def equal(self):
"""
Test of __eq__ operators
"""
a1 = myokit.Number(4)
a2 = myokit.Number(5)
self.assertEqual(a1, a1)
self.assertEqual(a1, myokit.Number(4))
self.assertEqual(a1, myokit.Number(4.0))
self.assertNotEqual(a1, a2)
b1 = myokit.Name('test')
b2 = myokit.Name('tost')
self.assertEqual(b1, b1)
self.assertNotEqual(b1, b2)
c1 = myokit.PrefixPlus(a1)
c2 = myokit.PrefixPlus(a1)
self.assertEqual(c1, c1)
self.assertEqual(c1, c2)
c2 = myokit.PrefixPlus(a2)
self.assertNotEqual(c1, c2)
d1 = myokit.Plus(a1, a2)
d2 = myokit.Plus(a1, a2)
self.assertEqual(d1, d1)
self.assertEqual(d1, d2)
d2 = myokit.Plus(a2, a1)
self.assertNotEqual(d2, d1)
e1 = myokit.Sqrt(a1)
e2 = myokit.Sqrt(a1)
self.assertEqual(e1, e1)
self.assertEqual(e1, e2)
e2 = myokit.Sqrt(a2)
self.assertNotEqual(e1, e2)
def _add_dose_compartment(model, drug_amount, time_unit):
"""
Adds a dose compartment to the model with a linear absorption rate to
the connected compartment.
"""
# Add a dose compartment to the model
dose_comp = model.add_component_allow_renaming('dose')
# Create a state variable for the drug amount in the dose compartment
dose_drug_amount = dose_comp.add_variable('drug_amount')
dose_drug_amount.set_rhs(0)
dose_drug_amount.set_unit(drug_amount.unit())
dose_drug_amount.promote()
# Create an absorption rate variable
absorption_rate = dose_comp.add_variable('absorption_rate')
absorption_rate.set_rhs(1)
absorption_rate.set_unit(1 / time_unit)
# Add outflow expression to dose compartment
dose_drug_amount.set_rhs(
myokit.Multiply(myokit.PrefixMinus(myokit.Name(absorption_rate)),
myokit.Name(dose_drug_amount)))
# Add inflow expression to connected compartment
rhs = drug_amount.rhs()
drug_amount.set_rhs(
myokit.Plus(
rhs,
myokit.Multiply(myokit.Name(absorption_rate),
myokit.Name(dose_drug_amount))))
return dose_drug_amount
def test_arithmetic(self):
# Test basic arithmetic
a = myokit.Name(self.avar)
b = myokit.Number('12', 'pF')
ca = '<ci>a</ci>'
cb = ('<cn cellml:units="picofarad">12.0</cn>')
# Prefix plus
x = myokit.PrefixPlus(b)
self.assertWrite(x, '<apply><plus/>' + cb + '</apply>')
# Prefix minus
x = myokit.PrefixMinus(b)
self.assertWrite(x, '<apply><minus/>' + cb + '</apply>')
# Plus
x = myokit.Plus(a, b)
self.assertWrite(x, '<apply><plus/>' + ca + cb + '</apply>')
# Minus
x = myokit.Minus(a, b)
self.assertWrite(x, '<apply><minus/>' + ca + cb + '</apply>')
# Multiply
x = myokit.Multiply(a, b)
self.assertWrite(x, '<apply><times/>' + ca + cb + '</apply>')
# Divide
x = myokit.Divide(a, b)
self.assertWrite(x, '<apply><divide/>' + ca + cb + '</apply>')
def create_dimless_tumour_growth_model():
r"""
Returns a tumour growth myokit model.
.. math::
\frac{\text{d}v}{\text{d}\tau} = \frac{a_1 v}
{v + a_0},
where the tumour volume :math:`v` and time :math:`\tau` are dimensionless
and measured in characteristic scales :math:`V^c_T` and :math:`t^c`.
The model parameters :math:`a_0` and :math:`a_1` are also dimensionless.
"""
# Instantiate model
model = Model()
# Add central compartment
central_comp = model.add_compartment('central')
# Add tumour growth variables to central compartment
volume_t = central_comp.add_variable('volume_t')
a_0 = central_comp.add_variable('a_0')
a_1 = central_comp.add_variable('a_1')
# Bind time
time = central_comp.add_variable('time')
time.set_binding('time')
# Set intial values (some default values) and units
time.set_rhs(0)
volume_t.set_rhs(0)
a_0.set_rhs(1) # Avoid ZeroDivisionError
a_1.set_rhs(0)
# Set units
time.set_unit('dimensionless')
volume_t.set_unit('dimensionless')
a_0.set_unit('dimensionless')
a_1.set_unit('dimensionless')
# Set rhs of tumor volume
# dot(volume_t) =
# (a_1 * volume_t) /
# (volume_t + a_0)
volume_t.promote()
volume_t.set_rhs(
myokit.Divide(myokit.Multiply(myokit.Name(a_1), myokit.Name(volume_t)),
myokit.Plus(myokit.Name(volume_t), myokit.Name(a_0))))
# Validate model
model.validate()
# Check units
model.check_units()
return model
def _test_maths(self, version):
# Test maths is written (in selected ``version``)
# Create model
m1 = cellml.Model('m', version)
c1 = m1.add_component('c')
p1 = c1.add_variable('p', 'mole')
p1.set_initial_value(2)
q1 = c1.add_variable('q', 'dimensionless')
r1 = c1.add_variable('r', 'second')
r1.set_initial_value(0.1)
t1 = c1.add_variable('t', 'second')
m1.set_variable_of_integration(t1)
# Add component without maths
d1 = m1.add_component('d')
s1 = d1.add_variable('s', 'volt')
s1.set_initial_value(1.23)
# Add two equations
# Note: Numbers without units become dimensionless in CellML
eq1 = myokit.Equation(
myokit.Name(q1),
myokit.Plus(myokit.Number(3, myokit.units.mole), myokit.Name(p1)))
er1 = myokit.Equation(myokit.Derivative(myokit.Name(r1)),
myokit.Power(myokit.Name(q1), myokit.Number(2)))
q1.set_equation(eq1)
r1.set_equation(er1)
# Write and read
xml = cellml.write_string(m1)
m2 = cellml.parse_string(xml)
# Check results
p2, q2, r2, s2 = m2['c']['p'], m2['c']['q'], m2['c']['r'], m2['d']['s']
subst = {
myokit.Name(p1): myokit.Name(p2),
myokit.Name(q1): myokit.Name(q2),
myokit.Name(r1): myokit.Name(r2),
}
eq2 = eq1.clone(subst)
er2 = er1.clone(subst)
self.assertEqual(q2.equation(), eq2)
self.assertEqual(r2.equation(), er2)
self.assertEqual(s2.initial_value(),
myokit.Number(1.23, myokit.units.volt))
self.assertFalse(p2.is_state())
self.assertFalse(q2.is_state())
self.assertTrue(r2.is_state())
self.assertFalse(s2.is_state())
self.assertIs(m2.variable_of_integration(), m2['c']['t'])
def _add_dose_rate(compartment, drug_amount, time_unit):
"""
Adds a dose rate variable to the state variable, which is bound to the
dosing regimen.
"""
# Register a dose rate variable to the compartment and bind it to
# pace, i.e. tell myokit that its value is set by the dosing regimen/
# myokit.Protocol
compartment = drug_amount.parent()
dose_rate = compartment.add_variable_allow_renaming(str('dose_rate'))
dose_rate.set_binding('pace')
# Set initial value to 0 and unit to unit of drug amount over unit of
# time
dose_rate.set_rhs(0)
dose_rate.set_unit(drug_amount.unit() / time_unit)
# Add the dose rate to the rhs of the drug amount variable
rhs = drug_amount.rhs()
drug_amount.set_rhs(myokit.Plus(rhs, myokit.Name(dose_rate)))
def test_arithmetic_binary(self):
# Tests parsing prefix operators
# Plus
a = myokit.Name('a')
b = myokit.Number(1.0)
e = myokit.Plus(a, b)
x = '<apply><plus/><ci>a</ci><cn>1.0</cn></apply>'
self.assertEqual(self.p(x), e)
# Minus
e = myokit.Minus(a, b)
x = '<apply><minus/><ci>a</ci><cn>1.0</cn></apply>'
self.assertEqual(self.p(x), e)
# Multiply
e = myokit.Multiply(a, b)
x = '<apply><times/><ci>a</ci><cn>1.0</cn></apply>'
self.assertEqual(self.p(x), e)
# Divide
e = myokit.Divide(a, b)
x = '<apply><divide/><ci>a</ci><cn>1.0</cn></apply>'
self.assertEqual(self.p(x), e)
# No operands
self.assertRaisesRegex(
mathml.MathMLError, 'at least one operand', self.p,
'<apply><times/></apply>')
# Only one operand
self.assertRaisesRegex(
mathml.MathMLError, 'at least two operands', self.p,
'<apply><times/><cn>1.0</cn></apply>')
# Several operands
e = myokit.Multiply(
myokit.Multiply(myokit.Multiply(a, b), myokit.Number(2)),
myokit.Number(3))
x = '<apply><times/><ci>a</ci><cn>1</cn><cn>2</cn><cn>3</cn></apply>'
self.assertEqual(self.p(x), e)
def test_arithmetic_binary(self):
# Tests writing basic arithmetic operators
a = myokit.Name(self.avar)
b = myokit.Number('12', 'pF')
ca = '<mi>c.a</mi>'
cb = '<mn>12.0</mn>'
# Plus
x = myokit.Plus(a, b)
self.assertWrite(x, '<mrow>' + ca + '<mo>+</mo>' + cb + '</mrow>')
# Minus
x = myokit.Minus(a, b)
self.assertWrite(x, '<mrow>' + ca + '<mo>-</mo>' + cb + '</mrow>')
# Multiply
x = myokit.Multiply(a, b)
self.assertWrite(x, '<mrow>' + ca + '<mo>*</mo>' + cb + '</mrow>')
# Divide
x = myokit.Divide(a, b)
self.assertWrite(x, '<mfrac>' + ca + cb + '</mfrac>')
def test_arithmetic_binary(self):
# Tests writing basic arithmetic operators
# Plus
a = myokit.Name('a')
b = myokit.Number(1)
e = myokit.Plus(a, b)
x = '<apply><plus/><ci>a</ci><cn>1.0</cn></apply>'
self.assertWrite(e, x)
# Minus
e = myokit.Minus(a, b)
x = '<apply><minus/><ci>a</ci><cn>1.0</cn></apply>'
self.assertWrite(e, x)
# Multiply
e = myokit.Multiply(a, b)
x = '<apply><times/><ci>a</ci><cn>1.0</cn></apply>'
self.assertWrite(e, x)
# Divide
e = myokit.Divide(a, b)
x = '<apply><divide/><ci>a</ci><cn>1.0</cn></apply>'
self.assertWrite(e, x)
def test_move_variable(self):
