Add API functions for setting rows / columns / sub-matrices

[mikera]

Ideas:

• (set-row m i v)
• (set-column m i j)
• (set-submatrix-at m i j small-matrix)

[kasterma]

If I understand the suggestion correctly, I would expand and suggest to add the elementary row operations. (switching, multiplication, and row addition; see http://en.wikipedia.org/wiki/Elementary_matrix).

Not sure what the semantics of the last function (set-submatrix-at) is supposed to be.

[mikera]

@kasterma: good suggestion, though I think that is worth a separate issue. I'll create one.

[mikera]

#40

[si14]

If I'm right it can be done using mutable "views" into original array (or at least can pretend to be done this way if underlying matrix representation doesn't support mutation).

[mikera]

Well we probably ultimately want two versions (immutable and mutable) of each: set-row and set-row! for example.

The mutable versions could certainly be implemented with an mutable view.

The immutable version would need to construct a new matrix. However structural sharing is possible, so parts of the new matrix could be shared with the original matrix - possibly via a view.

[alexott]

I've also thought already about implementing 2 APIs for Incanter - mutable & immutable.

[mikera]

We'll get mutable + immutable versions of most operations for free if we complete the Incanter / core.matrix integration.

Most core.matrix functions already have immutable and mutable versions where it makes sense, e.g. add and add!, where the ! versions generally mutate their first argument.

[si14]

I'm sorry for not being clear enough.

I meant something like this MATLAB/Octave code:

octave:1> a = eye(3)
a =

Diagonal Matrix

   1   0   0
   0   1   0
   0   0   1

octave:2> a(2,1:2) = [2,2]
a =

   1   0   0
   2   2   0
   0   0   1

The thing here is that we already need a powerful tool to take slices of array. Why don't reuse it to assign values as well, as it is done in MATLAB/Octave? From the point of API, I can imagine "slicing schemes" as first-class objects:

(def s (slicing-scheme [2 1 :to 2]))
(sub (eye 3) s) ; returns a slice
(set (eye 3) s) ; returns new matrix
(set! (eye 3) s) ; mutates in place

DSL for slicing is another issue, of course.

[mikera]

slicing schemes as first class objects is an interesting idea, I'd be interested to see an implementation that demonstrates that it can be done efficiently and in a general way.

But do note that core.matrix already includes an NDWrapper type that can wrap an arbitrary subset of a matrix. See clojure.core.matrix.impl.wrappers namespace and the submatrix function.

Use example:

(def A (array :ndarray [[1 2 3] [4 5 6] [7 8 9]]))
(def S (submatrix A [[1 1] [0 2]]))
S
=> #<NDWrapper [[4 5]]>

Currently NDWrapper doesn't support mutation, but it could easily be upgraded to do so. In which case, we would be able to do stuff that alters the original matrix like:

(assign! S 0)
S
=> #<NDWrapper [[0 0]]>
A
=> #<NDArray [[1 2 3] [0 0 6] [7 8 9]]>

Overall the NDWrapper is quite flexible and good for simple use cases. The problem is that it adds quite a lot of index lookup overhead for each element (Dmitry: we wouldn't need your shiny new NDArray if the NDWrapper was ultra-fast!)

[mikera]

Row setting implemented in this commit:
95993ea

Still not sure of how to handle the more general strategy....