def cluster(self, tokens, assign_clusters=False, trace=False):
assert chktype(1, tokens, [Token])
assert chktype(2, assign_clusters, bool)
assert chktype(3, trace, bool)
assert len(tokens) > 0
vectors = map(lambda tk: tk['FEATURES'], tokens)
# normalise the vectors
if self._should_normalise:
vectors = map(self._normalise, vectors)
# use SVD to reduce the dimensionality
if self._svd_dimensions and self._svd_dimensions < len(vectors[0]):
[u, d, vt] = numarray.linear_algebra.singular_value_decomposition(
numarray.transpose(numarray.array(vectors)))
S = d[:self._svd_dimensions] * \
numarray.identity(self._svd_dimensions, numarray.Float64)
T = u[:,:self._svd_dimensions]
Dt = vt[:self._svd_dimensions,:]
vectors = numarray.transpose(numarray.matrixmultiply(S, Dt))
self._Tt = numarray.transpose(T)
# call abstract method to cluster the vectors
self.cluster_vectorspace(vectors, trace)
# assign the tokens to clusters
if assign_clusters:
for token in tokens:
self.classify(token)
def regress(X):
"""
Apply a linear regression on X.
X is an numarray array of form [Y|X].
We split this up, do the regression and return the
regression coefficients, beta_i.
"""
X = N.array(X)
Y = X[:,0].copy()
X[:,0] = 1.0
a = N.dot(NL.inverse(N.dot(N.transpose(X), X)), N.transpose(X))
return N.dot(a, Y)
def stdForm(a, b):
def invert(L): # Inverts lower triangular matrix L
n = len(L)
for j in range(n - 1):
L[j, j] = 1.0 / L[j, j]
for i in range(j + 1, n):
L[i, j] = -dot(L[i, j:i], L[j:i, j]) / L[i, i]
L[n - 1, n - 1] = 1.0 / L[n - 1, n - 1]
n = len(a)
L = choleski(b)
invert(L)
h = matrixmultiply(b, matrixmultiply(a, transpose(L)))
return h, transpose(L)
def stdForm(a, b):
def invert(L): # Inverts lower triangular matrix L
n = len(L)
for j in range(n - 1):
L[j, j] = 1.0 / L[j, j]
for i in range(j + 1, n):
L[i, j] = -dot(L[i, j:i], L[j:i, j]) / L[i, i]
L[n - 1, n - 1] = 1.0 / L[n - 1, n - 1]
n = len(a)
L = choleski(b)
invert(L)
h = matrixmultiply(b, matrixmultiply(a, transpose(L)))
return h, transpose(L)
def __init__(self, parent, framesize = None, hopsize = 100, number_of_vectors_used = 15): if not framesize: lp = len(parent) #logfs = min(int(scipy.log2(lp / 32)), 10) log2 = lambda x: math.log(x) / math.log(2) logfs = min(int(log2(lp / 32)), 10) framesize = pow(2, logfs) print framesize if hopsize > framesize / 4: hopsize = framesize / 4 self.hopsize = hopsize self.framesize = framesize #if len(parent) < framesize: # self._delete_from_parents() # raise UnderflowError, "Thingy is too small...\nHere I pull the plug in order to avoid a segfaulty thingy." input_array = parent self.feature_vectors = None interesting_parts = input_array[:, :number_of_vectors_used] interesting_parts = numarray.transpose(interesting_parts) for row in interesting_parts: specspectrum = calculate_spectrogram(row, framesize = framesize, hopsize = hopsize) import cPickle z, lambdas, EOFs = svdeofs.svdeofs(specspectrum) print ".", s = z[:, :15] svd_fft_fft_vectors = numarray.transpose(s) #print "svd_eofs ok!" if self.feature_vectors is None: self.feature_vectors = numarray.transpose(svd_fft_fft_vectors) else: self.feature_vectors = numarray.concatenate((self.feature_vectors, numarray.transpose(svd_fft_fft_vectors)), 1) #print "svd_fft_fft_vectors shapes:", shape(svd_fft_fft_vectors), shape(self.feature_vectors) z, lambdas, EOFs = svdeofs.svdeofs(self.feature_vectors) self.feature_vectors = z[:, :15] self.arr = self.feature_vectors
def get_residual(pcanode, pts):
pvals = pcanode.execute(pts, pcanode.get_output_dim())
pproj = mat(pvals) * mat(transpose(pcanode.v))
res = pts - array(pproj) # orthogonal complement of projection onto PCs
resval_part = sqrt(sum(res**2))
resval = sqrt(sum(resval_part**2)) # ?!
return resval
def get_residual(pcanode, pts):
pvals = pcanode.execute(pts, pcanode.get_output_dim())
pproj = mat(pvals)*mat(transpose(pcanode.v))
res = pts-array(pproj) # orthogonal complement of projection onto PCs
resval_part = sqrt(sum(res**2))
resval = sqrt(sum(resval_part**2)) # ?!
return resval
def normalize(self, dim=-1):
""" If dim=-1 all elements sum to 1. Otherwise sum to specific dimension, such that
sum(Pr(x=i|Pa(x))) = 1 for all values of i and a specific set of values for Pa(x)
"""
if dim == -1 or len(self.cpt.shape) == 1:
self.cpt /= self.cpt.sum()
else:
ndim = self.assocdim[dim]
order = range(len(self.names_list))
order[0] = ndim
order[ndim] = 0
tcpt = na.transpose(self.cpt, order)
t1cpt = na.sum(tcpt, axis=0)
t1cpt = na.resize(t1cpt,tcpt.shape)
tcpt = tcpt/t1cpt
self.cpt = na.transpose(tcpt, order)
def _castCopyAndTranspose(type, *numarray, **kargs):
# This should work as a drop in replacement for LinearAlgegra2._castCopyAndTranspose
indices = kargs.get("indices")
cast_numarray = []
for a in numarray:
if indices is None:
a = na.transpose(a)
else:
a = na.transpose(a, indices)
if a.type() == type:
cast_numarray.append(a.copy())
else:
cast_numarray.append(a.astype(type))
if len(cast_numarray) == 1:
return cast_numarray[0]
else:
return cast_numarray
def testEq(self):
a = Table(['a','b'],[2,3],range(6),'Float32')
b = Table(['a','b'],[2,3],range(6),'Float32')
c = Table(['a'],[6],range(6),'Float32')
d = na.arange(6,shape=(2,3))
e = Table(['b','a'],[3,2], na.transpose(a.cpt))
assert(a == b and \
not a == c and \
a == d and \
a == e and e == a), \
"__eq__ does not work"
def testUnion(self):
""" test Union between two Tables """
a = Table(['a','b','c','d'],[2,3,4,5],range(2*3*4*5))
b = Table(['c','b','e'],[4,3,6],range(12*6))
ab,bb = a.union(b)
assert(ab.names_list == ['a','b','c','d','e'] and \
ab.shape == tuple([2,3,4,5,1]) and \
na.all(bb == na.transpose(b.cpt[...,na.NewAxis,na.NewAxis],axes=[3,1,0,4,2]))), \
""" union does not work ..."""
def Update(self, other):
""" updates this Table with the values contained in the other"""
# check that all variables in self are contained in other
if self.names != other.names:
return "error in update, all variables in other should be contained in self"
# find the correspondance vector
correspond = []
for vara in self.names_list:
correspond.append(other.assocdim[vara])
self.cpt = copy(na.transpose(other.cpt, axes=correspond))
def notes_roc (la, lb, eps):
from numarray import transpose, add, resize
""" creates a matrix of size len(la)*len(lb) then look for hit and miss
in it within eps tolerance windows """
gdn,fpw,fpg,fpa,fdo,fdp = 0,0,0,0,0,0
m = len(la)
n = len(lb)
x = resize(la[:][0],(n,m))
y = transpose(resize(lb[:][0],(m,n)))
teps = (abs(x-y) <= eps[0])
x = resize(la[:][1],(n,m))
y = transpose(resize(lb[:][1],(m,n)))
tpitc = (abs(x-y) <= eps[1])
res = teps * tpitc
res = add.reduce(res,axis=0)
for i in range(len(res)) :
if res[i] > 1:
gdn+=1
fdo+=res[i]-1
elif res [i] == 1:
gdn+=1
fpa = n - gdn - fpa
return gdn,fpw,fpg,fpa,fdo,fdp
def notes_roc(la, lb, eps):
from numarray import transpose, add, resize
""" creates a matrix of size len(la)*len(lb) then look for hit and miss
in it within eps tolerance windows """
gdn, fpw, fpg, fpa, fdo, fdp = 0, 0, 0, 0, 0, 0
m = len(la)
n = len(lb)
x = resize(la[:][0], (n, m))
y = transpose(resize(lb[:][0], (m, n)))
teps = (abs(x - y) <= eps[0])
x = resize(la[:][1], (n, m))
y = transpose(resize(lb[:][1], (m, n)))
tpitc = (abs(x - y) <= eps[1])
res = teps * tpitc
res = add.reduce(res, axis=0)
for i in range(len(res)):
if res[i] > 1:
gdn += 1
fdo += res[i] - 1
elif res[i] == 1:
gdn += 1
fpa = n - gdn - fpa
return gdn, fpw, fpg, fpa, fdo, fdp
def union(a,b):
""" Returns a new instance of same class as a that contains all
data contained in a but also has any new variables found in b with unary
dimensions. Also returns a view of b.cpt ready for an operation with
the returned instance.
eg. a= Pr(A,B,C,D,E)
b= Pr(C,G,A,F)
a.union(b) --> returns (Pr(A,B,C,D,E,1,1),numarray([A,1,C,1,1,G,F]))
Notes:
- a and b remain unchanged
- a and b must be Table instances (or something equivalent)
- a always keeps the same order of its existing variables
- any new variables found in b are added at the end of a in the order
they appear in b.
- new dimensions are added with numarray.NewAxis
- the two numarrays objects returns have exactly the same dimensions
and are ready for any kind of operation, *,/,...
