How MATLAB code generation infers output size with nested branches - matlab

Question

When generating C code using MATLAB Coder, the behaviour is different when an if happens in body of another if or in its elsesection. The following case easily creates C code with output having size 5x5:
function y = foo1(u)
if u > 0
y = zeros(2,2);
else
y = zeros(5,5);
end
Now this one works as well
function y = foo2(u,v)
if u > 0
y = zeros(2,2);
else
y = zeros(5,5);
if v > 0
y = 2 * y;
end
end
But this one fails to generate code, complaining about size mismatch:
function y = foo3(u,v)
if u > 0
y = zeros(2,2);
if v > 0
y = 2 * y;
end
else
y = zeros(5,5);
end
Here is the output in command-line:
>> codegen foo1.m -args {0}
>> codegen foo2.m -args {0,0}
>> codegen foo3.m -args {0,0}
??? Size mismatch (size [2 x 2] ~= size [5 x 5]).
The size to the left is the size of the left-hand side of the assignment.
Error in ==> foo3 Line: 8 Column: 5
Code generation failed: Open error report.
Error using codegen (line 144)
I have seen this behaviour in MATLAB R2013b and R2015a.

Answer 1

From the docs, Matlab codegen must know the size of a matrix at compile time unless codegen is told or infers that the matrix is of variable size. There are several ways to let Matlab know a matrix will be of variable size:
Using coder.varsize function, a matrix can be explicitly declared to be of variable size.
MATLAB can infer a matrix is of variable size from the structure of the code.
As your code suggests, option (2) apparently isn't robust. Matlab tries to infer in some cases when there's a simple if else statement, but that inference appears to be quite fragile, as shown by your example.
Rather than rely on MATLAB to correctly infer whether a matrix is variable size, a solution is to make an explicit declaration:
function y = foo3(u,v)
coder.varsize('y', []); % Let codegen know y is variable sized
% and can be arbitrary dimensions
% an alternative is: coder.varsize('y',[5,5]);
if u > 0
y = zeros(2,2);
if v > 0
y = 2 * y;
end
else
y = zeros(5,5);
end
Why might Matlab want to know this information? If a matrix's size is known at compile time, all kinds of additional optimizations may be possible (loop unrolling etc...).

Answer 2

I agree with Matthew Gunn's answer, this is to add some explanation for the behavior. A good mental model to have about how Coder analyzes your MATLAB code is that it looks at it from the top to the bottom.
Applying that mental model, in your first two examples, the assignments which determine sizes of y: y = zeros(2,2) and y = zeros(5,5), occur before the value of y is ever used. So Coder can merge both sizes to automatically make y a variable-sized array. In the third example, the assignment y = zeros(2,2) occurs and then y is used: y = 2 * y. At this point, Coder needs to determine the size and type of the multiplication 2 * y. Only the 2-by-2 assignment is seen so it is inferred that 2 * y must also return a 2-by-2 matrix.
Performing this inference then embeds the assumption that y is 2-by-2 into the code and essentially locks the size of y so that the subsequent assignment to y with a 5-by-5 matrix must fail.