def quadratic_denom_rule(integral):
integrand, symbol = integral
a = sympy.Wild('a', exclude=[symbol])
b = sympy.Wild('b', exclude=[symbol])
c = sympy.Wild('c', exclude=[symbol])
match = integrand.match(a / (b * symbol ** 2 + c))
if not match:
return
a, b, c = match[a], match[b], match[c]
return PiecewiseRule([(ArctanRule(a, b, c, integrand, symbol), sympy.Gt(c / b, 0)),
(ArccothRule(a, b, c, integrand, symbol), sympy.And(sympy.Gt(symbol ** 2, -c / b), sympy.Lt(c / b, 0))),
(ArctanhRule(a, b, c, integrand, symbol), sympy.And(sympy.Lt(symbol ** 2, -c / b), sympy.Lt(c / b, 0))),
], integrand, symbol)
def test_pheno(parser):
code = """$PK
IF(AMT.GT.0) BTIME=TIME
TAD=TIME-BTIME
TVCL=THETA(1)*WGT
TVV=THETA(2)*WGT
IF(APGR.LT.5) TVV=TVV*(1+THETA(3))
CL=TVCL*EXP(ETA(1))
V=TVV*EXP(ETA(2))
S1=V
"""
rec = parser.parse(code).records[0]
assert len(rec.statements) == 8
assert rec.statements[0].symbol == S('BTIME')
assert rec.statements[1].symbol == S('TAD')
assert rec.statements[2].symbol == S('TVCL')
assert rec.statements[3].symbol == S('TVV')
assert rec.statements[4].symbol == S('TVV')
assert rec.statements[5].symbol == S('CL')
assert rec.statements[6].symbol == S('V')
assert rec.statements[7].symbol == S('S1')
assert rec.statements[0].expression == sympy.Piecewise(
(S('TIME'), sympy.Gt(S('AMT'), 0)), (0, True))
assert rec.statements[1].expression == S('TIME') - S('BTIME')
assert rec.statements[2].expression == S('THETA(1)') * S('WGT')
assert rec.statements[3].expression == S('THETA(2)') * S('WGT')
assert rec.statements[4].expression == sympy.Piecewise(
(S('TVV') * (1 + S('THETA(3)')), sympy.Lt(S('APGR'), 5)),
(S('TVV'), True))
assert rec.statements[5].expression == S('TVCL') * sympy.exp(S('ETA(1)'))
assert rec.statements[6].expression == S('TVV') * sympy.exp(S('ETA(2)'))
assert rec.statements[7].expression == S('V')
symbol_names = {s.name for s in rec.statements.free_symbols}
assert symbol_names == {
'AMT',
'BTIME',
'TIME',
'TAD',
'TVCL',
'THETA(1)',
'WGT',
'TVV',
'THETA(2)',
'APGR',
'THETA(3)',
'CL',
'ETA(1)',
'V',
'ETA(2)',
'S1',
}
def extreme(fn, over, maximizing):
"""Maximizes [minimizes] the function fn for 'over'. Returns the
first extreme expression and a list of conditions for it to be a
maximum [minimum].
>>> sp.var('x p', positive=True)
(x, p)
>>> theta = sp.Symbol('theta', positive=True)
>>> fn = p*x - theta*x*x
>>> maximize(fn, x)
(p/(2*theta), 0 < theta)
>>> maximize(fn.subs(theta, 1), x)
(p/2, 0 <= p)
>>> maximize(fn.subs(theta, -1), x)
(None, False)
"""
first = sp.diff(fn, over)
extremes_at = sp.solve(first, over)
second = sp.diff(first, over)
for m in extremes_at:
positive = False
try:
## We only want values of over that are positive.
positive = sp.solve(sp.Ge(m, 0))
except:
## Inequality solve only works with a single variable.
## Assume it is true. We are missing a condition.
positive = True
## Checking for inequality to False because an inequality will
## evaluate as False even if present in positive
if positive is not False:
conditions = []
if positive is not True:
conditions.append(positive)
try:
if maximizing:
max_min_cond = sp.solve(sp.Lt(second.subs(over, m), 0))
else:
max_min_cond = sp.solve(sp.Gt(second.subs(over, m), 0))
except:
## Not always works. Assume it is true. We are
## missing a condition.
max_min_cond = True
if max_min_cond:
if max_min_cond is not True:
conditions.append(max_min_cond)
return m, reduce(sp.And, [True] + conditions)
return None, False
def sum_over_piecewise(expr: sympy.Piecewise,
sum_var: sympy.Symbol,
sum_start: typing.Union[sympy.Basic, int],
sum_end: sympy.Basic,
extra_condition: sympy.Basic = True) -> sympy.Expr:
"""
:return: equivalent to Sum(expr, (sum_var, sum_start, sum_end)), but we try to remove the piecewise.
