def test_complex():
t = Var('t')
s = Var('s')
assert str(Diff(Pow((t * 5), 2), t)) != '0'
# XXX: doesn't work without global
global p
p = Par('3.', 'p')
f = Fun(QuantSpec('f', str(2.0 + s - 10 * (t ** 2) + Exp(p))), ['s', 't'])
assert str(2 * f.eval(s=3, t=t)) == '2*((2.0+3)-10*Pow(t,2)+Exp(p))'
assert str(Diff('-10*Pow(t,2)', 't')) == '-20*t'
assert str(Diff(2 * f.eval(s=3, t=t), t)) == '2*-20*t'
assert str(Diff(3 + t * f.eval(s=3,
t=t),
t)) == '((2.0+3)-10*Pow(t,2)+Exp(p))+t*(-10*2*t)'
assert str(Diff(3 + t * f(s, t),
t).eval(s=3,
t=1,
p=p)) == '((2.0+3)-10*Pow(1,2)+Exp(p))+1*(-10*2*1)'
# FIXME: segmentation fault!
# assert_almost_equal(Diff(3 + t * f(s, t), t).eval(s=3,
# t=1,
# p=p()),
# -4.914463076812332)
assert Diff(str(f(s, t)), 't') == Diff(f(s, t), t)
q1 = Diff(f(s, t), t)
q2 = Diff(str(f(s, t)), t)
assert q1 == q2
assert str(Diff(f(t, s), t)) == '1'
assert str(Diff(2 * f(3, t * 5), t)) == '2*-100*t*5'
assert str(Diff(2 * f(3, t * 5), t)) != str(0)
assert f(s, t) != f(t, s)
assert str(f(s, t).eval()) == '(2.0+s)-10*Pow(t,2)+Exp(3.0)'
q = f(s, t)
assert str(q.eval()) == '(2.0+s)-10*Pow(t,2)+Exp(3.0)'
assert str(Diff('g(s)', s)) == 'g_0(s)'
assert str(Diff('g(s)', s).eval()) == 'g_0(s)'
# XXX: doesn't work without global
global dg_dt
dg_dt = Fun(QuantSpec('g_0', '2-Sin(t/2)'), ['t'])
assert str(Diff('g(t)', t).eval()) == '2-Sin(t/2)'
assert str(Diff('g(s)', s)) == 'g_0(s)'
assert str(Diff('g(s)', s).eval()) == '2-Sin(s/2)'
g = Fun('', [t], 'g') # declare empty function
assert str(g(t)) == 'g(t)'
assert str(Diff(g(s), s).eval()) == '2-Sin(s/2)'
assert eval(str(Diff('pow(1,2)*t', 't'))) == 1
assert eval(str(Diff(Pow(1, 2) * t, t))) == 1
assert str(Diff(Sin(Pow(t, 1)), t)) == 'Cos(t)'
q = QuantSpec('q', '-0+3+pow(g(x)*h(y,x),1)*1')
assert str(Diff(q, 'x')) == '(g_0(x)*h(y,x)+g(x)*h_1(y,x))'
def test_diff_point_3D():
x0 = Var('x0')
x1 = Var('x1')
x2 = Var('x2')
f5_x0 = Fun(x0 * x2, [x0, x1, x2], 'f5_x0')
f5_x1 = Fun(x0 * 5, [x0, x1, x2], 'f5_x1')
f5_x2 = Fun(x2 * 0.5, [x0, x1, x2], 'f5_x2')
z0 = Point({
'coordarray': [3., 2., 1.],
'coordnames': ['x0', 'x1', 'x2']
})
# could also have defined F directly from f5_x[i] definitions
F1 = Fun(
[
f5_x0(x0, x1, x2),
f5_x1(x0, x1, x2),
f5_x2(x0, x1, x2)
],
[x0, x1, x2],
'F'
)
F2 = [
f5_x0(x0, x1, x2),
f5_x1(x0, x1, x2),
f5_x2(x0, x1, x2)
]
assert Diff(F1, [x0, x1, x2]) == Diff(F2, [x0, x1, x2])
assert_array_almost_equal(
Diff(F1, [x0, x1, x2]).eval(z0).tonumeric(),
array([[1.0, 0, 3.0], [5, 0, 0], [0, 0, 0.5]])
)
assert_array_almost_equal(
Diff(F2, [x0, x1, x2]).eval(z0).tonumeric(),
array([[1.0, 0, 3.0], [5, 0, 0], [0, 0, 0.5]])
)
def F3(z):
return Point({
'coorddict': {
'x0': z('x0') * z('x2'),
'x1': z('x0') * 5.0,
'x2': z('x2') * 0.5
}
})
assert_array_almost_equal(
simplifyMatrixRepr(diff(F3, z0, axes=['x1', 'x2'])),
Diff(F1, [x0, x1, x2]).eval(z0).tonumeric()[1:]
)
# Comparing 1st order Taylor series for nearby point to actual value:
z1 = Point({
'coordarray': array([3.1, 2., .94]),
'coordnames': ['x0', 'x1', 'x2']
})
actual = F3(z1)
approx = F3(z0) + simplifyMatrixRepr(diff(F3, z0)).dot(z1 - z0)
assert all([err < 0.01 for err in abs(approx - actual)])
def test_symbolic_diff():
"""Showing the variety of ways that symbolic Diff() can be used."""
x = Var('x')
y = Var('y')
xx = QuantSpec('dummy', 'x')
function_variants = ('[-3*x**2+2*(x+y),-y/2]', ['-3*x**2+2*(x+y)', '-y/2'],
[-3 * Pow(x, 2) + 2 * (x + y), -y / 2])
for f in function_variants:
for v in ('x', x, xx):
assert str(Diff(f, v)) == '[-6*x+2,0]'
for f in function_variants:
for v in (['x', 'y'], [x, y], [xx, y]):
assert str(Diff(f, v)) == '[[-6*x+2,2],[0,-0.5]]'
"""
Cross-channel coupling for a biophysical neural network.
Example courtesy of Mark Olenik (Bristol University).
