def setdata(self, X, V):
A = self.bialtprodeye(2*self.F.J_coords)
"""Note: p, q <= min(n,m)"""
self.data.Brand = 2*(random((A.shape[0],self.data.p))-0.5)
self.data.Crand = 2*(random((A.shape[1],self.data.q))-0.5)
self.data.B = zeros((A.shape[0],self.data.p), Float)
self.data.C = zeros((A.shape[1],self.data.q), Float)
self.data.D = zeros((self.data.q,self.data.p), Float)
U, S, Vh = linalg.svd(A)
self.data.b = U[:,-1:]
self.data.c = num_transpose(Vh)[:,-1:]
if self.update:
self.data.B[:,1] = self.data.b
self.data.C[:,1] = self.data.c
U2, S2, Vh2 = linalg.svd(c_[r_[A, transpose(self.data.C[:,1])], r_[self.data.B[:,1], [[0]]]])
self.data.B[:,2] = U2[0:A.shape[0],-1:]
self.data.C[:,2] = num_transpose(Vh2)[0:A.shape[1],-1:]
self.data.D[0,1] = U2[A.shape[0],-1]
self.data.D[1,0] = num_transpose(Vh2)[A.shape[1],-1]
else:
self.data.B = self.data.Brand
self.data.C = self.data.Crand
def updatedata(self, A):
# Update b, c
try:
ALU = linalg.lu_factor(A)
BC = linalg.lu_solve(ALU, c_[linalg.lu_solve(ALU, self.data.b + 1e-8*self.data.Brand[:,:1]), \
self.data.c + 1e-8*self.data.Crand[:,:1]], trans=1)
C = linalg.lu_solve(ALU, BC[:,-1:])
B = BC[:,:1]
except:
if self.C.verbosity >= 1:
print 'Warning: Problem updating border vectors. Using svd...'
U, S, Vh = linalg.svd(A)
B = U[:,-1:]
C = num_transpose(Vh)[:,-1:]
bmult = cmult = 1
if matrixmultiply(transpose(self.data.b), B) < 0:
bmult = -1
if matrixmultiply(transpose(self.data.c), C) < 0:
cmult = -1
self.data.b = bmult*B*(linalg.norm(A,1)/linalg.norm(B))
self.data.c = cmult*C*(linalg.norm(A,Inf)/linalg.norm(C))
# Update
if self.update:
self.data.B[:,0] = self.data.b*(linalg.norm(A,1)/linalg.norm(self.data.b))
self.data.C[:,0] = self.data.c*(linalg.norm(A,Inf)/linalg.norm(self.data.c))
self.data.B[:,1] = self.data.w[:,2]*(linalg.norm(A,1)/linalg.norm(self.data.w,1))
self.data.C[:,1] = self.data.v[:,2]*(linalg.norm(A,Inf)/linalg.norm(self.data.v,1))
self.data.D[0,1] = self.data.g[0,1]
self.data.D[1,0] = self.data.g[1,0]
def updatedata(self, A):
if self.update:
if self.corr:
self.data.B = self.data.w*(linalg.norm(A,1)/linalg.norm(self.data.w,1))
self.data.C = self.data.v*(linalg.norm(A,Inf)/linalg.norm(self.data.v,1))
else:
# Note: Problem when singular vectors switch smallest singular value (See NewLorenz).
# To overcome this, I have implemented a 1e-8 random nudge.
try:
ALU = linalg.lu_factor(A)
BC = linalg.lu_solve(ALU, c_[linalg.lu_solve(ALU, self.data.B + 1e-8*self.data.Brand), \
self.data.C + 1e-8*self.data.Crand], trans=1)
C = linalg.lu_solve(ALU, BC[:,-1*self.data.q:])
B = BC[:,0:self.data.p]
except:
if self.C.verbosity >= 1:
print 'Warning: Problem updating border vectors. Using svd...'
U, S, Vh = linalg.svd(A)
B = U[:,-1*self.data.p:]
C = num_transpose(Vh)[:,-1*self.data.q:]
bmult = cmult = 1
if matrixmultiply(transpose(self.data.B), B) < 0:
bmult = -1
if matrixmultiply(transpose(self.data.C), C) < 0:
cmult = -1
self.data.B = bmult*B*(linalg.norm(A,1)/linalg.norm(B))
self.data.C = cmult*C*(linalg.norm(A,Inf)/linalg.norm(C))
def setdata(self, A):
"""Note: p, q <= min(n,m)"""
self.data.Brand = 2*(random((A.shape[0],self.data.p))-0.5)
self.data.Crand = 2*(random((A.shape[1],self.data.q))-0.5)
self.data.D = zeros((self.data.q,self.data.p), Float)
if self.update:
U, S, Vh = linalg.svd(A)
self.data.B = U[:,-1*self.data.p:]
self.data.C = num_transpose(Vh)[:,-1*self.data.q:]
else:
self.data.B = self.data.Brand
self.data.C = self.data.Crand
def newCurve(self, initargs):
"""Create new curve with arguments specified in the dictionary initargs."""
curvetype = initargs['type']
curvetype = curvetype.upper()
if curvetype not in curve_list:
raise TypeError(curvetype + ' not an allowable curve type')
# Check name
if initargs['name'] in self.curves.keys():
raise AttributeError('Ambiguous name field: ' + initargs['name'] + ' already exists')
# Check parameters
if self.model.pars == {}:
raise ValueError('No parameters defined for this system!')