"""
# make a copy of a
new = copy(a)
for varb in b.names_list:
# varb is the name of a variable in b
if not new.assocdim.has_key(varb):
new.addDim(varb) # add new variable to new
# new now contains all the variables contained in a and b
# new = A U B
correspond = []
b_assocdim = copy(b.assocdim)
bcpt = b.cpt.view()
for var in new.names_list:
# var is the name of a variable in new
if not b.assocdim.has_key(var):
bcpt = bcpt[...,na.NewAxis]
b_assocdim[var] = bcpt.rank - 1
correspond.append(b_assocdim[var])
# transpose dimensions in b to match those in a
btr = na.transpose(bcpt, axes = correspond)
# btr is now ready for any operation with new
return new, btr
def fig3b(t, m, w, p):
""" Plot image of age,metallicity weights -- nearest neighbor interpolation"""
NREP = 50
xi = pylab.linspace(0.1, 15, 512)
yi = pylab.linspace(-2.5, 0.9, 512)
z = numarray.zeros((len(xi), len(yi)),
numarray.Float) # create t, metallicity array
y = numarray.repeat(m, NREP)
dt = t[1] - t[0]
x = numarray.arange(t[0], t[-1] + 2 * dt, dt / NREP)
x = x[0:len(y)]
x = 10.**x / 1.e9
weight = numarray.repeat(w, NREP)
# Find the indices in the array
xindex = numarray.searchsorted(xi, x)
print "shape(x), shape(y), shape(weight)", numarray.shape(
x), numarray.shape(y), numarray.shape(weight)
if p.sigma > 0:
if p.dsigmadlogt == 0.:
for i in range(len(y)):
nstars = weight[i] * normgauss(yi, y[i], p.sigma)
j = xindex[i]
z[j, :] += nstars
if p.dsigmadlogt != 0.:
for i in range(len(y)):
logt0 = numarray.log10(x[0])
logt = numarray.log10(x[i])
sigma = p.sigma + p.dsigmadlogt * (logt - logt0)
nstars = weight[i] * normgauss(yi, y[i], sigma)
j = xindex[i]
z[j, :] += nstars
else:
sigma = 0.01
for i in range(len(y)):
nstars = weight[i] * normgauss(yi, y[i], sigma)
j = xindex[i]
z[j, :] += nstars
# yindex = numarray.searchsorted(yi,y)
# z[xindex,yindex] = z[xindex,yindex] + weight # increment the 2-d array
zz = numarray.transpose(z)
pylab.imshow(zz, extent=[0.1, 15, -2.5, 0.9], aspect='auto')
pylab.xlabel("Age (Gyr)")
pylab.ylabel("[Fe/H]")
return xi, yi, zz
def plot_PCA_residuals(data, D=None, newfig=True, marker='o'):
if D is None:
D = shape(data)[1]
p = doPCA(data, D, D)
spec = zeros((D, 1), Float)
for i in range(1, D):
spec[i] = norm(p.d[:i])
res = transpose(sqrt(spec[-1]**2 - spec**2) / spec[-1])[0]
print "2-norm of PCA spectrum =", spec[-1]
if newfig:
figure()
style = 'k' + marker
else:
style = marker
semilogy(res, style)
## title('PCA residuals')
xlabel(r'$\rm{Dimension}$', fontsize=20)
ylabel(r'$\rm{PCA \ residual}$', fontsize=20)
return p, res
def testMul(self):
""" test multiplication """
a = Table(['a','b','c','d'],[2,3,4,5],range(2*3*4*5))
b = Table(['c','b','e'],[4,3,6],range(12*6))
c = Table(['a','b','c','d','e'],[2,3,4,5,6],range(2*3*4*5*6))
acpt = a.cpt[...,na.NewAxis]
bcpt = b.cpt[...,na.NewAxis,na.NewAxis]
bcpt = na.transpose(bcpt,[3,1,0,4,2])
resab = acpt*bcpt
ab = a*b
cc = c*c
bb = b*b
assert (ab == Table(['a','b','c','d','e'],[2,3,4,5,6],resab) and \
cc == Table(['a','b','c','d','e'],[2,3,4,5,6],na.arange(2*3*4*5*6)**2) and \
bb == Table(['c','b','e'],[4,3,6],na.arange(12*6)**2)), \
" Multiplication does not work"
def fig3e(t,m,w,p):
""" Plot image of log(age),metallicity weights -- nearest neighbor interpolation"""
xi = pylab.linspace(8,10.25,512)
yi = pylab.linspace(-2.5,0.9,512)
z = numarray.zeros((len(xi),len(yi)),numarray.Float) # create t, metallicity array
x = t
y = m
# Find the indices in the array
xindex = numarray.searchsorted(xi,x)
if p.sigma > 0:
for i in range(len(y)):
nstars = w[i]*normgauss(yi,y[i],p.sigma)
print "shape(z),len(nstars)", numarray.shape(z), len(nstars)
z[xindex[i],:] += nstars
else:
yindex = numarray.searchsorted(yi,y)
z[xindex,yindex] = z[xindex,yindex] + weight # increment the 2-d array
zz = numarray.transpose(z)
pylab.imshow(zz,extent=[8,10.25,-2.5,0.9],aspect='auto')
def plot_PCA_residuals(data, D=None, newfig=True, marker='o'):
if D is None:
D = shape(data)[1]
p=doPCA(data, D, D)
spec=zeros((D,1),Float)
for i in range(1,D):
spec[i] = norm(p.d[:i])
res = transpose(sqrt(spec[-1]**2-spec**2)/spec[-1])[0]
print "2-norm of PCA spectrum =", spec[-1]
if newfig:
figure()
style='k'+marker
else:
style=marker
semilogy(res,style)
## title('PCA residuals')
xlabel(r'$\rm{Dimension}$',fontsize=20)
ylabel(r'$\rm{PCA \ residual}$',fontsize=20)
return p, res
def fig3b(t,m,w,p):
""" Plot image of age,metallicity weights -- nearest neighbor interpolation"""
NREP = 50
xi = pylab.linspace(0.1,15,512)
yi = pylab.linspace(-2.5,0.9,512)
z = numarray.zeros((len(xi),len(yi)),numarray.Float) # create t, metallicity array
y = numarray.repeat(m,NREP)
dt = t[1]-t[0]
x = numarray.arange(t[0],t[-1]+2*dt,dt/NREP)
x = x[0:len(y)]
x = 10.**x/1.e9
weight = numarray.repeat(w,NREP)
# Find the indices in the array
xindex = numarray.searchsorted(xi,x)
print "shape(x), shape(y), shape(weight)", numarray.shape(x),numarray.shape(y), numarray.shape(weight)
if p.sigma > 0:
if p.dsigmadlogt == 0.:
for i in range(len(y)):
nstars = weight[i]*normgauss(yi,y[i],p.sigma)
j = xindex[i]
z[j,:] += nstars
if p.dsigmadlogt != 0.:
for i in range(len(y)):
logt0 = numarray.log10(x[0])
logt = numarray.log10(x[i])
sigma = p.sigma + p.dsigmadlogt*(logt-logt0)
nstars = weight[i]*normgauss(yi,y[i],sigma)
j = xindex[i]
z[j,:] += nstars
else:
sigma = 0.01
for i in range(len(y)):
nstars = weight[i]*normgauss(yi,y[i],sigma)
j = xindex[i]
z[j,:] += nstars
# yindex = numarray.searchsorted(yi,y)
# z[xindex,yindex] = z[xindex,yindex] + weight # increment the 2-d array
zz = numarray.transpose(z)
pylab.imshow(zz,extent=[0.1,15,-2.5,0.9],aspect='auto')
pylab.xlabel("Age (Gyr)")
pylab.ylabel("[Fe/H]")
return xi,yi,zz
def testPrepareOther(self):
c = Table(['e','b'],[2,3],range(6))
d = Table(['a','b','c','d','e'],[2,3,2,2,2],range(3*2**4))
e = Table(['e','b','f'],[2,3,4],range(6*4))
src = Table(['s','r','c'],[2,3,4],range(24))
cr = Table(['c','r'],[4,3],range(12))
dc = d.prepareOther(c)
try:
d.prepareOther(e)
assert(0),""" this should produce an error..."""
except:
pass
cr_ = src.prepareOther(cr)
assert(dc.shape == tuple([1,3,1,1,2]) and \
na.all(dc[0,:,0,0,:] == na.transpose(c.cpt, axes=[1,0])) and \
cr_.shape == (1,3,4)), \
""" problem with prepareOther"""
def prepareOther(self, other):
"""
Prepares other for inplace multiplication/division with self. Returns
a *view* of other.cpt ready for an operation. other must contain a
subset of the variables of self. NON-DESTRUCTIVE!
eg. a= Pr(A,B,C,D)
b= Pr(D,B)
a.prepareOther(b) --> returns a numarray Pr(1,B,1,D)
a= Pr(A,B,C,D)
b= Pr(C,B,E)
a.prepareOther(b) --> ERROR (E not in {A,B,C,D})
Notes:
- a and b are not altered in any way. NON-DESTRUCTIVE
- b must contain a subset of a's variables
a=Pr(X),b=Pr(Y); Y entirely included in X
"""
#self contains all variables found in other
if len(other.names - self.names) > 0:
raise "ERROR :"+str((other.names-self.names))+"not in"+str(self.names)
# add new dimensions to b
bcpt = other.cpt.view()
b_assocdim = copy(other.assocdim)
for var in (self.names-other.names):
#for all variables found in self and not in other
#add a new dimension to other
bcpt = bcpt[...,na.NewAxis]
b_assocdim[var] = bcpt.rank - 1
#create the transposition vector
trans = list()
for var in self.names_list:
trans.append(b_assocdim[var])
bcpt_trans = na.transpose(bcpt, axes=trans)
# transpose and return bcpt
return bcpt_trans
def fig3e(t, m, w, p):
""" Plot image of log(age),metallicity weights -- nearest neighbor interpolation"""
xi = pylab.linspace(8, 10.25, 512)
yi = pylab.linspace(-2.5, 0.9, 512)
z = numarray.zeros((len(xi), len(yi)),
numarray.Float) # create t, metallicity array
x = t
y = m
# Find the indices in the array
xindex = numarray.searchsorted(xi, x)
if p.sigma > 0:
for i in range(len(y)):
nstars = w[i] * normgauss(yi, y[i], p.sigma)
print "shape(z),len(nstars)", numarray.shape(z), len(nstars)
z[xindex[i], :] += nstars
else:
yindex = numarray.searchsorted(yi, y)
z[xindex,
yindex] = z[xindex, yindex] + weight # increment the 2-d array
zz = numarray.transpose(z)
pylab.imshow(zz, extent=[8, 10.25, -2.5, 0.9], aspect='auto')
def solve_linear_equations(a, b):
"""solve_linear_equations(a, b) -> x such that dot(a,x) = b
*a* may be either rank-2 or rank-3, in either case, it
must be square along the last two axes *b* may either
have a rank one lower than *a*, in which case it
represents a vector or an array of vectors, or it may be
the same rank as *a* in which case it represents a matrix
or an array of matrices.
