def draw_bonds(self, ax, atom_coord=None, atom_names=None, **kwargs): """ Draw atomic bonds onto a matplotlib axis object. Params: - ax: Matplotlib axis object - atom_coord: List of atomic coordinates (not necessarily the original one in order to use a supercell). - atom_namse: List of atom names (same shape as atom_coord). Used to plot the proper color and atomic radius. """ from itertools import combinations_with_replacement as cwr if atom_coord is None: atom_coord = self.atoms_coord_cart if atom_names is None: atom_names = self.atoms_typ trees, names, rad = split_atom_list_by_name(atom_coord, atom_names) for rad_t, (tree1,tree2), (name1,name2) in zip(cwr(rad,2), cwr(trees,2), cwr(names,2)): bonds = tree1.query_ball_tree(tree2, sum(rad_t)) c1 = periodic_table[name1]['color'] c2 = periodic_table[name2]['color'] for i1,b in enumerate(bonds): for i2 in b: if i1 == i2 and tree1 == tree2: continue start = tree1.data[i1] end = tree2.data[i2] cg.draw_bond(ax, start, end, c1, c2, **kwargs)
def seq_gen(n):
p = [2, 3]
q = [6, 7, 8, 9]
r = []
if n > 1:
for i in p:
r += [(i, ) + j for j in cwr(q, n - 1)]
r += [i for i in cwr(q, n)]
r = [int(''.join(str(k) for k in i)) for i in r]
else:
r = [2, 3, 6, 7, 8, 9]
return r
def car2sph(sh, cart, orderedp=True):
"""Cartesian to spherical transform matrices.
.. code-block:: python
sh = solid_harmonics(8) # symbolic solid harmonics
cart = gen_enum_cartesian(8) # cartesian powers in a defined order
c2s = car2sph(sh, cart) # dictionary of {l: transform_matrix}
Args:
sh (OrderedDict): symbolic solid harmonics
cart (OrderedDict): cartesian powers in a defined order
orderedp (bool): order l=1 as ['x', 'y', 'z'], not [-1, 0, 1] (default True)
Returns:
c2s (OrderedDict): cartesian to spherical transform matrices
"""
c2s = OrderedDict([(L, np.zeros(((L + 1) * (L + 2) // 2, 2 * L + 1)))
for L in range(max(sh.keys()) + 1)])
for L, mls in sh.items():
if not L or (L == 1 and orderedp):
c2s[L] = np.array(cart[L])
continue
cdxs = [reduce(mul, xyz) for xyz in cwr((_x, _y, _z), L)]
for ml, sym in mls.items():
mli = ml + L
coefs = sym.expand().as_coefficients_dict()
#for crt, coef in coefs.items():
for crt, _ in coefs.items():
if isinstance(crt, (Integer, Float)): continue
idx = cdxs.index(crt)
c2s[L][idx, mli] = coefs[cdxs[idx]]
return c2s
def solution():
consecutives = {}
ops = (add, sub, mul, truediv)
ops = set(p for c in cwr(ops, 3) for p in permutations(c))
for key in combinations(range(10), 4):
generated = set()
for a, b, c, d in permutations(key):
for x, y, z in ops:
# Non-parenthesized case
try:
generated.add(x(y(z(a, b), c), d))
except ZeroDivisionError:
pass
# Parenthesized case
try:
generated.add(x(y(a, b), z(c, d)))
except ZeroDivisionError:
pass
consecutive = list(takewhile(lambda n: n in generated, count(1)))
if consecutive:
consecutives[tuple(sorted(key))] = max(consecutive)
return ''.join(map(str, max((v, k) for k, v in consecutives.items())[1]))
def test(n, rank):
"""
Using combinations with replacement to generate
index mappings and check against recursive implementation.
"""
dim = np.arange(n)
combos = np.asarray(list(cwr(dim, rank)))
arr = np.zeros(rank * (n,), dtype=int)
if rank == 2:
for a,idx in enumerate(combos):
i,j = idx
arr[i,j] = a
for idx in combos:
i,j = idx
print(flatten(n, rank, i,j))
print(flatten(n, rank, i,j) == arr[i,j], end=' ')
if rank == 3:
for a,idx in enumerate(combos):
i,j,k = idx
arr[i,j,k] = a
for idx in combos:
i,j,k = idx
print(flatten(n, rank, i,j,k) == arr[i,j,k], end=' ')
if rank == 4:
for a,idx in enumerate(combos):
i,j,k,l = idx
arr[i,j,k,l] = a
for idx in combos:
i,j,k,l = idx
print(flatten(n, rank, i,j,k,l) == arr[i,j,k,l], end=' ')
print(" ")
print(" ")
def solve():
links = dict()
for tri_count in range(10):
for pair in cwr(range(28 - 3 * tri_count), tri_count):
tup1 = ('t', ) + tuple(map(lambda x: x // 2, pair))
tup2 = ('b', ) + tuple(map(lambda x: (x + 1) // 2, pair))
if tup1 not in links: links[tup1] = []
if tup2 not in links: links[tup2] = []
links[tup1].append(tup2)
links[tup2].append(tup1)
configs = dict()
for layer in links:
configs[layer] = 1
for new_row in range(9):
new_configs = dict()
for layer in links:
for new_layer in links[layer]:
if new_layer in new_configs:
new_configs[new_layer] += configs[layer]
else:
new_configs[new_layer] = configs[layer]
configs = new_configs
result = 0
for layer in configs:
result += configs[layer]
return result
def problem030(n):
'''
Returns the sum of all the numbers which can be written as the sum of
n-th powers of their digits, where n is greater than 3. The function
first determines all the possible configurations of digits with
combinations_with_replacement in itertools. It subsequently calculates
the sum of those digits to the power n and determines whether this is
equal to the corresponding configuration.
With this method, this function can calculate sum of all numbers that
can be written as the 10-th powers of their digit in less than a second
'''
def convert(num):
'''
Convert an integer to an ordered tuple of its digits padded
by zeros. While this conversion can be done with the str() function
,this method is faster when n gets larger.
'''
digitList = []
while num != 0:
digitList.append(num % 10)
num = num // 10
return tuple([0] * (n - len(digitList) + 1) + sorted(digitList))
total = 0
possibleDigits = cwr(range(10), n + 1)
for perm in possibleDigits:
sumDigits = sum(d**n for d in perm)
digitTuple = convert(sumDigits)
if sumDigits > 1 and digitTuple == perm:
total += sumDigits
return total
def car2sph(sh, cart, orderedp=True):
"""Cartesian to spherical transform matrices.
