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randomInitialPair -- a random initial pair

Synopsis

Description

Generates a start system S that has and equal chance of reaching any of the solutions of the target system T.
i1 : T = randomSd {2,3};
i2 : (S,solsS) = randomInitialPair T

                                   2                                     
o2 = ({(.00170893 - .00536891*ii)x1  + (- .242657 - .304107*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                             2                                              
     .0241927 - .202294*ii)x2  + (.371141 - .0280178*ii)x1*x3 + (- .414057 -
     ------------------------------------------------------------------------
                                                      2            
     .00669294*ii)x2*x3 + (- .0876678 + .0594637*ii)x3 , (.286187 -
     ------------------------------------------------------------------------
                  3                           2                 
     .034459*ii)x1  + (.496131 + .488378*ii)x1 x2 + (- .125791 -
     ------------------------------------------------------------------------
                     2                            3             
     .110773*ii)x1*x2  + (.493416 + .0230773*ii)x2  + (.447525 +
     ------------------------------------------------------------------------
                  2                                                      
     .320914*ii)x1 x3 + (- .00476473 + .362909*ii)x1*x2*x3 + (- .164529 +
     ------------------------------------------------------------------------
                 2                                  2               
     .11936*ii)x2 x3 + (- .245475 + .210323*ii)x1*x3  + (- .127682 -
     ------------------------------------------------------------------------
                    2                              3
     .11088*ii)x2*x3  + (- .235554 - .0256742*ii)x3 }, {{-.462897+.797495*ii,
     ------------------------------------------------------------------------
     -.191159-.250664*ii, .141584-.174091*ii}})

o2 : Sequence
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{{-.301955+.353846*ii, .0167065-.128687*ii, .785187+.387631*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .581701}}

o3 : List

Ways to use randomInitialPair :