def comb(N,k,exact=0):
"""Combinations of N things taken k at a time.
If exact==0, then floating point precision is used, otherwise
exact long integer is computed.
Notes:
- Array arguments accepted only for exact=0 case.
- If k > N, N < 0, or k < 0, then a 0 is returned.
"""
if exact:
if (k > N) or (N < 0) or (k < 0):
return 0L
val = 1L
for j in xrange(min(k, N-k)):
val = (val*(N-j))//(j+1)
return val
else:
from scipy import special
k,N = asarray(k), asarray(N)
lgam = special.gammaln
cond = (k <= N) & (N >= 0) & (k >= 0)
sv = special.errprint(0)
vals = exp(lgam(N+1) - lgam(N-k+1) - lgam(k+1))
sv = special.errprint(sv)
return where(cond, vals, 0.0)
def comb(N,k,exact=0):
"""Combinations of N things taken k at a time.
If exact==0, then floating point precision is used, otherwise
exact long integer is computed.
Notes:
- Array arguments accepted only for exact=0 case.
- If k > N, N < 0, or k < 0, then a 0 is returned.
"""
if exact:
if (k > N) or (N < 0) or (k < 0):
return 0L
N,k = map(long,(N,k))
top = N
val = 1L
while (top > (N-k)):
val *= top
top -= 1
n = 1L
while (n < k+1L):
val /= n
n += 1
return val
else:
k,N = asarray(k), asarray(N)
lgam = special.gammaln
cond = (k <= N) & (N >= 0) & (k >= 0)
sv = special.errprint(0)
vals = exp(lgam(N+1) - lgam(N-k+1) - lgam(k+1))
sv = special.errprint(sv)
return where(cond, vals, 0.0)
def comb(N, k, exact=0):
"""Combinations of N things taken k at a time.
If exact==0, then floating point precision is used, otherwise
exact long integer is computed.
Notes:
- Array arguments accepted only for exact=0 case.
- If k > N, N < 0, or k < 0, then a 0 is returned.
"""
if exact:
if (k > N) or (N < 0) or (k < 0):
return 0L
val = 1L
for j in xrange(min(k, N - k)):
val = (val * (N - j)) // (j + 1)
return val
else:
from scipy import special
k, N = asarray(k), asarray(N)
lgam = special.gammaln
cond = (k <= N) & (N >= 0) & (k >= 0)
sv = special.errprint(0)
vals = exp(lgam(N + 1) - lgam(N - k + 1) - lgam(k + 1))
sv = special.errprint(sv)
return where(cond, vals, 0.0)
def factorial(n,exact=0):
"""n! = special.gamma(n+1)
If exact==0, then floating point precision is used, otherwise
exact long integer is computed.
Notes:
- Array argument accepted only for exact=0 case.
- If n<0, the return value is 0.
"""
if exact:
if n < 0:
return 0L
n = long(n)
val = 1L
k = 1L
while (k < n+1L):
val = val*k
k += 1
return val
else:
n = asarray(n)
sv = special.errprint(0)
vals = special.gamma(n+1)
sv = special.errprint(sv)
return where(n>=0,vals,0)
def wrapper(*a, **kw):
old_filters = list(getattr(warnings, 'filters', []))
old_errprint = sc.errprint(1)
warnings.filterwarnings("error", category=sc.SpecialFunctionWarning)
try:
return func(*a, **kw)
finally:
sc.errprint(old_errprint)
setattr(warnings, 'filters', old_filters)
def test_errprint():
flag = sc.errprint(True)
try:
assert_(isinstance(flag, bool))
with warnings.catch_warnings(record=True) as w:
sc.loggamma(0)
assert_(w[-1].category is sc.SpecialFunctionWarning)
finally:
sc.errprint(flag)
def wrapper(*a, **kw):
old_filters = list(getattr(warnings, 'filters', []))
old_errprint = sc.errprint(1)
warnings.filterwarnings("error", category=sc.SpecialFunctionWarning)
try:
return func(*a, **kw)
finally:
sc.errprint(old_errprint)
setattr(warnings, 'filters', old_filters)
def test_errprint():
flag = sc.errprint(True)
try:
assert_(isinstance(flag, bool))
with warnings.catch_warnings(record=True) as w:
sc.loggamma(0)
assert_(w[-1].category is sc.SpecialFunctionWarning)
finally:
sc.errprint(flag)
def comb(N,k,exact=0):
"""
The number of combinations of N things taken k at a time.
