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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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support for Complex operators
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@jaak-s
jaak-s committed Jan 3, 2015
commit b1517a6b12553a82a9d867f0e65fe5e489638f8d
34 changes: 26 additions & 8 deletions base/linalg/arnoldi.jl
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Expand Up @@ -110,22 +110,40 @@ end

## svds

type SVDOperator <: AbstractArray{Float64, 2}
X
type SVDOperator{T,S} <: AbstractArray{T, 2}
X::S
m::Int
n::Int
SVDOperator(X) = new(X, size(X,1), size(X,2))
SVDOperator(X::S) = new(X, size(X,1), size(X,2))
end

## 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]]
*{T,S}(s::SVDOperator{T,S}, v::Vector{T}) = [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, 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
function getOperatorType(X)
et = eltype(X)
if et <: Integer || et <: Float64
return Float64
end
if et <: Complex64
return Complex64
end
if et <: Complex
return Complex128
end
if et <: Float32
return Float32
end
error("Element type $et is not supported for 'svds'.")
end

function svds{S}(X::S; nsv::Int = 6, ritzvec::Bool = true, tol::Float64 = 0.0, maxiter::Int = 1000)
otype = getOperatorType(X)
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I think we can just simplify this to use just eltype(X) and avoid getOperatorType() altogether. The checks for whether eltype() is BlasFloat should ideally be in eigs. It should be possible to make SVDOperator free of types then.

ex = eigs(SVDOperator{otype,S}(X), I; ritzvec = ritzvec, nev = 2*nsv, tol = tol, maxiter = maxiter)
ind = [1:2:nsv*2]
sval = abs(ex[1][ind])

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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]
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38 changes: 38 additions & 0 deletions test/linalg/arnoldi.jl
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Expand Up @@ -18,3 +18,41 @@ let # svds test
s2_right = sign(S2[3][3,1]) * S2[3][:,1]
@test_approx_eq s1_right s2_right
end

let # svd test with boolean matrix
B = [true true false; false true false; true false true; false true true]
S1 = svds(B, nsv = 2)
S2 = svd(B)

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

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

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

let # complex svds test
A = sparse([1, 1, 2, 3, 4], [2, 1, 1, 3, 1], exp(im*[2.0:2:10]))
S1 = svds(A, nsv = 2)
S2 = svd(full(A))

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

## left singular vectors
s1_left = abs(S1[1][:,1:2])
s2_left = abs(S2[1][:,1:2])
@test_approx_eq s1_left s2_left

## right singular vectors
s1_right = abs(S1[3][:,1:2])
s2_right = abs(S2[3][:,1:2])
@test_approx_eq s1_right s2_right
end