def single_well_numerov_match(V0, dx, parity=1, overlapsize=5): "generate a candidate eigenfunction with given potential, assuming the potential well has a single allowed region bounded on both sides" assert len(V0) & 1, "Must have a grid with an odd number of points" vminchan=Numeric.argmin(V0) #position of bottom of well right_turn=Numeric.searchsorted(V0[vminchan:], 0.0)+vminchan #position of right-hand turning point #integrate from left end to right-hand turning point, at which point numerov method becomes unstable leftpsi=bare_numerov(V0[:right_turn], dx) #iterate backwards on right part to turning point, and flatten to normal array rightpsi= Numeric.array(bare_numerov(V0[right_turn-overlapsize:][::-1], dx)[::-1]) #remember that since Numeric handles slices without copying, leftend and rightend also scale here slopeweight=Numeric.array(range(overlapsize),Numeric.Float)-overlapsize/2.0 leftend=leftpsi[-overlapsize:] rightend=rightpsi[:overlapsize] scale=abs(Numeric.sum(leftend*rightend)/Numeric.sum(leftend**2)) #'least-squares' scale estimate #note that since leftend and rightend are Numeric slice references, modifying psi also changes them! rightpsi*=float(parity)/scale error=Numeric.sum((leftend-rightend)*slopeweight) #average derivative psi0=Numeric.concatenate((leftpsi, rightpsi[overlapsize:])) psi2=psi0*psi0 integral=psi2[0]+psi2[-1]+4.0*Numeric.sum(psi2[1:-1:2])+2.0*Numeric.sum(psi2[2:-2:2]) #use simpson's rule psimag=1.0/math.sqrt(integral*dx/3.0) return psi0*psimag, error*psimag
def recursive_remove_redundant_strains(self, cnd_entropy_matrix,
cnd_entropy_sum_vector,
no_of_strains_to_be_removed):
strain_to_be_deleted_index_list = []
if no_of_strains_to_be_removed > 0:
strain_to_be_deleted = num.argmin(cnd_entropy_sum_vector)
strain_to_be_deleted_index_list.append(strain_to_be_deleted)
for i in range(cnd_entropy_sum_vector.shape[0]): #remove
cnd_entropy_sum_vector[i] -= cnd_entropy_matrix[
strain_to_be_deleted, i]
cnd_entropy_sum_vector[
strain_to_be_deleted] = cnd_entropy_matrix.shape[
0] #set this deleted strain's cond entropy to maximum
no_of_strains_to_be_removed -= 1
if self.debug:
print
print 'strain_to_be_deleted:', strain_to_be_deleted
print 'strain_to_be_deleted_index_list'
print strain_to_be_deleted_index_list
print 'cnd_entropy_sum_vector'
print cnd_entropy_sum_vector
strain_to_be_deleted_index_list += self.recursive_remove_redundant_strains(
cnd_entropy_matrix, cnd_entropy_sum_vector,
no_of_strains_to_be_removed)
return strain_to_be_deleted_index_list
def input_numpy_array_output_geotiff(
self,
attribute_values_in_2d_array,
prototype_dataset=None,
format="GTiff",
output_directory=None,
output_file_name=None,
):
"""
This method accepts numpy array objects, x, y and attribute_values and converts them to a GeoTiff image.
twoD_attribute_values - 2d attribute values, could be return value from Dataset.get_2d_attribute();
prototype_dataset - prototype dataset that includes the same projection and goetransform info,
must be in a format that can be opened by gdal.Open();
format - default "GTiff" for GeoTiff format, possible options "PNG" and any other formats GDAL support;
output_directory and output_file_name indicate where to save the output,
if unspecified, save to current directory and use time stamp as file name (without file extension).
"""
import Numeric as numeric
import gdal.gdal as gdal
import gdal.gdalnumeric as gdalnumeric
driver = gdal.GetDriverByName(format)
tdata = numeric.array(attribute_values_in_2d_array.tolist())
tdata = numeric.transpose(tdata)
min_val = min(numeric.argmin(tdata))
if min_val >= 0:
null_substitute = -1
else:
null_substitute = min_val + min_val * 10
for i in range(len(tdata)):
for j in range(len(tdata[i])):
if tdata[i][j] == 999999:
tdata[i][j] = null_substitute
if prototype_dataset is not None:
imgds = gdalnumeric.OpenArray(tdata,
prototype_ds=prototype_dataset)
else:
imgds = gdalnumeric.OpenArray(tdata)
if output_directory is None:
output_directory = "."
