def _makeMapObjects(self):
if self.map is None:
self.map = InterpolatingFunction(
(self.x_axis, self.y_axis, self.z_axis), self.data, 0.)
self.map_gx = self.map.derivative(0)
self.map_gy = self.map.derivative(1)
self.map_gz = self.map.derivative(2)
def smooth_function_from_coordinates(
x,
y, # coordinates of some curve
sample_fraction=1.0, # fraction of x,y points used for resampling
spline_smoothing=4, # degree of spline (1 gives piecewise linear)
):
"""
Given a set of coordinates in the `x` and `y` arrays, create a
smooth function from these coordinates by 1) resampling n
uniformly distributed points by linear interpolation of the `x`
and `y` coordinates, where n is given by `sample_fraction` times
the length of `x`; and 2) interpolating the resampled points by
a smooth spline, where `spline_smoothing` is an integer holding
the degree of the piecewise polynomial pieces of the spline
(0 and 1 gives a piecewise linear function, 2 and higher gives
splines of that order). Return the smooth function as a
Python function of x, together with the (uniformly distributed)
resampled points on which the smooth function is based.
"""
# Construct linear interpolator of data points
from Scientific.Functions.Interpolation \
import InterpolatingFunction
linear = InterpolatingFunction([x], y)
# Resample
xp = np.linspace(x[0], x[-1], sample_fraction * len(x))
yp = np.array([linear(xi) for xi in xp])
# Spline smoothing or linear interpolation, based on (xp,yp)
if spline_smoothing >= 2:
from scipy.interpolate import UnivariateSpline as Spline
function = Spline(xp, yp, s=0, k=spline_smoothing)
else:
function = InterpolatingFunction([xp], yp)
return function, xp, yp
def findAlphaBeta(self):
if self.res_shells is None:
return
p = self.model_amplitudes*self.exp_amplitudes/self.epsilon
t = None
alpha = []
beta = []
for rsc, rsa in self.res_shells:
a = b = c = d = 0.
tw = len(rsc) + 2.*len(rsa)
for ri in rsc:
a += self.model_amplitudes[ri]**2/self.epsilon[ri]
b += self.exp_amplitudes[ri]**2/self.epsilon[ri]
c += p[ri]
d += p[ri]*p[ri]
for ri in rsa:
a += 2.*self.model_amplitudes[ri]**2/self.epsilon[ri]
b += 2.*self.exp_amplitudes[ri]**2/self.epsilon[ri]
c += 2.*p[ri]
d += 2.*p[ri]*p[ri]
a /= tw
b /= tw
c /= tw
d /= tw
if d < a*b:
t = 0.
else:
def g(t):
return N.sqrt(1.+4.*a*b*t*t)-2.*t*_l(t, p, rsc, rsa)-1.
if t is None:
t = 1.
while g(t) > 0.:
t = t/2.
t1 = t
while g(t) < 0.:
t = 2.*t
t2 = t
g1 = g(t1)
g2 = g(t2)
while t2-t1 > 1.e-3*t1:
t = t1-g1*(t2-t1)/(g2-g1)
gt = g(t)
if gt == 0.:
break
elif gt < 0:
t1 = t
g1 = gt
else:
t2 = t
g2 = gt
s = N.sqrt(1.+4.*a*b*t*t)
v = N.sqrt((s-1)/(2*a))
u = N.sqrt((s+1)/(2*b))
alpha.append(v/u)
beta.append(1./(u*u))
self.alpha = InterpolatingFunction((self.ssq_av_shell,),
N.array([alpha[0]]+alpha+[alpha[-1]]))
self.beta = InterpolatingFunction((self.ssq_av_shell,),
N.array([beta[0]]+beta+[beta[-1]]))
def Integrate(xdata,ydata):
x_array=Numeric.array(xdata)
y_array=Numeric.array(ydata)
# Create the interpolating function
f = InterpolatingFunction((x_array,), y_array)
f_integral=f.definiteIntegral()
return f_integral
def correlation(self, nsteps):
"""Return the autocorrelation function of the process (as estimated
from the AR model) up to |nsteps| times the sampling interval.
"""
poles = self.poles()
cpoles = N.conjugate(poles)
x = 0.
exponents = N.arange(self.order - 1, nsteps + self.order - 1)
for i in range(len(poles)):
pole = poles[i]
factor = N.multiply.reduce((pole-poles)[:i]) * \
N.multiply.reduce((pole-poles)[i+1:]) * \
N.multiply.reduce((pole-1./cpoles))
try:
x = x + pole**exponents / factor
except OverflowError:
# happens with some Python versions on some systems
power = N.zeros(exponents.shape, N.Complex)
for i in range(len(exponents)):
try:
power[i] = pole**exponents[i]
except ValueError:
pass
x = x + power / factor
cf = -self.sigsq * x / N.conjugate(self.coeff[0])
if not isComplex(self.coeff):
cf = realPart(cf)
return InterpolatingFunction((self.delta_t * N.arange(nsteps), ), cf)
def staticStructureFactor(self,
q_range=(1., 15.),
subset=None,
weights=None,
random_vectors=15,
first_mode=6):
"""
:param q_range: the range of angular wavenumber values
:type q_range: tuple
:param subset: the subset of the universe used in the calculation
(default: the whole universe)
:type subset: :class:~MMTK.Collections.GroupOfAtoms
:param weights: the weight to be given to each atom in the average
(default: coherent scattering lengths)
:type weights: :class:~MMTK.ParticleProperties.ParticleScalar
:param random_vectors: the number of random direction vectors
used in the orientational average
:type random_vectors: int
:param first_mode: the first mode to be taken into account for
the fluctuation calculation. The default value
of 6 is right for molecules in vacuum.
:type first_mode: int
:returns: the Static Structure Factor as a
function of angular wavenumber
:rtype: Scientific.Functions.Interpolation.InterpolatingFunction
"""
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.getParticleScalar('b_coherent')
mask = subset.booleanMask()
weights = N.repeat(weights.array, mask.array)
weights = weights / N.sqrt(N.add.reduce(weights * weights))
friction = N.repeat(self.friction.array, mask.array)
r = N.repeat(self.universe.configuration().array, mask.array)
first, last, step = (q_range + (None, ))[:3]
if step is None:
step = (last - first) / 50.
q = N.arange(first, last, step)
kT = Units.k_B * self.temperature
natoms = subset.numberOfAtoms()
sq = 0.
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
sab = N.zeros((natoms, natoms), N.Float)
for i in range(first_mode, self.nmodes):
irt = self.rawMode(i).inv_relaxation_time
d = N.repeat((self.rawMode(i)*v).array, mask.array) \
/ N.sqrt(friction)
sab = sab + (d[N.NewAxis, :] - d[:, N.NewAxis])**2 / irt
sab = sab[N.NewAxis, :, :] * q[:, N.NewAxis, N.NewAxis]**2
phase = N.exp(-1.j*q[:, N.NewAxis]
* N.dot(r, v.array)[N.NewAxis, :]) \
* weights[N.NewAxis, :]
temp = N.sum(phase[:, :, N.NewAxis] * N.exp(-0.5 * kT * sab), 1)
temp = N.sum(N.conjugate(phase) * temp, 1)
sq = sq + temp.real
return InterpolatingFunction((q, ), sq / len(random_vectors))
def EISF(self,
q_range=(0., 15.),
subset=None,
weights=None,
random_vectors=15,
first_mode=6):
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.getParticleScalar('b_incoherent')
weights = weights * weights
weights = weights * subset.booleanMask()
total = weights.sumOverParticles()
weights = weights / total
first, last, step = (q_range + (None, ))[:3]
if step is None:
step = (last - first) / 50.
q = N.arange(first, last, step)
f = ParticleProperties.ParticleTensor(self.universe)
for i in range(first_mode, self.nmodes):
mode = self.rawMode(i)
f = f + (1. / mode.inv_relaxation_time) * mode.dyadicProduct(mode)
f = Units.k_B * self.temperature * f / self.friction
eisf = N.zeros(q.shape, N.Float)
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
for a in subset.atomList():
exp = N.exp(-v * (f[a] * v))
N.add(eisf, weights[a] * exp**(q * q), eisf)
return InterpolatingFunction((q, ), eisf / len(random_vectors))
def __init__(self, data):
self.data = data # (x,y,f) data for an f(x,y) function
from Scientific.Functions.Interpolation \
import InterpolatingFunction # from ScientificPython
self.interpolating_function = \
InterpolatingFunction(self.data[:-1], self.data[-1])
self.ndims = len(self.data[:-1]) # no of spatial dim.