.. code-block:: python
sh = solid_harmonics(8) # symbolic solid harmonics
cart = gen_enum_cartesian(8) # cartesian powers in a defined order
c2s = car2sph(sh, cart) # dictionary of {l: transform_matrix}
Args:
sh (OrderedDict): symbolic solid harmonics
cart (OrderedDict): cartesian powers in a defined order
orderedp (bool): order l=1 as ['x', 'y', 'z'], not [-1, 0, 1] (default True)
Returns:
c2s (OrderedDict): cartesian to spherical transform matrices
"""
c2s = OrderedDict([(L, np.zeros(((L + 1) * (L + 2) // 2, 2 * L + 1)))
for L in range(max(sh.keys()) + 1)])
for L, mls in sh.items():
if not L or (L == 1 and orderedp):
c2s[L] = np.array(cart[L])
continue
cdxs = [reduce(mul, xyz) for xyz in cwr((_x, _y, _z), L)]
for ml, sym in mls.items():
mli = ml + L
coefs = sym.expand().as_coefficients_dict()
#for crt, coef in coefs.items():
for crt, _ in coefs.items():
if isinstance(crt, (Integer, Float)): continue
idx = cdxs.index(crt)
c2s[L][idx, mli] = coefs[cdxs[idx]]
return c2s
def genotype_combinations(ref: str, alt_list: list) -> list:
"""
The `GC` column (not VCF-standard) in the Wellderly tsv files represents the count of genotypes in the
following patterns.
Suppose a, b, c, ..., z represent the allele frequencies.
For n = 2 alleles, the genotype frequencies are expanded as (a+b)^2 = a^2 + 2ab + b^2.
For n = 3 alleles, (a+b+c)^2 = (a+b)^2 + 2(a+b)c + c^2 = a^2 + 2ab + b^2 + 2ac + 2bc + c^2
For n = 4 alleles, (a+b+c+d)^2 = (a+b+c)^2 + 2(a+b+c)d + d^2 = ...
Therefore, the genotype combinations (i.e. the order of the `GC` column) would be
0/0, 0/1, 1/1, 0/2, 1/2, 2/2, 0/3, 1/3, 2/3, 3/3, ...
...
Note that this expanding scheme seems only apply to the Wellderly tsv files.
For n alleles, there would be {(n+1) choose 2} genotypes regardless of the combination order.
"""
# The REF must be the first allele in the list
allele_list = [ref] + alt_list
genotype_list = [
Genotype(first_allele=q, second_allele=p)
for (p, q) in cwr(reversed(allele_list), 2)
]
genotype_list.reverse()
return genotype_list
def get_clothing(self, temperature):
warm_coef = Wardrobe._warmness_coefficient(temperature)
keys = self._data.keys()
lengths = [len(item) for item in self._data]
elms = list(range(max(lengths)))
indexes = list(cwr(elms, len(keys)))
best_error = 100000
diff = 100000
spread = 100000
best_index = None
for index in indexes:
try:
vals = list()
for i, key in enumerate(keys):
cloth_item = self._data[key][index[i]]
vals.append(cloth_item)
if not (cloth_item.temperature_range[0] <= temperature <= cloth_item.temperature_range[1]):
raise ValueError
cur_spread = max(val.warmness for val in vals) - \
min(val.warmness for val in vals)
cur_diff = abs(warm_coef - sum(val.warmness for val in vals))
cur_error = Wardrobe._estimation(cur_diff, cur_spread ** 2)
if cur_error < best_error:
best_index = index
best_error = cur_error
except:
pass
clothing = [self._data[key][best_index[i]] for i, key in enumerate(keys)]
return clothing
def find_fewest_coins(coins: list, target: int) -> list:
"""[Function to find the fewest coins in change]
Args:
coins ([list]): [List of the coins available]
target ([int]): [Value of which change is made]
Raises:
ValueError: [Target input is less than change]
ValueError: [Couldn't get the proper amount in coins]
Returns:
[list]: [List of coins for appropriate change]
"""
if target == 0:
return []
if target < min(coins):
raise ValueError("Somethins whack with your target")
# iterate up to target value divided by the minimum coin
# Seeing as at the very least you'd use all of that min coin
# to reach the target value.
# From those coins generate combinations with replacement
# ie - all possible coin combinations with the coins available
# If the sum is == to the target. You've got the mininum coins~!
for i in range(1, target // min(coins) + 1):
for c in cwr(coins, i):
if sum(c) == target:
return list(c)
raise ValueError("No entiendo! Change not possible!")
def _nbo_labels():
"""Generate dataframes of NBO label, L, and ml or l, m, n."""
sph = pd.DataFrame([(L, m) for L in range(7) for m in range(-L, L + 1)],
columns=('L', 'ml'))