# Test the method to move component variables to another component.
# Create a model
m = myokit.Model('LotkaVolterra')
X = m.add_component('X')
a = X.add_variable('a')
a.set_rhs(3)
b = X.add_variable('b')
b1 = b.add_variable('b1')
b2 = b.add_variable('b2')
b1.set_rhs(1)
b2.set_rhs(
myokit.Minus(myokit.Minus(myokit.Name(a), myokit.Name(b1)),
myokit.Number(1)))
b.set_rhs(myokit.Plus(myokit.Name(b1), myokit.Name(b2)))
x = X.add_variable('x')
x.promote()
Y = m.add_component('Y')
c = Y.add_variable('c')
c.set_rhs(myokit.Minus(myokit.Name(a), myokit.Number(1)))
d = Y.add_variable('d')
d.set_rhs(2)
y = Y.add_variable('y')
y.promote()
x.set_rhs(
myokit.Minus(
myokit.Multiply(myokit.Name(a), myokit.Name(x)),
myokit.Multiply(
myokit.Multiply(myokit.Name(b), myokit.Name(x)),
myokit.Name(y))))
x.set_state_value(10)
y.set_rhs(
myokit.Plus(
myokit.Multiply(myokit.PrefixMinus(myokit.Name(c)),
myokit.Name(y)),
myokit.Multiply(
myokit.Multiply(myokit.Name(d), myokit.Name(x)),
myokit.Name(y))))
y.set_state_value(5)
Z = m.add_component('Z')
t = Z.add_variable('total')
t.set_rhs(myokit.Plus(myokit.Name(x), myokit.Name(y)))
E = m.add_component('engine')
time = E.add_variable('time')
time.set_rhs(0)
time.set_binding('time')
# Move time variable into X
m.validate() # If not valid, this will raise an exception
E.move_variable(time, Z)
m.validate()
# Can't do it a second time
self.assertRaises(ValueError, E.move_variable, time, Z)
# Move to self
Z.move_variable(time, Z)
m.validate()
Z.move_variable(time, Z)
m.validate()
# Duplicate variable name
E.add_variable('time')
self.assertRaises(myokit.DuplicateName, Z.move_variable, time, E)
# Create a nested variable by moving
m = myokit.Model()
c = m.add_component('c')
v = c.add_variable('v')
w = c.add_variable('w')
self.assertFalse(w.is_nested())
c.move_variable(w, v)
self.assertTrue(w.is_nested())
v.move_variable(w, c)
self.assertFalse(w.is_nested())
# State variables can't be made nested
w.promote(0)
self.assertRaisesRegex(Exception, 'State variables', c.move_variable,
w, v)
def test_model_creation(self):
# Create a model
m = myokit.Model('LotkaVolterra')
# Add the first component
X = m.add_component('X')
self.assertEqual(X.qname(), 'X')
self.assertEqual(X.parent(), m)
self.assertIsInstance(X, myokit.Component)
self.assertIn(X.qname(), m)
self.assertEqual(len(m), 1)
# Add variable a
self.assertFalse(X.has_variable('a'))
a = X.add_variable('a')
self.assertTrue(X.has_variable('a'))
self.assertEqual(a, a)
self.assertIsInstance(a, myokit.Variable)
self.assertEqual(len(X), 1)
self.assertIn(a.name(), X)
a.set_rhs(3)
self.assertFalse(a.is_state())
self.assertFalse(a.is_intermediary())
self.assertTrue(a.is_constant())
self.assertEqual(a.lhs(), myokit.Name(a))
self.assertEqual(a.rhs(), myokit.Number(3))
self.assertEqual(a.rhs().eval(), 3)
self.assertEqual(a.code(), 'a = 3\n')
self.assertEqual(a.eq().code(), 'X.a = 3')
self.assertEqual(a.lhs().code(), 'X.a')
self.assertEqual(a.rhs().code(), '3')
self.assertEqual(
a.eq(), myokit.Equation(myokit.Name(a), myokit.Number(3)))
# Check lhs
a_name1 = myokit.Name(a)
a_name2 = myokit.Name(a)
self.assertEqual(a_name1, a_name1)
self.assertEqual(a_name2, a_name2)
self.assertEqual(a_name1, a_name2)
self.assertEqual(a_name2, a_name1)
# Add variable b with two temporary variables
b = X.add_variable('b')
self.assertIsInstance(b, myokit.Variable)
self.assertEqual(len(X), 2)
self.assertIn(b.name(), X)
self.assertFalse(b.has_variable('b1'))
b1 = b.add_variable('b1')
self.assertTrue(b.has_variable('b1'))
self.assertEqual(len(b), 1)
self.assertIn(b1.name(), b)
self.assertIsInstance(b1, myokit.Variable)
b2 = b.add_variable('b2')
self.assertEqual(len(b), 2)
self.assertIn(b2.name(), b)
self.assertIsInstance(b2, myokit.Variable)
b1.set_rhs(1)
b2.set_rhs(
myokit.Minus(
myokit.Minus(myokit.Name(a), myokit.Name(b1)),
myokit.Number(1))
)
b.set_rhs(myokit.Plus(myokit.Name(b1), myokit.Name(b2)))
self.assertEqual(b.rhs().eval(), 2)
self.assertFalse(b.is_state())
self.assertFalse(b.is_intermediary())
self.assertTrue(b.is_constant())
self.assertEqual(b.lhs(), myokit.Name(b))
# Add state variable x
x = X.add_variable('x')
x.set_rhs(10)
x.promote()
self.assertNotEqual(x, X)
self.assertIsInstance(x, myokit.Variable)
self.assertEqual(len(X), 3)
self.assertIn(x.name(), X)
self.assertTrue(x.is_state())
self.assertFalse(x.is_intermediary())
self.assertFalse(x.is_constant())
self.assertEqual(x.lhs(), myokit.Derivative(myokit.Name(x)))
self.assertEqual(x.indice(), 0)
# Test demoting, promoting
x.demote()
self.assertFalse(x.is_state())
self.assertFalse(x.is_intermediary())
self.assertTrue(x.is_constant())
self.assertEqual(x.lhs(), myokit.Name(x))
x.promote()
self.assertTrue(x.is_state())
self.assertFalse(x.is_intermediary())
self.assertFalse(x.is_constant())
self.assertEqual(x.lhs(), myokit.Derivative(myokit.Name(x)))
x.demote()
x.promote()
x.demote()
x.promote()
self.assertTrue(x.is_state())
self.assertFalse(x.is_intermediary())
self.assertFalse(x.is_constant())
self.assertEqual(x.lhs(), myokit.Derivative(myokit.Name(x)))
# Add second component, variables
Y = m.add_component('Y')
self.assertNotEqual(X, Y)
self.assertEqual(len(m), 2)
c = Y.add_variable('c')
c.set_rhs(myokit.Minus(myokit.Name(a), myokit.Number(1)))
d = Y.add_variable('d')
d.set_rhs(2)
y = Y.add_variable('y')
y.promote()
# Set rhs for x and y
x.set_rhs(myokit.Minus(
myokit.Multiply(myokit.Name(a), myokit.Name(x)),
myokit.Multiply(
myokit.Multiply(myokit.Name(b), myokit.Name(x)),
myokit.Name(y)
)
))
x.set_state_value(10)
self.assertEqual(x.rhs().code(), 'X.a * X.x - X.b * X.x * Y.y')
y.set_rhs(myokit.Plus(
myokit.Multiply(
myokit.PrefixMinus(myokit.Name(c)), myokit.Name(y)
),
myokit.Multiply(
myokit.Multiply(myokit.Name(d), myokit.Name(x)),
myokit.Name(y)
)
))
y.set_state_value(5)
self.assertEqual(y.rhs().code(), '-Y.c * Y.y + Y.d * X.x * Y.y')
# Add ano component, variables
Z = m.add_component('Z')
self.assertNotEqual(X, Z)
self.assertNotEqual(Y, Z)
self.assertEqual(len(m), 3)
t = Z.add_variable('total')
self.assertEqual(t.name(), 'total')
self.assertEqual(t.qname(), 'Z.total')
self.assertEqual(t.qname(X), 'Z.total')
self.assertEqual(t.qname(Z), 'total')
t.set_rhs(myokit.Plus(myokit.Name(x), myokit.Name(y)))
self.assertFalse(t.is_state())
self.assertFalse(t.is_constant())
self.assertTrue(t.is_intermediary())
self.assertEqual(t.rhs().code(), 'X.x + Y.y')
self.assertEqual(t.rhs().code(X), 'x + Y.y')
self.assertEqual(t.rhs().code(Y), 'X.x + y')
self.assertEqual(t.rhs().code(Z), 'X.x + Y.y')
# Add engine component
E = m.add_component('engine')
self.assertNotEqual(X, E)
self.assertNotEqual(Y, E)
self.assertNotEqual(Z, E)
self.assertEqual(len(m), 4)
time = E.add_variable('time')
time.set_rhs(0)
self.assertIsNone(time.binding())
time.set_binding('time')
self.assertIsNotNone(time.binding())
# Check state
state = [i for i in m.states()]
self.assertEqual(len(state), 2)
self.assertIn(x, state)
self.assertIn(y, state)
# Test variable iterators
def has(*v):
for var in v:
self.assertIn(var, vrs)
self.assertEqual(len(vrs), len(v))
vrs = [i for i in m.variables()]
has(a, b, c, d, x, y, t, time)
vrs = [i for i in m.variables(deep=True)]
has(a, b, c, d, x, y, t, b1, b2, time)
vrs = [i for i in m.variables(const=True)]
has(a, b, c, d)
vrs = [i for i in m.variables(const=True, deep=True)]
has(a, b, c, d, b1, b2)
vrs = [i for i in m.variables(const=False)]
has(x, y, t, time)
vrs = [i for i in m.variables(const=False, deep=True)]
has(x, y, t, time)
vrs = [i for i in m.variables(state=True)]
has(x, y)
vrs = [i for i in m.variables(state=True, deep=True)]
has(x, y)
vrs = [i for i in m.variables(state=False)]
has(a, b, c, d, t, time)
vrs = [i for i in m.variables(state=False, deep=True)]
has(a, b, c, d, t, b1, b2, time)
vrs = [i for i in m.variables(inter=True)]
has(t)
vrs = [i for i in m.variables(inter=True, deep=True)]
has(t)
vrs = [i for i in m.variables(inter=False)]
has(a, b, c, d, x, y, time)
vrs = [i for i in m.variables(inter=False, deep=True)]
has(a, b, c, d, x, y, b1, b2, time)
vrs = list(m.variables(const=True, state=True))
has()
vrs = list(m.variables(const=True, state=False))
has(a, b, c, d)
# Test sorted variable iteration
names = [v.name() for v in m.variables(deep=True, sort=True)]
self.assertEqual(names, [
'a', 'b', 'b1', 'b2', 'x', 'c', 'd', 'y', 'total', 'time'])
# Test equation iteration
# Deeper testing is done when testing the ``variables`` method.
eq = [eq for eq in X.equations(deep=False)]
self.assertEqual(len(eq), 3)
self.assertEqual(len(eq), X.count_equations(deep=False))
eq = [eq for eq in X.equations(deep=True)]
self.assertEqual(len(eq), 5)
self.assertEqual(len(eq), X.count_equations(deep=True))
eq = [eq for eq in Y.equations(deep=False)]
self.assertEqual(len(eq), 3)
self.assertEqual(len(eq), Y.count_equations(deep=False))
eq = [eq for eq in Y.equations(deep=True)]
self.assertEqual(len(eq), 3)
self.assertEqual(len(eq), Y.count_equations(deep=True))
eq = [eq for eq in Z.equations(deep=False)]
self.assertEqual(len(eq), 1)
self.assertEqual(len(eq), Z.count_equations(deep=False))
eq = [eq for eq in Z.equations(deep=True)]
self.assertEqual(len(eq), 1)
self.assertEqual(len(eq), Z.count_equations(deep=True))
eq = [eq for eq in E.equations(deep=False)]
self.assertEqual(len(eq), 1)
eq = [eq for eq in E.equations(deep=True)]
self.assertEqual(len(eq), 1)
eq = [eq for eq in m.equations(deep=False)]
self.assertEqual(len(eq), 8)
eq = [eq for eq in m.equations(deep=True)]
self.assertEqual(len(eq), 10)
# Test dependency mapping
def has(var, *dps):
lst = vrs[m.get(var).lhs() if isinstance(var, basestring) else var]
self.assertEqual(len(lst), len(dps))
for d in dps:
d = m.get(d).lhs() if isinstance(d, basestring) else d
self.assertIn(d, lst)
vrs = m.map_shallow_dependencies(omit_states=False)
self.assertEqual(len(vrs), 12)
has('X.a')
has('X.b', 'X.b.b1', 'X.b.b2')
has('X.b.b1')
has('X.b.b2', 'X.a', 'X.b.b1')
has('X.x', 'X.a', 'X.b', myokit.Name(x), myokit.Name(y))
has(myokit.Name(x))
has('Y.c', 'X.a')
has('Y.d')
has('Y.y', 'Y.c', 'Y.d', myokit.Name(x), myokit.Name(y))
has(myokit.Name(y))
has('Z.total', myokit.Name(x), myokit.Name(y))
vrs = m.map_shallow_dependencies()
self.assertEqual(len(vrs), 10)
has('X.a')
has('X.b', 'X.b.b1', 'X.b.b2')
has('X.b.b1')
has('X.b.b2', 'X.a', 'X.b.b1')
has('X.x', 'X.a', 'X.b')
has('Y.c', 'X.a')
has('Y.d')
has('Y.y', 'Y.c', 'Y.d')
has('Z.total')
vrs = m.map_shallow_dependencies(collapse=True)
self.assertEqual(len(vrs), 8)
has('X.a')
has('X.b', 'X.a')
has('X.x', 'X.a', 'X.b')
has('Y.c', 'X.a')
has('Y.d')
has('Y.y', 'Y.c', 'Y.d')
has('Z.total')
# Validate
m.validate()
# Get solvable order
order = m.solvable_order()
self.assertEqual(len(order), 5)
self.assertIn('*remaining*', order)
self.assertIn('X', order)
self.assertIn('Y', order)
self.assertIn('Z', order)
# Check that X comes before Y
pos = dict([(name, k) for k, name in enumerate(order)])
self.assertLess(pos['X'], pos['Y'])
self.assertEqual(pos['*remaining*'], 4)
# Check component equation lists
eqs = order['*remaining*']
self.assertEqual(len(eqs), 0)
eqs = order['Z']
self.assertEqual(len(eqs), 1)
self.assertEqual(eqs[0].code(), 'Z.total = X.x + Y.y')
eqs = order['Y']
self.assertEqual(len(eqs), 3)
self.assertEqual(
eqs[2].code(), 'dot(Y.y) = -Y.c * Y.y + Y.d * X.x * Y.y')
eqs = order['X']
self.assertEqual(len(eqs), 5)
self.assertEqual(eqs[0].code(), 'X.a = 3')
self.assertEqual(eqs[1].code(), 'b1 = 1')
self.assertEqual(eqs[2].code(), 'b2 = X.a - b1 - 1')
self.assertEqual(eqs[3].code(), 'X.b = b1 + b2')
# Test model export and cloning
code1 = m.code()
code2 = m.clone().code()
self.assertEqual(code1, code2)
def test_all(self):
w = myokit.formats.ewriter('easyml')
model = myokit.Model()
component = model.add_component('c')
avar = component.add_variable('a')
# Name
a = myokit.Name(avar)
self.assertEqual(w.ex(a), 'c.a')
# Number with unit
b = myokit.Number('12', 'pF')
self.assertEqual(w.ex(b), '12.0')
# Integer
c = myokit.Number(1)
self.assertEqual(w.ex(c), '1.0')
# Integer
# Prefix plus
x = myokit.PrefixPlus(b)
self.assertEqual(w.ex(x), '12.0')
# Prefix minus
x = myokit.PrefixMinus(b)
self.assertEqual(w.ex(x), '(-12.0)')
# Plus
x = myokit.Plus(a, b)
self.assertEqual(w.ex(x), 'c.a + 12.0')
# Minus
x = myokit.Minus(a, b)
self.assertEqual(w.ex(x), 'c.a - 12.0')
# Multiply
x = myokit.Multiply(a, b)
self.assertEqual(w.ex(x), 'c.a * 12.0')
# Divide
x = myokit.Divide(a, b)
self.assertEqual(w.ex(x), 'c.a / 12.0')
# Quotient
x = myokit.Quotient(a, b)
with WarningCollector() as c:
self.assertEqual(w.ex(x), 'floor(c.a / 12.0)')
# Remainder
x = myokit.Remainder(a, b)
with WarningCollector() as c:
self.assertEqual(w.ex(x), 'c.a - 12.0 * (floor(c.a / 12.0))')
# Power
x = myokit.Power(a, b)
self.assertEqual(w.ex(x), 'pow(c.a, 12.0)')
# Sqrt
x = myokit.Sqrt(b)
self.assertEqual(w.ex(x), 'sqrt(12.0)')
# Exp
x = myokit.Exp(a)
self.assertEqual(w.ex(x), 'exp(c.a)')
# Log(a)
x = myokit.Log(b)
self.assertEqual(w.ex(x), 'log(12.0)')
# Log(a, b)
x = myokit.Log(a, b)
self.assertEqual(w.ex(x), '(log(c.a) / log(12.0))')
# Log10
x = myokit.Log10(b)
self.assertEqual(w.ex(x), 'log10(12.0)')
# Sin
with WarningCollector() as c:
x = myokit.Sin(b)
self.assertEqual(w.ex(x), 'sin(12.0)')
# Cos
x = myokit.Cos(b)
self.assertEqual(w.ex(x), 'cos(12.0)')
# Tan
x = myokit.Tan(b)
self.assertEqual(w.ex(x), 'tan(12.0)')
# ASin
x = myokit.ASin(b)
self.assertEqual(w.ex(x), 'asin(12.0)')
# ACos
x = myokit.ACos(b)
self.assertEqual(w.ex(x), 'acos(12.0)')
# ATan
x = myokit.ATan(b)
self.assertEqual(w.ex(x), 'atan(12.0)')
with WarningCollector() as c:
# Floor
x = myokit.Floor(b)
self.assertEqual(w.ex(x), 'floor(12.0)')
# Ceil
x = myokit.Ceil(b)
self.assertEqual(w.ex(x), 'ceil(12.0)')
# Abs
x = myokit.Abs(b)
self.assertEqual(w.ex(x), 'fabs(12.0)')
# Equal
x = myokit.Equal(a, b)
self.assertEqual(w.ex(x), '(c.a == 12.0)')
# NotEqual
x = myokit.NotEqual(a, b)
self.assertEqual(w.ex(x), '(c.a != 12.0)')
# More
x = myokit.More(a, b)
self.assertEqual(w.ex(x), '(c.a > 12.0)')
# Less
x = myokit.Less(a, b)
self.assertEqual(w.ex(x), '(c.a < 12.0)')
# MoreEqual
x = myokit.MoreEqual(a, b)
self.assertEqual(w.ex(x), '(c.a >= 12.0)')
# LessEqual
x = myokit.LessEqual(a, b)
self.assertEqual(w.ex(x), '(c.a <= 12.0)')
# Not
cond1 = myokit.parse_expression('5 > 3')
cond2 = myokit.parse_expression('2 < 1')
x = myokit.Not(cond1)
self.assertEqual(w.ex(x), '!((5.0 > 3.0))')
# And
x = myokit.And(cond1, cond2)
self.assertEqual(w.ex(x), '((5.0 > 3.0) and (2.0 < 1.0))')
# Or
x = myokit.Or(cond1, cond2)
self.assertEqual(w.ex(x), '((5.0 > 3.0) or (2.0 < 1.0))')
# If
x = myokit.If(cond1, a, b)
self.assertEqual(w.ex(x), '((5.0 > 3.0) ? c.a : 12.0)')
# Piecewise
c = myokit.Number(1)
x = myokit.Piecewise(cond1, a, cond2, b, c)
self.assertEqual(w.ex(x),
'((5.0 > 3.0) ? c.a : ((2.0 < 1.0) ? 12.0 : 1.0))')
# Test without a Myokit expression
self.assertRaisesRegex(ValueError, 'Unknown expression type', w.ex, 7)
def model(self, E=-88, g=1, component='ikr', current='IKr'):
m = myokit.Model()
# Add time variable
ce = m.add_component('engine')
t = ce.add_variable('time')
t.set_rhs(0)
t.set_binding('time')
p = ce.add_variable('pace')
p.set_rhs(0)
p.set_binding('pace')
# Add membrane potential variable
cm = m.add_component('membrane')
v = cm.add_variable('V')
v.set_rhs(-80)#-80
v.set_label('membrane_potential')
# Add current component
cc = m.add_component(component)
cc.add_alias('V', v)
# Add parameters
i = 0
pvars = []
for rate in self.rates:
i += 1
p = cc.add_variable('p' + str(i))
p.set_rhs(rate.alpha)
pvars.append(p)
i += 1
p = cc.add_variable('p' + str(i))
p.set_rhs(rate.beta)
pvars.append(p)
i += 1
p = cc.add_variable('p' + str(i))
p.set_rhs(myokit.Number(g))
pvars.append(p)
# Add rates, store in map from names to variables
rvars = {}
for i, rate in enumerate(self.rates):
var = cc.add_variable(rate.name)
rvars[rate.name] = var
# Generate term a * exp(+-b * V)
alpha = myokit.Name(pvars[2 * i])
beta = myokit.Name(pvars[1 + 2 * i])
if not rate.positive:
beta = myokit.PrefixMinus(beta)
var.set_rhs(myokit.Multiply(
alpha, myokit.Exp(myokit.Multiply(beta, myokit.Name(v)))))
# Add reversal potential variable
e = cc.add_variable('E')
e.set_rhs(myokit.Number(E))
# Add maximum conductance variable
g = cc.add_variable('g')
g.set_rhs(myokit.Name(p))
# Create states, store in map from names to variables
svars = {}
for i, state in enumerate(self.states):
var = cc.add_variable(state.name)
if i==0: # Add initial condition of all probability in first state.
