def adapt_to_callable(f, nargs=None):
"""
Tries to make every function in f into a (fast) callable
function, returning a new list of functions and the expected
arguments.
INPUT:
- ``f`` -- a list of functions; these can be symbolic expressions,
polynomials, etc
- ``nargs`` -- number of input args to have in the output functions
OUTPUT: functions, expected arguments
"""
from sage.misc.misc import deprecation
deprecation(
"adapt_to_callable is a deprecated function. Please use functions from sage.misc.plot instead."
)
try:
from sage.symbolic.callable import is_CallableSymbolicExpression
if sum([is_CallableSymbolicExpression(z) for z in f]):
# Sum to get common universe; this works since f is
# callable, and summing gets the arguments in the right
# order.
vars = sum(f).args()
else:
# Otherwise any free variable names in any order
try:
vars = tuple(sorted(set(sum([z.variables() for z in f], ()))))
if len(vars) > 1:
from sage.misc.misc import deprecation
deprecation(
"Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)"
)
except AttributeError:
vars = ()
f = [fast_float_constant(x) for x in f]
except TypeError:
vars = ()
f = [fast_float_constant(x) for x in f]
if nargs is not None and len(vars) != nargs:
vars = (vars + ('_', ) * nargs)[:nargs]
return fast_float(f, *vars), vars
def adapt_to_callable(f, nargs=None):
"""
Tries to make every function in f into a (fast) callable
function, returning a new list of functions and the expected
arguments.
INPUT:
- ``f`` -- a list of functions; these can be symbolic expressions,
polynomials, etc
- ``nargs`` -- number of input args to have in the output functions
OUTPUT: functions, expected arguments
"""
from sage.misc.misc import deprecation
deprecation("adapt_to_callable is a deprecated function. Please use functions from sage.misc.plot instead.")
try:
from sage.symbolic.callable import is_CallableSymbolicExpression
if sum([is_CallableSymbolicExpression(z) for z in f]):
# Sum to get common universe; this works since f is
# callable, and summing gets the arguments in the right
# order.
vars = sum(f).args()
else:
# Otherwise any free variable names in any order
try:
vars = tuple(sorted(set(sum( [z.variables() for z in f], ()) )))
if len(vars) > 1:
from sage.misc.misc import deprecation
deprecation("Substitution using function-call syntax and unnamed arguments is deprecated and will be removed from a future release of Sage; you can use named arguments instead, like EXPR(x=..., y=...)")
except AttributeError:
vars = ()
f = [fast_float_constant(x) for x in f]
except TypeError:
vars = ()
f = [fast_float_constant(x) for x in f]
if nargs is not None and len(vars) != nargs:
vars = (vars + ('_',)*nargs)[:nargs]
return fast_float(f, *vars), vars
def setup_for_eval_on_grid(funcs, ranges, plot_points=None, return_vars=False):
"""
Calculate the necessary parameters to construct a list of points,
and make the functions fast_callable.
INPUT:
- ``funcs`` -- a function, or a list, tuple, or vector of functions
- ``ranges`` -- a list of ranges. A range can be a 2-tuple of
numbers specifying the minimum and maximum, or a 3-tuple giving
the variable explicitly.
- ``plot_points`` -- a tuple of integers specifying the number of
plot points for each range. If a single number is specified, it
will be the value for all ranges. This defaults to 2.
- ``return_vars`` -- (default ``False``) If ``True``, return the variables,
in order.
OUTPUT:
- ``fast_funcs`` - if only one function passed, then a fast
callable function. If funcs is a list or tuple, then a tuple
of fast callable functions is returned.
- ``range_specs`` - a list of range_specs: for each range, a
tuple is returned of the form (range_min, range_max,
range_step) such that ``srange(range_min, range_max,
range_step, include_endpoint=True)`` gives the correct points
for evaluation.
EXAMPLES::
sage: x,y,z=var('x,y,z')
sage: f(x,y)=x+y-z
sage: g(x,y)=x+y
sage: h(y)=-y
sage: sage.plot.misc.setup_for_eval_on_grid(f, [(0, 2),(1,3),(-4,1)], plot_points=5)
(<sage.ext...>, [(0.0, 2.0, 0.5), (1.0, 3.0, 0.5), (-4.0, 1.0, 1.25)])
sage: sage.plot.misc.setup_for_eval_on_grid([g,h], [(0, 2),(-1,1)], plot_points=5)
((<sage.ext...>, <sage.ext...>), [(0.0, 2.0, 0.5), (-1.0, 1.0, 0.5)])
sage: sage.plot.misc.setup_for_eval_on_grid([sin,cos], [(-1,1)], plot_points=9)
((<sage.ext...>, <sage.ext...>), [(-1.0, 1.0, 0.25)])
sage: sage.plot.misc.setup_for_eval_on_grid([lambda x: x^2,cos], [(-1,1)], plot_points=9)
((<function <lambda> ...>, <sage.ext...>), [(-1.0, 1.0, 0.25)])
sage: sage.plot.misc.setup_for_eval_on_grid([x+y], [(x,-1,1),(y,-2,2)])
((<sage.ext...>,), [(-1.0, 1.0, 2.0), (-2.0, 2.0, 4.0)])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,-1,1),(y,-1,1)], plot_points=[4,9])
(<sage.ext...>, [(-1.0, 1.0, 0.6666666666666666), (-1.0, 1.0, 0.25)])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,-1,1),(y,-1,1)], plot_points=[4,9,10])
Traceback (most recent call last):
...
