def mcosine(u, v):
r"""
Computes the Cosine distance between two n-vectors u and v, which
is defined as
.. math::
\frac{1-uv^T}
{||u||_2 ||v||_2}.
Parameters
----------
u : ndarray
An :math:`n`-dimensional vector.
v : ndarray
An :math:`n`-dimensional vector.
Returns
-------
d : double
The Cosine distance between vectors ``u`` and ``v``.
"""
u = ma.asarray(u, order='c')
v = ma.asarray(v, order='c')
return (1.0 - (ma.dot(u, v.T) / \
(ma.sqrt(ma.dot(u, u.T)) * ma.sqrt(ma.dot(v, v.T)))))
def filter(s0, s1):
for i, dindex in enumerate(s0.bands):
s1flux = ma.array(data=s1.flux[dindex], mask=s1.mask[dindex])
s0flux = ma.array(data=s0.flux[dindex], mask=s0.mask[dindex])
s1ivar = ma.array(data=s1.ivar[dindex], mask=s1.mask[dindex])
s0ivar = ma.array(data=s0.ivar[dindex], mask=s0.mask[dindex])
ston1 = s1.flux[dindex].sum(
axis=1) / (1 / ma.sqrt(s1.ivar[dindex])).sum(axis=1)
ston0 = s0.flux[dindex].sum(
axis=1) / (1 / ma.sqrt(s0.ivar[dindex])).sum(axis=1)
# ston1 = s1.flux[dindex].sum(axis=1) / ma.sqrt((1/s1.ivar[dindex]).sum(axis=1))
# ston0 = s0.flux[dindex].sum(axis=1) / ma.sqrt((1/s0.ivar[dindex]).sum(axis=1))
if i == 0:
ans = np.logical_and(np.greater(ston0, HasSignal.ston_cut),
np.greater(ston1, HasSignal.ston_cut))
else:
ans = np.logical_or(
ans,
np.logical_and(np.greater(ston0, HasSignal.ston_cut),
np.greater(ston1, HasSignal.ston_cut)))
return ans
def combine_nights(combined_catalog, filterlist, refcat):
header = [
'BEGIN CATALOG HEADER', 'nfields 13', ' ra 1 0 d degrees %10.6f',
' dec 2 0 d degrees %10.6f', ' id 3 0 c INDEF %3d'
]
for filt in filterlist:
header.append(' {} {:2d} 0 r INDEF %6.3f'.format(
filt,
len(header) - 1))
header.append(' {}err {:2d} 0 r INDEF %6.3f'.format(
filt,
len(header) - 1))
header += ['END CATALOG HEADER', '']
catalog = Table([refcat['ra'], refcat['dec'], refcat['id']],
meta={'comments': header},
masked=True)
for filt in filterlist:
mags = combined_catalog['mag'][combined_catalog['filter'] == filt]
median = np.median(mags, axis=0)
absdev_mag = mags - median
mad = np.median(np.abs(absdev_mag), axis=0) * np.sqrt(pi / 2)
mags.mask |= np.abs(absdev_mag) > 5 * mad
catalog[filt] = np.median(mags, axis=0)
catalog[filt + 'err'] = np.median(np.abs(mags - catalog[filt]),
axis=0) * np.sqrt(pi / 2)
return catalog
def cache_angles(tile_size=500):
half_size = float(tile_size - 1) / 2
get_zp = lambda x, y: arccos(1 / sqrt(x**2 + y**2 + 1))
get_zm = lambda x, y: arccos(-1 / sqrt(x**2 + y**2 + 1))
get_xypm = lambda x, y: arccos(y / sqrt(x**2 + y**2 + 1))
get_phi = lambda x, y: arctan(float(y) / x)
cache = {
'zp': np.zeros((tile_size, tile_size, ), dtype=np.float),
'zm': np.zeros((tile_size, tile_size, ), dtype=np.float),
'xypm': np.zeros((tile_size, tile_size, ), dtype=np.float),
'phi': np.zeros((tile_size, tile_size, ), dtype=np.float)
}
print 'Perform cache angles...'
for tile_y in xrange(tile_size):
y = float(tile_y) / half_size - 1
for tile_x in xrange(tile_size):
x = float(tile_x) / half_size - 1
cache['zp'][tile_y, tile_x] = get_zp(x, y)
cache['zm'][tile_y, tile_x] = get_zm(x, y)
cache['xypm'][tile_y, tile_x] = get_xypm(x, y)
if x != 0:
cache['phi'][tile_y, tile_x] = get_phi(x, y)
# print 'cache for: [{}, {}] -> [{},{}]'.format(tile_y, tile_x, y, x)
return cache
def gamma(self, mkt_dict_, engine_, unit_=None):
"""calculate option GAMMA with market data and engine"""
_rate, _spot, _vol, _div, _method, _param, _sign, _strike, _t = self._prepare_risk_data(
mkt_dict_, engine_)
_unit = unit_ or self.unit
if _method == EngineMethod.BS.value:
_d1 = (log(_spot / _strike) +
(_rate + _vol**2 / 2) * _t) / _vol / sqrt(_t)
return exp(-_d1**2 / 2) / sqrt(
2 * pi) / _spot / _vol / sqrt(_t) * exp(-_div * _t) * _unit
elif _method == EngineMethod.MC.value:
from utils.monte_carlo import MonteCarlo
_iteration = self._check_iter(
_param[EngineParam.MCIteration.value])
_spot = MonteCarlo.stock_price(_iteration,
isp=_spot,
rate=_rate,
div=_div,
vol=_vol,
t=_t)
_step = 0.01
_gamma = [
((max(_sign * (_s + 2 * _step - _strike), 0) -
max(_sign * (_s - _strike), 0)) -
(max(_sign * (_s - _strike), 0) -
max(_sign * (_s - 2 * _step - _strike), 0))) / (4 * _step**2)
for _s in _spot
]
return average(_gamma) * exp(-_rate * _t) * _unit
def showDataFigure(dataArr, *args):
m, n = shape(dataArr)
print m, n
example_width = round(sqrt(n))
print "特征数目：", n
print "example_width:", example_width # 20
example_height = n / example_width # 20
display_rows = floor(sqrt(m)) # 10
display_cols = ceil(m / display_rows) # 10
pad = 1
display_array = -ones((pad + display_rows * (example_height + pad), pad + display_cols * (example_width + pad)))
print "display_array 的维度为:", shape(display_array)
curr_ex = 0;
for j in range(0, int(display_rows)):
for i in range(0, int(display_cols)):
# for j in range(0, int(1)):
#for i in range(0, int(1)):
if curr_ex >= m:
break
max_val = max(abs(display_array[curr_ex, :]))
#print "##################maxval",max_val
display_array[
int(pad + j * (example_height + pad)): int(pad + j * (example_height + pad)) + int(example_height),
int(pad + i * (example_width + pad)):int(pad + i * (example_width + pad)) + int(example_width)] = \
reshape(dataArr[curr_ex, :], (example_height, example_width)) / max_val
curr_ex = curr_ex + 1;
if curr_ex >= m:
break;
plt.imshow(display_array.T, CM.gray) # 类似matlib中的imagesc
# scaledimage.scaledimage(display_array)
plt.show()
def _ttest_ind(Sample_mean_ArrayA,
Sample_var_ArrayA,
n_subjectsA,
Sample_mean_ArrayB,
Sample_var_ArrayB,
n_subjectsB,
equal_var=True,
sign=1):
if equal_var:
# force df to be an array for masked division not to throw a warning
df = ma.asanyarray(n_subjectsA + n_subjectsB - 2.0)
svar = ((n_subjectsA - 1) * Sample_var_ArrayA +
(n_subjectsB - 1) * Sample_var_ArrayB) / df
denom = ma.sqrt(
svar *
(1.0 / n_subjectsA + 1.0 / n_subjectsB)) # n-D computation here!