# See the NBO 6.0 manual for more details
# This is the basis function labeling scheme
# In order of increasing ml from most negative
# to most positive in the same order as the
# results from the solid_harmonics code.
sph['label'] = [
1, 101, 102, 103, 251, 253, 255, 252, 254, 357, 355, 353, 351, 352,
354, 356, 459, 457, 455, 453, 451, 452, 454, 456, 458, 561, 559, 557,
555, 553, 551, 552, 554, 556, 558, 560, 663, 661, 659, 657, 655, 653,
651, 652, 654, 656, 658, 660, 662
]
Ls, ls, ms, ns, label = [], [], [], [], []
# Even NBO 6.0 doesn't support cartesian basis
# functions with an l value greater than g functions
for i in range(5):
start = i * 100 + 1
label += list(range(start, start + cart_lml_count[i]))
car = [''.join(i) for i in list(cwr('xyz', i))]
Ls += [i for k in car]
ls += [i.count('x') for i in car]
ms += [i.count('y') for i in car]
ns += [i.count('z') for i in car]
car = pd.DataFrame({'L': Ls, 'l': ls, 'm': ms, 'n': ns, 'label': label})
return sph, car
def probability(dices,
sides,
value):
return round((
sum(factorial(len(set(shot))) for
shot in cwr(range(1,sides), dices) if
sum(shot) == value) /
sides ** dices), 4)
def sopdfe(ex):
s, p = 0, {str(i):i**ex for i in range(10)}
if ex >= 5: ex += 1
for cx in cwr('0123456789', ex):
t = sum(p[x] for x in cx)
sd = sum(p[x] for x in str(t))
if t == sd and t > 9: s += t
return (s if s > 0 else "NONE")
def find_minimum_coins(change, coins):
if change < 1:
raise ValueError('Impossible to change imaginary money')
cycles = 1 + (change // min(coins))
for i in range(1, cycles):
for found in filter(lambda x: sum(x) == change, cwr(coins, i)):
return sorted(found)
raise ValueError('Sorry, we cant change your money today')
def Euler023():
amic_map = {}
for i in range(12, 28124):
f = Factor(i)
if f > i:
amic_map[i] = f
nums = set([x for x in (sum(i) for i in cwr(amic_map, 2)) if x < 28124])
return sum(set(range(1, 28124)) - nums)
def get_random_mask(self):
schemeta = []
masks = list(cwr([0, 1], self.num_dim))
masks = masks[1:-1] # remove all zero or all one mask
s = np.random.randint(len(masks))
schema = list(masks[s])
np.random.shuffle(schema)
return schema
def main():
colin_probs = [0] * (36 - 6 + 1)
peter_probs = [0] * (36 - 9 + 1)
for combo in cwr(range(1, 7), 6):
score = sum(combo)
colin_probs[score - 6] += num_perms(combo)
for combo in cwr(range(1, 5), 9):
score = sum(combo)
peter_probs[score - 9] += num_perms(combo)
colin_denom = sum(colin_probs)
peter_denom = sum(peter_probs)
result = 0
for pete_score, pp in enumerate(peter_probs, 9):
result += (pp) * (sum(colin_probs[0:pete_score - 6]))
print(result / (colin_denom * peter_denom))
def solution(arr):
for i, j in cwr(range(len(arr)), 2):
new_arr = arr[:]
new_arr[i], new_arr[j] = new_arr[j], new_arr[i]
if new_arr == sorted(arr):
return True
break
else:
return False
def combrep(L, K):
sum = 0
choose = lambda L, K: cwr(list(range(L)), K)
for coordinate in choose(L, K):
#print("coordinate",coordinate)
occurence = [coordinate.count(k) for k in range(L)]
#print("occurence",occurence)
if all(occurence):
sum += multi_comb(occurence)
return sum
def replacer(n):
N = list(str(n))
swaps = getcombs(len(N))
for thisswap in swaps:
N_temp = N
reps = cwr('0123456789', len(thisswap))
for rep in reps:
for it, dig in enumerate(thisswap):
N_temp[int(dig)] = rep[it]
print(int(''.join(N_temp)))
def alphabet_columns():
alphabet = string.ascii_uppercase
length = 2
column_names = []
for letter in alphabet:
column_names.append(letter)
for comb in cwr(alphabet, length):
column_names.append(''.join(comb))
return column_names
def package_lipid(key):
body = classes[key][1][1]
N_Tails = classes[key][1][0]
if body == 'Glycerol':
lst = [list(comb) for comb in cwr(tails[0], N_Tails)]
elif body == 'SB':
lst = [
list(filter(None, comb)) for comb in product(
tails[1], [tail * N_Tails for tail in tails[0]])
] # Hacky, only works for 0 and 1.
return lst
def total_probs(base, count, comb):
''' Get the probability of rolling each possible total. Return it in a list
where the index is the total and the value is the probability. Indexes 0
through 'count-1' will have a value of 0 '''
perms = len(base)**count
probs = [0] * 37
for roll in cwr(base, count):
values = tuple(roll.count(n) for n in set(roll))
values = tuple(sorted(values))
probs[sum(roll)] += comb[values] / perms
return probs
def run_workloads(output, queries, workload_size, perf_model):
import time
x = 0
start = time.clock()
for workload in cwr(queries, workload_size):
partitions = eval_goodness(workload, perf_model)
results = {'workload': workload, 'partitions': partitions}
pickle.dump(results, output)
x += 1
if x % 100 == 0:
print x, x / (time.clock() - start)
def SmartForce():
t0 = clock()
totalsum = 0
for k in range(1, 7):
for i in cwr(range(9, -1, -1), k):
if sixty(i):
ctr = Counter(i)
totalsum += permut(ctr)
print(int(totalsum))
t1 = clock()
print("Took", t1 - t0)
def new_differentiate_nn(E, geom, order=3):
"""
geom must be a LIST of single-variable torch.tensors
"""
# Compute derivatives. Build up higher order tensors one dimension at a time.
nparam = len(geom) #.size()[0]
# indices of geometry parameters 0 --> n
indices = [i for i in range(nparam)]
# indices of unique tensor elements
h_idx = torch.tensor(list(cwr(indices, 2)), dtype=torch.long)
c_idx = torch.tensor(list(cwr(indices, 3)), dtype=torch.long)
gradient = torch.autograd.grad(E, geom, create_graph=True)
h1 = []
c1 = []
for i, g in enumerate(gradient):
for j in range(i, nparam):
h = torch.autograd.grad(g, geom[j], create_graph=True)[0]
h1.append(h)
for k in range(j, nparam):
c = torch.autograd.grad(h, geom[k], create_graph=True)[0]
c1.append(c)
# To build up tensors after finding unique derivatives:
with torch.no_grad():
hess = torch.zeros((nparam, nparam),
dtype=torch.float64,
requires_grad=False)
for i, idx in enumerate(h_idx):
hess[idx[0], idx[1]] = h1[i]
hess[idx[1], idx[0]] = h1[i]
cubic = torch.zeros((nparam, nparam, nparam),
dtype=torch.float64,
requires_grad=False)
for i, idx in enumerate(c_idx):
for p in list(itertools.permutations([0, 1, 2])):
cubic[idx[p[0]], idx[p[1]], idx[p[2]]] = c1[i]
return hess, cubic
def palindrome(num):
if not isinstance(num, int) or num < 0: return "Not valid"
num = str(num)
count = 0
# generate indexes for all possible list slices
for i, j in cwr(range(len(num) + 1), 2):
check = num[i:j]
if check == check[::-1] and len(check) > 1: count += 1
return count
def iterations(arr, length):
#<---This function generates all possible rows for connect 4 of a given length--->
possible = []
combs = list(cwr(arr, length))
for c in combs:
c = list(c)
if c not in possible:
perms = permutations(c)
for p in perms:
p = list(p)
if p not in possible:
possible.append(p)
return possible
def generate(key):
lipid_body = D.classes[key][1][1]
number_of_tails = D.classes[key][1][0]
if lipid_body == 'Glycerol':
lst = [list(comb) for comb in cwr(tails[0], number_of_tails)]
elif lipid_body == 'SB':
lst = [
list(filter(None, comb)) for comb in product(
tails[1], [tail * number_of_tails for tail in tails[0]])
] # Hacky, only works for 0 and 1.