ValueError: plot_points must be either an integer or a list of integers, one for each range
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(1,-1),(y,-1,1)], plot_points=[4,9,10])
Traceback (most recent call last):
...
ValueError: Some variable ranges specify variables while others do not
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(1,-1),(-1,1)], plot_points=5)
doctest:...: DeprecationWarning:
Unnamed ranges for more than one variable is deprecated and
will be removed from a future release of Sage; you can used
named ranges instead, like (x,0,2)
See http://trac.sagemath.org/7008 for details.
(<sage.ext...>, [(1.0, -1.0, 0.5), (-1.0, 1.0, 0.5)])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(y,1,-1),(x,-1,1)], plot_points=5)
(<sage.ext...>, [(1.0, -1.0, 0.5), (-1.0, 1.0, 0.5)])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,1,-1),(x,-1,1)], plot_points=5)
Traceback (most recent call last):
...
ValueError: range variables should be distinct, but there are duplicates
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,1,1),(y,-1,1)])
Traceback (most recent call last):
...
ValueError: plot start point and end point must be different
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,1,-1),(y,-1,1)], return_vars=True)
(<sage.ext...>, [(1.0, -1.0, 2.0), (-1.0, 1.0, 2.0)], [x, y])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(y,1,-1),(x,-1,1)], return_vars=True)
(<sage.ext...>, [(1.0, -1.0, 2.0), (-1.0, 1.0, 2.0)], [y, x])
"""
if max(map(len, ranges)) != min(map(len, ranges)):
raise ValueError(
"Some variable ranges specify variables while others do not")
if len(ranges[0]) == 3:
vars = [r[0] for r in ranges]
ranges = [r[1:] for r in ranges]
if len(set(vars)) < len(vars):
raise ValueError(
"range variables should be distinct, but there are duplicates")
else:
vars, free_vars = unify_arguments(funcs)
if len(free_vars) > 1:
from sage.misc.superseded import deprecation
deprecation(
7008,
"Unnamed ranges for more than one variable is deprecated and will be removed from a future release of Sage; you can used named ranges instead, like (x,0,2)"
)
# pad the variables if we don't have enough
nargs = len(ranges)
if len(vars) < nargs:
vars += ('_', ) * (nargs - len(vars))
ranges = [[float(z) for z in r] for r in ranges]
if plot_points is None:
plot_points = 2
if not isinstance(plot_points, (list, tuple)):
plot_points = [plot_points] * len(ranges)
elif len(plot_points) != nargs:
raise ValueError(
"plot_points must be either an integer or a list of integers, one for each range"
)
plot_points = [int(p) if p >= 2 else 2 for p in plot_points]
range_steps = [
abs(range[1] - range[0]) / (p - 1)
for range, p in zip(ranges, plot_points)
]
if min(range_steps) == float(0):
raise ValueError("plot start point and end point must be different")
options = {}
if nargs == 1:
options['expect_one_var'] = True
if is_Vector(funcs):
funcs = list(funcs)
#TODO: raise an error if there is a function/method in funcs that takes more values than we have ranges
if return_vars:
return fast_float(funcs, *vars, **options), [
tuple(range + [range_step])
for range, range_step in zip(ranges, range_steps)
], vars
else:
return fast_float(funcs, *vars, **options), [
tuple(range + [range_step])
for range, range_step in zip(ranges, range_steps)
]
def setup_for_eval_on_grid(funcs, ranges, plot_points=None, return_vars=False):
"""
Calculate the necessary parameters to construct a list of points,
and make the functions fast_callable.
INPUT:
- ``funcs`` - a function, or a list, tuple, or vector of functions
- ``ranges`` - a list of ranges. A range can be a 2-tuple of
numbers specifying the minimum and maximum, or a 3-tuple giving
the variable explicitly.
- ``plot_points`` - a tuple of integers specifying the number of
plot points for each range. If a single number is specified, it
will be the value for all ranges. This defaults to 2.
- ``return_vars`` - (default False) If True, return the variables,
in order.
OUTPUT:
- ``fast_funcs`` - if only one function passed, then a fast
callable function. If funcs is a list or tuple, then a tuple
of fast callable functions is returned.
- ``range_specs`` - a list of range_specs: for each range, a
tuple is returned of the form (range_min, range_max,
range_step) such that ``srange(range_min, range_max,
range_step, include_endpoint=True)`` gives the correct points
for evaluation.