else:
vn1 = Sample_var_ArrayA / n_subjectsA
vn2 = Sample_var_ArrayB / n_subjectsB
df = (vn1 + vn2)**2 / (vn1**2 / (n_subjectsA - 1) + vn2**2 /
(n_subjectsB - 1))
# If df is undefined, variances are zero.
# It doesn't matter what df is as long as it is not NaN.
df = np.where(np.isnan(df), 1, df)
denom = ma.sqrt(vn1 + vn2)
with np.errstate(divide='ignore', invalid='ignore'):
ttest_ind = (Sample_mean_ArrayA - Sample_mean_ArrayB) * sign / denom
pvalues = special.betainc(0.5 * df, 0.5,
df / (df + ttest_ind * ttest_ind)).reshape(
ttest_ind.shape)
# ttest_ind, pvalues = ma.filled(ttest_ind), ma.filled(pvalues)
return ttest_ind, pvalues
def pv(self, mkt_dict_, engine_, unit_=None):
"""calculate option PV with market data and engine"""
_rate, _spot, _vol, _div, _method, _param, _sign, _strike, _t = self._prepare_risk_data(
mkt_dict_, engine_)
_unit = unit_ or self.unit
if _method == EngineMethod.BS.value:
_d1 = (log(_spot / _strike) +
(_rate - _div + _vol**2 / 2) * _t) / _vol / sqrt(_t)
_d2 = _d1 - _vol * sqrt(_t)
return _sign * (
_spot * exp(-_div * _t) * norm.cdf(_sign * _d1) -
_strike * exp(-_rate * _t) * norm.cdf(_sign * _d2)) * _unit
elif _method == EngineMethod.MC.value:
from utils.monte_carlo import MonteCarlo
_iteration = self._check_iter(
_param[EngineParam.MCIteration.value])
_spot = MonteCarlo.stock_price(_iteration,
isp=_spot,
rate=_rate,
div=_div,
vol=_vol,
t=_t)
_price = [max(_sign * (_s - _strike), 0) for _s in _spot]
return average(_price) * exp(-_rate * _t) * _unit
def mcorrelation(u, v):
r"""
Computes the correlation distance between two n-vectors ``u`` and
``v``, which is defined as
.. math::
\frac{1 - (u - \bar{u}){(v - \bar{v})}^T}
{{||(u - \bar{u})||}_2 {||(v - \bar{v})||}_2^T}
where :math:`\bar{u}` is the mean of a vectors elements and ``n``
is the common dimensionality of ``u`` and ``v``.
Parameters
----------
u : ndarray
An :math:`n`-dimensional vector.
v : ndarray
An :math:`n`-dimensional vector.
Returns
-------
d : double
The correlation distance between vectors ``u`` and ``v``.
"""
umu = u.mean()
vmu = v.mean()
um = u - umu
vm = v - vmu
return 1.0 - (ma.dot(um, vm) /
(ma.sqrt(ma.dot(um, um)) \
* ma.sqrt(ma.dot(vm, vm))))
def test_forest_topology():
"""Test building a forest topology.
"""
t = build_forest_topology(2,
depth=3,
arity=3,
dx=2.5,
dy=1.25,
roe=0.4,
dt=5)
nodes = t.nodes.all(order_by='address')
connections = t.connections.all(order_by='from_addr')
assert len(nodes) == 80
assert len(connections) == 78
# - ranges on levels 0, 1, 2 are the same and determined by sufficient
# distances for level 1;
# - range on level 3 is determined by sufficient distances for connecting
# to parents on level 2.
range_1 = 1.4 * sqrt(22.5**2 + 1.25**2)
range_2 = 1.4 * sqrt(7.5**2 + 1.25**2)
# Estimate positions and addresses by level:
y = [3.75, 2.5, 1.25, 0]
x1 = [
np.asarray([32.5]), 10.0 + np.arange(3) * 22.5,
2.5 + np.arange(9) * 7.5,
np.arange(27) * 2.5
]
x = [x1, [pos + 70 for pos in x1]]
addr1 = [
np.asarray([1]),
np.arange(3) + 2,
np.arange(9) + 5,
np.arange(27) + 14
]
addr = [addr1, [a + 40 for a in addr1]]
# Validate nodes level by level:
for level in range(4):
for tree in range(2):
for index in range(3**level):
address = addr[tree][level][index]
expected_node = Node(
address, GATEWAY_NODE if level == 0 else SENSOR_NODE,
x[tree][level][index], y[level],
range_1 if level < 3 else range_2)
assert expected_node == t.nodes.get(address)
# Validate connections:
for level, tree in product(range(3), range(2)):
offset = 0 if tree == 0 else 41
for index in range(3**level):
address = addr[tree][level][index]
children_addresses = addr[tree][level +
1][(3 * index):(3 * (index + 1))]
for child_address in children_addresses:
assert (child_address, address) in connections
def ttest_ind(a, b, axis=0, equal_var=True):
"""
Calculates the T-test for the means of two independent samples of scores.
Parameters
----------
a, b : array_like
The arrays must have the same shape, except in the dimension
corresponding to `axis` (the first, by default).
axis : int or None, optional
Axis along which to compute test. If None, compute over the whole
arrays, `a`, and `b`.
equal_var : bool, optional
If True, perform a standard independent 2 sample test that assumes equal
population variances.
If False, perform Welch's t-test, which does not assume equal population
variance.
.. versionadded:: 0.17.0
Returns
-------
statistic : float or array
The calculated t-statistic.
pvalue : float or array
The two-tailed p-value.
Notes
-----
For more details on `ttest_ind`, see `stats.ttest_ind`.
"""
a, b, axis = _chk2_asarray(a, b, axis)
if a.size == 0 or b.size == 0:
return 'One of the vector is empty'
(mean1, mean2) = (a.mean(axis), b.mean(axis))
(var1, var2) = (a.var(axis=axis, ddof=1), b.var(axis=axis, ddof=1))
(n1, n2) = (a.count(axis), b.count(axis))
if equal_var:
# force df to be an array for masked division not to throw a warning
df = ma.asanyarray(n1 + n2 - 2.0)
svar = ((n1 - 1) * var1 + (n2 - 1) * var2) / df
denom = ma.sqrt(svar * (1.0 / n1 + 1.0 / n2)) # n-D computation here!
else:
vn1 = var1 / n1
vn2 = var2 / n2
with np.errstate(divide='ignore', invalid='ignore'):
df = (vn1 + vn2)**2 / (vn1**2 / (n1 - 1) + vn2**2 / (n2 - 1))
# If df is undefined, variances are zero.
# It doesn't matter what df is as long as it is not NaN.
df = np.where(np.isnan(df), 1, df)
denom = ma.sqrt(vn1 + vn2)
with np.errstate(divide='ignore', invalid='ignore'):
t = (mean1 - mean2) / denom
probs = special.betainc(0.5 * df, 0.5, df / (df + t * t)).reshape(t.shape)
return Ttest_ind(t, probs.squeeze())
def __getitem__(self, index):
data_r = self.arguments[0]
data = data_r if is_constant(data_r) else data_r[index]
if isinstance(data, PhysArray):
return PhysArray(sqrt(data),
units=self._units,
name='sqrt({})'.format(data.name),
dimensions=data.dimensions,
positive=data.positive)
else:
return sqrt(data)
def coscalc(arr1, arr2):
x = 0
y = 0
xy = 0
for num in range(0, arr1.size - 1):
x += arr1[num] * arr1[num]
y += arr2[num] * arr2[num]
xy += arr1[num] * arr2[num]
y = sqrt(y)
x = sqrt(x)
cosenocal = 1 - (xy / (x * y))
return cosenocal
def coscalc(arr1, arr2):
x = 0
y = 0
xy = 0
for num in range(0, arr1.size - 1):
x += arr1[num] * arr1[num]
y += arr2[num] * arr2[num]
xy += arr1[num] * arr2[num]
y = sqrt(y)
x = sqrt(x)
cosenocal = 1 - (xy / (x * y))
return cosenocal
def _get_noise_mask(size: int) -> np.matrix:
"""Return random noise"""
density = 0.1
mask = np.zeros((size, size))
for ind in np.random.choice(size - 1, int(floor(size * density))): # pylint: disable=no-member
how_many_elmns = random.randint(1, int(sqrt(ind)) + 1)
for var in range(1, how_many_elmns): # pylint: disable=unused-variable
if random.randint(0, 1):
length = random.randint(1, int(sqrt(size * density)))
rnd_from = random.randint(1, ind) - length
rnd_to = rnd_from + length
mask[rnd_from:rnd_to, ind] = 1
mask[ind, rnd_from:rnd_to] = 1
return mask
def filter(pspectra0, pspectra1, zbest, norm=False, ston_cut=7., frac_inc_cut= .50):
fibermap = pspectra0.fibermap #Table.read(datafile0, 'FIBERMAP')
isTGT = fibermap['OBJTYPE'] == 'TGT'
okFibers = np.logical_and(pspectra0.fibermap['FIBERSTATUS'] == 0, pspectra1.fibermap['FIBERSTATUS'] == 0)
isGalaxy = zbest['SPECTYPE']=='GALAXY'
hasSignal = HasSignal.filter(pspectra0,pspectra1)
if norm:
pspectra0, pspectra1 = renorm(pspectra0,pspectra1)
diff = difference(pspectra0,pspectra1)
skymask = maskskylines(diff)
nspec = diff.flux[diff.bands[0]].shape[0]
signal=np.zeros(nspec)
var=np.zeros(nspec)
ref_signal=np.zeros(nspec)
if 'b' in diff.bands:
for sindex in range(nspec):
nmask = diff.mask['b'][sindex,:]==0
signal[sindex] = diff.flux['b'][sindex,nmask].sum()
var[sindex] = (1/diff.ivar['b'][sindex,nmask]).sum()
ref_signal[sindex] = pspectra1.flux['b'][sindex,nmask].sum()
# nan's should fail here
brighter = np.logical_or(np.abs(signal/ref_signal) >= frac_inc_cut, ref_signal <=0)
significant = (np.abs(signal)/ma.sqrt(var) >= ston_cut)
triggered = np.logical_and.reduce((significant, isTGT, hasSignal, okFibers, isGalaxy, brighter))
return triggered, diff
def biweight(x, cst):
"""
Computes the biweight average and midvariance for a given 1D array.