elif not os.path.exists(output_directory):
os.mkdir(output_directory)
if output_file_name is None:
output_file_name = strftime("%Y_%m_%d_%H_%M.",
localtime()) + format.lower()
sfilename = os.path.join(output_directory, output_file_name)
#try:
imgds = driver.CreateCopy(sfilename, imgds)
def testSort (self):
"Test sort, argsort, argmax, argmin, searchsorted"
s = (3,2,5,1,4,0)
sm = [s, Numeric.array(s)[::-1]]
se = Numeric.array(s)[0:0]
assert_eq(Numeric.sort(s), self.a)
assert len(Numeric.sort(se)) == 0
assert_eq(Numeric.argsort(s), [5,3,1,0,4,2])
assert len(Numeric.argsort(se)) == 0
assert_eq(Numeric.sort(sm, axis = -1), [[0,1,2,3,4,5],[0,1,2,3,4,5]])
assert_eq(Numeric.sort(sm, axis = 0), [[0,2,1,1,2,0],[3,4,5,5,4,3]])
assert_eq(Numeric.searchsorted(Numeric.arange(10), (5,2)), [5,2])
assert Numeric.argmax(s) == 2
assert Numeric.argmin(s) == 5
assert_eq(Numeric.argmax(sm, axis=-1), [2,3])
assert_eq(Numeric.argmax(sm, axis=1), [2,3])
assert_eq(Numeric.argmax(sm, axis=0), [0,1,0,1,0,1])
assert_eq(Numeric.argmin(sm, axis=-1), [5,0])
assert_eq(Numeric.argmin(sm, axis=1), [5,0])
def input_numpy_array_output_geotiff(self, attribute_values_in_2d_array,
prototype_dataset=None,
format="GTiff",
output_directory=None,
output_file_name=None,
):
"""
This method accepts numpy array objects, x, y and attribute_values and converts them to a GeoTiff image.
twoD_attribute_values - 2d attribute values, could be return value from Dataset.get_2d_attribute();
prototype_dataset - prototype dataset that includes the same projection and goetransform info,
must be in a format that can be opened by gdal.Open();
format - default "GTiff" for GeoTiff format, possible options "PNG" and any other formats GDAL support;
output_directory and output_file_name indicate where to save the output,
if unspecified, save to current directory and use time stamp as file name (without file extension).
"""
import Numeric as numeric
import gdal.gdal as gdal
import gdal.gdalnumeric as gdalnumeric
driver = gdal.GetDriverByName(format)
tdata = numeric.array(attribute_values_in_2d_array.tolist())
tdata = numeric.transpose(tdata)
min_val = min(numeric.argmin(tdata))
if min_val >= 0:
null_substitute = -1
else:
null_substitute = min_val + min_val * 10
for i in range(len(tdata)):
for j in range(len(tdata[i])):
if tdata[i][j] == 999999:
tdata[i][j] = null_substitute
if prototype_dataset is not None:
imgds = gdalnumeric.OpenArray(tdata, prototype_ds=prototype_dataset)
else:
imgds = gdalnumeric.OpenArray(tdata)
if output_directory is None:
output_directory = "."
elif not os.path.exists(output_directory):
os.mkdir(output_directory)
if output_file_name is None:
output_file_name = strftime("%Y_%m_%d_%H_%M.", localtime()) + format.lower()
sfilename = os.path.join(output_directory, output_file_name)
#try:
imgds = driver.CreateCopy( sfilename, imgds )
def getDistance(V, X, mask):
"""
d(V, X) = (1/|X|) Sum[i = 1 to |X|]{ min[j = 1 to |V|] {|| x_i - v_j||} }
where x_i is in X and v_j is in V.
"""
min = []
sum = 0
for x in X:
for v in V:
min.append(euclideanDistance(x, v, mask))
sum += min[Numeric.argmin(min)]
return sum / len(X)
def getDistance(V, X, mask):
"""
d(V, X) = (1/|X|) Sum[i = 1 to |X|]{ min[j = 1 to |V|] {|| x_i - v_j||} }
where x_i is in X and v_j is in V.
