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What is the best way to return multiple inhomogeneous results from a LibraryLink function? Imagine that the result of a single computation is several tensors of different dimensions and several numbers. They should all be returned at the same time.

I see two ways:

  1. Get a MathLink connection and use MathLink API functions to return the results. Is there any advantage at all to using LibraryLink (instead of pure MathLink) in this case? Did anyone compare LibraryLink/MathLink data transfer performance so I can more easily assess what the performance hit would be?

  2. Have several LibraryLink functions: one will send the input, do the computation and store the result; there would be separate functions for retrieving each result; finally there would be a function to free up the library memory used to store those results.

    I'm not particularly keen on doing this. It seems more trouble and it forces me to manually manage memory from Mathematica.

Are there any better options?

Update for version 10

Version 10 brings changes both to MathLink (now WSTP) and to LibraryLink. MathLink now has the "IntraProcess" protocol for fast communication within a single process. LibraryLink now has managed library expressions which allows Mathematica to auto-free library side data structures (at the cost of more boilerplate code). We have now new data types and there are examples of generic looking type specifications in the documentation such as {_,_} (same linked page).

Does the answer change for version 10.0 or 10.2? Are there less cumbersome solutions available now? Imagine having to write an interface to a library that will commonly return multiple results from the same function.

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This question has an open bounty worth +100 reputation from Szabolcs ending in 4 days.

The current answer(s) are out-of-date and require revision given recent changes.

Are there better and more convenient solutions as of version 10.2?

Cross posted on W Community, mentioning this per the guidelines. –  Szabolcs Sep 2 '13 at 19:16
I think number 2 is the way to go. This was one of the reasons why LibraryLink was written. The TetGenLink interface is an example where multiple LibrayLink functions query a single tetgen c++ instance and this works very efficiently. –  user21 Sep 2 '13 at 19:37
@ruebenko Thanks for the comment, I'll probably just do that. Actually I for the idea from TetGenLink. But in TetGenLink it seems to make sense to do this (to create a Mathematica-accessible, library-side data type) for other reasons too, even at the expense of manual memory management. What I would love to have in Mathematica is support for automating memory management in these situations. As soon as a TetGenExpression is no longer referenced, it should be auto-freed on the library side too, similarly to how symbols with the Temporary attribute ... –  Szabolcs Sep 2 '13 at 20:02
@ruebenko ... get freed when they are no longer referenced. I'm sure that this isn't possible at the moment though: if it were possible, J/Link and .NET/Link would be making use of the mechanism, but they aren't. –  Szabolcs Sep 2 '13 at 20:02
@ruebenko Finally I used this approach. If you post it as an answer I'll accept it. –  Szabolcs Sep 2 '13 at 21:10

3 Answers 3

up vote 8 down vote accepted

I think number 2 is the way to go. This was one of the reasons why LibraryLink was written. The TetGenLink interface is an example where multiple LibrayLink functions query a single tetgen c++ instance and this works very efficiently.

Unfortunately, there is no LibrayFree function that you could connect to.

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I see a third way, which is a combination of your two choices, but its usefulness depends on the problem you are solving. I used this once to get the best from both worlds. What I needed was a similar thing to ComponentMeasurements in 3D. Therefore, I needed a component labeling algorithm (similar to MorphologicalComponents) which takes a volume, binarizes it and assigns each separate component a unique ID. For this I needed only read access to the volume and therefore, I wanted to use it inside the library without copying it.

For this part I wrote a function using your second point which stored the result, the labeled volume, statically inside the library instance.

For each component in the labeled volume I wanted to have certain measures. My result was therefore a list which consisted of a set of several measurements for each component. This was something like

{"ID"->1, "Volume"->123, "BoundingBox"->{{..},{..},{..}}}

for each component, so highly inhomogeneous. To retrieve this result I wrote another function using MathLink where it didn't matter that I couldn't use the memory advantages of LibraryLink because I didn't have to transfer the large volume data.

