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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 = ({(- .348955 - .115593*ii)x1  + (- .132971 + .381977*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                              2                                           
     .0789807 + .0246188*ii)x2  + (.326285 - .082274*ii)x1*x3 + (.167235 -
     ------------------------------------------------------------------------
                                                   2               
     .0137843*ii)x2*x3 + (- .195944 + .171432*ii)x3 , (- .0284688 -
     ------------------------------------------------------------------------
                  3                            2               
     .113539*ii)x1  + (- .59729 - .103328*ii)x1 x2 + (.392497 -
     ------------------------------------------------------------------------
                      2                             3               
     .0408871*ii)x1*x2  + (.0334718 + .0806152*ii)x2  + (- .396248 -
     ------------------------------------------------------------------------
                  2                                                 
     .387808*ii)x1 x3 + (.0159079 + .859446*ii)x1*x2*x3 + (.163641 -
     ------------------------------------------------------------------------
                  2                                   2              
     .302096*ii)x2 x3 + (- .074191 + .0689511*ii)x1*x3  + (.0611832 -
     ------------------------------------------------------------------------
                     2                           3
     .609064*ii)x2*x3  + (.194982 - .184194*ii)x3 }, {{.227196+.411856*ii,
     ------------------------------------------------------------------------
     .755863+.092988*ii, .381699-.230408*ii}})

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

o3 = {{{.557627+.434943*ii, .184533+.0181652*ii, -.264971-.628716*ii}, #steps
     ------------------------------------------------------------------------
     => 15, status  => REGULAR, last t => 1, cond#^{-1} => .294821}}

o3 : List

Ways to use randomInitialPair :