def correlation(self, nsteps):
"""
@param nsteps: the number of time steps for which the autocorrelation
function is to be evaluated
@type nsteps: C{int}
@returns: the autocorrelation function of the process as estimated
from the AR model
@rtype: L{Scientific.Functions.Interpolation.InterpolatingFunction}
"""
poles = self.poles()
cpoles = N.conjugate(poles)
x = 0.
exponents = N.arange(self.order - 1, nsteps + self.order - 1)
for i in range(len(poles)):
pole = poles[i]
factor = N.multiply.reduce((pole-poles)[:i]) * \
N.multiply.reduce((pole-poles)[i+1:]) * \
N.multiply.reduce((pole-1./cpoles))
try:
x = x + pole**exponents / factor
except OverflowError:
# happens with some Python versions on some systems
power = N.zeros(exponents.shape, N.Complex)
for i in range(len(exponents)):
try:
power[i] = pole**exponents[i]
except ValueError:
pass
x = x + power / factor
cf = -self.sigsq * x / N.conjugate(self.coeff[0])
if not _isComplex(self.coeff):
cf = _realPart(cf)
return InterpolatingFunction((self.delta_t * N.arange(nsteps), ), cf)
def meanSquareDisplacement(self,
subset=None,
weights=None,
time_range=(0., None, None),
first_mode=6):
"""Returns the averaged mean-square displacement of the
atoms in |subset| (default: all atoms) at time points
defined by |time_range| using |weights| in the average
(default: masses). |time_range| is a three element tuple
(first, last, step). The defaults are first=0., last=
three times the longest relaxation time, and step defined
such that 300 points are used in total.
"""
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.masses()
weights = weights * subset.booleanMask()
total = weights.sumOverParticles()
weights = weights / (total * self.friction)
first, last, step = (time_range + (None, None))[:3]
if last is None:
last = 3. / self.rawMode(first_mode).inv_relaxation_time
if step is None:
step = (last - first) / 300.
time = N.arange(first, last, step)
msd = N.zeros(time.shape, N.Float)
for i in range(first_mode, self.nmodes):
mode = self.rawMode(i)
rt = mode.inv_relaxation_time
d = (weights * (mode * mode)).sumOverParticles()
N.add(msd, d * (1. - N.exp(-rt * time)) / rt, msd)
N.multiply(msd, 2. * Units.k_B * self.temperature, msd)
return InterpolatingFunction((time, ), msd)
def spectrum(self, omega):
"""Return the frequency spectrum of the process at the
angular frequencies |omega| (an array).
"""
sum = 1.
for i in range(1, len(self.coeff) + 1):
sum = sum - self.coeff[-i] * N.exp(-1j * i * self.delta_t * omega)
s = 0.5 * self.delta_t * self.sigsq / (sum * N.conjugate(sum)).real
return InterpolatingFunction((omega, ), s)
def memoryFunction(self, nsteps):
"""Return the memory function corresponding to the autocorrelation
function of the process up to |nsteps| times the sampling interval.
"""
mz = self.memoryFunctionZapprox(nsteps + self.order)
mem = mz.divide(nsteps - 1)[0].coeff[::-1]
if len(mem) == nsteps + 1:
mem = mem[1:]
mem[0] = 2. * realPart(mem[0])
time = self.delta_t * N.arange(nsteps)
return InterpolatingFunction((time, ), mem)
def EISF(self,
q_range=(0., 15.),
subset=None,
weights=None,
random_vectors=15,
first_mode=6):
"""
:param q_range: the range of angular wavenumber values
:type q_range: tuple
:param subset: the subset of the universe used in the calculation
(default: the whole universe)
:type subset: :class:~MMTK.Collections.GroupOfAtoms
:param weights: the weight to be given to each atom in the average
(default: incoherent scattering lengths)
:type weights: :class:~MMTK.ParticleProperties.ParticleScalar
:param random_vectors: the number of random direction vectors
used in the orientational average
:type random_vectors: int
:param first_mode: the first mode to be taken into account for
the fluctuation calculation. The default value
of 6 is right for molecules in vacuum.
:type first_mode: int
:returns: the Elastic Incoherent Structure Factor (EISF) as a
function of angular wavenumber
:rtype: Scientific.Functions.Interpolation.InterpolatingFunction
"""
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.getParticleScalar('b_incoherent')
weights = weights * weights
weights = weights * subset.booleanMask()
total = weights.sumOverParticles()
weights = weights / total
first, last, step = (q_range + (None, ))[:3]
if step is None:
step = (last - first) / 50.
q = N.arange(first, last, step)
f = ParticleProperties.ParticleTensor(self.universe)
for i in range(first_mode, self.nmodes):
mode = self.rawMode(i)
f = f + (1. / mode.inv_relaxation_time) * mode.dyadicProduct(mode)
f = Units.k_B * self.temperature * f / self.friction
eisf = N.zeros(q.shape, N.Float)
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
for a in subset.atomList():
exp = N.exp(-v * (f[a] * v))
N.add(eisf, weights[a] * exp**(q * q), eisf)
return InterpolatingFunction((q, ), eisf / len(random_vectors))
def spectrum(self, omega):
"""
@param omega: the angular frequencies at which the spectrum
is to be evaluated
@type omega: C{Numeric.array} of C{float}
@returns: the frequency spectrum of the process
@rtype: C{Numeric.array} of C{float}
"""
sum = 1.
for i in range(1, len(self.coeff) + 1):
sum = sum - self.coeff[-i] * N.exp(-1j * i * self.delta_t * omega)
s = 0.5 * self.delta_t * self.sigsq / (sum * N.conjugate(sum)).real
return InterpolatingFunction((omega, ), s)
def memoryFunction(self, nsteps):
mz = self.memoryFunctionZ()
mem = mz.divide(nsteps - 1)[0].coeff[:]
mem.reverse()
if len(mem) == nsteps + 1:
mem = mem[1:]
if isComplex(self.coeff[0]):
mem = N.array([complex(m.real, m.imag) for m in mem])
else:
mem = N.array([float(m) for m in mem])
mem[0] = 2. * realPart(mem[0])
time = self.delta_t * N.arange(nsteps)
return InterpolatingFunction((time, ), mem)
def meanSquareDisplacement(self,
subset=None,
weights=None,
time_range=(0., None, None),
first_mode=6):
"""
:param subset: the subset of the universe used in the calculation
(default: the whole universe)
:type subset: :class:~MMTK.Collections.GroupOfAtoms
:param weights: the weight to be given to each atom in the average
(default: atomic masses)
:type weights: :class:~MMTK.ParticleProperties.ParticleScalar
:param time_range: the time values at which the mean-square
displacement is evaluated, specified as a
range tuple (first, last, step).
The defaults are first=0, last=
20 times the longest vibration perdiod,
and step defined such that 300 points are
used in total.
:type time_range: tuple
:param first_mode: the first mode to be taken into account for
the fluctuation calculation. The default value
of 6 is right for molecules in vacuum.
:type first_mode: int
:returns: the averaged mean-square displacement of the
atoms in subset as a function of time
:rtype: Scientific.Functions.Interpolation.InterpolatingFunction
"""
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.masses()
weights = weights * subset.booleanMask()
total = weights.sumOverParticles()
weights = weights / (total * self.friction)
first, last, step = (time_range + (None, None))[:3]
if last is None:
last = 3. / self.rawMode(first_mode).inv_relaxation_time
if step is None:
step = (last - first) / 300.
time = N.arange(first, last, step)
msd = N.zeros(time.shape, N.Float)
for i in range(first_mode, self.nmodes):
mode = self.rawMode(i)
rt = mode.inv_relaxation_time
d = (weights * (mode * mode)).sumOverParticles()
N.add(msd, d * (1. - N.exp(-rt * time)) / rt, msd)
N.multiply(msd, 2. * Units.k_B * self.temperature, msd)
return InterpolatingFunction((time, ), msd)
def memoryFunction(self, nsteps):
"""
@param nsteps: the number of time steps for which the memory
function is to be evaluated
@type nsteps: C{int}
@returns: the memory function of the process as estimated
from the AR model
@rtype: L{Scientific.Functions.Interpolation.InterpolatingFunction}
"""
mz = self.memoryFunctionZapprox(nsteps + self.order)
mem = mz.divide(nsteps - 1)[0].coeff[::-1]
if len(mem) == nsteps + 1:
mem = mem[1:]
mem[0] = 2. * _realPart(mem[0])
time = self.delta_t * N.arange(nsteps)
return InterpolatingFunction((time, ), mem)
def coherentScatteringFunction(self,
q,
time_range=(0., None, None),
subset=None,
weights=None,
random_vectors=15,
first_mode=6):
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.getParticleScalar('b_coherent')
mask = subset.booleanMask()
weights = N.repeat(weights.array, mask.array)
weights = weights / N.sqrt(N.add.reduce(weights * weights))
friction = N.repeat(self.friction.array, mask.array)
r = N.repeat(self.universe.configuration().array, mask.array)
first, last, step = (time_range + (None, None))[:3]
if last is None:
last = 3. / self.rawMode(first_mode).inv_relaxation_time
if step is None:
step = (last - first) / 300.
