How to properly use the `block` function - maxima

I'm attempting to write a little function where it takes 2 vectors, changes the sign on the first entry of the first vector and then perform the dot product on them. However, when I do this, the global value of the changed vector in the function is changed outside the function.
I've attempted to use the block function to protect the global values of the vectors, but this doesn't seem to change anything.
a: matrix([3],[4],[5]);
b: matrix([4],[5],[6]);
f(x,y):=block([x:x,y:y],x[1]:-x[1],x.y);
f(a,b);
I expect the answer to be 38, which it is on the first time I run f(a,b); but when I do it a second time, I get 62 because a has changed globally.

You pass a matrix to the function, and this matrix is not copied, it's a reference to the same matrix. As Maxima documentation says,
Matrices are handled with speed and memory-efficiency in mind. This means that assigning a matrix to a variable will create a reference to, not a copy of the matrix. If the matrix is modified all references to the matrix point to the modified object (See copymatrix for a way of avoiding this)
So you need to copy a matrix to handle it independently:
f(x,y):=block([x:x, y:y, m:m, n:n],
m:copymatrix(x),
n:copymatrix(y),
m[1]:-m[1],
m.n);

Related

Can you generate a scene graph after a plant has been finalized?

I'm working on a project that requires me to add a model through Parser (which requires the plant to be of the same type as the array used) before Setting the position of the model in said plant and taking distance queries. These queries only work when the query object generated from the scene graph is of type float.
I've run into a problem where setting the position doesn't work due to the array being used being of type AutoDiff. A possible solution would then be converting the plant of type float to Autodiff with plant.ToAutoDiff(), but this only creates a copy of the plant without coupling it to the scene graph (and in turn the query object) from which the queries are derived. Taking queries with a query object generated from the original plant would then fail to reflect the new position passed to the AutoDiff copy.
Is there a way to create a new scene graph from the already finalized symbolic copy of the original plant, so that I can perform the queries with it?
A couple of thoughts:
Don't just convert the plant to autodiff. Convert the whole diagram. That will give you a converted, connected network.
You're stuck with the current workflow. Presumably, your proximity geometries are specified in your parsed file (as <collision> tags). The parsing process is ephemeral. The declaration is consumed, passed through MultibodyPlant into SceneGraph. If there is no SceneGraph at parse time, all knowledge of the declared collision geometry is forgotten.
So, the typical workflow is:
Create a float-valued diagram.
Scalar convert it to an AutoDiff-valued diagram.
Keep both around to serve the different roles.
We don't have a tutorial that directly shows scalar converting an entire diagram, but it's akin to what is shown in this MultibodyPlant-specific tutorial. Just call ToScalarType() on the Diagram root.

How to use autoDiffToGradientMatrix to solve for Coriolis Matrix in drake?

I am trying to get the Coriolis matrix for my robot (need the matrix explicitly for the controller) based on the following approach which I have found online:
plant_.CalcBiasTerm(*context, &Cv_);
auto jac = autoDiffToGradientMatrix(Cv_);
C = 0.5*jac.rightCols(n_v_);
where Cv_, plant_, context are AutoDiffXd and n_v_ is the number of generalized velocities. So basically I have a 62-joint robot loaded from URDF into drake which is a free body (floating base system). After finalizing the robot I am using the DiagramBuilder.Build() method and then the CreateDefaultContext() in order to get the context. Next, I am trying to set up the AutoDiff environment like this:
plant_autodiff = drake::systems::System<double>::ToAutoDiffXd(*multibody_plant);
context_autodiff = plant_autodiff->CreateDefaultContext();
context_autodiff->SetTimeStateAndParametersFrom(*diagram_context);
The code above is contained in an initialization setup code. In another method, which is called on update events, the following lines of code are written:
drake::AutoDiffVecXd c_auto_diff_ = drake::AutoDiffVecXd::Zero(62);
plant_autodiff->CalcBiasTerm(*context_autodiff, &c_auto_diff_);
MatrixXd jac = drake::math::autoDiffToGradientMatrix(c_auto_diff_);
auto C = 0.5*jac.rightCols(jac.size());
This setup compiles and runs, however the size of the jac matrix is 0, whereas I would expect 62x62. I am also extracting and then exposing the Coriolis vector, which is 62x1 and seems to be more or less correct. The c_auto_diff_ variable is 62x1 as well, but all the elements are 0.
I am clearly making a mistake, but I do not know where exactly.
Any help is appreciated,
Thank you all,
Robert
You are close. You need to tell the autodiff pipeline what you want to take the derivative with respect to. In this case, I believe you want
auto v = drake::math::initializeAutoDiff(Eigen::VectorXd::Zero(62))
plant_autodiff->SetVelocities(context_autodiff.get(), v);
By calling initializeAutoDiff, you are initializing the autodiff terms to the identity matrix, which is saying that you want to take the derivative with respect to v. Then you should get non-zero derivatives.
Btw - I normally would use
plant_autodiff = multibody_plant->ToAutoDiffXd();
but I guess what you have must work, too!

