def expand_integer_powers(cls, expr):
"""
Convert integer powers in an expression to Muls, e.g. a**3 => a*a*a.
This is used when printing to C-style strings as it is more accurate.
"""
if isinstance(expr, sympy.Basic):
integer_pows = list(p for p in expr.atoms(sympy.Pow) if (
p.as_base_exp()[1].is_Integer and abs(p.as_base_exp()[1]) > 1))
to_replace = {}
for int_pow in integer_pows:
base, expn = int_pow.as_base_exp()
repl = sympy.Mul(*([base] * abs(expn)), evaluate=False)
if expn < 0:
repl = sympy.Pow(repl, -1)
to_replace[int_pow] = repl
if to_replace:
expr = cls._non_eval_xreplace(expr, to_replace)
return expr
def timeconst(self):
"""Convert rational function to time constant form with unity
lowest power of denominator.
See also canonical, general, partfrac, standard, and ZPK"""
N, D, delay, undef = self.as_ratfun_delay_undef()
var = self.var
Npoly = sym.Poly(N, var)
Dpoly = sym.Poly(D, var)
K = Dpoly.EC()
D = D / K
N = N / K
return sym.Mul(N, sym.Pow(D, -1), evaluate=False) * sym.exp(
self.var * delay) * undef
def convert_sympy(expr):
"converts top-level to sympy"
leaves = expr.get_leaves()
if isinstance(expr, Integer):
return sympy.Integer(expr.get_int_value())
if expr.has_form('Power', 2):
# sympy won't expand `(a + b) / x` to `a / x + b / x` if denom is False
# if denom is False we store negative powers to prevent this.
n1 = leaves[1].get_int_value()
if not denom and n1 is not None and n1 < 0:
return store_sub_expr(expr)
return sympy.Pow(*[convert_sympy(leaf) for leaf in leaves])
elif expr.has_form('Times', 2, None):
return sympy.Mul(*[convert_sympy(leaf) for leaf in leaves])
elif expr.has_form('Plus', 2, None):
return sympy.Add(*[convert_sympy(leaf) for leaf in leaves])
else:
return store_sub_expr(expr)
def calc(function, x0, eps):
# firstly, check if it's polynome
if is_polynome(function):
return function.subs({x: x0})
# then check if it's elementary
if is_elementary(function):
g = function.args[0]
f_du = function.diff()
_, b = estimate_abs(f_du, x0)
u = calc(g, float(x0), eps / b)
return calc_elem_func(function.func, u, eps)
# at last, check top-level term
if len(function.args) == 2:
# f(x) = g(x) + h(x)
if function.func == sp.Add:
g, h = function.args
u = calc(g, x0, eps / 2)
v = calc(h, x0, eps / 2)
return u + v
# f(x) = g(x) ** k
if function.func == sp.Pow:
k = function.args[1]
if isinstance(k, sp.Integer):
g = function.args[0]
derivative = k * sp.Pow(x, k - 1)
b_u0, b_u1 = estimate_abs(derivative, x0)
u = calc(g, x0, eps / b_u1)
return u**k
raise NotImplementedError(
f'calculating f(x) ** {k} it too hard for me yet')
# f(x) = g(x) * h(x)
if function.func == sp.Mul:
raise NotImplementedError(function.func)
raise NotImplementedError(function.func)
def convert_frac(frac):
diff_op = False
partial_op = False
lower_itv = frac.lower.getSourceInterval()
lower_itv_len = lower_itv[1] - lower_itv[0] + 1
if (frac.lower.start == frac.lower.stop
and frac.lower.start.type == PSLexer.DIFFERENTIAL):
wrt = get_differential_var_str(frac.lower.start.text)
diff_op = True
elif (lower_itv_len == 2 and frac.lower.start.type == PSLexer.SYMBOL
and frac.lower.start.text == '\\partial'
and (frac.lower.stop.type == PSLexer.LETTER
or frac.lower.stop.type == PSLexer.SYMBOL)):
partial_op = True
wrt = frac.lower.stop.text
if frac.lower.stop.type == PSLexer.SYMBOL:
wrt = wrt[1:]
if diff_op or partial_op:
wrt = sympy.Symbol(wrt)
if (diff_op and frac.upper.start == frac.upper.stop
and frac.upper.start.type == PSLexer.LETTER
and frac.upper.start.text == 'd'):
return [wrt]
elif (partial_op and frac.upper.start == frac.upper.stop
and frac.upper.start.type == PSLexer.SYMBOL
and frac.upper.start.text == '\\partial'):
return [wrt]
upper_text = rule2text(frac.upper)
expr_top = None
if diff_op and upper_text.startswith('d'):
expr_top = process_sympy(upper_text[1:])
elif partial_op and frac.upper.start.text == '\\partial':
expr_top = process_sympy(upper_text[len('\\partial'):])
if expr_top:
return sympy.Derivative(expr_top, wrt)
expr_top = convert_expr(frac.upper)
expr_bot = convert_expr(frac.lower)
return sympy.Mul(expr_top,
sympy.Pow(expr_bot, -1, evaluate=False),
evaluate=False)
def __init__(self, given, prove):
# Operators and modifiers of interest
self.operators = [sympy.Mul, sympy.Add] # , sympy.Pow]
self.modifiers = [sympy.sin, sympy.cos] # , sympy.exp]
print('Proof Generator initialized...')