time = N.arange(first, last, step)
natoms = subset.numberOfAtoms()
kT = Units.k_B * self.temperature
fcoh = N.zeros((len(time), ), N.Complex)
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
phase = N.exp(-1.j * q * N.dot(r, v.array))
for ai in range(natoms):
fbt = N.zeros((natoms, len(time)), N.Float)
for i in range(first_mode, self.nmodes):
irt = self.rawMode(i).inv_relaxation_time
d = q * N.repeat((self.rawMode(i)*v).array, mask.array) \
/ N.sqrt(friction)
ft = N.exp(-irt * time) / irt
N.add(fbt, d[ai] * d[:, N.NewAxis] * ft[N.NewAxis, :], fbt)
N.add(fbt, (-0.5 / irt) * (d[ai]**2 + d[:, N.NewAxis]**2),
fbt)
N.add(
fcoh, weights[ai] * phase[ai] *
N.dot(weights * N.conjugate(phase), N.exp(kT * fbt)), fcoh)
return InterpolatingFunction((time, ), fcoh.real / len(random_vectors))
def incoherentScatteringFunction(self,
q,
time_range=(0., None, None),
subset=None,
random_vectors=15,
first_mode=6):
if subset is None:
subset = self.universe
mask = subset.booleanMask()
weights_inc = self.universe.getParticleScalar('b_incoherent')
weights_inc = N.repeat(weights_inc.array**2, mask.array)
weights_inc = weights_inc / N.add.reduce(weights_inc)
friction = N.repeat(self.friction.array, mask.array)
mass = N.repeat(self.universe.masses().array, mask.array)
r = N.repeat(self.universe.configuration().array, mask.array)
first, last, step = (time_range + (None, None))[:3]
if last is None:
last = 3. / self.weighedMode(first_mode).inv_relaxation_time
if step is None:
step = (last - first) / 300.
time = N.arange(first, last, step)
natoms = subset.numberOfAtoms()
kT = Units.k_B * self.temperature
finc = N.zeros((len(time), ), N.Float)
eisf = 0.
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
phase = N.exp(-1.j * q * N.dot(r, v.array))
faat = N.zeros((natoms, len(time)), N.Float)
eisf_sum = N.zeros((natoms, ), N.Float)
for i in range(first_mode, self.nmodes):
irt = self.rawMode(i).inv_relaxation_time
d = q * N.repeat((self.rawMode(i)*v).array, mask.array) \
/ N.sqrt(friction)
ft = (N.exp(-irt * time) - 1.) / irt
N.add(faat, d[:, N.NewAxis]**2 * ft[N.NewAxis, :], faat)
N.add(eisf_sum, -d**2 / irt, eisf_sum)
N.add(finc, N.sum(weights_inc[:, N.NewAxis] * N.exp(kT * faat), 0),
finc)
eisf = eisf + N.sum(weights_inc * N.exp(kT * eisf_sum))
return InterpolatingFunction((time, ), finc / len(random_vectors))
def staticStructureFactor(self,
q_range=(1., 15.),
subset=None,
weights=None,
random_vectors=15,
first_mode=6):
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.getParticleScalar('b_coherent')
mask = subset.booleanMask()
weights = N.repeat(weights.array, mask.array)
weights = weights / N.sqrt(N.add.reduce(weights * weights))
friction = N.repeat(self.friction.array, mask.array)
r = N.repeat(self.universe.configuration().array, mask.array)
first, last, step = (q_range + (None, ))[:3]
if step is None:
step = (last - first) / 50.
q = N.arange(first, last, step)
kT = Units.k_B * self.temperature
natoms = subset.numberOfAtoms()
sq = 0.
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
sab = N.zeros((natoms, natoms), N.Float)
for i in range(first_mode, self.nmodes):
irt = self.rawMode(i).inv_relaxation_time
d = N.repeat((self.rawMode(i)*v).array, mask.array) \
/ N.sqrt(friction)
sab = sab + (d[N.NewAxis, :] - d[:, N.NewAxis])**2 / irt
sab = sab[N.NewAxis, :, :] * q[:, N.NewAxis, N.NewAxis]**2
phase = N.exp(-1.j*q[:, N.NewAxis]
* N.dot(r, v.array)[N.NewAxis, :]) \
* weights[N.NewAxis, :]
temp = N.sum(phase[:, :, N.NewAxis] * N.exp(-0.5 * kT * sab), 1)
temp = N.sum(N.conjugate(phase) * temp, 1)
sq = sq + temp.real
return InterpolatingFunction((q, ), sq / len(random_vectors))
from Gnuplot import plot
from RandomArray import random
dt = 1.
t = dt * N.arange(500)
if 1:
data = N.sin(t) + N.cos(3. * t) + 0.1 * (random(len(t)) - 0.5)
data = data + 0.1j * (random(len(t)) - 0.5)
if 0:
data = [0.]
for i in range(500 + len(t) - 1):
data.append(mean(data[-500:]) + gaussian(0., 0.1))
data = N.exp(1j * N.array(data[500:]))
if 0:
#data = readArray('~/scientific/Test/data')
string = open('/users1/hinsen/scientific/Test/data').read()[4:]
data = N.array(eval(string))
data = data[:, 0]
model = AutoRegressiveModel(20, data, dt)
print model.coeff
print model.poles()
c = model.correlation(200)
cref = InterpolatingFunction((t, ), AutoCorrelationFunction(data))[:200]
m = model.memoryFunction(200)
s = model.spectrum(N.arange(0., 5., 0.01))
#plot(c.real, cref.real); plot(c.imag, cref.imag)
print model.frictionConstant(), model.memoryFunctionZ()(
1.), m.definiteIntegral()
#plot(m.real, m.imag)
plot(m)
x = D(10, index=0, order=2)
y = D(0, index=1, order=2)
z = D(1, index=2, order=2)
r = somefunc(x, y, z)
print r
# (40, [3, -1, 20], [[0, 0, 0], [0, 0, 0], [0, 0, 20]])
print "d^2(somefunc)/dzdx:", r[2][2][0] # 0
print "d^2(somefunc)/dz^2:", r[2][2][2] # 20
print "\n\ntesting interpolation:"
from Scientific.Functions.Interpolation \
import InterpolatingFunction as Ip
t = sequence(0, 10, 0.1)
v = sin(t)
vi = Ip((t, ), v)
# interpolate and compare with exact result:
print "interpolated:", vi(5.05), " exact:", sin(5.05)
# interpolate the derivative of v:
vid = vi.derivative()
print "interpolated derivative:", vid(5.05), " exact:", cos(5.05)
# compute the integral of v over all t values:
print "definite integral:", vi.definiteIntegral(), \
" exact:", -cos(t[-1]) - (-cos(t[0]))
# add path to Grid2D:
sys.path.insert(0,
os.path.join(os.environ['scripting'], 'src', 'py', 'examples'))
from Grid2D import Grid2D
g = Grid2D(dx=0.1, dy=0.2)
f = g('sin(pi*x)*sin(pi*y)')
class EventDamageModel:
"""
Object for working out the damage and cost
"""
STRUCT_LOSS_TITLE = "STRUCT_LOSS_$" #"Structure Loss ($)"