Since that may be a bit confusing let's look at some examples.
First the simplest case, a square matrix A, and a vector of
results B.
>>> A = [[1,2,3], [3,5,5], [5,6,7]]
>>> B = [1,1,1]
>>> x = solve_linear_equations(A, B)
>>> _isClose(x, num.array([-0.5, 0. , 0.5]))
1
>>> _isClose(na.dot(A, x), # This should give us B
... num.array([ 1., 1., 1.]))
1
The next simplest case is a square matrix A and a matrix B.
>>> B = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
>>> _isClose(solve_linear_equations(A, B),
... num.array([[-0.625, -0.5 , 0.625],
... [-0.5 , 1. , -0.5 ],
... [ 0.875, -0.5 , 0.125]]))
1
If *a* is rank-3, then the first dimension of *a* **and** *b* is
interpreted as selecting different submatrices or subvectors to operate
on. In this case, *b* will be rank-2 in the vector case and rank-3 in
the matrix case. Here is what is looks like in the vector case.
>>> A = [[[1, 3], [2j, 3j]],
... [[2, 4], [4j, 4j]],
... [[3, 5], [6j, 5j]]]
>>> B = [[1, 0], [0, 1], [1, 1]]
>>> _isClose(solve_linear_equations(A, B),
... num.array([[-1. +0.j , 0.66666667+0.j ],
... [ 0. -0.5j , 0. +0.25j ],
... [-0.33333333-0.33333333j, 0.4 +0.2j ]]))
1
The first dimensions of *a* and *b* must either match or one of them must
be 1. In the latter case, the length-1 dimension is broadcast in the normal
way.
>>> B = [[1, 0], [0, 1]]
>>> solve_linear_equations(A, B)
Traceback (most recent call last):
...
LinearAlgebraError: first dimensions of a and b must match or be 1
>>> B = [[1, 0]]
>>> _isClose(solve_linear_equations(A, B),
... num.array([[-1. +0.j, 0.66666667+0.j],
... [-0.5 +0.j, 0.5 +0.j],
... [-0.33333333+0.j, 0.4 +0.j]]))
1
"""
a = na.asarray(a)
b = na.asarray(b)
_assertRank((2,3), a)
_assertSubmatrixSquareness(a)
rank_a = len(a.shape)
_assertRank((rank_a-1, rank_a), b)
stretched = (rank_a == 2)
if stretched:
a = a[na.NewAxis,]
b = b[na.NewAxis,]
one_eq = (len(b.shape) == len(a.shape)-1)
if one_eq:
b = b[:,:,na.NewAxis]
broadcast_a = (a.shape[0] == 1)
broadcast_b = (b.shape[0] == 1)
if not (broadcast_a or broadcast_b or a.shape[0] == b.shape[0]):
raise LinAlgError, "first dimensions of a and b must match or be 1"
#
n_cases = max(a.shape[0], b.shape[0])
n_eq = a.shape[1]
n_rhs = b.shape[2]
if n_eq != b.shape[1]:
raise LinAlgError, 'Incompatible dimensions'
t = _commonType(a, b)
if _array_kind[t] == 1: # Complex routines take different arguments
lapack_routine = lapack_lite2.zgesv
else:
lapack_routine = lapack_lite2.dgesv
a, b = _castCopyAndTranspose(t, a, b, indices=(0,2,1))
result = na.zeros([n_cases, n_rhs, n_eq], b.type())
result[:] = b
b = result
pivots = na.zeros(n_eq, 'l')
a_stride = n_eq * n_eq * a.itemsize()
b_stride = n_eq * n_rhs * b.itemsize()
a_view = a[0]
b_view = b[0]
a_i = a_view.copy()
b_i = b_view.copy()
for i in range(n_cases):
if i:
if not broadcast_a:
a_i._copyFrom(a_view)
b_i._copyFrom(b_view)
outcome = lapack_routine(n_eq, n_rhs, a_i, n_eq, pivots, b_i, n_eq, 0)
if outcome['info'] > 0:
raise LinAlgError, 'Singular matrix'
b_view._copyFrom(b_i)
a_view._byteoffset += a_stride
b_view._byteoffset += b_stride
b = na.transpose(b, (0,2,1))
if one_eq:
b = b[...,0]
if stretched:
b = b[0]
return b
for n in line.split():
U[row, col] = float(n)
col += 1
row += 1
rows, columns = [int(a) for a in vfile.readline().split()]
V = na.zeros((rows, columns), type="Float32")
row = 0
for line in vfile:
col = 0
for n in line.split():
V[row, col] = float(n)
col += 1
row += 1
return U, S, V
up = cPickle.Unpickler(file('artist_user.pickle', 'rb'))
artists, users = up.load()
#U is artists
U, S, V = load_svd(file('big_s', 'r'), file('big_ut', 'r'),
file('big_vt', 'r'))
#I believe that U is already transposed
tt = na.dot(na.transpose(U), na.dot(na.dot(S, S), U))
fout = file('lsi.out', 'wb')
cp = cPickle.Pickler(fout, -1)
cp.dump(tt)
fout.close()
def compute(self, trajname, ics=None):
assert self.funcspec.targetlang == 'python', \
('Wrong target language for functional specification. '
'Python needed for this class')
assert isinstance(self.funcspec, RHSfuncSpec), ('Map system '
'requires RHSfuncSpec type to proceed')
if self.defined:
self.validateSpec()
## assert remain(self.initialconditions.keys(),
## self._xdatadict.keys()+self.funcspec.auxvars) == [],\
## ('mismatching entries between initial conditions and '
## 'declared variable names')
self.clearWarnings()
self.clearErrors()
if ics is not None:
self.set(ics=ics)
xnames = self._var_ixmap # ensures correct order
# wrap up each dictionary initial value as a singleton list
alltData = [self.indepvariable.depdomain.get(0)]
allxDataDict = dict(zip(xnames, map(listid,
sortedDictValues(self.initialconditions,
self.funcspec.vars))))
rhsfn = eval("self."+self.funcspec.spec[1])
# Check i.c.'s are well defined (finite)
self.checkInitialConditions()
self.setEventICs(self.initialconditions, self.globalt0)
ic = sortedDictValues(self.initialconditions, self.funcspec.vars)
plist = sortedDictValues(self.pars)
extralist = copy(plist)
ilist = []
if self.inputs:
# inputVarList is a list of Variables
listend = self.numpars + len(self.inputs)
inputVarList = sortedDictValues(self.inputs)
try:
for f in inputVarList:
f.clearWarnings
ilist.append(f(alltData[0], self.checklevel))
except AssertionError:
print 'External input call has t out of range: t = ', \
self.indepvariable.depdomain.get(0)
print 'Maybe checklevel is 3 and initial time is not', \
'completely inside valid time interval'
raise
except ValueError:
print 'External input call has value out of range: t = ', \
self.indepvariable.depdomain.get(0)
for f in inputVarList:
if len(f.warnings):
print 'External input %s out of range:' % f.name
print ' t = ', repr(f.warnings[-1][0]), ', ', \
f.name, ' = ', repr(f.warnings[-1][1])
raise
else:
listend = self.numpars
inputVarList = []
extralist.extend(ilist)
precevents = self.eventstruct.query(['precise'])
if precevents != []:
raise PyDSTool_ValueError('precise events are not valid for map systems')
eventslist = self.eventstruct.query(['highlevel', 'active',
'notvarlinked'])
termevents = self.eventstruct.query(['term'], eventslist)
# initialize event info dictionaries
Evtimes = {}
Evpoints = {}
for (evname, ev) in eventslist:
Evtimes[evname] = []
Evpoints[evname] = []
if eventslist != []:
self.eventstruct.resetHighLevelEvents(self.indepvariable.depdomain.get(0),
eventslist)
self.eventstruct.validateEvents(self.funcspec.vars + \
self.funcspec.auxvars + \
['t'], eventslist)
# per-iteration storage of variable data (initial values are irrelevant)
xDataDict = {}
# storage of all auxiliary variable data
allaDataDict = {}
anames = self.funcspec.auxvars
avals = apply(eval("self."+self.funcspec.auxspec[1]),
[self.indepvariable.depdomain.get(0),
sortedDictValues(self.initialconditions,
self.funcspec.vars),
extralist])
for aix in range(len(anames)):
aname = anames[aix]
allaDataDict[aname] = [avals[aix]]
# temp storage of first time at which terminal events found
# (this is used for keeping the correct end point of new mesh)
first_found_t = None
tmesh = self.indepvariable.depdomain.uniformSample(self.tstep, strict=False,
avoidendpoints=self.checklevel>2)
# Main loop
breakwhile = False
success = False
x = ic
notdone = True
# did i=0 for initial condition already
i = 1
while notdone:
t = tmesh[i]
## COMPUTE NEXT STATE y from x
try:
y = rhsfn(t, x, extralist)
except:
print "Error in calling right hand side function:"
self.showSpec()
raise
for xi in xrange(self.dimension):
xDataDict[xnames[xi]] = y[xi]
if not self.contains(self.variables[xnames[xi]].depdomain,
y[xi], self.checklevel):
self.warnings.append((W_TERMSTATEBD,
(t, xnames[xi], y[xi],
self.variables[xnames[xi]].depdomain)))
breakwhile = True
break # for loop
if breakwhile:
notdone = False
continue
if eventslist != []:
dataDict = copy(xDataDict)
dataDict['t'] = t
evsflagged = self.eventstruct.pollHighLevelEvents(None,
dataDict,
self.pars,
eventslist)
termevsflagged = filter(lambda e: e in evsflagged, termevents)
nontermevsflagged = filter(lambda e: e not in termevsflagged,
evsflagged)
# register any non-terminating events in the warnings list
if len(nontermevsflagged) > 0:
evnames = [ev[0] for ev in nontermevsflagged]
self.warnings.append((W_NONTERMEVENT,
(t, evnames)))