# Parse into left and right expressions
sGivenLeft, sGivenRight = given.split('=')
self.givenLeft = parse_expr(sGivenLeft, evaluate=False)
self.givenRight = parse_expr(sGivenRight, evaluate=False)
print('Given: ', self.givenLeft, ' = ', self.givenRight)
sProveLeft, sProveRight = prove.split('=')
self.proveLeft = parse_expr(sProveLeft, evaluate=False)
self.proveRight = parse_expr(sProveRight, evaluate=False)
print('Prove: ', self.proveLeft, ' = ', self.proveRight)
# Setup full set of possible symbols
symbolsTemp = (self.givenLeft.free_symbols
| self.givenRight.free_symbols
| self.proveLeft.free_symbols
| self.proveRight.free_symbols)
self.symbols = []
self.symbols.extend(symbolsTemp)
for m in self.modifiers:
for s in symbolsTemp:
self.symbols.append(m(s))
symbolsTemp = self.symbols[:]
for s in symbolsTemp:
self.symbols.append(sympy.Pow(s, -1))
self.symbols.append(sympy.Mul(
-1,
s,
))
# Setup node handler
self.handler = NodeHandler()
tempDist = self.Distance(self.givenLeft, self.givenRight,
self.proveLeft, self.proveRight)
self.handler.Add(self.givenLeft, self.givenRight, tempDist, [])
def generate_Sa_Sb_Sn_operators(atom_list, Sp_list, Sm_list):
"""Generates Sa, Sb, Sn operators"""
Sa_list = []
Sb_list = []
Sn_list = []
N = len(atom_list)
S = sp.Symbol('S', commutative=True)
for i in range(N):
Sa = ((1 / 2) * (Sp_list[i] + Sm_list[i])).expand()
Sb = ((1 / 2) * (1 / I) * (Sp_list[i] - Sm_list[i])).expand()
Sn = (S - sp.Pow(2 * S, -1) * Sm_list[i].expand() *
Sp_list[i].expand()).expand()
Sa_list.append(Sa)
Sb_list.append(Sb)
Sn_list.append(Sn)
print "Operators Generated: Sa, Sb, Sn"
return (Sa_list, Sb_list, Sn_list)
def _arg_func_from_proto(
func: v2.program_pb2.ArgFunction,
*,
arg_function_language: str,
required_arg_name: Optional[str] = None,
) -> Optional[ARG_RETURN_LIKE]:
supported = SUPPORTED_FUNCTIONS_FOR_LANGUAGE.get(arg_function_language)
if supported is None:
raise ValueError(
f'Unrecognized arg_function_language: {arg_function_language!r}')
if func.type not in supported:
raise ValueError(
f'Unrecognized function type {func.type!r} '
f'for arg_function_language={arg_function_language!r}')
if func.type == 'add':
return sympy.Add(*[
arg_from_proto(
a,
arg_function_language=arg_function_language,
required_arg_name='An addition argument',
) for a in func.args
])
if func.type == 'mul':
return sympy.Mul(*[
arg_from_proto(
a,
arg_function_language=arg_function_language,
required_arg_name='A multiplication argument',
) for a in func.args
])
if func.type == 'pow':
return sympy.Pow(*[
arg_from_proto(
a,
arg_function_language=arg_function_language,
required_arg_name='A power argument',
) for a in func.args
])
return None
def make_term_depth_three(**kwargs):
if 'seed' in kwargs:
seed = kwargs['seed']
else:
seed = random.random()
random.seed(seed)
out = ''
if kwargs == {}:
oper3 = random.choice(['prod', 'quot', 'power'])
term1 = make_term_depth_two()
term2 = make_term_depth_two()
elif 'oper3' in kwargs:
oper3 = kwargs['oper3']
else:
oper3 = random.choice(['prod', 'quot', 'power'])
if 'oper1' in kwargs:
kwargs['oper'] = kwargs['oper1']
term1 = make_term_depth_two(**kwargs)
else:
term1 = make_term_depth_two(**kwargs)
if 'oper2' in kwargs:
kwargs['oper'] = kwargs['oper2']
kwargs['seed'] = 1 - kwargs['seed']
term2 = make_term_depth_two(**kwargs)
else:
kwargs['seed'] = 1 - kwargs['seed']
term2 = make_term_depth_two(**kwargs)
if oper3 == 'prod':
out += '\\left(' + term1['fmt'] + '\\right)'
out += '\\left(' + term2['fmt'] + '\\right)'
term = term1['sym'] * term2['sym']
if oper3 == 'quot':
out += '\\frac{{{expr1}}}{{{expr2}}}'.format(
expr1=term1['fmt'], expr2=term2['fmt'])
term = term1['sym'] / term2['sym']
if oper3 == 'power':
random.seed(seed)
power = random.randint(-5, 5)
out += '\\left({expr}\\right)^{{{power}}}'.format(
expr=term1['fmt'], power=power)
term = sy.Pow(term1['sym'], power)
return {'fmt': out, 'sym': term}
def convert_exp(exp):
if hasattr(exp, 'exp'):
exp_nested = exp.exp()
else:
exp_nested = exp.exp_nofunc()
if exp_nested:
base = convert_exp(exp_nested)
if isinstance(base, list):
raise LaTeXParsingError("Cannot raise derivative to power")
if exp.atom():
exponent = convert_atom(exp.atom())
elif exp.expr():
exponent = convert_expr(exp.expr())
return sympy.Pow(base, exponent, evaluate=False)
else:
if hasattr(exp, 'comp'):
return convert_comp(exp.comp())
else:
return convert_comp(exp.comp_nofunc())
def inverse_laplace_power(expr, s, t, **assumptions):
