In some case the Compile's syntax is quite straightforward. Es. for rank 1 e rank 2 tensors:

Quiet[Remove[cf]];
cf = Compile[
   {{x, _Real, 1}}
   , Total[x]
   ];

and

Quiet[Remove[cf]];
cf = Compile[
   {{x, _Real, 2}}
   , Inverse[x]
   ];

Or, even,

Quiet[Remove[cf]];
cf = Compile[
   {{x, _Real, 2}, {y, _Real, 2}}
   , Det[x] + Det[y]
   ];
cf[matrixA, matrixB]

But what if the arguments are intricated ? What is the syntax needed ?

A workaround to circumvent this question was proposed here : Not the most elegant but could you flatten and join and then "unflatten" and separate afterwards ?

Please, can you elucidate the topic and give examples for a function having as argument (all atomic expression are understood Real):

• a matrix of lists
• a matrix of matrices
• a matrix whose element are {x_Real , a matrix }
• a matrix whose element are {x_List , a matrix }
• etc.