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Julia v1.1 update #1

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89 changes: 62 additions & 27 deletions Pfaffian.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,7 @@
# (file, filename, data) = imp.find_module("pfaffian", [path]);
# pfaffian = imp.load_module(name, file, filename, data)

function Householder(x::Vector{Float64})::Tuple{Vector{Float64}, Float64, Float64}
function Householder(x::Vector{Float64})::Tuple{Vector{Float64},Float64,Float64}
@assert length(x) > 0

sigma = dot(x[2:end], x[2:end])
Expand All @@ -29,13 +29,13 @@ end

Householder(x::Vector{Int}) = Householder(convert(Vector{Float64}, x))

function Householder(x::Vector{Complex128})::Tuple{Vector{Complex128}, Float64, Complex128}
function Householder(x::Vector{ComplexF64})::Tuple{Vector{ComplexF64},Float64,ComplexF64}
@assert length(x) > 1

sigma = dot(x[2:end], x[2:end])

if sigma == 0
return (zeros(Complex128, length(x)), 0., x[1])
return (zeros(ComplexF64, length(x)), 0., x[1])
else
norm_x = sqrt(abs2(x[1]) + sigma)
v = copy(x)
Expand All @@ -46,9 +46,12 @@ function Householder(x::Vector{Complex128})::Tuple{Vector{Complex128}, Float64,
end
end

function skew_tridiagonalize(A::Matrix{T}; overwrite_A=false, calc_Q=true) where {T <: Number}
function skew_tridiagonalize(
A::Matrix{T};
overwrite_A = false, calc_Q = true
) where {T<:Number}
@assert size(A)[1] == size(A)[2] > 0
@assert maximum(abs, A + A.') < 1e-12
@assert maximum(abs, A + A') < 1e-12

n = size(A)[1]

Expand Down Expand Up @@ -92,18 +95,25 @@ function skew_tridiagonalize(A::Matrix{T}; overwrite_A=false, calc_Q=true) where
end
end

function skew_tridiagonalize(A::Matrix{Int}; overwrite_A=false, calc_Q=true)
return skew_tridiagonalize(convert(Matrix{Float64}, A), overwrite_A=overwrite_A, calc_Q=calc_Q)
function skew_tridiagonalize(A::Matrix{Int}; overwrite_A = false, calc_Q = true)
return skew_tridiagonalize(
convert(Matrix{Float64}, A),
overwrite_A = overwrite_A,
calc_Q = calc_Q
)
end

function Pfaffian_LTL(A::Union{Matrix{Float64}, Matrix{Complex128}}; overwrite_A=false, skewsymtol=1e-6)::Union{Float64, Complex128}
function Pfaffian_LTL(
A::Union{Matrix{Float64},Matrix{ComplexF64}};
overwrite_A = false, skewsymtol = 1e-6
)::Union{Float64,ComplexF64}
@assert size(A)[1] == size(A)[2] > 0
@assert maximum(abs, A + A.') < skewsymtol
@assert maximum(abs, A + A') < skewsymtol

T = eltype(A)
n = size(A)[1]

if n%2 == 1
if n % 2 == 1
return T(0.)
end

Expand All @@ -114,10 +124,10 @@ function Pfaffian_LTL(A::Union{Matrix{Float64}, Matrix{Complex128}}; overwrite_A

pf_val = T(1.)

for k in 1:2:n-1
kp = k + indmax(abs.(A[k+1:end, k]))
for k in 1:2:n - 1
kp = k + argmax(abs.(A[k+1:end, k]))[1]

if kp != k+1
if kp != k + 1
temp = copy(A[k+1, k:end])
A[k+1, k:end] = @view(A[kp, k:end])
A[kp, k:end] = temp
Expand All @@ -135,9 +145,19 @@ function Pfaffian_LTL(A::Union{Matrix{Float64}, Matrix{Complex128}}; overwrite_A

pf_val *= A[k, k+1]

