The best way of adding PSDMatrix types

[Nicholas Krämer]

Frequently, one has to compute C = A + B where A and B are of PSDMatrix type. A and B may have different forms, there is an entire zoo of options of computing this sum, and with different goals, different implementations might be optimal.

Potential test cases:

• Number of elements in A and B: say, <=100 and >=10,000)
• Square, tall, and wide matrices
• Ill-conditioned and well-conditioned matrices

Competitors:

• Cholesky (already implemented)
• Pivoted cholesky
• QR (already implemented)
• Pivoted QR
• iterated lowrankupdate

Plus each of the in-place versions, of course.

Desiderata:

• Run time
• Number of allocations
• Numerical stability
• Special properties of the output (i.e., if the return value is of Cholesky type).