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, \