for evname in evnames:
Evtimes[evname].append(t)
Evpoints[evname].append(y)
if termevsflagged != []:
# active terminal event flagged at this time point
# register the event in the warnings
evnames = [ev[0] for ev in termevsflagged]
self.warnings.append((W_TERMEVENT, \
(t, evnames)))
for evname in evnames:
Evtimes[evname].append(t)
Evpoints[evname].append(y)
notdone = False
continue
alltData.append(t)
for xi in range(self.dimension):
allxDataDict[xnames[xi]].append(y[xi])
avals = apply(eval("self."+self.funcspec.auxspec[1]), [t,
sortedDictValues(xDataDict),
extralist])
for aix in range(len(anames)):
aname = anames[aix]
allaDataDict[aname].append(avals[aix])
try:
extralist[self.numpars:listend] = [apply(f,
[t, self.checklevel]) \
for f in inputVarList]
except ValueError:
print 'External input call caused value out of range error:', \
't = ', t
for f in inputVarList:
if len(f.warnings):
print 'External input variable %s out of range:' % f.name
print ' t = ', repr(f.warnings[-1][0]), ', ', \
f.name, ' = ', repr(f.warnings[-1][1])
raise
except AssertionError:
print 'External input call caused t out of range error: t = ', t
raise
if i >= len(tmesh) - 1:
notdone = False
else:
i += 1
x = y
# update success flag
success = not notdone
# Check that any terminal events found terminated the code correctly
if first_found_t is not None:
assert self.warnings[-1][0] == W_TERMEVENT, ("Event finding code "
"for terminal event failed")
# Package up computed trajectory in Variable variables
# Add external inputs warnings to self.warnings, if any
for f in inputVarList:
for winfo in f.warnings:
self.warnings.append((W_NONTERMSTATEBD,
(winfo[0], f.name, winfo[1],
f.depdomain)))
# check for non-unique terminal event
termcount = 0
for (w,i) in self.warnings:
if w == W_TERMEVENT or w == W_TERMSTATEBD:
termcount += 1
if termcount > 1:
self.errors.append((E_NONUNIQUETERM, (alltData[-1], i[1])))
## print 'Time interval adjusted according to %s: %s' % \
## (self._warnmessages[w], str(i[0])+", "+ str(i[1]))
# Create variables (self.variables contains no actual data)
variables = copyVarDict(self.variables)
# build event pointset information (reset previous trajectory's)
self.trajevents = {}
for (evname, ev) in eventslist:
evpt = Evpoints[evname]
if evpt == []:
self.trajevents[evname] = None
else:
evpt = transpose(array(evpt))
self.trajevents[evname] = Pointset({'coordnames': xnames,
'indepvarname': 't',
'coordarray': evpt,
'indepvararray': Evtimes[evname],
'indepvartype': self.variables[xnames[0]].indepvartype})
for x in xnames:
if len(alltData) > 1:
variables[x] = Variable(Pointset({'coordnames': [x],
'coordarray': allxDataDict[x],
'coordtype': self.variables[x].coordtype,
'indepvarname': 't',
'indepvararray': alltData,
'indepvartype': self.variables[x].indepvartype}), 't', x, x)
else:
raise PyDSTool_ValueError, "Fewer than 2 data points computed"
for a in anames:
if len(alltData) > 1:
variables[a] = Variable(Pointset({'coordnames': [a],
'coordarray': allaDataDict[a],
'coordtype': self.variables[a].coordtype,
'indepvarname': 't',
'indepvararray': alltData,
'indepvartype': self.variables[a].indepvartype}), 't', a, a)
else:
raise PyDSTool_ValueError, "Fewer than 2 data points computed"
if success:
self.validateSpec()
self.defined = True
return Trajectory(trajname, variables.values(),
self.globalt0, self.checklevel)
else:
print 'Trajectory computation failed'
self.errors.append((E_COMPUTFAIL, (t, self._errorcodes[errcode])))
self.defined = False
def compute(self, trajname, dirn='f'):
continue_integ = ODEsystem.prepDirection(self, dirn)
if self._dircode == -1:
raise NotImplementedError, ('Backwards integration is not implemented')
# validate spec if there exists a prior trajectory computation
if self.defined:
self.validateSpec()
self.validateICs()
self.clearWarnings()
self.clearErrors()
pnames = sortedDictKeys(self.pars)
xnames = self._var_ixmap # ensures correct order
# Check i.c.'s are well defined (finite)
self.checkInitialConditions()
if self._algparams['stiff']:
methstr = 'bdf'
methcode = 2
else:
methstr = 'adams'
methcode = 1
if self.haveJacobian():
haveJac = 1
else:
haveJac = 0
if isinstance(self._algparams['atol'], list):
if len(self._algparams['atol']) != self.dimension:
raise ValueError, 'atol list must have same length as phase dimension'
else:
atol = self._algparams['atol']
self._algparams['atol'] = [atol for dimix in xrange(self.dimension)]
indepdom0 = self.indepvariable.depdomain.get(0)
indepdom1 = self.indepvariable.depdomain.get(1)
if continue_integ:
if self._tdata[0] != self._solver.t:
print "Previous end time is %f"%self._solver.t
raise ValueError, \
"Start time not correctly updated for continuing orbit"
x0 = self._solver.y
indepdom0 = self._solver.t
else:
x0 = sortedDictValues(self.initialconditions,
self.funcspec.vars)
if self._solver._integrator is None:
# Banded Jacobians not yet supported
#
# start a new integrator, because method may have been
# switched
self._solver.set_integrator('vode', method=methstr,
rtol=self._algparams['rtol'],
atol=self._algparams['atol'],
nsteps=self._algparams['max_pts'],
max_step=self._algparams['max_step'],
min_step=self._algparams['min_step'],
first_step=self._algparams['init_step'],
with_jacobian=haveJac)
# speed up repeated access to solver by making a temp name for it
solver = self._solver
else:
# speed up repeated access to solver by making a temp name for it
solver = self._solver
solver.with_jacobian = haveJac
# self.mu = lband
# self.ml = uband
solver.rtol = self._algparams['rtol']
solver.atol = self._algparams['atol']
solver.method = methcode
# self.order = order
solver.nsteps = self._algparams['max_pts']
solver.max_step = self._algparams['max_step']
solver.min_step = self._algparams['min_step']
solver.first_step = self._algparams['init_step']
solver.set_initial_value(x0, indepdom0)
## if self._dircode == 1:
## solver.set_initial_value(x0, indepdom0)
## else:
## solver.set_initial_value(x0, indepdom1)
# wrap up each dictionary initial value as a singleton list
alltData = [indepdom0]
allxDataDict = dict(zip(xnames, map(listid, x0)))
plist = sortedDictValues(self.pars)
extralist = copy(plist)
if self.inputs:
# inputVarList is a list of Variables
inames = sortedDictKeys(self.inputs)
listend = self.numpars + len(self.inputs)
inputVarList = sortedDictValues(self.inputs)
ilist = _pollInputs(inputVarList, alltData[0]+self.globalt0,
self.checklevel)
else:
ilist = []
inames = []
listend = self.numpars
inputVarList = []
extralist.extend(ilist)
solver.set_f_params(extralist)
if haveJac:
solver.set_jac_params(extralist)
dt = self._algparams['init_step']
strict = self._algparams['strictdt']
# Make t mesh
if not all(isfinite(self.indepvariable.depdomain.get())):
print "Time domain was: ", self.indepvariable.depdomain.get()
raise ValueError, "Ensure time domain is finite"
if dt == indepdom1 - indepdom0:
# single-step integration required
tmesh = [indepdom0, indepdom1]
else:
notDone = True
repeatTol = 10
count = 0
while notDone and count <= repeatTol:
try:
tmesh = self.indepvariable.depdomain.uniformSample(dt,
strict=strict,
avoidendpoints=self.checklevel>2)
notDone = False
except AssertionError:
count += 1
dt = dt/3.0
if count == repeatTol:
raise AssertionError, \
("supplied time step is too large for selected time"
" interval")
if len(tmesh)<=2:
# safety net, in case too few points in mesh
# too few points unless we can add endpoint
if tmesh[-1] != indepdom1:
# dt too large for tmesh to have more than one point
tmesh.append(indepdom1)
if not strict: # get actual time step used
# don't use [0] in case avoided end points
dt = tmesh[2]-tmesh[1]
if self.eventstruct.query(['lowlevel']) != []:
raise ValueError, "Only high level events can be passed to VODE"
eventslist = self.eventstruct.query(['highlevel', 'active',
'notvarlinked'])
termevents = self.eventstruct.query(['term'], eventslist)
# reverse time by reversing mesh doesn't work
## if self._dircode == -1:
## tmesh.reverse()
tmesh.pop(0) # get rid of first entry for initial condition
# per-iteration storage of variable data (initial values are irrelevant)
xDataDict = {}
xnames = self.funcspec.vars
# storage of all auxiliary variable data
allaDataDict = {}