var.promote(1)
else:
var.promote(0)
svars[state.name] = var
# Set equations for states
for state in self.states:
incoming = []
outgoing = []
for edge in self.edges:
# Gather info
if state == edge.state_from:
# Edge from this state to other state
state2 = edge.state_to
rate_in = edge.backward_rate
rate_out = edge.forward_rate
mult_in = edge.backward_multiplier
mult_out = edge.forward_multiplier
elif state == edge.state_to:
# Edge from other state to this state
state2 = edge.state_from
rate_in = edge.forward_rate
rate_out = edge.backward_rate
mult_in = edge.forward_multiplier
mult_out = edge.backward_multiplier
else:
continue
# Add incoming term
term = myokit.Name(svars[state2.name])
term = myokit.Multiply(
myokit.Name(rvars[rate_in.name]), term)
if mult_in != 1:
term = myokit.Multiply(myokit.Number(mult_in), term)
incoming.append(term)
# Add outgoing term
term = myokit.Name(rvars[rate_out.name])
if mult_out != 1:
term = myokit.Multiply(myokit.Number(mult_out), term)
outgoing.append(term)
# Start with outgoing terms (grouped)
outgoing = iter(outgoing)
rhs = next(outgoing)
for term in outgoing:
rhs = myokit.Plus(rhs, term)
rhs = myokit.PrefixMinus(rhs)
rhs = myokit.Multiply(rhs, myokit.Name(svars[state.name]))
# Add incoming terms (one by one)
incoming = iter(incoming)
for term in incoming:
rhs = myokit.Plus(rhs, term)
# Set rhs
svars[state.name].set_rhs(rhs)
# Add current variable
var = cc.add_variable(current)
rhs = myokit.Name(g)
for state in self.states:
if state.conducting:
rhs = myokit.Multiply(rhs, myokit.Name(svars[state.name]))
rhs = myokit.Multiply(
rhs, myokit.Minus(myokit.Name(v), myokit.Name(e)))
var.set_rhs(rhs)
print(m.code())
return m
def test_all(self):
w = myokit.formats.matlab.MatlabExpressionWriter()
model = myokit.Model()
component = model.add_component('c')
avar = component.add_variable('a')
# Name
a = myokit.Name(avar)
self.assertEqual(w.ex(a), 'c.a')
# Number with unit
b = myokit.Number('12', 'pF')
self.assertEqual(w.ex(b), '12.0')
# Prefix plus
x = myokit.PrefixPlus(b)
self.assertEqual(w.ex(x), '12.0')
# Prefix minus
x = myokit.PrefixMinus(b)
self.assertEqual(w.ex(x), '(-12.0)')
# Plus
x = myokit.Plus(a, b)
self.assertEqual(w.ex(x), 'c.a + 12.0')
# Minus
x = myokit.Minus(a, b)
self.assertEqual(w.ex(x), 'c.a - 12.0')
# Multiply
x = myokit.Multiply(a, b)
self.assertEqual(w.ex(x), 'c.a * 12.0')
# Divide
x = myokit.Divide(a, b)
self.assertEqual(w.ex(x), 'c.a / 12.0')
# Quotient
x = myokit.Quotient(a, b)
self.assertEqual(w.ex(x), 'floor(c.a / 12.0)')
# Remainder
x = myokit.Remainder(a, b)
self.assertEqual(w.ex(x), 'mod(c.a, 12.0)')
# Power
x = myokit.Power(a, b)
self.assertEqual(w.ex(x), 'c.a ^ 12.0')
# Sqrt
x = myokit.Sqrt(b)
self.assertEqual(w.ex(x), 'sqrt(12.0)')
# Exp
x = myokit.Exp(a)
self.assertEqual(w.ex(x), 'exp(c.a)')
# Log(a)
x = myokit.Log(b)
self.assertEqual(w.ex(x), 'log(12.0)')
# Log(a, b)
x = myokit.Log(a, b)
self.assertEqual(w.ex(x), '(log(c.a) / log(12.0))')
# Log10
x = myokit.Log10(b)
self.assertEqual(w.ex(x), 'log10(12.0)')
# Sin
x = myokit.Sin(b)
self.assertEqual(w.ex(x), 'sin(12.0)')
# Cos
x = myokit.Cos(b)
self.assertEqual(w.ex(x), 'cos(12.0)')
# Tan
x = myokit.Tan(b)
self.assertEqual(w.ex(x), 'tan(12.0)')
# ASin
x = myokit.ASin(b)
self.assertEqual(w.ex(x), 'asin(12.0)')
# ACos
x = myokit.ACos(b)
self.assertEqual(w.ex(x), 'acos(12.0)')
# ATan
x = myokit.ATan(b)
self.assertEqual(w.ex(x), 'atan(12.0)')
# Floor
x = myokit.Floor(b)
self.assertEqual(w.ex(x), 'floor(12.0)')
# Ceil
x = myokit.Ceil(b)
self.assertEqual(w.ex(x), 'ceil(12.0)')
# Abs
x = myokit.Abs(b)
self.assertEqual(w.ex(x), 'abs(12.0)')
# Equal
x = myokit.Equal(a, b)
self.assertEqual(w.ex(x), '(c.a == 12.0)')
# NotEqual
x = myokit.NotEqual(a, b)
self.assertEqual(w.ex(x), '(c.a != 12.0)')
# More
x = myokit.More(a, b)
self.assertEqual(w.ex(x), '(c.a > 12.0)')
# Less
x = myokit.Less(a, b)
self.assertEqual(w.ex(x), '(c.a < 12.0)')
# MoreEqual
x = myokit.MoreEqual(a, b)
self.assertEqual(w.ex(x), '(c.a >= 12.0)')
# LessEqual
x = myokit.LessEqual(a, b)
self.assertEqual(w.ex(x), '(c.a <= 12.0)')
# Not
cond1 = myokit.parse_expression('5 > 3')
cond2 = myokit.parse_expression('2 < 1')
x = myokit.Not(cond1)
self.assertEqual(w.ex(x), '!((5.0 > 3.0))')
# And
x = myokit.And(cond1, cond2)
self.assertEqual(w.ex(x), '((5.0 > 3.0) && (2.0 < 1.0))')
# Or
x = myokit.Or(cond1, cond2)
self.assertEqual(w.ex(x), '((5.0 > 3.0) || (2.0 < 1.0))')
# If (custom function)
x = myokit.If(cond1, a, b)
self.assertEqual(w.ex(x), 'ifthenelse((5.0 > 3.0), c.a, 12.0)')
# Piecewise
c = myokit.Number(1)
x = myokit.Piecewise(cond1, a, cond2, b, c)
self.assertEqual(
w.ex(x),
'ifthenelse((5.0 > 3.0), c.a, ifthenelse((2.0 < 1.0), 12.0, 1.0))')
# Test fetching using ewriter method
w = myokit.formats.ewriter('matlab')
self.assertIsInstance(w, myokit.formats.matlab.MatlabExpressionWriter)
# Test without a Myokit expression
self.assertRaisesRegex(ValueError, 'Unknown expression type', w.ex, 7)
def test_all(self):
w = myokit.formats.python.PythonExpressionWriter()
model = myokit.Model()
component = model.add_component('c')
avar = component.add_variable('a')
# Name
a = myokit.Name(avar)
self.assertEqual(w.ex(a), 'c.a')
# Number with unit
b = myokit.Number('12', 'pF')
self.assertEqual(w.ex(b), '12.0')
# Prefix plus
x = myokit.PrefixPlus(b)
self.assertEqual(w.ex(x), '12.0')
# Prefix minus
x = myokit.PrefixMinus(b)
self.assertEqual(w.ex(x), '(-12.0)')
# Plus
x = myokit.Plus(a, b)
self.assertEqual(w.ex(x), 'c.a + 12.0')
# Minus
x = myokit.Minus(a, b)
self.assertEqual(w.ex(x), 'c.a - 12.0')
# Multiply
x = myokit.Multiply(a, b)
self.assertEqual(w.ex(x), 'c.a * 12.0')
# Divide
x = myokit.Divide(a, b)
self.assertEqual(w.ex(x), 'c.a / 12.0')
# Quotient
x = myokit.Quotient(a, b)
self.assertEqual(w.ex(x), 'c.a // 12.0')
# Remainder
x = myokit.Remainder(a, b)
self.assertEqual(w.ex(x), 'c.a % 12.0')
# Power
x = myokit.Power(a, b)
self.assertEqual(w.ex(x), 'c.a ** 12.0')
# Sqrt
x = myokit.Sqrt(b)
self.assertEqual(w.ex(x), 'math.sqrt(12.0)')
# Exp
x = myokit.Exp(a)
self.assertEqual(w.ex(x), 'math.exp(c.a)')
# Log(a)
x = myokit.Log(b)
self.assertEqual(w.ex(x), 'math.log(12.0)')
# Log(a, b)
x = myokit.Log(a, b)
self.assertEqual(w.ex(x), 'math.log(c.a, 12.0)')
# Log10
x = myokit.Log10(b)
self.assertEqual(w.ex(x), 'math.log10(12.0)')
# Sin
x = myokit.Sin(b)
self.assertEqual(w.ex(x), 'math.sin(12.0)')
# Cos
x = myokit.Cos(b)
self.assertEqual(w.ex(x), 'math.cos(12.0)')
# Tan
x = myokit.Tan(b)
self.assertEqual(w.ex(x), 'math.tan(12.0)')
# ASin
x = myokit.ASin(b)
self.assertEqual(w.ex(x), 'math.asin(12.0)')
# ACos
x = myokit.ACos(b)
self.assertEqual(w.ex(x), 'math.acos(12.0)')
# ATan
x = myokit.ATan(b)
self.assertEqual(w.ex(x), 'math.atan(12.0)')
# Floor
x = myokit.Floor(b)
self.assertEqual(w.ex(x), 'math.floor(12.0)')
# Ceil
x = myokit.Ceil(b)
self.assertEqual(w.ex(x), 'math.ceil(12.0)')
# Abs
x = myokit.Abs(b)
self.assertEqual(w.ex(x), 'abs(12.0)')
# Equal
x = myokit.Equal(a, b)
self.assertEqual(w.ex(x), '(c.a == 12.0)')
# NotEqual
x = myokit.NotEqual(a, b)
self.assertEqual(w.ex(x), '(c.a != 12.0)')
# More
x = myokit.More(a, b)
self.assertEqual(w.ex(x), '(c.a > 12.0)')
# Less
x = myokit.Less(a, b)
self.assertEqual(w.ex(x), '(c.a < 12.0)')
# MoreEqual
x = myokit.MoreEqual(a, b)
self.assertEqual(w.ex(x), '(c.a >= 12.0)')
# LessEqual
x = myokit.LessEqual(a, b)
self.assertEqual(w.ex(x), '(c.a <= 12.0)')
# Not
cond1 = myokit.parse_expression('5 > 3')
cond2 = myokit.parse_expression('2 < 1')
x = myokit.Not(cond1)
self.assertEqual(w.ex(x), 'not ((5.0 > 3.0))')
# And
x = myokit.And(cond1, cond2)
self.assertEqual(w.ex(x), '((5.0 > 3.0) and (2.0 < 1.0))')
# Or
x = myokit.Or(cond1, cond2)
self.assertEqual(w.ex(x), '((5.0 > 3.0) or (2.0 < 1.0))')
# If
x = myokit.If(cond1, a, b)
self.assertEqual(w.ex(x), '(c.a if (5.0 > 3.0) else 12.0)')
# Piecewise
c = myokit.Number(1)
x = myokit.Piecewise(cond1, a, cond2, b, c)
self.assertEqual(
w.ex(x),
'(c.a if (5.0 > 3.0) else (12.0 if (2.0 < 1.0) else 1.0))')
# Test fetching using ewriter method
w = myokit.formats.ewriter('python')
self.assertIsInstance(w, myokit.formats.python.PythonExpressionWriter)
# Test lhs method
w.set_lhs_function(lambda x: 'sheep')
self.assertEqual(w.ex(a), 'sheep')
# Test without a Myokit expression
self.assertRaisesRegex(ValueError, 'Unknown expression type', w.ex, 7)
def test_reader_writer(self):
# Test using the proper reader/writer
try:
import sympy as sp
except ImportError:
print('Sympy not found, skipping test.')
