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 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 asym_sigmoidal(self, x, asym=1.0, mod_asym=1.0, xmid=None, lscale=1.0,
rscale=1.0):
if xmid is None:
xmid = ma.median(x)
return np.where(x <= xmid,
(asym * mod_asym) / (1 + ma.exp((xmid - x) / lscale)),
asym / (1 + ma.exp((xmid - x) / rscale)))
def test_log_returns_to_prices(self):
prices_values = array([1, exp(1), exp(2), exp(-1), exp(2)])
prices_dates = pd.date_range('2015-01-01', periods=5)
expected = PricesSeries(data=prices_values, index=prices_dates)
returns_tms = LogReturnsSeries(data=[1, 1, -3, 3], index=expected.index[1::])
actual = returns_tms.to_prices()
assert_series_equal(expected, actual)
def asym_sigmoidal(self,
x,
asym=1.0,
mod_asym=1.0,
xmid=None,
lscale=1.0,
rscale=1.0):
if xmid is None:
xmid = ma.median(x)
return np.where(x <= xmid, (asym * mod_asym) / (1 + ma.exp(
(xmid - x) / lscale)), asym / (1 + ma.exp((xmid - x) / rscale)))
def _pfromz_MA(z, lapse_rate, P_bott, T_bott, z_bott):
"""Pressure given altitude in a constant lapse rate layer.
The dry gas constant is used in calculations requiring the gas
constant. See the docstring for press2alt for references.
Input Arguments:
* z: Geopotential altitude [m].
* lapse_rate: -dT/dz [K/m] over the layer.
* P_bott: Pressure [hPa] at the base of the layer.
* T_bott: Temperature [K] at the base of the layer.
* z_bott: Geopotential altitude [m] of the base of the layer.
Output:
* Pressure [hPa] for each element given in the input arguments.
All input arguments can be either a scalar or an MA array. All
arguments that are MA arrays, however, are of the same size and
shape. If every input argument is a scalar, the output is a scalar.
If any of the input arguments is an MA array, the output is an MA
array of the same size and shape.
"""
#jfp was import Numeric as N
import numpy as N
#jfp was import MA
import numpy.ma as MA
from atmconst import AtmConst
const = AtmConst()
if MA.size(lapse_rate) == 1:
#jfp was if MA.array(lapse_rate)[0] == 0.0:
if MA.array(lapse_rate) == 0.0:
return P_bott * \
MA.exp( -const.g / (const.R_d*T_bott) * (z-z_bott) )
else:
exponent = const.g / (const.R_d * lapse_rate)
return P_bott * \
( (1.0 - (lapse_rate * (z-z_bott) / T_bott))**exponent )
else:
exponent = const.g / (const.R_d * lapse_rate)
P = P_bott * \
( (1.0 - (lapse_rate * (z-z_bott) / T_bott))**exponent )
P_at_0 = P_bott * \
MA.exp( -const.g / (const.R_d*T_bott) * (z-z_bott) )
zero_lapse_mask = MA.filled(MA.where(lapse_rate == 0., 1, 0), 0)
zero_lapse_mask_indices_flat = N.nonzero(N.ravel(zero_lapse_mask))
P_flat = MA.ravel(P)
MA.put( P_flat, zero_lapse_mask_indices_flat \
, MA.take(MA.ravel(P_at_0), zero_lapse_mask_indices_flat) )
return MA.reshape(P_flat, P.shape)
def _pfromz_MA(z, lapse_rate, P_bott, T_bott, z_bott):
"""Pressure given altitude in a constant lapse rate layer.
The dry gas constant is used in calculations requiring the gas
constant. See the docstring for press2alt for references.
Input Arguments:
* z: Geopotential altitude [m].
* lapse_rate: -dT/dz [K/m] over the layer.
* P_bott: Pressure [hPa] at the base of the layer.
* T_bott: Temperature [K] at the base of the layer.
* z_bott: Geopotential altitude [m] of the base of the layer.
Output:
* Pressure [hPa] for each element given in the input arguments.
All input arguments can be either a scalar or an MA array. All
arguments that are MA arrays, however, are of the same size and
shape. If every input argument is a scalar, the output is a scalar.
If any of the input arguments is an MA array, the output is an MA
array of the same size and shape.
"""
#jfp was import Numeric as N
import numpy as N
#jfp was import MA
import numpy.ma as MA
from atmconst import AtmConst
const = AtmConst()
if MA.size(lapse_rate) == 1:
#jfp was if MA.array(lapse_rate)[0] == 0.0:
if MA.array(lapse_rate) == 0.0:
return P_bott * \
MA.exp( -const.g / (const.R_d*T_bott) * (z-z_bott) )
else:
exponent = const.g / (const.R_d * lapse_rate)
return P_bott * \
( (1.0 - (lapse_rate * (z-z_bott) / T_bott))**exponent )
else:
exponent = const.g / (const.R_d * lapse_rate)
P = P_bott * \
( (1.0 - (lapse_rate * (z-z_bott) / T_bott))**exponent )
P_at_0 = P_bott * \
MA.exp( -const.g / (const.R_d*T_bott) * (z-z_bott) )
zero_lapse_mask = MA.filled(MA.where(lapse_rate == 0., 1, 0), 0)
zero_lapse_mask_indices_flat = N.nonzero(N.ravel(zero_lapse_mask))
P_flat = MA.ravel(P)
MA.put( P_flat, zero_lapse_mask_indices_flat \
, MA.take(MA.ravel(P_at_0), zero_lapse_mask_indices_flat) )
return MA.reshape(P_flat, P.shape)
def test_print_solved(self):
potential = lambda x: 2 * (exp(-2 * x) - 2 * exp(-x) + 1
) # 0.5 * x ** 2 + 0.5 * x ** 4
matrix_size = 501
left_boundary = -10
right_boundary = 10
solver = Schrodinger_equation_solver(potential, matrix_size,
left_boundary, right_boundary)
solver.solve()
solver.print_energies(1, 10)
solver.print_wave_functions((1, 2, 3, 4, 5))
solver.print_probability_density_function((1, 2, 3, 4, 5))
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 calculate_n_leaching(avail_n, n_added, dr_list, fc, calib_n_leach):
""" Estimate the amount of N leached by the draining water during this
time step.