"""
min = []
sum = 0
for x in X:
for v in V:
min.append(euclideanDistance(x,v,mask))
sum += min[Numeric.argmin(min)]
return sum / len(X)
def findTransformationAsQuaternion(self, conf1, conf2 = None):
if conf2 is None:
conf1, conf2 = conf2, conf1
ref = conf1
conf = conf2
weights = self.universe().masses()
weights = weights/self.mass()
ref_cms = self.centerOfMass(ref).array
pos = Numeric.zeros((3,), Numeric.Float)
possq = 0.
cross = Numeric.zeros((3, 3), Numeric.Float)
for a in self.atomList():
r = a.position(conf).array
r_ref = a.position(ref).array-ref_cms
w = weights[a]
pos = pos + w*r
possq = possq + w*Numeric.add.reduce(r*r) \
+ w*Numeric.add.reduce(r_ref*r_ref)
cross = cross + w*r[:, Numeric.NewAxis]*r_ref[Numeric.NewAxis, :]
k = Numeric.zeros((4, 4), Numeric.Float)
k[0, 0] = -cross[0, 0]-cross[1, 1]-cross[2, 2]
k[0, 1] = cross[1, 2]-cross[2, 1]
k[0, 2] = cross[2, 0]-cross[0, 2]
k[0, 3] = cross[0, 1]-cross[1, 0]
k[1, 1] = -cross[0, 0]+cross[1, 1]+cross[2, 2]
k[1, 2] = -cross[0, 1]-cross[1, 0]
k[1, 3] = -cross[0, 2]-cross[2, 0]
k[2, 2] = cross[0, 0]-cross[1, 1]+cross[2, 2]
k[2, 3] = -cross[1, 2]-cross[2, 1]
k[3, 3] = cross[0, 0]+cross[1, 1]-cross[2, 2]
for i in range(1, 4):
for j in range(i):
k[i, j] = k[j, i]
k = 2.*k
for i in range(4):
k[i, i] = k[i, i] + possq - Numeric.add.reduce(pos*pos)
import LinearAlgebra
e, v = LinearAlgebra.eigenvectors(k)
i = Numeric.argmin(e)
v = v[i]
if v[0] < 0: v = -v
if e[i] <= 0.:
rms = 0.
else:
rms = Numeric.sqrt(e[i])
return Quaternion.Quaternion(v), Vector(ref_cms), \
Vector(pos), rms
def recursive_remove_redundant_strains(self, cnd_entropy_matrix, cnd_entropy_sum_vector, no_of_strains_to_be_removed): strain_to_be_deleted_index_list = [] if no_of_strains_to_be_removed>0: strain_to_be_deleted = num.argmin(cnd_entropy_sum_vector) strain_to_be_deleted_index_list.append(strain_to_be_deleted) for i in range(cnd_entropy_sum_vector.shape[0]): #remove cnd_entropy_sum_vector[i] -= cnd_entropy_matrix[strain_to_be_deleted,i] cnd_entropy_sum_vector[strain_to_be_deleted] = cnd_entropy_matrix.shape[0] #set this deleted strain's cond entropy to maximum no_of_strains_to_be_removed -= 1 if self.debug: print print 'strain_to_be_deleted:', strain_to_be_deleted print 'strain_to_be_deleted_index_list' print strain_to_be_deleted_index_list print 'cnd_entropy_sum_vector' print cnd_entropy_sum_vector strain_to_be_deleted_index_list += self.recursive_remove_redundant_strains(cnd_entropy_matrix, cnd_entropy_sum_vector, no_of_strains_to_be_removed) return strain_to_be_deleted_index_list
def updateWinner(self):
"""
Calculate the current winner based on which model vector is
closest to the moving average.
"""
min = []
for m in self.models:
min.append(euclideanDistance(m.vector, self.movingAverage, self.mask))
if min == []:
self.winner = 'No Winner'
else:
self.previousWinnerIndex= self.newWinnerIndex
self.newWinnerIndex = Numeric.argmin(min)
if self.previousWinnerIndex == self.newWinnerIndex:
self.winnerCount += 1
else:
self.winnerCount = 0
winner = self.models[self.newWinnerIndex]
winner.counter += 1
#if winner.maxSize != -1:
winner.addItem(self.buffer[0])
self.winner = winner.vector
def updateWinner(self):
"""
Calculate the current winner based on which model vector is
closest to the moving average.