We assume that the piecewise conditions also depend on sum_var.
"""
assert sum_var.is_Integer or sum_var.assumptions0["integer"]
assert isinstance(expr, sympy.Piecewise)
res = sympy.sympify(0)
cond_start = sympy.Ge(sum_var, sum_start)
cond_end = sympy.Le(sum_var, sum_end)
prev_ranges = [(None, sum_start - 1), (sum_end + 1, None)]
def check(cond__):
false_cond = simplify_and(sympy.And(sympy.Not(cond__),
extra_condition))
if false_cond == sympy.sympify(False):
return True
true_cond = simplify_and(sympy.And(cond__, extra_condition))
if true_cond == sympy.sympify(False):
return False
return None
for value, cond in expr.args:
j = 0
while j < len(prev_ranges) - 1:
cond_r_start = sympy.Ge(sum_var, prev_ranges[j][1] + 1)
cond_r_end = sympy.Le(sum_var, prev_ranges[j + 1][0] - 1)
cond = sympy.And(cond, cond_start, cond_end, cond_r_start,
cond_r_end)
cond_ = simplify_and(cond,
sum_var,
extra_conditions=extra_condition)
# print(cond, "->", cond_)
if cond_ == sympy.sympify(False):
j += 1
continue
if isinstance(cond_, sympy.And):
if any(
[sum_var not in part.free_symbols for part in cond_.args]):
new_extra_conditions = [
part for part in cond_.args
if sum_var not in part.free_symbols
]
new_extra_condition = sympy.And(*new_extra_conditions)
if check(new_extra_condition) is False:
j += 1
continue
assert check(new_extra_condition)
cond_ = sympy.And(*[
part for part in cond_.args
if sum_var in part.free_symbols
])
r = range_from_relationals(cond_, sum_var)
if r[0] is None: # e.g. if cond_start == True because sum_var is >= 0 always
r = (sum_start, r[1])
if sympy.Eq(r[0], r[1]) == sympy.sympify(True):
res += value.subs(sum_var, r[0])
else:
res += sympy.Sum(value, (sum_var, r[0], r[1])).doit()
for i in range(1, len(prev_ranges) + 1):
assert i < len(prev_ranges), "where to insert %r?" % (
r, ) # should not get past here
assert check(sympy.Gt(r[0], prev_ranges[i - 1][1]))
if check(sympy.Eq(r[0] - 1, prev_ranges[i - 1][1])):
prev_ranges[i - 1] = (prev_ranges[i - 1][0], r[1])
break
if check(sympy.Lt(r[0], prev_ranges[i][0])) or check(
sympy.Lt(r[1], prev_ranges[i][0])):
if check(sympy.Eq(r[1] + 1, prev_ranges[i][0])):
prev_ranges[i] = (r[0], prev_ranges[i][1])
else:
prev_ranges.insert(i, r)
break
# print("prev ranges:", prev_ranges)
j = 0 # start over...
if len(prev_ranges) == 2 and sympy.Eq(
prev_ranges[0][1], prev_ranges[1][0]) == sympy.sympify(True):