EXAMPLES::
sage: x,y,z=var('x,y,z')
sage: f(x,y)=x+y-z
sage: g(x,y)=x+y
sage: h(y)=-y
sage: sage.plot.misc.setup_for_eval_on_grid(f, [(0, 2),(1,3),(-4,1)], plot_points=5)
(<sage.ext...>, [(0.0, 2.0, 0.5), (1.0, 3.0, 0.5), (-4.0, 1.0, 1.25)])
sage: sage.plot.misc.setup_for_eval_on_grid([g,h], [(0, 2),(-1,1)], plot_points=5)
((<sage.ext...>, <sage.ext...>), [(0.0, 2.0, 0.5), (-1.0, 1.0, 0.5)])
sage: sage.plot.misc.setup_for_eval_on_grid([sin,cos], [(-1,1)], plot_points=9)
((<sage.ext...>, <sage.ext...>), [(-1.0, 1.0, 0.25)])
sage: sage.plot.misc.setup_for_eval_on_grid([lambda x: x^2,cos], [(-1,1)], plot_points=9)
((<function <lambda> ...>, <sage.ext...>), [(-1.0, 1.0, 0.25)])
sage: sage.plot.misc.setup_for_eval_on_grid([x+y], [(x,-1,1),(y,-2,2)])
((<sage.ext...>,), [(-1.0, 1.0, 2.0), (-2.0, 2.0, 4.0)])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,-1,1),(y,-1,1)], plot_points=[4,9])
(<sage.ext...>, [(-1.0, 1.0, 0.6666666666666666), (-1.0, 1.0, 0.25)])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,-1,1),(y,-1,1)], plot_points=[4,9,10])
Traceback (most recent call last):
...
ValueError: plot_points must be either an integer or a list of integers, one for each range
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(1,-1),(y,-1,1)], plot_points=[4,9,10])
Traceback (most recent call last):
...
ValueError: Some variable ranges specify variables while others do not
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(1,-1),(-1,1)], plot_points=5)
doctest:...: DeprecationWarning:
Unnamed ranges for more than one variable is deprecated and
will be removed from a future release of Sage; you can used
named ranges instead, like (x,0,2)
See http://trac.sagemath.org/7008 for details.
(<sage.ext...>, [(1.0, -1.0, 0.5), (-1.0, 1.0, 0.5)])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(y,1,-1),(x,-1,1)], plot_points=5)
(<sage.ext...>, [(1.0, -1.0, 0.5), (-1.0, 1.0, 0.5)])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,1,-1),(x,-1,1)], plot_points=5)
Traceback (most recent call last):
...
ValueError: range variables should be distinct, but there are duplicates
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,1,1),(y,-1,1)])
Traceback (most recent call last):
...
ValueError: plot start point and end point must be different
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(x,1,-1),(y,-1,1)], return_vars=True)
(<sage.ext...>, [(1.0, -1.0, 2.0), (-1.0, 1.0, 2.0)], [x, y])
sage: sage.plot.misc.setup_for_eval_on_grid(x+y, [(y,1,-1),(x,-1,1)], return_vars=True)
(<sage.ext...>, [(1.0, -1.0, 2.0), (-1.0, 1.0, 2.0)], [y, x])
"""
if max(map(len, ranges)) != min(map(len, ranges)):
raise ValueError("Some variable ranges specify variables while others do not")
if len(ranges[0])==3:
vars = [r[0] for r in ranges]
ranges = [r[1:] for r in ranges]
if len(set(vars))<len(vars):
raise ValueError("range variables should be distinct, but there are duplicates")
else:
vars, free_vars = unify_arguments(funcs)
if len(free_vars)>1:
from sage.misc.superseded import deprecation
deprecation(7008, "Unnamed ranges for more than one variable is deprecated and will be removed from a future release of Sage; you can used named ranges instead, like (x,0,2)")
# pad the variables if we don't have enough
nargs = len(ranges)
if len(vars)<nargs:
vars += ('_',)*(nargs-len(vars))
ranges = [[float(z) for z in r] for r in ranges]
if plot_points is None:
plot_points=2
if not isinstance(plot_points, (list, tuple)):
plot_points = [plot_points]*len(ranges)
elif len(plot_points)!=nargs:
raise ValueError("plot_points must be either an integer or a list of integers, one for each range")
plot_points = [int(p) if p>=2 else 2 for p in plot_points]
range_steps = [abs(range[1] - range[0])/(p-1) for range, p in zip(ranges, plot_points)]
if min(range_steps) == float(0):
raise ValueError("plot start point and end point must be different")
options={}
if nargs==1:
options['expect_one_var']=True
if is_Vector(funcs):
funcs = list(funcs)
#TODO: raise an error if there is a function/method in funcs that takes more values than we have ranges
if return_vars:
return fast_float(funcs, *vars,**options), [tuple(range+[range_step]) for range,range_step in zip(ranges, range_steps)], vars
else:
return fast_float(funcs, *vars,**options), [tuple(range+[range_step]) for range,range_step in zip(ranges, range_steps)]