CONTENTS_LOSS_TITLE = "CONTENTS_LOSS_$" #"Contents Loss ($)"
CONTENTS_DAMAGE_TITLE = "CONTENTS_DAMAGE_fraction" #"Contents damaged (fraction)"
STRUCT_DAMAGE_TITLE = "STRUCT_DAMAGE_fraction" #"Structure damaged (fraction)"
COLLAPSE_CSV_INFO_TITLE = "COLLAPSE_CSV_INFO" #"Calculation notes"
MAX_DEPTH_TITLE = "MAX_DEPTH_m" #"Inundation height above ground floor (m)"
STRUCT_COLLAPSED_TITLE = "STRUCT_COLLAPSED" #"collapsed structure if 1"
STRUCT_INUNDATED_TITLE = "STRUCT_INUNDATED" #"inundated structure if 1"
double_brick_damage_array = num.array(
[ #[-kinds.default_float_kind.MAX, 0.0],
[-1000.0, 0.0], [0.0 - depth_epsilon, 0.0], [0.0, 0.016],
[0.1, 0.150], [0.3, 0.425], [0.5, 0.449], [1.0, 0.572],
[1.5, 0.582], [2.0, 0.587], [2.5, 0.647], [1000.0, 64.7]
#[kinds.default_float_kind.MAX,64.7]
])
if scipy_available:
double_brick_damage_curve = interp1d(double_brick_damage_array[:, 0],
double_brick_damage_array[:, 1])
else:
double_brick_damage_curve = InterpolatingFunction( \
(num.ravel(double_brick_damage_array[:,0:1]),),
num.ravel(double_brick_damage_array[:,1:]))
brick_veeer_damage_array = num.array(
[ #[-kinds.default_float_kind.MAX, 0.0],
[-1000.0, 0.0], [0.0 - depth_epsilon, 0.0], [0.0, 0.016],
[0.1, 0.169], [0.3, 0.445], [0.5, 0.472], [1.0, 0.618],
[1.5, 0.629], [2.0, 0.633], [2.5, 0.694], [1000.0, 69.4]
#[kinds.default_float_kind.MAX,69.4]
])
if scipy_available:
brick_veeer_damage_curve = interp1d(brick_veeer_damage_array[:, 0],
brick_veeer_damage_array[:, 1])
else:
brick_veeer_damage_curve = InterpolatingFunction( \
(num.ravel(brick_veeer_damage_array[:,0:1]),),
num.ravel(brick_veeer_damage_array[:,1:]))
struct_damage_curve = {
'Double Brick': double_brick_damage_curve,
'Brick Veneer': brick_veeer_damage_curve
}
default_struct_damage_curve = brick_veeer_damage_curve
contents_damage_array = num.array([ #[-kinds.default_float_kind.MAX, 0.0],
[-1000.0, 0.0], [0.0 - depth_epsilon, 0.0], [0.0, 0.013], [0.1, 0.102],
[0.3, 0.381], [0.5, 0.500], [1.0, 0.970], [1.5, 0.976], [2.0, 0.986],
[1000.0, 98.6]
#[kinds.default_float_kind.MAX,98.6]
])
if scipy_available:
contents_damage_curve = interp1d(contents_damage_array[:, 0],
contents_damage_array[:, 1])
else:
contents_damage_curve = InterpolatingFunction( \
(num.ravel(contents_damage_array[:,0:1]),),
num.ravel(contents_damage_array[:,1:]))
#building collapse probability
# inundation depth above ground floor, m
depth_upper_limits = [
depth_epsilon, 1.0, 2.0, 3.0, 5.0, kinds.default_float_kind.MAX
]
# shore mistance, m
shore_upper_limits = [125, 200, 250, kinds.default_float_kind.MAX]
# Building collapse probability
collapse_probability = [
[0.0, 0.0, 0.0, 0.0], #Code below assumes 0.0
[0.05, 0.02, 0.01, 0.0],
[0.6, 0.3, 0.1, 0.05],
[0.8, 0.4, 0.25, 0.15],
[0.95, 0.7, 0.5, 0.3],
[0.99, 0.9, 0.65, 0.45]
]
def __init__(self, max_depths, shore_distances, walls, struct_costs,
content_costs):
"""
max depth is Inundation height above ground floor (m), so
the ground floor has been taken into account.
"""
self.max_depths = [float(x) for x in max_depths]
self.shore_distances = [float(x) for x in shore_distances]
self.walls = walls
self.struct_costs = [float(x) for x in struct_costs]
self.content_costs = [float(x) for x in content_costs]
self.structure_count = len(self.max_depths)
#Fixme expand
assert self.structure_count == len(self.shore_distances)
assert self.structure_count == len(self.walls)
assert self.structure_count == len(self.struct_costs)
assert self.structure_count == len(self.content_costs)
#assert self.structure_count == len(self.)
def calc_damage_and_costs(self, verbose_csv=False, verbose=False):
"""
This is an overall method to calculate the % damage and collapsed
structures and then the $ loss.
"""
self.calc_damage_percentages()
collapse_probability = self.calc_collapse_probability()
self._calc_collapse_structures(collapse_probability,
verbose_csv=verbose_csv)
self.calc_cost()
results_dict = {
self.STRUCT_LOSS_TITLE: self.struct_loss,
self.STRUCT_DAMAGE_TITLE: self.struct_damage,
self.CONTENTS_LOSS_TITLE: self.contents_loss,
self.CONTENTS_DAMAGE_TITLE: self.contents_damage,
self.MAX_DEPTH_TITLE: self.max_depths,
self.STRUCT_COLLAPSED_TITLE: self.struct_collapsed,
self.STRUCT_INUNDATED_TITLE: self.struct_inundated
}
if verbose_csv:
results_dict[self.COLLAPSE_CSV_INFO_TITLE] = self.collapse_csv_info
return results_dict
def calc_damage_percentages(self):
"""
Using stage curves calc the damage to structures and contents
"""
# the data being created
struct_damage = num.zeros(self.structure_count, num.float)
contents_damage = num.zeros(self.structure_count, num.float)
self.struct_inundated = [''] * self.structure_count
for i, max_depth, shore_distance, wall in map(
None, range(self.structure_count), self.max_depths,
self.shore_distances, self.walls):
## WARNING SKIP IF DEPTH < 0.0
if 0.0 > max_depth:
continue
# The definition of inundated is if the max_depth is > 0.0
self.struct_inundated[i] = 1.0
#calc structural damage %
damage_curve = self.struct_damage_curve.get(
wall, self.default_struct_damage_curve)
struct_damage[i] = damage_curve(max_depth)
contents_damage[i] = self.contents_damage_curve(max_depth)
self.struct_damage = struct_damage
self.contents_damage = contents_damage
def calc_cost(self):
"""
Once the damage has been calculated, determine the $ cost.
"""
# ensure_numeric does not cut it.
self.struct_loss = self.struct_damage * \
ensure_numeric(self.struct_costs)
self.contents_loss = self.contents_damage * \
ensure_numeric(self.content_costs)
def calc_collapse_probability(self):
"""
return a dict of which structures have x probability of collapse.
key is collapse probability
value is list of struct indexes with key probability of collapse
"""
