FBAHelper

FBA helper class

The flux analysis problem is shaped as follows:

min c' * v s.t. A_{ub} * v_{ub} = b_{ub} A_{eq} * v_{eq} = b_{eq} lb < v < ub

With FBA, one has: S_{int} * v = 0 v_{lb} < v < v_{ub} and C * v = y (<=> C * v - y = 0) y = y_b y_lb < y < y_ub where S_{int} is the intracellular stoichimetric matrix y is the vector of measurement, y_b is the vector containing measured values y_{lb} is the vector containing lower bounds of measured values y_{ub} is the vector containing upper bounds of measured values

Then, the problem is reshaped as follows:

     [ S_{int} |  0      ]           [  r  ]
     [ --------|------   ]           [ --- ]

A_{eq} = [ C | -Id_{C} ], b_{eq} = [ 0 ] [---------|------ ] [-----] [ 0 | Id_{Y} ] [ y_b ]

 [  v  ]

x = [ --- ] [ y ]

 [ v_{lb} ]        [ v_{ub} ]

lb = [ ---- ], ub = [ ---- ] [ y_{lb} ] [ y_{ub} ]

Id_{C} and Id_{Y} are identity matrices.