On Apr 5, 2011, at 10:54 AM, Brian Granger wrote: > On Tue, Apr 5, 2011 at 9:26 AM, Aaron S. Meurer <asmeu...@gmail.com> wrote: >> >> On Apr 4, 2011, at 11:30 PM, Brian Granger wrote: >> >>> Hi, >>> >>>> Could you give an example of how you construct large sparse matrices. >>>> What sort of constructors would you like to see in the class ? >>> >>> Our big sparse matrices are formed out of tensor products of 2x2 >>> matrices, such as Pauli and Hadamard matrices. But these tensor >>> products have *many* identity matrices as well, which makes them >>> sparse. Here is our matrix tensor product code: >>> >>> https://github.com/sympy/sympy/blob/master/sympy/physics/quantum/matrixutils.py#L232 >>> >>> >>> Here is some specific examples: >>> >>> In [1]: from sympy.physics.quantum import * >>> >>> In [2]: from sympy.physics.quantum.gate import * >>> >>> In [3]: g = X(2) >>> >>> In [4]: represent(g, nqubits=4) >>> >>> You could also look at what happens when you increase nqubits and also look >>> at: >>> >>> g = Y(2) >>> g = H(2) >>> >>> 2 could also be any number < nqubits >>> >>> In many ways one of the most useful things we could have would be a >>> sparse tensor product. >>> >>>> Are there any special class of sparse matrices that you guys use >>>> often, like tridiagonal matrix or permutation matrix ? >>> >>> Nope, in practice we get matrices that look quite different and have >>> different sparsities. >>> >>>>>> I should also mention that we are >>>> pretty much only interested in matrix-vector multiplies, matrix- >>>> scalar >>>> mult. and matrix addition. >>> >>>> Arent you also interested in solving A * x = B, or matrix-matrix >>>> mult ? >>> >>> Nope for this particular application, we don't need linear solves or >>> matrix-matrix mul. >> >> So what do you do with the matrices? > > 90% of the time, we build them and them apply a sequence of them to a vector: > > A*B*C*D*E*...(Y*(Z*v)) > > We could do the matrix-matrix muls first and then apply to the vector: > > (A*B*C*D*E*...Y*Z)*v > > But the product of all the matrices is usually dense, and we don't > want to have to store the entire big dense matrix. > > Brian
This reminds me. Implementing symbolic matrices would allow us to optimize multiplication of several matrices of different sizes using the matrix chain multiplication algorithm. Aaron Meurer > > > > >> Aaron Meurer >> >>> >>> Cheers, >>> >>> Brian >>> >>>> Thank you for your help, >>>> Sherjil Ozair >>>> >>>> -- >>>> You received this message because you are subscribed to the Google Groups >>>> "sympy" group. >>>> To post to this group, send email to sympy@googlegroups.com. >>>> To unsubscribe from this group, send email to >>>> sympy+unsubscr...@googlegroups.com. >>>> For more options, visit this group at >>>> http://groups.google.com/group/sympy?hl=en. >>>> >>>> >>> >>> >>> >>> -- >>> Brian E. Granger >>> Cal Poly State University, San Luis Obispo >>> bgran...@calpoly.edu and elliso...@gmail.com >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "sympy" group. >>> To post to this group, send email to sympy@googlegroups.com. >>> To unsubscribe from this group, send email to >>> sympy+unsubscr...@googlegroups.com. >>> For more options, visit this group at >>> http://groups.google.com/group/sympy?hl=en. >>> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To post to this group, send email to sympy@googlegroups.com. >> To unsubscribe from this group, send email to >> sympy+unsubscr...@googlegroups.com. >> For more options, visit this group at >> http://groups.google.com/group/sympy?hl=en. >> >> > > > > -- > Brian E. Granger > Cal Poly State University, San Luis Obispo > bgran...@calpoly.edu and elliso...@gmail.com -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to sympy@googlegroups.com. To unsubscribe from this group, send email to sympy+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
