**********************************************************************
* GENERATING SERIES Approach for Structural Identifiability Analysis *
**********************************************************************

Model name:     ArabidopsisPoly
Matlab version: 9.1.0.441655 (R2016b)
Computer:       PCWIN64
Options:
                verbose: 1
         reportCompTime: 1
                 noRank: 0
            closeFigure: 1
                  store: 1
    problem_folder_path: 'D:\data\Tom\Research\GenSSI\Examples\ArabidopsisPoly\run1'

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

Maximum number of derivatives for the analysis: 7

State variables (x):
  x1
  x2
  x3
  x4
  x5
  x6
  x7
 xi1
 xi2
 xi3
 xi4
 xi5
 xi6
 xi7
 xi8
 xi9
 
Vector field for autonomous dynamics (f):
                         p1*x6*xi2 - p5*x1*xi3
          p19*x1 - p22*x2 + p23*x3 - p6*x2*xi4
                   p22*x2 - p23*x3 - p7*x3*xi5
                       p2*xi1*p4^2 - p8*x4*xi6
          p20*x4 - p24*x5 + p25*x6 - p9*x5*xi7
                  p24*x5 - p25*x6 - p10*x6*xi8
                              p21 - p11*x7*xi9
      2*x3*xi1^2*(p23*x3 - p22*x2 + p7*x3*xi5)
          xi2^2*(p25*x6 - p24*x5 + p10*x6*xi8)
                -xi3^2*(p1*x6*xi2 - p5*x1*xi3)
 -xi4^2*(p19*x1 - p22*x2 + p23*x3 - p6*x2*xi4)
           xi5^2*(p23*x3 - p22*x2 + p7*x3*xi5)
              -xi6^2*(p2*xi1*p4^2 - p8*x4*xi6)
 -xi7^2*(p20*x4 - p24*x5 + p25*x6 - p9*x5*xi7)
          xi8^2*(p25*x6 - p24*x5 + p10*x6*xi8)
                     -xi9^2*(p21 - p11*x7*xi9)
 
Control vector (g):
               p26*x7
                    0
                    0
                    0
                    0
                    0
       - p21 - p27*x7
                    0
                    0
        -p26*x7*xi3^2
                    0
                    0
                    0
                    0
                    0
 xi9^2*(p21 + p27*x7)
 
Initial conditions (x0):
      0
      0
      0
      0
      0
      0
      0
 1/p4^2
   1/p3
  1/p12
  1/p13
  1/p14
  1/p15
  1/p16
  1/p17
  1/p18
 
Observables (y):
 x1
 x4
 
Parameters considered for structural identifiability analysis:
  p1
  p2
  p5
  p8
 p10
 p11
 p12
 p15
 p18
 p26
 p27
 
Report inputs elapsed time: 0.10103
 
**********************************
* COMPUTATION OF 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  7.
   -> The rank of the next Jacobian is expected to be maximum 11.
.................................................................
 
 
COMPUTING LIE DERIVATIVES OF ORDER 4
.................................................................
   -> The rank of the Jacobian generated by 4 derivatives is  9.
   -> The rank of the next Jacobian is expected to be maximum 11.
.................................................................
 
 
COMPUTING LIE DERIVATIVES OF ORDER 5
.................................................................
   -> The rank of the Jacobian generated by 5 derivatives is 11.
 
Compute Lie derivatives elapsed time: 1.0778
 
******************************************
* COMPUTATION OF IDENTIFIABILITY TABLEAU *
******************************************

Rank of full Jacobian matrix: 11 
=> THE RANK OF THE FULL JACOBIAN IS COMPLETE, THUS AT LEAST LOCAL IDENTIFIABILITY IS GUARANTEED.

Compute tableau elapsed time: 0.58461
 
***************************************************
* COMPUTATION OF REDUCED IDENTIFIABILITY TABLEAUS *
***************************************************

Relations needed for computing parameters:
                                                                                                                     p2 - c1
                                                                                                          - c2 - (p2*p8)/p15
                                                                                                                p21*p26 - c3
                                                                      p2*(p8^2/p15^2 + (p2*p8)/p15^2) - c4 + (p2^2*p8)/p15^2
                                                                                                    - c5 - (p11*p21*p26)/p18
                                                                                                     - c6 - (p5*p21*p26)/p12
                                                                                                          - c7 - p21*p26*p27
                                                                                                     (p1*p2*p20*p24)/p3 - c8
                                                  p21*((p11^2*p26)/p18^2 + (p11*p21*p26)/p18^2) - c9 + (p11*p21^2*p26)/p18^2
 - c10 - p2*(p20*(p24*((p1*(p25 + p10/p17))/p3 + (p1*p5)/(p3*p12)) + (p1*p24*(p24 + p9/p16))/p3) + (p1*p8*p20*p24)/(p3*p15))
                                                             p21*((4*p5*p21*p26^2)/p12^2 - (p5*p11*p26*p27)/(p12*p18)) - c11
 
Compute reduced tableau  elapsed time: 1.6034
 
*****************************************************************************************************
* DETECTION OF (DIRECT) STRUCTURALLY GLOBALLY IDENTIFIABLE PARAMETERS AND REORGANIZATION OF TABLEAU *
*****************************************************************************************************

=> STRUCTURALLY GLOBALLY IDENTIFIABLE PARAMETERS DETERMINED DIRECTLY
   (parameters corresponding to one non-zero element in the reduced identifiability tableau)
--> The parameter p2 is structurally globally identifiable. It has the solution:
       p2 = c1.
--> The parameter p26 is structurally globally identifiable. It has the solution:
       p26 = c3/p21.
--> The parameter p27 is structurally globally identifiable. It has the solution:
       p27 = -c7/(p21*p26).
--> The parameter p1 is structurally globally identifiable. It has the solution:
       p1 = (c8*p3)/(p2*p20*p24).
=> NO STRUCTURALLY LOCALLY IDENTIFIABLE PARAMETER COULD BE DETERMINED DIRECTLY