How to apply changes to elements of a tensor/vector without changing its reference?

I am sharing parameters of a network and want to apply some operations to change to the elements of the parameter vector. I cannot do those operations directly on the parameter tensor because they will certainly change the parameter vector reference and sharing breaks. So :clone() the shared parameters vector and apply the changes I want on the new vector and use the :copy() function to replace the elements in the original parameter vector. I thought the tensor:copy() function does not change the vector/tensor reference but it seems that it does since the parameter sharing collapses soon after apply it. So I wonder, can anyone fix the code below and suggest a way to change the elements of the parameter vector without breaking the sharing?
tempParam = parameters:clone()
Do some operations on the tempParam vector
parameters:copy(tempParam) -- Do the replacement (the copy() function breaks the sharing)
One of the operations I'm interested in doing is clamping but the clamp() function also breaks the sharing if applied directly kon the parameter vector.
Basically, you need a pointer to the Tensor that will modify its raw data, preserve the reference and sharing. This link (Tensor doc) clearly explains it.
https://github.com/torch/torch7/blob/master/doc/tensor.md#result-datatensor-asnumber

Why does ELKI need db.in file in addition to distance matrix? Also what should db.in file contain?

I tried to follow this tutorial on using ELKI with pre-computed distances for clustering.
http://elki.dbs.ifi.lmu.de/wiki/HowTo/PrecomputedDistances
I used the following set of command line options:
-dbc.filter FixedDBIDsFilter -dbc.startid 0 -algorithm clustering.OPTICS
-algorithm.distancefunction external.FileBasedDoubleDistanceFunction
-distance.matrix /path/to/matrix -optics.minpts 5 -resulthandler ResultWriter
ELkI fails with a configuration error saying db.in file is needed to make the computation.
The following configuration errors prevented execution:
No value given for parameter "dbc.in":
Expected: The name of the input file to be parsed.
No value given for parameter "parser.distancefunction":
Expected: Distance function used for parsing values.
My question is what is db.in file? Why should I provide it in addition to the distance matrix file since the pair-wise distance matrix file completely specifies all the information about the point cloud. (also I don't have access to any other information other than the pair-wise distance information).
What should I do about db.in? Should I override it, or specify some dummy information etc. Kindly help me understand.
thank you.
This is documented in the ELKI HowTos:
http://elki.dbs.ifi.lmu.de/wiki/HowTo/PrecomputedDistances
Using without primary data
-dbc DBIDRangeDatabaseConnection -idgen.count 100
However, there is a bug (patch is on the howto page, and will be in the next release) so you right now can't fully use this; as a workaround you can use a text file that enumerates the objects.
The reason for this is that ELKI is designed to work on multi-relational data. It's not just processing matrixes. But some algorithms may e.g. need a geographic representation of an object, some measurements for this object, and a label for evaluation. That is three relations.
What the DBIDRange data source essentially does is create a single "fake" relation that is just the DBIDs 0 to 99. On algorithms that don't need actual data, but only distances (e.g. LOF or DBSCAN or OPTICS), it is sufficient to have object IDs and a distance matrix.

Efficient matrix copying in OpenCV

I have no idea for how to implement matrix implementation efficiently in OpenCV.
I have binary Mat nz(150,600) with 0 and 1 elements.
I have Mat mk(150,600) with double values.
I like to implement as in Matlab as
sk = mk(nz);
That command copy mk to sk only for those element of mk element at the location where nz has 1. Then make sk into a row matrix.
How can I implement it in OpenCV efficiently for speed and memory?
You should take a look at Mat::copyTo and Mat::clone.
copyTo will make an copy with optional mask where its non-zero elements indicate which matrix elements need to be copied.
mk.copyTo(sk, nz);
And if you really want a row matrix then call sk.reshape() as member sansuiso already suggested. This method ...
creates alternative matrix header for the same data, with different
number of channels and/or different number of rows.
bkausbk gave the best answer. However, a second way around:
A=bitwise_and(nz,mk);
If you access A, you can copy the non-zero into a std::vector. If you want your output to be a cv::Mat instance then you have to allocate the memory first:
S=countNonZero(A); //size of the final output matrix
Now, fast element access is an actual topic of itself. Google it. Or have a look at opencv/modules/core/src/stat.cpp where countNonZero() is implemented to get some ideas.
There are two steps involved in your task.
First, you convert to double the input matrix:
cv::Mat binaryMat; // source matrix, filled somewhere
cv::Mat doubleMat; // target matrix (with doubles)
binaryMat.convertTo(doubleMat, CV64F); // Perform the conversion
Then, reshape the result as a row matrix:
doubleMat = cv::reshape(doubleMat, 1, 1);
// Alternatively:
cv::Mat doubleRow = cv::reshape(doubleMat, 1, 1);
The cv::reshape operation is efficient in the sense that the data is not copied, only the structure header changes.
This function returns a new reference to a matrix (by creating a new header), thus you should not forget to assign its result.

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