"""
from PyDSTool import Var, Exp, Par, Pow, args
from PyDSTool.Toolbox.neuralcomp import voltage, \
ModelConstructor, makeSoma, channel
from matplotlib import pyplot as plt
v = Var(voltage)
# Create placeholder structs to collect together related symbols
# (not used internally by PyDSTool)
NMDA = args()
KCa = args()
# Calcium concentration through nmda channels
# Ca_nmda won't create a current but will be used for KCa.I
Ca_nmda = args()
Iapp = args()
NMDA.g = Par(0.75, 'g')
NMDA.erev = Par(0., 'erev')
KCa.g = Par(0.0072, 'g')
KCa.erev = Par(-80., 'erev')
Ca_nmda.erev = Par(20., 'Ca_erev')
Ca_nmda.rho = Par(0.0004, 'rho')
Ca_nmda.delta = Par(0.002, 'delta')
Iapp.amp = Par(0.0, 'amp')
NMDA.p = Var('p') # nmda gating variable
Ca_nmda.c = Var('c') # concentration
def test_symbolic():
assert doneg('-x-y') == 'x+y'
assert doneg('(-x-y)') == '(x+y)'
assert doneg('-(-x-y)') == '(-x-y)'
assert dosub('1', '-x-y') == '(1+x+y)'
g2 = expr2fun('1-max([0., -a+b*x])', **{'a': 3, 'b': 1.5})
assert g2._args == ['x']
assert g2(1) == 1.0
assert g2(10) == -11.0
ds = {'a': 3, 'bbb': 1}
f=expr2fun('1+ds["a"]')
assert f._args == ['ds']
assert f(ds) == 4
f2=expr2fun('1+ds["a"]')
assert f2(**{'ds':ds}) == 4
assert f2._args == ['ds']
g=expr2fun('1+ds["bbb"]', ds=ds)
assert g() == 2
# g must be dynamic and not based on static eval of ds on initialization
ds['bbb'] = 2
assert g._args == []
assert g() == 3
m = args(pars=copy(ds))
h = expr2fun('m.pars["a"]+c', m=m, c=1)
assert h() == 4
assert h._args == []
h2 = expr2fun('1 + m.pars["a"]/2.', m=m)
assert h2() == 2.5
assert h2._args == []
def func(x, y):
return x * (y+1)
m.func = func
i = expr2fun('1+func(x,y)+b', func=m.func, b=0.5)
assert 1+func(2,3)+0.5 == i(2,3)
j = expr2fun('i(x,func(2,y))*2', i=i, func=m.func)
assert j(1,0) == 9
fnspec = {'f': (['x','y'], 'x+1+2*y-a')}
# a is expected to be in scope like a FuncSpec parameter
# so can't use the above method of providing explicit functions
k = expr2fun('-f(c,d)+b', f=fnspec['f'], b=0.5, a=1)
assert k(1,2) == -4.5
s='1+a/(f(x,y)-3)+h(2)'
t=s.replace('y','g(x,z)')
u=t.replace('z','f(z)')
r1, d1 = replaceCallsWithDummies(s, ['f','g','h'])
r2, d2 = replaceCallsWithDummies(t, ['f','g','h'])
r3, d3 = replaceCallsWithDummies(u, ['f','g','h'])
assert r1 == '1+a/(__dummy1__-3)+__dummy2__'
assert len(d1) == 2
assert r2 == '1+a/(__dummy2__-3)+__dummy3__'
assert len(d2) == 3
assert r2 == '1+a/(__dummy2__-3)+__dummy3__'
assert len(d3) == 4
ps = 'abs((HB9_fs_Vq-HB9_fs_V)*(-((HB9_fs_Lk_g*(HB9_fs_V-HB9_fs_Lk_vrev))+(-HB9_fs_Iapp_Ibias)+((HB9_fs_Na_g*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1-HB9_fs_K_n))*(HB9_fs_V-HB9_fs_Na_vrev))+(HB9_fs_K_g*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*(HB9_fs_V-HB9_fs_K_vrev))+(HB9_fs_isyn_g*(HB9_fs_V-HB9_fs_isyn_vrev))+(HB9_fs_esyn_g*(HB9_fs_V-HB9_fs_esyn_vrev)))/HB9_fs_C)+(HB9_fs_Knq-HB9_fs_K_n)*(((1.0/(1.0+exp((HB9_fs_V-HB9_fs_K_theta_n)/HB9_fs_K_k_n)))-HB9_fs_K_n)/(HB9_fs_K_taun_bar/cosh((HB9_fs_V-HB9_fs_K_theta_n)/(2*HB9_fs_K_k_n)))))/(sqrt(HB9_fs_Vq*HB9_fs_Vq+HB9_fs_Knq*HB9_fs_Knq)+sqrt(pow((-((HB9_fs_Lk_g*(HB9_fs_V-HB9_fs_Lk_vrev))+(-HB9_fs_Iapp_Ibias)+((HB9_fs_Na_g*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1-HB9_fs_K_n))*(HB9_fs_V-HB9_fs_Na_vrev))+(HB9_fs_K_g*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*(HB9_fs_V-HB9_fs_K_vrev))+(HB9_fs_isyn_g*(HB9_fs_V-HB9_fs_isyn_vrev))+(HB9_fs_esyn_g*(HB9_fs_V-HB9_fs_esyn_vrev)))/HB9_fs_C),2)+pow((((1.0/(1.0+exp((HB9_fs_V-HB9_fs_K_theta_n)/HB9_fs_K_k_n)))-HB9_fs_K_n)/(HB9_fs_K_taun_bar/cosh((HB9_fs_V-HB9_fs_K_theta_n)/(2*HB9_fs_K_k_n)))),2)))'
parnames = ['HB9_fs_Vq', 'HB9_fs_Lk_g', 'HB9_fs_Lk_vrev', 'HB9_fs_Iapp_Ibias', 'HB9_fs_Na_g', 'HB9_fs_Na_theta_m', 'HB9_fs_Na_k_m', 'HB9_fs_Na_vrev', 'HB9_fs_K_g', 'HB9_fs_K_vrev', 'HB9_fs_isyn_g', 'HB9_fs_isyn_vrev', 'HB9_fs_esyn_g', 'HB9_fs_esyn_vrev', 'HB9_fs_C', 'HB9_fs_Knq', 'HB9_fs_K_theta_n', 'HB9_fs_K_k_n', 'HB9_fs_K_taun_bar']