return lst
def find_nr_chain_length_v2():
total = 0
for tup in cwr(range(1, 10), 6):
numstr = (''.join([str(i) for i in tup]))
num_leading_ones = get_num_leading_ones(numstr)
if num_leading_ones == len(numstr):
continue
for i in range(num_leading_ones + 1):
if find_nr_chain_length(int(numstr[i:])) == 60:
add = 0
for elem in include_zero_substitutions(numstr[i:]):
add = num_permutations(elem)
print(total, add, elem)
total += add
return total
def compute(self): numbers_sets = cwr([n for n in range(self.max, self.min - 1, -1)], numbers) # min - 1 to print min # generates the sets of n numbers to be multiplied pal_number = 0 for numbers_set in numbers_sets: # iterate the set of numbers product = 1 for number in numbers_set: product *= number # finds the product of the n numbers in the set if self.check(product) and product > pal_number: pal_number = product PalSet = numbers_set print(pal_number) # print(product, set) print(pal_number, PalSet) return
def solve():
#Declare variables
start = time.time()
facts, ans = [[i, fact(i)] for i in range(10)], 0
#Solve the problem
for digits in range(2, 8):
for comb in list(cwr(facts, digits)): #Note 1
num = ''.join(str(i[0]) for i in comb)
sumfacts = sum(i[1] for i in comb)
if sorted(str(sumfacts)) == sorted(num): ans += sumfacts #Note 2
#Print the results
print 'The sum of all numbers which are equal to the '
print 'sum of the factorial of their digits is ' + str(ans) + '.'
print 'This took ' + str(time.time() - start) + ' seconds to calculate.'
def M(p,q,N):
exp = ceil((log(N)-log(max([p,q])))/log(min([p,q])))
tmp = [0]
for e in range(1,exp+1):
combos = cwr([p,q],e)
nums = []
for i in combos:
if p in i and q in i:
j = reduce(mul,i)
if j<=N:
nums+=[j]
#nums = [j for j in reduce(mul,i) for i in combos if j<=N and p in i\
#and q in i]
if nums:
tmp+=[max(nums)]
#if N in tmp:return N
return max(tmp)
def get_expected_probability(probabilities):
"""
Calculates the expected probability of two variables
:param probabilities: dictionary with all the probabilites per element
:return: expected probabilites per pair of values
"""
expected = dict()
for a, b in cwr(probabilities.keys(), 2):
if a == b:
expected["".join(sorted([a, b
]))] = probabilities[a] * probabilities[b]
else:
expected["".join(sorted(
[a, b]))] = 2 * (probabilities[a] * probabilities[b])
return expected
def __init__( self, **kwargs ) :
from P2VV.RooFitWrappers import __check_req_kw__
__check_req_kw__('AmpNames',kwargs)
__check_req_kw__('Amplitudes',kwargs)
__check_req_kw__('AngFunctions',kwargs)
try : from itertools import combinations_with_replacement as cwr
except: from P2VV.Compatibility import cwr
# get amplitude names from arguments
self._ampNames = kwargs.pop('AmpNames')
# get amplitudes from arguments
self._amplitudes = kwargs.pop('Amplitudes')
for amp in self._ampNames : assert amp in self._amplitudes, 'Amplitudes_AngularPdfTerms: no amplitude \'%s\' found' % amp
# get keys for angular terms
keys = [ key for key in cwr( self._ampNames, 2 ) ]
# get angular functions from arguments
angFuncs = { }
angFuncsArg = kwargs.pop('AngFunctions')
for key in keys :
assert key in angFuncsArg, 'Amplitudes_AngularPdfTerms: no angular function %s found' % str(key)
angFuncs[key] = angFuncsArg[key]
# check if there are no arguments left
if kwargs: raise KeyError('Amplitudes_AngularPdfTerms: got unknown keyword%s: %s'\
% ( '' if len(kwargs) == 1 else 's', kwargs ))
# build angular coefficients
from P2VV.RooFitWrappers import FormulaVar
angCoefs = { }
Re = lambda Ai, Aj :\
FormulaVar( Name = 'Re_c_%s_%s' % ( Ai, Aj ), Formula = '@0*@2 + @1*@3', Arguments = [ Ai.Re, Ai.Im, Aj.Re, Aj.Im ] )
Im = lambda Ai, Aj :\
FormulaVar( Name = 'Im_c_%s_%s' % ( Ai, Aj ), Formula = '@0*@3 - @1*@2', Arguments = [ Ai.Re, Ai.Im, Aj.Re, Aj.Im ] )
for key in keys :
angCoefs[key] = ( Re( self._amplitudes[ key[0] ], self._amplitudes[ key[1] ] )
, Im( self._amplitudes[ key[0] ], self._amplitudes[ key[1] ] ) )
# initialize
Coefficients_AngularPdfTerms.__init__( self, Keys = keys, AngCoefficients = angCoefs, AngFunctions = angFuncs )
def add_polynomial_terms(X):
"""
Return matrix X augmented with columns representing 2-dgree polynomial
expansions of its columns.
Examples
--------
>>> X = np.array([[1,2,3,4],[5,6,7,8]]).T
array([[1, 5],
[2, 6],
[3, 7],
[4, 8]])
>>> add_polynomial_terms(X)
array([[ 1, 5, 1, 5, 25],
[ 2, 6, 4, 12, 36],
[ 3, 7, 9, 21, 49],
[ 4, 8, 16, 32, 64]])
"""
from itertools import combinations_with_replacement as cwr
# TODO: will need to combine column indices
col_combinations = [x for x in cwr(range(X.shape[1]), 2)]
poly_cols = [np.prod(X[:, c], axis=1) for c in col_combinations]
return np.hstack((X, np.array(poly_cols).T))
def precondition(self):
"""Get the indices through which we should run, and check if anything
is missing. Populate the dictionaries part_list (that has the
list of particle indices for each type) and pair_list (the
list of particle pair indices for each particle pair).