anames = self.funcspec.auxvars
avals = apply(getattr(self,self.funcspec.auxspec[1]),
[indepdom0, x0, extralist])
for aix in range(len(anames)):
aname = anames[aix]
try:
allaDataDict[aname] = [avals[aix]]
except IndexError:
print "\nVODE generator: There was a problem evaluating " \
+ "an auxiliary variable"
print "Debug info: avals (length", len(avals), ") was ", avals
print "Index out of range was ", aix
print self.funcspec.auxspec[1]
print hasattr(self, self.funcspec.auxspec[1])
print "Args were:", [indepdom0, x0, extralist]
raise
# Initialize signs of event detection objects at IC
dataDict = copy(self.initialconditions)
dataDict.update(dict(zip(anames, avals)))
dataDict['t'] = indepdom0
self.setEventICs(self.initialconditions, self.globalt0)
if self.inputs:
parsinps = copy(self.pars)
parsinps.update(dict(zip(inames,ilist)))
else:
parsinps = self.pars
if eventslist != []:
evsflagged = self.eventstruct.pollHighLevelEvents(None,
dataDict,
parsinps,
eventslist)
if len(evsflagged) > 0:
raise RuntimeError, "Some events flagged at initial condition"
if continue_integ:
# revert to prevprevsign, since prevsign changed after call
self.eventstruct.resetHighLevelEvents(indepdom0, eventslist, 'prev')
else:
self.eventstruct.resetHighLevelEvents(indepdom0, eventslist) #, 'off')
self.eventstruct.validateEvents(self.funcspec.vars + \
self.funcspec.auxvars + \
self.funcspec.inputs + \
['t'], eventslist)
# temp storage of first time at which terminal events found
# (this is used for keeping the correct end point of new mesh)
first_found_t = None
# list of precise non-terminal events to be resolved after integration
nontermprecevs = []
evnames = [ev[0] for ev in eventslist]
lastevtime = {}.fromkeys(evnames, None)
# initialize new event info dictionaries
Evtimes = {}
Evpoints = {}
if continue_integ:
for evname in evnames:
try:
# these are in global time, so convert to local time
lastevtime[evname] = self.eventstruct.Evtimes[evname][-1]-self.globalt0
except (IndexError, KeyError):
# IndexError: Evtimes[evname] was None
# KeyError: Evtimes does not have key evname
pass
for evname in evnames:
Evtimes[evname] = []
Evpoints[evname] = []
# temp storage for repeatedly used object attributes (for lookup efficiency)
depdomains = {}
for xi in xrange(self.dimension):
depdomains[xi] = self.variables[xnames[xi]].depdomain
# Main integration loop
num_points = 0
breakwhile = False
while not breakwhile:
try:
new_t = tmesh.pop(0) # this destroys tmesh for future use
except IndexError:
break
try:
errcode = solver.integrate(new_t)
except:
print "Error calling right hand side function:"
self.showSpec()
print "Numerical traceback information (current state, " \
+ "parameters, etc.)"
print "in generator dictionary 'traceback'"
self.traceback = {'vars': dict(zip(xnames,solver.y)),
'pars': dict(zip(pnames,plist)),
'inputs': dict(zip(inames,ilist)),
self.indepvariable.name: new_t}
raise
for xi in xrange(self.dimension):
xDataDict[xnames[xi]] = solver.y[xi]
if not self.contains(depdomains[xi],
solver.y[xi],
self.checklevel):
self.warnings.append((W_TERMSTATEBD,
(solver.t,
xnames[xi],solver.y[xi],
depdomains[xi].get())))
breakwhile = True
break # for loop
if breakwhile:
break
avals = apply(getattr(self,self.funcspec.auxspec[1]), [new_t,
sortedDictValues(xDataDict),
extralist])
# Uncomment the following assertion for debugging
# assert all([isfinite(a) for a in avals]), \
# "Some auxiliary variable values not finite"
aDataDict = dict(zip(anames,avals))
if eventslist != []:
dataDict = copy(xDataDict)
dataDict.update(aDataDict)
dataDict['t'] = new_t
if self.inputs:
parsinps = copy(self.pars)
parsinps.update(dict(zip(inames,
## extralist[self.numpars:listend])))
_pollInputs(inputVarList, new_t+self.globalt0,
self.checklevel))))
else:
parsinps = self.pars
evsflagged = self.eventstruct.pollHighLevelEvents(None,
dataDict,
parsinps,
eventslist)
## print new_t, evsflagged
# evsflagged = [ev for ev in evsflagged if solver.t-indepdom0 > ev[1].eventinterval]
termevsflagged = filter(lambda e: e in evsflagged, termevents)
nontermevsflagged = filter(lambda e: e not in termevsflagged,
evsflagged)
# register any non-terminating events in the warnings
# list, unless they are 'precise' in which case flag
# them to be resolved after integration completes
if len(nontermevsflagged) > 0:
evnames = [ev[0] for ev in nontermevsflagged]
precEvts = self.eventstruct.query(['precise'],
nontermevsflagged)
prec_evnames = [e[0] for e in precEvts]
# first register non-precise events
nonprec_evnames = remain(evnames, prec_evnames)
# only record events if they have not been previously
# flagged within their event interval
if nonprec_evnames != []:
temp_names = []
for evname in nonprec_evnames:
prevevt_time = lastevtime[evname]
if prevevt_time is None:
ignore_ev = False
else:
if solver.t-prevevt_time < e[1].eventinterval:
ignore_ev = True
else:
ignore_ev = False
if not ignore_ev:
temp_names.append(evname)
lastevtime[evname] = solver.t
self.warnings.append((W_NONTERMEVENT,
(solver.t, temp_names)))
for evname in temp_names:
Evtimes[evname].append(solver.t)
Evpoints[evname].append(solver.y)
for e in precEvts:
# only record events if they have not been previously
# flagged within their event interval
prevevt_time = lastevtime[e[0]]
if prevevt_time is None:
ignore_ev = False
else:
if solver.t-dt-prevevt_time < e[1].eventinterval:
ignore_ev = True
else:
ignore_ev = False
if not ignore_ev:
nontermprecevs.append((solver.t-dt, solver.t,e))
# be conservative as to where the event is, so
# that don't miss any events.
lastevtime[e[0]] = solver.t-dt
e[1].reset() #e[1].prevsign = None #
do_termevs = []
if termevsflagged != []:
# only record events if they have not been previously
# flagged within their event interval
for e in termevsflagged:
prevevt_time = lastevtime[e[0]]
## print "Event %s flagged."%e[0]
## print " ... last time was ", prevevt_time
## print " ... event interval = ", e[1].eventinterval
## print " ... t = %f, dt = %f"%(solver.t, dt)
if prevevt_time is None:
ignore_ev = False
else:
## print " ... comparison = %f < %f"%(solver.t-dt-prevevt_time, e[1].eventinterval)
if solver.t-dt-prevevt_time < e[1].eventinterval:
ignore_ev = True
## print "VODE ignore ev"
else:
ignore_ev = False
if not ignore_ev:
do_termevs.append(e)
if len(do_termevs) > 0:
# >= 1 active terminal event flagged at this time point
if all([not ev[1].preciseFlag for ev in do_termevs]):
# then none of the events specify greater accuracy
# register the event in the warnings
evnames = [ev[0] for ev in do_termevs]
self.warnings.append((W_TERMEVENT, \
(solver.t, evnames)))
for evname in evnames:
Evtimes[evname].append(solver.t)
Evpoints[evname].append(solver.y)
breakwhile = True # break while loop after appending t, x
else:
# find which are the 'precise' events that flagged
precEvts = self.eventstruct.query(['precise'],
do_termevs)
# these events have flagged once so eventdelay has
# been used. now switch it off while finding event
# precisely (should be redundant after change to
# eventinterval and eventdelay parameters)
evnames = [ev[0] for ev in precEvts]
if first_found_t is None:
## print "first time round at", solver.t
numtries = 0
first_found_t = solver.t
restore_evts = deepcopy(precEvts)
minbisectlimit = min([ev[1].bisectlimit for ev in precEvts])
for ev in precEvts:
ev[1].eventdelay = 0.
else:
numtries += 1
## print "time round: ", numtries
if numtries > minbisectlimit:
self.warnings.append((W_BISECTLIMIT,
(solver.t, evnames)))
breakwhile = True
# find minimum eventtol in precEvts
dt_min = min([e[1].eventtol for e in precEvts])
# get previous time point
if len(alltData)>=1:
# take one step back -> told, which will
# get dt added back to first new meshpoint
# (solver.t is the step *after* the event was
# detected)
told = solver.t-dt
else:
raise ValueError("Event %s found too "%evnames[0]+\
"close to local start time: try decreasing "
"initial step size (current size is "
"%f @ t=%f)"%(dt,solver.t+self.globalt0))
if dt_min >= dt:
## print "Registering event:", dt_min, dt
# register the event in the warnings
self.warnings.append((W_TERMEVENT,
(solver.t, evnames)))
for evname in evnames:
Evtimes[evname].append(solver.t)
Evpoints[evname].append(solver.y)
