def fneg(ctx, x, **kwargs):
"""
Negates the number *x*, giving a floating-point result, optionally
using a custom precision and rounding mode.
See the documentation of :func:`~mpmath.fadd` for a detailed description
of how to specify precision and rounding.
**Examples**
An mpmath number is returned::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = False
>>> fneg(2.5)
mpf('-2.5')
>>> fneg(-5+2j)
mpc(real='5.0', imag='-2.0')
Precise control over rounding is possible::
>>> x = fadd(2, 1e-100, exact=True)
>>> fneg(x)
mpf('-2.0')
>>> fneg(x, rounding='f')
mpf('-2.0000000000000004')
Negating with and without roundoff::
>>> n = 200000000000000000000001
>>> print int(-mpf(n))
-200000000000000016777216
>>> print int(fneg(n))
-200000000000000016777216
>>> print int(fneg(n, prec=log(n,2)+1))
-200000000000000000000001
>>> print int(fneg(n, dps=log(n,10)+1))
-200000000000000000000001
>>> print int(fneg(n, prec=inf))
-200000000000000000000001
>>> print int(fneg(n, dps=inf))
-200000000000000000000001
>>> print int(fneg(n, exact=True))
-200000000000000000000001
"""
prec, rounding = ctx._parse_prec(kwargs)
x = ctx.convert(x)
if hasattr(x, '_mpf_'):
return ctx.make_mpf(mpf_neg(x._mpf_, prec, rounding))
if hasattr(x, '_mpc_'):
return ctx.make_mpc(mpc_neg(x._mpc_, prec, rounding))
raise ValueError("Arguments need to be mpf or mpc compatible numbers")
def fneg(ctx, x, **kwargs):
"""
Negates the number *x*, giving a floating-point result, optionally
using a custom precision and rounding mode.
See the documentation of :func:`fadd` for a detailed description
of how to specify precision and rounding.
**Examples**
An mpmath number is returned::
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = False
>>> fneg(2.5)
mpf('-2.5')
>>> fneg(-5+2j)
mpc(real='5.0', imag='-2.0')
Precise control over rounding is possible::
>>> x = fadd(2, 1e-100, exact=True)
>>> fneg(x)
mpf('-2.0')
>>> fneg(x, rounding='f')
mpf('-2.0000000000000004')
Negating with and without roundoff::
>>> n = 200000000000000000000001
>>> print int(-mpf(n))
-200000000000000016777216
>>> print int(fneg(n))
-200000000000000016777216
>>> print int(fneg(n, prec=log(n,2)+1))
-200000000000000000000001
>>> print int(fneg(n, dps=log(n,10)+1))
-200000000000000000000001
>>> print int(fneg(n, prec=inf))
-200000000000000000000001
>>> print int(fneg(n, dps=inf))
-200000000000000000000001
>>> print int(fneg(n, exact=True))
-200000000000000000000001
"""
prec, rounding = ctx._parse_prec(kwargs)
x = ctx.convert(x)
if hasattr(x, '_mpf_'):
return ctx.make_mpf(mpf_neg(x._mpf_, prec, rounding))
if hasattr(x, '_mpc_'):
return ctx.make_mpc(mpc_neg(x._mpc_, prec, rounding))
raise ValueError("Arguments need to be mpf or mpc compatible numbers")
def __neg__(s):
cls, new, (prec, rounding) = s._ctxdata
v = new(cls)
v._mpf_ = mpf_neg(s._mpf_, prec, rounding)
return v
def conjugate(s):
a, b = s._mpci_
return s.ctx.make_mpc((a, mpf_neg(b)))
def conjugate(s):
a, b = s._mpci_
return s.ctx.make_mpc((a, mpf_neg(b)))
def __neg__(s):
cls, new, (prec, rounding) = s._ctxdata
v = new(cls)
v._mpf_ = mpf_neg(s._mpf_, prec, rounding)
return v
def fdot(ctx, A, B=None, conjugate=False):
r"""
Computes the dot product of the iterables `A` and `B`,
.. math ::
\sum_{k=0} A_k B_k.
Alternatively, :func:`~mpmath.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.
With ``conjugate=True``, the elements in the second vector
will be conjugated:
.. math ::
\sum_{k=0} A_k \overline{B_k}
**Examples**
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = False
>>> 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')
>>> A = [2, 1.5, 3j]
>>> B = [1+j, 3, -1-j]
>>> fdot(A, B)
mpc(real='9.5', imag='-1.0')
>>> fdot(A, B, conjugate=True)
mpc(real='3.5', imag='-5.0')
"""
if B:
A = zip(A, B)
prec, rnd = ctx._prec_rounding
real = []
imag = []
other = 0
hasattr_ = hasattr
types = (ctx.mpf, ctx.mpc)
for a, b in A:
if type(a) not in types: a = ctx.convert(a)
if type(b) not in types: b = ctx.convert(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_
if conjugate:
bim = mpf_neg(bim)
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)
are, aim = a._mpc_
bre, bim = b._mpc_
if conjugate:
bim = mpf_neg(bim)
real.append(mpf_mul(are, bre))
real.append(mpf_neg(mpf_mul(aim, bim)))
imag.append(mpf_mul(are, bim))
imag.append(mpf_mul(aim, bre))
else:
if conjugate:
other += a*ctx.conj(b)
else:
other += a*b
s = mpf_sum(real, prec, rnd)
if imag:
s = ctx.make_mpc((s, mpf_sum(imag, prec, rnd)))
else:
s = ctx.make_mpf(s)
if other is 0:
return s
else:
return s + other
def fdot(ctx, A, B=None, conjugate=False):
r"""
Computes the dot product of the iterables `A` and `B`,
.. math ::
\sum_{k=0} A_k B_k.
Alternatively, :func:`~mpmath.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.
With ``conjugate=True``, the elements in the second vector
will be conjugated:
.. math ::
\sum_{k=0} A_k \overline{B_k}
**Examples**
>>> from mpmath import *
>>> mp.dps = 15; mp.pretty = False
>>> 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')
>>> A = [2, 1.5, 3j]
>>> B = [1+j, 3, -1-j]
>>> fdot(A, B)
mpc(real='9.5', imag='-1.0')
>>> fdot(A, B, conjugate=True)
mpc(real='3.5', imag='-5.0')
"""
if B:
A = zip(A, B)
prec, rnd = ctx._prec_rounding
real = []
imag = []
other = 0
hasattr_ = hasattr
types = (ctx.mpf, ctx.mpc)
for a, b in A:
if type(a) not in types: a = ctx.convert(a)
if type(b) not in types: b = ctx.convert(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_
if conjugate:
bim = mpf_neg(bim)
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)
are, aim = a._mpc_
bre, bim = b._mpc_
if conjugate:
bim = mpf_neg(bim)
real.append(mpf_mul(are, bre))
real.append(mpf_neg(mpf_mul(aim, bim)))
imag.append(mpf_mul(are, bim))
imag.append(mpf_mul(aim, bre))
else:
if conjugate:
other += a * ctx.conj(b)
else:
other += a * b
s = mpf_sum(real, prec, rnd)
if imag:
s = ctx.make_mpc((s, mpf_sum(imag, prec, rnd)))
else:
s = ctx.make_mpf(s)
if other is 0:
return s
else:
return s + other