LAPACK and cuBLAS both support treating the diagonal of a triangular matrix as 1 and ignoring the actual matrix contents. Plumb this ability through to lax.
* add test case.
* add double and complex64 implementations.
Also add logic to all linalg methods to both coerce arguments to arrays, and to promote to an inexact (float or complex) type if the argument is not inexact.
Make Cholesky and TriangularSolve work for complex numbers on CPU. The HLO implementations are broken for complex numbers on GPU/TPU, so no tests enabled for these yet.
Implement np.linalg.det, and scipy.linalg.{lu,lu_factor,det}.
Add missing abstractification to loop arguments.
Implement XLA abstractification rules for AbstractTuple, ConcreteArray, and ShapedArray.
Remove np.linalg.{dot,matmul,trace}, because these aren't part of the numpy API. I had previously misinterpreted the np.linalg documentation to mean that they also existed in that module.
* Adds lax.{cholesky,triangular_solve,qr}. Adds a JVP for Cholesky.
* Adds a transpose rule for add_p, needed by the Cholesky JVP.
* Adds np.linalg.{cholesky,qr,dot,matmul,trace}.
* Adds scipy.linalg.{cholesky,qr,solve_triangular,tril,triu}.
Pair programmed with mattjj.
