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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 = ({(- .277641 - .146503*ii)x1  + (.0442706 - .257926*ii)x1*x2 + (.035408
     ------------------------------------------------------------------------
                     2                                                 
     - .0435325*ii)x2  + (- .234478 + .00275509*ii)x1*x3 + (- .417596 +
     ------------------------------------------------------------------------
                                                   2               
     .145181*ii)x2*x3 + (- .217537 - .0145327*ii)x3 , (- .0734913 +
     ------------------------------------------------------------------------
                  3                            2              
     .303188*ii)x1  + (.0301244 - .501885*ii)x1 x2 + (.43382 +
     ------------------------------------------------------------------------
                      2                             3             
     .0883412*ii)x1*x2  + (- .334184 + .140605*ii)x2  + (.713798 -
     ------------------------------------------------------------------------
                  2                                                    
     .070418*ii)x1 x3 + (- .187944 - .434345*ii)x1*x2*x3 + (- .421655 +
     ------------------------------------------------------------------------
                  2                                2               
     .230621*ii)x2 x3 + (.283138 - .365836*ii)x1*x3  + (- .105201 -
     ------------------------------------------------------------------------
                       2                              3
     .00168599*ii)x2*x3  + (- .145979 - .0896992*ii)x3 },
     ------------------------------------------------------------------------
     {{-.565075+.066809*ii, .313995-.0261628*ii, .099688+.753002*ii}})

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

o3 = {{{-.0928066+.0953792*ii, .901302+.234836*ii, .325123+.0953495*ii},
     ------------------------------------------------------------------------
     #steps => 11, status  => REGULAR, last t => 1, cond#^{-1} => .408694}}

o3 : List

Ways to use randomInitialPair :