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

--> Parameters: 
  p5
  p8
 p10
 p11
 p12
 p15
 p18
 
--> Relations: 
                                                                                                          - c2 - (p2*p8)/p15
                                                                      p2*(p8^2/p15^2 + (p2*p8)/p15^2) - c4 + (p2^2*p8)/p15^2
                                                                                                    - c5 - (p11*p21*p26)/p18
                                                                                                     - c6 - (p5*p21*p26)/p12
                                                  p21*((p11^2*p26)/p18^2 + (p11*p21*p26)/p18^2) - c9 + (p11*p21^2*p26)/p18^2
 - c10 - p2*(p20*(p24*((p1*(p25 + p10/p17))/p3 + (p1*p5)/(p3*p12)) + (p1*p24*(p24 + p9/p16))/p3) + (p1*p8*p20*p24)/(p3*p15))
                                                             p21*((4*p5*p21*p26^2)/p12^2 - (p5*p11*p26*p27)/(p12*p18)) - c11
 
******************************************************************
* COMPUTATION OF HIGHER ORDER REDUCED IDENTIFIABILITY TABLEAU(S) *
*  (display the group of 2/more depending parameters,            *
*           the associated algebraic relations,                  *
*           the corresponding solution (solutions))              *
******************************************************************

The group of parameters to be considered in the calculus and the corresponding relations:

--> Parameters: 
  p8
 p15
 
--> Relations: 
                                     - c2 - (p2*p8)/p15
 p2*(p8^2/p15^2 + (p2*p8)/p15^2) - c4 + (p2^2*p8)/p15^2
 
--> Symbolic solution(s) of the remaining parameters: 
--> The parameter p8 has the solution/solutions: 
  (2*c2^2*p2)/(c4*p2 - c2^2)
--> The parameter p15 has the solution/solutions: 
  -(2*c2*p2^2)/(c4*p2 - c2^2)
....................................................................................................

The group of parameters to be considered in the calculus and the corresponding relations:

--> Parameters: 
 p11
 p18
 
--> Relations: 
                                                   - c5 - (p11*p21*p26)/p18
 p21*((p11^2*p26)/p18^2 + (p11*p21*p26)/p18^2) - c9 + (p11*p21^2*p26)/p18^2
 
--> Symbolic solution(s) of the remaining parameters: 
--> The parameter p11 has the solution/solutions: 
  -(2*c5^2*p21)/(c5^2 - c9*p21*p26)
--> The parameter p18 has the solution/solutions: 
  (2*c5*p21^2*p26)/(c5^2 - c9*p21*p26)
....................................................................................................

The remaining group of parameters, relations and the corresponding solutions:

--> Parameters: 
  p5
 p10
 p12
 
--> Relations: 
                                                                                                     - c6 - (p5*p21*p26)/p12
 - c10 - p2*(p20*(p24*((p1*(p25 + p10/p17))/p3 + (p1*p5)/(p3*p12)) + (p1*p24*(p24 + p9/p16))/p3) + (p1*p8*p20*p24)/(p3*p15))
                                                             p21*((4*p5*p21*p26^2)/p12^2 - (p5*p11*p26*p27)/(p12*p18)) - c11
 
*******************************************************
* THE REDUCED TABLEAUS OF THE REDUCED TABLEAU         *
* (for the remaining set of parameters and relations) *
*******************************************************

The group of parameters to be considered in the calculus and the corresponding relations:

--> Parameters: 
  p5
 p12
 
--> Relations: 
                                         - c6 - (p5*p21*p26)/p12
 p21*((4*p5*p21*p26^2)/p12^2 - (p5*p11*p26*p27)/(p12*p18)) - c11
 
--> Symbolic solution(s) of the remaining parameters: 
--> The parameter p5 has the solution/solutions: 
  (4*c6^2*p18)/(c11*p18 - c6*p11*p27)
--> The parameter p12 has the solution/solutions: 
  -(4*c6*p18*p21*p26)/(c11*p18 - c6*p11*p27)
....................................................................................................

The remaining group of parameters, relations and the corresponding solutions:

--> Parameters: 
p10
 
--> Relations: 
- c10 - p2*(p20*(p24*((p1*(p25 + p10/p17))/p3 + (p1*p5)/(p3*p12)) + (p1*p24*(p24 + p9/p16))/p3) + (p1*p8*p20*p24)/(p3*p15))
 
--> Symbolic solution(s) of the remaining parameters: 
--> The parameter p10 has the solution/solutions: 
  -(p3*p17*(c10 + p2*(p20*(p24*((p1*p25)/p3 + (p1*p5)/(p3*p12)) + (p1*p24*(p24 + p9/p16))/p3) + (p1*p8*p20*p24)/(p3*p15))))/(p1*p2*p20*p24)
 
Order tableau elapsed time: 2.5992
 
***************************************
* RESULTS OF IDENTIFIABILITY ANALYSIS *
***************************************

=> THE MODEL IS STRUCTURALLY GLOBALLY IDENTIFIABLE 

Structurally globally identifiable parameters: 
  p2
 p26
 p27
  p1
  p8
 p15
 p11
 p18
  p5
 p12
 p10
 
Structurally locally identifiable parameters: 
 []
 
Structurally non-identifiable parameters: 
 []
 
Report results elapsed time: 0.016504
 
Total elapsed time: 5.9859
