def test_product():
k = pystencils.TypedSymbol('k', create_type('int64'))
sum = sympy.Product(k, (k, 1, 10))
expanded_sum = sum.doit()
print(sum)
print(expanded_sum)
x = pystencils.fields('x: int64[1d]')
assignments = pystencils.AssignmentCollection({x.center(): sum})
ast = pystencils.create_kernel(assignments)
code = str(pystencils.show_code(ast))
kernel = ast.compile()
print(code)
assert 'int64_t product' in code
array = np.zeros((10, ), np.int64)
kernel(x=array)
assert np.allclose(array, int(expanded_sum) * np.ones_like(array))
def handle_sum_or_prod(func, name):
val = convert_mp(func.mp())
iter_var = convert_expr(func.subeq().equality().expr(0))
start = convert_expr(func.subeq().equality().expr(1))
end = convert_expr(func.supexpr().expr())
if name == "summation":
return sympy.Sum(val, (iter_var, start, end))
elif name == "product":
return sympy.Product(val, (iter_var, start, end))
def __handle_sum_or_prod(func, name):
val = Math.__convert_mp(func.mp())
iter_var = Math.__convert_expr(func.subeq().equality().expr(0))
start = Math.__convert_expr(func.subeq().equality().expr(1))
if func.supexpr().expr(): # ^{expr}
end = Math.__convert_expr(func.supexpr().expr())
else: # ^atom
end = Math.__convert_atom(func.supexpr().atom())
if name == "summation":
return sympy.Sum(val, (iter_var, start, end))
elif name == "product":
return sympy.Product(val, (iter_var, start, end))
def handle_sum_or_prod(func, name):
val = convert_mp(func.mp())
iter_var = None
start = None
if func.subeq(): # e.g. _{i=0}
iter_var = convert_expr(func.subeq().equality().expr(0))
start = convert_expr(func.subeq().equality().expr(1))
elif func.subexpr().expr(): # _{expr}
iter_var = convert_expr(func.subexpr().expr())
else: # _atom
iter_var = convert_atom(func.subexpr().atom())
if func.supexpr():
if func.supexpr().expr(): # ^{expr}
end = convert_expr(func.supexpr().expr())
else: # ^atom
end = convert_atom(func.supexpr().atom())
if name == "summation":
if start is not None:
return sympy.Sum(val, (iter_var, start, end))
else:
return sympy.Function('sum_{' + str(iter_var) + '}')(val)
elif name == "product":
return sympy.Product(val, (iter_var, start, end))
# In[172]:
x = sympy.Sum(1 / (n**2), (n, 1, oo))
# In[173]:
x
# In[174]:
x.doit()
# In[175]:
x = sympy.Product(n, (n, 1, 7))
# In[176]:
x
# In[177]:
x.doit()
# In[178]:
x = sympy.Symbol("x")
# In[179]:
sympy.limit(f, x, y) # sin(y)/y
# Example:
# limit(x→y){sin(x)/x}
sympy.limit(sympy.sin(x) / x, x, y) # sin(y)/y
sympy.limit(sympy.sin(x) / x, x, 0) # 1
sympy.limit(sympy.sin(x) / x, x, sympy.oo) # 0 (The reality is none)
expr = (x**2 - 3 * x) / (2 * x - 2)
p = sympy.limit(expr / x, x, sympy.oo)
q = sympy.limit(expr - p * x, x, sympy.oo)
p, q # (1/2, -1)
#%% Sums and Products
import numpy as np
import sympy
import math
from sympy import I, pi, oo
n = sympy.symbols("n", integer=True)
# Sums:
S = sympy.Sum(1 / (n**2), (n, 1, oo))
S # Sum(n**(-2), (n, 1, oo))
S.doit() # pi**2/6
# Products:
X = sympy.Product(n, (n, 1, 16))
X # Product(n, (n, 1, 512))
X.doit() # 20922789888000
("\\sqrt[y]{\\sin x}", sympy.root(sympy.sin(x), y)),
("\\sqrt[\\theta]{\\sin x}", sympy.root(sympy.sin(x), theta)),
("x < y", sympy.StrictLessThan(x, y)), ("x \\leq y", sympy.LessThan(x, y)),
("x > y", sympy.StrictGreaterThan(x, y)),
("x \\geq y", sympy.GreaterThan(x, y)), ("\\mathit{x}", sympy.Symbol('x')),
("\\mathit{test}", sympy.Symbol('test')),
("\\mathit{TEST}", sympy.Symbol('TEST')),
("\\mathit{HELLO world}", sympy.Symbol('HELLO world')),
("\\sum_{k = 1}^{3} c", sympy.Sum(c, (k, 1, 3))),
("\\sum_{k = 1}^3 c", sympy.Sum(c, (k, 1, 3))),
("\\sum^{3}_{k = 1} c", sympy.Sum(c, (k, 1, 3))),
("\\sum^3_{k = 1} c", sympy.Sum(c, (k, 1, 3))),
("\\sum_{k = 1}^{10} k^2", sympy.Sum(k**2, (k, 1, 10))),
("\\sum_{n = 0}^{\\infty} \\frac{1}{n!}",
sympy.Sum(_Pow(_factorial(n), -1), (n, 0, sympy.oo))),
("\\prod_{a = b}^{c} x", sympy.Product(x, (a, b, c))),
("\\prod_{a = b}^c x", sympy.Product(x, (a, b, c))),
("\\prod^{c}_{a = b} x", sympy.Product(x, (a, b, c))),
("\\prod^c_{a = b} x", sympy.Product(x, (a, b, c))),
("\\ln x", _log(x, sympy.E)), ("\\ln xy", _log(x * y, sympy.E)),
("\\log x", _log(x, 10)), ("\\log xy", _log(x * y, 10)),
("\\log_2 x", _log(x, 2)), ("\\log_{2} x", _log(x, 2)),
("\\log_a x", _log(x, a)), ("\\log_{a} x", _log(x, a)),
("\\log_{11} x", _log(x, 11)), ("\\log_{a^2} x", _log(x, _Pow(a, 2))),
("[x]", x), ("[a + b]", _Add(a, b)),
("\\frac{d}{dx} [ \\tan x ]", sympy.Derivative(sympy.tan(x), x))
]
# These bad latex strings should raise an exception when parsed
BAD_STRINGS = [
"(", ")", "a / b /", "\\frac{d}{dx}", "(\\frac{d}{dx})"