# Handle expressions with a power of s.
if not (expr.is_Pow and expr.args[0] == s):
raise ValueError('Expression %s is not a power of s' % expr)
exponent = expr.args[1]
# Have many possible forms; the common ones are:
# s**a, s**-a, s**(1+a), s**(1-a), s**-(1+a), s**(a-1)
# Cannot tell if 1-a is positive.
if exponent.is_positive:
# Unfortunately, SymPy does not seem to support fractional
# derivatives...
return sym.Derivative(sym.DiracDelta(t), t, exponent, evaluate=False)
if exponent.is_negative:
return sym.Pow(t, -exponent - 1) / sym.Gamma(-exponent)
raise ValueError('Cannot determine sign of exponent for %s' % expr)
def eval_default(*args):
func, symbol = args[-2], args[-1]
if isinstance(func, sympy.Symbol):
func = sympy.Pow(func, 1, evaluate=False)
# Automatically derive and apply the rule (don't use diff() directly as
# chain rule is a separate step)
substitutions = []
mapping = {}
constant_symbol = sympy.Dummy()
for arg in func.args:
if symbol in arg.free_symbols:
mapping[symbol] = arg
substitutions.append(symbol)
else:
mapping[constant_symbol] = arg
substitutions.append(constant_symbol)
rule = func.func(*substitutions).diff(symbol)
return rule.subs(mapping)
def convert_mp(mp):
if hasattr(mp, 'mp'):
mp_left = mp.mp(0)
mp_right = mp.mp(1)
else:
mp_left = mp.mp_nofunc(0)
mp_right = mp.mp_nofunc(1)
if mp.MUL() or mp.CMD_TIMES() or mp.CMD_CDOT():
lh = convert_mp(mp_left)
rh = convert_mp(mp_right)
return sympy.Mul(lh, rh, evaluate=False)
elif mp.DIV() or mp.CMD_DIV() or mp.COLON():
lh = convert_mp(mp_left)
rh = convert_mp(mp_right)
return sympy.Mul(lh, sympy.Pow(rh, -1, evaluate=False), evaluate=False)
else:
if hasattr(mp, 'unary'):
return convert_unary(mp.unary())
else:
return convert_unary(mp.unary_nofunc())
def test_derivatives_wrt_t(self):
''' Compare the derivative w.r.t. t of the symbolic and the implemented
Legendre Polynomials'''
for item in range(0, 100):
Bimpl = cBasis1000()
tau_ = 10.0 * np.random.rand()
s_ = np.random.rand() * 2.0 - 1.0
ddeg = np.random.randint(1, 6)
B = [
Bi.diff(self.ssym_, ddeg) * sp.Pow(2 / self.tausym_, ddeg)
for Bi in self.Bsym_
]
B = [Bi.subs({self.tausym_: tau_}) for Bi in B]
B = [sp.lambdify(self.ssym_, Bi) for Bi in B]
B = np.array([Bi(s_) for Bi in B])
e = np.max(np.abs(B - Bimpl.evalDerivOnWindow(s_, tau_, ddeg)))
assert (
e < 5.0e-3
), 'Large error on derivatives wrt t, error = {:+.3e}'.format(e)
def pow_to_mul(expr):
if expr.is_Atom or expr.is_Indexed:
return expr
elif expr.is_Pow:
base, exp = expr.as_base_exp()
if exp > 10 or exp < -10 or int(exp) != exp or exp == 0:
# Large and non-integer powers remain untouched
return expr
elif exp == -1:
# Reciprocals also remain untouched, but we traverse the base
# looking for other Pows
return expr.func(pow_to_mul(base), exp, evaluate=False)
elif exp > 0:
return sympy.Mul(*[base]*int(exp), evaluate=False)
else:
# SymPy represents 1/x as Pow(x,-1). Also, it represents
# 2/x as Mul(2, Pow(x, -1)). So we shouldn't end up here,
# but just in case SymPy changes its internal conventions...
posexpr = sympy.Mul(*[base]*(-int(exp)), evaluate=False)
return sympy.Pow(posexpr, -1, evaluate=False)
else:
return expr.func(*[pow_to_mul(i) for i in expr.args], evaluate=False)
def handle_func_normal(func):
if func.L_PAREN(): # function called with parenthesis
arg = convert_func_arg(func.func_arg())
else:
arg = convert_func_arg(func.func_arg_noparens())
name = func.func_normal().start.text[1:]
# change arc<trig> -> a<trig>
if name in ["arcsin", "arccos", "arctan", "arccsc", "arcsec", "arccot", "asin", "acos", "atan"]:
if len(name) > 4:
name = "a" + name[3:]
expr = getattr(sympy.functions, name)(arg, evaluate=False)
if name in ["arsinh", "arcosh", "artanh"]:
name = "a" + name[2:]
expr = getattr(sympy.functions, name)(arg, evaluate=False)
if name == 'overline':
expr = sympy.functions.conjugate(arg, evaluate=False)
if name == 'exp':
expr = sympy.exp(arg, evaluate=False)
func_pow = None
should_pow = True
if func.supexpr():
if func.supexpr().expr():
func_pow = convert_expr(func.supexpr().expr())
else:
func_pow = convert_atom(func.supexpr().atom())
if name in ["sin", "cos", "tan", "csc", "sec", "cot", "sinh", "cosh", "tanh"]:
if func_pow == -1:
name = "a" + name
should_pow = False
expr = getattr(sympy.functions, name)(arg, evaluate=False)
if func_pow and should_pow:
expr = sympy.Pow(expr, func_pow, evaluate=False)
return expr
def parse_expr(expr, local_dict=None):
"""
Parses a json-object created with 'expr_to_json' into a Sympy expression.
If a local_dict argument is passed, symbols with be looked up by name, and a new symbol will
be created only if the name is not in local_dict.
"""
if local_dict is None:
local_dict = {}
if expr["type"] == "Add":
return sympy.Add._from_args([parse_expr(arg, local_dict) for arg in expr["args"]])
elif expr["type"] == "Mul":
return sympy.Mul._from_args([parse_expr(arg, local_dict) for arg in expr["args"]])
elif expr["type"] == "Pow":
return sympy.Pow(parse_expr(arg, local_dict) for arg in expr["args"])
elif expr["type"] == "Symbol":
try:
return local_dict[expr["name"]]
except KeyError:
return sympy.Symbol(expr["name"])
elif expr["type"] == "Number":
return sympy.sympify(expr["value"])
else:
raise NotImplementedError(expr["type"] + " is not implemented")
def convert_exp(exp):
if hasattr(exp, 'exp'):
exp_nested = exp.exp()
else:
exp_nested = exp.exp_nofunc()
if exp_nested:
base = convert_exp(exp_nested)
if isinstance(base, list):
raise Exception("Cannot raise derivative to power")
if exp.atom():
if exp.atom().LETTER(): # Transpose
if exp.atom().LETTER().getText() == 'T':
return sympy.Function('T')(base)
else:
exponent = convert_atom(exp.atom())
elif exp.expr():
exponent = convert_expr(exp.expr())
return sympy.Pow(base, exponent, evaluate=False)
else:
if hasattr(exp, 'comp'):
return convert_comp(exp.comp())
else:
return convert_comp(exp.comp_nofunc())
def fit_poly(x_vals, y_vals, degree, plot=False):
""" fit a polynomial based on points list """
x_vals = np.asarray(x_vals)
y_vals = np.asarray(y_vals)
coeffs = np.polyfit(x_vals, y_vals, degree)
func = 0
for i in range(len(coeffs)):
if coeffs[i] < 0.0000000001:
coeffs[i] = 0
func = func + sp.Pow(x, degree - i) * coeffs[i]
if plot:
x_min = x_vals.min()
x_max = x_vals.max()
x_axis = np.linspace(x_min - abs(x_max - x_min),
x_max + abs(x_max - x_min), 100)
y_axis = [func.subs(x, elem) for elem in x_axis]
#print(y_axis)
plt.plot(x_axis, y_axis)
plt.scatter(x_vals, y_vals, color='r')
plt.show()
return func
def main():
"""
main
"""
res_t, count_t = TrailValue(func_1_expr, 1, 2, 1.0/sympy.Pow(10, 5))
print('试值法 func 1 根: %.5f, 迭代次数: %d' % (res_t, count_t))
res_n, count_n = Newton(func_1_expr, 1, 2, 1.0/sympy.Pow(10, 5))
print('牛顿法 func 1 根: %.5f, 迭代次数: %d' % (res_n, count_n))
res_t, count_t = TrailValue(func_2_expr, 2, 3, 1.0/sympy.Pow(10, 5))
print('试值法 func 2 根: %.5f, 迭代次数: %d' % (res_t, count_t))
res_n, count_n = Newton(func_2_expr, 2, 3, 1.0/sympy.Pow(10, 5))
print('牛顿法 func 2 根: %.5f, 迭代次数: %d' % (res_n, count_n))
res_t, count_t = TrailValue(func_3_expr, -2.5, -1.5, 1.0/sympy.Pow(10, 5))
print('试值法 func 3 根: %.5f, 迭代次数: %d' % (res_t, count_t))
res_n, count_n = Newton(func_3_expr, -2.5, -1.5, 1.0/sympy.Pow(10, 5))
print('牛顿法 func 3 根: %.5f, 迭代次数: %d' % (res_n, count_n))
def fourier_transform(self) -> sy.Expr:
r"""
The 2D Fourier transform of :math:`Z^m_n`.