"""
self.part_list = {}
for j in self.names:
self.part_list[j] = \
[i for i, _x in enumerate(self.name) if _x == j]
#Create all pair_list arrays
self.pair_list = {}
for pair_name in cwr(self.names, 2):
self.pair_list[tuple(sorted(pair_name))] = []
#Populate pair_list
for pair in combinations(xrange(self.N), 2):
name_1 = self.name[pair[0]]
name_2 = self.name[pair[1]]
pair_name = tuple(sorted((name_1, name_2)))
self.pair_list[pair_name].append((pair[0], pair[1]))
from operator import add, sub, mul, truediv
from itertools import combinations_with_replacement as cwr
INDEXES = [tuple(map(int,i)) for k in range(1,7) for
i in cwr("123456",k) if
sum(int(j) for j in i) == 6]
OPER = [op for op in cwr((add,sub,mul, truediv),5)]
print(INDEXES)
print(OPER)
import csv
from pandas import DataFrame, ExcelFile, Series
from pandas.io.parsers import read_csv as rc
from pandas.io.json import read_json
import re
import numpy as np
DATA_TYPE_TYPES = {
"float64": float,
"int64": int,
"object" : object,
}
import string
from itertools import product as cwr
stuff = string.ascii_lowercase
# We generate a hexavigecimal alphabet which allows us to convert between base 26 letter codes and numbers
alphabet = ["".join(comb) for comb in cwr(stuff, repeat=1)]
alphabet += ["".join(comb) for comb in cwr(stuff, repeat=2)]
alphabet += ["".join(comb) for comb in cwr(stuff, repeat=3)]
def get_data_frame(read_csv, skiprows=0, header=None, names=None):
'''Returns a dataframe from a csv buffer'''
pd = rc(read_csv, infer_datetime_format=True,index_col=None, header=header, skiprows=skiprows,names=names,)
return pd
def get_excel_data_frame(read_excel, skiprows=0, header=None, names=None):
data = ExcelFile(read_excel)
df = data.parse(data.sheet_names[0], header=header,index_col=None, skiprows=skiprows,names=names, )
return df
def rename_column(df, position, new_name):
#Changes:
# OFFSET(B2,0,4)
#To:
# INDIRECT("'New Matrix'!$F$" & ROW($A2))
import string
from itertools import combinations_with_replacement as cwr
alphabet = string.ascii_lowercase
length = 2
alpha1 = ["".join(letter) for letter in string.ascii_lowercase]
alpha2 = ["".join(comb) for comb in cwr(alphabet, length)]
extended_alphabet = alpha1+alpha2
string = r'IF(ISBLANK(OFFSET(B2,0,4)),"",OFFSET(B2,0,4)&"?"&"utm_source=facebook&utm_medium="&IF(OR(OFFSET(B2,0,13)="des",OFFSET(B2,0,13)="mob",OFFSET(B2,0,13)="mob-tab",OFFSET(B2,0,13)="a",OFFSET(B2,0,13)="mob-all"),"pla","banr")&"&utm_term="&SUBSTITUTE(LOWER(AlphaNumericOnly(SUBSTITUTE(SUBSTITUTE(SUBSTITUTE(OFFSET(B2,0,19),"e","e"),"&","and"),"+","and")))," ","_")&"&utm_content="&OFFSET(B2,0,17)&"&utm_campaign="&OFFSET(B2,0,2)&"&db_dest="&OFFSET(B2,0,21)&"&db_unit=d&db_cid=60&db_terms="&OFFSET(B2,0,23)&"-"&OFFSET(B2,0,24)&"&db_class="&IF(OR(OFFSET(B2,0,13)="des",OFFSET(B2,0,13)="banr"),"des",OFFSET(B2,0,13))&"&db_seg="&OFFSET(B2,0,22)&"&db_sku=&c3ch=Facebook&c3nid="&OFFSET(B2,0,2)&"&db_vref1="&IF(ISBLANK(OFFSET(B2,0,25)),"n",OFFSET(B2,0,25))&"&db_vref2="&IF(ISBLANK(OFFSET(B2,0,26)),"n",OFFSET(B2,0,26))&"&lb=force")'
substring = 'OFFSET'
# for substring in string:
# print substring
start = string.find('OFFSET')
end = string.find(')', start)
num_reference = string[start+6:end].split(',')[2]
letter_reference = extended_alphabet[int(num_reference)+1]
text_to_replace = string[start:end+1]
print text_to_replace
ind_reference = r'INDIRECT("\'New Matrix\'!${0}$" & ROW($A2))'.format(letter_reference.upper())
print ind_reference
from itertools import combinations_with_replacement as cwr
x,y = input().split()
[print(''.join(c)) for c in cwr(sorted(x),int(y))]
lmap = OrderedDict()
rlmap = OrderedDict()
spher_ml_count = OrderedDict()
cart_ml_count = OrderedDict()
spher_lml_count = OrderedDict()
cart_lml_count = OrderedDict()
enum_cartesian = OrderedDict()
for i, L in enumerate(lorder):
lmap[L] = i
rlmap[i] = L
spher_ml_count[L] = 2 * i + 1
cart_ml_count[L] = (i + 1) * (i + 2) // 2
spher_lml_count[i] = spher_ml_count[L]
cart_lml_count[i] = cart_ml_count[L]
enum_cartesian[i] = []
cnts = [Counter(c) for c in cwr('xyz', i)]
enum_cartesian[i] = np.array([[0, 0, 0]]) if not cnts \
else np.array([[c[x] for x in 'xyz'] for c in cnts])
lmap.update([('px', 1), ('py', 1), ('pz', 1)])
gaussian_cartesian = enum_cartesian.copy()
gaussian_cartesian[2] = np.array([[2, 0, 0], [0, 2, 0], [0, 0, 2],
[1, 1, 0], [1, 0, 1], [0, 1, 1]])
def _hermite_gaussians(lmax):
"""Symbolic hermite gaussians up to order lmax.
Args:
lmax (int): highest order angular momentum quantum number
"""
order = 2 * lmax + 1
def __init__(self, angFuncs, Amplitudes,CP, itag, dilution, order ) :
def combine( name, afun, A, CPparams, tag, i, j) :
# TODO: deal with tag = None: create the untagged PDF in that case!
from P2VV.RooFitWrappers import ConstVar, Product
plus = ConstVar( Name = 'plus', Value = 1 )
minus = ConstVar( Name = 'minus', Value = -1 )
if type(CP['C'])==ConstVar and CP['C'].getVal() == 0 :
Norm = [ ]
else :
Norm = [ self._parseArg( 'Norm', kwargs, Formula = '1.0/(1.0+sign(@0)*@1)', Arguments = [ tag, CP['C'] ]
, ObjectType = 'FormulaVar' ) ]
Norm[0].setAttribute("CacheAndTrack")
# define functions which return Re(Conj(Ai) Aj), Im( Conj(Ai) Aj)
Re = lambda ai, aj : self._parseArg( 'Re_c_%s_%s' % ( ai, aj ), { }, Type = 'ProdCarthCToRe', ObjectType = 'ConvertPolAmp'
, Arguments=[ ai.Re,ai.Im,aj.Re,aj.Im ] )
Im = lambda ai, aj : self._parseArg( 'Im_c_%s_%s' % ( ai, aj ), { }, Type = 'ProdCarthCToIm', ObjectType = 'ConvertPolAmp'
, Arguments=[ ai.Re,ai.Im,aj.Re,aj.Im ] )