This is often expressed as "N choose k".
Parameters
----------
N : int, ndarray
Number of things.
k : int, ndarray
Number of elements taken.
exact : int, optional
If `exact` is 0, then floating point precision is used, otherwise
exact long integer is computed.
Returns
-------
val : int, ndarray
The total number of combinations.
Notes
-----
- Array arguments accepted only for exact=0 case.
- If k > N, N < 0, or k < 0, then a 0 is returned.
Examples
--------
>>> k = np.array([3, 4])
>>> n = np.array([10, 10])
>>> sc.comb(n, k, exact=False)
array([ 120., 210.])
>>> sc.comb(10, 3, exact=True)
120L
"""
if exact:
if (k > N) or (N < 0) or (k < 0):
return 0
val = 1
for j in xrange(min(k, N-k)):
val = (val*(N-j))//(j+1)
return val
else:
from scipy import special
k,N = asarray(k), asarray(N)
lgam = special.gammaln
cond = (k <= N) & (N >= 0) & (k >= 0)
sv = special.errprint(0)
vals = exp(lgam(N+1) - lgam(N-k+1) - lgam(k+1))
sv = special.errprint(sv)
return where(cond, vals, 0.0)
def comb(N, k, exact=0):
"""
The number of combinations of N things taken k at a time.
This is often expressed as "N choose k".
Parameters
----------
N : int, ndarray
Number of things.
k : int, ndarray
Number of elements taken.
exact : int, optional
If `exact` is 0, then floating point precision is used, otherwise
exact long integer is computed.
Returns
-------
val : int, ndarray
The total number of combinations.
Notes
-----
- Array arguments accepted only for exact=0 case.
- If k > N, N < 0, or k < 0, then a 0 is returned.
Examples
--------
>>> k = np.array([3, 4])
>>> n = np.array([10, 10])
>>> sc.comb(n, k, exact=False)
array([ 120., 210.])
>>> sc.comb(10, 3, exact=True)
120L
"""
if exact:
if (k > N) or (N < 0) or (k < 0):
return 0
val = 1
for j in xrange(min(k, N - k)):
val = (val * (N - j)) // (j + 1)
return val
else:
from scipy import special
k, N = asarray(k), asarray(N)
lgam = special.gammaln
cond = (k <= N) & (N >= 0) & (k >= 0)
sv = special.errprint(0)
vals = exp(lgam(N + 1) - lgam(N - k + 1) - lgam(k + 1))
sv = special.errprint(sv)
return where(cond, vals, 0.0)
def test_errprint():
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, "`errprint` is deprecated!")
flag = sc.errprint(True)
try:
assert_(isinstance(flag, bool))
with warnings.catch_warnings(record=True) as w:
sc.loggamma(0)
assert_(w[-1].category is sc.SpecialFunctionWarning)
finally:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, "`errprint` is deprecated!")
sc.errprint(flag)
def test_errprint():
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, "`errprint` is deprecated!")
flag = sc.errprint(True)
try:
assert_(isinstance(flag, bool))
with pytest.warns(sc.SpecialFunctionWarning):
sc.loggamma(0)
finally:
with suppress_warnings() as sup:
sup.filter(DeprecationWarning, "`errprint` is deprecated!")
sc.errprint(flag)
def factorial(n,exact=0):
"""
The factorial function, n! = special.gamma(n+1).
If exact is 0, then floating point precision is used, otherwise
exact long integer is computed.
- Array argument accepted only for exact=0 case.
- If n<0, the return value is 0.