# I could've done this is the calc_damage_percentages and
# Just had one loop.
# But for ease of testing and bug finding I'm seperating the loops.
# I'm make the outer loop for both of them the same though,
# so this loop can easily be folded into the other loop.
# dict of which structures have x probability of collapse.
# key of collapse probability
# value of list of struct indexes
struct_coll_prob = {}
for i, max_depth, shore_distance, wall in map(
None, range(self.structure_count), self.max_depths,
self.shore_distances, self.walls):
# WARNING ASSUMING THE FIRST BIN OF DEPTHS GIVE A ZERO PROBABILITY
depth_upper_limits = self.depth_upper_limits
shore_upper_limits = self.shore_upper_limits
collapse_probability = self.collapse_probability
if max_depth <= depth_upper_limits[0]:
continue
start = 1
for i_depth, depth_limit in enumerate(depth_upper_limits[start:]):
#Have to change i_depth so it indexes into the lists correctly
i_depth += start
if max_depth <= depth_limit:
for i_shore, shore_limit in enumerate(shore_upper_limits):
if shore_distance <= shore_limit:
coll_prob = collapse_probability[i_depth][i_shore]
if 0.0 == collapse_probability[i_depth][i_shore]:
break
struct_coll_prob.setdefault(coll_prob,
[]).append(i)
break
break
return struct_coll_prob
def _calc_collapse_structures(self,
collapse_probability,
verbose_csv=False):
"""
Given the collapse probabilities, throw the dice
and collapse some houses
"""
self.struct_collapsed = [''] * self.structure_count
if verbose_csv:
self.collapse_csv_info = [''] * self.structure_count
#for a given 'bin', work out how many houses will collapse
for probability, house_indexes in collapse_probability.iteritems():
collapse_count = round(len(house_indexes) * probability)
if verbose_csv:
for i in house_indexes:
# This could be sped up I think
self.collapse_csv_info[i] = str(probability) + ' prob.( ' \
+ str(int(collapse_count)) + ' collapsed out of ' \
+ str(len(house_indexes)) + ')'
for _ in range(int(collapse_count)):
house_index = choice(house_indexes)
self.struct_damage[house_index] = 1.0
self.contents_damage[house_index] = 1.0
house_indexes.remove(house_index)
self.struct_collapsed[house_index] = 1
class DensityMap:
def __init__(self, filename):
if filename is None:
return
filetype = os.path.splitext(filename)[1]
if filetype.lower() == '.ezd':
self.readEZD(filename)
elif filetype.lower() == '.ccp4':
self.readCCP4(filename)
else:
raise ValueError("Unknown file type %s" % filetype)
self.map = None
self.box = Box(
Vector(self.x_axis[0], self.y_axis[0], self.z_axis[0]),
Vector(self.x_axis[-1], self.y_axis[-1], self.z_axis[-1]))
self.normalize()
def readEZD(filename):
file = open(filename)
while 1:
line = file.readline()
if not line:
raise IOError, "unexpected end of file"
words = string.split(line)
if words[0] == 'MAP':
break
if words[0] == 'CELL':
cell_x, cell_y, cell_z, alpha, beta, gamma = \
map(float, words[1:])
if alpha != 90. or beta != 90. or gamma != 90.:
raise ValueError, "cell must be rectangular"
if words[0] == 'EXTENT':
self.nx, self.ny, self.nz = map(float, words[1:])
if words[0] == 'GRID':
gnx, gny, gnz = map(float, words[1:])
data = []
while 1:
line = file.readline()
if not line:
raise IOError, "unexpected end of file"
line = string.join(string.split(line, '.-'), '. -')
words = string.split(line)
if words[0] == 'END':
break
for value in map(float, words):
data.append(value)
data = N.array(data)
data.shape = (self.nz, self.ny, self.nx)
self.data = N.transpose(data)
self.x_axis = N.arange(self.nx) * (cell_x / gnx) * Units.Ang
self.y_axis = N.arange(self.ny) * (cell_y / gny) * Units.Ang
self.z_axis = N.arange(self.nz) * (cell_z / gnz) * Units.Ang
def readCCP4(self, filename):
mapfile = file(filename)
header_data = mapfile.read(1024)
NC, NR, NS, MODE, NCSTART, NRSTART, NSSTART, NX, NY, NZ, X, Y, Z, \
ALPHA, BETA, GAMMA, MAPC, MAPR, MAPS, AMIN, AMAX, AMEAN, \
ISPG, NSYMBT, LSKFLG = struct.unpack('=10l6f3l3f3l',
header_data[:4*25])
if MODE == 2:
byte_order = '='
elif MODE == 33554432:
NC, NR, NS, MODE, NCSTART, NRSTART, NSSTART, NX, NY, NZ, X, Y, Z, \
ALPHA, BETA, GAMMA, MAPC, MAPR, MAPS, AMIN, AMAX, AMEAN, \
ISPG, NSYMBT, LSKFLG = struct.unpack('>10l6f3l3f3l',
header_data[:4*25])
byte_order = '>'
if MODE == 33554432:
NC, NR, NS, MODE, NCSTART, NRSTART, NSSTART, NX, NY, NZ, \
X, Y, Z, ALPHA, BETA, GAMMA, MAPC, MAPR, MAPS, \
AMIN, AMAX, AMEAN, ISPG, NSYMBT, LSKFLG \
= struct.unpack('<10l6f3l3f3l', header_data[:4*25])
byte_order = '<'
else:
raise IOError("Not a mode 2 CCP4 map file")
symmetry_data = mapfile.read(NSYMBT)
map_data = mapfile.read(4 * NS * NR * NC)
if byte_order == '=':
array = N.fromstring(map_data, N.Float32, NC * NR * NS)
else:
array = N.zeros((NS * NR * NC, ), N.Float32)
index = 0
while len(map_data) >= 4 * 10000:
values = struct.unpack(byte_order + '10000f',
map_data[:4 * 10000])
array[index:index + 10000] = N.array(values, N.Float32)
index += 10000
map_data = map_data[4 * 10000:]
values = struct.unpack(byte_order + '%df' % (len(map_data) / 4),
map_data)
array[index:] = N.array(values, N.Float32)
del map_data
array.shape = (NS, NR, NC)
self.data = N.transpose(array)
resolution_x = X * Units.Ang / NX
resolution_y = Y * Units.Ang / NY
resolution_z = Z * Units.Ang / NZ
self.x_axis = (NCSTART + N.arange(NC)) * resolution_x
self.y_axis = (NRSTART + N.arange(NR)) * resolution_y
self.z_axis = (NSSTART + N.arange(NS)) * resolution_z
def __getitem__(self, item):
if not isinstance(item, tuple) or len(item) != 3:
raise ValueError("indexation requires three slices")
sx, sy, sz = item
if not (isinstance(sx, slice) and isinstance(sy, slice) \
and isinstance(sz, slice)):
raise ValueError("indexation requires three slices")
new_map = DensityMap(None)
new_map.data = self.data[sx, sy, sz]
new_map.x_axis = self.x_axis[sx]
new_map.y_axis = self.y_axis[sy]
new_map.z_axis = self.z_axis[sz]
new_map.map = None
new_map.box = Box(
Vector(new_map.x_axis[0], new_map.y_axis[0], new_map.z_axis[0]),
Vector(new_map.x_axis[-1], new_map.y_axis[-1], new_map.z_axis[-1]))
return new_map
def normalize(self):
self.data /= N.sum(N.ravel(self.data))
def makePositive(self):
min = N.minimum.reduce(N.ravel(self.data))
if min < 0:
nonzero_mask = self.data != 0
self.data = (self.data - min) * nonzero_mask
def _makeMapObjects(self):
if self.map is None:
self.map = InterpolatingFunction(
(self.x_axis, self.y_axis, self.z_axis), self.data, 0.)
self.map_gx = self.map.derivative(0)
self.map_gy = self.map.derivative(1)
self.map_gz = self.map.derivative(2)
def center(self):
self.map = None
x_center = N.sum(
N.ravel(self.x_axis[:, N.NewAxis, N.NewAxis] * self.data))
y_center = N.sum(
N.ravel(self.y_axis[N.NewAxis, :, N.NewAxis] * self.data))
z_center = N.sum(
N.ravel(self.z_axis[N.NewAxis, N.NewAxis, :] * self.data))
self.x_axis = self.x_axis - x_center
self.y_axis = self.y_axis - y_center
self.z_axis = self.z_axis - z_center
self.box = Box(
Vector(self.x_axis[0], self.y_axis[0], self.z_axis[0]),
Vector(self.x_axis[-1], self.y_axis[-1], self.z_axis[-1]))
def principalAxes(self):
r = self._rGrid()
cm = N.sum(N.sum(N.sum(self.data[..., N.NewAxis] * r)))
r = r - cm[N.NewAxis, N.NewAxis, N.NewAxis, :]
nx, ny, nz = self.data.shape
t = 0.
for i in range(nx): # make loops explicit to conserve memory
for j in range(ny):
for k in range(nz):
t = t + self.data[i, j, k] * r[i, j, k, N.NewAxis, :] * \
r[i, j, k, :, N.NewAxis]
ev, axes = eigenvectors(t)
return map(lambda a, b: (Vector(a), b), axes, ev)
def principalPoints(self):
(ex, vx), (ey, vy), (ez, vz) = self.principalAxes()
axes = N.array([ex.array, ey.array, ez.array])
r = self._rGrid()
cm = N.sum(N.sum(N.sum(self.data[..., N.NewAxis] * r)))
r = r - cm[N.NewAxis, N.NewAxis, N.NewAxis, :]
regions = N.greater(N.dot(r, N.transpose(axes)), 0)
regions = N.sum(N.array([[[[1, 2, 4]]]]) * regions, -1)
points = []
for i in range(8):
mask = N.equal(regions, i)
weight = N.sum(N.sum(N.sum(mask * self.data)))
cmr = N.sum(N.sum(N.sum((mask*self.data)[..., N.NewAxis]*r))) \
/ weight + cm
points.append(Vector(cmr))
return points
def overlap(self, object):
self._makeMapObjects()
sum = 0.
