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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 = ({(- .0183252 + .134743*ii)x1  + (.333844 + .0377658*ii)x1*x2 + (.236739
     ------------------------------------------------------------------------
                   2                                           
     + .47573*ii)x2  + (.54784 + .203469*ii)x1*x3 + (.0790032 +
     ------------------------------------------------------------------------
                                                   2               
     .303893*ii)x2*x3 + (- .0388666 + .062386*ii)x3 , (- .0498785 -
     ------------------------------------------------------------------------
                   3                            2               
     .0547583*ii)x1  + (.381026 - .0116485*ii)x1 x2 + (.164583 +
     ------------------------------------------------------------------------
                     2                              3               
     .195507*ii)x1*x2  + (- .210975 - .0205286*ii)x2  + (- .475233 -
     ------------------------------------------------------------------------
                 2                                               
     .15229*ii)x1 x3 + (.176976 + .6212*ii)x1*x2*x3 + (.0397812 -
     ------------------------------------------------------------------------
                  2                                2                
     .441712*ii)x2 x3 + (.243384 + .191105*ii)x1*x3  + (- .0511738 +
     ------------------------------------------------------------------------
                      2                             3
     .0396236*ii)x2*x3  + (.0635979 + .0133546*ii)x3 }, {{.486087+.185034*ii,
     ------------------------------------------------------------------------
     -.078401-.58145*ii, .483426+.389294*ii}})

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

o3 = {{{-.125308+.545176*ii, .345624-.354406*ii, .351744-.564179*ii}, #steps
     ------------------------------------------------------------------------
     => 11, status  => REGULAR, last t => 1, cond#^{-1} => .341934}}

o3 : List

Ways to use randomInitialPair :