**********************************************************************************
*                                                                                                      
* GENERATING SERIES approach for Structural Identifiability Analysis   
*                                                                                                      
* Oana Chis, Julio R. Banga and Eva Balsa-Canto                                
*  BioProcess Engineering Group, IIM-CSIC, Vigo-Spain                        
*  contact: [chisoana,julio,ebalsa]@iim.csic.es                                     
*                                                                                                        
**********************************************************************************

Matlab version=9.0.0.341360 (R2016a)
Computer=PCWIN64
options:
                verbose: 1
                 noRank: 0
    problem_folder_path: 'D:\data\Tom\Research\Raedler\mRNA-Helmholtz\Tom\GenSSI\Results\Bilirubin2\run4'

STRUCTURAL IDENTIFIABILITY ANALYSIS FOR: Bilirubin2 Model
 

***************
* INPUT DATA 
***************

-----> Maximum number of derivatives for the analysis: 10
-----> Dynamic model:
	A1=k12*x2 + k13*x3 + k14*x4 - x1*(k01 + k21 + k31 + k41)
 
	A2=- k12*x2 - k21*x1
 
	A3=k31*x1 - k13*x3
 
	A4=k41*x1 - k14*x4
 
-----> Control variables:
	G1=[ 1, 0, 0, 0]
 
-----> Observables:
	H1=x1
 
-----> Initial conditions:
	[ 1, 1, 1, 1]
 
-----> Parameters to be considered in the analysis:
	[ k01, k12, k13, k14, k21, k31, k41]
 



Report inputs elapsed time: 0.10459
*******************************
-> COMPUTE LIE DERIVATIVES
*******************************

COMPUTING LIE DERIVATIVES OF ORDER 1
.................................................................
   ->The rank of the Jacobian generated by 1 derivatives is  1.
   ->The rank of the next Jacobian is expected to be maximum 2.
.................................................................
  
COMPUTING LIE DERIVATIVES OF ORDER 2
.................................................................
   ->The rank of the Jacobian generated by 2 derivatives is  3.
   ->The rank of the next Jacobian is expected to be maximum 5.
.................................................................
  
COMPUTING LIE DERIVATIVES OF ORDER 3
.................................................................
   ->The rank of the Jacobian generated by 3 derivatives is  5.
   ->The rank of the next Jacobian is expected to be maximum 7.
.................................................................
  
COMPUTING LIE DERIVATIVES OF ORDER 4
.................................................................
   ->The rank of the Jacobian generated by 4 derivatives is 7.
Compute Lie derivatives elapsed time: 0.24559


***************************************
-> COMPUTE IDENTIFIABILITY TABLEAU
***************************************

 ----->The rank of the full Jacobian matrix is 7 

 ---->THE RANK OF THE FULL JACOBIAN IS COMPLETE, THUS AT LEAST LOCAL IDENTIFIABILITY IS GUARANTEED.
Compute tableau elapsed time: 1.9465


************************************************
-> COMPUTE REDUCED IDENTIFIABILITY TABLEAUS
************************************************


*****************************************************
-> THE RELATIONS NEEDED FOR COMPUTING THE PARAMETERS
*****************************************************

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         k12 - k01 - c1 + k13 + k14 - k21 - k31 - k41
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         (k01 + k21 + k31 + k41)*(k01 - k12 - k13 - k14 + k21 + k31 + k41) - k13*(k13 - k31) - k14*(k14 - k41) - c2 - k12*(k12 + k21)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         - c3 - k01 - k21 - k31 - k41
                                                                                                                                                                                                                                                                                                                                                                                 (k12 + k21)*(k12^2 + (k01 + k21 + k31 + k41)*k12) - (k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2)*(k01 - k12 - k13 - k14 + k21 + k31 + k41) - c4 + (k13 - k31)*(k13^2 + (k01 + k21 + k31 + k41)*k13) + (k14 - k41)*(k14^2 + (k01 + k21 + k31 + k41)*k14)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         k13*k31 - k12*k21 - c5 + k14*k41 + (k01 + k21 + k31 + k41)^2
 (k31*(k13^2 + (k01 + k21 + k31 + k41)*k13) - k21*(k12^2 + (k01 + k21 + k31 + k41)*k12) + k41*(k14^2 + (k01 + k21 + k31 + k41)*k14) + (k01 + k21 + k31 + k41)*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2))*(k01 - k12 - k13 - k14 + k21 + k31 + k41) - (k13*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2) + k13*(k13^2 + (k01 + k21 + k31 + k41)*k13))*(k13 - k31) - (k14*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2) + k14*(k14^2 + (k01 + k21 + k31 + k41)*k14))*(k14 - k41) - c6 - (k12 + k21)*(k12*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2) + k12*(k12^2 + (k01 + k21 + k31 + k41)*k12))
                                                                                                                                                                                                                                                                                                                                                                                                                           k21*(k12^2 + (k01 + k21 + k31 + k41)*k12) - c7 - k31*(k13^2 + (k01 + k21 + k31 + k41)*k13) - k41*(k14^2 + (k01 + k21 + k31 + k41)*k14) - (k01 + k21 + k31 + k41)*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2)
 