# define functions which return the coefficients that define the time-dependence...
_minus_if = lambda b, x : [ minus ] + x if b else x
coef = { 'cosh' : lambda ai,aj,CP : ( plus if ai.CP == aj.CP else CP['C']
, None )
, 'cos' : lambda ai,aj,CP : ( tag if ai.CP != aj.CP else Product('Re_%s_%s_cos' %(ai,aj), [ tag, CP['C'] ] )
, None )
, 'sinh' : lambda ai,aj,CP : ( None if ai.CP != aj.CP else Product('Re_%s_%s_sinh'%(ai,aj), _minus_if( ai.CP < 0 , [ CP['D'] ] ))
, None if ai.CP == aj.CP else Product('Im_%s_%s_sinh'%(ai,aj), _minus_if( ai.CP < aj.CP , [ CP['S'] ] )) )
, 'sin' : lambda ai,aj,CP : ( None if ai.CP != aj.CP else Product('Re_%s_%s_sin' %(ai,aj), _minus_if( ai.CP > 0 , [ tag, CP['S'] ] ))
, None if ai.CP == aj.CP else Product('Im_%s_%s_sin' %(ai,aj), _minus_if( ai.CP < aj.CP , [ tag, CP['D'] ] )) )
}
(c_re,c_im) = coef[name](A[i],A[j],CPparams)
(f_re,f_im) = afun[(i,j)]
(a_re,a_im) = ( Re(A[i],A[j]),Im(A[i],A[j]) )
# NOTE: thes sign are just the obvious Re(a b c) = Re(a)Re(b)Re(c) - Re(a)Im(b)Im(c) - Im(a)Re(b)Im(c) - Im(a)Im(b)Re(c),
# i.e. there is a minus in case there are 2 imaginary contributions
prod = lambda name, args : [ Product(name, args) ] if all(args) else []
s = prod('ReReRe_%s_%s_%s'%(name,A[i],A[j]), [ a_re , c_re, f_re ]+Norm ) \
+ prod('ImImRe_%s_%s_%s'%(name,A[i],A[j]), [ minus, a_im , c_im, f_re ]+Norm ) \
+ prod('ImReIm_%s_%s_%s'%(name,A[i],A[j]), [ minus, a_im , c_re, f_im ]+Norm ) \
+ prod('ReImIm_%s_%s_%s'%(name,A[i],A[j]), [ minus, a_re , c_im, f_im ]+Norm )
assert len(s) == 1 # for now, coefficients are either real, or imaginary, but not both... (not true in general, but I'm lazy today ;-)
return s[0]
args = dict()
from P2VV.RooFitWrappers import Addition,Product, RealCategory
try : # this requires python 2.7 or later...
from itertools import combinations_with_replacement as cwr
except:
from P2VV.Compatibility import cwr
tag = Product('tag',( RealCategory('tag_real', itag ),dilution))
for name in [ 'cosh', 'sinh', 'cos', 'sin' ] :
# NOTE: 'Amplitudes' must be traversed 'in order' -- so we cannot use Amplitudes.keys() out of the box, but use the
# specified order (which also selects which ones to include!)...
args[ name ] = Addition( 'a_%s'% name, [ combine(name,angFuncs,Amplitudes,CP,tag,i,j) for (i,j) in cwr( order, 2 ) ] )
BDecayBasisCoefficients.__init__( self, **args )
def configure_features(self, orders=range(1, 5), **extras):
from itertools import combinations_with_replacement as cwr
all_features = [t for order in orders for t in cwr(['logt', 'logg', 'feh'], order)]
return get_energy(output_file)
DISP = 0.005
os.makedirs('disp/', exist_ok=True)
# Run the reference geometry
e0_in = 'disp/e0.in'
write_input(e0_in, mol)
run(e0_in)
e0 = get_energy('disp/e0.out')
print("E0: " + str(e0))
# Iterate over all pairs of coordinates in the upper triangle
for q1, q2 in cwr(range(3*len(mol)), r=2):
# Displace forwards and back
for disp in [DISP, -DISP]:
sign = '+' if disp > 0 else '-'
if q1 == q2:
print(q1, sign)
inp_name = single_displace_form.format(q1, sign) + '.in'
displaced = displace(mol, q1, disp, q2, 0)
else:
print(q1, q2, sign)
inp_name = double_displace_form.format(q1, sign, q2, sign) + '.in'
displaced = displace(mol, q1, disp, q2, disp)
write_input(inp_name, displaced)
run(inp_name)
def __init__( self, AngFuncs, Amplitudes, CPParams, Order ) :
def combine( tCoefType, angFuncs, amplitudes, CPParams, iIndex, jIndex ) :
from P2VV.RooFitWrappers import ConstVar
one = ConstVar( Name = 'one', Value = 1 )
minus = ConstVar( Name = 'minus', Value = -1 )
# define functions which return Re(Ai* Aj), Im( Ai* Aj)
Re = lambda Ai, Aj : self._parseArg( 'Re_amps_%s_%s' % ( Ai, Aj ), { }, Type = 'ProdCarthCToRe', ObjectType = 'ConvertPolAmp'
, Arguments = [ Ai.Re, Ai.Im, Aj.Re, Aj.Im ] )
Im = lambda Ai, Aj : self._parseArg( 'Im_amps_%s_%s' % ( Ai, Aj ), { }, Type = 'ProdCarthCToIm', ObjectType = 'ConvertPolAmp'
, Arguments = [ Ai.Re, Ai.Im, Aj.Re, Aj.Im ] )
# define functions which return the coefficients of the time dependence
def CPVDec( termInd, iInd, jInd, amps, CPPar ) :
# get parameters for CP violation in decay
assert termInd in ( 'plus', 'min', 'Re', 'Im' )
if CPPar.CPVInDecay() : return CPPar.R( termInd, iInd, jInd )
# only CP violation in mixing (or lambdas for all polarizations identical):
# R^+ = ( 1 + eta_i * eta_j ) / 2
# R^- = ( 1 - eta_i * eta_j ) / 2
# R^Re = ( eta_i + eta_j ) / 2
# R^Im = i * ( eta_i - eta_j ) / 2
if termInd == 'plus' : return ( None if amps[iInd].CP != amps[jInd].CP else one, None )
if termInd == 'min' : return ( None if amps[iInd].CP == amps[jInd].CP else one, None )
if termInd == 'Re' : return ( None if amps[iInd].CP != amps[jInd].CP else one if amps[iInd].CP > 0 else minus, None )
if termInd == 'Im' : return ( None, None if amps[iInd].CP == amps[jInd].CP else one if amps[iInd].CP > 0 else minus )
def tCoefTerm( name, dec, mix, sign ) :
# build one of the two terms within the time function coefficient:
# + R^+ * 1, + R^- * C, + R^- * 1, + R^+ * C, + R^Re * D, + R^Im * S, + R^Im * D, - R^Re * S
if not dec or not mix : return None