# Cannot continue -- dt_min no smaller than
# previous dt. If this is more than the first time
# in this code then have found the event to within
# the minimum 'precise' event's eventtol, o/w need
# to set eventtol smaller.
breakwhile = True # while loop
if not breakwhile:
dt_new = dt/5.0
# calc new tmesh
trangewidth = 2*dt #first_found_t - told
numpoints = int(math.ceil(trangewidth/dt_new))
# choose slightly smaller dt to fit trange exactly
dt = trangewidth/numpoints
tmesh = [told + i*dt for i in xrange(1, numpoints+1)]
# reset events according to new time mesh,
# setting known previous event state to be their
# "no event found" state
self.eventstruct.resetHighLevelEvents(told,
precEvts,
state='off')
# build new ic with last good values (at t=told)
if len(alltData)>1:
new_ic = [allxDataDict[xname][-1] \
for xname in xnames]
else:
new_ic = x0
# reset integrator
solver.set_initial_value(new_ic, told)
extralist[self.numpars:listend] = \
[apply(f, [told+self.globalt0,
self.checklevel]) \
for f in inputVarList]
solver.set_f_params(extralist)
# continue integrating over new mesh
continue # while
alltData.append(solver.t)
for xi in xrange(self.dimension):
allxDataDict[xnames[xi]].append(solver.y[xi])
for aix in xrange(len(anames)):
aname = anames[aix]
allaDataDict[aname].append(avals[aix])
num_points += 1
if not breakwhile:
try:
extralist[self.numpars:listend] = [apply(f, \
[solver.t+self.globalt0,
self.checklevel]) \
for f in inputVarList]
except ValueError:
print 'External input call caused value out of range error:',\
't = ', solver.t
for f in inputVarList:
if len(f.warnings):
print 'External input variable %s out of range:' % f.name
print ' t = ', repr(f.warnings[-1][0]), ', ', \
f.name, ' = ', repr(f.warnings[-1][1])
raise
except AssertionError:
print 'External input call caused t out of range error: t = ', \
solver.t
raise
solver.set_f_params(extralist)
breakwhile = not solver.successful()
# Check that any terminal events found terminated the code correctly
if first_found_t is not None:
# ... then terminal events were found. Those that were 'precise' had
# their 'eventdelay' attribute temporarily set to 0. It now should
# be restored.
for evname1, ev1 in termevents:
# restore_evts are copies of the originally flagged 'precise'
# events
for evname2, ev2 in restore_evts:
if evname2 == evname1:
ev1.eventdelay = ev2.eventdelay
try:
if self.warnings[-1][0] not in [W_TERMEVENT, W_TERMSTATEBD]:
raise RuntimeError("Event finding code for terminal event "
"failed in Generator " + self.name + \
": try decreasing eventdelay or "
"eventinterval below eventtol")
except IndexError:
print "Output stats: ", self.outputstats
raise RuntimeError("Event finding failed in Generator " + \
self.name + ": try decreasing eventdelay "
"or eventinterval below eventtol")
# Package up computed trajectory in Variable variables
# Add external inputs warnings to self.warnings, if any
for f in inputVarList:
for winfo in f.warnings:
self.warnings.append((W_NONTERMSTATEBD,
(winfo[0], f.name, winfo[1],
f.depdomain.get())))
# check for non-unique terminal event
termcount = 0
for (w,i) in self.warnings:
if w == W_TERMEVENT or w == W_TERMSTATEBD:
termcount += 1
if termcount > 1:
self.errors.append((E_NONUNIQUETERM, (alltData[-1], i[1])))
# uncomment the following lines for debugging
# assert len(alltData) == len(allxDataDict.values()[0]) \
# == len(allaDataDict.values()[0]), "Output data size mismatch"
# for val_list in allaDataDict.values():
# assert all([isfinite(x) for x in val_list])
# Create variables (self.variables contains no actual data)
# These versions of the variables are only final if no non-terminal
# events need to be inserted.
variables = copyVarDict(self.variables)
for x in xnames:
if len(alltData) > 1:
variables[x] = Variable(interp1d(alltData, allxDataDict[x]),
't', x, x)
else:
print "Error in Generator:", self.name
print "t = ", alltData
print "x = ", allxDataDict
raise PyDSTool_ValueError, "Fewer than 2 data points computed"
for a in anames:
if len(alltData) > 1:
variables[a] = Variable(interp1d(alltData, allaDataDict[a]),
't', a, a)
else:
print "Error in Generator:", self.name
print "t = ", alltData
print "x = ", allxDataDict
raise PyDSTool_ValueError, "Fewer than 2 data points computed"
# Resolve non-terminal 'precise' events that were flagged, using the
# variables created. Then, add them to a new version of the variables.
ntpe_tdict = {}
for (et0,et1,e) in nontermprecevs:
lost_evt = False
search_dt = max((et1-et0)/5,e[1].eventinterval)
et_precise_list = e[1].searchForEvents(trange=[et0,et1],
dt=search_dt,
checklevel=self.checklevel,
parDict=self.pars,
vars=variables,
inputs=self.inputs,
abseps=self._abseps,
eventdelay=False,
globalt0=self.globalt0)
if et_precise_list == []:
lost_evt = True
for et_precise in et_precise_list:
if et_precise[0] is not None:
if et_precise[0] in ntpe_tdict:
# add event name at this time (that already exists in the dict)
ntpe_tdict[et_precise[0]].append(e[0])
else:
# add event name at this time (when time is not already in dict)
ntpe_tdict[et_precise[0]] = [e[0]]
else:
lost_evt = True
if lost_evt:
raise PyDSTool_ExistError, \
("Internal error: A non-terminal, 'precise' event '"
+e[0]+"' was lost after integration!")
# add non-terminal event points to variables
if ntpe_tdict != {}:
# find indices of times at which event times will be inserted
tix = 0
evts = ntpe_tdict.keys()
evts.sort()
for evix in xrange(len(evts)):
evt = evts[evix]
evnames = ntpe_tdict[evt]
self.warnings.append((W_NONTERMEVENT, (evt, evnames)))
xval = [variables[x](evt) for x in xnames]
for evname in evnames:
Evtimes[evname].append(evt)
Evpoints[evname].append(array(xval))
tcond = less_equal(alltData[tix:], evt).tolist()
try:
tix = tcond.index(0) + tix # lowest index for t > evt
do_insert = (alltData[tix-1] != evt)
except ValueError:
# evt = last t value so no need to add it
do_insert = False
if do_insert:
alltData.insert(tix, evt)
xvaldict = dict(zip(xnames, xval))
for x in xnames:
allxDataDict[x].insert(tix, xvaldict[x])
for a in anames:
allaDataDict[a].insert(tix, variables[a](evt))
for x in xnames:
variables[x] = Variable(interp1d(alltData, allxDataDict[x]),
't', x, x)
for a in anames:
variables[a] = Variable(interp1d(alltData, allaDataDict[a]),
't', a, a)
self.outputstats = {'last_step': dt,
'num_fcns': num_points,
'num_steps': num_points,
'errorStatus': errcode
}
if solver.successful():
self.validateSpec()
for evname, evtlist in Evtimes.iteritems():
try:
self.eventstruct.Evtimes[evname].extend([et+self.globalt0 \
for et in evtlist])
except KeyError:
self.eventstruct.Evtimes[evname] = [et+self.globalt0 \
for et in evtlist]
# build event pointset information (reset previous trajectory's)
self.trajevents = {}
for (evname, ev) in eventslist:
evpt = Evpoints[evname]
if evpt == []:
self.trajevents[evname] = None
else:
evpt = transpose(array(evpt))
self.trajevents[evname] = Pointset({'coordnames': xnames,
'indepvarname': 't',
'coordarray': evpt,
'indepvararray': Evtimes[evname],
'indepvartype': Float})
self.defined = True
return Trajectory(trajname, variables.values(),
self.globalt0, self.checklevel)
else:
try:
self.errors.append((E_COMPUTFAIL, (solver.t,
self._errorcodes[errcode])))
except TypeError:
# e.g. when errcode has been used to return info list
print "Error information: ", errcode
self.errors.append((E_COMPUTFAIL, (solver.t,
self._errorcodes[0])))
self.defined = False
col = 0
for n in line.split():
U[row, col] = float(n)
col += 1
row += 1
rows, columns = [int(a) for a in vfile.readline().split()]
V = na.zeros((rows, columns), type="Float32")
row = 0
for line in vfile:
col = 0
for n in line.split():
V[row, col] = float(n)
col += 1
row += 1
return U, S, V
up = cPickle.Unpickler(file('artist_user.pickle', 'rb'))
artists, users = up.load()
#U is artists
U, S, V = load_svd(file('big_s', 'r'), file('big_ut', 'r'), file('big_vt', 'r'))
#I believe that U is already transposed
tt = na.dot(na.transpose(U), na.dot(na.dot(S, S), U))
fout = file('lsi.out', 'wb')
cp = cPickle.Pickler(fout, -1)
cp.dump(tt)
fout.close()
def logistic_regression(x,y,beta_start=None,verbose=False,CONV_THRESH=1.e-3,
MAXIT=500):
"""
Uses the Newton-Raphson algorithm to calculate a maximum
likelihood estimate logistic regression.
The algorithm is known as 'iteratively re-weighted least squares', or IRLS.
x - rank-1 or rank-2 array of predictors. If x is rank-2,
the number of predictors = x.shape[0] = N. If x is rank-1,
it is assumed N=1.
y - binary outcomes (if N>1 len(y) = x.shape[1], if N=1 len(y) = len(x))
beta_start - initial beta vector (default zeros(N+1,x.dtype.char))
if verbose=True, diagnostics printed for each iteration (default False).
MAXIT - max number of iterations (default 500)
CONV_THRESH - convergence threshold (sum of absolute differences
of beta-beta_old, default 0.001)
returns beta (the logistic regression coefficients, an N+1 element vector),
J_bar (the (N+1)x(N+1) information matrix), and l (the log-likeliehood).
J_bar can be used to estimate the covariance matrix and the standard
error for beta.
l can be used for a chi-squared significance test.
covmat = inverse(J_bar) --> covariance matrix of coefficents (beta)
stderr = sqrt(diag(covmat)) --> standard errors for beta
deviance = -2l --> scaled deviance statistic
chi-squared value for -2l is the model chi-squared test.
