def rcosfir(beta, sps, span=None):
"""Generates a raised cosine FIR filter.
:param beta: shape of the raised cosine filter (0-1)
:param sps: number of samples per symbol
:param span: length of the filter in symbols (None => automatic selection)
>>> import arlpy
>>> rc = arlpy.comms.rcosfir(0.25, 6)
>>> bb = arlpy.comms.modulate(arlpy.comms.random_data(100), arlpy.comms.psk())
>>> pb = arlpy.comms.upconvert(bb, 6, 27000, 18000, rc)
"""
if beta < 0 or beta > 1:
raise ValueError('Beta must be between 0 and 1')
if span is None:
# from http://www.commsys.isy.liu.se/TSKS04/lectures/3/MichaelZoltowski_SquareRootRaisedCosine.pdf
# since this recommendation is for root raised cosine filter, it is conservative for a raised cosine filter
span = 33 - int(44 * beta) if beta < 0.68 else 4
delay = int(span * sps / 2)
t = _np.arange(-delay, delay + 1, dtype=_np.float) / sps
denom = 1 - (2 * beta * t)**2
eps = _np.finfo(float).eps
idx1 = _np.nonzero(_np.abs(denom) > _sqrt(eps))
b = _np.full_like(t, beta * _sin(_pi / (2 * beta)) / (2 * sps))
b[idx1] = _np.sinc(t[idx1]) * _cos(
_pi * beta * t[idx1]) / denom[idx1] / sps
b /= _sqrt(_np.sum(b**2))
return b
def imfp_TPP2M(energy_k,
rho,
molar_mass,
n_valence,
energy_bg,
units='angstroms'):
"""The TPP-2M is the modified TPP-2 equation for estimating inelastic
mean free paths (IMFP) [1]
Parameters
----------
energy_k : float
Kinetic energy [eV]
rho : float
Density (g/cm**3)
molar_mass : float
Atomic or molar mass
n_valence : float
Valence electrons
energy_bg : float
Bandgap energy [eV]
units : str
'angstroms' or 'si' (the default is 'angstroms')
Returns
-------
float
Inelastic mean free path (IMFP)
References
--------
.. [1] S. Tanuma, C. J. Powell, D. R. Penn: Surf. Interf. Anal.,Vol. 21, 165 (1994)
"""
# NOTE gamma, betaM, u, c, d are fitting parameters as in ref.
u = n_valence * rho / molar_mass
c = 1.97 - 0.91 * u
d = 53.4 - 20.8 * u
energy_plasmon = _sqrt(829.4 * u)
gamma = 0.191 * rho**-0.50
betaM = -0.10 + 0.944 / _sqrt(energy_plasmon**2 + energy_bg**2)
betaM += 0.069 * rho**0.1
imfp = energy_k
imfp /= (energy_plasmon**2 *
(betaM * _log(gamma * energy_k) - c / energy_k + d / energy_k**2))
if units.lower() == 'si':
# Convert to meters
return imfp * 1E-10
# Leave units unmodified in Angstroms
return imfp
def langevin(alpha, mass1, mass2):
"""
:param alpha: alpha: polarizability of neutral reactant (A^3)
:param mass1: mass of first particle (amu)
:param mass2: mass of second particle (amu)
:return: ion-neutral interaction rate constant (cm^3/s)
"""
mu = reduced_mass(mass1, mass2) * 1.660538782e-24
alpha = alpha * 1e-24
top = 2 * _pi * _e * _sqrt(alpha)
bot = _sqrt(mu)
output = top / bot
return output
def upconvert(x, sps, fc, fs=2.0, g=None):
"""Upconvert a complex baseband signal with pulse shaping.
This function supports upconversion by an integer factor. For a more general
passband conversion (but without pulse shaping), see :func:`arlpy.signal.bb2pb`.
If the carrier frequency is 0, the upsampled (at passband sampling rate) and
pulse shaped complex baseband data is returned. If the pulse shape is None,
a rectangular pulse shape is assumed.