Returns a tuple (biweight mean, biweight variance).
Parameters
----------
x: {ndarray}
Input Array
cst : {float}
Parameter controlling how outliers are censored.
Notes
-----
The function is restricted to 1D data only.
"""
assert (x.ndim == 1, "1D array only !")
xmed = ma.median(x, 0)
manom = x - xmed
mad = ma.median(ma.absolute(manom))
u_i = (manom/float(cst*mad))
u_i *= ma.less_equal(ma.absolute(u_i), 1.).astype(float)
w_i = (1-u_i**2)
if ma.count(w_i) > 0:
biw_m = xmed + ma.sum(manom * w_i**2)/ma.sum(w_i**2)
else:
biw_m = xmed
biw_sd = ma.sqrt(ma.count(x)*ma.sum(manom**2 * w_i**4))
biw_sd *= 1./ma.absolute(ma.sum(w_i * (1-5*u_i**2)))
return (biw_m, biw_sd.item())
def mag(u, v, missing=MISSING):
'''
Compute the magnitude of a vector from its components
Parameters
----------
u : number, array_like
U-component of the wind
v : number, array_like
V-component of the wind
missing : number (optional)
Optional missing parameter. If not given, assume default missing
value from sharppy.sharptab.constants.MISSING
Returns
-------
mag : number, array_like
The magnitude of the vector (units are the same as input)
'''
u = np.ma.asanyarray(u).astype(np.float64)
v = np.ma.asanyarray(v).astype(np.float64)
u.set_fill_value(missing)
v.set_fill_value(missing)
if u.shape:
u[u == missing] = ma.masked
v[v == missing] = ma.masked
else:
if u == missing or v == missing:
return ma.masked
return ma.sqrt(u**2 + v**2)
def calculateCentroidMeasurements(self):
self.X[self.badFrames, :] = ma.masked
if not self.useSmoothingFilterDerivatives:
self.v[1:-1] = (self.X[2:, :] - self.X[0:-2])/(2.0/self.frameRate)
else:
# use a cubic polynomial filter to estimate the velocity
self.v = ma.zeros(self.X.shape)
halfWindow = int(np.round(self.filterWindow/2.*self.frameRate))
for i in xrange(halfWindow, self.v.shape[0]-halfWindow):
start = i-halfWindow
mid = i
finish = i+halfWindow+1
if not np.any(self.X.mask[start:finish,:]):
px = np.polyder(np.polyfit(self.t[start:finish]-self.t[mid],
self.X[start:finish, 0], 3))
py = np.polyder(np.polyfit(self.t[start:finish]-self.t[mid],
self.X[start:finish, 1], 3))
self.v[i,:] = [np.polyval(px, 0), np.polyval(py, 0)]
else:
self.v[i,:] = ma.masked
self.s = ma.sqrt(ma.sum(ma.power(self.v, 2), axis=1))
self.phi = ma.arctan2(self.v[:, 1], self.v[:, 0])
self.t[self.badFrames] = ma.masked
self.X[self.badFrames, :] = ma.masked
self.v[self.badFrames, :] = ma.masked
self.s[self.badFrames] = ma.masked
self.phi[self.badFrames] = ma.masked
def _calc_correlation(self, values_1, values_2, conf_level=0.95):
""" Calculates Pearson's correlation coeffcient.
Arguments:
values_1 -- first data
values_2 -- second data
conf_level -- confidence level
Returns:
(corr_coeff, significance) -- correlation coefficient and significance arrays
"""
n_samples = values_1.shape[0] # Sample length
# Calculate Pearson's correlatiob coefficient
values_cov = ma.sum((values_1 - ma.mean(values_1, axis=0)) *
(values_2 - ma.mean(values_2, axis=0)),
axis=0)
corr_coef = values_cov / (ma.std(values_1, axis=0) *
ma.std(values_2, axis=0)) / n_samples
# Calculate significance using t-distribution with n-2 degrees of freedom.
deg_fr = n_samples - 2 # Degrees of freedom.
t_distr = ma.abs(
corr_coef *
ma.sqrt(deg_fr / (1. - corr_coef**2))) # Student's t-distribution.
prob = 0.5 + conf_level / 2 # Probability for two tails.
cr_value = student_t.ppf(prob, deg_fr) # Student's Critical value.
significance = ma.greater(t_distr, cr_value)
return corr_coef, significance
def column_stdevs(dataset, means):
stdevs = [0 for i in range(len(dataset[0]))]
for i in range(len(dataset[0])):
variance = [pow(row[i] - means[i], 2) for row in dataset]
stdevs[i] = sum(variance)
stdevs = [sqrt(x / (float(len(dataset) - 1))) for x in stdevs]
return stdevs
def all_pairs_euclidean(M):
C = np.zeros((len(M), len(M)))
for i in xrange(len(M)):
for j in xrange(i+1, len(M)):
q=M[i]-M[j]
C[i][j] = ma.sqrt((q*q.T).sum())
return C
def find_an_approximation(self, function_table: dict) -> Function:
try:
SLNX = sum(log(x) for x in function_table.keys())
SLNXX = sum(log(x) * log(x) for x in function_table.keys())
SLNY = sum(log(y) for y in function_table.values())
SLNXY = sum(log(x) * log(y) for x, y in function_table.items())
n = len(function_table)
except ValueError:
return None
try:
b, a = self.solve_matrix22([[n, SLNX], [SLNX, SLNXX]],
[SLNY, SLNXY])
if a is None:
return None
a = exp(a)
fun = lambda x: a * (x**b)
s = sum(
(fun(x) - function_table[x])**2 for x in function_table.keys())
root_mean_square_deviation = sqrt(s / n)
f = Function(fun, f'ф = {round(a, 3)}*x^({round(b, 3)})', s,
root_mean_square_deviation)
self.print_approximation_table(function_table, f,
self.function_type)
return f
except TypeError:
return None
def mmahalanobis(u, v, VI):
r"""
Computes the Mahalanobis distance between two n-vectors ``u`` and ``v``,
which is defiend as
.. math::
(u-v)V^{-1}(u-v)^T
where ``VI`` is the inverse covariance matrix :math:`V^{-1}`.
Parameters
----------
u : ndarray
An :math:`n`-dimensional vector.
v : ndarray
An :math:`n`-dimensional vector.
Returns
-------
d : double
The Mahalanobis distance between vectors ``u`` and ``v``.
