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initial svds support based on eigs #9425

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merged 9 commits into from
Jan 11, 2015
Merged

initial svds support based on eigs #9425

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9ea6b51
initial svds support based on eigs
jaak-s Dec 20, 2014
8b061df
removed extra spaces, added ritzvec param to svds
jaak-s Dec 21, 2014
d654afa
manual for svds
jaak-s Dec 21, 2014
6e91217
renamed to SVDOperator
jaak-s Dec 21, 2014
95e2d6c
svds now uses eigs of [0 A; A' 0]
jaak-s Jan 2, 2015
b1517a6
support for Complex operators
jaak-s Jan 3, 2015
be1f1bb
removed trailing whitespace
jaak-s Jan 3, 2015
f8edd41
replaced getOperatorType to eltype
jaak-s Jan 3, 2015
b9d7a30
added check for nsv
jaak-s Jan 3, 2015
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manual for svds
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@jaak-s
jaak-s committed Dec 21, 2014
commit d654afaf7d1d7068814f258db1c12077d7191da2
19 changes: 18 additions & 1 deletion doc/stdlib/linalg.rst
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Expand Up @@ -564,7 +564,7 @@ Linear algebra functions in Julia are largely implemented by calling functions f

Conjugate transpose array ``src`` and store the result in the preallocated array ``dest``, which should have a size corresponding to ``(size(src,2),size(src,1))``. No in-place transposition is supported and unexpected results will happen if `src` and `dest` have overlapping memory regions.

.. function:: eigs(A, [B,]; nev=6, which="LM", tol=0.0, maxiter=1000, sigma=nothing, ritzvec=true, v0=zeros((0,))) -> (d,[v,],nconv,niter,nmult,resid)
.. function:: eigs(A, [B,]; nev=6, which="LM", tol=0.0, maxiter=300, sigma=nothing, ritzvec=true, v0=zeros((0,))) -> (d,[v,],nconv,niter,nmult,resid)

``eigs`` computes eigenvalues ``d`` of ``A`` using Lanczos or Arnoldi iterations for real symmetric or general nonsymmetric matrices respectively. If ``B`` is provided, the generalized eigen-problem is solved. The following keyword arguments are supported:
* ``nev``: Number of eigenvalues
Expand Down Expand Up @@ -600,6 +600,23 @@ Linear algebra functions in Julia are largely implemented by calling functions f
real or complex inverse with level shift ``sigma`` :math:`(A - \sigma I )^{-1}`
=============== ================================== ==================================

.. function:: svds(A; ritzvec=true, args...) -> (left_sv, s, right_sv, nconv, niter, nmult, resid)

``svds`` computes singular values ``s`` of ``A`` using Lanczos or Arnoldi iterations. Uses ``eigs`` underneath so following keyword arguments are supported:
* ``nev``: Number of singular values.
* ``ncv``: Number of Krylov vectors used in the computation; see ``eigs`` manual.
* ``ritzvec``: Whether to return the left and right singular vectors ``left_sv`` and ``right_sv``, default is ``true``. If ``false`` the singular vectors are omitted from the output.
* ``which``: type of singular values (and vectors) to compute, default is largest values. See ``eigs`` manual.
* ``tol``: tolerance, see ``eigs``.
* ``maxiter``: Maximum number of iterations, see ``eigs``.
* ``sigma``: See ``eigs``.
* ``v0``: starting vector of right singular vector from which to start the iterations.

**Example**::

X = sprand(10, 5, 0.2)
svds(X, nev = 2)

.. function:: peakflops(n; parallel=false)

``peakflops`` computes the peak flop rate of the computer by using double precision :func:`Base.LinAlg.BLAS.gemm!`. By default, if no arguments are specified, it multiplies a matrix of size ``n x n``, where ``n = 2000``. If the underlying BLAS is using multiple threads, higher flop rates are realized. The number of BLAS threads can be set with ``blas_set_num_threads(n)``.
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