The upconversion process introduces a group delay depending on the pulse shaping
filter. It is usually (len(g)-1)/2 passband samples. When g is None, the group
delay is (sps-1)/2 passband samples.
:param x: complex baseband data
:param sps: number of passband samples per baseband symbol
:param fc: carrier frequency in Hz
:param fs: passband sampling rate
:param g: pulse shaping filter
>>> import arlpy
>>> rrc = arlpy.comms.rrcosfir(0.25, 6)
>>> bb = arlpy.comms.modulate(arlpy.comms.random_data(100), arlpy.comms.psk())
>>> pb = arlpy.comms.upconvert(bb, 6, 27000, 108000, rrc)
"""
x = _np.asarray(x, dtype=_np.complex)
if g is None:
y = _np.repeat(x, sps) / _np.sqrt(sps)
else:
y = _sp.upfirdn(g, x, up=sps)
if fc != 0:
y *= _sqrt(2) * _np.exp(2j * _pi * fc * _time(y, fs))
y = y.real
return y
def awgn(x, snr, measured=False, complex=None):
"""Add Gaussian noise to signal.
:param x: real passband or complex baseband signal
:param snr: SNR in dB
:param measured: True to measure signal strength, False to assume unit strength signal
:param complex: True for complex noise, False for real noise, None to automatically decide
>>> import arlpy
>>> d1 = arlpy.comms.random_data(100, 4)
>>> qpsk = arlpy.comms.psk(4)
>>> x = arlpy.comms.modulate(d1, qpsk)
>>> y = arlpy.comms.awgn(x, 6)
>>> d2 = arlpy.comms.demodulate(y, qpsk)
>>> arlpy.comms.ser(d1, d2)
0.02
"""
signal = _np.std(x) if measured else 1.0
noise = signal * _np.power(10, -snr / 20.0)
if complex is None:
complex = (x.dtype == _np.complex)
if complex:
noise /= _sqrt(2)
y = x + _np.random.normal(
0, noise,
_np.shape(x)) + 1j * _np.random.normal(0, noise, _np.shape(x))
else:
y = x + _np.random.normal(0, noise, _np.shape(x))
return y
def qam(m=16, gray=True):
"""Generate a QAM constellation with m signal points.
The constellation represents the baseband values for symbols 0 through m-1
respectively. The constellation is scaled for unit average energy per
sample, assuming the symbols are randomly distributed.
:param m: symbol alphabet size (must be a square of an integer)
:param gray: True to use Gray coding, False otherwise
>>> import arlpy
>>> arlpy.comms.iqplot(arlpy.comms.qam(16))
"""
n = int(_sqrt(m))
if n * n != m:
raise ValueError('m must be an integer squared')
x = _np.empty((n, n), dtype=_np.complex)
for r in range(n):
for i in range(n):
x[r, i] = r + 1j * i
x -= _np.mean(x)
x /= _np.std(x)
x = _np.ravel(x)
if gray:
ndx = _np.reshape(gray_code(m), (n, n))
for i in range(1, n, 2):
ndx[i] = _np.flipud(ndx[i])
ndx = invert_map(_np.ravel(ndx))
x = x[ndx]
return x
def pam(m=2, gray=True, centered=True):
"""Generate a PAM constellation with m signal points.
The constellation represents the baseband values for symbols 0 through m-1
respectively. The constellation is scaled for unit average energy per
sample, assuming the symbols are randomly distributed.
