# Detailed Description of CVX output fields using SeDuMi

I have the following semi-definite programming problem

\max_{x_{i,j}}\sum_{i \in \mathbf{F} }^{ }\sum_{j \in \mathbf{F} }^{ } w_{i,j}^{+}x_{i,j}+w^{-}\left(1- x_{i,j}\right )

subject to the constraints

C1: x_{i,i}=1, \forall i\in \mathbf{F}
C2: x_{i,j}+x_{j,k}-x_{i,k} \leq 1, \forall i,j,k \in \mathbf{F}:k>i, j \neq i,k
C3: \sum_{j \in F}^{ }x_{i,j} \leq M, \forall i \in \mathbf{F}
C4:x_{i,j} \geq 0, \forall i,j \in \mathbf{F}
C5: X=\left(x_{i,j} \right )\succeq 0

where, M \in R^+ and X is a PSD (F \times F) symmetric matrix.

I want to estimate its order of complexity using the expression O((mn^3+m^2n^2+m^3)\sqrt{n}\log\frac{1}{\epsilon}) where, n is the dimensions of the final matrix X and m is the number of equality constraints.
To help me with this issue i proceeded in a standard fashion by adding slack variables to the inequality constraints. However, the reported number of variables and equality constraints in SeDuMi output is below what i have estimated. So, is there any tutorial describing how SeDuMi in CVX estimates those values ? In other words i need a detailed description of SeDuMi output fields and how they were estimated
Regards,