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Add function for machine precision number to avoid expensive calculations in the Givens rotation algorithms #8660

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Oct 14, 2014
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Add function for machine precision number to avoid expensive calculations in the Givens rotation algorithms #8660

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Add function for machine precision number to avoid expensive calculat… 
…ion in the Givens rotation algorithms. Remove subtype relation to AbstractMatrix and therefore also the now unnecessary ambiguity warning avoiding method definitions. Use @simd and @inbounds in methods for applying Givens rotations.
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@andreasnoack
andreasnoack committed Oct 14, 2014
commit dadd6ca842d345f89e015a83a1a091294e9c65ad
2 changes: 2 additions & 0 deletions NEWS.md
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Expand Up @@ -75,6 +75,8 @@ Library improvements

* `deepcopy` recurses through immutable types and makes copies of their mutable fields ([#8560]).

* Givens type doesn't have a size anymore and is no longer a subtype of AbstractMatrix ([#8660])

Deprecated or removed
---------------------

Expand Down
46 changes: 23 additions & 23 deletions base/linalg/givens.jl
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@@ -1,5 +1,4 @@
immutable Givens{T} <: AbstractMatrix{T}
size::Int
immutable Givens{T}
i1::Int
i2::Int
c::T
Expand All @@ -11,14 +10,18 @@ type Rotation{T}
end
typealias AbstractRotation Union(Givens, Rotation)

realmin2(::Type{Float32}) = reinterpret(Float32, 0x26000000)
realmin2(::Type{Float64}) = reinterpret(Float64, 0x21a0000000000000)
realmin2{T}(::Type{T}) = (twopar = 2one(T); twopar^itrunc(log(realmin(T)/eps(T))/log(twopar)/twopar))

function givensAlgorithm{T<:FloatingPoint}(f::T, g::T)
zeropar = zero(T)
onepar = one(T)
twopar = 2one(T)

safmin = realmin(T)
epspar = eps(T)
safmn2 = twopar^itrunc(log(safmin/epspar)/log(twopar)/twopar)
safmn2 = realmin2(T)
safmx2 = onepar/safmn2

if g == 0
Expand Down Expand Up @@ -84,7 +87,7 @@ function givensAlgorithm{T<:FloatingPoint}(f::Complex{T}, g::Complex{T})
abs1(ff) = max(abs(real(ff)), abs(imag(ff)))
safmin = realmin(T)
epspar = eps(T)
safmn2 = twopar^itrunc(log(safmin/epspar)/log(twopar)/twopar)
safmn2 = realmin2(T)
safmx2 = onepar/safmn2
scalepar = max(abs1(f), abs1(g))
fs = f
Expand Down Expand Up @@ -181,33 +184,25 @@ function givensAlgorithm{T<:FloatingPoint}(f::Complex{T}, g::Complex{T})
return cs, sn, r
end

function givens{T}(f::T, g::T, i1::Integer, i2::Integer, size::Integer)
i2 <= size || error("indices cannot be larger than size Givens rotation matrix")
function givens{T}(f::T, g::T, i1::Integer, i2::Integer)
i1 < i2 || error("second index must be larger than the first")
h = givensAlgorithm(f, g)
Givens(size, i1, i2, convert(T, h[1]), convert(T, h[2]), convert(T, h[3]))
c, s, r = givensAlgorithm(f, g)
Givens(i1, i2, convert(T, c), convert(T, s), convert(T, r))
end

function givens{T}(A::AbstractMatrix{T}, i1::Integer, i2::Integer, col::Integer)
i1 < i2 || error("second index must be larger than the first")
h = givensAlgorithm(A[i1,col], A[i2,col])
Givens(size(A, 1), i1, i2, convert(T, h[1]), convert(T, h[2]), convert(T, h[3]))
c, s, r = givensAlgorithm(A[i1,col], A[i2,col])
Givens(i1, i2, convert(T, c), convert(T, s), convert(T, r))
end

*{T}(G1::Givens{T}, G2::Givens{T}) = Rotation(push!(push!(Givens{T}[], G2), G1))
*(G::Givens, B::BitArray{2}) = error("method not defined")
*{TBf,TBi}(G::Givens, B::SparseMatrixCSC{TBf,TBi}) = error("method not defined")
*(R::AbstractRotation, A::AbstractMatrix) = A_mul_B!(R, copy(A))

A_mul_Bc(A::AbstractMatrix, R::Rotation) = A_mul_Bc!(copy(A), R)

getindex(G::Givens, i::Integer, j::Integer) = i == j ? (i == G.i1 || i == G.i2 ? G.c : one(G.c)) : (i == G.i1 && j == G.i2 ? G.s : (i == G.i2 && j == G.i1 ? -G.s : zero(G.s)))
size(G::Givens) = (G.size, G.size)
size(G::Givens, i::Integer) = 1 <= i <= 2 ? G.size : 1

A_mul_B!(G1::Givens, G2::Givens) = error("Operation not supported. Consider *")
function A_mul_B!(G::Givens, A::AbstractMatrix)
m, n = size(A)
for i = 1:n
G.i2 <= m || throw(DimensionMismatch("column indices for rotation are outside the matrix"))
@inbounds @simd for i = 1:n
tmp = G.c*A[G.i1,i] + G.s*A[G.i2,i]
A[G.i2,i] = G.c*A[G.i2,i] - conj(G.s)*A[G.i1,i]
A[G.i1,i] = tmp
Expand All @@ -216,7 +211,8 @@ function A_mul_B!(G::Givens, A::AbstractMatrix)
end
function A_mul_Bc!(A::AbstractMatrix, G::Givens)
m, n = size(A)
for i = 1:m
G.i2 <= n || throw(DimensionMismatch("column indices for rotation are outside the matrix"))
@inbounds @simd for i = 1:m
tmp = G.c*A[i,G.i1] + conj(G.s)*A[i,G.i2]
A[i,G.i2] = G.c*A[i,G.i2] - G.s*A[i,G.i1]
A[i,G.i1] = tmp
Expand All @@ -228,14 +224,18 @@ function A_mul_B!(G::Givens, R::Rotation)
return R
end
function A_mul_B!(R::Rotation, A::AbstractMatrix)
for i = 1:length(R.rotations)
@inbounds for i = 1:length(R.rotations)
A_mul_B!(R.rotations[i], A)
end
return A
end
function A_mul_Bc!(A::AbstractMatrix, R::Rotation)
for i = 1:length(R.rotations)
@inbounds for i = 1:length(R.rotations)
A_mul_Bc!(A, R.rotations[i])
end
return A
end
*{T}(G1::Givens{T}, G2::Givens{T}) = Rotation(push!(push!(Givens{T}[], G2), G1))
*(R::AbstractRotation, A::AbstractMatrix) = A_mul_B!(R, copy(A))

A_mul_Bc(A::AbstractMatrix, R::AbstractRotation) = A_mul_Bc!(copy(A), R)