Compute reduced tableau  elapsed time: 2.0874


******************************************************************************************
-> DETECT (DIRECT) STRUCTURALLY GLOBALLY IDENTIFIABLE PARAMETERS AND REORGANIZES TABLEAU
*******************************************************************************************



 -> STRUCTURALLY GLOBALLY IDENTIFIABLE PARAMETERS DETERMINED DIRECTLY 
   (parameters corresponding to one non-zero element in the reduced identifiability tableau)



************************************************************************************************************
->THE REMAINING PARAMETERS (APART FROM IDENTIFIABLE OR NON-IDENTIFIABLE), AND THE CORRESPONDING RELATIONS  
************************************************************************************************************

-----> Parameters: 
[ k01, k12, k13, k14, k21, k31, k41]
 
-----> Relations: 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         k12 - k01 - c1 + k13 + k14 - k21 - k31 - k41
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         (k01 + k21 + k31 + k41)*(k01 - k12 - k13 - k14 + k21 + k31 + k41) - k13*(k13 - k31) - k14*(k14 - k41) - c2 - k12*(k12 + k21)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         - c3 - k01 - k21 - k31 - k41
                                                                                                                                                                                                                                                                                                                                                                                 (k12 + k21)*(k12^2 + (k01 + k21 + k31 + k41)*k12) - (k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2)*(k01 - k12 - k13 - k14 + k21 + k31 + k41) - c4 + (k13 - k31)*(k13^2 + (k01 + k21 + k31 + k41)*k13) + (k14 - k41)*(k14^2 + (k01 + k21 + k31 + k41)*k14)
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         k13*k31 - k12*k21 - c5 + k14*k41 + (k01 + k21 + k31 + k41)^2
 (k31*(k13^2 + (k01 + k21 + k31 + k41)*k13) - k21*(k12^2 + (k01 + k21 + k31 + k41)*k12) + k41*(k14^2 + (k01 + k21 + k31 + k41)*k14) + (k01 + k21 + k31 + k41)*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2))*(k01 - k12 - k13 - k14 + k21 + k31 + k41) - (k13*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2) + k13*(k13^2 + (k01 + k21 + k31 + k41)*k13))*(k13 - k31) - (k14*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2) + k14*(k14^2 + (k01 + k21 + k31 + k41)*k14))*(k14 - k41) - c6 - (k12 + k21)*(k12*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2) + k12*(k12^2 + (k01 + k21 + k31 + k41)*k12))
                                                                                                                                                                                                                                                                                                                                                                                                                           k21*(k12^2 + (k01 + k21 + k31 + k41)*k12) - c7 - k31*(k13^2 + (k01 + k21 + k31 + k41)*k13) - k41*(k14^2 + (k01 + k21 + k31 + k41)*k14) - (k01 + k21 + k31 + k41)*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2)
 
-----> THE SYMBOLIC SOLUTION OF THE REMAINING PARAMETERS: 
<a href="matlab: opentoline('D:\data\Tom\Research\Raedler\mRNA-Helmholtz\Tom\GenSSI\genssiOrderTableau.m',682,1)">682 </a>        Solution=solve(equation_relations{:}, constants{:});
equation_relations{:}
 
ans =
 
k12 - k01 - c1 + k13 + k14 - k21 - k31 - k41
 
 
ans =
 
(k01 + k21 + k31 + k41)*(k01 - k12 - k13 - k14 + k21 + k31 + k41) - k13*(k13 - k31) - k14*(k14 - k41) - c2 - k12*(k12 + k21)
 
 
ans =
 
- c3 - k01 - k21 - k31 - k41
 
 
ans =
 
(k12 + k21)*(k12^2 + (k01 + k21 + k31 + k41)*k12) - (k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2)*(k01 - k12 - k13 - k14 + k21 + k31 + k41) - c4 + (k13 - k31)*(k13^2 + (k01 + k21 + k31 + k41)*k13) + (k14 - k41)*(k14^2 + (k01 + k21 + k31 + k41)*k14)
 