if dec == minus : sign = -sign
if mix == minus : sign = -sign
sign = minus if sign < 0 else None
if dec in [ one, minus ] : dec = None
if mix in [ one, minus ] : mix = None
facs = [ fac for fac in ( sign, dec, mix ) if fac ]
return self._parseArg( name, { }, Arguments = facs, ObjectType = 'Product' ) if len(facs) > 1\
else facs[0] if len(facs) == 1 else one
def tCoef( tCType, iInd, jInd, amps, CPPar ) :
# build the coefficient of the time function:
# cosh: + R^+ * 1 + R^- * C
# cos: + R^- * 1 + R^+ * C
# sinh: + R^Re * D + R^Im * S
# sin: + R^Im * D - R^Re * S
assert tCType in ( 'cosh', 'sinh', 'cos', 'sin' )
CPVDecInds = [ 'plus', 'min' ] if tCType in ( 'cosh', 'cos' ) else [ 'Re', 'Im' ]
if tCType in ( 'cos', 'sin' ) : CPVDecInds = [ CPVDecInds[1], CPVDecInds[0] ]
CPVDecs = [ CPVDec( CPVDecInd, iInd, jInd, amps, CPPar ) for CPVDecInd in CPVDecInds ]
CPVMixs = [ one, CPPar.C() ] if tCType in ( 'cosh', 'cos' ) else [ CPPar.D(), CPPar.S() ]
signs = [ +1, +1 ] if tCType in ( 'cosh', 'cos', 'sinh' ) else [ +1, -1 ]
name = '%s_%s_%s' % ( iInd , jInd, tCType )
terms = [ ( tCoefTerm( 'Re_%s%d_%s_%s' % ( tCType, ind, iInd, jInd ), dec[0], mix, sign )
, tCoefTerm( 'Im_%s%d_%s_%s' % ( tCType, ind, iInd, jInd ), dec[1], mix, sign )
) for ind, ( dec, mix, sign ) in enumerate( zip( CPVDecs, CPVMixs, signs ) )
]
assert any( comp for term in terms for comp in term )
add = lambda name, args : self._parseArg( name, { }, Arguments = args, ObjectType = 'Addition' ) if len(args) > 1\
else args[0] if len(args) == 1 else None
return ( add( 'Re_%s_%s_%s' % ( tCType, iInd, jInd ), [ term[0] for term in terms if term[0] ] )
, add( 'Im_%s_%s_%s' % ( tCType, iInd, jInd ), [ term[1] for term in terms if term[1] ] )
)
# create complex amplitude, time and angular factors
( reAmps, imAmps ) = ( Re( amplitudes[iIndex], amplitudes[jIndex] ), Im( amplitudes[iIndex], amplitudes[jIndex] ) )\
if iIndex != jIndex else ( amplitudes[iIndex].Mag2, None )
( reTime, imTime ) = tCoef( tCoefType, iIndex, jIndex, amplitudes, CPParams )
( reAng, imAng ) = angFuncs[ ( iIndex, jIndex ) ]
# (real part of) product of amplitude, time and angular (complex) factors:
# Re(abc) = Re(a)Re(b)Re(c) - Im(a)Im(b)Re(c) - Re(a)Im(b)Im(c) - Im(a)Re(b)Im(c)
# (there is a minus in case there are 2 imaginary contributions)
prod = lambda name, args : [ self._parseArg( name, { }, Arguments = args, ObjectType = 'Product' ) ] if all(args) else [ ]
return prod( 'ReReRe_%s_%s_%s' % ( tCoefType, amplitudes[iIndex], amplitudes[jIndex] ), [ reAmps , reTime, reAng ] ) \
+ prod( 'ImImRe_%s_%s_%s' % ( tCoefType, amplitudes[iIndex], amplitudes[jIndex] ), [ minus, imAmps , imTime, reAng ] ) \
+ prod( 'ReImIm_%s_%s_%s' % ( tCoefType, amplitudes[iIndex], amplitudes[jIndex] ), [ minus, reAmps , imTime, imAng ] ) \
+ prod( 'ImReIm_%s_%s_%s' % ( tCoefType, amplitudes[iIndex], amplitudes[jIndex] ), [ minus, imAmps , reTime, imAng ] )
try : # this requires python 2.7 or later...
from itertools import combinations_with_replacement as cwr
except:
from P2VV.Compatibility import cwr
args = dict()
for tCoefType in [ 'cosh', 'sinh', 'cos', 'sin' ] :
# NOTE: 'Amplitudes' must be traversed 'in order' : A0, Apar, Aperp, AS, so we cannot use Amplitudes.keys() out of the box
coef = self._parseArg( '%sCoef' % tCoefType, { }, ObjectType = 'Addition'
, Arguments = [ term for ( i, j ) in cwr( Order, 2 )\
for term in combine( tCoefType, AngFuncs, Amplitudes, CPParams, i, j ) ]
)
# same B/Bbar sign for cosh and sinh coefficients ("even"), opposite B/Bbar sign for cos and sin coefficients ("odd")
args[ tCoefType ] = ( coef, None ) if tCoefType in [ 'cosh', 'sinh' ] else ( None, coef )
BDecayBasisCoefficients.__init__( self, **args )
from itertools import combinations_with_replacement as cwr
with open('sensor.in') as fin:
N = int(fin.read())
k = set()
for i in range(1, N + 1):
for j in cwr([1, 2, 3, 4, 5, 6], r=i):
if sum(j) == N:
print(j)
new_sum = sum([7 - i for i in j])
print(new_sum)
k.add(new_sum)
with open('sensor.out', 'w') as fout:
print(len(k), file=fout)
from itertools import combinations_with_replacement as cwr
s,k = input().split()
print("\n".join("".join(it) for it in cwr(sorted(s),int(k))))
def __init__( self, **kwargs ) :
ampNames = kwargs.pop('AmplitudeNames')
amps = kwargs.pop('Amplitudes')
magNames = kwargs.pop('MagnitudeNames')
phaseNames = kwargs.pop('PhaseNames')
RPlusDict = { }
RMinDict = { }
RReDict = { }
RImDict = { }
try : from itertools import combinations_with_replacement as cwr # this requires python 2.7 or later
except: from P2VV.Compatibility import cwr
for ampComb in cwr( ampNames, 2 ) :
eta0 = amps[ ampComb[0] ].CP
eta1 = amps[ ampComb[1] ].CP
RPlusDict[ampComb] = tuple( [ self._parseArg( '%sRPlus_%s_%s' % ( comp, ampComb[0], ampComb[1] ), kwargs
, Formula = '(%s@0*@1*%s(@2-@3)) / 2.'\
% ( '1. + ' if comp == 'Re' and eta0 == eta1\
else '1. - ' if comp == 'Re' and eta0 != eta1\
else '' if eta0 == eta1 else '-'
, func
)
, Arguments = [ getattr( self, '_%s' % magNames[ ampComb[0] ] )