Args:
avail_n: Grid of available N at end of previous step (kg/ha).
n_added: N added during this step (kg/ha).
dr_list: List of drainage grids from drainage.estimate_drainage().
fc: Soil field capacity grid.
calib_n_leach: Calibrating parameter determining the leaching rate.
Returns:
List of grids: [leached_n, new_avail_n].
"""
import numpy.ma as ma
# Extract individual parameters from drainage_list
snow_pk, wat_lev, surf_ro, lat_dr, vert_dr, tot_dr = dr_list
# Add today's N to the existing amount in the soil
intermed_n = avail_n + n_added
intermed_n[intermed_n<0]=0
# Calculate the fraction of the available N that leaches
exponent = -1*calib_n_leach*(lat_dr+vert_dr)/fc
leach_frac = 1 - ma.exp(exponent)
# Calculate the amount of N that leaches
leached_n = leach_frac*intermed_n
# Calculate amount of N left
new_avail_n = intermed_n - leached_n
return [leached_n, new_avail_n]
def geometric_mean(array, axis=0):
'''return the geometric mean of an array removing all zero-values but
retaining total length
'''
non_zero = ma.masked_values(array, 0)
log_a = ma.log(non_zero)
return ma.exp(log_a.mean(axis=axis))
def stats(op, infiles, band, log, area_weighted):
whats, years = get_domain(infiles)
df = pd.DataFrame(columns=whats, index=sorted(years))
for arg in infiles:
with rasterio.open(arg) as src:
data = src.read(band, masked=True)
if log:
data = ma.exp(data)
if area_weighted:
data *= rcs(data.shape[0], src.res, *src.bounds)
data.mask = np.logical_or(data.mask,
ma.where(np.isnan(data), True, False))
if op == 'sum':
op = 'total'
res = eval("%s(data)" % op)
if re.search(r'-hpd-(\d){4}.tif', arg):
print('%s: %8.4f %8.4f' %
(os.path.basename(arg), res, np.log(res + 1) / 10.02083))
else:
print('%s: %8.4f' % (os.path.basename(arg), res))
scenario, what, year = os.path.splitext(arg)[0].split('-')
df.ix[int(year), what] = res
print(df)
df.plot.bar()
plt.savefig('lu-comp.png')
plt.show()
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 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'Ñ„ = {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 _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 saturation_vapor_pressure(temperature):
r'''Calculate the saturation water vapor (partial) pressure
Parameters
----------
temperature : array_like
The temperature in degrees Celsius.
Returns
-------
array_like
The saturation water vapor (partial) presure in mb.
See Also
--------
vapor_pressure, dewpoint
Notes
-----
Instead of temperature, dewpoint may be used in order to calculate
the actual (ambient) water vapor (partial) pressure.
The formula used is that from Bolton 1980 [2] for T in degrees Celsius:
.. math:: 6.112 e^\frac{17.67T}{T + 243.5}
References
----------
.. [2] Bolton, D., 1980: The Computation of Equivalent Potential
Temperature. Mon. Wea. Rev., 108, 1046-1053.
'''
return sat_pressure_0c * exp(17.67 * temperature / (temperature + 243.5))
def zonal_avg(data,Log=False):
"""
Compute the zonal average of field on POP gx3v5 grid.
Shape of input data is expected to be either [nfoo,nlat,nlon]
or [nlat,nlon]. Log=True computes the geometric average.
Output: arrays zavg and lat
"""
print 'computing zonal average'
# get lat and lon for new regular grid
# fpin = Nio.open_file('/home/ivan/Python/data/lat_t.nc','r')
fpin = Nio.open_file('/home/emunoz/Python/mapping/model_grid/lat_t.nc','r')
lat_t = fpin.variables['lat_t'][:]
lat_t_edges = fpin.variables['lat_t_edges'][:]
fpin.close()
# fpin = Nio.open_file('/home/ivan/Python/data/gx3v5.nc','r')
fpin = Nio.open_file('/home/emunoz/Python/mapping/model_grid/gx3v5.nc','r')
lon_t = N.sort(fpin.variables['TLONG'][0,:])
ulon = N.sort(fpin.variables['ULONG'][0,:])
lon_t_edges = N.concatenate((ulon,ulon[0,N.newaxis]+360.),0)
# get gx3v5 lat and lon
tlon = fpin.variables['TLONG'][:]
tlat = fpin.variables['TLAT'][:]
fpin.close()
# compute area of cells in new regular grid
area = grid_area(lon_t_edges,lat_t_edges)
nlat = lat_t.shape[0]
nlon = lon_t.shape[0]
if data.ndim == 3:
new_data = MA.zeros((data.shape[0],nlat,nlon),dtype=float)
elif data.ndim == 2:
new_data = MA.zeros((nlat,nlon),dtype=float)
else:
print 'Check field dimensions'
sys.exit()