 
ans =
 
k13*k31 - k12*k21 - c5 + k14*k41 + (k01 + k21 + k31 + k41)^2
 
 
ans =
 
(k31*(k13^2 + (k01 + k21 + k31 + k41)*k13) - k21*(k12^2 + (k01 + k21 + k31 + k41)*k12) + k41*(k14^2 + (k01 + k21 + k31 + k41)*k14) + (k01 + k21 + k31 + k41)*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2))*(k01 - k12 - k13 - k14 + k21 + k31 + k41) - (k13*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2) + k13*(k13^2 + (k01 + k21 + k31 + k41)*k13))*(k13 - k31) - (k14*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2) + k14*(k14^2 + (k01 + k21 + k31 + k41)*k14))*(k14 - k41) - c6 - (k12 + k21)*(k12*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2) + k12*(k12^2 + (k01 + k21 + k31 + k41)*k12))
 
 
ans =
 
k21*(k12^2 + (k01 + k21 + k31 + k41)*k12) - c7 - k31*(k13^2 + (k01 + k21 + k31 + k41)*k13) - k41*(k14^2 + (k01 + k21 + k31 + k41)*k14) - (k01 + k21 + k31 + k41)*(k13*k31 - k12*k21 + k14*k41 + (k01 + k21 + k31 + k41)^2)
 
constant{:}
{Undefined variable "constant" or class "constant".
} 
constants{:}
 
ans =
 
k01
 
 
ans =
 
k12
 
 
ans =
 
k13
 
 
ans =
 
k14
 
 
ans =
 
k21
 
 
ans =
 
k31
 
 
ans =
 
k41
 
if system_dependent('IsDebugMode')==1, dbstep; end
[Warning: Cannot find explicit solution.] 
[> In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('solve', 'C:\Program Files\MATLAB\R2016a\toolbox\symbolic\symbolic\solve.m', 316)" style="font-weight:bold">solve</a> (<a href="matlab: opentoline('C:\Program Files\MATLAB\R2016a\toolbox\symbolic\symbolic\solve.m',316,0)">line 316</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('genssiOrderTableau>solveRemPar', 'D:\data\Tom\Research\Raedler\mRNA-Helmholtz\Tom\GenSSI\genssiOrderTableau.m', 682)" style="font-weight:bold">genssiOrderTableau>solveRemPar</a> (<a href="matlab: opentoline('D:\data\Tom\Research\Raedler\mRNA-Helmholtz\Tom\GenSSI\genssiOrderTableau.m',682,0)">line 682</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('genssiOrderTableau', 'D:\data\Tom\Research\Raedler\mRNA-Helmholtz\Tom\GenSSI\genssiOrderTableau.m', 216)" style="font-weight:bold">genssiOrderTableau</a> (<a href="matlab: opentoline('D:\data\Tom\Research\Raedler\mRNA-Helmholtz\Tom\GenSSI\genssiOrderTableau.m',216,0)">line 216</a>)
  In <a href="matlab:matlab.internal.language.introspective.errorDocCallback('genssiMain', 'D:\data\Tom\Research\Raedler\mRNA-Helmholtz\Tom\GenSSI\genssiMain.m', 87)" style="font-weight:bold">genssiMain</a> (<a href="matlab: opentoline('D:\data\Tom\Research\Raedler\mRNA-Helmholtz\Tom\GenSSI\genssiMain.m',87,0)">line 87</a>)] 
if system_dependent('IsDebugMode')==1, dbcont; end
-----> The parameter k01 has the solution/solutions: 
  matrix(0, 1, [])
-----> The parameter k12 has the solution/solutions: 
  matrix(0, 1, [])
-----> The parameter k13 has the solution/solutions: 
  matrix(0, 1, [])
-----> The parameter k14 has the solution/solutions: 
  matrix(0, 1, [])
-----> The parameter k21 has the solution/solutions: 
  matrix(0, 1, [])
-----> The parameter k31 has the solution/solutions: 
  matrix(0, 1, [])
-----> The parameter k41 has the solution/solutions: 
  matrix(0, 1, [])
Order tableau elapsed time: 53256.9804


***************************************************************

 -----> THE MODEL IS STRUCTURALLY LOCALLY IDENTIFIABLE 

***************************************************************

        The structurally globally identifiable parameters are: 

         	None

        The structurally locally identifiable parameters are: 

     	[      k01	      k12	      k13	      k14	      k21	      k31	      k41	]


Report results elapsed time: 0.01634
Total elapsed time: 53261.3848
