Expose MatrixSymbol, BlockMatrix, BlockDiagMatrix, etc.

[translunar]

It'd be great if I could do differentiation on vectors and matrices. (Is this something that can be done in Python SymEngine right now?)

http://docs.sympy.org/latest/modules/matrices/expressions.html

I'd like to be able to compute (and evaluate) Jacobians.

[isuruf]

MatrixSymbol, BlockMatrix, BlockDiagMatrix are not in SymEngine yet. They are only in SymPy.

In SymEngine there's support for DenseMatrix which can do jacobian among other functionalities.

I have a question about how to wrap this. Should symengine.rb wrap DenseMatrix class and its functionalities or use NMatrix with dtype equal to object.

I tried matrix functionalities with NMatrix and most algorithms require a < operator defined on the objects, but SymEngine doesn't have < operator overloaded, because in SymEngine only structural comparison is implemented. Mathematical comparison is not yet implemented.

[translunar]

I'm confused about what you're asking in the last paragraph. Can you give me an example?

[isuruf]

See here, https://gist.github.com/isuruf/79a7d30ee03731d5e623871535974601

[translunar]

Okay, so I believe this is the (or a) cause (then also a few other similar lines, like 52). That doesn't necessarily help you, but I wanted to track it down and make sure I understood the problem. It's called by the C version of getrf we've written for Ruby objects.

The problem is that the LAPACK/BLAS functions are primarily numeric algorithms, so they do use </> comparisons.

What happens if you call det_exact on an NMatrix object instead of det? This one shouldn't call any LAPACK functions, so I think it'd skip the calls to < and >.

[isuruf]

I get this

DataTypeError: Conversion to RubyObject requested from unknown/invalid data type (did you try to convert from a VALUE?)
(pry):32:in `det_exact'
(pry):32:in `<main>'
/home/isuru/.gem/ruby/2.1.0/gems/pry-0.10.3/lib/pry/pry_instance.rb:355:in `eval'
/home/isuru/.gem/ruby/2.1.0/gems/pry-0.10.3/lib/pry/pry_instance.rb:355:in `evaluate_ruby'
/home/isuru/.gem/ruby/2.1.0/gems/pry-0.10.3/lib/pry/pry_instance.rb:323:in `handle_line'
/home/isuru/.gem/ruby/2.1.0/gems/pry-0.10.3/lib/pry/pry_instance.rb:243:in `block (2 levels) in eval'
/home/isuru/.gem/ruby/2.1.0/gems/pry-0.10.3/lib/pry/pry_instance.rb:242:in `catch'
/home/isuru/.gem/ruby/2.1.0/gems/pry-0.10.3/lib/pry/pry_instance.rb:242:in `block in eval'
/home/isuru/.gem/ruby/2.1.0/gems/pry-0.10.3/lib/pry/pry_instance.rb:241:in `catch'
/home/isuru/.gem/ruby/2.1.0/gems/pry-0.10.3/lib/pry/pry_instance.rb:241:in `eval'
/home/isuru/.gem/ruby/2.1.0/gems/iruby-0.2.8/lib/iruby/backend.rb:65:in `eval'
/home/isuru/.gem/ruby/2.1.0/gems/iruby-0.2.8/lib/iruby/backend.rb:12:in `eval'
/home/isuru/.gem/ruby/2.1.0/gems/iruby-0.2.8/lib/iruby/kernel.rb:87:in `execute_request'
/home/isuru/.gem/ruby/2.1.0/gems/iruby-0.2.8/lib/iruby/kernel.rb:47:in `dispatch'
/home/isuru/.gem/ruby/2.1.0/gems/iruby-0.2.8/lib/iruby/kernel.rb:37:in `run'
/home/isuru/.gem/ruby/2.1.0/gems/iruby-0.2.8/lib/iruby/command.rb:70:in `run_kernel'
/home/isuru/.gem/ruby/2.1.0/gems/iruby-0.2.8/lib/iruby/command.rb:34:in `run'
/home/isuru/.gem/ruby/2.1.0/gems/iruby-0.2.8/bin/iruby:5:in `<top (required)>'
/home/isuru/.gem/ruby/2.1.0/bin/iruby:23:in `load'
/home/isuru/.gem/ruby/2.1.0/bin/iruby:23:in `<main>'

[translunar]

This puzzled me for a while, and then I realized it's definitely a bug in NMatrix. Let me get back to you.