# geometric mean?
if Log:
work = MA.log(data)
else:
work = data
# remap data to new regular grid
for i in range(nlat):
#print 'lat = %.2f'%(lat_t[i])
for j in range(nlon):
new_data[:,i,j] = extract_loc(lon_t[j],lat_t[i],tlon,tlat,work)
# compute zonal average
if Log:
za_data = (MA.exp(MA.average(new_data,axis=-1,
weights=N.resize(area,new_data.shape))))
else:
za_data = (MA.average(new_data,axis=-1,
weights=N.resize(area,new_data.shape)))
return za_data, lat_t
def saturation_vapor_pressure(temperature):
r'''Calculate the saturation water vapor (partial) pressure
Parameters
----------
temperature : array_like
The temperature in degrees Celsius.
Returns
-------
array_like
The saturation water vapor (partial) presure in mb.
See Also
--------
vapor_pressure, dewpoint
Notes
-----
Instead of temperature, dewpoint may be used in order to calculate
the actual (ambient) water vapor (partial) pressure.
The formula used is that from Bolton 1980 [2] for T in degrees Celsius:
.. math:: 6.112 e^\frac{17.67T}{T + 243.5}
References
----------
.. [2] Bolton, D., 1980: The Computation of Equivalent Potential
Temperature. Mon. Wea. Rev., 108, 1046-1053.
'''
return sat_pressure_0c * exp(17.67 * temperature / (temperature + 243.5))
def stock_price(cls, iteration_=1, **kwargs):
"""generate stock spot through stochastic process"""
_rand = rand_norm(0, 1, iteration_)
_isp, _rate, _div, _vol, _t = parse_kwargs(
kwargs, ['isp', 'rate', 'div', 'vol', 't'], 0)
return _isp * exp((_rate - _div - _vol**2 / 2) * _t +
_vol * sqrt(_t) * _rand)
def relative_humidity(p, q, t, A=17.625, B=-30.11, C=610.94, masked=False):
"""
From Mark G. Lawrence, BAMS Feb 2005, eq. (6)
RH = relative_humidity(p,q,t,A,B,C)
inputs: p = pressure (Pa)
q = specific humidity (kg/kg)
t = temperature (K)
keywords: A, B and C are optional fitting parameters
from Alduchov and Eskridge (1996).
Masked = False (if True, perform operation on masked arrays)
output: RH = relative humidity (0-1)
p, q and t can be arrays.
"""
if masked == False:
es = C * exp(A * (t - 273.15) / (B + t))
ws = 0.62198 * es / (maximum(p, es) - (1 - 0.62198) * es)
RH = q / ws
else:
es = C * ma.exp(A * (t - 273.15) / (B + t))
ws = 0.62198 * es / (maximum(p, es) - (1 - 0.62198) * es)
RH = q / ws
return RH
def geometric_mean(array, axis=0):
'''return the geometric mean of an array removing all zero-values but
retaining total length
'''
non_zero = ma.masked_values(array, 0)
log_a = ma.log(non_zero)
return ma.exp(log_a.mean(axis=axis))
def findEout(self, numSamples=1000):
e_out = 0
dataSamples = [self.createDataPoint() for _ in range(numSamples)]
for x, y in dataSamples:
e_out += log(1 +
exp(-1 * multiply(y, np.dot(transpose(self.w), x))))
e_out /= float(numSamples)
return e_out
def profit_discount(self, mkt_dict_, time_):
"""get instrument pnl for given spot"""
_rate, _spot = tuple(
self._load_market(
mkt_dict_,
[EnvParam.RiskFreeRate.value, EnvParam.UdSpotForPrice.value]))
return self.payoff(_spot) * exp(
-_rate * time_) - self.unit * self.price
def transform(self, a):
sign = np.sign(a)
masked = ma.masked_inside(a, -self.linthresh, self.linthresh, copy=False)
exp = sign * self.linthresh * ma.exp(sign * masked / self.linthresh - 1)
if masked.mask.any():
return ma.where(masked.mask, a, exp)
else:
return exp
def to_simple_returns(self) -> "SimpleReturnsSeries":
from qf_lib.containers.series.simple_returns_series import SimpleReturnsSeries
simple_rets_values = [exp(log_ret) - 1 for log_ret in self.values]
simple_returns_tms = SimpleReturnsSeries(
index=self.index.copy(),
data=simple_rets_values).__finalize__(self)
return simple_returns_tms
def transform(self, a):
sign = np.sign(a)
masked = ma.masked_inside(a,
-self.linthresh,
self.linthresh,
copy=False)
exp = sign * self.linthresh * ma.exp(sign * masked /
self.linthresh - 1)
if masked.mask.any():
return ma.where(masked.mask, a, exp)
else:
return exp
def delta(self, mkt_dict_, engine_, unit_=None):
"""calculate option DELTA 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 _sign * norm.cdf(_sign * _d1) * exp(-_div * _t) * _unit
elif _method == EngineMethod.MC.value:
from utils.monte_carlo import MonteCarlo
_iteration = _param.get(EngineParam.MCIteration.value)
if not _iteration:
raise ValueError("iteration not specified")
if not isinstance(_iteration, int):
raise ValueError("type <int> is required for iteration, not {}".format(type(_iteration)))
_spot = MonteCarlo.stock_price(_iteration, isp=_spot, rate=_rate, div=_div, vol=_vol, t=_t)
_step = 0.01
_delta = [(max(_sign * (_s + _step - _strike), 0) - max(_sign * (_s - _step - _strike), 0)) /
(_step * 2) for _s in _spot]
return average(_delta) * exp(-_rate * _t) * _unit