varnames = ['HB9_fs_V', 'HB9_fs_K_n']
ps2 = convertPowers(ps, 'pow')
for n in parnames+varnames:
v=rand(1)[0]+1e-5
ps2=ps2.replace(n,str(v))
ps=ps.replace(n,str(v))
eps=eval(ps)
eps2=eval(ps2)
assert eps==eps2
a = Par('3.5', 'a')
qa = Var(['a*3', 'b'], 'array_test')
assert str(qa.eval(a=1)) == '[3,b]'
# explicit exporting 'a' to globals to make this work as expected
globals()['a'] = a
assert str(qa.eval()) == '[10.5,b]'
testq = QuantSpec('d', 'a')
testq.simplify()
assert testq() == 'a'
assert str(testq.eval(a=3)) == '3'
q = QuantSpec('q', 'zeta(yrel(y,initcond(y)),z)-1')
print q.eval({})
assert 'initcond' in str(q.eval({}))
q2=QuantSpec('q','Exp(-spikeTable+b)/k')
assert 'spikeTable' in q2.freeSymbols
# x = Var('x')
# print x.isDefined()
# xs = QuantSpec('x', '1-rel - 2*x + cos(z) + 2e10', 'RHSfuncSpec')
# x.bindSpec(xs)
# print x.isDefined(),"\n"
x = Var(QuantSpec('x', '1-rel - 2*x + cos(z) + 2e10', 'RHSfuncSpec'))
p = Par('p')
az = Var(QuantSpec('z', 'myfunc(0,z)+abs(x+1)', 'RHSfuncSpec'))
w = Var('x-1/w[i]', 'w[i,0,1]', specType='RHSfuncSpec')
myLeaf1.compatibleContainers=(myNode,)
myLeaf2.compatibleContainers=(myNode,)
myNode.compatibleSubcomponents=(myLeaf1,myLeaf2)
c = myLeaf1('leaf1')
assert c.isDefined() == False
c.add(x)
print c.freeSymbols, c.isDefined()
c.add(az)
print c.freeSymbols, c.isDefined()
c.add(w)
print c.freeSymbols, c.isDefined()
c.compileFuncSpec()
print c.funcSpecDict
empty_fn = Fun('1+exp(1)', [], 'dumb_fn')
print empty_fn()
q = Par('qpar')
y = Var(QuantSpec('rel', 'v+p'), domain=[0,1])
g = Fun(QuantSpec('qfunc', '-1.e-05+sin(qpar)*(10.e-5-xtol)'), ['xtol'])
d = myLeaf2('leaf2')
## d.add(y)
q_dummy = Var(QuantSpec('q_notpar', '-2+sin(30)'))
g_dummy = Fun(QuantSpec('qfunc_dummy', 'sin(q_notpar)*(10.e-5-xtol)'), ['xtol'])
d.add([q_dummy, g_dummy]) # will delete these later
d.add([q,g])
d2 = myLeaf2('leaf3')
d2.add([q,g])
v = Var(QuantSpec('v', 'v * myfunc(rel,v) - sin(p)*t', 'RHSfuncSpec'))
# p is a global parameter so this is ok in v
f = Fun(QuantSpec('myfunc', '2.0+s-t+exp(p)'), ['s','t'])
# t is just a local argument here, so it won't clash with its
# occurrence in v (which we'll see is declared as a global
# when we call flattenSpec()).
ipar = Par('ipar')
z = Var('z[i]+v/(i*ipar)', 'z[i,0,5]', specType='RHSfuncSpec')
a = myNode('sys1')
a.add([f,p,y])
print a.isDefined(True)
a.add(c)
print a.freeSymbols, a.isDefined(), a.isComplete()
a.add(d)
print a.freeSymbols, a.isDefined(), a.isComplete()
a.add(d2)
print a.freeSymbols, a.isDefined(), a.isComplete()
a.add(v)
print "Added v"
print a.freeSymbols, a.isDefined(), a.isComplete()
print "Removed v"
a.remove(v)
print a.freeSymbols, a.isDefined(), a.isComplete()
a.add([z,ipar])
print a.freeSymbols, a.isDefined(), a.isComplete()
print "\na._registry --> "
print a._registry
print "Re-added v"
a.add(v)
print a.freeSymbols, a.isDefined(), a.isComplete()
print "\nv in a -->", v in a
print "\n"
with pytest.raises(TypeError):
a.compileFuncSpec()
a.remove(['leaf2.qfunc_dummy', 'leaf2.q_notpar'])
print "--------- sys1: funcSpecDict ---------------------"
a.compileFuncSpec()
info(a.funcSpecDict)
print "\n\n------------- Flatten spec with unravelling\n"
print "\n\ninfo(a.flattenSpec()) --> \n"
info(a.flattenSpec(globalRefs=['t']), "Model specification")
print "\n\n------------- Flatten spec with no unravelling\n"
print "\n\ninfo(a.flattenSpec(False, globalRefs=['t'])) --> \n"
info(a.flattenSpec(False, globalRefs=['t']), "Model specification")
print "\n\nDemos for functions (results are strings):\n"
h = f(p, -x)
z = QuantSpec('zero','0')
print "h = f(p, -x) --> ", h
print "z = QuantSpec('zero','0') --> ", z
print "f(g(3)*1,h) --> ", f(g(3)*1,h)
print "f(g(p),h) --> ", f(g(p),h)
print "f(g(p),0*h) --> ", f(g(p),0*h)
print "f(g(x),h+z) --> ", f(g(x),h+z)