"""
u = ma.asarray(u, order='c')
v = ma.asarray(v, order='c')
VI = ma.asarray(VI, order='c')
return ma.sqrt(ma.dot(ma.dot((u - v), VI), (u - v).T).sum())
def _apply_function(func, arg):
# type: (QuilParser.FunctionContext, Any) -> Any
if isinstance(arg, Expression):
if func.SIN():
return parameters.quil_sin(arg)
elif func.COS():
return parameters.quil_cos(arg)
elif func.SQRT():
return parameters.quil_sqrt(arg)
elif func.EXP():
return parameters.quil_exp(arg)
elif func.CIS():
return parameters.quil_cis(arg)
else:
raise RuntimeError("Unexpected function to apply: " + func.getText())
else:
if func.SIN():
return sin(arg)
elif func.COS():
return cos(arg)
elif func.SQRT():
return sqrt(arg)
elif func.EXP():
return exp(arg)
elif func.CIS():
return cos(arg) + complex(0, 1) * sin(arg)
else:
raise RuntimeError("Unexpected function to apply: " + func.getText())
def train_step_batch(self, epoch):
D1 = ma.dot(self.vectors**2, self.weight_matrix)
D2 = ma.dot(self.vectors, self.constant_matrix)
Dist = D1 - D2
best_nodes = ma.argmin(Dist, 0)
distances = ma.min(Dist, 0)
## print "q error:", ma.mean(ma.sqrt(distances + self.dist_cons)), self.radius(epoch)
self.qerror.append(ma.mean(ma.sqrt(distances + self.dist_cons)))
if self.neighbourhood == Map.NeighbourhoodGaussian:
H = numpy.exp(-self.unit_distances / (2 * self.radius(epoch))) * (
self.unit_distances <= self.radius(epoch))
elif self.neighbourhood == Map.NeighbourhoodEpanechicov:
H = 1.0 - (self.unit_distances / self.radius(epoch))**2
H = H * (H >= 0.0)
else:
H = 1.0 * (self.unit_distances <= self.radius(epoch))
P = numpy.zeros((self.vectors.shape[0], self.data.shape[0]))
P[(best_nodes,
list(range(len(best_nodes))))] = numpy.ones(len(best_nodes))
S = ma.dot(H, ma.dot(P, self.data))
A = ma.dot(H, ma.dot(P, ~self.data._mask))
## nonzero = (range(epoch%2, len(self.vectors), 2), )
nonzero = (numpy.array(sorted(set(ma.nonzero(A)[0]))), )
self.vectors[nonzero] = S[nonzero] / A[nonzero]
def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.cos(x), cos(xm)))
assert_(eq(np.cosh(x), cosh(xm)))
assert_(eq(np.sin(x), sin(xm)))
assert_(eq(np.sinh(x), sinh(xm)))
assert_(eq(np.tan(x), tan(xm)))
assert_(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.sqrt(abs(x)), sqrt(xm)))
assert_(eq(np.log(abs(x)), log(xm)))
assert_(eq(np.log10(abs(x)), log10(xm)))
assert_(eq(np.exp(x), exp(xm)))
assert_(eq(np.arcsin(z), arcsin(zm)))
assert_(eq(np.arccos(z), arccos(zm)))
assert_(eq(np.arctan(z), arctan(zm)))
assert_(eq(np.arctan2(x, y), arctan2(xm, ym)))
assert_(eq(np.absolute(x), absolute(xm)))
assert_(eq(np.equal(x, y), equal(xm, ym)))
assert_(eq(np.not_equal(x, y), not_equal(xm, ym)))
assert_(eq(np.less(x, y), less(xm, ym)))
assert_(eq(np.greater(x, y), greater(xm, ym)))
assert_(eq(np.less_equal(x, y), less_equal(xm, ym)))
assert_(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
assert_(eq(np.conjugate(x), conjugate(xm)))
assert_(eq(np.concatenate((x, y)), concatenate((xm, ym))))
assert_(eq(np.concatenate((x, y)), concatenate((x, y))))
assert_(eq(np.concatenate((x, y)), concatenate((xm, y))))
assert_(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def compare_medians_ms(group_1, group_2, axis=None):
"""Compares the medians from two independent groups along the given axis.
The comparison is performed using the McKean-Schrader estimate of the standard
error of the medians.
Parameters
----------
group_1 : {sequence}
First dataset.
group_2 : {sequence}
Second dataset.
axis : {integer}
Axis along which the medians are estimated. If None, the arrays are flattened.
Returns
-------
A (p,) array of comparison values.
"""
(med_1, med_2) = (ma.median(group_1,
axis=axis), ma.median(group_2, axis=axis))
(std_1, std_2) = (mstats.stde_median(group_1, axis=axis),
mstats.stde_median(group_2, axis=axis))
W = np.abs(med_1 - med_2) / ma.sqrt(std_1**2 + std_2**2)
return 1 - norm.cdf(W)
def forward(self, graph: dgl.DGLGraph) -> torch.Tensor:
start_index = 0
subtoken_ids = []
node_slices = []
for node in graph.ndata['token_id']:
node_id = node.item()
if node_id in self.full_token_id_to_subtokens:
cur_subtokens = self.full_token_id_to_subtokens[node_id]
else:
unk_id = self.subtoken_to_id[UNK]
cur_subtokens = [
self.subtoken_to_id.get(st, unk_id)
for st in self.full_token_id_to_token[node_id].split(self.delimiter)
]
subtoken_ids += cur_subtokens
node_slices.append(slice(start_index, start_index + len(cur_subtokens)))
start_index += len(cur_subtokens)
full_subtokens_embeds = self.subtoken_embedding(
graph.ndata['token_id'].new_tensor(subtoken_ids)
)
token_embeds = graph.ndata['token_id'].new_empty((graph.number_of_nodes(), self.h_emb), dtype=torch.float)
for node in range(graph.number_of_nodes()):
token_embeds[node] = full_subtokens_embeds[node_slices[node]].sum(0)
if self.normalize:
return token_embeds * sqrt(self.h_emb)
return token_embeds
def test_testUfuncs1(self):
# Test various functions such as sin, cos.
(x, y, a10, m1, m2, xm, ym, z, zm, xf, s) = self.d
assert_(eq(np.cos(x), cos(xm)))
assert_(eq(np.cosh(x), cosh(xm)))
assert_(eq(np.sin(x), sin(xm)))
assert_(eq(np.sinh(x), sinh(xm)))
assert_(eq(np.tan(x), tan(xm)))
assert_(eq(np.tanh(x), tanh(xm)))
with np.errstate(divide='ignore', invalid='ignore'):
assert_(eq(np.sqrt(abs(x)), sqrt(xm)))
assert_(eq(np.log(abs(x)), log(xm)))
assert_(eq(np.log10(abs(x)), log10(xm)))
assert_(eq(np.exp(x), exp(xm)))
assert_(eq(np.arcsin(z), arcsin(zm)))
assert_(eq(np.arccos(z), arccos(zm)))
assert_(eq(np.arctan(z), arctan(zm)))
assert_(eq(np.arctan2(x, y), arctan2(xm, ym)))
assert_(eq(np.absolute(x), absolute(xm)))
assert_(eq(np.equal(x, y), equal(xm, ym)))
assert_(eq(np.not_equal(x, y), not_equal(xm, ym)))
assert_(eq(np.less(x, y), less(xm, ym)))
assert_(eq(np.greater(x, y), greater(xm, ym)))
assert_(eq(np.less_equal(x, y), less_equal(xm, ym)))
assert_(eq(np.greater_equal(x, y), greater_equal(xm, ym)))
assert_(eq(np.conjugate(x), conjugate(xm)))
assert_(eq(np.concatenate((x, y)), concatenate((xm, ym))))
assert_(eq(np.concatenate((x, y)), concatenate((x, y))))
assert_(eq(np.concatenate((x, y)), concatenate((xm, y))))
assert_(eq(np.concatenate((x, y, x)), concatenate((x, ym, x))))
def compare_medians_ms(group_1, group_2, axis=None):
"""
Compares the medians from two independent groups along the given axis.
The comparison is performed using the McKean-Schrader estimate of the
standard error of the medians.
Parameters
----------
group_1 : array_like
First dataset.
group_2 : array_like
Second dataset.
axis : int, optional
Axis along which the medians are estimated. If None, the arrays are
flattened. If `axis` is not None, then `group_1` and `group_2`
should have the same shape.
Returns
-------
compare_medians_ms : {float, ndarray}
If `axis` is None, then returns a float, otherwise returns a 1-D
ndarray of floats with a length equal to the length of `group_1`
along `axis`.
"""
(med_1, med_2) = (ma.median(group_1, axis=axis), ma.median(group_2, axis=axis))
(std_1, std_2) = (mstats.stde_median(group_1, axis=axis),
mstats.stde_median(group_2, axis=axis))
W = np.abs(med_1 - med_2) / ma.sqrt(std_1 ** 2 + std_2 ** 2)
return 1 - norm.cdf(W)
def train_step_batch(self, epoch):
"""A single step of batch training algorithm.
"""
D1 = ma.dot(self.vectors**2, self.weight_matrix)
D2 = ma.dot(self.vectors, self.constant_matrix)
Dist = D1 - D2
best_nodes = ma.argmin(Dist, 0)
distances = ma.min(Dist, 0)
## print "q error:", ma.mean(ma.sqrt(distances + self.dist_cons)), self.radius(epoch)
self.qerror.append(ma.mean(ma.sqrt(distances + self.dist_cons)))
if self.neighbourhood == Map.NeighbourhoodGaussian:
H = numpy.exp(-self.unit_distances**2/(2*self.radius(epoch)**2)) * (self.unit_distances**2 <= self.radius(epoch)**2)
elif self.neighbourhood == Map.NeighbourhoodEpanechicov:
H = 1.0 - (self.unit_distances/self.radius(epoch))**2
H = H * (H >= 0.0)
else:
H = 1.0*(self.unit_distances <= self.radius(epoch))
P = numpy.zeros((self.vectors.shape[0], self.data.shape[0]))
P[(best_nodes, range(len(best_nodes)))] = numpy.ones(len(best_nodes))
S = ma.dot(H, ma.dot(P, self.data))
A = ma.dot(H, ma.dot(P, ~self.data._mask))
## nonzero = (range(epoch%2, len(self.vectors), 2), )
nonzero = (numpy.array(sorted(set(ma.nonzero(A)[0]))), )
self.vectors[nonzero] = S[nonzero] / A[nonzero]
def compare_medians_ms(group_1, group_2, axis=None):
"""
Compares the medians from two independent groups along the given axis.
