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initial svds support based on eigs #9425

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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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1 change: 1 addition & 0 deletions base/exports.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -690,6 +690,7 @@ export
svd,
svdfact!,
svdfact,
svds,
svdvals!,
svdvals,
sylvester,
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1 change: 1 addition & 0 deletions base/linalg.jl
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Expand Up @@ -102,6 +102,7 @@ export
svd,
svdfact!,
svdfact,
svds,
svdvals!,
svdvals,
sylvester,
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20 changes: 20 additions & 0 deletions base/linalg/arnoldi.jl
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Expand Up @@ -106,3 +106,23 @@ function eigs(A, B;
resid, ncv, v, ldv, sigma, iparam, ipntr, workd, workl, lworkl, rwork)

end


## svds

type SvdX <: 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.

end

*(s::SvdX, v::Vector{Float64}) = s.X' * (s.X * v)
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This approach ruins the precision of the small values. I think that the documentation suggests op = [0 A;A' 0] for the SVD. I'd also like to see the allocation free version, A_mul_B! for later use.

size(s::SvdX) = size(s.X, 2), size(s.X, 2)
issym(s::SvdX) = true

function svds(X; args...)
ex = eigs(SvdX(X), I; args...)
## 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]
end


20 changes: 20 additions & 0 deletions test/linalg/arnoldi.jl
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@@ -0,0 +1,20 @@
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)
S2 = svd(full(A))

## singular values match:
@test_approx_eq S1[2] S2[2][1:2]

## 1st left singular vector
s1_left = sign(S1[1][3,1]) * S1[1][:,1]
s2_left = sign(S2[1][3,1]) * S2[1][:,1]
@test_approx_eq s1_left s2_left

## 1st right singular vector
s1_right = sign(S1[3][3,1]) * S1[3][:,1]
s2_right = sign(S2[3][3,1]) * S2[3][:,1]
@test_approx_eq s1_right s2_right
end