# e is the math constant, but it doesn't evaluate to a float!
print "f(g(x()),(e+h)/2) --> ", f(g(x()),(e+h)/2)
print "f(g(x()),-h) --> ", f(g(x()),-h)
print "f(g(x()),.5-h+0) --> ", f(g(x()),.5-h+0)
print "Sin(pi+q) --> ", Sin(pi+q)
qsin=QuantSpec('qsin','zv-sin(beta)')
assert str(qsin.eval()) == 'zv-sin(beta)'
print "\n\nDemos for local scope evaluation and **:\n"
print "q=Var('xv+1','qv')"
print "x=Var('3','xv')"
q=Var('xv+1','qv')
x=Var('3','xv')
globals()['x'] = x
globals()['q'] = q
sc1 = str(q.eval()) == '4'
print "q.eval() == 4? ", sc1
assert sc1
print "a=x/q"
a=x/q
sc2 = str(a) == 'xv/qv'
print "a == xv/qv? ", sc2
assert sc2
sc3 = str(a.eval())=='0.75'
print "a.eval() == 0.75? ", sc3
assert sc3
sc4 = str(a.eval(xv=5))=='5/qv'
print "a.eval(xv=5) == 5/q? ", sc4
assert sc4
sc5 = (str(a.eval(xv=5,qv=q())),'0.83333333333333337')
assert_approx_equal(*sc5)
print "assert_approx_equal(%s,%s)" % sc5
sc6 = (str(a.eval({'xv': 10, 'qv': q()})),'0.90909090909090906')
print "assert_approx_equal(%s,%s)" % sc6
assert_approx_equal(*sc6)
print "qs=QuantSpec('qsv','xsv+1')"
print "xs=QuantSpec('xsv','3')"
qs=QuantSpec('qsv','xsv+1')
xs=QuantSpec('xsv','3')
globals()['qs'] = qs
globals()['xs'] = xs
qse = qs.eval()
qt1 = str(qse) == '4'
print "qs.eval() == 4? ", qt1
assert qt1
assert qse.tonumeric() == 4
print "asq = xs/qs"
asq=xs/qs
qt2 = str(asq) == '3/(xsv+1)'
print "asq == 3/(xsv+1)? ", qt2
assert qt2
qt3 = str(asq.eval()) == '0.75'
print "as.eval() == 0.75? ", qt3
assert qt3
ps = asq**xs
print "ps = as**xs"
qt4 = str(ps) == 'Pow(3/(xsv+1),3)'
print "ps == Pow(3/(xsv+1),3)? ", qt4
assert qt4
qt5 = str(ps.eval()) == str(0.75**3)
print "ps.eval() == 0.421875? ", qt5
assert qt5
print "sq=QuantSpec('sv','sin(xsv)')"
print "s2q=QuantSpec('s2v','Sin(xv)')"
sq=QuantSpec('sv','sin(xsv)')
s2q=QuantSpec('s2v','Sin(xv)')
print "sq.eval() --> ", sq.eval()
print "s2q.eval() --> ", s2q.eval()
assert sq.eval().tonumeric() == s2q.eval().tonumeric()
assert sq[:] == ['sin','(','xsv',')']
print "\n\nDemos for multiple quantity definitions:\n"
mp=QuantSpec('p','a + 3*z[4*i-2]')
m=Var(mp, 'z[i,2,5]', specType='RHSfuncSpec')
v=Var('3*z[i-1]+z4-i', 'z[i,1,5]', specType='RHSfuncSpec')
print "mp=QuantSpec('p','a + 3*z[4*i-2]')"
print "m=Var(mp, 'z[i,2,5]', specType='RHSfuncSpec')"
print "v=Var('3*z[i-1]+z4-i', 'z[i,1,5]', specType='RHSfuncSpec')"
print "v[3] -->", v[3]
assert str(v[3])=='z3'
print "v.freeSymbols -->", v.freeSymbols
assert v.freeSymbols == ['z0']
print "\nModelSpec a already contains 'z0', which was defined as part of"
print "a multiple quantity definition, so check that attempting to add"
print "v to a results in an error ..."
with pytest.raises(AttributeError):
a.add(v)
print "\nTest of eval method, e.g. on a function f(s,t)..."
print "f.eval(s='1', t='t_val') -->", f.eval(s='1', t='t_val')
print "f.eval(s=1, t='t_val', p=0.5) -->", f.eval(s=1, t='t_val', p=0.5)
print "\nTesting convertPowers():"
cp_tests = ["phi1dot^m3", "1+phi1dot^m3*s",
"phi1dot**m3", "1+phi1dot**m3*s",
"sin(x^3)**4", "(2/3)^2.5", "3^cos(x)-pi",
"3^(cos(x)-pi)", "2^(sin(y**p))"]
for spec in cp_tests:
print spec, " --> ", convertPowers(spec)
globals().pop('a')
qc=QuantSpec('t', "a+coot+b/'coot'")
assert str(qc.eval()) == 'a+coot+b/"coot"'
coot=QuantSpec('coot', "1.05")
globals()['coot'] = coot
assert str(qc.eval()) == 'a+1.05+b/"coot"'
print "\nTest of function calling with argument names that clash with"
print "bound names inside the function."
x0=Var('x0')
x1=Var('x1')
x2=Var('x2')
F=Fun([x0*x2,x0*5,x2**0.5], [x0,x1,x2], 'F')
print "F=Fun([x0*x2,x0*5,x2**0.5], [x0,x1,x2], 'F')"
print "F(3,2,Sin(x0))) = [3*Sin(x0),15,Pow(Sin(x0),0.5)] ..."
print " ... even though x0 is a bound name inside definition of F"
assert str(F(3,2,Sin(x0)))=='[3*Sin(x0),15,Pow(Sin(x0),0.5)]'
def test_symbolic():
assert doneg('-x-y') == 'x+y'
assert doneg('(-x-y)') == '(x+y)'
assert doneg('-(-x-y)') == '(-x-y)'
assert dosub('1', '-x-y') == '(1+x+y)'
g2 = expr2fun('1-max([0., -a+b*x])', **{'a': 3, 'b': 1.5})
assert g2._args == ['x']
assert g2(1) == 1.0
assert g2(10) == -11.0
ds = {'a': 3, 'bbb': 1}
f = expr2fun('1+ds["a"]')
assert f._args == ['ds']
assert f(ds) == 4
f2 = expr2fun('1+ds["a"]')
assert f2(**{'ds': ds}) == 4
assert f2._args == ['ds']
g = expr2fun('1+ds["bbb"]', ds=ds)
assert g() == 2
# g must be dynamic and not based on static eval of ds on initialization
ds['bbb'] = 2
assert g._args == []
assert g() == 3
m = args(pars=copy(ds))
h = expr2fun('m.pars["a"]+c', m=m, c=1)
assert h() == 4
assert h._args == []
h2 = expr2fun('1 + m.pars["a"]/2.', m=m)