The comparison is performed using the McKean-Schrader estimate of the
standard error of the medians.
Parameters
----------
group_1 : array_like
First dataset.
group_2 : array_like
Second dataset.
axis : int, optional
Axis along which the medians are estimated. If None, the arrays are
flattened. If `axis` is not None, then `group_1` and `group_2`
should have the same shape.
Returns
-------
compare_medians_ms : {float, ndarray}
If `axis` is None, then returns a float, otherwise returns a 1-D
ndarray of floats with a length equal to the length of `group_1`
along `axis`.
"""
(med_1, med_2) = (ma.median(group_1, axis=axis), ma.median(group_2, axis=axis))
(std_1, std_2) = (mstats.stde_median(group_1, axis=axis), mstats.stde_median(group_2, axis=axis))
W = np.abs(med_1 - med_2) / ma.sqrt(std_1 ** 2 + std_2 ** 2)
return 1 - norm.cdf(W)
def mseuclidean(u, v, V):
"""
Returns the standardized Euclidean distance between two n-vectors
``u`` and ``v``. ``V`` is an m-dimensional vector of component
variances. It is usually computed among a larger collection
vectors.
Parameters
----------
u : ndarray
An :math:`n`-dimensional vector.
v : ndarray
An :math:`n`-dimensional vector.
Returns
-------
d : double
The standardized Euclidean distance between vectors ``u`` and ``v``.
"""
u = ma.asarray(u, order='c')
v = ma.asarray(v, order='c')
V = ma.asarray(V, order='c')
if len(V.shape
) != 1 or V.shape[0] != u.shape[0] or u.shape[0] != v.shape[0]:
raise TypeError(
'V must be a 1-D array of the same dimension as u and v.')
return ma.sqrt(((u - v)**2 / V).sum())
def mag(u, v, missing=MISSING):
'''
Compute the magnitude of a vector from its components
Parameters
----------
u : number, array_like
U-component of the wind
v : number, array_like
V-component of the wind
missing : number (optional)
Optional missing parameter. If not given, assume default missing
value from sharppy.sharptab.constants.MISSING
Returns
-------
mag : number, array_like
The magnitude of the vector (units are the same as input)
'''
u = np.ma.asanyarray(u).astype(np.float64)
v = np.ma.asanyarray(v).astype(np.float64)
u.set_fill_value(missing)
v.set_fill_value(missing)
if u.shape:
u[u == missing] = ma.masked
v[v == missing] = ma.masked
else:
if u == missing or v == missing:
return ma.masked
return ma.sqrt(u**2 + v**2)
def cryo_CTF_Relion(square_side, star_record):
"""
Compute the contrast transfer function corresponding an n x n image with
the sampling interval DetectorPixelSize.
"""
# wavelength in nm
wave_length = 1.22639 / math.sqrt(star_record.voltage * 1000 +
0.97845 * star_record.voltage**2)
# Divide by 10 to make pixel size in nm. BW is the bandwidth of
# the signal corresponding to the given pixel size
bw = 1 / (star_record.pixel_size / 10)
s, theta = radius_norm(square_side, origin=fctr(square_side))
# RadiusNorm returns radii such that when multiplied by the
# bandwidth of the signal, we get the correct radial frequnecies
# corresponding to each pixel in our nxn grid.
s = s * bw
DFavg = (star_record.DefocusU + star_record.DefocusV) / 2
DFdiff = (star_record.DefocusU - star_record.DefocusV)
df = DFavg + DFdiff * np.cos(2 * (theta - star_record.DefocusAngle)) / 2
k2 = math.pi * wave_length * df
# 10**6 converts spherical_aberration from mm to nm
k4 = math.pi / 2 * 10**6 * star_record.spherical_aberration * wave_length**3
chi = k4 * s**4 - k2 * s**2
return (sqrt(1 - star_record.amplitude_contrast**2) * np.sin(chi) -
star_record.amplitude_contrast * np.cos(chi))
def compare_medians_ms(group_1, group_2, axis=None):
"""Compares the medians from two independent groups along the given axis.
The comparison is performed using the McKean-Schrader estimate of the standard
error of the medians.
Parameters
----------
group_1 : {sequence}
First dataset.
group_2 : {sequence}
Second dataset.
axis : {integer}
Axis along which the medians are estimated. If None, the arrays are flattened.
Returns
-------
A (p,) array of comparison values.
"""
(med_1, med_2) = (ma.median(group_1,axis=axis), ma.median(group_2,axis=axis))
(std_1, std_2) = (mstats.stde_median(group_1, axis=axis),
mstats.stde_median(group_2, axis=axis))
W = np.abs(med_1 - med_2) / ma.sqrt(std_1**2 + std_2**2)
return 1 - norm.cdf(W)
def _get_filament_dx(self):
''' Displacement of filament end-point to become stretched. '''
y_arr, z_arr = self.cut_data[1:3]
dy_free = self._free_length(y_arr)
dz_free = self._free_length(z_arr)
dx = ma.sqrt(self.fs_bond_free_length ** 2
- dy_free ** 2
- dz_free ** 2) - self.fs_bond_free_length_x
return dx
def combine_nights(combined_catalog, filterlist, refcat):
header = ['BEGIN CATALOG HEADER',
'nfields 13',
' ra 1 0 d degrees %10.6f',
' dec 2 0 d degrees %10.6f',
' id 3 0 c INDEF %3d']
for filt in filterlist:
header.append(' {} {:2d} 0 r INDEF %6.3f'.format(filt, len(header) - 1))
header.append(' {}err {:2d} 0 r INDEF %6.3f'.format(filt, len(header) - 1))
header += ['END CATALOG HEADER', '']
catalog = Table([refcat['ra'], refcat['dec'], refcat['id']], meta={'comments': header}, masked=True)
for filt in filterlist:
mags = combined_catalog['mag'][combined_catalog['filter'] == filt]
median = np.median(mags, axis=0)
absdev_mag = mags - median
mad = np.median(np.abs(absdev_mag), axis=0) * np.sqrt(pi / 2)
mags.mask |= np.abs(absdev_mag) > 5 * mad
catalog[filt] = np.median(mags, axis=0)
catalog[filt+'err'] = np.median(np.abs(mags - catalog[filt]), axis=0) * np.sqrt(pi / 2)
return catalog
def DD_FF(u,v):
''' calculates wind/current speed and direction from u and v components
#
if u and v are easterly and northerly components,
DD is heading direction of the wind.
to get meteorological-standard, call DD_FF(-u, -v)
'''
DD = ma.arctan2(u, v)*180/sp.pi
DD[DD < 0] = 360 + DD[DD < 0]
FF = ma.sqrt(u**2 + v**2)
return DD, FF
def _get_fs_length_between_cuts(self):
'''
Return linear filament length between cuts.
Matrix contain mask information.
'''
x_arr = self.cut_data[0]
y_arr = self.cut_data[1]
z_arr = self.cut_data[2]
length = ma.sqrt((x_arr[:, 1:] - x_arr[:, :-1]) ** 2
+ (y_arr[:, 1:] - y_arr[:, :-1]) ** 2
+ (z_arr[:, 1:] - z_arr[:, :-1]) ** 2)
return length
def vector_sum(x_arr, y_arr):
"""
Calculate the vector sum of arrays of
x and y vectors.
:param x_arr: array of x-directed vectors
:type x_arr: numpy.array
:param y_arr: array of y-directed vectors
:type y_arr: numpy.array
:return: array of vector sums
:rtype: numpy.array
"""
return ma.sqrt(x_arr**2 + y_arr**2)
def result(self):
ddof = self.kwargs['ddof']
if self.masked:
mask = self.running_count == 0
denominator = ma.array(self.running_count, mask=mask) - ddof
q = ma.array(self.q, mask=mask) / denominator
result = ma.sqrt(q)
result.shape = self.array[0].shape
else:
self.q /= (self.k - ddof)
result = np.sqrt(self.q)
# Promote array-scalar to 0-dimensional array.
if result.ndim == 0:
result = self._mod.array(result)
return result
def cart2polar(x, y, degrees=True):
"""
Convert cartesian X and Y to polar RHO and THETA.
