mirror of
https://igit.ific.uv.es/alramos/latticegpu.jl.git
synced 2025-05-14 19:23:42 +02:00
72 lines
No EOL
3 KiB
Julia
72 lines
No EOL
3 KiB
Julia
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SU2fund(a::T, b::T) where T <: AbstractFloat = SU2fund{T}(complex(a), complex(b))
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"""
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dag(a::SU2fund{T})
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Returns the conjugate of a fundamental element.
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"""
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dag(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(conj(a.t1), conj(a.t2))
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"""
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norm(a::SU2fund{T})
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Returns the norm of a fundamental element. Same result as dot(a,a).
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"""
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norm(a::SU2fund{T}) where T <: AbstractFloat = sqrt((abs2(a.t1) + abs2(a.t2)))
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"""
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norm(a::SU2fund{T})
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Returns the norm of a fundamental element. Same result as sqrt(dot(a,a)).
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"""
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norm2(a::SU2fund{T}) where T <: AbstractFloat = (abs2(a.t1) + abs2(a.t2))
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"""
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dot(a::SU2fund{T},b::SU2fund{T})
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Returns the scalar product of two fundamental elements. The convention is for the product to the linear in the second argument, and anti-linear in the first argument.
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"""
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dot(g1::SU2fund{T},g2::SU2fund{T}) where T <: AbstractFloat = conj(g1.t1)*g2.t1+conj(g1.t2)*g2.t2
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"""
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*(g::SU2{T},b::SU2fund{T})
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Returns ga
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"""
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Base.:*(g::SU2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(g.t1*b.t1 + g.t2*b.t2,-conj(g.t2)*b.t1 + conj(g.t1)*b.t2)
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"""
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\\(g::SU2{T},b::SU2fund{T})
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Returns g^dag b
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"""
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Base.:\(g::SU2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(conj(g.t1)*b.t1 - g.t2 * b.t2,conj(g.t2)*b.t1 + g.t1 * b.t2)
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"""
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*(a::SU2alg{T},b::SU2fund{T})
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Returns a*b
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"""
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Base.:*(a::SU2alg{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(complex(0.0, a.t3)*b.t1/2 + complex(a.t2,a.t1)*b.t2/2,
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complex(-a.t2,a.t1)*b.t1/2 + complex(0.0, -a.t3)*b.t1/2)
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Base.:+(a::SU2fund{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1+b.t1,a.t2+b.t2)
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Base.:-(a::SU2fund{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1-b.t1,a.t2-b.t2)
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Base.:+(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.t1,a.t2)
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Base.:-(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(-a.t1,-a.t2)
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imm(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(complex(-imag(a.t1),real(a.t1)),
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complex(-imag(a.t2),real(a.t2)))
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mimm(a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(complex(imag(a.t1),-real(a.t1)),
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complex(imag(a.t2),-real(a.t2)))
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# Operations with numbers
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Base.:*(a::SU2fund{T},b::Number) where T <: AbstractFloat = SU2fund{T}(b*a.t1,b*a.t2)
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Base.:*(b::Number,a::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(b*a.t1,b*a.t2)
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Base.:/(a::SU2fund{T},b::Number) where T <: AbstractFloat = SU2fund{T}(a.t1/b,a.t2/b)
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Base.:*(a::M2x2{T},b::SU2fund{T}) where T <: AbstractFloat = SU2fund{T}(a.u11*b.t1 + a.u12*b.t2,
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a.u21*b.t1 + a.u22*b.t2) |