assert h2() == 2.5
assert h2._args == []
def func(x, y):
return x * (y + 1)
m.func = func
i = expr2fun('1+func(x,y)+b', func=m.func, b=0.5)
assert 1 + func(2, 3) + 0.5 == i(2, 3)
j = expr2fun('i(x,func(2,y))*2', i=i, func=m.func)
assert j(1, 0) == 9
fnspec = {'f': (['x', 'y'], 'x+1+2*y-a')}
# a is expected to be in scope like a FuncSpec parameter
# so can't use the above method of providing explicit functions
k = expr2fun('-f(c,d)+b', f=fnspec['f'], b=0.5, a=1)
assert k(1, 2) == -4.5
s = '1+a/(f(x,y)-3)+h(2)'
t = s.replace('y', 'g(x,z)')
u = t.replace('z', 'f(z)')
r1, d1 = replaceCallsWithDummies(s, ['f', 'g', 'h'])
r2, d2 = replaceCallsWithDummies(t, ['f', 'g', 'h'])
r3, d3 = replaceCallsWithDummies(u, ['f', 'g', 'h'])
assert r1 == '1+a/(__dummy1__-3)+__dummy2__'
assert len(d1) == 2
assert r2 == '1+a/(__dummy2__-3)+__dummy3__'
assert len(d2) == 3
assert r2 == '1+a/(__dummy2__-3)+__dummy3__'
assert len(d3) == 4
ps = 'abs((HB9_fs_Vq-HB9_fs_V)*(-((HB9_fs_Lk_g*(HB9_fs_V-HB9_fs_Lk_vrev))+(-HB9_fs_Iapp_Ibias)+((HB9_fs_Na_g*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1-HB9_fs_K_n))*(HB9_fs_V-HB9_fs_Na_vrev))+(HB9_fs_K_g*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*(HB9_fs_V-HB9_fs_K_vrev))+(HB9_fs_isyn_g*(HB9_fs_V-HB9_fs_isyn_vrev))+(HB9_fs_esyn_g*(HB9_fs_V-HB9_fs_esyn_vrev)))/HB9_fs_C)+(HB9_fs_Knq-HB9_fs_K_n)*(((1.0/(1.0+exp((HB9_fs_V-HB9_fs_K_theta_n)/HB9_fs_K_k_n)))-HB9_fs_K_n)/(HB9_fs_K_taun_bar/cosh((HB9_fs_V-HB9_fs_K_theta_n)/(2*HB9_fs_K_k_n)))))/(sqrt(HB9_fs_Vq*HB9_fs_Vq+HB9_fs_Knq*HB9_fs_Knq)+sqrt(pow((-((HB9_fs_Lk_g*(HB9_fs_V-HB9_fs_Lk_vrev))+(-HB9_fs_Iapp_Ibias)+((HB9_fs_Na_g*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1.0/(1.0+exp((HB9_fs_V-HB9_fs_Na_theta_m)/HB9_fs_Na_k_m)))*(1-HB9_fs_K_n))*(HB9_fs_V-HB9_fs_Na_vrev))+(HB9_fs_K_g*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*HB9_fs_K_n*(HB9_fs_V-HB9_fs_K_vrev))+(HB9_fs_isyn_g*(HB9_fs_V-HB9_fs_isyn_vrev))+(HB9_fs_esyn_g*(HB9_fs_V-HB9_fs_esyn_vrev)))/HB9_fs_C),2)+pow((((1.0/(1.0+exp((HB9_fs_V-HB9_fs_K_theta_n)/HB9_fs_K_k_n)))-HB9_fs_K_n)/(HB9_fs_K_taun_bar/cosh((HB9_fs_V-HB9_fs_K_theta_n)/(2*HB9_fs_K_k_n)))),2)))'
parnames = [
'HB9_fs_Vq', 'HB9_fs_Lk_g', 'HB9_fs_Lk_vrev', 'HB9_fs_Iapp_Ibias',
'HB9_fs_Na_g', 'HB9_fs_Na_theta_m', 'HB9_fs_Na_k_m', 'HB9_fs_Na_vrev',
'HB9_fs_K_g', 'HB9_fs_K_vrev', 'HB9_fs_isyn_g', 'HB9_fs_isyn_vrev',
'HB9_fs_esyn_g', 'HB9_fs_esyn_vrev', 'HB9_fs_C', 'HB9_fs_Knq',
'HB9_fs_K_theta_n', 'HB9_fs_K_k_n', 'HB9_fs_K_taun_bar'
]
varnames = ['HB9_fs_V', 'HB9_fs_K_n']
ps2 = convertPowers(ps, 'pow')
for n in parnames + varnames:
v = rand(1)[0] + 1e-5
ps2 = ps2.replace(n, str(v))
ps = ps.replace(n, str(v))
eps = eval(ps)
eps2 = eval(ps2)
assert eps == eps2
a = Par('3.5', 'a')
qa = Var(['a*3', 'b'], 'array_test')
assert str(qa.eval(a=1)) == '[3,b]'
# explicit exporting 'a' to globals to make this work as expected
globals()['a'] = a
assert str(qa.eval()) == '[10.5,b]'
testq = QuantSpec('d', 'a')
testq.simplify()
assert testq() == 'a'
assert str(testq.eval(a=3)) == '3'
q = QuantSpec('q', 'zeta(yrel(y,initcond(y)),z)-1')
print(q.eval({}))
assert 'initcond' in str(q.eval({}))
q2 = QuantSpec('q', 'Exp(-spikeTable+b)/k')
assert 'spikeTable' in q2.freeSymbols
# x = Var('x')
# print x.isDefined()
# xs = QuantSpec('x', '1-rel - 2*x + cos(z) + 2e10', 'RHSfuncSpec')
# x.bindSpec(xs)
# print x.isDefined(),"\n"
x = Var(QuantSpec('x', '1-rel - 2*x + cos(z) + 2e10', 'RHSfuncSpec'))
p = Par('p')
az = Var(QuantSpec('z', 'myfunc(0,z)+abs(x+1)', 'RHSfuncSpec'))
w = Var('x-1/w[i]', 'w[i,0,1]', specType='RHSfuncSpec')
myLeaf1.compatibleContainers = (myNode, )
myLeaf2.compatibleContainers = (myNode, )
myNode.compatibleSubcomponents = (myLeaf1, myLeaf2)
c = myLeaf1('leaf1')
assert c.isDefined() == False
c.add(x)
print(c.freeSymbols, c.isDefined())
c.add(az)
print(c.freeSymbols, c.isDefined())
c.add(w)
print(c.freeSymbols, c.isDefined())
c.compileFuncSpec()
print(c.funcSpecDict)
empty_fn = Fun('1+exp(1)', [], 'dumb_fn')
print(empty_fn())
q = Par('qpar')
y = Var(QuantSpec('rel', 'v+p'), domain=[0, 1])
g = Fun(QuantSpec('qfunc', '-1.e-05+sin(qpar)*(10.e-5-xtol)'), ['xtol'])
d = myLeaf2('leaf2')
## d.add(y)
q_dummy = Var(QuantSpec('q_notpar', '-2+sin(30)'))
g_dummy = Fun(QuantSpec('qfunc_dummy', 'sin(q_notpar)*(10.e-5-xtol)'),
['xtol'])
d.add([q_dummy, g_dummy]) # will delete these later
d.add([q, g])
d2 = myLeaf2('leaf3')
d2.add([q, g])
v = Var(QuantSpec('v', 'v * myfunc(rel,v) - sin(p)*t', 'RHSfuncSpec'))
# p is a global parameter so this is ok in v
f = Fun(QuantSpec('myfunc', '2.0+s-t+exp(p)'), ['s', 't'])