if k+2 <= n
BLAS.ger!(T(1.), tau, conj(@view(A[k+2:end, k+1])), @view(A[k+2:end, k+2:end]))
BLAS.ger!(T(-1.), @view(A[k+2:end, k+1]), conj(tau), @view(A[k+2:end, k+2:end]))
if k + 2 <= n
BLAS.ger!(
T(1.),
tau,
conj(@view(A[k+2:end, k+1])),
@view(A[k+2:end, k+2:end])
)
BLAS.ger!(
T(-1.),
@view(A[k+2:end, k+1]),
conj(tau),
@view(A[k+2:end, k+2:end])
)
end
else
return T(0.)
Expand All @@ -147,18 +167,25 @@ function Pfaffian_LTL(A::Union{Matrix{Float64}, Matrix{Complex128}}; overwrite_A
return pf_val
end

function Pfaffian_LTL(A::Matrix{Int}; overwrite_A=false, skewsymtol=1e-6)::Float64
return Pfaffian_LTL(convert(Matrix{Float64}, A), overwrite_A=overwrite_A, skewsymtol=skewsymtol)
function Pfaffian_LTL(A::Matrix{Int}; overwrite_A = false, skewsymtol = 1e-6)::Float64
return Pfaffian_LTL(
convert(Matrix{Float64}, A),
overwrite_A = overwrite_A,
skewsymtol = skewsymtol
)
end

function Pfaffian_Householder(A::Union{Matrix{Float64}, Matrix{Complex128}}; overwrite_A=false, skewsymtol=1e-6)::Union{Float64, Complex128}
function Pfaffian_Householder(
A::Union{Matrix{Float64},Matrix{ComplexF64}};
overwrite_A = false, skewsymtol = 1e-6
)::Union{Float64,ComplexF64}
@assert size(A)[1] == size(A)[2] > 0
@assert maximum(abs, A + A.') < skewsymtol
@assert maximum(abs, A + A') < skewsymtol

T = eltype(A)
n = size(A)[1]

if n%2 == 1
if n % 2 == 1
return T(0.)
end

Expand All @@ -183,7 +210,7 @@ function Pfaffian_Householder(A::Union{Matrix{Float64}, Matrix{Complex128}}; ove
if tau != 0
pf_val *= 1. - tau
end
if i%2 == 1
if i % 2 == 1
pf_val *= -alpha
end
end
Expand All @@ -193,13 +220,21 @@ function Pfaffian_Householder(A::Union{Matrix{Float64}, Matrix{Complex128}}; ove
return pf_val
end

function Pfaffian_Householder(A::Matrix{Int}; overwrite_A=false, skewsymtol=1e-6)::Float64
return Pfaffian_Householder(convert(Matrix{Float64}, A), overwrite_A=overwrite_A, skewsymtol=skewsymtol)
function Pfaffian_Householder(
A::Matrix{Int};
overwrite_A = false, skewsymtol = 1e-6
)::Float64
return Pfaffian_Householder(
convert(Matrix{Float64}, A),
overwrite_A = overwrite_A,
skewsymtol = skewsymtol
)
end

# default to LTL for speed
Pfaffian(A::Matrix; overwrite_A=false, skewsymtol=1e-6)::Union{Float64, Complex128} = Pfaffian_LTL(A, overwrite_A=overwrite_A, skewsymtol=skewsymtol)
# Pfaffian(A::Matrix; overwrite_A=false, skewsymtol=1e-6)::Union{Float64, Complex128} = Pfaffian_Householder(A, overwrite_A=overwrite_A, skewsymtol=skewsymtol)
Pfaffian(A::Matrix; overwrite_A = false, skewsymtol = 1e-6)::Union{Float64,ComplexF64} =
Pfaffian_LTL(A, overwrite_A = overwrite_A, skewsymtol = skewsymtol)
# Pfaffian(A::Matrix; overwrite_A=false, skewsymtol=1e-6)::Union{Float64, ComplexF64} = Pfaffian_Householder(A, overwrite_A=overwrite_A, skewsymtol=skewsymtol)