return
# Create writer and reader
w = mypy.SymPyExpressionWriter()
r = mypy.SymPyExpressionReader(self._model)
# Name
a = self._a
ca = sp.Symbol('c.a')
self.assertEqual(w.ex(a), ca)
self.assertEqual(r.ex(ca), a)
# Number with unit
b = myokit.Number('12', 'pF')
cb = sp.Float(12)
self.assertEqual(w.ex(b), cb)
# Note: Units are lost in sympy im/ex-port!
#self.assertEqual(r.ex(cb), b)
# Number without unit
b = myokit.Number('12')
cb = sp.Float(12)
self.assertEqual(w.ex(b), cb)
self.assertEqual(r.ex(cb), b)
# Prefix plus
x = myokit.PrefixPlus(b)
self.assertEqual(w.ex(x), cb)
# Note: Sympy doesn't seem to have a prefix plus
self.assertEqual(r.ex(cb), b)
# Prefix minus
# Note: SymPy treats -x as Mul(NegativeOne, x)
# But for numbers just returns a number with a negative value
x = myokit.PrefixMinus(b)
self.assertEqual(w.ex(x), -cb)
self.assertEqual(float(r.ex(-cb)), float(x))
# Plus
x = myokit.Plus(a, b)
self.assertEqual(w.ex(x), ca + cb)
# Note: SymPy likes to re-order the operands...
self.assertEqual(float(r.ex(ca + cb)), float(x))
# Minus
x = myokit.Minus(a, b)
self.assertEqual(w.ex(x), ca - cb)
self.assertEqual(float(r.ex(ca - cb)), float(x))
# Multiply
x = myokit.Multiply(a, b)
self.assertEqual(w.ex(x), ca * cb)
self.assertEqual(float(r.ex(ca * cb)), float(x))
# Divide
x = myokit.Divide(a, b)
self.assertEqual(w.ex(x), ca / cb)
self.assertEqual(float(r.ex(ca / cb)), float(x))
# Quotient
x = myokit.Quotient(a, b)
self.assertEqual(w.ex(x), ca // cb)
self.assertEqual(float(r.ex(ca // cb)), float(x))
# Remainder
x = myokit.Remainder(a, b)
self.assertEqual(w.ex(x), ca % cb)
self.assertEqual(float(r.ex(ca % cb)), float(x))
# Power
x = myokit.Power(a, b)
self.assertEqual(w.ex(x), ca**cb)
self.assertEqual(float(r.ex(ca**cb)), float(x))
# Sqrt
x = myokit.Sqrt(a)
cx = sp.sqrt(ca)
self.assertEqual(w.ex(x), cx)
# Note: SymPy converts sqrt to power
self.assertEqual(float(r.ex(cx)), float(x))
# Exp
x = myokit.Exp(a)
cx = sp.exp(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Log(a)
x = myokit.Log(a)
cx = sp.log(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Log(a, b)
x = myokit.Log(a, b)
cx = sp.log(ca, cb)
self.assertEqual(w.ex(x), cx)
self.assertEqual(float(r.ex(cx)), float(x))
# Log10
x = myokit.Log10(b)
cx = sp.log(cb, 10)
self.assertEqual(w.ex(x), cx)
self.assertAlmostEqual(float(r.ex(cx)), float(x))
# Sin
x = myokit.Sin(a)
cx = sp.sin(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Cos
x = myokit.Cos(a)
cx = sp.cos(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Tan
x = myokit.Tan(a)
cx = sp.tan(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# ASin
x = myokit.ASin(a)
cx = sp.asin(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# ACos
x = myokit.ACos(a)
cx = sp.acos(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# ATan
x = myokit.ATan(a)
cx = sp.atan(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Floor
x = myokit.Floor(a)
cx = sp.floor(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Ceil
x = myokit.Ceil(a)
cx = sp.ceiling(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Abs
x = myokit.Abs(a)
cx = sp.Abs(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Equal
x = myokit.Equal(a, b)
cx = sp.Eq(ca, cb)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# NotEqual
x = myokit.NotEqual(a, b)
cx = sp.Ne(ca, cb)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# More
x = myokit.More(a, b)
cx = sp.Gt(ca, cb)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Less
x = myokit.Less(a, b)
cx = sp.Lt(ca, cb)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# MoreEqual
x = myokit.MoreEqual(a, b)
cx = sp.Ge(ca, cb)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# LessEqual
x = myokit.LessEqual(a, b)
cx = sp.Le(ca, cb)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Not
x = myokit.Not(a)
cx = sp.Not(ca)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# And
cond1 = myokit.More(a, b)
cond2 = myokit.Less(a, b)
c1 = sp.Gt(ca, cb)
c2 = sp.Lt(ca, cb)
x = myokit.And(cond1, cond2)
cx = sp.And(c1, c2)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Or
x = myokit.Or(cond1, cond2)
cx = sp.Or(c1, c2)
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# If
# Note: sympy only does piecewise, not if
x = myokit.If(cond1, a, b)
cx = sp.Piecewise((ca, c1), (cb, True))
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x.piecewise())
# Piecewise
c = myokit.Number(1)
cc = sp.Float(1)
x = myokit.Piecewise(cond1, a, cond2, b, c)
cx = sp.Piecewise((ca, c1), (cb, c2), (cc, True))
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Myokit piecewise's (like CellML's) always have a final True
# condition (i.e. an 'else'). SymPy doesn't require this, so test if
# we can import this --> It will add an "else 0"
x = myokit.Piecewise(cond1, a, myokit.Number(0))
cx = sp.Piecewise((ca, c1))
self.assertEqual(r.ex(cx), x)
# SymPy function without Myokit equivalent --> Should raise exception
cu = sp.principal_branch(cx, cc)
self.assertRaisesRegex(ValueError, 'Unsupported type', r.ex, cu)
# Derivative
m = self._model.clone()
avar = m.get('c.a')
r = mypy.SymPyExpressionReader(self._model)
avar.promote(4)
x = myokit.Derivative(self._a)
cx = sp.symbols('dot(c.a)')
self.assertEqual(w.ex(x), cx)
self.assertEqual(r.ex(cx), x)
# Equation
e = myokit.Equation(a, b)
ce = sp.Eq(ca, cb)
self.assertEqual(w.eq(e), ce)
# There's no backwards equivalent for this!
# The ereader can handle it, but it becomes and Equals expression.
# Test sympy division
del (m, avar, x, cx, e, ce)
a = self._model.get('c.a')
b = self._model.get('c').add_variable('bbb')
b.set_rhs('1 / a')
e = b.rhs()
ce = w.ex(b.rhs())
e = r.ex(ce)
self.assertEqual(
e,
myokit.Multiply(myokit.Number(1),
myokit.Power(myokit.Name(a), myokit.Number(-1))))
# Test sympy negative numbers
a = self._model.get('c.a')
e1 = myokit.PrefixMinus(myokit.Name(a))
ce = w.ex(e1)
e2 = r.ex(ce)
self.assertEqual(e1, e2)
def test_all(self):
w = myokit.formats.latex.LatexExpressionWriter()
model = myokit.Model()
component = model.add_component('c')
avar = component.add_variable('a')
# Model needs to be validated --> sets unames
avar.set_rhs(12)
avar.set_binding('time')
model.validate()
# Name
a = myokit.Name(avar)
self.assertEqual(w.ex(a), '\\text{a}')
# Number with unit
b = myokit.Number('12', 'pF')
self.assertEqual(w.ex(b), '12.0')
# Prefix plus
x = myokit.PrefixPlus(b)
self.assertEqual(w.ex(x), '12.0')
# Prefix minus
x = myokit.PrefixMinus(b)
self.assertEqual(w.ex(x), '\\left(-12.0\\right)')
# Prefix minus with bracket
x = myokit.PrefixMinus(myokit.Plus(a, b))
self.assertEqual(w.ex(x),
'\\left(-\\left(\\text{a}+12.0\\right)\\right)')
# Plus
x = myokit.Plus(a, b)
self.assertEqual(w.ex(x), '\\text{a}+12.0')
# Minus
x = myokit.Minus(a, b)
self.assertEqual(w.ex(x), '\\text{a}-12.0')
# Multiply
x = myokit.Multiply(a, b)
self.assertEqual(w.ex(x), '\\text{a}*12.0')
# Divide
x = myokit.Divide(a, b)
self.assertEqual(w.ex(x), '\\frac{\\text{a}}{12.0}')
# Quotient
# Not supported in latex!
x = myokit.Quotient(a, b)
self.assertEqual(
w.ex(x), '\\left\\lfloor\\frac{\\text{a}}{12.0}\\right\\rfloor')
# Remainder
x = myokit.Remainder(a, b)
self.assertEqual(w.ex(x), '\\bmod\\left(\\text{a},12.0\\right)')
# Power
x = myokit.Power(a, b)
self.assertEqual(w.ex(x), '\\text{a}^{12.0}')
# Power with brackets
x = myokit.Power(myokit.Plus(a, b), b)
self.assertEqual(w.ex(x), '\\left(\\text{a}+12.0\\right)^{12.0}')
# Sqrt
x = myokit.Sqrt(b)
self.assertEqual(w.ex(x), '\\sqrt{12.0}')
# Exp
x = myokit.Exp(a)
self.assertEqual(w.ex(x), '\\exp\\left(\\text{a}\\right)')
# Log(a)
x = myokit.Log(b)
self.assertEqual(w.ex(x), '\\log\\left(12.0\\right)')
# Log(a, b)
x = myokit.Log(a, b)
self.assertEqual(w.ex(x), '\\log_{12.0}\\left(\\text{a}\\right)')
# Log10
x = myokit.Log10(b)
self.assertEqual(w.ex(x), '\\log_{10.0}\\left(12.0\\right)')
# Sin
x = myokit.Sin(b)
self.assertEqual(w.ex(x), '\\sin\\left(12.0\\right)')
# Cos
x = myokit.Cos(b)
self.assertEqual(w.ex(x), '\\cos\\left(12.0\\right)')
# Tan
x = myokit.Tan(b)
self.assertEqual(w.ex(x), '\\tan\\left(12.0\\right)')
# ASin
x = myokit.ASin(b)
self.assertEqual(w.ex(x), '\\arcsin\\left(12.0\\right)')
# ACos
x = myokit.ACos(b)
self.assertEqual(w.ex(x), '\\arccos\\left(12.0\\right)')
# ATan
x = myokit.ATan(b)
self.assertEqual(w.ex(x), '\\arctan\\left(12.0\\right)')
# Floor
x = myokit.Floor(b)
self.assertEqual(w.ex(x), '\\left\\lfloor{12.0}\\right\\rfloor')
# Ceil
x = myokit.Ceil(b)
self.assertEqual(w.ex(x), '\\left\\lceil{12.0}\\right\\rceil')
# Abs
x = myokit.Abs(b)
self.assertEqual(w.ex(x), '\\lvert{12.0}\\rvert')
# Equal
x = myokit.Equal(a, b)
self.assertEqual(w.ex(x), '\\left(\\text{a}=12.0\\right)')
# NotEqual
x = myokit.NotEqual(a, b)
self.assertEqual(w.ex(x), '\\left(\\text{a}\\neq12.0\\right)')
# More
x = myokit.More(a, b)
self.assertEqual(w.ex(x), '\\left(\\text{a}>12.0\\right)')
# Less
x = myokit.Less(a, b)
self.assertEqual(w.ex(x), '\\left(\\text{a}<12.0\\right)')
# MoreEqual
x = myokit.MoreEqual(a, b)
self.assertEqual(w.ex(x), '\\left(\\text{a}\\geq12.0\\right)')
# LessEqual
x = myokit.LessEqual(a, b)
self.assertEqual(w.ex(x), '\\left(\\text{a}\\leq12.0\\right)')
# Not
cond1 = myokit.parse_expression('5 > 3')
cond2 = myokit.parse_expression('2 < 1')
x = myokit.Not(cond1)
self.assertEqual(w.ex(x), '\\not\\left(\\left(5.0>3.0\\right)\\right)')
# And
x = myokit.And(cond1, cond2)
self.assertEqual(
w.ex(x), '\\left(\\left(5.0>3.0\\right)\\and'
'\\left(2.0<1.0\\right)\\right)')
# Or
x = myokit.Or(cond1, cond2)
self.assertEqual(
w.ex(x), '\\left(\\left(5.0>3.0\\right)\\or'
'\\left(2.0<1.0\\right)\\right)')
# If
x = myokit.If(cond1, a, b)
self.assertEqual(
w.ex(x), 'if\\left(\\left(5.0>3.0\\right),\\text{a},12.0\\right)')
# Piecewise
c = myokit.Number(1)
x = myokit.Piecewise(cond1, a, cond2, b, c)
self.assertEqual(
w.ex(x), 'piecewise\\left(\\left(5.0>3.0\\right),\\text{a},'
'\\left(2.0<1.0\\right),12.0,1.0\\right)')
# Test fetching using ewriter method
w = myokit.formats.ewriter('latex')
self.assertIsInstance(w, myokit.formats.latex.LatexExpressionWriter)
# Test without a Myokit expression
self.assertRaisesRegex(ValueError, 'Unknown expression type', w.ex, 7)
def convert_hh_states_to_inf_tau_form(model, v=None):
"""
Scans a :class:`myokit.Model` for Hodgkin-Huxley style states written in
"alpha-beta form", and converts them to "inf-tau form".
For any state ``x`` written in the form
``dot(x) = alpha * (1 - x) - beta * x`` this method will calculate the
steady state and time constant, and add variables for both. Next, the state
RHS will be replaced by an expression of the form
``dot(x) = (x_inf - x) / tau_x``, where ``x_inf`` and ``tau_x`` are the
new variables.