:param x: x cartesian coordinate
:param y: y cartesian coordinate
:param degrees: True = return theta in degrees, False = return theta in
radians. [default: True]
:return: r, theta
"""
rho = ma.sqrt(x ** 2 + y ** 2)
theta = ma.arctan2(y, x)
if degrees:
theta *= (180 / math.pi)
return rho, theta
def crossmatch(cat0, cat1, threshold=1., racol0='ra', deccol0='dec', racol1='ra', deccol1='dec', right_join=False):
dra = cat0[racol0] - cat1[racol1][:, newaxis]
ddec = cat0[deccol0] - cat1[deccol1][:, newaxis]
sep = np.sqrt(dra**2 + ddec**2) * 3600.
matches = np.min(sep, axis=1) < threshold
inds = np.argmin(sep, axis=1)
out = Table(cat0[inds], masked=True)
if right_join:
for col in out.colnames:
out[col].mask = ~matches
cat1 = cat1.copy()
else:
out = out[matches]
cat1 = cat1[matches]
return out, cat1
def DD_FF(u,v,met=True):
''' calculates wind/current speed and direction from u and v components
#
if u and v are easterly and northerly components,
returns:
FF : wind speed
DD : wind direction in meteorological standard (directions the wind is coming from)
call with met=False for oceanographic standard
'''
if met==False:
u,v = -u, -v
DD = ma.arctan2(-u, -v)*180/sp.pi
DD[DD < 0] = 360 + DD[DD < 0]
FF = ma.sqrt(u**2 + v**2)
return DD, FF
def attest_ind(a, b, dim=None):
""" Return the t-test statistics on arrays a and b over the dim axis.
Returns both the t statistic as well as the p-value
"""
# dim = a.ndim - 1 if dim is None else dim
x1, x2 = ma.mean(a, dim), ma.mean(b, dim)
v1, v2 = ma.var(a, dim), ma.var(b, dim)
n1, n2 = (a.shape[dim], b.shape[dim]) if dim is not None else (a.size, b.size)
df = float(n1+n2-2)
svar = ((n1-1)*v1+(n2-1)*v2) / df
t = (x1-x2)/ma.sqrt(svar*(1.0/n1 + 1.0/n2))
if t.ndim == 0:
return (t, scipy.stats.betai(0.5*df,0.5,df/(df+t**2)) if t is not ma.masked and df/(df+t**2) <= 1.0 else ma.masked)
else:
prob = [scipy.stats.betai(0.5*df,0.5,df/(df+tsq)) if tsq is not ma.masked and df/(df+tsq) <= 1.0 else ma.masked for tsq in t*t]
return t, prob
def flatten(ech, method='average'):
"""Flatten 2-D echelle spectrum to 1-D flat spectrum
"""
wav = ech.wav[0]
assert np.allclose(ech.wav - wav, 0), "ech.wav rows must be identical"
ech.flux = ma.masked_invalid(ech.flux)
ech.uflux = ma.masked_invalid(ech.uflux)
if method=='average':
ivar = ech.uflux**-2
# Weighted mean and uncertanty on weighted mean
flux = ma.sum( ech.flux * ivar, axis=0 ) / ma.sum(ivar, axis=0)
uflux = ma.sqrt( 1 / ma.sum(ivar, axis=0) )
flux.fill_value = np.nan
uflux.fill_value = np.nan
flux = flux.filled()
uflux = uflux.filled()
return flux, uflux
def _get_gamma_cdf(aseries, condition):
"""
Returns the CDF values for aseries.
Parameters
----------
aseries : TimeSeries
Annual series of data (one column per period)
condition : TimeSeries
Period mask.
"""
# Mask the months for which no precipitations were recorded
aseries_ = ma.masked_values(aseries, 0)
# Get the proportion of 0 precipitation for each period (MM/WW)
pzero = 1. - aseries_.count(axis=0) / aseries.count(axis=0).astype(float)
# Mask outside the reference period
aseries_._mask |= condition._data
meanrain = aseries_.mean(axis=0)
aleph = ma.log(meanrain) - ma.log(aseries_).mean(axis=0)
alpha = (1. + ma.sqrt(1.+4./3*aleph)) / (4.*aleph)
beta = meanrain/alpha
# Get the Gamma CDF (per month)
gcdf = pzero + (1.-pzero) * ssd.gamma.cdf(aseries,alpha,scale=beta)
return gcdf
variables[var]['slabel'],total,variables[var]['tunits'])
print('%s'%(variables[var]['label']))
# compute min & max of annual (temporal) mean
mdatamin = vars()[var].min()
mdatamax = vars()[var].max()
# compute spatial mean & R.M.S. of annual (temporal) mean
mmask = MA.masked_values(vars()[var]/vars()[var],variables[var]['fillvalue'])
mdatamean = MA.masked_values(MA.sum(vars()[var] * area * mmask) / MA.sum(area * mmask),
variables[var]['fillvalue'])
mdatarms = MA.masked_values(MA.sqrt(MA.sum(vars()[var] * vars()[var] * area * mmask) /
MA.sum(area * mmask)),variables[var]['fillvalue'])
if POPDIAGPY == 'TRUE':
if var in vintlist: # vertically integrated
variables[var]['title_mod'] = '%s: Min:%.2f, Max:%.2f, Mean:%.2f, RMS:%.2f '%(
variables[var]['klabel'],mdatamin,mdatamax,mdatamean,mdatarms)
elif 'FLUX_IN' in var: # particle flux
variables[var]['title_mod'] = '%s at %.0f m: Min:%.2f, Max:%.2f, Mean:%.2f, RMS:%.2f '%(
variables[var]['slabel'],depth,mdatamin,mdatamax,mdatamean,mdatarms)
else:
variables[var]['title_mod'] = '%s: Min:%.2f, Max:%.2f, Mean:%.2f, RMS:%.2f '%(
variables[var]['slabel'],mdatamin,mdatamax,mdatamean,mdatarms)
else:
variables[var]['title_mod'] = variables[var]['label']
# plot maps -----------------------------------------------------------
def MSE(statistic, knownParameter=THETA):
return sqrt(np.mean((statistic - knownParameter) ** 2))
def multiply_by_cal(Data, CalData) :
"""Function scales data by the noise cal temperature.
"""
# For now we just assume that the cal and polarizations are arranged in a
# certain way and then check to make sure we are right.
calibrate_to_I = False
if tuple(Data.field['CRVAL4']) == (-5, -7, -8, -6) :
xx_ind = 0
yy_ind = 3
xy_inds = [1,2]
elif tuple(Data.field['CRVAL4']) == (1, 2, 3, 4) :
# This is a hack. Completly temporairy.
calibrate_to_I = True
else :
raise ce.DataError('Polarization types not as expected in data.')
cal_xx_ind = 0
cal_yy_ind = 1
if (CalData.field['CRVAL4'][cal_xx_ind] != -5 or
CalData.field['CRVAL4'][cal_yy_ind] != -6) :
raise ce.DataError('Polarization types not as expected in cal.')
# Cal should only have 1 time, 1 cal state and 2 polarizations.
if CalData.dims[:3] != (1,2,1) :
raise ce.DataError('Cal temperature data has wrong dimensions.')
# Cal state should be special state 'R'.
if CalData.field['CAL'][0] != 'R' :
raise ce.DataError("Cal state in cal temperture data should be "
"'R'.")
# Bring the Cal data to the same frequencies as the other data.
Data.calc_freq()
CalData.calc_freq()
if sp.allclose(Data.freq, CalData.freq) :
cdata = CalData.data
elif abs(Data.field['CDELT1']) <= abs(CalData.field['CDELT1']) :
calfunc = interpolate.interp1d(CalData.freq, CalData.data,
fill_value=sp.nan, bounds_error=False)
cdata = ma.array(calfunc(Data.freq))
cdata[sp.logical_not(sp.isfinite(cdata))] = ma.masked
else :
nf = len(Data.freq)
width = abs(Data.field['CDELT1'])
cdata = ma.empty((1,2,1,nf))
for find in range(nf) :
f = Data.freq[find]
inds, = sp.where(sp.logical_and(CalData.freq >= f - width/2.0,
CalData.freq < f + width/2.0))
cdata[:,:,:,find] = ma.mean(CalData.data[:,:,:,inds], 3)
if calibrate_to_I :
Data.data *= (cdata[0,cal_xx_ind,0,:] + cdata[0,cal_yy_ind,0,:])/2.0
else :
# Loop over times and cal and scale each polarization appropriately.
for tind in range(Data.dims[0]) :
for cind in range(Data.dims[2]) :
Data.data[tind,xx_ind,cind,:] *= cdata[0,cal_xx_ind,0,:]
Data.data[tind,yy_ind,cind,:] *= cdata[0,cal_yy_ind,0,:]
Data.data[tind,xy_inds,cind,:] *= ma.sqrt(
cdata[0,cal_yy_ind,0,:] * cdata[0,cal_xx_ind,0,:])
def scale_by_cal(Data, scale_t_ave=True, scale_f_ave=False, sub_med=False,
scale_f_ave_mod=False, rotate=False) :
"""Puts all data in units of the cal temperature.
