def split_filter(sols, dim, tol, verbose=True): r""" Given in *sols* is a list of solutions of dimension *dim*, which contain a variable with name 'zz' + str(*dim*), which is the name of the last slack variable. The tolerance *tol* is used to split the list of solution in two. On return is a tuple of two lists of solutions (possibly empty). The first list of solutions has the last slack variable equal to zero (with respect to the tolerance *tol) and the last slack variable of each solution in the second list has a magnitude larger than *tol*. If *verbose*, then the length of each solution list is printed. """ from phcpy.solutions import filter_zero_coordinates as filter lastslack = 'zz' + str(dim) zerosols = filter(sols, lastslack, tol, 'select') nonzsols = filter(sols, lastslack, tol, 'remove') if verbose: print 'number of candidate generic points :', len(zerosols) print 'number of nonsolutions :', len(nonzsols) return (zerosols, nonzsols)
def split_filter(sols, dim, tol, verbose=True): r""" Given in *sols* is a list of solutions of dimension *dim*, which contain a variable with name 'zz' + str(*dim*), which is the name of the last slack variable. The tolerance *tol* is used to split the list of solution in two. On return is a tuple of two lists of solutions (possibly empty). The first list of solutions has the last slack variable equal to zero (with respect to the tolerance *tol) and the last slack variable of each solution in the second list has a magnitude larger than *tol*. If *verbose*, then the length of each solution list is printed. """ from phcpy.solutions import filter_zero_coordinates as filter lastslack = 'zz' + str(dim) zerosols = filter(sols, lastslack, tol, 'select') nonzsols = filter(sols, lastslack, tol, 'remove') if verbose: print 'number of candidate generic points :', len(zerosols) print 'number of nonsolutions :', len(nonzsols) return (zerosols, nonzsols)
""" Illustration of the witness set computation of the cyclic 4-roots system. """ from phcpy.families import cyclic c4 = cyclic(4) from phcpy.sets import embed c4e1 = embed(4, 1, c4) print 'the embedded cyclic 4-roots problem :' for pol in c4e1: print pol from phcpy.solver import solve sols = solve(c4e1) print 'computed', len(sols), 'solutions' from phcpy.solutions import filter_zero_coordinates as filter genpts = filter(sols, 'zz1', 1.0e-8, 'select') print 'generic points :' for sol in genpts: print sol from phcpy.sets import membertest sdpoint = [-1, 0, -1, 0, 1, 0, 1, 0] print 'testing in standard double precision ...' print membertest(c4e1, genpts, 1, sdpoint, verbose=True, precision='d') raw_input('*** hit enter to continue ***') print 'testing in double double precision ...' ddpoint = [-1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0] print membertest(c4e1, genpts, 1, ddpoint, verbose=True, precision='dd') raw_input('*** hit enter to continue ***') print 'testing in quad double precision ...' ddpoint = [-1, 0, 0, 0, 0, 0, 0, 0, \ -1, 0, 0, 0, 0, 0, 0, 0, \ 1, 0, 0, 0, 0, 0, 0, 0, \