:param m: symbol alphabet size
:param gray: True to use Gray coding, False otherwise
:param centered: True to center constellation around 0, False otherwise
>>> import arlpy
>>> arlpy.comms.pam()
array([-1, 1])
>>> arlpy.comms.pam(m=4, gray=False, centered=False)
array([0, 0.535, 1.069, 1.604])
"""
if gray and 2**int(_np.log2(m)) != m:
raise ValueError('m must be a power of 2 if Gray coding is desired')
x = _np.arange(m, dtype=_np.float)
if centered:
x -= _np.mean(x)
x /= _sqrt(_np.mean(x**2))
if gray:
x = x[invert_map(gray_code(m))]
return x
def dipole(temperature, mass1, mass2, mu_d, c):
"""
Calculates ion-dipole interaction component to rate constant
:param temperature: collision temperature (K)
:param mass1: mass of first particle (amu)
:param mass2: mass of second particle (amu)
:param mu_d: dipole moment of neutral reactant (D)
:param c: unitless factor parameterized by mu_d and alpha
:return: ion-dipole interaction rate constant (cm^3/s)
"""
mu = reduced_mass(mass1, mass2) * 1.660538782e-24
mu_d = mu_d * 1e-18
top = 2 * _sqrt(2) * _pi * _e * c * mu_d
bot = _sqrt(mu * _pi * _kb * temperature)
output = top / bot
return output
def ook():
"""Generate an on-off keying constellation.
The constellation represents the baseband values for bits 0 and 1
respectively. The constellation is scaled for unit average
energy per bit, assuming the bits are randomly distributed.
>>> import arlpy
>>> arlpy.comms.ook()
array([0, 1.414])
"""
return _np.array([0, _sqrt(2)], dtype=_np.float)
def mb_mean_velocity(temperature, mass):
"""
Calculates the mean velocity of a Maxwell Boltzmann distribution
:param temperature: temperature of distribution
:param mass: mass of gas particle
:return: velocity
"""
top = 8 * _u.k * temperature
bot = mass * _pi
output = _sqrt(top / bot)
return output
def max_supersonic_velocity(temperature, mu, gamma):
"""
Maximum velocity of a supersonic beam
:param temperature: temperature of initial gas sample
:param mu: reduced mass of gas particles
:param gamma: heat capacity ratio (1+1/f) where f is the number of degrees of freedom
:return: velocity
"""
top = 2 * _u.k * temperature * gamma
bot = mu * (gamma - 1)
output = _sqrt(top / bot)
return output
def rrcosfir(beta, sps, span=None):
"""Generates a root raised cosine FIR filter.
:param beta: shape of the root raised cosine filter (0-1)
:param sps: number of samples per symbol
:param span: length of the filter in symbols (None => automatic selection)
>>> import arlpy
>>> rrc = arlpy.comms.rrcosfir(0.25, 6)
>>> bb = arlpy.comms.modulate(arlpy.comms.random_data(100), arlpy.comms.psk())
>>> pb = arlpy.comms.upconvert(bb, 6, 27000, 18000, rrc)
"""
if beta < 0 or beta > 1:
raise ValueError('Beta must be between 0 and 1')
if span is None:
# from http://www.commsys.isy.liu.se/TSKS04/lectures/3/MichaelZoltowski_SquareRootRaisedCosine.pdf
span = 33 - int(44 * beta) if beta < 0.68 else 4
delay = int(span * sps / 2)
t = _np.arange(-delay, delay + 1, dtype=_np.float) / sps
b = _np.empty_like(t)
b[delay] = -1 / (_pi * sps) * (_pi * (beta - 1) - 4 * beta)
eps = _np.finfo(float).eps
idx2 = _np.nonzero(_np.abs(_np.abs(4 * beta * t) - 1) < _sqrt(eps))
if len(idx2) > 0:
b[idx2] = (_pi * (beta + 1) * _sin(_pi * (beta + 1) / (4 * beta)) -
4 * beta * _sin(_pi * (beta - 1) / (4 * beta)) + _pi *
(beta - 1) * _cos(_pi * (beta - 1) /
(4 * beta))) / (2 * _pi * sps)
ind = _np.arange(len(t))
ind = _np.delete(ind, _np.append(idx2, delay))
nind = t[ind]
b[ind] = -4 * beta / sps * (_cos((1 + beta) * _pi * nind) + _sin(
(1 - beta) * _pi * nind) / (4 * beta * nind)) / (_pi * (
(4 * beta * nind)**2 - 1))
b /= _sqrt(_np.sum(b**2))
return b
def downconvert(x, sps, fc, fs=2.0, g=None):
"""Downconvert a passband signal with a matched pulse shaping filter.
