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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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2 changes: 2 additions & 0 deletions NEWS.md
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Original file line number Diff line number Diff line change
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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Original file line number Diff line number Diff line change
@@ -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)