mirror of
https://igit.ific.uv.es/alramos/latticegpu.jl.git
synced 2025-05-15 11:43:42 +02:00
130 lines
6.6 KiB
Julia
130 lines
6.6 KiB
Julia
###
|
|
### "THE BEER-WARE LICENSE":
|
|
### Alberto Ramos wrote this file. As long as you retain this
|
|
### notice you can do whatever you want with this stuff. If we meet some
|
|
### day, and you think this stuff is worth it, you can buy me a beer in
|
|
### return. <alberto.ramos@cern.ch>
|
|
###
|
|
### file: M3x3.jl
|
|
### created: Sun Oct 3 09:03:34 2021
|
|
###
|
|
|
|
|
|
Base.:*(a::M3x3{T},b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31,
|
|
a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32,
|
|
a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33,
|
|
a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31,
|
|
a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32,
|
|
a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33,
|
|
a.u31*b.u11 + a.u32*b.u21 + a.u33*b.u31,
|
|
a.u31*b.u12 + a.u32*b.u22 + a.u33*b.u32,
|
|
a.u31*b.u13 + a.u32*b.u23 + a.u33*b.u33)
|
|
|
|
function Base.:*(a::SU3{T},b::M3x3{T}) where T <: AbstractFloat
|
|
|
|
au31 = conj(a.u12*a.u23 - a.u13*a.u22)
|
|
au32 = conj(a.u13*a.u21 - a.u11*a.u23)
|
|
au33 = conj(a.u11*a.u22 - a.u12*a.u21)
|
|
|
|
return M3x3{T}(a.u11*b.u11 + a.u12*b.u21 + a.u13*b.u31,
|
|
a.u11*b.u12 + a.u12*b.u22 + a.u13*b.u32,
|
|
a.u11*b.u13 + a.u12*b.u23 + a.u13*b.u33,
|
|
a.u21*b.u11 + a.u22*b.u21 + a.u23*b.u31,
|
|
a.u21*b.u12 + a.u22*b.u22 + a.u23*b.u32,
|
|
a.u21*b.u13 + a.u22*b.u23 + a.u23*b.u33,
|
|
au31*b.u11 + au32*b.u21 + au33*b.u31,
|
|
au31*b.u12 + au32*b.u22 + au33*b.u32,
|
|
au31*b.u13 + au32*b.u23 + au33*b.u33)
|
|
end
|
|
|
|
|
|
function Base.:*(a::M3x3{T},b::SU3{T}) where T <: AbstractFloat
|
|
|
|
bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
|
|
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
|
|
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
|
|
|
|
return M3x3{T}(a.u11*b.u11 + a.u12*b.u21 + a.u13*bu31,
|
|
a.u11*b.u12 + a.u12*b.u22 + a.u13*bu32,
|
|
a.u11*b.u13 + a.u12*b.u23 + a.u13*bu33,
|
|
a.u21*b.u11 + a.u22*b.u21 + a.u23*bu31,
|
|
a.u21*b.u12 + a.u22*b.u22 + a.u23*bu32,
|
|
a.u21*b.u13 + a.u22*b.u23 + a.u23*bu33,
|
|
a.u31*b.u11 + a.u32*b.u21 + a.u33*bu31,
|
|
a.u31*b.u12 + a.u32*b.u22 + a.u33*bu32,
|
|
a.u31*b.u13 + a.u32*b.u23 + a.u33*bu33)
|
|
end
|
|
|
|
function Base.:/(a::M3x3{T},b::SU3{T}) where T <: AbstractFloat
|
|
|
|
bu31 = (b.u12*b.u23 - b.u13*b.u22)
|
|
bu32 = (b.u13*b.u21 - b.u11*b.u23)
|
|
bu33 = (b.u11*b.u22 - b.u12*b.u21)
|
|
|
|
return M3x3{T}(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
|
|