Parameters
----------
n : int or array_like of ints
Calculate ``n!``. Arrays are only supported with `exact` set
to False. If ``n < 0``, the return value is 0.
exact : bool, optional
The result can be approximated rapidly using the gamma-formula
above. If `exact` is set to True, calculate the
answer exactly using integer arithmetic. Default is False.
Returns
-------
nf : float or int
Factorial of `n`, as an integer or a float depending on `exact`.
Examples
--------
>>> arr = np.array([3,4,5])
>>> sc.factorial(arr, exact=False)
array([ 6., 24., 120.])
>>> sc.factorial(5, exact=True)
120L
"""
if exact:
if n < 0:
return 0L
val = 1L
for k in xrange(1,n+1):
val *= k
return val
else:
from scipy import special
n = asarray(n)
sv = special.errprint(0)
vals = special.gamma(n+1)
sv = special.errprint(sv)
return where(n>=0,vals,0)
def factorial(n,exact=0):
"""
The factorial function, n! = special.gamma(n+1).
If exact is 0, then floating point precision is used, otherwise
exact long integer is computed.
- Array argument accepted only for exact=0 case.
- If n<0, the return value is 0.
Parameters
----------
n : int or array_like of ints
Calculate ``n!``. Arrays are only supported with `exact` set
to False. If ``n < 0``, the return value is 0.
exact : bool, optional
The result can be approximated rapidly using the gamma-formula
above. If `exact` is set to True, calculate the
answer exactly using integer arithmetic. Default is False.
Returns
-------
nf : float or int
Factorial of `n`, as an integer or a float depending on `exact`.
Examples
--------
>>> arr = np.array([3,4,5])
>>> sc.factorial(arr, exact=False)
array([ 6., 24., 120.])
>>> sc.factorial(5, exact=True)
120L
"""
if exact:
if n < 0:
return 0L
val = 1L
for k in xrange(1,n+1):
val *= k
return val
else:
from scipy import special
n = asarray(n)
sv = special.errprint(0)
vals = special.gamma(n+1)
sv = special.errprint(sv)
return where(n>=0,vals,0)
def comb(N, k, exact = 0):
if exact:
if (k > N) or (N < 0) or (k < 0):
return 0
val = 1
for j in xrange(min(k, N-k)):
val = (val*(N-j))//(j+1)
return val
else:
from scipy import special
k,N = asarray(k), asarray(N)
lgam = special.gammaln
cond = (k <= N) & (N >= 0) & (k >= 0)
sv = special.errprint(0)
vals = exp(lgam(N + 1) - lgam(N - k + 1) - lgam(k + 1))
sv = special.errprint(sv)
return where(cond, vals, 0.0)
def comb(N, k, exact=0):
if exact:
if (k > N) or (N < 0) or (k < 0):
return 0
val = 1
for j in xrange(min(k, N - k)):
val = (val * (N - j)) // (j + 1)
return val
else:
from scipy import special
k, N = asarray(k), asarray(N)
lgam = special.gammaln
cond = (k <= N) & (N >= 0) & (k >= 0)
sv = special.errprint(0)
vals = exp(lgam(N + 1) - lgam(N - k + 1) - lgam(k + 1))
sv = special.errprint(sv)
return where(cond, vals, 0.0)
def factorial(n, exact=0):
"""n! = special.gamma(n+1)
If exact==0, then floating point precision is used, otherwise
exact long integer is computed.
Notes:
- Array argument accepted only for exact=0 case.
- If n<0, the return value is 0.
"""
if exact:
if n < 0:
return 0L
val = 1L
for k in xrange(1, n + 1):
val *= k
return val
else:
from scipy import special
n = asarray(n)
sv = special.errprint(0)
vals = special.gamma(n + 1)
sv = special.errprint(sv)
return where(n >= 0, vals, 0)
def factorial(n,exact=0):
"""n! = special.gamma(n+1)
If exact==0, then floating point precision is used, otherwise
exact long integer is computed.
Notes:
- Array argument accepted only for exact=0 case.
- If n<0, the return value is 0.
