Contents

%mat_transform2.m
%
%Transforms a general rank 2 tensor according to a chosen transformation
%matrix. Generating matrices can be loaded by entering their number.
%General, already created group elements can be loaded by entering their
%file name (no file extension necessary). The tensor will be tranformed and
%a system of 6 equations will be created via the invariance condition
%(h_ij = g_ij, with h_ij the transformed tensor). The transformed tensor as
%well as the resulting independent elements will be shown at the end.
%
%input:  nam ... name or # of tranforming matrix
%
%output: hs  ... transformed rank 2 tensor
%        hi  ... resulting tensor with independent elements
%
%Valentin Zauner
%
%05.2008

clear all;
clc;

rep = 1;
while rep
    clear all;

    %initialize general rank 2 tensor with elements named according to 1-d
    %representation for symmetric tensors
    syms g1 g2 g3 g4 g5 g6 h g
    g = [g1,g6,g5;g6,g2,g4;g5,g4,g3];

load transformation matrix

    nam = input('Transforming matrix: ','s');
    if isempty(nam)
        %if nothing is entered identity matrix will be loaded
        M = eye(3);
    elseif ~isempty(str2num(nam));
        %if only a number is entered the corresponding generating matrix will
        %be loaded
        t = struct2cell(load(['M',nam]));
        M = t{1};
    else
        t = struct2cell(load(nam));
        M = t{1};
    end;

transform tensor

    h = simple(inv(M)*g*M);
    ind = [1,5,9,8,7,4];%mask for vector - representation for symmetric matrices
    t = h(ind);%map to vector - representation for symmetric matrices
    x = [g1,g2,g3,g4,g5,g6];

solve for independent elements

    y = cell(1,6);
    for k = 1:6
        y{k} = [char(t(k)),'=',char(x(k))];%generate defining equations for each element
    end;
    S = struct2cell(solve(y{:},'g1','g2','g3','g4','g5','g6'));%solve system of eqns

    hi = sym(zeros(3,3));
    hs = sym(zeros(3,3));

    hs(ind) = t;%representation with 0 below diagonal for symmetric matrix
    for k = 1:6
        hi(ind(k)) = S{k};
    end;

display results

    disp('Transformed matrix:');
    disp(hs);

    disp('Independent elements:');
    disp(hi);

    rep = input('repeat: ');
    if isempty(rep),rep=1;end;
end;

Published with MATLAB® 7.4