for a in object.atomList():
x, y, z = a.position()
sum = sum + self.map(x, y, z)
return sum
def gradient(self, object):
self._makeMapObjects()
g = ParticleVector(object.universe())
for a in object.atomList():
x, y, z = a.position()
g[a] = Vector(self.map_gx(x, y, z), self.map_gy(x, y, z),
self.map_gz(x, y, z))
return g
def atomMap(self, object, r0=0.3):
r = self._rGrid()
atom_map = N.zeros(self.data.shape, N.Float)
cutoff = 4. * r0
for a in object.atomList():
# An over-eager optimization: it should use
# an enlarged box
#if not self.box.enclosesPoint(a.position()):
# continue
ra = a.position().array
xi1 = N.sum(self.x_axis < ra[0] - cutoff)
xi2 = N.sum(self.x_axis < ra[0] + cutoff)
yi1 = N.sum(self.y_axis < ra[1] - cutoff)
yi2 = N.sum(self.y_axis < ra[1] + cutoff)
zi1 = N.sum(self.z_axis < ra[2] - cutoff)
zi2 = N.sum(self.z_axis < ra[2] + cutoff)
if xi2 > xi1 and yi2 > yi1 and zi2 > zi1:
dr = r[xi1:xi2, yi1:yi2, zi1:zi2] - \
ra[N.NewAxis, N.NewAxis, N.NewAxis, :]
w = N.exp(-0.5 * N.sum(dr**2, axis=-1) / r0**2)
lmap = atom_map[xi1:xi2, yi1:yi2, zi1:zi2]
N.add(lmap, w, lmap)
N.divide(atom_map, N.sum(N.sum(N.sum(atom_map))), atom_map)
return atom_map
def fit(self, object, r0=0.4, w_neg=1.):
diff = self.atomMap(object, r0) - self.data
N.multiply(diff, 1. + (w_neg - 1.) * N.less(diff, 0.), diff)
return N.sum(N.sum(N.sum(diff**2)))
def fitWithGradient(self, object, r0=0.4, w_neg=1.):
r = self._rGrid()
atom_map = N.zeros(self.data.shape, N.Float)
cutoff = 4. * r0
for a in object.atomList():
ra = a.position().array
xi1 = N.sum(self.x_axis < ra[0] - cutoff)
xi2 = N.sum(self.x_axis < ra[0] + cutoff)
yi1 = N.sum(self.y_axis < ra[1] - cutoff)
yi2 = N.sum(self.y_axis < ra[1] + cutoff)
zi1 = N.sum(self.z_axis < ra[2] - cutoff)
zi2 = N.sum(self.z_axis < ra[2] + cutoff)
if xi2 > xi1 and yi2 > yi1 and zi2 > zi1:
dr = r[xi1:xi2, yi1:yi2, zi1:zi2] - \
ra[N.NewAxis, N.NewAxis, N.NewAxis, :]
w = N.exp(-0.5 * N.sum(dr**2, axis=-1) / r0**2)
lmap = atom_map[xi1:xi2, yi1:yi2, zi1:zi2]
N.add(lmap, w, lmap)
norm_factor = 1. / N.sum(N.sum(N.sum(atom_map)))
N.multiply(atom_map, norm_factor, atom_map)
N.subtract(atom_map, self.data, atom_map)
weight = 1. + (w_neg - 1.) * N.less(atom_map, 0.)
N.multiply(atom_map, weight, atom_map)
g = ParticleVector(object.universe())
for a in object.atomList():
ra = a.position().array
xi1 = N.sum(self.x_axis < ra[0] - cutoff)
xi2 = N.sum(self.x_axis < ra[0] + cutoff)
yi1 = N.sum(self.y_axis < ra[1] - cutoff)
yi2 = N.sum(self.y_axis < ra[1] + cutoff)
zi1 = N.sum(self.z_axis < ra[2] - cutoff)
zi2 = N.sum(self.z_axis < ra[2] + cutoff)
if xi2 > xi1 and yi2 > yi1 and zi2 > zi1:
dr = r[xi1:xi2, yi1:yi2, zi1:zi2] - \
ra[N.NewAxis, N.NewAxis, N.NewAxis, :]
lmap = atom_map[xi1:xi2, yi1:yi2, zi1:zi2]
lw = weight[xi1:xi2, yi1:yi2, zi1:zi2]
w = N.exp(-0.5 * N.sum(dr**2, axis=-1) / r0**2)
v = N.sum(
N.sum(
N.sum(lmap[..., N.NewAxis] * lw[..., N.NewAxis] * dr *
w[..., N.NewAxis])))
g[a] = Vector(v)
return N.sum(N.sum(N.sum(atom_map**2))), -2 * norm_factor * g / r0**2
def _rGrid(self):
x = N.add.outer(N.add.outer(self.x_axis, 0 * self.y_axis),
0 * self.z_axis)[..., N.NewAxis]
y = N.add.outer(N.add.outer(0 * self.x_axis, self.y_axis),
0 * self.z_axis)[..., N.NewAxis]
z = N.add.outer(N.add.outer(0 * self.x_axis, 0 * self.y_axis),
self.z_axis)[..., N.NewAxis]
return N.concatenate((x, y, z), axis=-1)
def clipBelow(self, cutoff):
mask = self.clipMask(cutoff)
self.data *= mask
self.data /= N.add.reduce(N.ravel(self.data))
self.map = None
def clipAbove(self, cutoff):
mask = self.clipMask(cutoff)
self.data *= (1 - mask)
self.data /= N.add.reduce(N.ravel(self.data))
self.map = None
def clipMask(self, cutoff):
max_value = N.maximum.reduce(N.ravel(self.data))
mask = N.greater_equal(self.data, cutoff * max_value)
gradient_masks = []
for i in range(len(mask.shape)):
upper_index = i * index_expression[::] + index_expression[1::]
lower_index = i * index_expression[::] + index_expression[:-1:]
gmask1 = N.greater(self.data[upper_index], self.data[lower_index])
gmask2 = N.greater(self.data[lower_index], self.data[upper_index])
gradient_masks.append((gmask1, gmask2))
while 1:
new_mask = 0 * mask
for i in range(len(mask.shape)):
upper_index = i * index_expression[::] + index_expression[1::]
lower_index = i * index_expression[::] + index_expression[:-1:]
upper_mask, lower_mask = gradient_masks[i]
N.logical_or(new_mask[upper_index],
N.logical_and(mask[lower_index], lower_mask),
new_mask[upper_index])
N.logical_or(new_mask[lower_index],
N.logical_and(mask[upper_index], upper_mask),
new_mask[lower_index])
N.logical_and(new_mask, N.logical_not(mask), new_mask)
N.logical_or(mask, new_mask, mask)
if N.sum(N.ravel(new_mask)) == 0:
break
return mask
def dataDump(self, filename):
outfile = file(filename, 'w')
data = N.ravel(N.transpose(self.data))
data = 10000. * data / N.maximum.reduce(data)
data.shape = (len(data) / 7, 7)
for line in data:
for number in line:
outfile.write('%.1f ' % number)
outfile.write('\n')
outfile.close()
def writeVTK(self, filename):
import pyvtk
origin = N.array([self.x_axis[0], self.y_axis[0], self.z_axis[0]])
spacing = N.array([self.x_axis[1], self.y_axis[1], self.z_axis[1]]) \
- origin
values = pyvtk.Scalars(N.ravel(N.transpose(self.data)),
'electron density')
data = pyvtk.VtkData(
pyvtk.StructuredPoints(self.data.shape, origin, spacing),
'Density map', pyvtk.PointData(values))
data.tofile(filename, format='binary')
def view(self, gmodule, lower, upper, file=None):
scene = gmodule.Scene()
scale = gmodule.ColorScale(1.)
size = 0.5 * min(self.x_axis[1], self.y_axis[1], self.z_axis[1])
for i in range(self.nx):
for j in range(self.ny):
for k in range(self.nz):
value = self.data[i, j, k]
if value > lower and value < upper:
center = Vector(self.x_axis[i], self.y_axis[j],
self.z_axis[k])
m = gmodule.Material(diffuse_color=scale(value))
object = gmodule.Sphere(center, size, material=m)
scene.addObject(object)
if file is None:
scene.view()
else:
scene.writeToFile(file)
def viewVMD(self, filename=None, pdb_filename=None):
run_vmd = 0
if filename is None:
filename = tempfile.mktemp()
run_vmd = 1
file = open(filename, 'w')
if pdb_filename is not None:
file.write('mol load pdb %s\n' % pdb_filename)
file.write('mol volume top "Electron Density" \\\n')
x_origin = self.x_axis[0] / Units.Ang
y_origin = self.y_axis[0] / Units.Ang
z_origin = self.z_axis[0] / Units.Ang
x_length = self.x_axis[-1] / Units.Ang - x_origin
y_length = self.y_axis[-1] / Units.Ang - y_origin
z_length = self.z_axis[-1] / Units.Ang - z_origin
file.write(' {%f %f %f} \\\n' % (x_origin, y_origin, z_origin))
file.write(' {%f 0. 0.} \\\n' % x_length)
file.write(' {0. %f 0.} \\\n' % y_length)
file.write(' {0. 0. %f} \\\n' % z_length)
file.write(' %d %d %d \\\n' % self.data.shape)
file.write(' {')
factor = 1. / N.maximum.reduce(N.ravel(self.data))
for iz in range(self.data.shape[2]):
for iy in range(self.data.shape[1]):
for ix in range(self.data.shape[0]):
file.write(str(factor * self.data[ix, iy, iz]) + ' ')
file.write('}\n')
file.write('mol addrep top\nmol modstyle 1 top isosurface\n')
if run_vmd:
file.write('file delete %s\n' % filename)
file.close()
if run_vmd:
os.system('vmd -e ' + filename + ' 1> /dev/null 2>&1')
def writeXPlor(self, filename):
from Scientific.IO.FortranFormat import FortranFormat, FortranLine
file = open(filename, 'w')
file.write('\n 1 !NTITLE\n')
file.write('REMARKS Electronic density map\n')
data = [
self.data.shape[0], 1, self.data.shape[0], self.data.shape[1], 1,
self.data.shape[1], self.data.shape[2], 1, self.data.shape[2]
]
file.write(str(FortranLine(data, '9I8')) + '\n')
x = (self.x_axis[-1] - self.x_axis[0]) / Units.Ang
y = (self.y_axis[-1] - self.y_axis[0]) / Units.Ang
z = (self.z_axis[-1] - self.z_axis[0]) / Units.Ang
data = [x, y, z] + 3 * [90.]