"""
if x.shape[-1] != len(y):
raise ValueError, "x.shape[-1] and y should be the same length!"
try:
N, npreds = x.shape[1], x.shape[0]
except: # single predictor, use simple logistic regression routine.
return _simple_logistic_regression(x,y,beta_start=beta_start,
CONV_THRESH=CONV_THRESH,MAXIT=MAXIT,verbose=verbose)
if beta_start is None:
beta_start = NA.zeros(npreds+1,x.dtype.char)
X = NA.ones((npreds+1,N), x.dtype.char)
X[1:, :] = x
Xt = NA.transpose(X)
iter = 0; diff = 1.; beta = beta_start # initial values
if verbose:
print 'iteration beta log-likliehood |beta-beta_old|'
while iter < MAXIT:
beta_old = beta
ebx = NA.exp(NA.dot(beta, X))
p = ebx/(1.+ebx)
l = NA.sum(y*NA.log(p) + (1.-y)*NA.log(1.-p)) # log-likeliehood
s = NA.dot(X, y-p) # scoring function
J_bar = NA.dot(X*p,Xt) # information matrix
beta = beta_old + NA.dot(LA.inverse(J_bar),s) # new value of beta
diff = NA.sum(NA.fabs(beta-beta_old)) # sum of absolute differences
if verbose:
print iter+1, beta, l, diff
if diff <= CONV_THRESH: break
iter = iter + 1
if iter == MAXIT and diff > CONV_THRESH:
print 'warning: convergence not achieved with threshold of %s in %s iterations' % (CONV_THRESH,MAXIT)
return beta, J_bar, l
#! /usr/bin/env python # -*- compile-command: "python hello.py" -*- print "Calcul numerique en Python" A=[[1,2],[3,4]] print A print A[1] # selectionne la deuxieme ligne (indice commence a 1) print [A[i][0] for i in range(len(A))] # selectionne la premiere colonne print [i[0] for i in A] # selectionne la premiere colonne (+ court) B=[[1,2],[3,4]] #print add(A,B) # voir pour les operations import numarray as np A_num = np.array([[1,2],[3,4]]) print np.transpose(A_num)[0]
r12 = 0.5 # average correlation between the first predictor and the obs.
r13 = 0.25 # avg correlation between the second predictor and the obs.
r23 = 0.125 # avg correlation between predictors.
# random draws from trivariate normal distribution
x = multivariate_normal(
NA.array([0, 0, 0]),
NA.array([[1, r12, r13], [r12, 1, r23], [r13, r23, 1]]), nsamps)
x2 = multivariate_normal(
NA.array([0, 0, 0]),
NA.array([[1, r12, r13], [r12, 1, r23], [r13, r23, 1]]), nsamps)
print 'correlations (r12,r13,r23) = ', r12, r13, r23
print 'number of realizations = ', nsamps
# training data.
obs = x[:, 0]
climprob = NA.sum((obs > 0).astype('f')) / nsamps
fcst = NA.transpose(x[:, 1:]) # 2 predictors.
obs_binary = obs > 0.
# independent data for verification.
obs2 = x2[:, 0]
fcst2 = NA.transpose(x2[:, 1:])
# compute logistic regression.
beta, Jbar, llik = logistic_regression(fcst, obs_binary, verbose=True)
covmat = LA.inverse(Jbar)
stderr = NA.sqrt(mlab.diag(covmat))
print 'beta =', beta
print 'standard error =', stderr
# forecasts from independent data.
prob = calcprob(beta, fcst2)
# compute Brier Skill Score
verif = (obs2 > 0.).astype('f')
bs = mlab.mean((0.01 * prob - verif)**2)
def logistic_regression(x,
y,
beta_start=None,
verbose=False,
CONV_THRESH=1.e-3,
MAXIT=500):
"""
Uses the Newton-Raphson algorithm to calculate a maximum
likelihood estimate logistic regression.
The algorithm is known as 'iteratively re-weighted least squares', or IRLS.
x - rank-1 or rank-2 array of predictors. If x is rank-2,
the number of predictors = x.shape[0] = N. If x is rank-1,
it is assumed N=1.
y - binary outcomes (if N>1 len(y) = x.shape[1], if N=1 len(y) = len(x))
beta_start - initial beta vector (default zeros(N+1,x.dtype.char))
if verbose=True, diagnostics printed for each iteration (default False).
MAXIT - max number of iterations (default 500)
CONV_THRESH - convergence threshold (sum of absolute differences
of beta-beta_old, default 0.001)
returns beta (the logistic regression coefficients, an N+1 element vector),
J_bar (the (N+1)x(N+1) information matrix), and l (the log-likeliehood).
J_bar can be used to estimate the covariance matrix and the standard
error for beta.
l can be used for a chi-squared significance test.
covmat = inverse(J_bar) --> covariance matrix of coefficents (beta)
stderr = sqrt(diag(covmat)) --> standard errors for beta
deviance = -2l --> scaled deviance statistic
chi-squared value for -2l is the model chi-squared test.
"""
if x.shape[-1] != len(y):
raise ValueError, "x.shape[-1] and y should be the same length!"
try:
N, npreds = x.shape[1], x.shape[0]
except: # single predictor, use simple logistic regression routine.
return _simple_logistic_regression(x,
y,
beta_start=beta_start,
CONV_THRESH=CONV_THRESH,
MAXIT=MAXIT,
verbose=verbose)
if beta_start is None:
beta_start = NA.zeros(npreds + 1, x.dtype.char)
X = NA.ones((npreds + 1, N), x.dtype.char)
X[1:, :] = x
Xt = NA.transpose(X)
iter = 0
diff = 1.
beta = beta_start # initial values
if verbose:
print 'iteration beta log-likliehood |beta-beta_old|'
while iter < MAXIT:
beta_old = beta
ebx = NA.exp(NA.dot(beta, X))
p = ebx / (1. + ebx)
l = NA.sum(y * NA.log(p) +
(1. - y) * NA.log(1. - p)) # log-likeliehood
s = NA.dot(X, y - p) # scoring function
J_bar = NA.dot(X * p, Xt) # information matrix
beta = beta_old + NA.dot(LA.inverse(J_bar), s) # new value of beta
diff = NA.sum(NA.fabs(beta - beta_old)) # sum of absolute differences
if verbose:
print iter + 1, beta, l, diff
if diff <= CONV_THRESH: break
iter = iter + 1
if iter == MAXIT and diff > CONV_THRESH:
print 'warning: convergence not achieved with threshold of %s in %s iterations' % (
CONV_THRESH, MAXIT)
return beta, J_bar, l
#!/usr/bin/python
## example2_8
from numarray import array,matrixmultiply,transpose
from choleski import *
a = array([[ 1.44, -0.36, 5.52, 0.0], \
[-0.36, 10.33, -7.78, 0.0], \
[ 5.52, -7.78, 28.40, 9.0], \
[ 0.0, 0.0, 9.0, 61.0]])
L = choleski(a)
print 'L =\n',L
print '\nCheck: L*L_transpose =\n', \
matrixmultiply(L,transpose(L))
raw_input("\nPress return to exit")
#! /usr/bin/env python # -*- compile-command: "python hello.py" -*- print "Calcul numerique en Python" A=[[1,2],[3,4]] print A print A[1] # selectionne la deuxieme ligne (indice commence a 1) print [A[i][0] for i in range(len(A))] # selectionne la premiere colonne print [i[0] for i in A] # selectionne la premiere colonne (+ court) B=[[1,2],[3,4]] #print add(A,B) # voir pour les operations import numarray A_num = numarray.array([[1,2],[3,4]]) print numarray.transpose(A_num)[0]
def exportPointset(thepointset,
infodict,
separator=' ',
linesep='\n',
precision=12,
suppress_small=0,
varvaldir='col',
ext='',
append=False):
assert varvaldir in ['col', 'row'], \
"invalid variable value write direction"
# in order to avoid import cycles, cannot explicitly check that
# thepointset is of type Pointset, because Points.py imports this file
# (utils.py), so check an attribute instead.
try:
thepointset.coordnames
except AttributeError:
raise TypeError, "Must pass Pointset to this function: use arrayToPointset first!"