# Wimmer's version
# Pfaffian(A::Matrix; overwrite_A=false, skewsymtol=1e-6)::Union{Float64, Complex128} = pfaffian[:pfaffian](A, overwrite_a=overwrite_A, method="P")
# Pfaffian(A::Matrix; overwrite_A=false, skewsymtol=1e-6)::Union{Float64, ComplexF64} = pfaffian[:pfaffian](A, overwrite_a=overwrite_A, method="P")
30 changes: 15 additions & 15 deletions test-Pfaffian.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -7,7 +7,7 @@ using PyCall
@pyimport imp
path = dirname("pfapack/python/pfaffian.py")
name = basename("pfapack/python/pfaffian.py")
(file, filename, data) = imp.find_module("pfaffian", [path]);
(file, filename, data) = imp.find_module("pfaffian", [path])
pfaffian = imp.load_module(name, file, filename, data)

N = 100
Expand Down Expand Up @@ -39,15 +39,15 @@ T_w, Q_w = pfaffian[:skew_tridiagonalize](A)
println()

pf_ltl = Pfaffian_LTL(A)
pf_ltl_w = pfaffian[:pfaffian](A, method="P")
pf_ltl_w = pfaffian[:pfaffian](A, method = "P")

@show abs((pf_ltl - pf_ltl_w)/pf_ltl_w)
@show abs((pf_ltl - pf_ltl_w) / pf_ltl_w)
println()

pf_h = Pfaffian_Householder(A)
pf_h_w = pfaffian[:pfaffian](A, method="H")
pf_h_w = pfaffian[:pfaffian](A, method = "H")

@show abs((pf_h - pf_h_w)/pf_h_w)
@show abs((pf_h - pf_h_w) / pf_h_w)
println()

println()
Expand Down Expand Up @@ -75,22 +75,22 @@ T_w, Q_w = pfaffian[:skew_tridiagonalize](convert(Matrix{Float64}, A))
println()

pf_ltl = Pfaffian_LTL(A)
pf_ltl_w = pfaffian[:pfaffian](A, method="P")
pf_ltl_w = pfaffian[:pfaffian](A, method = "P")

@show abs((pf_ltl - pf_ltl_w)/pf_ltl_w)
@show abs((pf_ltl - pf_ltl_w) / pf_ltl_w)
println()

pf_h = Pfaffian_Householder(A)
pf_h_w = pfaffian[:pfaffian](A, method="H")
pf_h_w = pfaffian[:pfaffian](A, method = "H")

@show abs((pf_h - pf_h_w)/pf_h_w)
@show abs((pf_h - pf_h_w) / pf_h_w)
println()

println()
println("Testing complex methods:")
println()

x = rand(Complex128, N)
x = rand(ComplexF64, N)

v, tau, alpha = Householder(x)
v_w, tau_w, alpha_w = pfaffian[:householder_complex](x)
Expand All @@ -100,7 +100,7 @@ v_w, tau_w, alpha_w = pfaffian[:householder_complex](x)
@show abs(alpha - alpha_w)
println()

A = rand(Complex128, (N, N))
A = rand(ComplexF64, (N, N))
A = A - A.'

T, Q = skew_tridiagonalize(A)
Expand All @@ -111,13 +111,13 @@ T_w, Q_w = pfaffian[:skew_tridiagonalize](A)
println()

pf_ltl = Pfaffian_LTL(A)
pf_ltl_w = pfaffian[:pfaffian](A, method="P")
pf_ltl_w = pfaffian[:pfaffian](A, method = "P")

@show abs((pf_ltl - pf_ltl_w)/pf_ltl_w)
@show abs((pf_ltl - pf_ltl_w) / pf_ltl_w)
println()

pf_h = Pfaffian_Householder(A)
pf_h_w = pfaffian[:pfaffian](A, method="H")
pf_h_w = pfaffian[:pfaffian](A, method = "H")

@show abs((pf_h - pf_h_w)/pf_h_w)
@show abs((pf_h - pf_h_w) / pf_h_w)
println()