See also: :meth:`get_alpha_and_beta()`.
Arguments:
``model``
A :class:`myokit.Model` object to convert.
``v``
An optional :class:`myokit.Variable`` representing the membrane
potential. If not given, the method will search for a variable labelled
``membrane_potential``. An error is raised if no membrane potential
variable can be found.
Returns an updated copy of the given model.
"""
# Clone the model before editing
if not isinstance(model, myokit.Model):
raise ValueError('Given `model` must be a myokit.Model.')
model = model.clone()
# Check membrane potential variable is known.
if v is None:
v = model.label('membrane_potential')
if v is None:
raise ValueError(
'Membrane potential must be given as `v` or by setting the'
' label `membrane_potential` in the model.')
else:
# Ensure v is a variable, and from the cloned model
if isinstance(v, myokit.Variable):
v = v.qname()
v = model.get(v)
# Loop over states
# - If they're in alpha-beta form, add new (nested) variables inf and tau
for x in model.states():
res = get_alpha_and_beta(x, v)
if res is not None:
# Create variabless for inf and tau
a = myokit.Name(res[0])
b = myokit.Name(res[1])
tau = x.add_variable_allow_renaming('tau')
tau.set_rhs(myokit.Divide(myokit.Number(1), myokit.Plus(a, b)))
inf = x.add_variable_allow_renaming('inf')
inf.set_rhs(myokit.Multiply(a, myokit.Name(tau)))
# Update RHS expression for state
x.set_rhs(
myokit.Divide(myokit.Minus(myokit.Name(inf), myokit.Name(x)),
myokit.Name(tau)))
return model
def test_split_factor(self):
# Tests _split_factor
# Load model, to create interesting RHS
fname = os.path.join(DIR_DATA, 'clancy-1999-fitting.mmt')
model = myokit.load_model(fname)
v1 = model.get('ina.C1')
v2 = model.get('ina.C2')
v3 = model.get('ina.C3')
v4 = model.get('ina.IF')
# Test simplest cases
v4.set_rhs('C1')
self.assertEqual(markov._split_factor(v4.rhs(), [v1]),
(myokit.Name(v1), myokit.Number(1)))
v4.set_rhs('+++C1')
self.assertEqual(markov._split_factor(v4.rhs(), [v1]),
(myokit.Name(v1), myokit.Number(1)))
v4.set_rhs('--C1')
self.assertEqual(markov._split_factor(v4.rhs(), [v1]),
(myokit.Name(v1), myokit.Number(1)))
v4.set_rhs('---C1')
self.assertEqual(
markov._split_factor(v4.rhs(), [v1]),
(myokit.Name(v1), myokit.PrefixMinus(myokit.Number(1))))
# Test multiplication
v4.set_rhs('C1 * 3')
self.assertEqual(markov._split_factor(v4.rhs(), [v1]),
(myokit.Name(v1), myokit.Number(3)))
v4.set_rhs('C1 * (sqrt(C2) + C3)')
self.assertEqual(
markov._split_factor(v4.rhs(), [v1]),
(myokit.Name(v1),
myokit.Plus(myokit.Sqrt(myokit.Name(v2)), myokit.Name(v3))))
# Test division
v4.set_rhs('C1 / (sqrt(C2) + C3)')
self.assertEqual(
markov._split_factor(v4.rhs(), [v1]),
(myokit.Name(v1),
myokit.Divide(
myokit.Number(1),
myokit.Plus(myokit.Sqrt(myokit.Name(v2)), myokit.Name(v3)))))
# Test division that's not allowed
v4.set_rhs('(sqrt(C2) + C3) / C1')
self.assertRaisesRegex(ValueError, r'Non-linear function \(division\)',
markov._split_factor, v4.rhs(), [v1])
# Test with list of variables
v4.set_rhs('C2 * 3')
self.assertEqual(markov._split_factor(v4.rhs(), [v1, v2, v3]),
(myokit.Name(v2), myokit.Number(3)))
# Multiple variables is not allowed
v4.set_rhs('C2 * C1')
self.assertRaisesRegex(ValueError,
'must reference exactly one variable',
markov._split_factor, v4.rhs(), [v1, v2, v3])
# Zero variables is not allowed
v4.set_rhs('C3')
self.assertRaisesRegex(ValueError,
'must reference exactly one variable',
markov._split_factor, v4.rhs(), [v1, v2])
# Non-linear term is not allowed
v4.set_rhs('sqrt(C1)')
self.assertRaisesRegex(ValueError, 'Non-linear function',
markov._split_factor, v4.rhs(), [v1, v2])
# Multiple terms is not allowed
v4.set_rhs('C2 - C2')
self.assertRaisesRegex(ValueError, 'must be a single term',
markov._split_factor, v4.rhs(), [v1, v2, v3])
def _ex_plus(self, e):
a, b = e.as_two_terms()
return myokit.Plus(self.ex(a), self.ex(b))
def test_remove_variable(self):
# Test the removal of a variable.
# Create a model
m = myokit.Model('LotkaVolterra')
# Add a variable 'a'
X = m.add_component('X')
# Simplest case
a = X.add_variable('a')
self.assertEqual(X.count_variables(), 1)
X.remove_variable(a)
self.assertEqual(X.count_variables(), 0)
self.assertRaises(Exception, X.remove_variable, a)
# Test re-adding
a = X.add_variable('a')
a.set_rhs(myokit.Number(5))
self.assertEqual(X.count_variables(), 1)
# Test deleting dependent variables
b = X.add_variable('b')
self.assertEqual(X.count_variables(), 2)
b.set_rhs(myokit.Plus(myokit.Number(3), myokit.Name(a)))
# Test blocking of removal
self.assertRaises(myokit.IntegrityError, X.remove_variable, a)
self.assertEqual(X.count_variables(), 2)
# Test removal in the right order
X.remove_variable(b)
self.assertEqual(X.count_variables(), 1)
X.remove_variable(a)
self.assertEqual(X.count_variables(), 0)
# Test reference to current state variable values
a = X.add_variable('a')
a.set_rhs(myokit.Number(5))
a.promote()
b = X.add_variable('b')
b.set_rhs(myokit.Plus(myokit.Number(3), myokit.Name(a)))
self.assertRaises(myokit.IntegrityError, X.remove_variable, a)
X.remove_variable(b)
X.remove_variable(a)
self.assertEqual(X.count_variables(), 0)
# Test reference to current state variable values with "self"-ref
a = X.add_variable('a')
a.promote()
a.set_rhs(myokit.Name(a))
X.remove_variable(a)
# Test it doesn't interfere with normal workings
a = X.add_variable('a')
a.promote()
a.set_rhs(myokit.Name(a))
b = X.add_variable('b')
b.set_rhs(myokit.Name(a))
self.assertRaises(myokit.IntegrityError, X.remove_variable, a)
X.remove_variable(b)
X.remove_variable(a)
# Test reference to dot
a = X.add_variable('a')
a.set_rhs(myokit.Number(5))
a.promote()
b = X.add_variable('b')
b.set_rhs(myokit.Derivative(myokit.Name(a)))
self.assertRaises(myokit.IntegrityError, X.remove_variable, a)
X.remove_variable(b)
X.remove_variable(a)
# Test if orphaned
self.assertIsNone(b.parent())
# Test deleting variable with nested variables
a = X.add_variable('a')
b = a.add_variable('b')
b.set_rhs(myokit.Plus(myokit.Number(2), myokit.Number(2)))
a.set_rhs(myokit.Multiply(myokit.Number(3), myokit.Name(b)))
self.assertRaises(myokit.IntegrityError, X.remove_variable, a)
self.assertEqual(a.count_variables(), 1)
self.assertEqual(X.count_variables(), 1)
# Test recursive deleting
X.remove_variable(a, recursive=True)
self.assertEqual(a.count_variables(), 0)
self.assertEqual(X.count_variables(), 0)
# Test deleting variable with nested variables that depend on each
# other
a = X.add_variable('a')
b = a.add_variable('b')
c = a.add_variable('c')
d = a.add_variable('d')
a.set_rhs('b + c - d')
a.promote(0.1)
b.set_rhs('2 * a - d')
c.set_rhs('a + b + d')
d.set_rhs('3 * a')
self.assertRaises(myokit.IntegrityError, X.remove_variable, a)
self.assertEqual(a.count_variables(), 3)
self.assertEqual(X.count_variables(), 1)
X.remove_variable(a, recursive=True)
self.assertEqual(a.count_variables(), 0)
self.assertEqual(X.count_variables(), 0)
# Test if removed from model's label and binding lists
m = myokit.Model()
c = m.add_component('c')
x = c.add_variable('x')
y = c.add_variable('y')
x.set_rhs(0)
y.set_rhs(0)
x.set_binding('time')
y.set_label('membrane_potential')
self.assertIs(m.binding('time'), x)
self.assertIs(m.label('membrane_potential'), y)
c.remove_variable(x)
self.assertIs(m.binding('time'), None)
self.assertIs(m.label('membrane_potential'), y)
c.remove_variable(y)
self.assertIs(m.binding('time'), None)
self.assertIs(m.label('membrane_potential'), None)
def set_roa(self, dose_comp, indirect):
"""
Sets route of administration.
Arguments:
dose_comp -- Compartment that is either infused with drug (direct)
or connected to the depot compartment (indirect).
indirect -- Flag whether dose is administered directly (False) into
the dose compartment or indriectly (True) through a
depot.
"""
# Check that model contains dose_comp
if not self._model.has_component(dose_comp):
raise ValueError
# Check that dose compartment has a variable called amount
amount = dose_comp + '.amount'
if not self._model.has_variable(amount):
raise ValueError
# Check that amount is a state variable
amount = self._model.var(amount)
if not amount.is_state():
raise ValueError
# Check that model has time bound variable
time = self._model.binding(binding='time')
if time is None:
raise ValueError
# Get amount and time unit from dose compartment
amount_unit = amount.unit()
time_unit = time.unit()
# TODO: Remove previously set roa compartments, variables and
# expressions.
# Remember name of dose_comp
self._dose_comp = dose_comp
# Get dose compartment object
dose_comp = self._model.get(dose_comp)
# Add depot compartment if dose is administered indirectly
if indirect:
# Add depot compartment
depot_comp = self._model.add_component_allow_renaming('depot')
# Remember name of depot compartment
self._depot_comp = depot_comp.name()
# Add drug amount and absorption rate to the depot compartment
amount_de = depot_comp.add_variable('amount')
k_a = depot_comp.add_variable('k_a')
# Set default values for amount and absorption rate
amount_de.set_rhs(0)
k_a.set_rhs(0)
# Set units
amount_de.set_unit(amount_unit)
k_a.set_unit(1 / time_unit)
# Promote amount to state variable
amount_de.promote()
# Add outflow expression to depot compartment
amount_de.set_rhs(
myokit.Multiply(myokit.PrefixMinus(myokit.Name(k_a)),
myokit.Name(amount_de)))
# Add inflow expression to dose compartment
expr = amount.rhs()
amount.set_rhs(
myokit.Plus(
expr,
myokit.Multiply(myokit.Name(k_a), myokit.Name(amount_de))))
# Set the depot to the dose compartment
dose_comp = depot_comp
amount = amount_de
del depot_comp
del amount_de
# Add dose rate and regimen variables
dose_rate = dose_comp.add_variable_allow_renaming('dose_rate')
regimen = dose_comp.add_variable_allow_renaming('regimen')
# Remember dose rate variable name
comp_name = dose_comp.name()
self._dose_rate = comp_name + '.' + dose_rate.name()
# Set default values for dose_rate and regimen
dose_rate.set_rhs(0)
regimen.set_rhs(0)
# Set units
dose_rate.set_unit(amount_unit / time_unit)
regimen.set_unit('dimensionless')
# Bind regimen to myokit pacer (so regimen can be adjusted with
# myokit.Protocol)
regimen.set_binding('pace')
# Add dose infusion expression to dose compartment
expr = amount.rhs()
amount.set_rhs(
myokit.Plus(
expr,
myokit.Multiply(myokit.Name(dose_rate), myokit.Name(regimen))))
# Flag route of administration to be set
self._roa_set = True
# Check whether a valid model has been created
self.validate()
def create_tumour_growth_model():
r"""
Returns a tumour growth myokit model.
.. math::
\frac{\text{d}V^s_T}{\text{d}t} = \frac{2\lambda _0\lambda _1 V^s_T}
{2\lambda _0 V^s_T + \lambda _1},
where the tumour volume :math:`V^s_T` is measured in :math:`\text{cm}^3`,
the exponential growth rate :math:`\lambda _0` is mesured in
:math:`\text{day}` and the linear growth rate :math:`\lambda _1` is
measured in :math:`\text{cm}^3/\text{day}`.
"""
# Instantiate model
model = Model()
# add central compartment
central_comp = model.add_compartment('central')
# add tumour growth variables to central compartment
volume_t = central_comp.add_variable('volume_t')
lambda_0 = central_comp.add_variable('lambda_0')
lambda_1 = central_comp.add_variable('lambda_1')
# bind time
time = central_comp.add_variable('time')
time.set_binding('time')
# set preferred representation of units
# time in days
unit = myokit.parse_unit('day')
myokit.Unit.register_preferred_representation('day', unit)
# rates in 1 / day
unit = myokit.parse_unit('1/day')
myokit.Unit.register_preferred_representation('1/day', unit)
# tumor volume
unit = myokit.parse_unit('cm^3')
myokit.Unit.register_preferred_representation('cm^3', unit)
# linear growth
unit = myokit.parse_unit('cm^3/day')
myokit.Unit.register_preferred_representation('cm^3/day', unit)
# set intial values (some default values) and units
time.set_rhs(0)
volume_t.set_rhs(0)
lambda_0.set_rhs(0)
lambda_1.set_rhs(1) # avoid ZeroDivisionError
# set units
time.set_unit('day') # time in days
volume_t.set_unit('cm^3') # milimeter cubed
lambda_0.set_unit('1 / day') # per day
lambda_1.set_unit('cm^3 / day') # milimiter cubed per day
# set rhs of tumor volume
# dot(volume_t) =
# (2 * lambda_0 * lambda_1 * volume_t) /
# (2 * lambda_0 * volume_t + lambda_1)
volume_t.promote()
volume_t.set_rhs(
myokit.Divide(
myokit.Multiply(
myokit.Number(2),
myokit.Multiply(
myokit.Name(lambda_0),
myokit.Multiply(myokit.Name(lambda_1),
myokit.Name(volume_t)))),
myokit.Plus(
myokit.Multiply(
myokit.Number(2),
myokit.Multiply(myokit.Name(lambda_0),
myokit.Name(volume_t))),
myokit.Name(lambda_1))))
# Validate model
model.validate()
# TODO: Check units
# model.check_units()
return model
def create_pktgi_model():
"""
Returns 1 compartmental PK model.