I personally like how you can build very complex expressions with MathLink and for me it would have been very inconvenient if I had to write a LibraryLink function to retrieve every single property of my components.

void MLPutComponentProperties(MLINK mlp, const Component3d<mint> &c) {
    MLPutFunction(mlp, "List", c.number_of_properties);
    MLPutFunction(mlp, "Rule", 2); MLPutString(mlp, "Id"); MLPutInteger(mlp, c.label);
    MLPutFunction(mlp, "Rule", 2); MLPutString(mlp, "Volume"); MLPutInteger(mlp, c.volume);
    MLPutFunction(mlp, "Rule", 2); MLPutString(mlp, "BoundingBox");
        MLPutFunction(mlp, "List", 3);
        MLPutFunction(mlp, "List", 2);
          MLPutInteger(mlp, c.bounding_box.x1+1);
          MLPutInteger(mlp, c.bounding_box.x2+1);
        MLPutFunction(mlp, "List", 2);
          MLPutInteger(mlp, c.bounding_box.y1+1);
          MLPutInteger(mlp, c.bounding_box.y2+1);
        MLPutFunction(mlp, "List", 2);
          MLPutInteger(mlp, c.bounding_box.z1+1);
          MLPutInteger(mlp, c.bounding_box.z2+1);

void MLPutComponentList(MLINK mlp, const Component3dList components) {
    MLPutFunction(mlp, "List", components->size());
    Component3dListIterator it;
    for (it = components->begin(); it != components->end(); ++it) {
        MLPutComponentProperties(mlp, **it);
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Summary: I vouch for option 2 as LibraryLink is great with memory (sharing as opposed to copying). Furthermore I did a little investigation into the possible types of tensors with a negative/conservative result. The main point of posting the analysis to prevent that other people do the same.


Addressing: "Did anyone compare LibraryLink/MathLink data transfer performance so I can more easily assess what the performance hit would be"?

I think sending data over a MathLink connection always causes a copy of the data. In LibraryLink this is not necessary.

Firstly, you can load a function with the instruction that a tensor argument has to be shared between Mathematica and LibraryLink. This prevents copying information when giving the information from the kernel to the C program. Secondly, I think any tensor "returned" from a LibraryLink function using MArgument_setMTensor most likely does not have to be copied either. The main evidence for this is that the docs say

"Arguments passed to and from a library function can share data, saving on memory consumption and the time to copy large amounts of data."

in LibraryLink/tutorial/Introduction#163333181. This doc page also lists other differences between LibraryLink and MathLink. In particular the overhead of calling a LibraryLink function is much lower.


Please see my answer here for an example of returning multiple outputs. It involves calling a separate function to access a global variable. I hope to learn more about this so that I can improve this code. At the moment it crashes for large inputs.


From the LibraryLink user guide we have: "You can exchange not only C-like data types such as integers, reals, packed arrays, and strings, but also arbitrary Mathematica expressions".

Of course, from LibraryLink we can call MathLink, so I guess in this sense that statement is true (I am now quite confident that MathLink is necessary for this). However, I was hoping we could maybe make ragged arrays.

I investigated a bit, and found in WolframLibrary.h

#define MType_Integer 2
#define MType_Real 3
#define MType_Complex 4

My hope was now that there would be another type corresponding to 1. The following code can be used to investigate this further

DLLEXPORT int raggedArray_T_I(WolframLibraryData libData, mint Argc, MArgument *Args, MArgument Res) {

    MTensor T_arg = MArgument_getMTensor(Args[0]);
    int type = libData->MTensor_getType(T_arg);
    MArgument_setInteger(Res, type);
    return 0;

It doesn't even really matter what the code above is. The point was to see if we could call a library function with something other than the usual "packable" arrays as arguments. I loaded the function above as follows

rAFu = LibraryFunctionLoad[libraryName, "raggedArray_T_I", {{_, _}}, 

Of course for the usual arrays the output was expected. One interesting thing is that any combinations of empty lists apparently has type 3 as a tensor, corresponding to an array of reals.

Unfortunately, I was unable to find any other input that qualified as a tensor. For example raFu[{{1},1}] gives an error that {{1},1} is not a tensor (of rank -1 of Removed[$$Failure] oddly).

Far fetched

My suspicion is now that maybe the valid types are 2,3 and 4 instead of 1, 2 and 3 is because of the following reason. Possibly expressions contain an indicator (maybe in the sense that they are structs have the indicator as an attribute, I read somewhere that expressions "are" structs (and unions)) containing the information what kind of expression the expression is. Then 1 could stand for "normal expression" and 2, 3 and 4 for the PackedArrays. Other types of expressions could be Integer, Real or Complex. That is what I did when I programmed my own little prototype of Mathematica anyway. I would be glad if somebody could shine more light on this.

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Wow that was a fast upvote for a long answer :) –  Jacob Akkerboom Dec 1 '13 at 17:50
NTensor->MTensor –  Jacob Akkerboom Dec 2 '13 at 0:55

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