Data is put into units of the cal temperature, thus removing dependence on
the gain. This can be done by dividing by the time average of the cal
(scale_t_ave=True, Default) thus removing dependence on the frequency-
dependant gain. Alternatively, you can scale by the frequency average to
remove the time-dependent gain (scale_f_ave=True). Data is then in units of
the frequency averaged cal temperture. You can also do both (recommended).
After some scaling the data ends up in units of the cal temperture as a
funciton of frequency.
Optionally you can also subtract the time average of the data off here
(subtract_time_median), since you might be done with the cal information at
this point.
"""
on_ind = 0
off_ind = 1
if (Data.field['CAL'][on_ind] != 'T' or
Data.field['CAL'][off_ind] != 'F') :
raise ce.DataError('Cal states not in expected order.')
if tuple(Data.field['CRVAL4']) == (-5, -7, -8, -6) :
# Here we check the polarizations and cal indicies
xx_ind = 0
yy_ind = 3
xy_inds = [1,2]
# A bunch of calculations used to test phase closure. Not acctually
# relevant to what is being done here.
#a = (Data.data[5, xy_inds, on_ind, 15:20]
# - Data.data[5, xy_inds, off_ind, 15:20])
#a /= sp.sqrt( Data.data[5, xx_ind, on_ind, 15:20]
# - Data.data[5, xx_ind, off_ind, 15:20])
#a /= sp.sqrt( Data.data[5, yy_ind, on_ind, 15:20]
# - Data.data[5, yy_ind, off_ind, 15:20])
#print a[0,:]**2 + a[1,:]**2
diff_xx = Data.data[:,xx_ind,on_ind,:] - Data.data[:,xx_ind,off_ind,:]
diff_yy = Data.data[:,yy_ind,on_ind,:] - Data.data[:,yy_ind,off_ind,:]
if scale_t_ave :
# Find the cal means (in time) and scale by them.
# Means work much better than medians. Medians seems to bias the
# result by up to 10%. This seems to be discretization noise. Cal
# switches fast enough that we shouldn't need this anyway.
cal_tmed_xx = ma.mean(diff_xx, 0)
cal_tmed_yy = ma.mean(diff_yy, 0)
cal_tmed_xx[sp.logical_or(cal_tmed_xx<=0, cal_tmed_yy<=0)] = ma.masked
cal_tmed_yy[cal_tmed_xx.mask] = ma.masked
Data.data[:,xx_ind,:,:] /= cal_tmed_xx
Data.data[:,yy_ind,:,:] /= cal_tmed_yy
Data.data[:,xy_inds,:,:] /= ma.sqrt(cal_tmed_yy*cal_tmed_xx)
if scale_f_ave :
# The frequency gains have have systematic structure to them,
# they are not by any approximation gaussian distributed. Use
# means, not medians across frequency.
operation = ma.mean
cal_fmea_xx = operation(diff_xx, -1)
cal_fmea_yy = operation(diff_yy, -1)
# Flag data with wierd cal power. Still Experimental.
cal_fmea_xx[sp.logical_or(cal_fmea_xx<=0,cal_fmea_yy<=0)] = ma.masked
cal_fmea_yy[cal_fmea_xx.mask] = ma.masked
cal_xx = ma.mean(cal_fmea_xx)
cal_yy = ma.mean(cal_fmea_yy)
cal_fmea_xx[sp.logical_or(abs(cal_fmea_xx.anom()) >= 0.1*cal_xx,
abs(cal_fmea_yy.anom()) >= 0.1*cal_yy)] = ma.masked
cal_fmea_yy[cal_fmea_xx.mask] = ma.masked
ntime = len(cal_fmea_xx)
cal_fmea_xx.shape = (ntime, 1, 1)
cal_fmea_yy.shape = (ntime, 1, 1)
Data.data[:,xx_ind,:,:] /= cal_fmea_xx
Data.data[:,yy_ind,:,:] /= cal_fmea_yy
cal_fmea_xx.shape = (ntime, 1, 1, 1)
cal_fmea_yy.shape = (ntime, 1, 1, 1)
Data.data[:,xy_inds,:,:] /= ma.sqrt(cal_fmea_yy*cal_fmea_xx)
if scale_f_ave_mod :
# The frequency gains have have systematic structure to them,
# they are not by any approximation gaussian distributed. Use
# means, not medians across frequency.
operation = ma.mean
cal_fmea_xx = operation(diff_xx, -1)
cal_fmea_yy = operation(diff_yy, -1)
cal_fmea_xx_off = operation(Data.data[:,xx_ind,off_ind,:], -1)
cal_fmea_yy_off = operation(Data.data[:,yy_ind,off_ind,:], -1)
sys_xx = cal_fmea_xx_off/cal_fmea_xx
sys_yy = cal_fmea_yy_off/cal_fmea_yy
percent_ok = 0.03
sys_xx_tmed = ma.median(sys_xx)
sys_yy_tmed = ma.median(sys_yy)
maskbad_xx = (sys_xx > sys_xx_tmed + sys_xx_tmed*percent_ok)|(sys_xx < sys_xx_tmed - sys_xx_tmed*percent_ok)
maskbad_yy = (sys_yy > sys_yy_tmed + sys_yy_tmed*percent_ok)|(sys_yy < sys_yy_tmed - sys_yy_tmed*percent_ok)
cal_fmea_xx[sp.logical_or(cal_fmea_xx<=0,cal_fmea_yy<=0)] = ma.masked
cal_fmea_yy[cal_fmea_xx.mask] = ma.masked
cal_fmea_xx[maskbad_xx] = ma.masked
cal_fmea_yy[maskbad_yy] = ma.masked
cal_xx = ma.mean(cal_fmea_xx)
cal_yy = ma.mean(cal_fmea_yy)
ntime = len(cal_fmea_xx)
cal_fmea_xx.shape = (ntime, 1, 1)
cal_fmea_yy.shape = (ntime, 1, 1)
Data.data[:,xx_ind,:,:] /= cal_fmea_xx
Data.data[:,yy_ind,:,:] /= cal_fmea_yy
cal_fmea_xx.shape = (ntime, 1, 1, 1)
cal_fmea_yy.shape = (ntime, 1, 1, 1)
Data.data[:,xy_inds,:,:] /= ma.sqrt(cal_fmea_yy*cal_fmea_xx)
if scale_f_ave and scale_t_ave :
# We have devided out t_cal twice so we need to put one factor back
# in.
cal_xx = operation(cal_tmed_xx)
cal_yy = operation(cal_tmed_yy)
Data.data[:,xx_ind,:,:] *= cal_xx
Data.data[:,yy_ind,:,:] *= cal_yy
Data.data[:,xy_inds,:,:] *= ma.sqrt(cal_yy*cal_xx)
if scale_f_ave_mod and scale_t_ave :
#Same divide out twice problem.
cal_xx = operation(cal_tmed_xx)
cal_yy = operation(cal_tmed_yy)
Data.data[:,xx_ind,:,:] *= cal_xxcal_imag_mean
Data.data[:,yy_ind,:,:] *= cal_yy
Data.data[:,xy_inds,:,:] *= ma.sqrt(cal_yy*cal_xx)
if scale_f_ave and scale_f_ave_mod :
raise ce.DataError("time averaging twice")
if rotate:
# Define the differential cal phase to be zero and rotate all data
# such that this is true.
cal_real_mean = ma.mean(Data.data[:,1,0,:] - Data.data[:,1,1,:], 0)
cal_imag_mean = ma.mean(Data.data[:,2,0,:] - Data.data[:,2,1,:], 0)
# Get the cal phase angle as a function of frequency.
cal_phase = -ma.arctan2(cal_imag_mean, cal_real_mean)
# Rotate such that the cal phase is zero. Imperative to have a
# temporary variable.
New_data_real = (ma.cos(cal_phase) * Data.data[:,1,:,:]
- ma.sin(cal_phase) * Data.data[:,2,:,:])
New_data_imag = (ma.sin(cal_phase) * Data.data[:,1,:,:]
+ ma.cos(cal_phase) * Data.data[:,2,:,:])
Data.data[:,1,:,:] = New_data_real
Data.data[:,2,:,:] = New_data_imag
elif tuple(Data.field['CRVAL4']) == (1, 2, 3, 4) :
# For the shot term, just devide everything by on-off in I.
I_ind = 0
cal_I_t = Data.data[:,I_ind,on_ind,:] - Data.data[:,I_ind,off_ind,:]
cal_I = ma.mean(cal_I_t, 0)
Data.data /= cal_I
else :
raise ce.DataError("Unsupported polarization states.")
