WIP: fix querying dual of symmetric equality constraints

src/sd.jl

@@ -174,6 +174,29 @@ function reshape_set(
     return PSDCone()
 end
 
+"""
+    DualSymmetricMatrixShape(side_dimension)
+
+A shape used when quering the dual of a symmetic matrix.
+"""
+struct DualSymmetricMatrixShape <: AbstractShape
+    side_dimension::Int
+end
+
+function reshape_vector(v::Vector{T}, shape::DualSymmetricMatrixShape) where {T}
+    matrix = Matrix{T}(undef, shape.side_dimension, shape.side_dimension)
+    k = 0
+    for j in 1:shape.side_dimension
+        for i in 1:j-1
+            k += 1
+            matrix[j, i] = matrix[i, j] = 0.5 * v[k]
+        end
+        k += 1
+        matrix[j, j] = v[k]
+    end
+    return LinearAlgebra.Symmetric(matrix)
+end
+
 """
     triangle_vec(matrix::Matrix)
 
@@ -479,6 +502,34 @@ function reshape_vector(v::Vector{T}, shape::HermitianMatrixShape) where {T}
     return LinearAlgebra.Hermitian(matrix)
 end
 
+"""
+    DualHermitianMatrixShape(side_dimension)
+
+A shape used when quering the dual of a symmetic matrix.
+"""
+struct DualHermitianMatrixShape <: AbstractShape
+    side_dimension::Int
+end
+
+function reshape_vector(v::Vector{T}, shape::DualHermitianMatrixShape) where {T}
+    NewType = _MA.promote_operation(_MA.add_mul, T, Complex{Bool}, T)
+    n = shape.side_dimension
+    matrix = Matrix{NewType}(undef, n, n)
+    real_k = 0
+    imag_k = MOI.dimension(MOI.PositiveSemidefiniteConeTriangle(n))
+    for j in 1:n
+        for i in 1:(j-1)
+            real_k += 1
+            imag_k += 1
+            matrix[i, j] = (v[real_k] + im * v[imag_k]) / 2
+            matrix[j, i] = (v[real_k] - im * v[imag_k]) / 2
+        end
+        real_k += 1
+        matrix[j, j] = v[real_k]
+    end
+    return LinearAlgebra.Hermitian(matrix)
+end
+
 function _vectorize_complex_variables(error_fn::Function, matrix::Matrix)
     if any(_is_binary, matrix) || any(_is_integer, matrix)
         # We would then need to fix the imaginary value to zero. Let's wait to
@@ -557,6 +608,20 @@ function build_constraint(
     return VectorConstraint(x, MOI.Zeros(length(x)), shape)
 end
 
+function dual(
+    con_ref::ConstraintRef{
+        <:AbstractModel,
+        MOI.ConstraintIndex{F,MOI.Zeros},
+        HermitianMatrixShape,
+    };
+    result::Int = 1,
+) where {F}
+    return reshape_vector(
+        _constraint_dual(con_ref, result),
+        DualHermitianMatrixShape(con_ref.shape.side_dimension),
+    )
+end
+
 reshape_set(s::MOI.Zeros, ::HermitianMatrixShape) = Zeros()
 
 function build_constraint(
@@ -570,6 +635,20 @@ function build_constraint(
     return VectorConstraint(x, MOI.Zeros(length(x)), shape)
 end
 
+function dual(
+    con_ref::ConstraintRef{
+        <:AbstractModel,
+        MOI.ConstraintIndex{F,MOI.Zeros},
+        SymmetricMatrixShape,
+    };
+    result::Int = 1,
+) where {F}
+    return reshape_vector(
+        _constraint_dual(con_ref, result),
+        DualSymmetricMatrixShape(con_ref.shape.side_dimension),
+    )
+end
+
 function build_constraint(error_fn::Function, ::AbstractMatrix, ::Nonnegatives)
     return error_fn(
         "Unsupported matrix in vector-valued set. Did you mean to use the " *