This function essentially implements eq. (7) of [Tatulli_2013]_.
.. note::
Compared to [Tatulli_2013]_, we are using a slightly
different notation. Instead of indexing the dimensions of
the Fourier space (or :math:`k`-space) using :math:`\kappa`
and :math:`\alpha`, we use :math:`k_1` and :math:`k_2`.
Returns:
The 2D Fourier transform of :math:`Z^m_n`, that is,
:math:`\mathcal{F}\lbrace Z^m_n \rbrace (k_1, k_2)`,
as a `sy.Expr`.
"""
# Define symbols for k1 and k2
k1 = sy.Symbol('k1')
k2 = sy.Symbol('k2')
# Define the first factor, which only depends on n
factor_1 = (sy.Pow(-1, self.n) * sy.sqrt(self.n + 1) / (sy.pi * k1) *
sy.besselj(2 * sy.pi * k1, self.n + 1))
# Define the second factor that also depends on m
if self.m == 0:
factor_2 = sy.Pow(-1, self.n / 2)
elif self.m > 0:
factor_2 = (sy.sqrt(2) * sy.Pow(-1, (self.n - self.m) / 2) *
sy.Pow(sy.I, self.m) * sy.cos(self.m * k2))
else:
factor_2 = (sy.sqrt(2) * sy.Pow(-1, (self.n + self.m) / 2) *
sy.Pow(sy.I, -self.m) * sy.sin(-self.m * k2))
return sy.nsimplify(sy.simplify(factor_1 * factor_2))
print("Sigma = 0.5")
stability(u, False, 0.5)
print("Sigma = 1")
stability(u, False, 1)
refresh()
print("Вариант 3")
print("Уравнение вида:")
print("du/dt = (d^2u/dx^2) + (x^2 + 1) * du/dx + f(x, t)")
print("u(x,0) = phi(x), 0 <= x <= 1")
print("du/dx, (x = 0) = alpha(t), u(1,t) = beta(t), 0 <= t <= 0.1")
print("u(x, t) = x + t")
algorithm()
print("u(x,t) = 3 * x - 0.12 * t")
u_symbol = 3 * x - 0.12 * t
u = sympy.lambdify([x, t], 3 * x - 0.12 * t)
algorithm()
print("u(x,t) = x^3 + t^3")
u_symbol = sympy.Pow(x, 3) + sympy.Pow(t, 3)
u = sympy.lambdify([x, t], x * x * x + t * t * t)
algorithm()
print("u(x,t) = sin(2t + 1) + cos(2x)")
u_symbol = sympy.sin(2 * t + 1) + sympy.cos(2 * x)
u = sympy.lambdify([x, t], sympy.sin(2 * t + 1) + sympy.cos(2 * x))
algorithm()
def convert_func(func):
if func.func_normal():
if func.L_PAREN(): # function called with parenthesis
arg = convert_func_arg(func.func_arg())
else:
arg = convert_func_arg(func.func_arg_noparens())
name = func.func_normal().start.text[1:]
# change arc<trig> -> a<trig>
if name in [
"arcsin", "arccos", "arctan", "arccsc", "arcsec", "arccot"
]:
name = "a" + name[3:]
expr = getattr(sympy.functions, name)(arg, evaluate=False)
if name in ["arsinh", "arcosh", "artanh"]:
name = "a" + name[2:]
expr = getattr(sympy.functions, name)(arg, evaluate=False)
if name == "exp":
expr = sympy.exp(arg, evaluate=False)
if (name == "log" or name == "ln"):
if func.subexpr():
if func.subexpr().expr():
base = convert_expr(func.subexpr().expr())
else:
base = convert_atom(func.subexpr().atom())
elif name == "log":
base = 10
elif name == "ln":
base = sympy.E
expr = sympy.log(arg, base, evaluate=False)
func_pow = None
should_pow = True
if func.supexpr():
if func.supexpr().expr():
func_pow = convert_expr(func.supexpr().expr())
else:
func_pow = convert_atom(func.supexpr().atom())
if name in [
"sin", "cos", "tan", "csc", "sec", "cot", "sinh", "cosh",
"tanh"
]:
if func_pow == -1:
name = "a" + name
should_pow = False
expr = getattr(sympy.functions, name)(arg, evaluate=False)
if func_pow and should_pow:
expr = sympy.Pow(expr, func_pow, evaluate=False)
return expr
elif func.LETTER() or func.SYMBOL():
if func.LETTER():
fname = func.LETTER().getText()
elif func.SYMBOL():
fname = func.SYMBOL().getText()[1:]
fname = str(fname) # can't be unicode
if func.subexpr():
subscript = None
if func.subexpr().expr(): # subscript is expr
subscript = convert_expr(func.subexpr().expr())
else: # subscript is atom
subscript = convert_atom(func.subexpr().atom())
subscriptName = StrPrinter().doprint(subscript)
fname += '_{' + subscriptName + '}'
input_args = func.args()
output_args = []
while input_args.args(): # handle multiple arguments to function
output_args.append(convert_expr(input_args.expr()))
input_args = input_args.args()
output_args.append(convert_expr(input_args.expr()))