"""
min = []
for m in self.models:
min.append(
euclideanDistance(m.vector, self.movingAverage, self.mask))
if min == []:
self.winner = 'No Winner'
else:
self.previousWinnerIndex = self.newWinnerIndex
self.newWinnerIndex = Numeric.argmin(min)
if self.previousWinnerIndex == self.newWinnerIndex:
self.winnerCount += 1
else:
self.winnerCount = 0
winner = self.models[self.newWinnerIndex]
winner.counter += 1
#if winner.maxSize != -1:
winner.addItem(self.buffer[0])
self.winner = winner.vector
def __init__(self, trajectory, object, first=0, last=None, skip=1,
reference = None):
self.trajectory = trajectory
universe = trajectory.universe
if last is None: last = len(trajectory)
first_conf = trajectory.configuration[first]
offset = universe.contiguousObjectOffset([object], first_conf, 1)
if reference is None:
reference = first_conf
reference = universe.contiguousObjectConfiguration([object],
reference)
steps = (last-first+skip-1)/skip
mass = object.mass()
ref_cms = object.centerOfMass(reference)
atoms = object.atomList()
possq = Numeric.zeros((steps,), Numeric.Float)
cross = Numeric.zeros((steps, 3, 3), Numeric.Float)
rcms = Numeric.zeros((steps, 3), Numeric.Float)
# cms of the CONTIGUOUS object made of CONTINUOUS atom trajectories
for a in atoms:
r = trajectory.readParticleTrajectory(a, first, last, skip,
"box_coordinates").array
w = a._mass/mass
Numeric.add(rcms, w*r, rcms)
if offset is not None:
Numeric.add(rcms, w*offset[a].array, rcms)
# relative coords of the CONTIGUOUS reference
r_ref = Numeric.zeros((len(atoms), 3), Numeric.Float)
for a in range(len(atoms)):
r_ref[a] = atoms[a].position(reference).array - ref_cms.array
# main loop: storing data needed to fill M matrix
for a in range(len(atoms)):
r = trajectory.readParticleTrajectory(atoms[a],
first, last, skip,
"box_coordinates").array
r = r - rcms # (a-b)**2 != a**2 - b**2
if offset is not None:
Numeric.add(r, offset[atoms[a]].array,r)
trajectory._boxTransformation(r, r)
w = atoms[a]._mass/mass
Numeric.add(possq, w*Numeric.add.reduce(r*r, -1), possq)
Numeric.add(possq, w*Numeric.add.reduce(r_ref[a]*r_ref[a],-1),
possq)
Numeric.add(cross, w*r[:,:,Numeric.NewAxis]*r_ref[Numeric.NewAxis,
a,:],cross)
self.trajectory._boxTransformation(rcms, rcms)
# filling matrix M (formula no 40)
k = Numeric.zeros((steps, 4, 4), Numeric.Float)
k[:, 0, 0] = -cross[:, 0, 0]-cross[:, 1, 1]-cross[:, 2, 2]
k[:, 0, 1] = cross[:, 1, 2]-cross[:, 2, 1]
k[:, 0, 2] = cross[:, 2, 0]-cross[:, 0, 2]
k[:, 0, 3] = cross[:, 0, 1]-cross[:, 1, 0]
k[:, 1, 1] = -cross[:, 0, 0]+cross[:, 1, 1]+cross[:, 2, 2]
k[:, 1, 2] = -cross[:, 0, 1]-cross[:, 1, 0]
k[:, 1, 3] = -cross[:, 0, 2]-cross[:, 2, 0]
k[:, 2, 2] = cross[:, 0, 0]-cross[:, 1, 1]+cross[:, 2, 2]
k[:, 2, 3] = -cross[:, 1, 2]-cross[:, 2, 1]
k[:, 3, 3] = cross[:, 0, 0]+cross[:, 1, 1]-cross[:, 2, 2]
del cross
for i in range(1, 4):
for j in range(i):
k[:, i, j] = k[:, j, i]
Numeric.multiply(k, 2., k)
for i in range(4):
Numeric.add(k[:,i,i], possq, k[:,i,i])
del possq
quaternions = Numeric.zeros((steps, 4), Numeric.Float)
fit = Numeric.zeros((steps,), Numeric.Float)
import LinearAlgebra
for i in range(steps):
e, v = LinearAlgebra.eigenvectors(k[i])
j = Numeric.argmin(e)
if e[j] < 0.:
fit[i] = 0.