This function supports downconversion by an integer factor. For a more general
baseband conversion (but without matched filtering), see :func:`arlpy.signal.pb2bb`.
If the carrier frequency is 0, the input is assumed to be complex baseband, and only
undergoes matched filtering and downsampling. If the pulse shape is None, a
rectangular pulse shape is assumed.
The downconversion process introduces a group delay depending on the matched
filter. It is usually (len(g)-1)/2 passband samples.
:param x: real passband data (or complex baseband data at passband sampling rate, if fc=0)
:param sps: number of passband samples per baseband symbol
:param fc: carrier frequency in Hz
:param fs: passband sampling rate
:param g: pulse shaping filter (for matched filtering)
>>> import arlpy
>>> d1 = arlpy.comms.random_data(100, 4)
>>> qpsk = arlpy.comms.psk(4)
>>> bb1 = arlpy.comms.modulate(d1, qpsk)
>>> rrc = arlpy.comms.rrcosfir(0.25, 6)
>>> pb = arlpy.comms.upconvert(bb1, 6, 27000, 108000, rrc)
>>> bb2 = arlpy.comms.downconvert(pb, 6, 27000, 108000, rrc)
>>> delay = (len(rrc)-1)/2 # compute passband group delay of rrc FIR filter
>>> delay = 2*delay/6 # compute baseband group delay after filtering twice
>>> d2 = arlpy.comms.demodulate(bb2[delay:-delay], qpsk)
>>> arlpy.comms.ser(d1, d2)
0.0
"""
if fc == 0:
y = _np.asarray(x, dtype=_np.complex)
else:
y = _sp.hilbert(x) / 2
y *= _sqrt(2) * _np.exp(-2j * _pi * fc * _time(y, fs))
if g is None:
y = _np.sum(_np.reshape(y,
(sps, -1), order='F'), axis=0) / _np.sqrt(sps)
else:
y = _sp.upfirdn(g, y, down=sps)
return y
def _update_ps(self, es):
"""update path with isotropic delta mean, possibly clipped.
From input argument `es`, the attributes isotropic_mean_shift,
opts['CSA_clip_length_value'], and N are used.
opts['CSA_clip_length_value'] can be a single value, the upper
bound parameter, such that::
max_len = sqrt(N) + opts['CSA_clip_length_value'] * N / (N+2)
or a list with lower and upper bound parameters.
"""
if not self.is_initialized:
self.initialize(es)
if self._ps_updated_iteration == es.countiter:
return
z = es.isotropic_mean_shift
if es.opts['CSA_clip_length_value'] is not None:
vals = es.opts['CSA_clip_length_value']
try:
len(vals)
except TypeError:
vals = [-np.inf, vals]
if vals[0] > 0 or vals[1] < 0:
raise ValueError(
"""value(s) for option 'CSA_clip_length_value' = %s
not allowed""" % str(es.opts['CSA_clip_length_value']))
min_len = es.N**0.5 + vals[0] * es.N / (es.N + 2)
max_len = es.N**0.5 + vals[1] * es.N / (es.N + 2)
act_len = _norm(z)
new_len = Mh.minmax(act_len, min_len, max_len)
if new_len != act_len:
z *= new_len / act_len
# z *= (es.N / sum(z**2))**0.5 # ==> sum(z**2) == es.N
# z *= es.const.chiN / sum(z**2)**0.5
self.ps = (1 - self.cs) * self.ps + _sqrt(self.cs * (2 - self.cs)) * z
self._ps_updated_iteration = es.countiter
def ball_and_stick_2D(target,
pore_area='pore.area',
throat_area='throat.area',
pore_diameter='pore.diameter',
throat_diameter='throat.diameter',
conduit_lengths='throat.conduit_lengths'):
r"""
Calculate conduit shape factors for throat conductance associated with
diffusion-like physics (ex. thermal/diffusive/electrical conductance),
assuming pores and throats are circles (balls) and rectangles (sticks).