, getattr( self, '_%s' % magNames[ ampComb[1] ] )
, getattr( self, '_%s' % phaseNames[ ampComb[0] ] )
, getattr( self, '_%s' % phaseNames[ ampComb[1] ] )
]
, ObjectType = 'FormulaVar'
) for ( comp, func ) in [ ( 'Re', 'cos' ), ( 'Im', 'sin' ) ]
] )
RMinDict[ampComb] = tuple( [ self._parseArg( '%sRMin_%s_%s' % ( comp, ampComb[0], ampComb[1] ), kwargs
, Formula = '(%s@0*@1*%s(@2-@3)) / 2.'\
% ( '1. - ' if comp == 'Re' and eta0 == eta1\
else '1. + ' if comp == 'Re' and eta0 != eta1\
else '-' if eta0 == eta1 else ''
, func
)
, Arguments = [ getattr( self, '_%s' % magNames[ ampComb[0] ] )
, getattr( self, '_%s' % magNames[ ampComb[1] ] )
, getattr( self, '_%s' % phaseNames[ ampComb[0] ] )
, getattr( self, '_%s' % phaseNames[ ampComb[1] ] )
]
, ObjectType = 'FormulaVar'
) for ( comp, func ) in [ ( 'Re', 'cos' ), ( 'Im', 'sin' ) ]
] )
RReDict[ampComb] = tuple( [ self._parseArg( '%sRRe_%s_%s' % ( comp, ampComb[0], ampComb[1] ), kwargs
, Formula = '(%s@0*%s(@2) %s @1*%s(-@3)) / 2.'\
% ( '' if eta0 > 0 else '-', func, '+' if eta1 > 0 else '-', func )
, Arguments = [ getattr( self, '_%s' % magNames[ ampComb[0] ] )
, getattr( self, '_%s' % magNames[ ampComb[1] ] )
, getattr( self, '_%s' % phaseNames[ ampComb[0] ] )
, getattr( self, '_%s' % phaseNames[ ampComb[1] ] )
]
, ObjectType = 'FormulaVar'
) for ( comp, func ) in [ ( 'Re', 'cos' ), ( 'Im', 'sin' ) ]
] )
RImDict[ampComb] = tuple( [ self._parseArg( '%sRIm_%s_%s' % ( comp, ampComb[0], ampComb[1] ), kwargs
, Formula = '(%s@0*%s(@2) %s @1*%s(-@3)) / 2.'\
% ( '-' if ( eta0 > 0 and comp == 'Re' )\
or ( eta0 < 0 and comp == 'Im' ) else ''
, func
, '+' if ( eta1 > 0 and comp == 'Re' )\
or ( eta1 < 0 and comp == 'Im' ) else '-'
, func
)
, Arguments = [ getattr( self, '_%s' % magNames[ ampComb[0] ] )
, getattr( self, '_%s' % magNames[ ampComb[1] ] )
, getattr( self, '_%s' % phaseNames[ ampComb[0] ] )
, getattr( self, '_%s' % phaseNames[ ampComb[1] ] )
]
, ObjectType = 'FormulaVar'
) for ( comp, func ) in [ ( 'Re', 'sin' ), ( 'Im', 'cos' ) ]
] )
self._check_extraneous_kw( kwargs )
CPParam.__init__( self, AmplitudeNames = ampNames
, C = self._parseArg( 'C', kwargs
, Formula = '(1. - @0*@0) / (1. + @0*@0)'
, Arguments = [ getattr( self, '_%s' % magNames['mix'] ) ]
, ObjectType = 'FormulaVar'
)
, D = self._parseArg( 'D', kwargs
, Formula = '-2. * @0 * cos(@1) / (1. + @0*@0)'
, Arguments = [ getattr( self, '_%s' % magNames['mix'] )
, getattr( self, '_%s' % phaseNames['mix'] ) ]
, ObjectType = 'FormulaVar'
)
, S = self._parseArg( 'S', kwargs
, Formula = '-2. * @0 * sin(@1) / (1. + @0*@0)'
, Arguments = [ getattr( self, '_%s' % magNames['mix'] )
, getattr( self, '_%s' % phaseNames['mix'] ) ]
, ObjectType = 'FormulaVar'
)
, RPlusDict = RPlusDict
, RMinDict = RMinDict
, RReDict = RReDict
, RImDict = RImDict
)
bounds = {}
features = {}
def pad_bounds(inbounds, tpad=500., gpad=0.5, zpad=0.1, **extras):
mm = np.array([-1,1])
outbounds = {}
outbounds['logt'] = tuple(np.log10(10**np.array(inbounds['logt']) + mm * tpad))
outbounds['logg'] = tuple(np.array(inbounds['logg']) + mm*gpad)
outbounds['feh'] = tuple(np.array(inbounds['feh']) + mm*zpad)
return outbounds
#you get (order + 3 - 1)!/(order! * 2!) combinations for each order
# terms_of_order = [t for t in cwr(['logt', 'logg', 'feh'], order)]
all_features = [t for order in [1, 2, 3 ,4, 5] for t in cwr(['logt', 'logg', 'feh'], order)]
bounds["Test"] = {'logt': (np.log10(2549.0), np.log10(4249)),
'logg': (3.49, 5.51),
'feh': (-2.01, 0.51)}
features["Test"] = (['logt'],
['feh'],
['logg'],
# Quadratic
['logt', 'logt'],
['logg', 'logg'],
['feh', 'feh'],
# Cross-quadratic
['logt', 'feh'],
# A palindromic number reads the same both ways.
# The largest palindrome made from the product of two 2-digit numbers
# is 9009 = 91 × 99.
#
# Find the largest palindrome made from the product of two 3-digit numbers.
from itertools import combinations_with_replacement as cwr
def ispalindrome(x):
y = str(x)
if y == y[::-1]:
return True
else:
return False
combinations = cwr(range(999, 99, -1), 2)
products = [x * y for x, y in combinations]
print(max([x for x in products if ispalindrome(x)]))
from itertools import permutations, combinations, combinations_with_replacement as cwr
import sys
from util import isprime
# iterate over each combination of 4 numbers
for digits in cwr("0123456789", 4):
# all permutations of digits, in numerical order
perms = [int("".join(p)) for p in permutations(digits)]
perms = sorted(perms)
# each increasting pair
for t1, t2 in combinations(perms, 2):
if t1 < 1000:
continue # must be 4 digits
if t2 == t1:
continue # must be increasing
if t1 == 1487:
continue
t3 = t2 + (t2 - t1)
if not isprime(t1) or not isprime(t2):
continue
if not isprime(t3) or t3 not in perms:
continue
print "%4.4i%4.4i%4.4i" % (t1, t2, t3)
sys.exit(1)
from itertools import combinations_with_replacement as cwr #take input word and length k input_str = raw_input().split() keyword = input_str[0] keyword = sorted(keyword) k = int(input_str[1]) L = list(cwr(keyword,k)) #print the formatted answer for i in range(0,len(L)): print ''.join(L[i])