# We have the full range covered.
break
return res.simplify()
def gen_greaterthan(self, ident, val):
return sym.Gt(val.exp_a, val.exp_b)
def __bool__(self):
return bool(self.shape_env.evaluate_expr(self.expr))
# Methods that have a `__foo__` as well as `__rfoo__`
reflectable_magic_methods = {
'add': lambda a, b: a + b,
'sub': lambda a, b: a - b,
'mul': lambda a, b: a * b,
'mod': lambda a, b: a % b,
}
magic_methods = {
**reflectable_magic_methods,
'eq': lambda a, b: sympy.Eq(a, b),
'gt': lambda a, b: sympy.Gt(a, b),
'lt': lambda a, b: sympy.Lt(a, b),
'le': lambda a, b: sympy.Le(a, b),
'ge': lambda a, b: sympy.Ge(a, b),
}
for method, _func in magic_methods.items():
method_name = f'{method}'
def _create_magic_impl(func):
def magic_impl(self, other):
if isinstance(other, PySymInt):
other = other.expr
return PySymInt(func(self.expr, other), self.shape_env)
return magic_impl
def _ex_more(self, e):
return sp.Gt(self.ex(e[0]), self.ex(e[1]))
sympy.atan(1) - sympy.asin(S('X')) / sympy.acos(S('X'))),
('$PRED CL = INT(-2.2)', S('CL'), -2),
('$PRED CL = INT(0.2)', S('CL'), 0),
('$PRED CL = MOD(1, 2)', S('CL'), sympy.Mod(1, 2)),
('$PRED CL = GAMLN(2 + X) ;COMMENT', S('CL'),
sympy.loggamma(S('X') + 2)),
('$PRED IF (X.EQ.2) CL=23', S('CL'),
sympy.Piecewise((23, sympy.Eq(S('X'), 2)))),
('$PRED IF (X.NE.1.5) CL=THETA(1)', S('CL'),
sympy.Piecewise((S('THETA(1)'), sympy.Ne(S('X'), 1.5)))),
('$PRED IF (X.EQ.2+1) CL=23', S('CL'),
sympy.Piecewise((23, sympy.Eq(S('X'), 3)))),
('$PRED IF (X < ETA(1)) CL=23', S('CL'),
sympy.Piecewise((23, sympy.Lt(S('X'), S('ETA(1)'))))),
('$PK IF(AMT.GT.0) BTIME=TIME', S('BTIME'),
sympy.Piecewise((S('TIME'), sympy.Gt(S('AMT'), 0)))),
('$PRED IF (X.EQ.2.AND.Y.EQ.3) CL=23', S('CL'),
sympy.Piecewise(
(23, sympy.And(sympy.Eq(S('X'), 2), sympy.Eq(S('Y'), 3))))),
('$PRED IF (X.EQ.2.OR.Y.EQ.3) CL=23', S('CL'),
sympy.Piecewise(
(23, sympy.Or(sympy.Eq(S('X'), 2), sympy.Eq(S('Y'), 3))))),
('$PRED IF (.NOT.X.EQ.2) CL=25', S('CL'),
sympy.Piecewise((25, sympy.Not(sympy.Eq(S('X'), 2))))),
('$PRED IF (Q.EQ.(R+C)/D) L=0', S('L'),
sympy.Piecewise(
(0, sympy.Eq(S('Q'), sympy.Mul(sympy.Add(S('R'), S('C')),
1 / S('D')))))),
('$PRED IF (Q.EQ.R+C/D) L=0', S('L'),
sympy.Piecewise((0, sympy.Eq(S('Q'),
S('R') + S('C') / S('D'))))),
def _make_comparison_question(context, left, right):
"""Makes a question for comparing two values."""
if random.choice([False, True]) and sympy.Ne(left.value, right.value):
# Do question of form: "Which is bigger: a or b?".
if random.choice([False, True]):
answer = (left.handle
if sympy.Gt(left.value, right.value) else right.handle)
template = random.choice([
'Mana yang lebih besar: {left} atau {right}?',
])
else:
answer = (left.handle
if sympy.Lt(left.value, right.value) else right.handle)
template = random.choice([
'Mana yang lebih kecil: {left} atau {right}?',
])
return example.Problem(question=example.question(context,
template,
left=left,
right=right),
answer=answer)
comparisons = {
'<': sympy.Lt,
'<=': sympy.Le,
'>': sympy.Gt,
'>=': sympy.Ge,
'=': sympy.Eq,
'!=': sympy.Ne,
}
templates = {
'<': [
'Apakah {left} ' + ops.LT_SYMBOL + ' {right}?',
'Apakah {left} kurang dari {right}?',
'Apakah {left} lebih kecil dari {right}?',
],
'<=': [
'Apakah {left} ' + ops.LE_SYMBOL + ' {right}?',
'Apakah {left} kurang dari atau sama dengan {right}?',
'Apakah {left} lebih banyak {right}?',
'Apakah {left} paling tidak sama dengan {right}?',
],
'>': [
'Apakah {left} ' + ops.GT_SYMBOL + ' {right}?',
'Apakah {left} lebih dari {right}?',
'Apakah {left} lebih besar dari {right}?',
],
'>=': [
'Apakah {left} ' + ops.GE_SYMBOL + ' {right}?',
'Apakah {left} lebih dari atau sama dengan {right}?',
'Apakah {left} setidaknya {right}?',