def thelenTensonForce(self, tendonLength, tendonSlackLength):
self.tendonLength = tendonLength
self.tendonSlackLength = tendonSlackLength
self.relativeTendonLength = ( self.tendonLength - self.tendonSlackLength ) / self.tendonSlackLength
if self.relativeTendonLength <= 0 :
self.tendonForce = 0
elif self.relativeTendonLength > 0 and self.relativeTendonLength <= self.tendonStrainLinear :
self.tendonForce = self.tendonNormalizedMaximalForceLinear * (exp(self.tendonNonlinearShapeFactor * self.relativeTendonLength / self.tendonStrainLinear) - 1) / ( exp( self.tendonNonlinearShapeFactor ) - 1)
else :# self.relativeTendonLength > self.tendonStrainLinear :
self.tendonForce = self.tendonLinearShapeFactor * (self.relativeTendonLength - self.tendonStrainLinear ) + self.tendonNormalizedMaximalForceLinear
return self.tendonForce + 0.001 * (1 + self.relativeTendonLength)
def thelenPassiveForce(self, muscleLength, muscleOptimaleLength):
self.muscleLength = muscleLength
self.muscleOptimaleLength = muscleOptimaleLength
self.normalizedMuscleLength = self.muscleLength / self.muscleOptimaleLength
if self.normalizedMuscleLength <= 1 + self.passiveNormalizedMaximalForce :
passiveMuscleForce = (exp(self.passiveExpoShapeFactor*(self.normalizedMuscleLength-1)/self.passiveNormalizedMaximalForce)) / (exp(self.passiveExpoShapeFactor))
elif self.normalizedMuscleLength > 1 + self.passiveNormalizedMaximalForce :
passiveMuscleForce = 1+ self.passiveExpoShapeFactor/self.passiveNormalizedMaximalForce * (self.normalizedMuscleLength-(1+self.passiveNormalizedMaximalForce))
else :# self.relativeTendonLength > self.tendonStrainLinear :
passiveMuscleForce = 0
return passiveMuscleForce
def _apply_function(func, arg):
# type: (QuilParser.FunctionContext, Any) -> Any
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: " + str(func))
def entropyScore(dist, labels, label, cache=None):
indices = np.where(labels == label)[0]
if cache is not None:
tindices = tuple(indices)
if tindices in cache:
return cache[tindices]
if CYTHON:
if conf.clustering == 'FastDBSCAN':
result = cchen.entropyScoreDistIndex(dist, indices)
else:
result = cchen.entropyScore(dist, indices)
else:
if dist is None:
return None
# E(X) = - S_j( 1/m log( S_i( exp(-d(x_i, x_j, t ) 1/m ) )
# = - 1/m S_j( log( 1/m S_i( exp(-d(x_i, x_j, t ) ) )
s1 = 0
for j in indices:
s2 = 0
for i in indices:
if conf.clustering == 'FastDBSCAN':
s2 = s2 + exp(-dist.get(i,j))
else:
s2 = s2 + exp(-dist[i,j])
s2 = s2 / len(indices)
s1 = s1 + log(s2)
s1 = s1 /len(indices)
result = -s1
if cache is not None:
cache[tindices] = result
return result
def runLogisticRegression(self):
diff = 1
while diff > 0.01:
permutation = np.random.permutation(self.N)
newWeights = self.w.copy()
for i in permutation:
x, y = self.trainingData[i]
gradient = divide(
multiply(-1.0, multiply(x, y)),
(1.0 + exp(multiply(y, np.dot(transpose(self.w), x)))))
newWeights = subtract(newWeights,
multiply(self.learningRate, gradient))
self.epoch += 1
diff = norm(self.w - newWeights)
self.w = newWeights
def geoMean(array):
'''
Generate the geometric mean of a list or array,
removing all zero-values but retaining total length
'''
if isinstance(array, pandas.core.frame.DataFrame):
array = array.as_matrix()
else:
pass
non_zero = ma.masked_values(array, 0)
log_a = ma.log(non_zero)
geom_mean = ma.exp(log_a.mean())
return geom_mean
def sigmodFunction(dataArr, theta):
z = dot(dataArr, theta)
p = 1e-5
hx = 1 / (1 + exp(-z))
# print "sigmod Function ä¸hx 的值为:",hx
hx_new = []
for f in hx.flat:
if f == 1:
hx_new.append([f - p])
elif f == 0:
hx_new.append([f + p])
else:
hx_new.append([f])
hx = asarray(hx_new)
return hx
def sigmodGradient(z):
gz = 1.0 / (1 + exp(-z))
p = 1e-5
m, n = shape(gz)
gz_new = []
for f in gz.flat:
if f == 1:
gz_new.append([f - p])
elif f == 0:
gz_new.append([f + p])
else:
gz_new.append([f])
gz = asarray(gz_new)
gz = reshape(gz, (m, n))
return gz * (1 - gz)
def sigmodFunction(z2):
p = 1e-5
hx = 1.0 / (1 + exp(-z2))
# print "sigmod Function ä¸hx 的值为:",hx
m, n = shape(hx)
hx_new = []
for f in hx.flat:
if f == 1:
hx_new.append([f - p])
elif f == 0:
hx_new.append([f + p])
else:
hx_new.append([f])
hx = asarray(hx_new)
hx = reshape(hx, (m, n))
return hx
def geoMean(array):
'''
Generate the geometric mean of a list or array,
removing all zero-values but retaining total length
'''
if isinstance(array, pandas.core.frame.DataFrame):
array = array.as_matrix()
else:
pass
non_zero = ma.masked_values(array,
0)
log_a = ma.log(non_zero)
geom_mean = ma.exp(log_a.mean())
return geom_mean
def vapor_pressure(temp):
'''
Calculate the saturation water vapor (partial) pressure given
*temperature*.