"""
if exact:
if n < 0:
return 0L
val = 1L
for k in xrange(1,n+1):
val *= k
return val
else:
from scipy import special
n = asarray(n)
sv = special.errprint(0)
vals = special.gamma(n+1)
sv = special.errprint(sv)
return where(n>=0,vals,0)
def beambeam_Gaussian_grid(sigmax,
sigmay,
rangex=10.0,
rangey=10.0,
epsilon=1e-3,
gridpoints=10,
sdds_file=None):
if abs(sigmax - sigmay) / (sigmax + sigmay) < epsilon:
xlist = np.linspace(-rangex * sigmax,
rangex * sigmax,
num=int(rangex * gridpoints) + 1,
endpoint=True)
ylist = np.linspace(-rangey * sigmay,
rangey * sigmay,
num=int(rangey * gridpoints) + 1,
endpoint=True)
xlist, ylist = np.meshgrid(xlist, ylist)
sigr = (sigmax + sigmay) / 2.0
rabs = np.sqrt(xlist * xlist + ylist * ylist)
mask = (rabs == 0)
invmask = np.logical_not(mask)
eabs = np.zeros_like(rabs)
ex = np.zeros_like(rabs)
ey = np.zeros_like(rabs)
eabs[invmask] = (1 - np.exp(-rabs[invmask] * rabs[invmask] / 2 / sigr /
sigr)) / rabs[invmask] / 2 / np.pi
ex[invmask] = eabs[invmask] * xlist[invmask] / rabs[invmask]
ey[invmask] = eabs[invmask] * ylist[invmask] / rabs[invmask]
eabs[mask] = 0
ex[mask] = 0
ey[mask] = 0
else:
xlist = np.linspace(-rangex * sigmax,
rangex * sigmax,
num=int(rangex * gridpoints) + 1,
endpoint=True)
ylist = np.linspace(-rangey * sigmay,
rangey * sigmay,
num=int(rangey * gridpoints) + 1,
endpoint=True)
spefunc.errprint(1)
if sigmax < sigmay:
su = sigmay
sv = sigmax
ulist = ylist
vlist = xlist
ulist, vlist = np.meshgrid(ulist, vlist)
else:
su = sigmax
sv = sigmay
ulist = xlist
vlist = ylist
ulist, vlist = np.meshgrid(ulist, vlist)
xmask = ulist > 0
ymask = vlist > 0
xmask = xmask * 2.0 - 1.0
ymask = ymask * 2.0 - 1.0
sqrtsigma = math.sqrt(2 * su * su - 2 * sv * sv)
w1 = spefunc.wofz((np.abs(ulist) + 1j * np.abs(vlist)) / sqrtsigma)
w2 = spefunc.wofz(
(np.abs(ulist) * sv / su + 1j * np.abs(vlist) * su / sv) /
sqrtsigma)
expterm = np.exp(-ulist * ulist / 2.0 / su / su -
vlist * vlist / 2.0 / sv / sv)
ecompx = (w1 - expterm * w2) / math.sqrt(
np.pi) / 2.0 / 1.0j / sqrtsigma
eu = np.real(ecompx)
ev = -np.imag(ecompx)
if sigmax < sigmay:
ex = ev * xmask
ey = eu * ymask
xlist = vlist
ylist = ulist
else:
ex = eu * xmask
ey = ev * ymask
xlist = ulist
ylist = vlist
#if sdds_file is not None:
# import SDDSIO.sdds as sdds
# output=sdds.SDDS(0)
# output.columnName=['x','y','Fx','Fy']
# output.columnDefinition[['', 'm', 'x', '', output.SDDS_DOUBLE, 0L],
# ['', 'm', 'y', '', output.SDDS_DOUBLE, 0L],
# ['', '', 'Fx', '', output.SDDS_DOUBLE, 0L],
# ['', '', 'Fy', '', output.SDDS_DOUBLE, 0L],
# ]
# output.columnData[[xlist.tolist(),],[ylist.tolist(),][ex.tolist(),][ey.tolist(),]]
# output.save(sdds_file)
return xlist, ylist, ex, ey
