From fec60834e094f79f43d21a69e7ff6d9c046ee095 Mon Sep 17 00:00:00 2001
From: amitjamadagni <bitsjamadagni@gmail.com>
Date: Mon, 29 Jun 2015 17:34:25 +0530
Subject: [PATCH] Dot, trace implemented. Test added.

---
 src/arrays/arraymath.jl | 15 +++++++++++++++
 test/multest.jl         | 13 +++++++++++++
 2 files changed, 28 insertions(+)

diff --git a/src/arrays/arraymath.jl b/src/arrays/arraymath.jl
index d924ccb..ffec121 100644
--- a/src/arrays/arraymath.jl
+++ b/src/arrays/arraymath.jl
@@ -124,6 +124,21 @@ end
 #  Vectorize QuArray
 Base.vec{B<:OrthonormalBasis}(vec1::AbstractQuArray{B}) = QuArray(vec(coeffs(vec1)))
 
+# 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
index fddce6e..542e280 100644
--- a/test/multest.jl
+++ b/test/multest.jl
@@ -38,5 +38,18 @@ 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)
+
 # Vectorize
 @assert vec(qv) == vec(qv')