'Apakah {left} setidaknya sama besar dengan {right}?',
],
'=': [
'Apakah {left} ' + ops.EQ_SYMBOL + ' {right}?',
'Apakah {left} dan {right} sama?',
'Apakah {left} sama dengan {right}?',
'Apakah {left} dan {right} memiliki nilai yang sama?',
],
'!=': [
'Apakah {left} ' + ops.NE_SYMBOL + ' {right}?',
'Apakah {left} tidak sama dengan {right}?',
'Apakah {left} dan {right} berbeda?',
'Apakah {left} dan {right} tidak sama?',
'Apakah {left} dan {right} memiliki nilai yang berbeda?',
],
}
comparison = random.choice(list(comparisons.keys()))
template = random.choice(templates[comparison])
question = example.question(context, template, left=left, right=right)
answer = comparisons[comparison](left.value, right.value)
return example.Problem(question=question, answer=answer)
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 xml_to_sympy_expr(self, xml_node):
if isTag(xml_node, '/MathML}cn'):
return float(xml_node.text)
elif isTag(xml_node, '/MathML}ci'):
if xml_node.text not in self.symbol_table:
self.symbol_table[xml_node.text] = sp.Symbol(xml_node.text)
self.extra_assignments[self.symbol_table[xml_node.text]] = None
return self.symbol_table[xml_node.text]
elif not isTag(xml_node, '/MathML}apply'):
raise ValueError("Do not know hot to parse node %s" % xml_node)
try:
func, *arg_children = filterTags(xml_node.getchildren())
except ValueError:
raise
processed_args = []
for child in arg_children:
processed_args.append(self.xml_to_sympy_expr(child))
if isTag(func, '/MathML}plus'):
out_expr = sp.Add(*processed_args)
elif isTag(func, '/MathML}times'):
out_expr = sp.Mul(*processed_args)
elif isTag(func, '/MathML}power'):
if len(processed_args) != 2:
raise ValueError("Power is a binary operation!")
out_expr = sp.Pow(*processed_args)
elif isTag(func, '/MathML}divide'):
if len(processed_args) != 2:
raise ValueError("Division is a binary operation!")
out_expr = sp.Mul(processed_args[0], sp.Pow(processed_args[1], -1))
elif isTag(func, '/MathML}minus'):
if (len(processed_args) > 2) or (len(processed_args) == 0):
raise ValueError("Subtraction is a unitary or binary operation!")
elif len(processed_args) == 2:
out_expr = sp.Add(processed_args[0], sp.Mul(processed_args[1], -1))
elif len(processed_args) == 1:
out_expr = sp.Mul(processed_args[0], -1)
elif isTag(func, '/MathML}abs'):
if len(processed_args) != 1:
raise ValueError("Absolute value is a unitary operation!")
out_expr = sp.Abs(processed_args[0])
elif isTag(func, '/MathML}cos'):
if len(processed_args) != 1:
raise ValueError("cos is a unitary operation!")
out_expr = sp.cos(processed_args[0])
elif isTag(func, '/MathML}sin'):
if len(processed_args) != 1:
raise ValueError("sin is a unitary operation!")
out_expr = sp.sin(processed_args[0])
elif isTag(func, '/MathML}csymbol'):
if func.text == 'atan2':
if len(processed_args) != 2:
raise ValueError("atan2 is a binary operation!")
out_expr = sp.atan2(*processed_args)
else:
raise ValueError("Unknown csymbol %s" % func.text)
elif isTag(func, '/MathML}piecewise'):
*pieces, otherwise = func.getchildren()
otherwise_children = filterTags(otherwise.getchildren())
conditions = []
values = []
if len(otherwise_children) != 1:
raise ValueError("Too many `otherwise` children")
for piece in filterTags(pieces):
value_child, condition_child = filterTags(piece.getchildren())
values.append(self.xml_to_sympy_expr(value_child))
conditions.append(self.xml_to_sympy_expr(condition_child))
values.append(self.xml_to_sympy_expr(otherwise_children[0]))
conditions.append(True)
out_expr = sp.Piecewise(*[(value, condition) for value, condition in zip(values, conditions)])
elif isTag(func, '/MathML}lt'):
if len(processed_args) != 2:
raise ValueError("Less than is a binary operation!")
