def thresh_Naka_Rushton_fndef(N=2, half_on=120, max_val=100, with_if=True,
sys_pars=None):
"""Can specify strings or numbers for half_on and max_val arguments, in case of
including parameters or other variables in the definitions.
(Don't forget to declare those parameters, in that case.)
Use the with_if=False case to ensure Jacobians can be calculated.
Use sys_pars list to provide names of any model parameters or functions
that will be declared elsewhere.
"""
assert N == int(N), "Provide integer N"
extra_pars = []
if sys_pars is None:
sys_pars = []
if not isinstance(half_on, str):
half_on = str(half_on)
else:
Q = QuantSpec('h', half_on)
# don't add model system parameters to function parameter list
extra_pars.extend(remain(Q.freeSymbols, sys_pars))
if not isinstance(max_val, str):
max_val = str(max_val)
else:
Q = QuantSpec('m', max_val)
extra_pars.extend(remain(Q.freeSymbols, sys_pars))
if with_if:
return (['x']+extra_pars,
'if(x>0,%s*pow(x,%i)/(pow(%s,%i) + pow(x,%i)),0)' % (max_val, N, half_on, N, N))
else:
return (['x']+extra_pars,
'%s*pow(x,%i)/(pow(%s,%i) + pow(x,%i))' % (max_val, N, half_on, N, N))
def test_nested_functions_diff():
"""Examples of differentiation using nested functions.
This functionality is built in to Symbolic.prepJacobian
"""
func_ma_spec = (["p", "v"], "0.32*(v+54)/(1-exp(-p*(v+54)/4))")
ma = Fun(func_ma_spec[1], func_ma_spec[0], "ma")
ma_1 = Fun(Diff(ma, "v"), ["v"], "ma_1")
func_mb_spec = (["v"], "0.28*(v+27)/(exp((v+27)/5)-1)")
mb = Fun(func_mb_spec[1], func_ma_spec[0], "mb")
mb_0 = Fun(Diff(mb, "v"), ["v"], "mb_0")
func_ma_1_spec = (["p", "v"], str(ma_1.spec))
func_mb_0_spec = (["v"], str(mb_0.spec))
# artificial example to introduce time dependence
rhs_m = "exp(-2*t)*(100-v) + ma(1, v)*(1-m)-mb(v)*m"
jac_part = Diff(rhs_m, ["v", "m"])
f = expr2fun(jac_part, ma_1=func_ma_1_spec, mb_0=func_mb_0_spec, ma=func_ma_spec, mb=func_mb_spec)
assert remain(f._args, ["t", "v", "m"]) == []
assert abs(norm(f(0, -50, 0.2)) - 8.565615) < 1e-6
# alternative usage syntax
assert abs(norm(f(**{"t": 0, "v": -50, "m": 0.2})) - 8.565615) < 1e-6
def test_nested_functions_diff():
"""Examples of differentiation using nested functions.
This functionality is built in to Symbolic.prepJacobian
"""
func_ma_spec = (['p', 'v'], '0.32*(v+54)/(1-exp(-p*(v+54)/4))')
ma = Fun(func_ma_spec[1], func_ma_spec[0], 'ma')
ma_1 = Fun(Diff(ma, 'v'), ['v'], 'ma_1')
func_mb_spec = (['v'], '0.28*(v+27)/(exp((v+27)/5)-1)')
mb = Fun(func_mb_spec[1], func_ma_spec[0], 'mb')
mb_0 = Fun(Diff(mb, 'v'), ['v'], 'mb_0')
func_ma_1_spec = (['p', 'v'], str(ma_1.spec))
func_mb_0_spec = (['v'], str(mb_0.spec))
# artificial example to introduce time dependence
rhs_m = 'exp(-2*t)*(100-v) + ma(1, v)*(1-m)-mb(v)*m'
jac_part = Diff(rhs_m, ['v', 'm'])
f = expr2fun(jac_part,
ma_1=func_ma_1_spec,
mb_0=func_mb_0_spec,
ma=func_ma_spec,
mb=func_mb_spec)
assert remain(f._args, ['t', 'v', 'm']) == []
assert abs(norm(f(0, -50, 0.2)) - 8.565615) < 1e-6
# alternative usage syntax
assert abs(norm(f(**{'t': 0, 'v': -50, 'm': 0.2})) - 8.565615) < 1e-6
def make_Jac(DS, varnames=None):
if varnames is None:
varnames = DS.funcspec.vars
subdomain = {}
fixedvars = remain(DS.funcspec.vars, varnames)
for k in fixedvars:
subdomain[k] = DS.initialconditions[k]
jac, new_fnspecs = prepJacobian(DS.funcspec._initargs['varspecs'], varnames,
DS.funcspec._initargs['fnspecs'])
scope = copy.copy(DS.pars)
scope.update(subdomain)
scope.update(new_fnspecs)
return expr2fun(jac, ensure_args=['t'], **scope)