temp : scalar or array
The temperature in degrees Celsius.
Returns : scalar or array
The saturation water vapor (partial) presure in millibars, with
the same shape as *temp*.
Instead of temperature, dewpoint may be used in order to calculate
the actual (ambient) water vapor (partial) pressure.
'''
return sat_pressure_0c * exp(17.67 * temp / (temp + 243.5))
def saturation_vapor_pressure(temp):
"""
Calculate the saturation water vapor (partial) pressure given
*temperature*.
temp : scalar or array
The temperature in degrees Celsius.
Returns : scalar or array
The saturation water vapor (partial) presure in millibars, with
the same shape as *temp*.
Instead of temperature, dewpoint may be used in order to calculate
the actual (ambient) water vapor (partial) pressure.
"""
return sat_pressure_0c * exp(17.67 * temp / (temp + 243.5))
def compute_centroid(im,sigw=None,nb_iter=4):
""" Computes centroid.
#TODO: would be interesting to compare with Sam's moments based computation
Calls:
* gaussfitter.gaussfit
"""
if sigw is None:
param=gaussfitter.gaussfit(im,returnfitimage=False)
#print param
sigw = (param[3]+param[4])/2
sigw = float(sigw)
n1 = im.shape[0]
n2 = im.shape[1]
rx = array(range(0,n1))
ry = array(range(0,n2))
Wc = ones((n1,n2))
centroid = zeros((1,2))
# Four iteration loop to compute the centroid
i=0
for i in range(0,nb_iter):
xx = npma.outerproduct(rx-centroid[0,0],ones(n2))
yy = npma.outerproduct(ones(n1),ry-centroid[0,1])
W = npma.exp(-(xx**2+yy**2)/(2*sigw**2))
centroid = zeros((1,2))
# Estimate Centroid
Wc = copy(W)
if i == 0:Wc = ones((n1,n2))
totx=0.0
toty=0.0
cx=0
cy=0
for cx in range(0,n1):
centroid[0,0] += (im[cx,:]*Wc[cx,:]).sum()*(cx)
totx += (im[cx,:]*Wc[cx,:]).sum()
for cy in range(0,n2):
centroid[0,1] += (im[:,cy]*Wc[:,cy]).sum()*(cy)
toty += (im[:,cy]*Wc[:,cy]).sum()
centroid = centroid*array([1/totx,1/toty])
return (centroid,Wc)
def compute_centroid(im, sigw=None, nb_iter=4):
""" Computes centroid.
