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WIP: Efficient eigenvalue/vector and singular value/vector computations for special LAPACK matrices #4593

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WIP: Efficient eigenvalue/vector and singular value/vector computations for special LAPACK matrices #4593

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jiahao
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@jiahao jiahao commented Oct 20, 2013

Provides new LAPACK wrappers where necessary to provide specialized eigenvalue/vector and singular value/vector routines for Triangular, Tridiagonal, SymTridiagonal, Bidiagonal and Diagonal matrices.

Related issue: #3688

@andreasnoack
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I know that we already have eigvecs for some types, but I wonder if eig, eigfact and eigvecs are too many functions for the same functionality and the same for the singular vectors. We have to have eigvals because we don't have dispatch on output arguments, but when the vectors are requested I personally prefer to use the Eigen type for the result.

The rest looks good to me.

@jiahao
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jiahao commented Oct 20, 2013

@andreasnoackjensen are you suggesting that we should have just eigvecs and eigfact? I did wonder why eig and eigfact are separate functions.

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The presence of both eig and eigfact is kind of a compromise. Personally, I would prefer only to return the Eigen type instead of the tuple, but the MATLAB compatible version was requested by some users. As I remember it, the eigvecs was introduced for the special case where you want to calculate the vector for a specific eigenvalue of a tridiagonal matrix (by xstein, I think).

@jiahao
Add zeros, ones, infs and nans methods taking an AbstractMatrix argument
5ef3701
@jiahao
Generic linear solver for upper triangular matrices
0356cf3 
- Generic inverse replaced with generic solve on identity matrix
- Specialized transpose, ctranspose, istril, istriu
@jiahao
Provides cond(A::Triangular)
9b3c213 
- wraps LAPACK wrapper trcon!, reciprocal of condition number estimate for triangular matrices
- type stability bugfixes to generic cond()
- Triangular-specific tests for linear solver and cond()
@jiahao
Provide eigvals(A::Triangular)
a7ae943
@jiahao
Provides methods and tests for eigvecs, eigfact
4cb19f5
@jiahao
Update News.md
92e71c3
@jiahao
Adds eig, eigfact, eigvals and eigvecs for Bidiagonal
53e43ff 
Addresses #3688
@jiahao
Wrapper for LAPACK.trevc
10583b8
@jiahao
Provides diag, eig, eigfact eigvals and eigvecs for upper and lower T…
20cc7e9 
…riangular matrices

Addresses #3688
- Also provides simple wrappers around the full routines for svd, svdfact, svdfact!, svdvals, svdvecs for Triangular
- Adds convert routine from Triangular to dense Matrix
- Clean up bidiagonal Matrix tests
@jiahao
More efficient eigenvector computation for lower Triangular matrices
a7f25ed
@jiahao
Clean up eigensystem and singular system solvers
63fe73a
@jiahao
Clean up miscellaneous functions
c8861f8
@jiahao
Add generic multiplication
fa00d18
@jiahao
Fix trevc! wrapper for complex arguments
63bd619
@jiahao jiahao closed this Dec 29, 2013
@jiahao jiahao deleted the cjh/special_eig branch December 29, 2013 23:08
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jiahao commented Dec 30, 2013

This is a lot of code, so I'm going to break it up into several pieces.

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@jiahao @andreasnoack