# rigidtform2d: why not accept double type homogenous matrix?

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cui on 29 Oct 2022
Edited: cui on 29 Oct 2022
I found out by accident why the function rigidtform2d does not accept a 3 by 3 flush matrix of type double?
T = [ 1.0000 0.0004 -0.2102
-0.0004 1.0000 3.3896
0 0 1.0000]; % T is default double type
A = rigidtform2d(single(T)); % ok
B = rigidtform2d(T);
Error using rigidtform2d>parseOneInputSyntaxes
Invalid transformation matrix.

Error in rigidtform2d (line 40)
self = parseOneInputSyntaxes(self,varargin{1});
I then test to see if it is close to the singular matrix：
rcond(T)
ans =
0.0473
However it doesn't, which means double is more sensitive than single? Or that the function is not robust enough?

cui on 29 Oct 2022
Edited: cui on 29 Oct 2022
A rigidtform2d object stores only rotation and translation information, and the shear 0.0004 exists in the T matrix above. It is actually a robustness problem, Hopefully future versions enhance the double type of issue，caused by the following functions：
the constrained matrix is not within floating-point round-off error of the original matrix, then the original matrix is not a valid transformation matrix for the subclass.
function tf = matricesNearlyEqual(A,B)
% matricesNearlyEqual
% matricesNearlyEqual(A,B) returns true if A and B are the
% same, within floating-point round-off error. A and B are assumed to
% be square and of the same class, and this is not checked.
coder.inline('always');
coder.internal.prefer_const(A,B);
t = eps(class(A)) ^ (3/4);
R = max(norm(A),norm(B));
R0 = 100 * realmin(class(A)) / t;
R = max(R,R0);
tf = (norm(A - B) / R) <= t;
end

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