out_expr = sp.Le(*processed_args)
elif isTag(func, '/MathML}gt'):
if len(processed_args) != 2:
raise ValueError("Greater than is a binary operation!")
out_expr = sp.Gt(*processed_args)
elif isTag(func, '/MathML}leq'):
if len(processed_args) != 2:
raise ValueError("Less than equal to is a binary operation!")
out_expr = sp.Le(*processed_args)
elif isTag(func, '/MathML}geq'):
if len(processed_args) != 2:
raise ValueError("Greater than equal to is a binary operation!")
out_expr = sp.Ge(*processed_args)
else:
raise ValueError("Unknown func tag, %s" % func.tag)
if out_expr is None:
raise ValueError("Calculated None")
else:
return out_expr
def _make_comparison_question(context, left, right):
"""Makes a question for comparing two values."""
if random.choice([False, True]) and sympy.Ne(left.value, right.value):
# Do question of form: "Which is bigger: a or b?".
if random.choice([False, True]):
answer = (left.handle
if sympy.Gt(left.value, right.value) else right.handle)
template = random.choice([
'Which is bigger: {left} or {right}?',
'Which is greater: {left} or {right}?',
])
else:
answer = (left.handle
if sympy.Lt(left.value, right.value) else right.handle)
template = random.choice([
'Which is smaller: {left} or {right}?',
])
return example.Problem(question=example.question(context,
template,
left=left,
right=right),
answer=answer)
comparisons = {
'<': sympy.Lt,
'<=': sympy.Le,
'>': sympy.Gt,
'>=': sympy.Ge,
'=': sympy.Eq,
'!=': sympy.Ne,
}
templates = {
'<': [
'Is {left} ' + ops.LT_SYMBOL + ' {right}?',
'Is {left} less than {right}?',
'Is {left} smaller than {right}?',
],
'<=': [
'Is {left} ' + ops.LE_SYMBOL + ' {right}?',
'Is {left} less than or equal to {right}?',
'Is {left} at most {right}?',
'Is {left} at most as big as {right}?',
],
'>': [
'Is {left} ' + ops.GT_SYMBOL + ' {right}?',
'Is {left} greater than {right}?',
'Is {left} bigger than {right}?',
],
'>=': [
'Is {left} ' + ops.GE_SYMBOL + ' {right}?',
'Is {left} greater than or equal to {right}?',
'Is {left} at least {right}?',
'Is {left} at least as big as {right}?',
],
'=': [
'Does {left} ' + ops.EQ_SYMBOL + ' {right}?',
'Are {left} and {right} equal?',
'Is {left} equal to {right}?',
'Do {left} and {right} have the same value?',
],
'!=': [
'Is {left} ' + ops.NE_SYMBOL + ' {right}?',
'Is {left} not equal to {right}?',
'Are {left} and {right} unequal?',
'Are {left} and {right} nonequal?',
'Are {left} and {right} non-equal?',
'Do {left} and {right} have different values?',
],
}
comparison = random.choice(list(comparisons.keys()))
template = random.choice(templates[comparison])
question = example.question(context, template, left=left, right=right)
answer = comparisons[comparison](left.value, right.value)
return example.Problem(question=question, answer=answer)
def _make_comparison_question(context, left, right):
"""Makes a question for comparing two values."""
if random.choice([False, True]) and sympy.Ne(left.value, right.value):
# Do question of form: "Which is bigger: a or b?".
if random.choice([False, True]):
answer = (left.handle
if sympy.Gt(left.value, right.value) else right.handle)
template = random.choice([
'Что больше: {left} или {right}?',
'Какое из чисел больше: {left} или {right}?',
])
else:
answer = (left.handle
if sympy.Lt(left.value, right.value) else right.handle)
template = random.choice([
'Что меньше: {left} или {right}?',
'Какое число меньше: {left} или {right}?'