file.write(str(FortranLine(data, '6E12.5')) + '\n')
file.write('ZYX\n')
map_data = N.ravel(self.data)
map_data = map_data / N.maximum.reduce(map_data)
average = N.sum(map_data) / len(map_data)
sd = N.sqrt(N.sum((map_data - average)**2) / len(map_data))
map_data.shape = self.data.shape
for i in range(self.data.shape[2]):
file.write(str(FortranLine([i], 'I8')) + '\n')
data = list(N.ravel(N.transpose(map_data[:, :, i])))
while data:
file.write(str(FortranLine(data[:6],
'%dE12.5' % min(6, len(data)))) \
+ '\n')
data = data[6:]
file.write(str(FortranLine([-9999], 'I8')) + '\n')
file.write(str(FortranLine([average, sd], '2(E12.4,1X)')) + '\n')
file.close()
x = D(10, index=0, order=2)
y = D(0, index=1, order=2)
z = D(1, index=2, order=2)
r = somefunc(x, y, z)
print r
# (40, [3, -1, 20], [[0, 0, 0], [0, 0, 0], [0, 0, 20]])
print 'd^2(somefunc)/dzdx:', r[2][2][0] # 0
print 'd^2(somefunc)/dz^2:', r[2][2][2] # 20
print '\n\ntesting interpolation:'
from Scientific.Functions.Interpolation \
import InterpolatingFunction as Ip
t = linspace(0, 10, 101)
v = sin(t)
vi = Ip((t, ), v)
# interpolate and compare with exact result:
print 'interpolated:', vi(5.05), ' exact:', sin(5.05)
# interpolate the derivative of v:
vid = vi.derivative()
print 'interpolated derivative:', vid(5.05), ' exact:', cos(5.05)
# compute the integral of v over all t values:
print 'definite integral:', vi.definiteIntegral(), \
' exact:', -cos(t[-1]) - (-cos(t[0]))
# add path to Grid2D (for testing interpolation on a 2D grid):
sys.path.insert(0,
os.path.join(os.environ['scripting'], 'src', 'py', 'examples'))
from Grid2D import Grid2D
g = Grid2D(dx=0.1, dy=0.2)
f = g(lambda x, y: sin(pi * x) * sin(pi * y))
def get_ld_grid(photband, **kwargs):
"""
Retrieve an interpolating grid for the LD coefficients
Check outcome:
#>>> bands = ['GENEVA.U', 'GENEVA.B', 'GENEVA.G', 'GENEVA.V']
#>>> f_ld_grid = get_ld_grid(bands)
#>>> ff = pyfits.open(_atmos['file'])
#>>> all(ff['GENEVA.U'].data[257][2:]==f_ld_grid(ff['GENEVA.U'].data[257][0],ff['GENEVA.U'].data[257][1])[0:5])
#True
#>>> all(ff['GENEVA.G'].data[257][2:]==f_ld_grid(ff['GENEVA.G'].data[257][0],ff['GENEVA.G'].data[257][1])[10:15])
#True
#>>> ff.close()
#Make some plots:
#>>> photband = ['GENEVA.V']
#>>> f_ld = get_ld_grid(photband)
#>>> logg = 4.0
#>>> mu = linspace(0,1,100)
#>>> p = figure()
#>>> p = gcf().canvas.set_window_title('test of function <get_ld_grid>')
#>>> for teff in linspace(9000,12000,19):
#... out = f_ld(teff,logg)
#... a1x,a2x,a3x,a4x, I_x1 = out.reshape((len(photband),5)).T
#... p = subplot(221);p = title('Interpolation of absolute intensities')
#... p = plot(teff,I_x1,'ko')
#... p = subplot(222);p = title('Interpolation of LD coefficients')
#... p = scatter(4*[teff],[a1x,a2x,a3x,a4x],c=range(4),vmin=0,vmax=3,cmap=cm.spectral,edgecolors='none')
#... p = subplot(223);p = title('Without absolute intensity')
#... p = plot(mu,ld_eval(mu,[a1x,a2x,a3x,a4x]),'-')
#... p = subplot(224);p = title('With absolute intensity')
#... p = plot(mu,I_x1*ld_eval(mu,[a1x,a2x,a3x,a4x]),'-')
"""
#-- retrieve the grid points (unique values)
teffs, loggs = get_ld_grid_dimensions(**kwargs)
teffs_grid = np.sort(np.unique1d(teffs))
loggs_grid = np.sort(np.unique1d(loggs))
coeff_grid = np.zeros(
(len(teffs_grid), len(loggs_grid), 5 * len(photband)))
#-- get the FITS-file containing the tables
gridfile = get_file(**kwargs)
#-- fill the grid
ff = pyfits.open(gridfile)
for pp, iband in enumerate(photband):
teffs = ff[iband].data.field('Teff')
loggs = ff[iband].data.field('logg')
for ii, (iteff, ilogg) in enumerate(zip(teffs, loggs)):
indext = np.searchsorted(teffs_grid, iteff)
indexg = np.searchsorted(loggs_grid, ilogg)
#-- array and list are added for backwards compatibility with some
# pyfits versions
coeff_grid[indext, indexg, 5 * pp:5 * (pp + 1)] = np.array(
list(ff[iband].data[ii]))[2:]
ff.close()
#-- make an interpolating function
f_ld_grid = InterpolatingFunction([teffs_grid, loggs_grid], coeff_grid)
return f_ld_grid
import pandas as pd
import numpy as np
from Scientific.Functions.Interpolation import InterpolatingFunction
df_EC = pd.read_csv("EC.csv")
df_DL = pd.read_csv("DL.csv")
gt = np.arange(1,4,1)
g1 = np.arange(20,55,15)
g2 = np.arange(20,55,15)
WCU = np.arange(2,7,2)
temp = df_EC.iloc[0:27]
temp2 = temp.as_matrix()
data = temp2.reshape(len(gt),len(g1),len(g2))
axes = (gt,g1,g2)
print(axes)
print(data)
f = InterpolatingFunction(axes, data)
print(f(2.5,25.5,40.5))
def incoherentScatteringFunction(self,
q,
time_range=(0., None, None),
subset=None,
random_vectors=15,
first_mode=6):
"""
:param q: the angular wavenumber
:type q: float
:param time_range: the time values at which the mean-square
displacement is evaluated, specified as a
range tuple (first, last, step).
The defaults are first=0, last=
20 times the longest vibration perdiod,
and step defined such that 300 points are
used in total.
:type time_range: tuple
:param subset: the subset of the universe used in the calculation
(default: the whole universe)
:type subset: :class:~MMTK.Collections.GroupOfAtoms
:param random_vectors: the number of random direction vectors
used in the orientational average
:type random_vectors: int
:param first_mode: the first mode to be taken into account for
the fluctuation calculation. The default value
of 6 is right for molecules in vacuum.
:type first_mode: int
:returns: the Incoherent Scattering Function as a function of time
:rtype: Scientific.Functions.Interpolation.InterpolatingFunction
"""
if subset is None:
subset = self.universe
mask = subset.booleanMask()
weights_inc = self.universe.getParticleScalar('b_incoherent')
weights_inc = N.repeat(weights_inc.array**2, mask.array)
weights_inc = weights_inc / N.add.reduce(weights_inc)
friction = N.repeat(self.friction.array, mask.array)
mass = N.repeat(self.universe.masses().array, mask.array)
r = N.repeat(self.universe.configuration().array, mask.array)
first, last, step = (time_range + (None, None))[:3]
if last is None:
last = 3. / self.weighedMode(first_mode).inv_relaxation_time
if step is None:
step = (last - first) / 300.
time = N.arange(first, last, step)
natoms = subset.numberOfAtoms()
kT = Units.k_B * self.temperature
finc = N.zeros((len(time), ), N.Float)
eisf = 0.