"""
# Instantiate model
model = Model()
# Add central compartment
central_comp = model.add_compartment('central')
# Add PK variables and constants to central compartment
amount = central_comp.add_variable('amount')
volume_c = central_comp.add_variable('volume_c')
k_e = central_comp.add_variable('k_e')
conc = central_comp.add_variable('conc')
# add PD variables to central compartment
volume_t = central_comp.add_variable('volume_t')
lambda_0 = central_comp.add_variable('lambda_0')
lambda_1 = central_comp.add_variable('lambda_1')
kappa = central_comp.add_variable('kappa')
# bind time
time = central_comp.add_variable('time')
time.set_binding('time')
# set intial values (some default values)
time.set_rhs(0)
amount.set_rhs(0)
volume_c.set_rhs(1) # avoid ZeroDivisionError
k_e.set_rhs(0)
conc.set_rhs(0)
volume_t.set_rhs(0)
lambda_0.set_rhs(0)
lambda_1.set_rhs(1) # avoid ZeroDivisionError
kappa.set_rhs(0)
# set units
time.set_unit('day') # time in days
amount.set_unit('mg') # miligram
volume_c.set_unit('L') # liter
k_e.set_unit('1 / day') # 1 / day
conc.set_unit('mg / L') # miligram / liter
volume_t.set_unit('cm^3') # milimeter cubed
lambda_0.set_unit('1 / day') # per day
lambda_1.set_unit('cm^3 / day') # milimiter cubed per day
kappa.set_unit('L / mg / day') # in reference L / ug / day,
# set preferred representation of units
# time days
unit = myokit.parse_unit('day')
myokit.Unit.register_preferred_representation('day', unit)
# rates in 1 / day
unit = myokit.parse_unit('1/day')
myokit.Unit.register_preferred_representation('1/day', unit)
# amount in mg
unit = myokit.parse_unit('mg')
myokit.Unit.register_preferred_representation('mg', unit)
# dose rate in mg / day
unit = myokit.parse_unit('mg/day')
myokit.Unit.register_preferred_representation('mg/day', unit)
# concentration mg / L
unit = myokit.parse_unit('mg/L')
myokit.Unit.register_preferred_representation('mg/L', unit)
# tumor volume
unit = myokit.parse_unit('cm^3')
myokit.Unit.register_preferred_representation('cm^3', unit)
# linear growth
unit = myokit.parse_unit('cm^3/day')
myokit.Unit.register_preferred_representation('cm^3/day', unit)
# potency
unit = myokit.parse_unit('L/mg/day')
myokit.Unit.register_preferred_representation('L/mg/day', unit)
# set rhs of drug amount
# (dot(amount) = - k_e * amount)
amount.promote()
amount.set_rhs(
myokit.Multiply(myokit.PrefixMinus(myokit.Name(k_e)),
myokit.Name(amount)))
# set rhs of tumor volume
# dot(volume_t) =
# (2 * lambda_0 * lambda_1 * volume_t) /
# (2 * lambda_0 * volume_t + lambda_1) -
# kappa * conc * volume_t
volume_t.promote()
volume_t.set_rhs(
myokit.Minus(
myokit.Divide(
myokit.Multiply(
myokit.Number(2),
myokit.Multiply(
myokit.Name(lambda_0),
myokit.Multiply(myokit.Name(lambda_1),
myokit.Name(volume_t)))),
myokit.Plus(
myokit.Multiply(
myokit.Number(2),
myokit.Multiply(myokit.Name(lambda_0),
myokit.Name(volume_t))),
myokit.Name(lambda_1))),
myokit.Multiply(
myokit.Name(kappa),
myokit.Multiply(myokit.Name(conc), myokit.Name(volume_t)))))
# set algebraic relation between drug and concentration
# conc = amount / volume_c
conc.set_rhs(myokit.Divide(myokit.Name(amount), myokit.Name(volume_c)))
return model
def get_rl_expression(x, dt, v=None):
"""
For states ``x`` with RHS expressions written in the "inf-tau form" (see
:meth:`has_inf_tau_form`) this returns a Rush-Larsen (RL) update expression
of the form ``x_inf + (x - x_inf) * exp(-(dt / tau_x))``.
If the state does not have the "inf-tau form", ``None`` is returned.
Arguments:
``x``
A state variable for which to return the RL update expression.
``dt``
A :class:`myokit.Name` expression to use for the time step in the RL
expression.
``v``
An optional variable representing the membrane potential.
Returns a :class:`myokit.Expression` if succesful, or ``None`` if not.
Example:
# Load a Myokit model
model = myokit.load_model('example')
v = model.get('membrane.V')
# Get a copy where all HH-state variables are written in inf-tau form
model = myokit.lib.hh.convert_hh_states_to_inf_tau_form(model, v)
# Create an expression for the time step
dt = myokit.Name('dt')
# Show an RL-update for the variable ina.h
h = model.get('ina.h')
e = myokit.lib.hh.get_rl_expression(h, dt, v)
print('h[t + dt] = ' + str(e))
See:
[1] Rush, Larsen (1978) A Practical Algorithm for Solving Dynamic Membrane
Equations. IEEE Transactions on Biomedical Engineering,
https://doi.org/10.1109/TBME.1978.326270
[2] Marsh, Ziaratgahi, Spiteri (2012) The secrets to the success of the
Rush-Larsen method and its generalization. IEEE Transactions on Biomedical
Engineering, https://doi.org/10.1109/TBME.2012.2205575
"""
# Test dt is an expression
if not isinstance(dt, myokit.Expression):
raise ValueError('Argument `dt` must be a myokit.Expression.')
# Get x_inf and tau_x, if possible
res = get_inf_and_tau(x, v)
if res is None:
return None
# Create expression for RL update
# x_inf + (x - x_inf) * exp(-(dt / tau_x))
x = myokit.Name(x)
x_inf = myokit.Name(res[0])
tau_x = myokit.Name(res[1])
return myokit.Plus(
x_inf,
myokit.Multiply(
myokit.Minus(x, x_inf),
myokit.Exp(myokit.PrefixMinus(myokit.Divide(dt, tau_x)))))
def test_basic(self):
# Single and double precision and native maths
ws = myokit.formats.opencl.OpenCLExpressionWriter()
wd = myokit.formats.opencl.OpenCLExpressionWriter(
myokit.DOUBLE_PRECISION)
wn = myokit.formats.opencl.OpenCLExpressionWriter(native_math=False)
a = myokit.Name(myokit.Model().add_component('c').add_variable('a'))
b = myokit.Number('12', 'pF')
# Name
self.assertEqual(ws.ex(a), 'c.a')
self.assertEqual(wd.ex(a), 'c.a')
self.assertEqual(wn.ex(a), 'c.a')
# Number with unit
self.assertEqual(ws.ex(b), '12.0f')
self.assertEqual(wd.ex(b), '12.0')
self.assertEqual(wn.ex(b), '12.0f')
# Prefix plus
x = myokit.PrefixPlus(b)
self.assertEqual(ws.ex(x), '12.0f')
self.assertEqual(wd.ex(x), '12.0')
self.assertEqual(wn.ex(x), '12.0f')
# Prefix minus
x = myokit.PrefixMinus(b)
self.assertEqual(ws.ex(x), '(-12.0f)')
self.assertEqual(wd.ex(x), '(-12.0)')
self.assertEqual(wn.ex(x), '(-12.0f)')
# Plus
x = myokit.Plus(a, b)
self.assertEqual(ws.ex(x), 'c.a + 12.0f')
self.assertEqual(wd.ex(x), 'c.a + 12.0')
self.assertEqual(wn.ex(x), 'c.a + 12.0f')
# Minus
x = myokit.Minus(a, b)
self.assertEqual(ws.ex(x), 'c.a - 12.0f')
self.assertEqual(wd.ex(x), 'c.a - 12.0')
self.assertEqual(wn.ex(x), 'c.a - 12.0f')
# Multiply
x = myokit.Multiply(a, b)
self.assertEqual(ws.ex(x), 'c.a * 12.0f')
self.assertEqual(wd.ex(x), 'c.a * 12.0')
self.assertEqual(wn.ex(x), 'c.a * 12.0f')
# Divide
x = myokit.Divide(a, b)
self.assertEqual(ws.ex(x), 'c.a / 12.0f')
self.assertEqual(wd.ex(x), 'c.a / 12.0')
self.assertEqual(wn.ex(x), 'c.a / 12.0f')
# Quotient
x = myokit.Quotient(a, b)
self.assertEqual(ws.ex(x), 'floor(c.a / 12.0f)')
self.assertEqual(wd.ex(x), 'floor(c.a / 12.0)')
self.assertEqual(wn.ex(x), 'floor(c.a / 12.0f)')
# Remainder
x = myokit.Remainder(a, b)
self.assertEqual(ws.ex(x), 'c.a - 12.0f * (floor(c.a / 12.0f))')
self.assertEqual(wd.ex(x), 'c.a - 12.0 * (floor(c.a / 12.0))')
self.assertEqual(wn.ex(x), 'c.a - 12.0f * (floor(c.a / 12.0f))')
def _parse_apply(self, apply_element):
"""
Parses an ``<apply>`` element.
"""
# Apply must have kids
if len(apply_element) == 0:
raise MathMLError('Apply must contain at least one child element.',
apply_element)
# Get first child
iterator = iter(apply_element)
element = self._next(iterator)
# Decide what to do based on first child
_, name = split(element.tag)
# Handle derivative
if name == 'diff':
return self._parse_derivative(element, iterator)
# Algebra (unary/binary/n-ary operators)
elif name == 'plus':
return self._parse_nary(element, iterator, myokit.Plus,
myokit.PrefixPlus)
elif name == 'minus':
return self._parse_nary(element, iterator, myokit.Minus,
myokit.PrefixMinus)
elif name == 'times':
return self._parse_nary(element, iterator, myokit.Multiply)
elif name == 'divide':
return self._parse_nary(element, iterator, myokit.Divide)
# Basic functions
elif name == 'exp':
return myokit.Exp(*self._eat(element, iterator))
elif name == 'ln':
return myokit.Log(*self._eat(element, iterator))
elif name == 'log':
return self._parse_log(element, iterator)
elif name == 'root':
return self._parse_root(element, iterator)
elif name == 'power':
return myokit.Power(*self._eat(element, iterator, 2))
elif name == 'floor':
return myokit.Floor(*self._eat(element, iterator))
elif name == 'ceiling':
return myokit.Ceil(*self._eat(element, iterator))
elif name == 'abs':
return myokit.Abs(*self._eat(element, iterator))
elif name == 'quotient':
return myokit.Quotient(*self._eat(element, iterator, 2))
elif name == 'rem':
return myokit.Remainder(*self._eat(element, iterator, 2))
# Logic
elif name == 'and':
return self._parse_nary(element, iterator, myokit.And)
elif name == 'or':
return self._parse_nary(element, iterator, myokit.Or)
elif name == 'xor':
# Becomes ``(x or y) and not(x and y)``
x, y = self._eat(element, iterator, 2)
return myokit.And(myokit.Or(x, y), myokit.Not(myokit.And(x, y)))
elif name == 'not':
return myokit.Not(*self._eat(element, iterator))
elif name == 'eq' or name == 'equivalent':
return myokit.Equal(*self._eat(element, iterator, 2))
elif name == 'neq':
return myokit.NotEqual(*self._eat(element, iterator, 2))
elif name == 'gt':
return myokit.More(*self._eat(element, iterator, 2))
elif name == 'lt':
return myokit.Less(*self._eat(element, iterator, 2))
elif name == 'geq':
return myokit.MoreEqual(*self._eat(element, iterator, 2))
elif name == 'leq':
return myokit.LessEqual(*self._eat(element, iterator, 2))
# Trigonometry
elif name == 'sin':
return myokit.Sin(*self._eat(element, iterator))
elif name == 'cos':
return myokit.Cos(*self._eat(element, iterator))
elif name == 'tan':
return myokit.Tan(*self._eat(element, iterator))
elif name == 'arcsin':
return myokit.ASin(*self._eat(element, iterator))
elif name == 'arccos':
return myokit.ACos(*self._eat(element, iterator))
elif name == 'arctan':
return myokit.ATan(*self._eat(element, iterator))
# Redundant trigonometry (CellML includes this)
elif name == 'csc':
# Cosecant: csc(x) = 1 / sin(x)
return myokit.Divide(self._const(1),
myokit.Sin(*self._eat(element, iterator)))
elif name == 'sec':
# Secant: sec(x) = 1 / cos(x)
return myokit.Divide(self._const(1),
myokit.Cos(*self._eat(element, iterator)))
elif name == 'cot':
# Contangent: cot(x) = 1 / tan(x)
return myokit.Divide(self._const(1),
myokit.Tan(*self._eat(element, iterator)))
elif name == 'arccsc':
# ArcCosecant: acsc(x) = asin(1/x)
return myokit.ASin(
myokit.Divide(self._const(1), *self._eat(element, iterator)))
elif name == 'arcsec':
# ArcSecant: asec(x) = acos(1/x)
return myokit.ACos(
myokit.Divide(self._const(1), *self._eat(element, iterator)))
elif name == 'arccot':
# ArcCotangent: acot(x) = atan(1/x)
return myokit.ATan(
myokit.Divide(self._const(1), *self._eat(element, iterator)))
# Hyperbolic trig
elif name == 'sinh':
# Hyperbolic sine: sinh(x) = 0.5 * (e^x - e^-x)
x = self._eat(element, iterator)[0]
return myokit.Multiply(
self._const(0.5),
myokit.Minus(myokit.Exp(x), myokit.Exp(myokit.PrefixMinus(x))))
elif name == 'cosh':
# Hyperbolic cosine: cosh(x) = 0.5 * (e^x + e^-x)
x = self._eat(element, iterator)[0]
return myokit.Multiply(
self._const(0.5),
myokit.Plus(myokit.Exp(x), myokit.Exp(myokit.PrefixMinus(x))))
elif name == 'tanh':
# Hyperbolic tangent: tanh(x) = (e^2x - 1) / (e^2x + 1)
x = self._eat(element, iterator)[0]
e2x = myokit.Exp(myokit.Multiply(self._const(2), x))
return myokit.Divide(myokit.Minus(e2x, self._const(1)),
myokit.Plus(e2x, self._const(1)))
elif name == 'arcsinh':
# Inverse hyperbolic sine: asinh(x) = log(x + sqrt(x*x + 1))
x = self._eat(element, iterator)[0]
return myokit.Log(
myokit.Plus(
x,
myokit.Sqrt(
myokit.Plus(myokit.Multiply(x, x), self._const(1)))))
elif name == 'arccosh':
# Inverse hyperbolic cosine:
# acosh(x) = log(x + sqrt(x*x - 1))
x = self._eat(element, iterator)[0]
return myokit.Log(
myokit.Plus(
x,
myokit.Sqrt(
myokit.Minus(myokit.Multiply(x, x), self._const(1)))))
elif name == 'arctanh':
# Inverse hyperbolic tangent:
# atanh(x) = 0.5 * log((1 + x) / (1 - x))
x = self._eat(element, iterator)[0]
return myokit.Multiply(
self._const(0.5),
myokit.Log(
myokit.Divide(myokit.Plus(self._const(1), x),
myokit.Minus(self._const(1), x))))
# Hyperbolic redundant trig
elif name == 'csch':
# Hyperbolic cosecant: csch(x) = 2 / (exp(x) - exp(-x))
x = self._eat(element, iterator)[0]
return myokit.Divide(
self._const(2),
myokit.Minus(myokit.Exp(x), myokit.Exp(myokit.PrefixMinus(x))))
elif name == 'sech':
# Hyperbolic secant: sech(x) = 2 / (exp(x) + exp(-x))
x = self._eat(element, iterator)[0]
return myokit.Divide(
self._const(2),
myokit.Plus(myokit.Exp(x), myokit.Exp(myokit.PrefixMinus(x))))
elif name == 'coth':
# Hyperbolic cotangent:
# coth(x) = (exp(2*x) + 1) / (exp(2*x) - 1)
x = self._eat(element, iterator)[0]
e2x = myokit.Exp(myokit.Multiply(self._const(2), x))
return myokit.Divide(myokit.Plus(e2x, self._const(1)),
myokit.Minus(e2x, self._const(1)))
elif name == 'arccsch':
# Inverse hyperbolic cosecant:
# arccsch(x) = log(1 / x + sqrt(1 / x^2 + 1))
x = self._eat(element, iterator)[0]
return myokit.Log(
myokit.Plus(
myokit.Divide(self._const(1), x),
myokit.Sqrt(
myokit.Plus(
myokit.Divide(self._const(1),
myokit.Multiply(x, x)),
self._const(1)))))
elif name == 'arcsech':
# Inverse hyperbolic secant:
# arcsech(x) = log(1 / x + sqrt(1 / x^2 - 1))
x = self._eat(element, iterator)[0]
return myokit.Log(
myokit.Plus(
myokit.Divide(self._const(1), x),
myokit.Sqrt(
myokit.Minus(
myokit.Divide(self._const(1),
myokit.Multiply(x, x)),
self._const(1)))))
elif name == 'arccoth':
# Inverse hyperbolic cotangent:
# arccoth(x) = 0.5 * log((x + 1) / (x - 1))
x = self._eat(element, iterator)[0]
return myokit.Multiply(
self._const(0.5),
myokit.Log(
myokit.Divide(myokit.Plus(x, self._const(1)),
myokit.Minus(x, self._const(1)))))