# t is just a local argument here, so it won't clash with its
# occurrence in v (which we'll see is declared as a global
# when we call flattenSpec()).
ipar = Par('ipar')
z = Var('z[i]+v/(i*ipar)', 'z[i,0,5]', specType='RHSfuncSpec')
a = myNode('sys1')
a.add([f, p, y])
print(a.isDefined(True))
a.add(c)
print(a.freeSymbols, a.isDefined(), a.isComplete())
a.add(d)
print(a.freeSymbols, a.isDefined(), a.isComplete())
a.add(d2)
print(a.freeSymbols, a.isDefined(), a.isComplete())
a.add(v)
print("Added v")
print(a.freeSymbols, a.isDefined(), a.isComplete())
print("Removed v")
a.remove(v)
print(a.freeSymbols, a.isDefined(), a.isComplete())
a.add([z, ipar])
print(a.freeSymbols, a.isDefined(), a.isComplete())
print("\na._registry --> ")
print(a._registry)
print("Re-added v")
a.add(v)
print(a.freeSymbols, a.isDefined(), a.isComplete())
print("\nv in a -->", v in a)
print("\n")
with pytest.raises(TypeError):
a.compileFuncSpec()
a.remove(['leaf2.qfunc_dummy', 'leaf2.q_notpar'])
print("--------- sys1: funcSpecDict ---------------------")
a.compileFuncSpec()
info(a.funcSpecDict)
print("\n\n------------- Flatten spec with unravelling\n")
print("\n\ninfo(a.flattenSpec()) --> \n")
info(a.flattenSpec(globalRefs=['t']), "Model specification")
print("\n\n------------- Flatten spec with no unravelling\n")
print("\n\ninfo(a.flattenSpec(False, globalRefs=['t'])) --> \n")
info(a.flattenSpec(False, globalRefs=['t']), "Model specification")
print("\n\nDemos for functions (results are strings):\n")
h = f(p, -x)
z = QuantSpec('zero', '0')
print("h = f(p, -x) --> ", h)
print("z = QuantSpec('zero','0') --> ", z)
print("f(g(3)*1,h) --> ", f(g(3) * 1, h))
print("f(g(p),h) --> ", f(g(p), h))
print("f(g(p),0*h) --> ", f(g(p), 0 * h))
print("f(g(x),h+z) --> ", f(g(x), h + z))
# e is the math constant, but it doesn't evaluate to a float!
print("f(g(x()),(e+h)/2) --> ", f(g(x()), (e + h) / 2))
print("f(g(x()),-h) --> ", f(g(x()), -h))
print("f(g(x()),.5-h+0) --> ", f(g(x()), .5 - h + 0))
print("Sin(pi+q) --> ", Sin(pi + q))
qsin = QuantSpec('qsin', 'zv-sin(beta)')
assert str(qsin.eval()) == 'zv-sin(beta)'
print("\n\nDemos for local scope evaluation and **:\n")
print("q=Var('xv+1','qv')")
print("x=Var('3','xv')")
q = Var('xv+1', 'qv')
x = Var('3', 'xv')
globals()['x'] = x
globals()['q'] = q
sc1 = str(q.eval()) == '4'
print("q.eval() == 4? ", sc1)
assert sc1
print("a=x/q")
a = x / q
sc2 = str(a) == 'xv/qv'
print("a == xv/qv? ", sc2)
assert sc2
sc3 = str(a.eval()) == '0.75'
print("a.eval() == 0.75? ", sc3)
assert sc3
sc4 = str(a.eval(xv=5)) == '5/qv'
print("a.eval(xv=5) == 5/q? ", sc4)
assert sc4
sc5 = (str(a.eval(xv=5, qv=q())), '0.83333333333333337')
assert_approx_equal(*sc5)
print("assert_approx_equal(%s,%s)" % sc5)
sc6 = (str(a.eval({'xv': 10, 'qv': q()})), '0.90909090909090906')
print("assert_approx_equal(%s,%s)" % sc6)
assert_approx_equal(*sc6)
print("qs=QuantSpec('qsv','xsv+1')")
print("xs=QuantSpec('xsv','3')")
qs = QuantSpec('qsv', 'xsv+1')
xs = QuantSpec('xsv', '3')
globals()['qs'] = qs
globals()['xs'] = xs
qse = qs.eval()
qt1 = str(qse) == '4'
print("qs.eval() == 4? ", qt1)
assert qt1
assert qse.tonumeric() == 4
print("asq = xs/qs")
asq = xs / qs
qt2 = str(asq) == '3/(xsv+1)'
print("asq == 3/(xsv+1)? ", qt2)
assert qt2
qt3 = str(asq.eval()) == '0.75'
print("as.eval() == 0.75? ", qt3)
assert qt3
ps = asq**xs
print("ps = as**xs")
qt4 = str(ps) == 'Pow(3/(xsv+1),3)'
print("ps == Pow(3/(xsv+1),3)? ", qt4)
assert qt4
qt5 = str(ps.eval()) == str(0.75**3)
print("ps.eval() == 0.421875? ", qt5)
assert qt5
print("sq=QuantSpec('sv','sin(xsv)')")
print("s2q=QuantSpec('s2v','Sin(xv)')")
sq = QuantSpec('sv', 'sin(xsv)')
s2q = QuantSpec('s2v', 'Sin(xv)')
print("sq.eval() --> ", sq.eval())
print("s2q.eval() --> ", s2q.eval())
assert sq.eval().tonumeric() == s2q.eval().tonumeric()
assert sq[:] == ['sin', '(', 'xsv', ')']
print("\n\nDemos for multiple quantity definitions:\n")
mp = QuantSpec('p', 'a + 3*z[4*i-2]')
m = Var(mp, 'z[i,2,5]', specType='RHSfuncSpec')
v = Var('3*z[i-1]+z4-i', 'z[i,1,5]', specType='RHSfuncSpec')
print("mp=QuantSpec('p','a + 3*z[4*i-2]')")
print("m=Var(mp, 'z[i,2,5]', specType='RHSfuncSpec')")
print("v=Var('3*z[i-1]+z4-i', 'z[i,1,5]', specType='RHSfuncSpec')")
print("v[3] -->", v[3])
assert str(v[3]) == 'z3'
print("v.freeSymbols -->", v.freeSymbols)
assert v.freeSymbols == ['z0']
print("\nModelSpec a already contains 'z0', which was defined as part of")
print("a multiple quantity definition, so check that attempting to add")
print("v to a results in an error ...")
with pytest.raises(AttributeError):
a.add(v)
print("\nTest of eval method, e.g. on a function f(s,t)...")