#TODO: would be interesting to compare with Sam's moments based computation
Calls:
* gaussfitter.gaussfit
"""
if sigw is None:
param = gaussfitter.gaussfit(im, returnfitimage=False)
#print param
sigw = (param[3] + param[4]) / 2
sigw = float(sigw)
n1 = im.shape[0]
n2 = im.shape[1]
rx = array(range(0, n1))
ry = array(range(0, n2))
Wc = ones((n1, n2))
centroid = zeros((1, 2))
# Four iteration loop to compute the centroid
i = 0
for i in range(0, nb_iter):
xx = npma.outerproduct(rx - centroid[0, 0], ones(n2))
yy = npma.outerproduct(ones(n1), ry - centroid[0, 1])
W = npma.exp(-(xx**2 + yy**2) / (2 * sigw**2))
centroid = zeros((1, 2))
# Estimate Centroid
Wc = copy(W)
if i == 0: Wc = ones((n1, n2))
totx = 0.0
toty = 0.0
cx = 0
cy = 0
for cx in range(0, n1):
centroid[0, 0] += (im[cx, :] * Wc[cx, :]).sum() * (cx)
totx += (im[cx, :] * Wc[cx, :]).sum()
for cy in range(0, n2):
centroid[0, 1] += (im[:, cy] * Wc[:, cy]).sum() * (cy)
toty += (im[:, cy] * Wc[:, cy]).sum()
centroid = centroid * array([1 / totx, 1 / toty])
return (centroid, Wc)
def predictRes(x, theta, y, threshold):
dataArr = asarray(x)
labelArr = asarray(y)
n = shape(y)[0]
# print theta
z = dot(x, theta)
p = 1.0 / (1 + exp(-1 * z))
p[p < threshold] = 0
p[p >= threshold] = 1
# print p
res = p - labelArr
count = 0
for r in res.flat:
if r != 0:
count += 1
print count
print n
return (n - count * 1.0) / n
def ljung_box_pierce(cross_correlation_array, length, n_lag):
"""Calculate Ljung-Box-Pierce statistics
Args:
cross_correlation_array: array of spatial maps of correlations, for
each lag
length: length of the time series
n_lag: integer, maximum temporal lag to sum
Return:
2d array, same shape as value_map[0, :, :], contains lbp statistics
"""
statistic = ma.empty_like(cross_correlation_array[0])
statistic[np.logical_not(statistic.mask)] = 0
for i in range(n_lag + 1):
statistic += (ma.exp(2 * ma.log(cross_correlation_array[i]) -
math.log(length - i)))
return statistic
def compute_centroid(im,sigw,nb_iter=4):
n1 = im.shape[0]
n2 = im.shape[1]
rx = array(range(0,n1))
ry = array(range(0,n2))
Wc = ones((n1,n2))
centroid = zeros((1,2))
# Four iteration loop to compute the centroid
i=0
for i in range(0,nb_iter):
xx = npma.outerproduct(rx-centroid[0,0],ones(n2))
yy = npma.outerproduct(ones(n1),ry-centroid[0,1])
W = npma.exp(-(xx**2+yy**2)/(2*sigw**2))
centroid = zeros((1,2))
# Estimate Centroid
Wc = copy(W)
if i == 0:Wc = ones((n1,n2))
totx=0.0
toty=0.0
cx=0
cy=0
for cx in range(0,n1):
centroid[0,0] += (im[cx,:]*Wc[cx,:]).sum()*(cx)
totx += (im[cx,:]*Wc[cx,:]).sum()
for cy in range(0,n2):
centroid[0,1] += (im[:,cy]*Wc[:,cy]).sum()*(cy)
toty += (im[:,cy]*Wc[:,cy]).sum()
centroid = centroid*array([1/totx,1/toty])
return (centroid,Wc)
def thelenActiveMuscleForce(self, muscleLength, muscleOptimaleLength):
self.muscleOptimalLength = muscleOptimaleLength
self.muscleLength = muscleLength
return exp(- (muscleLength / self.muscleOptimalLength - 1) ** 2 / self.kShapeActive)
def run_model(self):
"""
Run the model
:return:
"""
shape = self._shape
tew = self._tew
taw = self._taw
start_time = datetime.now()
pkcb = zeros(shape)
swe = zeros(shape)
tot_snow = zeros(shape)
tot_mass = zeros(shape)
cum_mass = zeros(shape)
ref_et = zeros(shape)
a_min = ones(shape) * 0.45
a_max = ones(shape) * 0.90
a = a_max
pA = a_min
days = list(rrule.rrule(rrule.DAILY, dtstart=self._start, until=self._end))
nsteps = len(days)
plt_day = zeros(nsteps)
plt_rain = zeros(nsteps)
plt_eta = zeros(nsteps)
plt_snow_fall = zeros(nsteps)
plt_ro = zeros(nsteps)
plt_dr = zeros(nsteps)
plt_de = zeros(nsteps)
plt_drew = zeros(nsteps)
plt_temp = zeros(nsteps)
plt_dp_r = zeros(nsteps)
plt_ks = zeros(nsteps)
plt_pdr = zeros(nsteps)
plt_etrs = zeros(nsteps)
plt_kcb = zeros(nsteps)
plt_ppt = zeros(nsteps)
plt_ke = zeros(nsteps)
plt_kr = zeros(nsteps)
plt_mlt = zeros(nsteps)
plt_swe = zeros(nsteps)
plt_tempm = zeros(nsteps)
plt_fs1 = zeros(nsteps)
plt_mass = zeros(nsteps)
p_mo_et = zeros(shape)
p_mo_precip = zeros(shape)
p_mo_ro = zeros(shape)
p_mo_deps = self._dr + self._de + self._drew
p_mo_infil = zeros(shape)
p_mo_etrs = zeros(shape)
p_yr_et = zeros(shape)
p_yr_precip = zeros(shape)
p_yr_ro = zeros(shape)
p_yr_deps = self._dr + self._de + self._drew
p_yr_infil = zeros(shape)
p_yr_etrs = zeros(shape)
start_month = self._start_month
end_month = self._end_month
for i, dday in enumerate(days):
if i > 0:
pkcb = kcb
doy = dday.timetuple().tm_yday
year = dday.year
month = dday.month
day = dday.day
msg = 'Time : {} day {}_{}'.format(datetime.now() - start_time, doy, year)
logging.debug(msg)
# -------------- kcb -------------------
if year == 2000:
ndvi = self.calculate_ndvi_2000(doy)
elif year == 2001:
ndvi = self.calculate_ndvi_2001(doy)
else:
ndvi = self.calculate_ndvi(year, doy)
kcb = ndvi * 1.25
kcb = maximum(kcb, self._min_val)
kcb = where(isnan(kcb), pkcb, kcb)
# -------------- PRISM -------------------
ppt, ppt_tom, max_temp, min_temp, mid_temp = self.load_prism(dday)
# -------------- PM -------------------
# PM data to etrs
name = os.path.join('PM{}'.format(year),
'PM_NM_{}_{:03n}'.format(year, doy))
etrs = tif_to_array(self._pm_data_root, name)
etrs = maximum(etrs, self._min_val)
name = os.path.join('PM{}'.format(year),
'RLIN_NM_{}_{:03n}'.format(year, doy))
rlin = tif_to_array(self._pm_data_root, name)
rlin = maximum(rlin, zeros(shape))
name = os.path.join('rad{}'.format(year),
'RTOT_{}_{:03n}'.format(year, doy))
rg = tif_to_array(self._pm_data_root, name)
rg = maximum(rg, zeros(shape))
if i == 0:
# Total evaporable water is depth of water in the evaporable
# soil layer, i.e., the water available to both stage 1 and 2 evaporation
rew = minimum((2 + (tew / 3.)), 0.8 * tew)
# del tew1, tew2
# you should have all these from previous model runs
pDr = self._dr
pDe = self._de
pDrew = self._drew
dr = self._dr
de = self._de
drew = self._drew
nom = 2 if start_month <= doy <= end_month else 6
ksat = self._ksat * nom / 24.