# Process initial point
if 'initpoint' not in initargs:
# Default to initial conditions for model
if self.model.icdict == {}:
raise ValueError('No initial point defined for this system!')
initargs['initpoint'] = self.model.icdict.copy()
#for p in initargs['freepars']:
# initargs['initpoint'][p] = self.model.pars[p]
else:
if isinstance(initargs['initpoint'], dict):
initargs['initpoint'] = initargs['initpoint'].copy()
#for p in initargs['freepars']:
# if p not in initargs['initpoint'].keys():
# initargs['initpoint'][p] = self.model.pars[p]
elif isinstance(initargs['initpoint'], str):
curvename, pointname = initargs['initpoint'].split(':')
pointtype = pointname.strip('0123456789')
if not self.curves.has_key(curvename):
raise KeyError('No curve of name ' + curvename + ' exists.')
else:
point = self.curves[curvename].getSpecialPoint(pointtype, pointname)
if point is None:
raise KeyError('No point of name ' + pointname + ' exists.')
else:
initargs['initpoint'] = point
# Separate from if-else above since 'str' clause returns type Point
if isinstance(initargs['initpoint'], Point):
# Check to see if point contains a cycle. If it does, assume
# we are starting at a cycle and save it in initcycle
for v in initargs['initpoint'].labels.itervalues():
if v.has_key('cycle'):
initargs['initcycle'] = v # Dictionary w/ cycle, name, and tangent information
# Save initial point information
initargs['initpoint'] = initargs['initpoint'].todict()
#for p in initargs['freepars']:
# if p not in initargs['initpoint'].keys():
# initargs['initpoint'][p] = self.model.pars[p]
# Process cycle
if 'initcycle' in initargs:
if isinstance(initargs['initcycle'], NumArray):
c0 = {}
c0['data'] = args(V = {'udotps': None, 'rldot': None})
c0['cycle'] = Pointset({'coordnames': self.gensys.funcspec.vars,
'coordarray': num_transpose(initargs['initcycle'][:,1:]).copy(),
'indepvarname': 't',
'indepvararray': num_transpose(initargs['initcycle'][:,0]).copy()
})
initargs['initcycle'] = c0
elif isinstance(initargs['initcycle'], Pointset):
c0 = {}
c0['data'] = args(V = {'udotps': None, 'rldot': None})
c0['cycle'] = initargs['initcycle']
initargs['initcycle'] = c0
# Load auto module if required
automod = None
if curvetype in auto_list:
if self._autoMod is None:
self.loadAutoMod()
automod = self._autoMod
self.curves[initargs['name']] = curve_list[curvetype](self.model, self.gensys, automod, self.plot, initargs)
def newCurve(self, initargs):
"""Create new curve with arguments specified in the dictionary initargs."""
curvetype = initargs['type']
curvetype = curvetype.upper()
if curvetype not in curve_list:
raise TypeError(curvetype + ' not an allowable curve type')
# Check name
if initargs['name'] in self.curves.keys():
raise AttributeError('Ambiguous name field: ' + initargs['name'] +
' already exists')
# Check parameters
if self.model.pars == {}:
raise ValueError('No parameters defined for this system!')
# Process initial point
if 'initpoint' not in initargs:
# Default to initial conditions for model
if self.model.icdict == {}:
raise ValueError('No initial point defined for this system!')
initargs['initpoint'] = self.model.icdict.copy()
#for p in initargs['freepars']:
# initargs['initpoint'][p] = self.model.pars[p]
else:
if isinstance(initargs['initpoint'], dict):
initargs['initpoint'] = initargs['initpoint'].copy()
#for p in initargs['freepars']:
# if p not in initargs['initpoint'].keys():
# initargs['initpoint'][p] = self.model.pars[p]
elif isinstance(initargs['initpoint'], str):
curvename, pointname = initargs['initpoint'].split(':')
pointtype = pointname.strip('0123456789')
if not self.curves.has_key(curvename):
raise KeyError('No curve of name ' + curvename +
' exists.')
else:
point = self.curves[curvename].getSpecialPoint(
pointtype, pointname)
if point is None:
raise KeyError('No point of name ' + pointname +
' exists.')
else:
initargs['initpoint'] = point
# Separate from if-else above since 'str' clause returns type Point
if isinstance(initargs['initpoint'], Point):
# Check to see if point contains a cycle. If it does, assume
# we are starting at a cycle and save it in initcycle
for v in initargs['initpoint'].labels.itervalues():
if v.has_key('cycle'):
initargs[
'initcycle'] = v # Dictionary w/ cycle, name, and tangent information
# Save initial point information
initargs['initpoint'] = initargs['initpoint'].todict()
#for p in initargs['freepars']:
# if p not in initargs['initpoint'].keys():
# initargs['initpoint'][p] = self.model.pars[p]
# Process cycle
if 'initcycle' in initargs:
if isinstance(initargs['initcycle'], NumArray):
c0 = {}
c0['data'] = args(V={'udotps': None, 'rldot': None})
c0['cycle'] = Pointset({
'coordnames':
self.gensys.funcspec.vars,
'coordarray':
num_transpose(initargs['initcycle'][:, 1:]).copy(),
'indepvarname':
't',
'indepvararray':
num_transpose(initargs['initcycle'][:, 0]).copy()
})
initargs['initcycle'] = c0
elif isinstance(initargs['initcycle'], Pointset):
c0 = {}
c0['data'] = args(V={'udotps': None, 'rldot': None})
c0['cycle'] = initargs['initcycle']
initargs['initcycle'] = c0
# Load auto module if required
automod = None
if curvetype in auto_list:
if self._autoMod is None:
self.loadAutoMod()
automod = self._autoMod
self.curves[initargs['name']] = curve_list[curvetype](self.model,
self.gensys,
automod,
self.plot,
initargs)