a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
|
|
a.u11*(bu31) + a.u12*(bu32) + a.u13*(bu33),
|
|
a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
|
|
a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
|
|
a.u21*(bu31) + a.u22*(bu32) + a.u23*(bu33),
|
|
a.u31*conj(b.u11) + a.u32*conj(b.u12) + a.u33*conj(b.u13),
|
|
a.u31*conj(b.u21) + a.u32*conj(b.u22) + a.u33*conj(b.u23),
|
|
a.u31*(bu31) + a.u32*(bu32) + a.u33*(bu33))
|
|
end
|
|
|
|
function Base.:\(a::SU3{T},b::M3x3{T}) where T <: AbstractFloat
|
|
|
|
au31 = (a.u12*a.u23 - a.u13*a.u22)
|
|
au32 = (a.u13*a.u21 - a.u11*a.u23)
|
|
au33 = (a.u11*a.u22 - a.u12*a.u21)
|
|
|
|
return M3x3{T}(conj(a.u11)*b.u11 + conj(a.u21)*b.u21 + (au31)*b.u31,
|
|
conj(a.u11)*b.u12 + conj(a.u21)*b.u22 + (au31)*b.u32,
|
|
conj(a.u11)*b.u13 + conj(a.u21)*b.u23 + (au31)*b.u33,
|
|
conj(a.u12)*b.u11 + conj(a.u22)*b.u21 + (au32)*b.u31,
|
|
conj(a.u12)*b.u12 + conj(a.u22)*b.u22 + (au32)*b.u32,
|
|
conj(a.u12)*b.u13 + conj(a.u22)*b.u23 + (au32)*b.u33,
|
|
conj(a.u13)*b.u11 + conj(a.u23)*b.u21 + (au33)*b.u31,
|
|
conj(a.u13)*b.u12 + conj(a.u23)*b.u22 + (au33)*b.u32,
|
|
conj(a.u13)*b.u13 + conj(a.u23)*b.u23 + (au33)*b.u33)
|
|
|
|
end
|
|
|
|
Base.:*(a::Number,b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a*b.u11, a*b.u12, a*bu13,
|
|
a*b.u21, a*b.u22, a*bu23,
|
|
a*b.u31, a*b.u32, a*bu33)
|
|
|
|
Base.:*(b::M3x3{T},a::Number) where T <: AbstractFloat = M3x3{T}(a*b.u11, a*b.u12, a*bu13,
|
|
a*b.u21, a*b.u22, a*bu23,
|
|
a*b.u31, a*b.u32, a*bu33)
|
|
|
|
Base.:+(a::M3x3{T},b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a.u11+b.u11, a.u12+b.u12, a.u13+bu13,
|
|
a.u21+b.u21, a.u22+b.u22, a.u23+bu23,
|
|
a.u31+b.u31, a.u32+b.u32, a.u33+bu33)
|
|
|
|
Base.:-(a::M3x3{T},b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(a.u11-b.u11, a.u12-b.u12, a.u13-bu13,
|
|
a.u21-b.u21, a.u22-b.u22, a.u23-bu23,
|
|
a.u31-b.u31, a.u32-b.u32, a.u33-bu33)
|
|
|
|
Base.:-(b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(-b.u11, -b.u12, -bu13,
|
|
-b.u21, -b.u22, -bu23,
|
|
-b.u31, -b.u32, -bu33)
|
|
|
|
Base.:+(b::M3x3{T}) where T <: AbstractFloat = M3x3{T}(b.u11, b.u12, bu13,
|
|
b.u21, b.u22, bu23,
|
|
b.u31, b.u32, bu33)
|
|
function projalg(a::M3x3{T}) where T <: AbstractFloat
|
|
|
|
sr3ov2::T = 0.866025403784438646763723170752
|
|
|
|
ditr = ( imag(a.u11) + imag(a.u22) - 2.0*imag(a.u33) )/3.0
|
|
m12 = (a.u12 - conj(a.u21))/2.0
|
|
m13 = (a.u13 - conj(a.u31))/2.0
|
|
m23 = (a.u23 - conj(a.u32))/2.0
|
|
|
|
return SU3alg{T}(imag( m12 ), imag( m13 ), imag( m23 ),
|
|
real( m12 ), real( m13 ), real( m23 ),
|
|
(imag(a.u11)-imag(a.u22))/2.0,
|
|
sr3ov2*(ditr))
|
|
end
|
|
|