# Subtract the time median if desired.
if sub_med :
Data.data -= ma.median(Data.data, 0)
sys.exit()
fpmod.close()
# compute temporal mean
datam[var] = datam[var].mean(axis=0)
if 'cfac' in variables[var]: # apply unit conversions if any
datam[var] = datam[var] * variables[var]['cfac']
# compute max & min
mdatamin = datam[var].min()
mdatamax = datam[var].max()
# compute mean & r.m.s.
mdatamean = MA.sum(datam[var] * area) / MA.sum(area)
mdatarms = MA.sqrt(MA.sum(datam[var] * datam[var] * area) / MA.sum(area))
# compute annual totals and include them in plot labels
if 'tcfac' in variables[var]:
totalm = MA.sum(datam[var] * area) * variables[var]['tcfac']
if 'FLUX_IN' in var: # particle flux
variables[var]['title_exp'] = 'Total %s at %.0f m = %.2f %s'%(
variables[var]['label'],depth,totalm,variables[var]['tunits'])
else: # vertical integrals
variables[var]['title_exp'] = 'Total %s = %.2f %s'%(
variables[var]['label'],totalm,variables[var]['tunits'])
if POPDIAGPY == 'TRUE':
variables[var]['title_exp'] = '%s: Min:%.2f, Max:%.2f, Mean:%.2f, RMS:%.2f '%(
variables[var]['slabel'],mdatamin,mdatamax,mdatamean,mdatarms)
def __call__(self, value, clip=None):
#read in parameters
method = self.stretch
exponent = self.exponent
midpoint = self.midpoint
# ORIGINAL MATPLOTLIB CODE
if clip is None:
clip = self.clip
if cbook.iterable(value):
vtype = 'array'
val = ma.asarray(value).astype(np.float)
else:
vtype = 'scalar'
val = ma.array([value]).astype(np.float)
self.autoscale_None(val)
vmin, vmax = self.vmin, self.vmax
if vmin > vmax:
raise ValueError("minvalue must be less than or equal to maxvalue")
elif vmin==vmax:
return 0.0 * val
else:
if clip:
mask = ma.getmask(val)
val = ma.array(np.clip(val.filled(vmax), vmin, vmax),
mask=mask)
result = (val-vmin) * (1.0/(vmax-vmin))
# CUSTOM APLPY CODE
# Keep track of negative values
negative = result < 0.
if self.stretch == 'linear':
pass
elif self.stretch == 'log':
result = ma.log10(result * (self.midpoint - 1.) + 1.) \
/ ma.log10(self.midpoint)
elif self.stretch == 'sqrt':
result = ma.sqrt(result)
elif self.stretch == 'arcsinh':
result = ma.arcsinh(result/self.midpoint) \
/ ma.arcsinh(1./self.midpoint)
elif self.stretch == 'power':
result = ma.power(result, exponent)
else:
raise Exception("Unknown stretch in APLpyNormalize: %s" %
self.stretch)
# Now set previously negative values to 0, as these are
# different from true NaN values in the FITS image
result[negative] = -np.inf
if vtype == 'scalar':
result = result[0]
return result
def weighted_rms_var_from_yr(var,reg_name,reg_num,mask_var,wgt_var,year,hist_dict,ave_info,file_dict,avg_test_slice,obs_file,nlev):
'''
Computes the weighted rms for a year
@param var The name of the variable that is being averaged.
@reg_name The name of the region to average over.
@reg_num The number of the region in the region_mask.
@mask_var The name of the netCDF variable that contain the region mask.
@wgt_var The name of the netCDF variable that contains the weight information.
@param year The year to average over.
@param hist_dict A dictionary that holds file references for all years/months.
@param ave_info A dictionary of the type of average that is to be done.
Includes: type, months_to_average, fn, and weights
(weights are not used in this function/average)
@param file_dict A dictionary which holds file pointers to the input files that
are needed by this average calculation.
@param avg_test_slice Averaged slice used in this calculation.
@param obs_file Observation file that contains the values to be used in the caluculation.
@param nlev Number of ocean vertical levels
@return nrms The normalized rms results for this variable.
'''
import warnings
# Get the weighted values from the yearly average file
slev_weights = rover.fetch_slice(hist_dict,year,0,wgt_var,file_dict,time=False)
# Get the region mask
slev_mask = rover.fetch_slice(hist_dict,year,0,mask_var,file_dict,time=False)
# Since weights and region mask are only one level, we need to expand them to all levels
region_mask = MA.expand_dims(slev_mask, axis=0)
weights = MA.expand_dims(slev_weights, axis=0)
for lev in range(1,nlev):
new_region_mask = MA.expand_dims(slev_mask, axis=0)
region_mask = np.vstack((region_mask,new_region_mask))
new_weights = MA.expand_dims(slev_weights, axis=0)
weights = np.vstack((weights,new_weights))
# Calculate the weighted average
# First, we need to reshape the arrays to average along two dims
if (reg_name == 'Glo'):
temp_mask = MA.masked_where(region_mask<=int(reg_num),avg_test_slice)
else:
temp_mask = MA.masked_where(region_mask!=int(reg_num),avg_test_slice)
ma_to_average = temp_mask.reshape(temp_mask.shape[0], -1)
weights_flattened = weights.reshape(weights.shape[0],-1)
warnings.filterwarnings("ignore")
rms_Ave = MA.sqrt(MA.average((ma_to_average*ma_to_average), axis=1, weights=weights_flattened))
warnings.filterwarnings("default")
#nrms = rms_Ave/(MA.max(rms_Ave) - MA.min(rms_Ave))
nrms = rms_Ave
return nrms
def initialize_cluster_centers(self, pXY, K):
""" Initializes the cluster assignments along each axis, by first selecting k centers,
and then map each row to its closet center under cosine similarity.
Args:
pXY: original data matrix
K: numbers of clusters desired in each dimension
Return:
new_C: a list of list of cluster id that the current index in the current axis is assigned to.
"""
if not isinstance(pXY, SparseMatrix):
raise Exception("Matrix argument to initialize_cluster_centers is not an instance of SparseMatrix.")
new_C = [[-1] * Ni for Ni in pXY.N]
for axis in xrange(len(K)): # loop over each dimension
# choose cluster centers
axis_length = pXY.N[axis]
center_indices = random.sample(xrange(axis_length), K[axis])
cluster_ids = {}
for i in xrange(K[axis]): # assign identifiers to clusters
center_index = center_indices[i]
cluster_ids[center_index] = i
centers = defaultdict(lambda: defaultdict(float)) # all nonzero indices for each center
for coords in pXY.nonzero_elements:
coord_this_axis = coords[axis]
if coord_this_axis in cluster_ids: # is a center
reduced_coords = tuple([coords[i] for i in xrange(len(coords)) if i != axis]) # coords without the current axis
centers[cluster_ids[coord_this_axis]][reduced_coords] = pXY.nonzero_elements[coords] # (cluster_id, other coords) -> value
# assign rows to clusters
scores = np.zeros(shape=(pXY.N[axis], K[axis])) # scores: axis_size x cluster_number
denoms_P = np.zeros(shape=(pXY.N[axis]))
denoms_Q = np.zeros(shape=(K[axis]))
for coords in pXY.nonzero_elements:
coord_this_axis = coords[axis]
if coord_this_axis in center_indices:
continue # don't reassign cluster centers, please
reduced_coords = tuple([coords[i] for i in xrange(len(coords)) if i != axis])
for cluster_index in cluster_ids:
xhat = cluster_ids[cluster_index] # need cluster ID, not the axis index
if reduced_coords in centers[xhat]: # overlapping point
P_i = pXY.nonzero_elements[coords]
Q_i = centers[xhat][reduced_coords]
scores[coords[axis]][xhat] += P_i * Q_i # now doing based on cosine similarity
denoms_P[coords[axis]] += P_i * P_i # magnitude of this slice of original matrix
denoms_Q[xhat] += Q_i * Q_i # magnitude of cluster centers
# normalize scores
scores = divide(scores, outer(sqrt(denoms_P), sqrt(denoms_Q)))
scores[scores == 0] = -1.0
# add random jitter to scores to handle tie-breaking
scores += self.jitter_max * random_sample(scores.shape)
new_cXYi = list(scores.argmax(1)) # this needs to be argmax because cosine similarity
# make sure to assign the cluster centers to themselves
for center_index in cluster_ids:
new_cXYi[center_index] = cluster_ids[center_index]
# ensure numbers of clusters are correct
self.ensure_correct_number_clusters(new_cXYi, K[axis])
new_C[axis] = new_cXYi
return new_C
