dcp.jl.cov

        - #############################################################################
        - # dcp.jl
        - # This file handles the basic rules on interactions of mathematical expressions
        - # to create new expressions.
        - #
        - # For example: negative of a concaveVexity expression is convexVexity, or multiplication
        - # of two positive expressions continue to be positive.
        - #
        - # See: http://dcp.stanford.edu/rules or the original paper at
        - # http://web.stanford.edu/~boyd/papers/disc_cvx_prog.html
        - #############################################################################
        - 
        - export Vexity, ConstVexity, AffineVexity, ConvexVexity, ConcaveVexity, NotDcp
        - export Monotonicity, Nonincreasing, Nondecreasing, NoMonotonicity
        - export Sign, Positive, Negative, NoSign
        - export -, +, *
        - 
        - # Vexity subtypes
        - abstract Vexity
        - type ConstVexity <: Vexity              end
        - type AffineVexity <: Vexity             end
        - type ConvexVexity <: Vexity             end
        - type ConcaveVexity <: Vexity            end
        - 
        - type NotDcp <: Vexity
        - 	function NotDcp()
        - 		warn("Expression not DCP compliant")
        -     return new()
        - 	end
        - end
        - 
        - # Monotonocity subtypes
        - abstract Monotonicity
        - type Nonincreasing <: Monotonicity      end
        - type Nondecreasing <: Monotonicity      end
        - type ConstMonotonicity <: Monotonicity  end
        - type NoMonotonicity <: Monotonicity     end
        - 
        - # Sign subtypes
        - abstract Sign
        - type Positive <: Sign                   end
        - type Negative <: Sign                   end
        - type NoSign <: Sign                     end
        - 
      257 -(v::Vexity) = v
        9 -(v::ConcaveVexity) = ConvexVexity()
        - -(v::ConvexVexity) = ConcaveVexity()
        - 
        - -(m::Monotonicity) = m
        - -(m::Nonincreasing) = Nondecreasing()
        - -(m::Nondecreasing) = Nonincreasing()
        - 
        4 -(s::Sign) = s
        - -(s::Positive) = Negative()
        - -(s::Negative) = Positive()
        - 
        - +(v::NotDcp, w::NotDcp) = v
        - +(v::NotDcp, w::Vexity) = v
        - +(v::Vexity, w::NotDcp) = w
        - 
       69 +(v::ConstVexity, w::ConstVexity) = v
        - +(v::ConstVexity, w::NotDcp) = w
        - +(v::NotDcp, w::ConstVexity) = v
      403 +(v::ConstVexity, w::Vexity) = w
      186 +(v::Vexity, w::ConstVexity) = v
        - 
      155 +(v::AffineVexity, w::AffineVexity) = v
        3 +(v::AffineVexity, w::ConvexVexity) = w
       57 +(v::ConvexVexity, w::AffineVexity) = v
        2 +(v::AffineVexity, w::ConcaveVexity) = w
       12 +(v::ConcaveVexity, w::AffineVexity) = v
        - 
        8 +(v::ConvexVexity, w::ConvexVexity) = v
        2 +(v::ConcaveVexity, w::ConcaveVexity) = v
        - +(v::ConcaveVexity, w::ConvexVexity) = NotDcp()
        - +(v::ConvexVexity, w::ConcaveVexity) = NotDcp()
        - 
        - +(s::Positive, t::Positive) = s
        - +(s::Negative, t::Negative) = s
        - +(s::Positive, t::Negative) = NoSign()
        - +(s::Negative, t::Positive) = NoSign()
        1 +(s::NoSign, t::NoSign) = s
        4 +(s::NoSign, t::Sign) = s
        - +(s::Sign, t::NoSign) = t
        - 
        1 *(s::NoSign, t::NoSign) = s
        - *(s::NoSign, t::Sign) = s
       18 *(s::Sign, t::NoSign) = t
        - *(s::Positive, t::Positive) = s
        - *(s::Positive, t::Negative) = t
        - *(s::Negative, t::Positive) = s
        - *(s::Negative, t::Negative) = Positive()
        - 
       91 *(s::Positive, m::Monotonicity) = m
        1 *(s::Negative, m::Monotonicity) = -m
       89 *(s::NoSign, m::Monotonicity) = NoMonotonicity()
       12 *(m::Monotonicity, s::Sign) = s * m
        - 
      372 *(m::Nondecreasing, v::Vexity) = v
       21 *(m::Nonincreasing, v::Vexity) = -v
      101 *(m::NoMonotonicity, v::Vexity) = v
        - *(m::NoMonotonicity, v::ConvexVexity) = NotDcp()
        - *(m::NoMonotonicity, v::ConcaveVexity) = NotDcp()
        -