])
return example.Problem(question=example.question(context,
template,
left=left,
right=right),
answer=answer)
comparisons = {
'<': sympy.Lt,
'<=': sympy.Le,
'>': sympy.Gt,
'>=': sympy.Ge,
'=': sympy.Eq,
'!=': sympy.Ne,
}
templates = {
'<': [
'Правда ли, что {left} ' + ops.LT_SYMBOL + ' {right}?',
'{left} меньше, чем {right}?',
'Число {left} меньше числа {right}?',
],
'<=': [
'Правда ли, что {left} ' + ops.LE_SYMBOL + ' {right}?',
'Правда ли, что {left} меньше или равно {right}?',
'Число {left} не больше {right}?',
'Число {left} не превосходит {right}?',
],
'>': [
'Правда ли, что {left} ' + ops.GT_SYMBOL + ' {right}?',
'{left} больше, чем {right}?',
'Число {left} больше числа {right}?',
],
'>=': [
'Правда ли, что {left} ' + ops.GE_SYMBOL + ' {right}?',
'Правда ли, что {left} больше или равно {right}?',
'Число {left} не меньше {right}?',
],
'=': [
'Правда ли, что {left} ' + ops.EQ_SYMBOL + ' {right}?',
'Равны ли {left} и {right}?',
'Число {left} равно числу {right}?',
'Одинаковы ли {left} и {right}?',
],
'!=': [
'Правда ли, что {left} ' + ops.NE_SYMBOL + ' {right}?',
'Число {left} не равно {right}?',
'Числа {left} и {right} не равны?',
'Значения числа {left} и числа {right} отличаются?',
'{left} и {right} не равны друг другу?',
],
}
comparison = random.choice(list(comparisons.keys()))
template = random.choice(templates[comparison])
question = example.question(context, template, left=left, right=right)
answer = comparisons[comparison](left.value, right.value)
return example.Problem(question=question, answer=answer)
def _symcheck():
# import sympy as sym
# # Create the index for our indexable sequence objects
# i = sym.symbols('i', cls=sym.Idx)
# measured = list(map(sym.IndexedBase, ['A_m', 'B_m', 'C_m']))
# smoothed = list(map(sym.IndexedBase, ['A_s', 'B_s', 'C_s']))
# for S in smoothed:
# S[0] = 0
# for M, S in zip(measured, smoothed):
# M[i]
# pass
# for r in raw_values:
# z = r[i]
# .is_nonnegative = True
# r.is_real = True
###########
# I'm not sure how to used index objects correctly, so lets hack it
import sympy as sym
kw = dict(is_nonnegative=True, is_real=True)
measured = {'A_m': [], 'B_m': [], 'C_m': [], 'T_m': []}
smoothed = {'A_s': [], 'B_s': [], 'C_s': [], 'T_s': []}
for i in range(3):
_syms = sym.symbols('A_m{i}, B_m{i}, C_m{i}, T_m{i}'.format(i=i), **kw)
for _sym in _syms:
prefix = _sym.name[0:-1]
measured[prefix].append(_sym)
_syms = sym.symbols('A_s{i}, B_s{i}, C_s{i}, T_s{i}'.format(i=i), **kw)
for _sym in _syms:
prefix = _sym.name[0:-1]
smoothed[prefix].append(_sym)
# alpha, beta = sym.symbols('α, β', is_real=1, is_positive=True)
# constraints.append(sym.Eq(beta, 1 - alpha))
# constraints.append(sym.Le(alpha, 1))
# constraints.append(sym.Ge(alpha, 0))
constraints = []
N = 2
alpha = 0.6
beta = 1 - 0.6
for i in range(N):
# Total measure constraints
constr = sym.Eq(
measured['T_m'][i],
measured['A_m'][i] + measured['B_m'][i] + measured['C_m'][i])
# EWMA constraints
for s_key in smoothed.keys():
m_key = s_key.replace('_s', '_m')
S = smoothed[s_key]
M = measured[m_key]
if i == 0:
constr = sym.Eq(S[i], M[i])
constraints.append(constr)
else:
constr = sym.Eq(S[i], M[i] * alpha + beta * S[i - 1])
constraints.append(constr)
constr = sym.Eq(
measured['T_m'][i],
measured['A_m'][i] + measured['B_m'][i] + measured['C_m'][i])
constraints.append(constr)
from sympy.solvers.solveset import linear_eq_to_matrix
from sympy.solvers.solveset import linsolve
import itertools as it
import ubelt as ub
all_symbols = list(
ub.flatten(it.chain(measured.values(), smoothed.values())))
# WE WANT TO KNOW IF THIS IS POSSIBLE
constraints.append(sym.Gt(measured['A_m'][-1], measured['T_m'][-1]), )
A, b = linear_eq_to_matrix(constraints, all_symbols)
linsolve((A, b))