print("f.eval(s='1', t='t_val') -->", f.eval(s='1', t='t_val'))
print("f.eval(s=1, t='t_val', p=0.5) -->", f.eval(s=1, t='t_val', p=0.5))
print("\nTesting convertPowers():")
cp_tests = [
"phi1dot^m3", "1+phi1dot^m3*s", "phi1dot**m3", "1+phi1dot**m3*s",
"sin(x^3)**4", "(2/3)^2.5", "3^cos(x)-pi", "3^(cos(x)-pi)",
"2^(sin(y**p))"
]
for spec in cp_tests:
print(spec, " --> ", convertPowers(spec))
globals().pop('a')
qc = QuantSpec('t', "a+coot+b/'coot'")
assert str(qc.eval()) == 'a+coot+b/"coot"'
coot = QuantSpec('coot', "1.05")
globals()['coot'] = coot
assert str(qc.eval()) == 'a+1.05+b/"coot"'
print("\nTest of function calling with argument names that clash with")
print("bound names inside the function.")
x0 = Var('x0')
x1 = Var('x1')
x2 = Var('x2')
F = Fun([x0 * x2, x0 * 5, x2**0.5], [x0, x1, x2], 'F')
print("F=Fun([x0*x2,x0*5,x2**0.5], [x0,x1,x2], 'F')")
print("F(3,2,Sin(x0))) = [3*Sin(x0),15,Pow(Sin(x0),0.5)] ...")
print(" ... even though x0 is a bound name inside definition of F")
assert str(F(3, 2, Sin(x0))) == '[3*Sin(x0),15,Pow(Sin(x0),0.5)]'
def test_symbolic_vector():
# XXX: doesn't work without global
global q0, q1
p0 = Var("p0")
q0 = Var(p0 + 3, "q0")
q1 = Var(Diff(1 + Sin(Pow(p0, 3) + q0), p0), "q1")
qv = Var([q0, q1], "q")
assert str(qv()) == "[q0,q1]"
assert str(qv.eval()) == "[(p0+3),(3*Pow(p0,2)*Cos(Pow(p0,3)+(p0+3)))]"
v = Var("v")
w = Var("w")
f = Var([-3 * Pow((2 * v + 1), 3) + 2 * (w + v), -w / 2], "f")
df = Diff(f, [v, w])
assert str(df) == "[[-3*6*Pow((2*v+1),2)+2,2],[0,-0.5]]"
dfe = df.eval(v=3, w=10).tonumeric()
assert_allclose(dfe, [[-880.0, 2.0], [0.0, -0.5]])
assert isinstance(dfe, ndarray)
assert isinstance(df.fromvector(), list)
y0 = Var("y0")
y1 = Var("y1")
y2 = Var("y2")
t = Var("t")
ydot0 = Fun(-0.04 * y0 + 1e4 * y1 * y2, [y0, y1, y2], "ydot0")
ydot2 = Fun(3e7 * y1 * y1, [y0, y1, y2], "ydot2")
ydot1 = Fun(-ydot0(y0, y1, y2) - ydot2(y0, y1, y2), [y0, y1, y2], "ydot1")
F = Fun([ydot0(y0, y1, y2), ydot1(y0, y1, y2), ydot2(y0, y1, y2)], [y0, y1, y2], "F")
assert F.dim == 3
DF = Diff(F, [y0, y1, y2])
DF0, DF1, DF2 = DF.fromvector()
assert_approx_equal(DF0.fromvector()[0].tonumeric(), -0.04)
# str(Diff(F,[y0,y1,y2])) should be (to within numerical rounding errors):
# '[[-0.04,10000*y2,10000*y1],[0.040000000000000001,(-10000*y2)-30000000*2*y1,-10000*y1],[0,30000000*2*y1,0]]')
jac = Fun(Diff(F, [y0, y1, y2]), [t, y0, y1, y2], "Jacobian")
assert jac(t, 0.1, y0 + 1, 0.5).eval(y0=0) == jac(t, 0.1, 1 + y0, 0.5).eval(y0=0)
assert jac(t, 0.1, y0, 0.5) == jac(t, 0.1, 0 + y0, 0.5)
x = Var("x")
y = Var("y")
f1 = Fun([-3 * x ** 3 + 2 * (x + y), -y / 2], [x, y], "f1")
f2 = ["-3*x**3+2*(x+y)", "-y/2"]
f3 = [-3 * x ** 3.0 + 2 * (x + y), -y / 2.0]
assert str(f1) == "f1"
assert str(f2) == "['-3*x**3+2*(x+y)', '-y/2']"
assert str(f3) == "[QuantSpec __result__ (ExpFuncSpec), QuantSpec __result__ (ExpFuncSpec)]"
f4 = [-3 * Pow((2 * x + 1), 3) + 2 * (x + y), -y / 2]
xx = QuantSpec("dummy", "x")
f5 = Var([-3 * Pow((2 * x + 1), 3) + 2 * (x + y), -y / 2], "f5")
assert Diff(f1, x) == Diff(f1, "x")
assert str(Diff(f1, x)) == "[-3*3*Pow(x,2)+2,0]"
assert str(Diff(f3, x)) == "[-3*3*Pow(x,2)+2,0]"
assert str(Diff(f3, xx)) == "[-3*3*Pow(x,2)+2,0]"
assert str(Diff(f4, x)) == "[-3*6*Pow((2*x+1),2)+2,0]"
assert str(Diff(f4, xx)) == "[-3*6*Pow((2*x+1),2)+2,0]"
# Examples of Jacobian Diff(f, [x,y])...
assert Diff(f1, [x, y]) == Diff(f1, ["x", "y"]) == Diff(f1(x, y), [x, y])
assert str(Diff(f2, ["x", "y"])) == "[[-3*3*Pow(x,2)+2,2],[0,-0.5]]"
assert str(Diff(f3, ["x", "y"])) == "[[-3*3*Pow(x,2)+2,2],[0,-0.5]]"
assert str(Diff(f1, [xx, y])) == "[[-3*3*Pow(x,2)+2,2],[0,-0.5]]"
assert str(Diff(f1, [xx, "y"])) == "[[-3*3*Pow(x,2)+2,2],[0,-0.5]]"
assert str(Diff(f2, [x, y])) == "[[-3*3*Pow(x,2)+2,2],[0,-0.5]]"
assert str(Diff(f3, [x, y])) == "[[-3*3*Pow(x,2)+2,2],[0,-0.5]]"
assert str(Diff(f4, [x, y])) == "[[-3*6*Pow((2*x+1),2)+2,2],[0,-0.5]]"
df5 = Diff(f5, [x, y])
assert str(df5) == "[[-3*6*Pow((2*x+1),2)+2,2],[0,-0.5]]"
assert_allclose(df5.eval(x=3, y=10).tonumeric(), [[-880.0, 2.0], [0.0, -0.5]])