kc_max_1 = kcb + 0.0001
min_val = ones(shape) * 0.0001
kc_max = maximum(min_val, kc_max_1)
self._nlcd_plt_hgt = self._nlcd_plt_hgt * 0.5 + 1
numr = maximum(kcb - self._kc_min, min_val * 10)
denom = maximum((kc_max - self._kc_min), min_val * 10)
fcov_ref = (numr / denom) ** self._nlcd_plt_hgt
fcov_min = minimum(fcov_ref, ones(shape))
fcov = maximum(fcov_min, min_val * 10)
few = maximum(1 - fcov, 0.01) # exposed ground
pKr = kr
kr = minimum(((tew - de) / (tew - rew)), ones(shape))
kr = where(isnan(kr), pKr, kr)
pKs = ks
ks_ref = where(((taw - pDr) / (0.6 * taw)) < zeros(shape), ones(shape) * 0.001,
((taw - pDr) / (0.6 * taw)))
ks_ref = where(isnan(ks), pKs, ks_ref)
ks = minimum(ks_ref, ones(shape))
# Ke evaporation reduction coefficient; stage 1 evaporation
fsa = where(isnan((rew - drew) / (KE_MAX * etrs)), zeros(shape),
(rew - drew) / (KE_MAX * etrs))
fsb = minimum(fsa, ones(shape))
fs1 = maximum(fsb, zeros(shape))
ke = where(drew < rew, minimum((fs1 + (1 - fs1) * kr) * (kc_max - ks * kcb), few * kc_max),
zeros(shape))
transp = (ks * kcb) * etrs
et_init = (ks * kcb + ke) * etrs
eta = maximum(et_init, zeros(shape))
evap_init = ke * etrs
evap_min = maximum(evap_init, zeros(shape))
evap = minimum(evap_min, kc_max)
# Load temp, find swe, melt, and precipitation, load Ksat
# Use SNOTEL data for precip and temps:
# df_snow : (stel_date, stel_snow, stel_precip, stel_tobs, stel_tmax, stel_tmin, stel_tavg, stel_snwd)
snow_fall = where(mid_temp <= 0.0, ppt, zeros(shape))
rain = where(mid_temp >= 0.0, ppt, zeros(shape))
pA = a
a = where(snow_fall > 3.0, ones(shape) * a_max, a)
a = where(snow_fall <= 3.0, a_min + (pA - a_min) * exp(-0.12), a)
a = where(snow_fall == 0.0, a_min + (pA - a_min) * exp(-0.05), a)
a = where(a < a_min, a_min, a)
swe += snow_fall
mlt_init = maximum(((1 - a) * rg * 0.2) + (mid_temp - 1.8) * 11.0,
zeros(shape)) # use calibrate coefficients
mlt = minimum(swe, mlt_init)
swe -= mlt
# Find depletions
pDr = dr
pDe = de
pDrew = drew
watr = rain + mlt
deps = dr + de + drew
ro = zeros(shape)
ro = where(watr > ksat + deps, watr - ksat - deps, ro)
ro = maximum(ro, zeros(shape))
dp_r = zeros(shape)
id1 = where(watr > deps, ones(shape), zeros(shape))
id2 = where(ksat > watr - deps, ones(shape), zeros(shape))
dp_r = where(id1 + id2 > 1.99, maximum(watr - deps, zeros(shape)), dp_r)
dp_r = where(watr > ksat + deps, ksat, dp_r)
dp_r = maximum(dp_r, zeros(shape))
drew_1 = minimum((pDrew + ro + (evap - (rain + mlt))), rew)
drew = maximum(drew_1, zeros(shape))
diff = maximum(pDrew - drew, zeros(shape))
de_1 = minimum((pDe + (evap - (rain + mlt - diff))), tew)
de = maximum(de_1, zeros(shape))
diff = maximum(((pDrew - drew) + (pDe - de)), zeros(shape))
dr_1 = minimum((pDr + ((transp + dp_r) - (rain + mlt - diff))), taw)
dr = maximum(dr_1, zeros(shape))
# Create cumulative rasters to show net over entire run
infil += dp_r
infil = maximum(infil, zeros(shape))
prev_et = et
ref_et += etrs
et = et + evap + transp
et_ind = et / ref_et
et = where(isnan(et) == True, prev_et, et)
et = where(et > ref_et, ref_et / 2., et)
et = maximum(et, ones(shape) * 0.001)
precip = precip + rain + snow_fall
precip = maximum(precip, zeros(shape))
runoff += ro