return sympy.Function(fname)(*output_args)
elif func.FUNC_INT():
return handle_integral(func)
elif func.FUNC_SQRT():
expr = convert_expr(func.base)
if func.root:
r = convert_expr(func.root)
return sympy.root(expr, r, evaluate=False)
else:
return sympy.sqrt(expr, evaluate=False)
elif func.FUNC_OVERLINE():
expr = convert_expr(func.base)
return sympy.conjugate(expr, evaluate=False)
elif func.FUNC_SUM():
return handle_sum_or_prod(func, "summation")
elif func.FUNC_PROD():
return handle_sum_or_prod(func, "product")
elif func.FUNC_LIM():
return handle_limit(func)
"help(%s)",
no_pre_output,
multivariate=False,
eval_method=eval_function_docs,
format_input_function=format_function_docs_input,
format_output_function=format_nothing),
'root_to_polynomial':
ResultCard("Polynomial with this root",
"minpoly(%s)",
no_pre_output,
multivariate=False),
'matrix_inverse':
ResultCard(
"Inverse of matrix",
"(%s).inv()",
lambda statement, var, *args: sympy.Pow(statement, -1, evaluate=False),
multivariate=False),
'matrix_eigenvals':
ResultCard("Eigenvalues",
"(%s).eigenvals()",
no_pre_output,
multivariate=False,
format_output_function=format_dict_title(
"Eigenvalue", "Multiplicity")),
'matrix_eigenvectors':
ResultCard("Eigenvectors",
"(%s).eigenvects()",
no_pre_output,
multivariate=False,
format_output_function=format_list),
'satisfiable':
def basic_pow_term(**kwargs):
if 'seed' in kwargs:
seed = kwargs['seed']
else:
seed = random.random()
# print('basic pow term seed', seed)
random.seed(seed)
if 'const_range' in kwargs:
a, b = kwargs['const_range']
A = random_non_zero_integer(a, b)
else:
A = random_non_zero_integer(-9, 9)
if 'const_power_range' in kwargs:
a, b = kwargs['const_power_range']
e_const = random.randint(a, b)
else:
e_const = random.randint(-9, 9)
if 'variables' in kwargs:
variables = []
for variable in kwargs['variables']:
variables.append(variable)
else:
n = random.randint(0, 3)
variables = []
if n > 0:
variables.append('x')
if n > 1:
variables.append('y')
if n > 2:
variables.append('z')
e = []
if 'var_power_ranges' in kwargs:
for r in kwargs['var_power_ranges']:
a, b = r
e.append(random.randint(a, b))
else:
for var in variables:
e.append(random.randint(-5, 5))
fmt_out = ''
term = 1
if A < 0:
parens = random.choice([True, False])
if parens and e_const != 1:
# print('parens:', A, e_const)
fmt_out += pow_neg_style('\\left({A}\\right)'.format(A=A),
e_const)
term *= sy.Pow(A, e_const)
# print('term:', term)
else:
fmt_out += pow_neg_style(A, e_const)
term *= -sy.Pow(abs(A), e_const)
elif A != 1:
fmt_out = pow_neg_style(A, e_const)
term *= sy.Pow(A, e_const)
elif A == -1:
fmt_out += '-'
term *= -1
i = 0
for var in variables:
fmt_out += pow_neg_style(var, e[i])
term *= sy.Pow(sy.Symbol(var), e[i])
i += 1
return {'fmt': fmt_out, 'sym': term}
(
1 - sympy.Symbol("x") * sympy.Symbol("y"),
(1, FunctionCall("mul", (Symbol("x"), Symbol("y")))),
),
],
)
def test_add_resulting_from_subtraction_is_converted_to_sub_function_call(
sympy_addition, expected_args):
assert expression_from_sympy(sympy_addition) == FunctionCall(
"sub", expected_args)
@pytest.mark.parametrize(
"sympy_power, expected_args",
[
(sympy.Pow(sympy.Symbol("x"), 2), (Symbol("x"), 2)),
(sympy.Pow(2, sympy.Symbol("x")), (2, Symbol("x"))),
(
sympy.Pow(sympy.Symbol("x"), sympy.Symbol("y")),
(Symbol("x"), Symbol("y")),
),
],
)
def test_sympy_pow_is_converted_to_pow_function_call(sympy_power,
expected_args):
assert expression_from_sympy(sympy_power) == FunctionCall(
"pow", expected_args)
@pytest.mark.parametrize(
"sympy_power, expected_denominator",
def cirq_class_resolver_dictionary(self) -> Dict[str, Type]:
if self._crd is None:
import cirq
from cirq.devices.noise_model import _NoNoiseModel
from cirq.experiments import (CrossEntropyResult,
GridInteractionLayer)
from cirq.google.devices.known_devices import (
_NamedConstantXmonDevice)
def _identity_operation_from_dict(qubits, **kwargs):