# Last option: A single atomic inside an apply
# Do this one last to stop e.g. <apply><times /></apply> returning the
# error 'Unsupported element' (which is what parse_atomic would call).
elif len(apply_element) == 1:
return self._parse_atomic(element)
# Unexpected element
else:
raise MathMLError(
'Unsupported element in apply: ' + str(element.tag) + '.',
element)
def test_functions(self):
# Single and double precision and native maths
ws = myokit.formats.opencl.OpenCLExpressionWriter()
wd = myokit.formats.opencl.OpenCLExpressionWriter(
myokit.DOUBLE_PRECISION)
wn = myokit.formats.opencl.OpenCLExpressionWriter(native_math=False)
a = myokit.Name(myokit.Model().add_component('c').add_variable('a'))
b = myokit.Number('12', 'pF')
# Power
x = myokit.Power(a, b)
self.assertEqual(ws.ex(x), 'pow(c.a, 12.0f)')
self.assertEqual(wd.ex(x), 'pow(c.a, 12.0)')
self.assertEqual(wn.ex(x), 'pow(c.a, 12.0f)')
# Square
x = myokit.Power(a, myokit.Number(2))
self.assertEqual(ws.ex(x), '(c.a * c.a)')
self.assertEqual(wd.ex(x), '(c.a * c.a)')
self.assertEqual(wn.ex(x), '(c.a * c.a)')
# Square with brackets
x = myokit.Power(myokit.Plus(a, b), myokit.Number(2))
self.assertEqual(ws.ex(x), '((c.a + 12.0f) * (c.a + 12.0f))')
self.assertEqual(wd.ex(x), '((c.a + 12.0) * (c.a + 12.0))')
self.assertEqual(wn.ex(x), '((c.a + 12.0f) * (c.a + 12.0f))')
# Sqrt
x = myokit.Sqrt(b)
self.assertEqual(ws.ex(x), 'native_sqrt(12.0f)')
self.assertEqual(wd.ex(x), 'native_sqrt(12.0)')
self.assertEqual(wn.ex(x), 'sqrt(12.0f)')
# Exp
x = myokit.Exp(a)
self.assertEqual(ws.ex(x), 'native_exp(c.a)')
self.assertEqual(wd.ex(x), 'native_exp(c.a)')
self.assertEqual(wn.ex(x), 'exp(c.a)')
# Log(a)
x = myokit.Log(b)
self.assertEqual(ws.ex(x), 'native_log(12.0f)')
self.assertEqual(wd.ex(x), 'native_log(12.0)')
self.assertEqual(wn.ex(x), 'log(12.0f)')
# Log(a, b)
x = myokit.Log(a, b)
self.assertEqual(ws.ex(x), '(native_log(c.a) / native_log(12.0f))')
self.assertEqual(wd.ex(x), '(native_log(c.a) / native_log(12.0))')
self.assertEqual(wn.ex(x), '(log(c.a) / log(12.0f))')
# Log10
x = myokit.Log10(b)
self.assertEqual(ws.ex(x), 'native_log10(12.0f)')
self.assertEqual(wd.ex(x), 'native_log10(12.0)')
self.assertEqual(wn.ex(x), 'log10(12.0f)')
# Sin
x = myokit.Sin(b)
self.assertEqual(ws.ex(x), 'native_sin(12.0f)')
self.assertEqual(wd.ex(x), 'native_sin(12.0)')
self.assertEqual(wn.ex(x), 'sin(12.0f)')
# Cos
x = myokit.Cos(b)
self.assertEqual(ws.ex(x), 'native_cos(12.0f)')
self.assertEqual(wd.ex(x), 'native_cos(12.0)')
self.assertEqual(wn.ex(x), 'cos(12.0f)')
# Tan
x = myokit.Tan(b)
self.assertEqual(ws.ex(x), 'native_tan(12.0f)')
self.assertEqual(wd.ex(x), 'native_tan(12.0)')
self.assertEqual(wn.ex(x), 'tan(12.0f)')
# ASin
x = myokit.ASin(b)
self.assertEqual(ws.ex(x), 'asin(12.0f)')
self.assertEqual(wd.ex(x), 'asin(12.0)')
self.assertEqual(wn.ex(x), 'asin(12.0f)')
# ACos
x = myokit.ACos(b)
self.assertEqual(ws.ex(x), 'acos(12.0f)')
self.assertEqual(wd.ex(x), 'acos(12.0)')
self.assertEqual(wn.ex(x), 'acos(12.0f)')
# ATan
x = myokit.ATan(b)
self.assertEqual(ws.ex(x), 'atan(12.0f)')
self.assertEqual(wd.ex(x), 'atan(12.0)')
self.assertEqual(wn.ex(x), 'atan(12.0f)')
# Floor
x = myokit.Floor(b)
self.assertEqual(ws.ex(x), 'floor(12.0f)')
self.assertEqual(wd.ex(x), 'floor(12.0)')
self.assertEqual(wn.ex(x), 'floor(12.0f)')
# Ceil
x = myokit.Ceil(b)
self.assertEqual(ws.ex(x), 'ceil(12.0f)')
self.assertEqual(wd.ex(x), 'ceil(12.0)')
self.assertEqual(wn.ex(x), 'ceil(12.0f)')
# Abs
x = myokit.Abs(b)
self.assertEqual(ws.ex(x), 'fabs(12.0f)')
self.assertEqual(wd.ex(x), 'fabs(12.0)')
self.assertEqual(wn.ex(x), 'fabs(12.0f)')
def parsex(node):
"""
Parses a mathml expression.
"""
def chain(kind, node, unary=None):
"""
Parses operands for chained operators (for example plus, minus,
times and division).
The argument ``kind`` must be the myokit expression type being
parsed, ``node`` is a DOM node and ``unary``, if given, should be
the unary expression type (unary Plus or unary Minus).
"""
ops = []
node = dom_next(node)
while node:
ops.append(parsex(node))
node = dom_next(node)
n = len(ops)
if n < 1:
raise MathMLError('Operator needs at least one operand.')
if n < 2:
if unary:
return unary(ops[0])
else:
raise MathMLError('Operator needs at least two operands')
ex = kind(ops[0], ops[1])
for i in range(2, n):
ex = kind(ex, ops[i])
return ex
# Start parsing
name = node.tagName
if name == 'apply':
# Brackets, can be ignored in an expression tree.
return parsex(dom_child(node))
elif name == 'ci':
# Reference
var = str(node.firstChild.data).strip()
if var_table is not None:
try:
var = var_table[var]
except KeyError:
if logger:
logger.warn('Unable to resolve reference to <' +
str(var) + '>.')
return myokit.Name(var)
elif name == 'diff':
# Derivative
# Check time variable
bvar = dom_next(node, 'bvar')
if derivative_post_processor:
derivative_post_processor(parsex(dom_child(bvar, 'ci')))
# Check degree, if given
d = dom_child(bvar, 'degree')
if d is not None:
d = parsex(dom_child(d, 'cn')).eval()
if not d == 1:
raise MathMLError(
'Only derivatives of degree one are supported.')
# Create derivative and return
x = dom_next(node, 'ci')
if x is None:
raise MathMLError(
'Derivative of an expression found: only derivatives of'
' variables are supported.')
return myokit.Derivative(parsex(x))
elif name == 'cn':
# Number
number = parse_mathml_number(node, logger)
if number_post_processor:
return number_post_processor(node, number)
return number
#
# Algebra
#
elif name == 'plus':
return chain(myokit.Plus, node, myokit.PrefixPlus)
elif name == 'minus':
return chain(myokit.Minus, node, myokit.PrefixMinus)
elif name == 'times':
return chain(myokit.Multiply, node)
elif name == 'divide':
return chain(myokit.Divide, node)
#
# Functions
#
elif name == 'exp':
return myokit.Exp(parsex(dom_next(node)))
elif name == 'ln':
return myokit.Log(parsex(dom_next(node)))
elif name == 'log':
if dom_next(node).tagName != 'logbase':
return myokit.Log10(parsex(dom_next(node)))
else:
return myokit.Log(parsex(dom_next(dom_next(node))),
parsex(dom_child(dom_next(node))))
elif name == 'root':
# Check degree, if given
nxt = dom_next(node)
if nxt.tagName == 'degree':
# Degree given, return x^(1/d) unless d is 2
d = parsex(dom_child(nxt))
x = parsex(dom_next(nxt))
if d.is_literal() and d.eval() == 2:
return myokit.Sqrt(x)
return myokit.Power(x, myokit.Divide(myokit.Number(1), d))
else:
return myokit.Sqrt(parsex(nxt))
elif name == 'power':
n2 = dom_next(node)
return myokit.Power(parsex(n2), parsex(dom_next(n2)))
elif name == 'floor':
return myokit.Floor(parsex(dom_next(node)))
elif name == 'ceiling':
return myokit.Ceil(parsex(dom_next(node)))
elif name == 'abs':
return myokit.Abs(parsex(dom_next(node)))
elif name == 'quotient':
n2 = dom_next(node)
return myokit.Quotient(parsex(n2), parsex(dom_next(n2)))
elif name == 'rem':
n2 = dom_next(node)
return myokit.Remainder(parsex(n2), parsex(dom_next(n2)))
#
# Trigonometry
#
elif name == 'sin':
return myokit.Sin(parsex(dom_next(node)))
elif name == 'cos':
return myokit.Cos(parsex(dom_next(node)))
elif name == 'tan':
return myokit.Tan(parsex(dom_next(node)))
elif name == 'arcsin':
return myokit.ASin(parsex(dom_next(node)))
elif name == 'arccos':
return myokit.ACos(parsex(dom_next(node)))
elif name == 'arctan':
return myokit.ATan(parsex(dom_next(node)))
#
# Redundant trigonometry (CellML includes this)
#
elif name == 'csc':
# Cosecant: csc(x) = 1 / sin(x)
return myokit.Divide(myokit.Number(1),
myokit.Sin(parsex(dom_next(node))))
elif name == 'sec':
# Secant: sec(x) = 1 / cos(x)
return myokit.Divide(myokit.Number(1),
myokit.Cos(parsex(dom_next(node))))
elif name == 'cot':
# Contangent: cot(x) = 1 / tan(x)
return myokit.Divide(myokit.Number(1),
myokit.Tan(parsex(dom_next(node))))
elif name == 'arccsc':
# ArcCosecant: acsc(x) = asin(1/x)
return myokit.ASin(
myokit.Divide(myokit.Number(1), parsex(dom_next(node))))
elif name == 'arcsec':
# ArcSecant: asec(x) = acos(1/x)
return myokit.ACos(
myokit.Divide(myokit.Number(1), parsex(dom_next(node))))
elif name == 'arccot':
# ArcCotangent: acot(x) = atan(1/x)
return myokit.ATan(
myokit.Divide(myokit.Number(1), parsex(dom_next(node))))
#
# Hyperbolic trigonometry (CellML again)
#
elif name == 'sinh':
# Hyperbolic sine: sinh(x) = 0.5 * (e^x - e^-x)
x = parsex(dom_next(node))
return myokit.Multiply(
myokit.Number(0.5),
myokit.Minus(myokit.Exp(x), myokit.Exp(myokit.PrefixMinus(x))))
elif name == 'cosh':
# Hyperbolic cosine: cosh(x) = 0.5 * (e^x + e^-x)
x = parsex(dom_next(node))
return myokit.Multiply(
myokit.Number(0.5),
myokit.Plus(myokit.Exp(x), myokit.Exp(myokit.PrefixMinus(x))))
elif name == 'tanh':
# Hyperbolic tangent: tanh(x) = (e^2x - 1) / (e^2x + 1)
x = parsex(dom_next(node))
e2x = myokit.Exp(myokit.Multiply(myokit.Number(2), x))
return myokit.Divide(myokit.Minus(e2x, myokit.Number(1)),
myokit.Plus(e2x, myokit.Number(1)))
