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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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svds now uses eigs of [0 A; A' 0]
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@jaak-s
jaak-s committed Jan 2, 2015
commit 95e2d6c5a34355324a2326df922a15d27f3acabc
30 changes: 19 additions & 11 deletions base/linalg/arnoldi.jl
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Expand Up @@ -112,19 +112,27 @@ end

type SVDOperator <: AbstractArray{Float64, 2}
X
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I think we'd like to parametrize this type on the input element and matrix type (and use capital letters), i.e. something like

type SVDOperator{T,S}
data::S
end

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I addition, we'll have to support more than Float64 and the type should reflect that. The type can probably not be subtype of AbstractMatrix either, as the input might not be a subtype of AbstractMatrix.

m::Int
n::Int
SVDOperator(X) = new(X, size(X,1), size(X,2))
end

*(s::SVDOperator, v::Vector{Float64}) = s.X' * (s.X * v)
size(s::SVDOperator) = size(s.X, 2), size(s.X, 2)
## v = [ left_singular_vector; right_singular_vector ]
*(s::SVDOperator, v::Vector{Float64}) = [s.X * v[s.m+1:end]; s.X' * v[1:s.m]]
size(s::SVDOperator) = s.m + s.n, s.m + s.n
issym(s::SVDOperator) = true

function svds(X; ritzvec::Bool = true, args...)
ex = eigs(SVDOperator(X), I; ritzvec = ritzvec, args...)
if ! ritzvec
return sqrt(ex[1]), ex[2], ex[3], ex[4], ex[5]
end

## calculating left-side singular vectors
left_sv = X * ex[2]
return left_sv ./ sqrt(sum(left_sv.^2, 1)), sqrt(ex[1]), ex[2], ex[3], ex[4], ex[5], ex[6]
function svds(X; ritzvec::Bool = true, nsv::Int = 6, tol::Float64 = 0.0, maxiter::Int = 1000)
ex = eigs(SVDOperator(X), I; ritzvec = ritzvec, nev = 2*nsv, tol = tol, maxiter = maxiter)
ind = [1:2:nsv*2]
sval = (abs(ex[1][ind]) + abs(ex[1][ind + 1])) / 2

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travis doesn't like the trailing whitespace here or on line 151

if ! ritzvec
return sval, ex[2], ex[3], ex[4], ex[5]
end

## calculating singular vectors
left_sv = sqrt(2) * ex[2][ 1:size(X,1), ind ] .* sign(ex[1][ind]')
right_sv = sqrt(2) * ex[2][ size(X,1)+1:end, ind ]
return left_sv, sval, right_sv, ex[3], ex[4], ex[5], ex[6]
end
2 changes: 1 addition & 1 deletion test/linalg/arnoldi.jl
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Expand Up @@ -2,7 +2,7 @@ using Base.Test

let # svds test
A = sparse([1, 1, 2, 3, 4], [2, 1, 1, 3, 1], [2.0, -1.0, 6.1, 7.0, 1.5])
S1 = svds(A, nev = 2)
S1 = svds(A, nsv = 2)
S2 = svd(full(A))

## singular values match:
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