def fsum(terms):
"""
Calculates a sum containing a finite number of terms (for infinite
series, see :func:`nsum`). The terms will be converted to
mpmath numbers. For len(terms) > 2, this function is generally
faster and produces more accurate results than the builtin
Python function :func:`sum`.
>>> from sympy.mpmath import *
>>> mp.dps = 15
>>> fsum([1, 2, 0.5, 7])
mpf('10.5')
"""
prec, rnd = prec_rounding
real = []
imag = []
other = 0
for term in terms:
if hasattr(term, "_mpf_"):
val = term._mpf_
elif hasattr(term, "_mpc_"):
val, im = term._mpc_
imag.append(im)
else:
term = mpmathify(term)
if hasattr(term, "_mpf_"):
val = term._mpf_
elif hasattr(term, "_mpc_"):
val, im = term._mpc_
imag.append(im)
else:
other += term
continue
real.append(val)
s = mpf_sum(real, prec, rnd)
if imag:
s = make_mpc((s, mpf_sum(imag, prec, rnd)))
else:
s = make_mpf(s)
if other is 0:
return s
else:
return s + other
def fdot(A, B=None):
r"""
Computes the dot product of the iterables `A` and `B`,
.. math ::
\sum_{k=0} A_k B_k.
Alternatively, :func:`fdot` accepts a single iterable of pairs.
In other words, ``fdot(A,B)`` and ``fdot(zip(A,B))`` are equivalent.
The elements are automatically converted to mpmath numbers.
Examples::
>>> from sympy.mpmath import *
>>> mp.dps = 15
>>> A = [2, 1.5, 3]
>>> B = [1, -1, 2]
>>> fdot(A, B)
mpf('6.5')
>>> zip(A, B)
[(2, 1), (1.5, -1), (3, 2)]
>>> fdot(_)
mpf('6.5')
"""
if B:
A = zip(A, B)
prec, rnd = prec_rounding
real = []
imag = []
other = 0
hasattr_ = hasattr
types = (mpf, mpc)
for a, b in A:
if type(a) not in types: a = mpmathify(a)
if type(b) not in types: b = mpmathify(b)
a_real = hasattr_(a, "_mpf_")
b_real = hasattr_(b, "_mpf_")
if a_real and b_real:
real.append(mpf_mul(a._mpf_, b._mpf_))
continue
a_complex = hasattr_(a, "_mpc_")
b_complex = hasattr_(b, "_mpc_")
if a_real and b_complex:
aval = a._mpf_
bre, bim = b._mpc_
real.append(mpf_mul(aval, bre))
imag.append(mpf_mul(aval, bim))
elif b_real and a_complex:
are, aim = a._mpc_
bval = b._mpf_
real.append(mpf_mul(are, bval))
imag.append(mpf_mul(aim, bval))
elif a_complex and b_complex:
re, im = mpc_mul(a._mpc_, b._mpc_, prec+20)
real.append(re)
imag.append(im)
else:
other += a*b
s = mpf_sum(real, prec, rnd)
if imag:
s = make_mpc((s, mpf_sum(imag, prec, rnd)))
else:
s = make_mpf(s)
if other is 0:
return s
else:
return s + other
