uitable() do not store table() objects.
The following code looks at the column names to create variables for the table objects. It does not assume that names are already present ('ColumnName' 'numbered' is valid). It does not assume that there are enough column names provided, and does not assume that any entries provided are valid unique variable names. If more headers are present than data columns then it extends the data columns.
Most of the work below is to ensure that valid headers of the right size are put in place. The actual work of creating the table and writing it is pretty short, so if you already know that your headers are valid and the right size then potentially you could make this code significantly shorter.
fullpathAndFilename = '/home/mytable.txt';
data = get(handles.uitable1, 'Data');
if ~iscell(data); data = num2cell(data); end
nc = size(data, 2);
cn = get(handles.uitable1, 'ColumnName');
if isempty(cn) || ~iscell(cn)
cn = cell(1, nc);
end
nch = length(cn);
if nc < nch
data{end, nch} = [];
nc = nch;
elseif nch < nc
cn{nc} = [];
nch = nc;
end
mask = cellfun(@isempty, cn);
cn(mask) = sprintfc('var%d', find(mask));
cn = matlab.lang.makeUniqueStrings( matlab.lang.makeValidName(cn, 'ReplacementStyle', 'hex') );
T = cell2table(data, 'VariableNames', cn);
writetable(T, fullpathAndFilename);
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