else:
fit[i] = Numeric.sqrt(e[j])
if v[j,0] < 0.: quaternions[i] = -v[j] # eliminate jumps
else: quaternions[i] = v[j]
self.fit = fit
self.cms = rcms
self.quaternions = quaternions
else:
x2=Numeric.take(var_list,inds2)
y2=Numeric.take(var2_list,inds2)
g.itemlist.append(Gnuplot.Data(x2,y2,with='points 2 1',title='{/Symbol G}_{max}> %g'%ref_g))
for i in range(len(matching)):
if matching[i].data['num']==ref:
ref_ind = i
break
minx = min(var_list)
maxx = max(var_list)
g('set xrange [%g:%g]'%(minx,maxx))
if var_key=='epsVz' and var_key2=='Vz0':
xl = Numeric.arange(minx-abs(minx)*2,maxx+abs(maxx)*2,.01)
g.itemlist.append(Gnuplot.Data(xl,2./abs(xl),with='lines'))
if wb==None:
indmin=Numeric.argmin(matching[ref_ind].evals.imag)
wb=matching[ref_ind].evals[indmin].real
print wb
data = matching[ref_ind].data
g.itemlist.append(Gnuplot.Data(xl,abs(wb)/abs(data['k']*(1-xl*r0**2)),with='lines'))
g.refresh()
ttl = ''
for tt1 in tt:
ttl=ttl+'%s=%g, '%(tt1,matching[ref_ind].data[tt1])
ttl = ttl[:-2]
if notitle==False:
g.title(ttl)#'V_z(r=a)=%g'%matching[0].Vz([matching[0].data['a']]))
else:
g('unset title')
fn = 'plots/%d_%s_%s_stability_boundary.eps'%(min([mat.data['num'] for mat in matching]),var_key,var_key2)
print 'Output to %s'%fn
evec_num = int(round(evec_num+eimag/abs(eimag)))
else:
EV.imag = True
del EV.sevecs
(y1,yl) = EV.get_evec1(coord,evec_num,x)
acoef = EV.get_EVrot(minr=minr,maxr=maxr)
y2 = (acoef*y+1j*acoef*y1).real
y3 = (acoef*y+1j*acoef*y1).imag
#print acoef, y[-1],y1[-1],y2[-1],y3[-1]
norm = EV.get_EVnorm()
y2 = y2*norm
y3 = y3*norm
amp.append(1./((max(y2)+abs(min(y2)))/2.))
try:
x_zero = x[Numeric.nonzero(y2[1:]*y2[:-1]<0)[0]]
ind = Numeric.argmin(Numeric.absolute(EV.grid-x_zero))
zero.append(EV.grid[ind])
except:
zero.append(0)
dr = Gnuplot.Data(x,y2,title='Re',with='lines 3')
di = Gnuplot.Data(x,y3,title='Im',with='lines 2')
inds = Numeric.nonzero((EV.grid>=minx)*(EV.grid<=maxx))
dg = Gnuplot.Data(Numeric.take(EV.grid,inds),0*inds,with='points 1',title='Grid')
d[-1]=[dg,dr,di]
if 'nolegend' in sys.argv:
for i in range(len(d[-1])):
d[-1][i].set_option(title=None)
EV.imag=False
fn = 'plots/%g_var_%s_evec%s_%dunstable.eps'%(num0,var_key,coord,unst_ind)
if 'xr' in sys.argv:
d=d,
nomatch_keys=get_EV.get_numeric_nomatch_keys() +
[var_key, var_key2])
var_list = []
var2_list = []
min_eval = []
nums = []
for i in range(len(matching)):
var_list.append(matching[i].data[var_key])
var2_list.append(matching[i].data[var_key2])
nums.append(matching[i].num)
evals = matching[i].evals
if 'neg' in sys.argv:
inds = Numeric.nonzero(evals.real < 1e-5)
evals = Numeric.take(evals, inds)
ind = Numeric.argmin(evals.imag)
min_eval.append(evals[ind].real)
print nums
for u2 in Numeric.sort(list(sets.Set(var2_list))):
inds = Numeric.nonzero(Numeric.array(var2_list) == u2)
v1 = Numeric.take(var_list, inds)
ev1 = Numeric.take(min_eval, inds)
d1 = matching[inds[0]]
g.itemlist.append(
Gnuplot.Data(v1, ev1, title='%s=%g' % (var_key2, d1.data[var_key2])))
g.itemlist.append(
Gnuplot.Data(v1,
d1.data['k'] *
Numeric.array([matching[j].Vz([r0])[0] for j in inds]) +
ev1[0] - d1.data['k'] * d1.Vz([r0]),
title='V_z(r=%g)' % r0))
