Dot product, Trace Implemented.Tests added.

JuliaAttic · Jun 29, 2015 · b457ec2 · b457ec2
1 parent 055bce8
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diff --git a/src/arrays/arraymath.jl b/src/arrays/arraymath.jl
@@ -121,6 +121,21 @@ function \{B<:OrthonormalBasis}(op::AbstractQuMatrix{B}, vec::AbstractQuVector{B
     return QAT(div, bases(op,1))
 end
 
+# Trace of AbstractQuMatrix
+Base.trace{B<:OrthonormalBasis}(qm1::AbstractQuMatrix{B}) = trace(coeffs(qm1))
+
+# dot product of QuArray's
+Base.dot{B<:OrthonormalBasis}(vec1::AbstractQuVector{B}, vec2::AbstractQuVector{B}) = dot(coeffs(vec1), coeffs(vec2))
+Base.dot{B<:OrthonormalBasis}(vec1::DualVector{B}, vec2::DualVector{B}) = dot(vec(coeffs(vec1)), vec(coeffs(vec2)))
+Base.dot{B<:OrthonormalBasis}(vec1::AbstractQuVector{B}, vec2::DualVector{B}) = error("Inner product of a dual vector and a vector is not supported.")
+Base.dot{B<:OrthonormalBasis}(vec1::DualVector{B}, vec2::AbstractQuVector{B}) = error("Inner product of a dual vector and a vector is not supported.")
+
+# Reference : http://en.wikipedia.org/wiki/Dot_product#Dyadics_and_matrices
+Base.dot{B<:OrthonormalBasis}(qm1::AbstractQuMatrix{B}, qm2::AbstractQuMatrix{B}) = trace(qm1'*qm2)
+Base.dot{B<:OrthonormalBasis}(qm1::DualMatrix{B}, qm2::AbstractQuMatrix{B}) = trace(qm1*qm2)
+Base.dot{B<:OrthonormalBasis}(qm1::DualMatrix{B}, qm2::DualMatrix{B}) = trace(qm1*qm2')
+Base.dot{B<:OrthonormalBasis}(qm1::AbstractQuMatrix{B}, qm2::DualMatrix{B}) = trace(qm1'*qm2')
+
 # matrix operations returning a scalar
 # normalization
 Base.norm(qarr::AbstractQuArray) = vecnorm(rawcoeffs(qarr))

diff --git a/test/multest.jl b/test/multest.jl
@@ -37,3 +37,16 @@ v1 =  [0.5+0*im, 0.+0.*im]
 qv1 = normalize!(QuArray(v1))
 @assert coeffs(\(sigmax,qv1)) == [0.+0.*im, 1.+0.*im]
 @assert coeffs(\(sigmaz, sigmax)) == [0. 1.;-1. 0.]
+
+# Trace
+# Pauli matrices sigmax, sigmay, sigmaz are traceless
+# Ref : http://en.wikipedia.org/wiki/Pauli_matrices#Algebraic_properties
+@assert trace(sigmax) == zero(eltype(sigmax))
+@assert trace(sigmax) == trace(sigmaz)
+
+# Dot product
+# Being defined both for vectors and dual vectors
+# Related Ref : https://github.com/JuliaLang/julia/issues/11064
+@assert dot(qv,qv) == dot(qv',qv')
+# dot(A,B)=trace(A'*B) for the case of sigmax, sigmay results in no trace.
+@assert dot(sigmax, sigmay) == trace(sigmaz)