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
phase = N.exp(-1.j * q * N.dot(r, v.array))
faat = N.zeros((natoms, len(time)), N.Float)
eisf_sum = N.zeros((natoms, ), N.Float)
for i in range(first_mode, self.nmodes):
irt = self.rawMode(i).inv_relaxation_time
d = q * N.repeat((self.rawMode(i)*v).array, mask.array) \
/ N.sqrt(friction)
ft = (N.exp(-irt * time) - 1.) / irt
N.add(faat, d[:, N.NewAxis]**2 * ft[N.NewAxis, :], faat)
N.add(eisf_sum, -d**2 / irt, eisf_sum)
N.add(finc, N.sum(weights_inc[:, N.NewAxis] * N.exp(kT * faat), 0),
finc)
eisf = eisf + N.sum(weights_inc * N.exp(kT * eisf_sum))
return InterpolatingFunction((time, ), finc / len(random_vectors))
def coherentScatteringFunction(self,
q,
time_range=(0., None, None),
subset=None,
weights=None,
random_vectors=15,
first_mode=6):
"""
:param q: the angular wavenumber
:type q: float
:param time_range: the time values at which the mean-square
displacement is evaluated, specified as a
range tuple (first, last, step).
The defaults are first=0, last=
20 times the longest vibration perdiod,
and step defined such that 300 points are
used in total.
:type time_range: tuple
:param subset: the subset of the universe used in the calculation
(default: the whole universe)
:type subset: :class:~MMTK.Collections.GroupOfAtoms
:param weights: the weight to be given to each atom in the average
(default: coherent scattering lengths)
:type weights: :class:~MMTK.ParticleProperties.ParticleScalar
:param random_vectors: the number of random direction vectors
used in the orientational average
:type random_vectors: int
:param first_mode: the first mode to be taken into account for
the fluctuation calculation. The default value
of 6 is right for molecules in vacuum.
:type first_mode: int
:returns: the Coherent Scattering Function as a function of time
:rtype: Scientific.Functions.Interpolation.InterpolatingFunction
"""
if subset is None:
subset = self.universe
if weights is None:
weights = self.universe.getParticleScalar('b_coherent')
mask = subset.booleanMask()
weights = N.repeat(weights.array, mask.array)
weights = weights / N.sqrt(N.add.reduce(weights * weights))
friction = N.repeat(self.friction.array, mask.array)
r = N.repeat(self.universe.configuration().array, mask.array)
first, last, step = (time_range + (None, None))[:3]
if last is None:
last = 3. / self.rawMode(first_mode).inv_relaxation_time
if step is None:
step = (last - first) / 300.
time = N.arange(first, last, step)
natoms = subset.numberOfAtoms()
kT = Units.k_B * self.temperature
fcoh = N.zeros((len(time), ), N.Complex)
random_vectors = Random.randomDirections(random_vectors)
for v in random_vectors:
phase = N.exp(-1.j * q * N.dot(r, v.array))
for ai in range(natoms):
fbt = N.zeros((natoms, len(time)), N.Float)
for i in range(first_mode, self.nmodes):
irt = self.rawMode(i).inv_relaxation_time
d = q * N.repeat((self.rawMode(i)*v).array, mask.array) \
/ N.sqrt(friction)
ft = N.exp(-irt * time) / irt
N.add(fbt, d[ai] * d[:, N.NewAxis] * ft[N.NewAxis, :], fbt)
N.add(fbt, (-0.5 / irt) * (d[ai]**2 + d[:, N.NewAxis]**2),
fbt)
N.add(
fcoh, weights[ai] * phase[ai] *
N.dot(weights * N.conjugate(phase), N.exp(kT * fbt)), fcoh)
return InterpolatingFunction((time, ), fcoh.real / len(random_vectors))
x = D(10, index=0, order=2) y = D(0, index=1, order=2) z = D(1, index=2, order=2) r = somefunc(x, y, z) print r # (40, [3, -1, 20], [[0, 0, 0], [0, 0, 0], [0, 0, 20]]) print "d^2(somefunc)/dzdx:", r[2][2][0] # 0 print "d^2(somefunc)/dz^2:", r[2][2][2] # 20 print "\n\ntesting interpolation:" from Scientific.Functions.Interpolation import InterpolatingFunction as Ip t = linspace(0, 10, 101) v = sin(t) vi = Ip((t,), v) # interpolate and compare with exact result: print "interpolated:", vi(5.05), " exact:", sin(5.05) # interpolate the derivative of v: vid = vi.derivative() print "interpolated derivative:", vid(5.05), " exact:", cos(5.05) # compute the integral of v over all t values: print "definite integral:", vi.definiteIntegral(), " exact:", -cos(t[-1]) - (-cos(t[0])) # add path to Grid2D (for testing interpolation on a 2D grid): sys.path.insert(0, os.path.join(os.environ["scripting"], "src", "py", "examples")) from Grid2D import Grid2D g = Grid2D(dx=0.1, dy=0.2) f = g(lambda x, y: sin(pi * x) * sin(pi * y)) fi = Ip((g.xcoor, g.ycoor), f)
def get_grid_mesh(wave=None, teffrange=None, loggrange=None, **kwargs):
"""
Return InterpolatingFunction spanning the available grid of spectrum models.
WARNING: the grid must be entirely defined on a mesh grid, but it does not
need to be equidistant.
It is thus the user's responsibility to know whether the grid is evenly
spaced in logg and teff
You can supply your own wavelength range, since the grid models'
resolution are not necessarily homogeneous. If not, the first wavelength
array found in the grid will be used as a template.
It might take a long a time and cost a lot of memory if you load the entire
grid. Therefor, you can also set range of temperature and gravity.
@param wave: wavelength to define the grid on
@type wave: ndarray
@param teffrange: starting and ending of the grid in teff
@type teffrange: tuple of floats
@param loggrange: starting and ending of the grid in logg
@type loggrange: tuple of floats
@return: wavelengths, teffs, loggs and fluxes of grid, and the interpolating
function
@rtype: (1Darray,1Darray,1Darray,3Darray,InterpolatingFunction)
"""
#-- get the dimensions of the grid
teffs, loggs = get_grid_dimensions(**kwargs)
#-- build flux grid, assuming a perfectly sampled grid (needs not to be
# equidistant)
if teffrange is not None:
sa = (teffrange[0] <= teffs) & (teffs <= teffrange[1])
teffs = teffs[sa]
if loggrange is not None:
sa = (loggrange[0] <= loggs) & (loggs <= loggrange[1])
loggs = loggs[sa]
#-- clip if necessary
teffs = list(set(list(teffs)))
loggs = list(set(list(loggs)))
teffs = np.sort(teffs)
loggs = np.sort(loggs)
if wave is not None:
flux = np.ones((len(teffs), len(loggs), len(wave)))
cont = np.ones((len(teffs), len(loggs), len(wave)))
#-- run over teff and logg, and interpolate the models onto the supplied
# wavelength range
gridfile = get_file(**kwargs)
ff = pf.open(gridfile)
for i, teff in enumerate(teffs):
for j, logg in enumerate(loggs):
try:
mod_name = "T%05d_logg%01.02f" % (teff, logg)
mod = ff[mod_name]
wave_ = mod.data.field(
'wavelength') #array(mod.data.tolist())[:,0]
flux_ = mod.data.field('flux') #array(mod.data.tolist())[:,1]
cont_ = mod.data.field('cont') #array(mod.data.tolist())[:,1]
#-- if there is no wavelength range given, we assume that
# the whole grid has the same resolution, and the first
# wave-array will be used as a template
if wave is None:
wave = wave_
flux = np.ones((len(teffs), len(loggs), len(wave)))
cont = np.ones((len(teffs), len(loggs), len(wave)))
except KeyError:
continue
#-- it could be that we're lucky and the grid is completely
# homogeneous. In that case, there is no need for interpolation
try:
flux[i, j, :] = flux_
cont[i, j, :] = cont_
except:
flux[i, j, :] = np.interp(wave, wave_, flux_)
cont[i, j, :] = np.interp(wave, wave_, cont_)
flux_grid = InterpolatingFunction([np.log10(teffs), loggs], flux)
cont_grid = InterpolatingFunction([np.log10(teffs), loggs], cont)
#logger.info('Constructed spectrum interpolation grid')
return wave, teffs, loggs, flux, flux_grid, cont_grid
