,gnd_ind,mat_ref,zc,v_f,df,tol,perm_sym); This function calculates the Jacobian (sensitivity) matrix of the system wrt to conductivity. -------------------------------------------------------------------------- [16] function [Jrr,Jri,Jir,Jii] = jacobian_3d_comp(I,elec,vtx,simp,gnd_ind,mat_ref,no_pl,zc,v_f,df,tol,perm_sym); This function calculates the Jacobian matrices (wrt conductivity) for the complex EIT system. -------------------------------------------------------------------------- [17] function [JTb] = adjoint_spin(vtx,simp,elec,x,gnd_ind,zc,I,no_pl,Vmes); The function calculates the product J'*b, i.e. Jacobian transpose times a (measurements) vector b, using the adjoint sources formulation. ---------------------------------------------------------------------------- [18] function [IntGrad] = integrofgrad(vtx,simp,mat_ref); function that calculates the integral of the gradients for first order tetrahedral elements. Required for the calculation of the Jacobian. -------------------------------------------------------------------------- [19] function [elec_face,sels,cnts,VV] = set_electrodes(vtx,srf,elec_face,sels,cnts,VV); You need to call this function recursively to select boundary faces building up the ele_face. You will need to reshape this matrix appropriately to get the elec matrix, depending on how many faces there are in each electrode. -------------------------------------------------------------------------- [20] function [mat,grp] = set_inho(srf,simp,vtx,mat_ref,val); Auxiliary functions used to set small local inhomogeneities in a volume (graphically). -------------------------------------------------------------------------- [21] function [sel] = laserbeam(vtx,srf,cnts); Auxiliary plotting function Licenced -------------------------------------------------------------------------- [22] function paint_electrodes(sel,srf,vtx); Auxiliary function which plots the electrodes red at the boundaries. -------------------------------------------------------------------------- [23] function repaint_inho(mat,mat_ref,vtx,simp); Repaints the simulated inhomogeneity according to the reference distribution. (Increase -> Red, Decrease -> Blue) ------------------------------------------------------------------------- [24] function potplot(vtx,srf,V); Animates the forward solution in 3D. -------------------------------------------------------------------------- [25] function [dd] = db23d(x1,y1,z1,x2,y2,z2); Auxiliary function that calculates the distance between two points in 3D. -------------------------------------------------------------------------- [26] function [srf] = find_boundary(simp); Auxiliary function that calculates the boundary faces of a given 3D volume. Useful in electrode assignment. -------------------------------------------------------------------------- [27] function [vtx_n,simp_n] = delfix(vtx,simp) Auxiliary function to remove the zero area faces produced by Matlab's delaunay triangulation --------------------------------------------------------------------------- [28] function [vols] = check_vols(simp,vtx); Auxiliary function which calculates the volume of each tetrahedron in the mesh. -------------------------------------------------------------------------- [29] function [ta] = triarea3d(V); Function that calculates the area of a triangle in the 3D Cartesian space. -------------------------------------------------------------------------- [30] function [Reg] = iso_f_smooth(vtx,simp,deg,w); Calculates a first order discrete Gaussian smoothing operator -------------------------------------------------------------------------- [31] function [Reg] = iso_s_smooth(simp,w); Calculates a second order discrete Gaussian smoothing operator -------------------------------------------------------------------------- [32] function [solf,solp] = inverse_solver(I,voltage,tol,mat_ref,vtx,simp,elec,no_pl,zc,perm_sym,gnd_ind,tfac,Reg,it); Calculates a Newton non-linear inverse solution. -------------------------------------------------------------------------- [33] function demo_real( ... ); Demonstrates an ERT (conductivity only) image reconstruction example. -------------------------------------------------------------------------- [33] function demo_comp( ... ); Demonstrates an EIT (conductivity and permittivity) image reconstruction example. -------------------------------------------------------------------------- [34] function demo_complex(....); An alternative fully complex formulation for the complex EIT problem -------------------------------------------------------------------------- --------------------------------------------------------------------------