Start adding support for matrix functions

[mtfishman]

Start adding support for matrix functions such as exp(A), cos(A), inv(A), etc. on square block diagonal matrices. The operations are applied to the diagonal blocks. Care is taken to instantiate unstored diagonal blocks in case they are nontrivial (or even if they remain zero they get instantiated for simplicity).

Matrix functions supported by Julia can be found:

• https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/#Standard-functions
• https://github.com/JuliaLang/LinearAlgebra.jl/blob/b265feabec34f492ea072a7acacd361a17e5fed7/src/diagonal.jl#L928-L990
• https://github.com/JuliaLang/LinearAlgebra.jl/blob/b265feabec34f492ea072a7acacd361a17e5fed7/src/dense.jl

The strategy to handle this generically is to use Base.promote_op to use type inference on the block type of the input block sparse matrix to determine the block type of the output. A number of operations are broken right now because the LinearAlgebra.jl dense implementations are type unstable, I'll look into fixing those manually. Maybe we can provide an interface like initialize_output(f, A) (inspired by MatrixAlgebraKit.initialize_output) for customizing/specifying the output type. It can default to Base.promote_op. This issue is fixed by introducing initialize_output_blocksparse(f, A), which defaults to Base.promote_op but then uses similartype in cases that are type unstable.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 75.15%. Comparing base (81003b1) to head (82f7c13).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #135      +/-   ##
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+ Coverage   74.84%   75.15%   +0.31%     
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  Files          35       35              
  Lines        1749     1771      +22     
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+ Hits         1309     1331      +22     
  Misses        440      440              

Flag	Coverage Δ
docs	6.44% <0.00%> (-0.09%)	⬇️

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