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• Singular Value Decomposition

  Implement a Singular Value Decompositions based on Divide and Conquer and Jacobi rotations

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• QR Decomposition with pivoting

  Implement a Householder rotation based QR decomposition that supports pivoting if desired by the user.

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• Dense LU Decomposition

  Implement a dense LU decomposition based on blocked BLAS3 operations to achieve performance.

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• Linear Algebra backend

  There already exists a very good library for array operations with ndarray. However, it does not not use low-level expression templates, can be complicated in its syntax (due to it being built around general n-dimensional arrays), and is also still evolving. We should strive for simple very clean structures that have just the right complexity for what we need to implement higher order linear algebra functions. On top we should have good compatibility routines so that users can use advanced array operations from ndarray on our data structures (e.g. by being able to create ndarray object views to our data, etc.).

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• Householder 1.0

  These are the goals to achieving a 1.0 status - Easy to use backend for working with one and two dimensional arrays (implemented through ndarray, but encapsulated so that other backends can be used). - Implementations of dense LU, QR, SVD, and Eigenvalue decomposition - Sparse data structures, sparse iterative solvers and sparse LU decomposition - Performance similar to Lapack (not necessarily identical but within acceptable range) - Where possible multithreaded routines

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