#
# Inverse hyperbolic trigonometry (CellML...)
#
elif name == 'arcsinh':
# Inverse hyperbolic sine: asinh(x) = log(x + sqrt(1 + x*x))
x = parsex(dom_next(node))
return myokit.Log(
myokit.Plus(
x,
myokit.Sqrt(
myokit.Plus(myokit.Number(1), myokit.Multiply(x, x)))))
elif name == 'arccosh':
# Inverse hyperbolic cosine:
# acosh(x) = log(x + sqrt(x + 1) * sqrt(x - 1))
x = parsex(dom_next(node))
return myokit.Log(
myokit.Plus(
x,
myokit.Multiply(
myokit.Sqrt(myokit.Plus(x, myokit.Number(1))),
myokit.Sqrt(myokit.Minus(x, myokit.Number(1))))))
elif name == 'arctanh':
# Inverse hyperbolic tangent:
# atanh(x) = 0.5 * (log(1 + x) - log(1 - x))
x = parsex(dom_next(node))
return myokit.Multiply(
myokit.Number(0.5),
myokit.Minus(myokit.Log(myokit.Plus(myokit.Number(1), x)),
myokit.Log(myokit.Minus(myokit.Number(1), x))))
#
# Hyperbolic redundant trigonometry (CellML...)
#
elif name == 'csch':
# Hyperbolic cosecant: csch(x) = 2 / (exp(x) - exp(-x))
x = parsex(dom_next(node))
return myokit.Divide(
myokit.Number(2),
myokit.Minus(myokit.Exp(x), myokit.Exp(myokit.PrefixMinus(x))))
elif name == 'sech':
# Hyperbolic secant: sech(x) = 2 / (exp(x) + exp(-x))
x = parsex(dom_next(node))
return myokit.Divide(
myokit.Number(2),
myokit.Plus(myokit.Exp(x), myokit.Exp(myokit.PrefixMinus(x))))
elif name == 'coth':
# Hyperbolic cotangent:
# coth(x) = (exp(2*x) + 1) / (exp(2*x) - 1)
x = parsex(dom_next(node))
e2x = myokit.Exp(myokit.Multiply(myokit.Number(2), x))
return myokit.Divide(myokit.Plus(e2x, myokit.Number(1)),
myokit.Minus(e2x, myokit.Number(1)))
#
# Inverse hyperbolic redundant trigonometry (CellML has a lot to answer
# for...)
#
elif name == 'arccsch':
# Inverse hyperbolic cosecant:
# arccsch(x) = log(sqrt(1/(x*x) + 1) + 1/x)
x = parsex(dom_next(node))
return myokit.Log(
myokit.Plus(
myokit.Sqrt(
myokit.Plus(
myokit.Divide(myokit.Number(1),
myokit.Multiply(x, x)),
myokit.Number(1))),
myokit.Divide(myokit.Number(1), x)))
elif name == 'arcsech':
# Inverse hyperbolic secant:
# arcsech(x) = log(sqrt(1/(x*x) - 1) + 1/x)
x = parsex(dom_next(node))
return myokit.Log(
myokit.Plus(
myokit.Sqrt(
myokit.Minus(
myokit.Divide(myokit.Number(1),
myokit.Multiply(x, x)),
myokit.Number(1))),
myokit.Divide(myokit.Number(1), x)))
elif name == 'arccoth':
# Inverse hyperbolic cotangent:
# arccoth(x) = 0.5 * (log(3 + 1) - log(3 - 1))
x = parsex(dom_next(node))
return myokit.Multiply(
myokit.Number(0.5),
myokit.Log(
myokit.Divide(myokit.Plus(x, myokit.Number(1)),
myokit.Minus(x, myokit.Number(1)))))
#
# Logic
#
elif name == 'and':
return chain(myokit.And, node)
elif name == 'or':
return chain(myokit.Or, node)
elif name == 'not':
return chain(None, node, myokit.Not)
elif name == 'eq' or name == 'equivalent':
n2 = dom_next(node)
return myokit.Equal(parsex(n2), parsex(dom_next(n2)))
elif name == 'neq':
n2 = dom_next(node)
return myokit.NotEqual(parsex(n2), parsex(dom_next(n2)))
elif name == 'gt':
n2 = dom_next(node)
return myokit.More(parsex(n2), parsex(dom_next(n2)))
elif name == 'lt':
n2 = dom_next(node)
return myokit.Less(parsex(n2), parsex(dom_next(n2)))
elif name == 'geq':
n2 = dom_next(node)
return myokit.MoreEqual(parsex(n2), parsex(dom_next(n2)))
elif name == 'leq':
n2 = dom_next(node)
return myokit.LessEqual(parsex(n2), parsex(dom_next(n2)))
elif name == 'piecewise':
# Piecewise contains at least one piece, optionally contains an
# "otherwise". Syntax doesn't ensure this statement makes sense.
conds = []
funcs = []
other = None
piece = dom_child(node)
while piece:
if piece.tagName == 'otherwise':
if other is None:
other = parsex(dom_child(piece))
elif logger:
logger.warn(
'Multiple <otherwise> tags found in <piecewise>'
' statement.')
elif piece.tagName == 'piece':
n2 = dom_child(piece)
funcs.append(parsex(n2))
conds.append(parsex(dom_next(n2)))
elif logger:
logger.warn('Unexpected tag type in <piecewise>: <' +
piece.tagName + '>.')
piece = dom_next(piece)
if other is None:
if logger:
logger.warn('No <otherwise> tag found in <piecewise>')
other = myokit.Number(0)
# Create string of if statements
args = []
f = iter(funcs)
for c in conds:
args.append(c)
args.append(next(f))
args.append(other)
return myokit.Piecewise(*args)
#
# Constants
#
elif name == 'pi':
return myokit.Number('3.14159265358979323846')
elif name == 'exponentiale':
return myokit.Exp(myokit.Number(1))
elif name == 'true':
# This is corrent, even in Python True == 1 but not True == 2
return myokit.Number(1)
elif name == 'false':
return myokit.Number(0)
#
# Unknown/unhandled elements
#
else:
if logger:
logger.warn('Unknown element: ' + name)
ops = []
node = dom_child(node) if dom_child(node) else dom_next(node)
while node:
ops.append(parsex(node))
node = dom_next(node)
return myokit.UnsupportedFunction(name, ops)
def test_all(self):
# Single and double precision
ws = myokit.formats.cuda.CudaExpressionWriter()
wd = myokit.formats.cuda.CudaExpressionWriter(myokit.DOUBLE_PRECISION)
model = myokit.Model()
component = model.add_component('c')
avar = component.add_variable('a')
# Name
a = myokit.Name(avar)
self.assertEqual(ws.ex(a), 'c.a')
self.assertEqual(wd.ex(a), 'c.a')
# Number with unit
b = myokit.Number('12', 'pF')
self.assertEqual(ws.ex(b), '12.0f')
self.assertEqual(wd.ex(b), '12.0')
# Prefix plus
x = myokit.PrefixPlus(b)
self.assertEqual(ws.ex(x), '12.0f')
self.assertEqual(wd.ex(x), '12.0')
# Prefix minus
x = myokit.PrefixMinus(b)
self.assertEqual(ws.ex(x), '(-12.0f)')
self.assertEqual(wd.ex(x), '(-12.0)')
# Plus
x = myokit.Plus(a, b)
self.assertEqual(ws.ex(x), 'c.a + 12.0f')
self.assertEqual(wd.ex(x), 'c.a + 12.0')
# Minus
x = myokit.Minus(a, b)
self.assertEqual(ws.ex(x), 'c.a - 12.0f')
self.assertEqual(wd.ex(x), 'c.a - 12.0')
# Multiply
x = myokit.Multiply(a, b)
self.assertEqual(ws.ex(x), 'c.a * 12.0f')
self.assertEqual(wd.ex(x), 'c.a * 12.0')
# Divide
x = myokit.Divide(a, b)
self.assertEqual(ws.ex(x), 'c.a / 12.0f')
self.assertEqual(wd.ex(x), 'c.a / 12.0')
# Quotient
x = myokit.Quotient(a, b)
self.assertEqual(ws.ex(x), 'floorf(c.a / 12.0f)')
self.assertEqual(wd.ex(x), 'floor(c.a / 12.0)')
# Remainder
x = myokit.Remainder(a, b)
self.assertEqual(ws.ex(x), 'c.a - 12.0f * (floorf(c.a / 12.0f))')
self.assertEqual(wd.ex(x), 'c.a - 12.0 * (floor(c.a / 12.0))')
# Power
x = myokit.Power(a, b)
self.assertEqual(ws.ex(x), 'powf(c.a, 12.0f)')
self.assertEqual(wd.ex(x), 'pow(c.a, 12.0)')
# Square
x = myokit.Power(a, myokit.Number(2))
self.assertEqual(ws.ex(x), '(c.a * c.a)')
self.assertEqual(wd.ex(x), '(c.a * c.a)')
# Square with brackets
x = myokit.Power(myokit.Plus(a, b), myokit.Number(2))
self.assertEqual(ws.ex(x), '((c.a + 12.0f) * (c.a + 12.0f))')
self.assertEqual(wd.ex(x), '((c.a + 12.0) * (c.a + 12.0))')
# Sqrt
x = myokit.Sqrt(b)
self.assertEqual(ws.ex(x), 'sqrtf(12.0f)')
self.assertEqual(wd.ex(x), 'sqrt(12.0)')
# Exp
x = myokit.Exp(a)
self.assertEqual(ws.ex(x), 'expf(c.a)')
self.assertEqual(wd.ex(x), 'exp(c.a)')
# Log(a)
x = myokit.Log(b)
self.assertEqual(ws.ex(x), 'logf(12.0f)')
self.assertEqual(wd.ex(x), 'log(12.0)')
# Log(a, b)
x = myokit.Log(a, b)
self.assertEqual(ws.ex(x), '(logf(c.a) / logf(12.0f))')
self.assertEqual(wd.ex(x), '(log(c.a) / log(12.0))')
# Log10
x = myokit.Log10(b)
self.assertEqual(ws.ex(x), 'log10f(12.0f)')
self.assertEqual(wd.ex(x), 'log10(12.0)')
# Sin
x = myokit.Sin(b)
self.assertEqual(ws.ex(x), 'sinf(12.0f)')
self.assertEqual(wd.ex(x), 'sin(12.0)')
# Cos
x = myokit.Cos(b)
self.assertEqual(ws.ex(x), 'cosf(12.0f)')
self.assertEqual(wd.ex(x), 'cos(12.0)')
# Tan
x = myokit.Tan(b)
self.assertEqual(ws.ex(x), 'tanf(12.0f)')
self.assertEqual(wd.ex(x), 'tan(12.0)')
# ASin
x = myokit.ASin(b)
self.assertEqual(ws.ex(x), 'asinf(12.0f)')
self.assertEqual(wd.ex(x), 'asin(12.0)')
# ACos
x = myokit.ACos(b)
self.assertEqual(ws.ex(x), 'acosf(12.0f)')
self.assertEqual(wd.ex(x), 'acos(12.0)')
# ATan
x = myokit.ATan(b)
self.assertEqual(ws.ex(x), 'atanf(12.0f)')
self.assertEqual(wd.ex(x), 'atan(12.0)')
# Floor
x = myokit.Floor(b)
self.assertEqual(ws.ex(x), 'floorf(12.0f)')
self.assertEqual(wd.ex(x), 'floor(12.0)')
# Ceil
x = myokit.Ceil(b)
self.assertEqual(ws.ex(x), 'ceilf(12.0f)')
self.assertEqual(wd.ex(x), 'ceil(12.0)')
# Abs
x = myokit.Abs(b)
self.assertEqual(ws.ex(x), 'fabsf(12.0f)')
self.assertEqual(wd.ex(x), 'fabs(12.0)')
# Equal
x = myokit.Equal(a, b)
self.assertEqual(ws.ex(x), '(c.a == 12.0f)')
self.assertEqual(wd.ex(x), '(c.a == 12.0)')
# NotEqual
x = myokit.NotEqual(a, b)
self.assertEqual(ws.ex(x), '(c.a != 12.0f)')
self.assertEqual(wd.ex(x), '(c.a != 12.0)')
# More
x = myokit.More(a, b)
self.assertEqual(ws.ex(x), '(c.a > 12.0f)')
self.assertEqual(wd.ex(x), '(c.a > 12.0)')
# Less
x = myokit.Less(a, b)
self.assertEqual(ws.ex(x), '(c.a < 12.0f)')
self.assertEqual(wd.ex(x), '(c.a < 12.0)')
# MoreEqual
x = myokit.MoreEqual(a, b)
self.assertEqual(ws.ex(x), '(c.a >= 12.0f)')
self.assertEqual(wd.ex(x), '(c.a >= 12.0)')
# LessEqual
x = myokit.LessEqual(a, b)
self.assertEqual(ws.ex(x), '(c.a <= 12.0f)')
self.assertEqual(wd.ex(x), '(c.a <= 12.0)')
# Not
cond1 = myokit.parse_expression('5 > 3')
cond2 = myokit.parse_expression('2 < 1')
x = myokit.Not(cond1)
self.assertEqual(ws.ex(x), '!((5.0f > 3.0f))')
self.assertEqual(wd.ex(x), '!((5.0 > 3.0))')
# And
x = myokit.And(cond1, cond2)
self.assertEqual(ws.ex(x), '((5.0f > 3.0f) && (2.0f < 1.0f))')
self.assertEqual(wd.ex(x), '((5.0 > 3.0) && (2.0 < 1.0))')
# Or
x = myokit.Or(cond1, cond2)
self.assertEqual(ws.ex(x), '((5.0f > 3.0f) || (2.0f < 1.0f))')
self.assertEqual(wd.ex(x), '((5.0 > 3.0) || (2.0 < 1.0))')
# If
x = myokit.If(cond1, a, b)
self.assertEqual(ws.ex(x), '((5.0f > 3.0f) ? c.a : 12.0f)')
self.assertEqual(wd.ex(x), '((5.0 > 3.0) ? c.a : 12.0)')
# Piecewise
c = myokit.Number(1)
x = myokit.Piecewise(cond1, a, cond2, b, c)
self.assertEqual(
ws.ex(x), '((5.0f > 3.0f) ? c.a : ((2.0f < 1.0f) ? 12.0f : 1.0f))')
self.assertEqual(wd.ex(x),
'((5.0 > 3.0) ? c.a : ((2.0 < 1.0) ? 12.0 : 1.0))')
# Test fetching using ewriter method
w = myokit.formats.ewriter('cuda')
self.assertIsInstance(w, myokit.formats.cuda.CudaExpressionWriter)
# Test without a Myokit expression
self.assertRaisesRegex(ValueError, 'Unknown expression type', w.ex, 7)