return cirq.identity_each(*qubits)
def single_qubit_matrix_gate(matrix):
if not isinstance(matrix, np.ndarray):
matrix = np.array(matrix, dtype=np.complex128)
return cirq.MatrixGate(matrix, qid_shape=(matrix.shape[0],))
def two_qubit_matrix_gate(matrix):
if not isinstance(matrix, np.ndarray):
matrix = np.array(matrix, dtype=np.complex128)
return cirq.MatrixGate(matrix, qid_shape=(2, 2))
self._crd = {
'AmplitudeDampingChannel': cirq.AmplitudeDampingChannel,
'AsymmetricDepolarizingChannel':
cirq.AsymmetricDepolarizingChannel,
'BitFlipChannel': cirq.BitFlipChannel,
'CCNotPowGate': cirq.CCNotPowGate,
'CCXPowGate': cirq.CCXPowGate,
'CCZPowGate': cirq.CCZPowGate,
'CNotPowGate': cirq.CNotPowGate,
'ControlledGate': cirq.ControlledGate,
'ControlledOperation': cirq.ControlledOperation,
'CSwapGate': cirq.CSwapGate,
'CXPowGate': cirq.CXPowGate,
'CZPowGate': cirq.CZPowGate,
'CrossEntropyResult': CrossEntropyResult,
'Circuit': cirq.Circuit,
'DepolarizingChannel': cirq.DepolarizingChannel,
'ConstantQubitNoiseModel': cirq.ConstantQubitNoiseModel,
'Duration': cirq.Duration,
'FSimGate': cirq.FSimGate,
'DensePauliString': cirq.DensePauliString,
'MutableDensePauliString': cirq.MutableDensePauliString,
'GateOperation': cirq.GateOperation,
'GeneralizedAmplitudeDampingChannel':
cirq.GeneralizedAmplitudeDampingChannel,
'GlobalPhaseOperation': cirq.GlobalPhaseOperation,
'GridInteractionLayer': GridInteractionLayer,
'GridQid': cirq.GridQid,
'GridQubit': cirq.GridQubit,
'HPowGate': cirq.HPowGate,
'ISwapPowGate': cirq.ISwapPowGate,
'IdentityGate': cirq.IdentityGate,
'IdentityOperation': _identity_operation_from_dict,
'LineQubit': cirq.LineQubit,
'LineQid': cirq.LineQid,
'MatrixGate': cirq.MatrixGate,
'MeasurementGate': cirq.MeasurementGate,
'Moment': cirq.Moment,
'_NamedConstantXmonDevice': _NamedConstantXmonDevice,
'_NoNoiseModel': _NoNoiseModel,
'NamedQubit': cirq.NamedQubit,
'_PauliX': cirq.ops.pauli_gates._PauliX,
'_PauliY': cirq.ops.pauli_gates._PauliY,
'_PauliZ': cirq.ops.pauli_gates._PauliZ,
'ParamResolver': cirq.ParamResolver,
'PasqalDevice': cirq.pasqal.PasqalDevice,
'PauliString': cirq.PauliString,
'PhaseDampingChannel': cirq.PhaseDampingChannel,
'PhaseFlipChannel': cirq.PhaseFlipChannel,
'PhaseGradientGate': cirq.PhaseGradientGate,
'PhasedISwapPowGate': cirq.PhasedISwapPowGate,
'PhasedXPowGate': cirq.PhasedXPowGate,
'PhasedXZGate': cirq.PhasedXZGate,
'PhysicalZTag': cirq.google.PhysicalZTag,
'QuantumFourierTransformGate': cirq.QuantumFourierTransformGate,
'ResetChannel': cirq.ResetChannel,
'SingleQubitMatrixGate': single_qubit_matrix_gate,
'SingleQubitPauliStringGateOperation':
cirq.SingleQubitPauliStringGateOperation,
'SingleQubitReadoutCalibrationResult':
cirq.experiments.SingleQubitReadoutCalibrationResult,
'SwapPowGate': cirq.SwapPowGate,
'SycamoreGate': cirq.google.SycamoreGate,
'TaggedOperation': cirq.TaggedOperation,
'ThreeDGridQubit': cirq.pasqal.ThreeDGridQubit,
'TrialResult': cirq.TrialResult,
'TwoQubitMatrixGate': two_qubit_matrix_gate,
'_UnconstrainedDevice':
cirq.devices.unconstrained_device._UnconstrainedDevice,
'WaitGate': cirq.WaitGate,
'_QubitAsQid': raw_types._QubitAsQid,
'XPowGate': cirq.XPowGate,
'XXPowGate': cirq.XXPowGate,
'YPowGate': cirq.YPowGate,
'YYPowGate': cirq.YYPowGate,
'ZPowGate': cirq.ZPowGate,
'ZZPowGate': cirq.ZZPowGate,
# not a cirq class, but treated as one:
'pandas.DataFrame': pd.DataFrame,
'pandas.Index': pd.Index,
'pandas.MultiIndex': pd.MultiIndex.from_tuples,
'sympy.Symbol': sympy.Symbol,
'sympy.Add': lambda args: sympy.Add(*args),
'sympy.Mul': lambda args: sympy.Mul(*args),
'sympy.Pow': lambda args: sympy.Pow(*args),
'sympy.Float': lambda approx: sympy.Float(approx),
'sympy.Integer': sympy.Integer,
'sympy.Rational': sympy.Rational,
'complex': complex,
}
return self._crd
def op_divide(*args):
if not len(args) == 2:
raise Exception('divide given wrong number of arguments!')