# FIXME: segmentation fault!
# assert_allclose(df5.eval(x=3,y=10).fromvector(0), [-880.0,2.0])
assert str(df5.eval(x=3, y=10).fromvector(0)) == "[-880.0,2]"
assert str(df5.fromvector(0)) == "[-3*6*Pow((2*x+1),2)+2,2]"
assert isinstance(df5.fromvector(), list)
a = df5.fromvector(0).eval(x=3, y=10).tonumeric()
b = df5.eval(x=3, y=10).tonumeric()[0]
assert a[0] == b[0] and a[1] == b[1]
def test_symbolic_vector():
# XXX: doesn't work without global
global q0, q1
p0 = Var('p0')
q0 = Var(p0 + 3, 'q0')
q1 = Var(Diff(1 + Sin(Pow(p0, 3) + q0), p0), 'q1')
qv = Var([q0, q1], 'q')
assert str(qv()) == '[q0,q1]'
assert str(qv.eval()) == '[(p0+3),(3*Pow(p0,2)*Cos(Pow(p0,3)+(p0+3)))]'
v = Var('v')
w = Var('w')
f = Var([-3 * Pow((2 * v + 1), 3) + 2 * (w + v), -w / 2], 'f')
df = Diff(f, [v, w])
assert str(df) == '[[-3*6*Pow((2*v+1),2)+2,2],[0,-0.5]]'
dfe = df.eval(v=3, w=10).tonumeric()
assert_allclose(dfe, [[-880.0, 2.0], [0.0, -0.5]])
assert isinstance(dfe, ndarray)
assert isinstance(df.fromvector(), list)
y0 = Var('y0')
y1 = Var('y1')
y2 = Var('y2')
t = Var('t')
ydot0 = Fun(-0.04 * y0 + 1e4 * y1 * y2, [y0, y1, y2], 'ydot0')
ydot2 = Fun(3e7 * y1 * y1, [y0, y1, y2], 'ydot2')
ydot1 = Fun(-ydot0(y0, y1, y2) - ydot2(y0, y1, y2), [y0, y1, y2], 'ydot1')
F = Fun([ydot0(y0, y1, y2),
ydot1(y0, y1, y2),
ydot2(y0, y1, y2)], [y0, y1, y2], 'F')
assert F.dim == 3
DF = Diff(F, [y0, y1, y2])
DF0, DF1, DF2 = DF.fromvector()
assert_approx_equal(DF0.fromvector()[0].tonumeric(), -0.04)
# str(Diff(F,[y0,y1,y2])) should be (to within numerical rounding errors):
# '[[-0.04,10000*y2,10000*y1],[0.040000000000000001,(-10000*y2)-30000000*2*y1,-10000*y1],[0,30000000*2*y1,0]]')
jac = Fun(Diff(F, [y0, y1, y2]), [t, y0, y1, y2], 'Jacobian')
assert jac(t, 0.1, y0 + 1, 0.5).eval(y0=0) == jac(t, 0.1, 1 + y0,
0.5).eval(y0=0)
assert jac(t, 0.1, y0, 0.5) == jac(t, 0.1, 0 + y0, 0.5)
x = Var('x')
y = Var('y')
f1 = Fun([-3 * x**3 + 2 * (x + y), -y / 2], [x, y], 'f1')
f2 = ['-3*x**3+2*(x+y)', '-y/2']
f3 = [-3 * x**3. + 2 * (x + y), -y / 2.]
assert str(f1) == 'f1'
assert str(f2) == '[\'-3*x**3+2*(x+y)\', \'-y/2\']'
assert str(
f3
) == '[QuantSpec __result__ (ExpFuncSpec), QuantSpec __result__ (ExpFuncSpec)]'
f4 = [-3 * Pow((2 * x + 1), 3) + 2 * (x + y), -y / 2]
xx = QuantSpec('dummy', 'x')
f5 = Var([-3 * Pow((2 * x + 1), 3) + 2 * (x + y), -y / 2], 'f5')
assert Diff(f1, x) == Diff(f1, 'x')
assert str(Diff(f1, x)) == '[-3*3*Pow(x,2)+2,0]'
assert str(Diff(f3, x)) == '[-3*3*Pow(x,2)+2,0]'
assert str(Diff(f3, xx)) == '[-3*3*Pow(x,2)+2,0]'
assert str(Diff(f4, x)) == '[-3*6*Pow((2*x+1),2)+2,0]'
assert str(Diff(f4, xx)) == '[-3*6*Pow((2*x+1),2)+2,0]'
# Examples of Jacobian Diff(f, [x,y])...
assert Diff(f1, [x, y]) == Diff(f1, ['x', 'y']) == Diff(f1(x, y), [x, y])
assert str(Diff(f2, ['x', 'y'])) == '[[-3*3*Pow(x,2)+2,2],[0,-0.5]]'
assert str(Diff(f3, ['x', 'y'])) == '[[-3*3*Pow(x,2)+2,2],[0,-0.5]]'
assert str(Diff(f1, [xx, y])) == '[[-3*3*Pow(x,2)+2,2],[0,-0.5]]'
assert str(Diff(f1, [xx, 'y'])) == '[[-3*3*Pow(x,2)+2,2],[0,-0.5]]'
assert str(Diff(f2, [x, y])) == '[[-3*3*Pow(x,2)+2,2],[0,-0.5]]'
assert str(Diff(f3, [x, y])) == '[[-3*3*Pow(x,2)+2,2],[0,-0.5]]'
assert str(Diff(f4, [x, y])) == '[[-3*6*Pow((2*x+1),2)+2,2],[0,-0.5]]'
df5 = Diff(f5, [x, y])
assert str(df5) == '[[-3*6*Pow((2*x+1),2)+2,2],[0,-0.5]]'
assert_allclose(
df5.eval(x=3, y=10).tonumeric(), [[-880.0, 2.0], [0.0, -0.5]])
# FIXME: segmentation fault!
# assert_allclose(df5.eval(x=3,y=10).fromvector(0), [-880.0,2.0])
assert str(df5.eval(x=3, y=10).fromvector(0)) == '[-880.0,2]'
assert str(df5.fromvector(0)) == '[-3*6*Pow((2*x+1),2)+2,2]'
assert isinstance(df5.fromvector(), list)
a = df5.fromvector(0).eval(x=3, y=10).tonumeric()
b = df5.eval(x=3, y=10).tonumeric()[0]
assert a[0] == b[0] and a[1] == b[1]