Parameters
----------
target : OpenPNM Object
The object which this model is associated with. This controls the
length of the calculated array, and also provides access to other
necessary properties.
pore_area : string
Dictionary key of the pore area values
throat_area : string
Dictionary key of the throat area values
pore_diameter : string
Dictionary key of the pore diameter values
throat_diameter : string
Dictionary key of the throat diameter values
conduit_lengths : string
Dictionary key of the conduit lengths' values
Returns
-------
SF : dictionary
Dictionary containing conduit shape factors to be used in conductance
models associated with diffusion-like physics. Shape factors are
accessible via the keys: 'pore1', 'pore2' and 'throat'.
Notes
-----
(1) This model accounts for the variable cross-section area in circles.
(2) WARNING: This model could break if `conduit_lengths` does not
correspond to an actual ball and stick! Example: pore length is greater
than pore radius --> :(
"""
_np.warnings.filterwarnings('ignore', category=RuntimeWarning)
network = target.project.network
throats = network.map_throats(throats=target.Ts, origin=target)
cn = network['throat.conns'][throats]
# Get pore diameter
D1 = network[pore_diameter][cn[:, 0]]
D2 = network[pore_diameter][cn[:, 1]]
# Get conduit lengths
L1 = network[conduit_lengths + '.pore1'][throats]
L2 = network[conduit_lengths + '.pore2'][throats]
Lt = network[conduit_lengths + '.throat'][throats]
# Get pore/throat baseline areas (the one used in generic conductance)
A1 = network[pore_area][cn[:, 0]]
A2 = network[pore_area][cn[:, 1]]
At = network[throat_area][throats]
# Preallocating F, SF
# F is INTEGRAL(1/A) dx , x : 0 --> L
F1, F2, Ft = _np.zeros((3, len(Lt)))
SF1, SF2, SFt = _np.ones((3, len(Lt)))
# Setting SF to 1 when Li = 0 (ex. boundary pores)
# INFO: This is needed since area could also be zero, which confuses NumPy
m1, m2, mt = [Li != 0 for Li in [L1, L2, Lt]]
SF1[~m1] = SF2[~m2] = SFt[~mt] = 1
F1[m1] = (0.5 * _atanh(2 * L1 / _sqrt(D1**2 - 4 * L1**2)))[m1]
F2[m2] = (0.5 * _atanh(2 * L2 / _sqrt(D2**2 - 4 * L2**2)))[m2]
Ft[mt] = (Lt / At)[mt]
# Calculate conduit shape factors
SF1[m1] = (L1 / (A1 * F1))[m1]
SF2[m2] = (L2 / (A2 * F2))[m2]
SFt[mt] = (Lt / (At * Ft))[mt]
_np.warnings.filterwarnings('default', category=RuntimeWarning)
return {'pore1': SF1, 'throat': SFt, 'pore2': SF2}
def RMSE(p1, p2):
return _sqrt(MSE(p1, p2))
'value': 0.11,
'units': None,
'symbol': symbols(r'\alpha_s', positive=True)
}
αem = {
'value': 1.0 / 137.0,
'units': None,
'symbol': symbols(r'\alpha_{e}', positive=True)
}
cW = {
'value': mW['value'] / mZ['value'],
'units': 'GeV',
'symbol': symbols('c_W', real=True)
}
sW = {
'value': _sqrt(1 - cW['value']**2),
'units': 'GeV',
'symbol': symbols('s_W', real=True)
}
g = {
'value': 2 * (mW['value'] / SMvev['value']),
'unit': None,
'symbol': symbols('g', real=True)
}
ge = {
'value': _sqrt(4 * _pi * αem['value']),
'unit': None,
'symbol': symbols('g_e', real=True)
}
gw = {
'value': ge['value'] / sW['value'],