# print "divide: arg0=%s, arg1=%s" % (args[0],args[1])
return sympy.Mul(args[0], sympy.Pow(args[1], -1))
def _arg_from_proto(
arg_proto,
*,
arg_function_language,
required_arg_name=None,
):
"""Extracts a python value from an argument value proto.
Args:
arg_proto: The proto containing a serialized value.
arg_function_language: The `arg_function_language` field from
`Program.Language`.
required_arg_name: If set to `None`, the method will return `None` when
given an unset proto value. If set to a string, the method will
instead raise an error complaining that the value is missing in that
situation.
Returns:
The deserialized value, or else None if there was no set value and
`required_arg_name` was set to `None`.
"""
supported = SUPPORTED_FUNCTIONS_FOR_LANGUAGE.get(arg_function_language)
if supported is None:
raise ValueError(f'Unrecognized arg_function_language: '
f'{arg_function_language!r}')
which = arg_proto.WhichOneof('arg')
if which == 'arg_value':
arg_value = arg_proto.arg_value
which_val = arg_value.WhichOneof('arg_value')
if which_val == 'float_value' or which_val == 'double_value':
if which_val == 'double_value':
result = float(arg_value.double_value)
else:
result = float(arg_value.float_value)
if math.ceil(result) == math.floor(result):
result = int(result)
return result
if which_val == 'bool_values':
return list(arg_value.bool_values.values)
if which_val == 'string_value':
return str(arg_value.string_value)
raise ValueError(f'Unrecognized value type: {which_val!r}')
if which == 'symbol':
return sympy.Symbol(arg_proto.symbol)
if which == 'func':
func = arg_proto.func
if func.type not in supported:
raise ValueError(
f'Unrecognized function type {func.type!r} '
f'for arg_function_language={arg_function_language!r}')
if func.type == 'add':
return sympy.Add(*[
_arg_from_proto(a,
arg_function_language=arg_function_language,
required_arg_name='An addition argument')
for a in func.args
])
if func.type == 'mul':
return sympy.Mul(*[
_arg_from_proto(a,
arg_function_language=arg_function_language,
required_arg_name='A multiplication argument')
for a in func.args
])
if func.type == 'pow':
return sympy.Pow(*[
_arg_from_proto(a,
arg_function_language=arg_function_language,
required_arg_name='A power argument')
for a in func.args
])
if required_arg_name is not None:
raise ValueError(
f'{required_arg_name} is missing or has an unrecognized '
f'argument type (WhichOneof("arg")={which!r}).')
return None
A = np.multiply(np.subtract(1, moisture_content), np.divide(mf, rho_cs))
B = np.divide(1, np.subtract(1, porosity))
return np.multiply(
B,
np.divide(
A,
np.add(
A,
np.add(np.divide(np.subtract(1, mf), rho_solvent),
np.multiply(moisture_content, np.divide(mf,
rho_water))))))
sigma, sigma_star, phi, phi_m, phi_o, mu_f, beta = sy.symbols(
'sigma sigma_star phi phi_m phi_o mu_f beta', real=True)
e_f = sy.exp(-1. * (sy.Pow((sigma_star / sigma), beta)))
e_phij = e_f * (phi_m - phi_o) + phi_o
e_mu = mu_f * sy.Pow(1 - (phi / e_phij), -2.0)
e_gd = sigma / e_mu
e_dgds = sy.diff(e_gd, sigma)
e_sigj = sigma_star / sy.Pow(-sy.log(
(phi - phi_o) / (phi_m - phi_o)), 1. / beta)
f_f = sy.lambdify([sigma, sigma_star, beta], e_f, 'numpy')
f_phij = sy.lambdify([sigma, sigma_star, beta, phi_m, phi_o], e_phij, 'numpy')
f_mu = sy.lambdify([sigma, sigma_star, beta, phi_m, phi_o, phi, mu_f], e_mu,
'numpy')
f_gd = sy.lambdify([sigma, sigma_star, beta, phi_m, phi_o, phi, mu_f], e_gd,
'numpy')
f_dgds = sy.lambdify([sigma, sigma_star, beta, phi_m, phi_o, phi, mu_f],
e_dgds, 'numpy')