runoff = maximum(runoff, zeros(shape))
snow_ras = swe + snow_fall - mlt
snow_ras = maximum(snow_ras, zeros(shape))
tot_snow += snow_fall
mo_date = calendar.monthrange(year, month)
if day == mo_date[1]:
infil_mo = infil - p_mo_infil
infil_mo = maximum(infil_mo, zeros(shape))
ref_et_mo = etrs - p_mo_etrs
et_mo = et - p_mo_et
et_mo = where(isnan(et_mo) == True, p_mo_et, et_mo)
et_mo = where(et_mo > ref_et, ref_et / 2., et_mo)
et_mo = maximum(et_mo, ones(shape) * 0.001)
precip_mo = precip - p_mo_precip
precip_mo = maximum(precip_mo, zeros(shape))
runoff_mo = ro - p_mo_ro
runoff_mo = maximum(runoff_mo, zeros(shape))
snow_ras_mo = swe
snow_ras_mo = maximum(snow_ras_mo, zeros(shape))
deps_mo = drew + de + dr
delta_s_mo = p_mo_deps - deps_mo
outputs = (('infil', infil_mo), ('et', et_mo), ('precip', precip_mo), ('runoff', runoff_mo),
('snow_ras', snow_ras_mo), ('delta_s_mo', delta_s_mo), ('deps_mo', deps_mo))
self.save_month_step(outputs, month, year)
p_mo_et = et
p_mo_precip = precip
p_mo_ro = ro
p_mo_deps = deps_mo
p_mo_infil = infil
p_mo_etrs = etrs
if day == 31 and month == 12:
infil_yr = infil - p_yr_infil
infil_yr = maximum(infil_yr, zeros(shape))
ref_et_yr = etrs - p_yr_etrs
et_yr = et - p_yr_et
et_yr = where(isnan(et_yr) == True, p_yr_et, et_yr)
et_yr = where(et_yr > ref_et, ref_et / 2., et_yr)
et_yr = maximum(et_yr, ones(shape) * 0.001)
precip_yr = precip - p_yr_precip
precip_yr = maximum(precip_yr, zeros(shape))
runoff_yr = ro - p_yr_ro
runoff_yr = maximum(runoff_yr, zeros(shape))
snow_ras_yr = swe
snow_ras_yr = maximum(snow_ras_yr, zeros(shape))
deps_yr = drew + de + dr
delta_s_yr = p_yr_deps - deps_yr
outputs = (('infil', infil_yr), ('et', et_yr), ('precip', precip_yr), ('runoff', runoff_yr),
('snow_ras', snow_ras_yr), ('delta_s_yr', delta_s_yr), ('deps_yr', deps_yr))
p_yr_et = et
p_yr_precip = precip
p_yr_ro = ro
p_yr_deps = deps_yr # this was originally p_mo_deps = deps_yr im assuming this is a typo
p_yr_infil = infil
p_yr_etrs = etrs
self.save_year_step(outputs, month, year)
# Check MASS BALANCE for the love of WATER!!!
mass = rain + mlt - (ro + transp + evap + dp_r + ((pDr - dr) + (pDe - de) + (pDrew - drew)))
tot_mass += abs(mass)
cum_mass += mass
plt_day[i] = dday
plt_rain[i] = rain[S, E]
plt_eta[i] = eta[S, E]
plt_snow_fall[i] = snow_fall[S, E]
plt_ro[i] = ro[S, E]
plt_dr[i] = dr[S, E]
plt_de[i] = de[S, E]
plt_drew[i] = drew[S, E]
plt_temp[i] = mid_temp[S, E]
plt_dp_r[i] = dp_r[S, E]
plt_ks[i] = ks[S, E]
plt_pdr[i] = pDr[S, E]
plt_etrs[i] = etrs[S, E]
plt_kcb[i] = kcb[S, E]
plt_ppt[i] = ppt[S, E]
plt_ke[i] = ke[S, E]
plt_kr[i] = kr[S, E]
plt_mlt[i] = mlt[S, E]
plt_swe[i] = swe[S, E]
plt_tempm[i] = max_temp[S, E]
plt_fs1[i] = fs1[S, E]
plt_mass[i] = mass[S, E]
def logist(x, loc_, scale_):
return exp((loc_ - x) / scale_) / (scale_ * (1 + exp((loc_ - x) / scale_)) ** 2)
def sigmoid(inX):
return 1.0 / (1 + exp(-inX))
def py_sigmoidal(x, asym=1.0, xmid=None, scale=1.0):
if xmid is None:
xmid = ma.median(x)
return asym / (1 + ma.exp((xmid - x) / scale))
def sigmoidal(self, x, asym=1.0, xmid=None, xmod=0, scale=1.0):
if xmid is None:
xmid = ma.median(x)
xmid = xmid + xmod
return asym / (1 + ma.exp((xmid - x) / scale))