infodict_usedkeys = []
for key, info in infodict.iteritems():
if isinstance(info, str):
infodict_usedkeys += [info]
elif info == []:
infodict[key] = copy.copy(thepointset.coordnames)
infodict_usedkeys.extend(thepointset.coordnames)
else:
infodict_usedkeys += list(info)
allnames = copy.copy(thepointset.coordnames)
if thepointset._parameterized:
allnames.append(thepointset.indepvarname)
remlist = remain(infodict_usedkeys, allnames + range(len(allnames)))
if remlist != []:
print "Coords not found in pointset:", remlist
raise ValueError, \
"invalid keys in infodict - some not present in thepointset"
assert isinstance(ext, str), "'ext' extension argument must be a string"
if ext != '':
if ext[0] != '.':
ext = '.' + ext
if append:
assert varvaldir == 'col', ("append mode not supported for row"
"format of data ordering")
modestr = 'a'
else:
modestr = 'w'
totlen = len(thepointset)
if totlen == 0:
raise ValueError, ("Pointset is empty")
for fname, tup in infodict.iteritems():
try:
f = open(fname + ext, modestr)
except IOError:
print "There was a problem opening file " + fname + ext
raise
try:
if isinstance(tup, str):
try:
varray = thepointset[tup]
except TypeError:
raise ValueError, "Invalid specification of coordinates"
elif isinstance(tup, int):
try:
varray = thepointset[:, tup].toarray()
except TypeError:
raise ValueError, "Invalid specification of coordinates"
elif type(tup) in [list, tuple]:
if alltrue([type(ti) == str for ti in tup]):
thetup = list(tup)
if thepointset.indepvarname in tup:
tix = thetup.index(thepointset.indepvarname)
thetup.remove(thepointset.indepvarname)
try:
vlist = thepointset[thetup].toarray().tolist()
except TypeError:
raise ValueError, "Invalid specification of coordinates"
if len(thetup) == 1:
vlist = [vlist]
if thepointset.indepvarname in tup:
vlist.insert(tix, thepointset.indepvararray.tolist())
varray = array(vlist)
elif alltrue([type(ti) == int for ti in tup]):
try:
varray = thepointset[:, tup].toarray()
except TypeError:
raise ValueError, "Invalid specification of coordinates"
else:
raise ValueError, "Invalid specification of coordinates"
else:
f.close()
raise TypeError, \
"infodict values must be singletons or tuples/lists of strings or integers"
except IOError:
f.close()
print "Problem writing to file" + fname + ext
raise
except KeyError:
f.close()
raise KeyError, ("Keys in infodict not found in pointset")
if varvaldir == 'row':
write_array(f,
varray,
separator,
linesep,
precision,
suppress_small,
keep_open=0)
else:
write_array(f,
transpose(varray),
separator,
linesep,
precision,
suppress_small,
keep_open=0)
def transform(self, t): tmp = transpose(array(sequence=self.points, shape=(len(self.points), 3))) self.points = transpose(matrixmultiply(t, tmp)).tolist()
def get_evec(p, dim):
# extra call to array() to make it contiguous
v = array(transpose(p.v)[dim - 1])
v.shape = (totdim, 3)
return v
def compute(self, trajname, ics=None):
assert self.funcspec.targetlang == "python", (
"Wrong target language for functional specification. " "Python needed for this class"
)
assert isinstance(self.funcspec, RHSfuncSpec), "Map system " "requires RHSfuncSpec type to proceed"
if self.defined:
self.validateSpec()
## assert remain(self.initialconditions.keys(),
## self._xdatadict.keys()+self.funcspec.auxvars) == [],\
## ('mismatching entries between initial conditions and '
## 'declared variable names')
self.clearWarnings()
self.clearErrors()
if ics is not None:
self.set(ics=ics)
xnames = self._var_ixmap # ensures correct order
# wrap up each dictionary initial value as a singleton list
alltData = [self.indepvariable.depdomain.get(0)]
allxDataDict = dict(zip(xnames, map(listid, sortedDictValues(self.initialconditions, self.funcspec.vars))))
rhsfn = eval("self." + self.funcspec.spec[1])
# Check i.c.'s are well defined (finite)
self.checkInitialConditions()
self.setEventICs(self.initialconditions, self.globalt0)
ic = sortedDictValues(self.initialconditions, self.funcspec.vars)
plist = sortedDictValues(self.pars)
extralist = copy(plist)
ilist = []
if self.inputs:
# inputVarList is a list of Variables
listend = self.numpars + len(self.inputs)
inputVarList = sortedDictValues(self.inputs)
try:
for f in inputVarList:
f.clearWarnings
ilist.append(f(alltData[0], self.checklevel))
except AssertionError:
print "External input call has t out of range: t = ", self.indepvariable.depdomain.get(0)
print "Maybe checklevel is 3 and initial time is not", "completely inside valid time interval"
raise
except ValueError:
print "External input call has value out of range: t = ", self.indepvariable.depdomain.get(0)
for f in inputVarList:
if len(f.warnings):
print "External input %s out of range:" % f.name
print " t = ", repr(f.warnings[-1][0]), ", ", f.name, " = ", repr(f.warnings[-1][1])
raise
else:
listend = self.numpars
inputVarList = []
extralist.extend(ilist)
precevents = self.eventstruct.query(["precise"])
if precevents != []:
raise PyDSTool_ValueError("precise events are not valid for map systems")
eventslist = self.eventstruct.query(["highlevel", "active", "notvarlinked"])
termevents = self.eventstruct.query(["term"], eventslist)
# initialize event info dictionaries
Evtimes = {}
Evpoints = {}
for (evname, ev) in eventslist:
Evtimes[evname] = []
Evpoints[evname] = []
if eventslist != []:
self.eventstruct.resetHighLevelEvents(self.indepvariable.depdomain.get(0), eventslist)
self.eventstruct.validateEvents(self.funcspec.vars + self.funcspec.auxvars + ["t"], eventslist)
# per-iteration storage of variable data (initial values are irrelevant)
xDataDict = {}
# storage of all auxiliary variable data
allaDataDict = {}
anames = self.funcspec.auxvars
avals = apply(
eval("self." + self.funcspec.auxspec[1]),
[
self.indepvariable.depdomain.get(0),
sortedDictValues(self.initialconditions, self.funcspec.vars),
extralist,
],
)
for aix in range(len(anames)):
aname = anames[aix]
allaDataDict[aname] = [avals[aix]]
# temp storage of first time at which terminal events found
# (this is used for keeping the correct end point of new mesh)
first_found_t = None
tmesh = self.indepvariable.depdomain.uniformSample(self.tstep, strict=False, avoidendpoints=self.checklevel > 2)
# Main loop
breakwhile = False
success = False
x = ic
notdone = True
# did i=0 for initial condition already
i = 1
while notdone:
t = tmesh[i]
## COMPUTE NEXT STATE y from x
try:
y = rhsfn(t, x, extralist)
except:
print "Error in calling right hand side function:"
self.showSpec()
raise
for xi in xrange(self.dimension):
xDataDict[xnames[xi]] = y[xi]
if not self.contains(self.variables[xnames[xi]].depdomain, y[xi], self.checklevel):
self.warnings.append((W_TERMSTATEBD, (t, xnames[xi], y[xi], self.variables[xnames[xi]].depdomain)))
breakwhile = True
break # for loop
if breakwhile:
notdone = False
continue
if eventslist != []:
dataDict = copy(xDataDict)
dataDict["t"] = t
evsflagged = self.eventstruct.pollHighLevelEvents(None, dataDict, self.pars, eventslist)
termevsflagged = filter(lambda e: e in evsflagged, termevents)
nontermevsflagged = filter(lambda e: e not in termevsflagged, evsflagged)
# register any non-terminating events in the warnings list
if len(nontermevsflagged) > 0:
evnames = [ev[0] for ev in nontermevsflagged]
self.warnings.append((W_NONTERMEVENT, (t, evnames)))
for evname in evnames:
Evtimes[evname].append(t)
Evpoints[evname].append(y)
if termevsflagged != []:
# active terminal event flagged at this time point
# register the event in the warnings
evnames = [ev[0] for ev in termevsflagged]
self.warnings.append((W_TERMEVENT, (t, evnames)))
for evname in evnames:
Evtimes[evname].append(t)
Evpoints[evname].append(y)
notdone = False
continue
alltData.append(t)
for xi in range(self.dimension):
allxDataDict[xnames[xi]].append(y[xi])
avals = apply(eval("self." + self.funcspec.auxspec[1]), [t, sortedDictValues(xDataDict), extralist])
for aix in range(len(anames)):
aname = anames[aix]
allaDataDict[aname].append(avals[aix])
try:
extralist[self.numpars : listend] = [apply(f, [t, self.checklevel]) for f in inputVarList]
except ValueError:
print "External input call caused value out of range error:", "t = ", t
for f in inputVarList:
if len(f.warnings):
print "External input variable %s out of range:" % f.name
print " t = ", repr(f.warnings[-1][0]), ", ", f.name, " = ", repr(f.warnings[-1][1])
raise
except AssertionError:
print "External input call caused t out of range error: t = ", t
raise
if i >= len(tmesh) - 1:
notdone = False
else:
i += 1
x = y
# update success flag
success = not notdone
# Check that any terminal events found terminated the code correctly
if first_found_t is not None:
assert self.warnings[-1][0] == W_TERMEVENT, "Event finding code " "for terminal event failed"
# Package up computed trajectory in Variable variables
# Add external inputs warnings to self.warnings, if any
for f in inputVarList:
for winfo in f.warnings:
self.warnings.append((W_NONTERMSTATEBD, (winfo[0], f.name, winfo[1], f.depdomain)))
# check for non-unique terminal event
termcount = 0
for (w, i) in self.warnings:
if w == W_TERMEVENT or w == W_TERMSTATEBD:
termcount += 1
if termcount > 1:
self.errors.append((E_NONUNIQUETERM, (alltData[-1], i[1])))
## print 'Time interval adjusted according to %s: %s' % \
## (self._warnmessages[w], str(i[0])+", "+ str(i[1]))
# Create variables (self.variables contains no actual data)
variables = copyVarDict(self.variables)
# build event pointset information (reset previous trajectory's)
self.trajevents = {}
for (evname, ev) in eventslist:
evpt = Evpoints[evname]
if evpt == []:
self.trajevents[evname] = None
else:
evpt = transpose(array(evpt))
self.trajevents[evname] = Pointset(
{
"coordnames": xnames,
"indepvarname": "t",
"coordarray": evpt,
"indepvararray": Evtimes[evname],
"indepvartype": self.variables[xnames[0]].indepvartype,
}
)
for x in xnames:
if len(alltData) > 1:
variables[x] = Variable(
Pointset(
{
"coordnames": [x],
"coordarray": allxDataDict[x],
"coordtype": self.variables[x].coordtype,
"indepvarname": "t",
"indepvararray": alltData,
"indepvartype": self.variables[x].indepvartype,
}
),
"t",
x,
x,
)
else:
raise PyDSTool_ValueError, "Fewer than 2 data points computed"
for a in anames:
if len(alltData) > 1:
variables[a] = Variable(
Pointset(
{
"coordnames": [a],
"coordarray": allaDataDict[a],
"coordtype": self.variables[a].coordtype,
"indepvarname": "t",
"indepvararray": alltData,
"indepvartype": self.variables[a].indepvartype,
}
),
"t",
a,
a,
)
else:
raise PyDSTool_ValueError, "Fewer than 2 data points computed"
if success:
self.validateSpec()
self.defined = True
return Trajectory(trajname, variables.values(), self.globalt0, self.checklevel)
else:
print "Trajectory computation failed"
self.errors.append((E_COMPUTFAIL, (t, self._errorcodes[errcode])))
self.defined = False
import numpy.oldnumeric.mlab as mlab
# number of realizations.
nsamps = 100000
# correlations
r12 = 0.5 # average correlation between the first predictor and the obs.
r13 = 0.25 # avg correlation between the second predictor and the obs.
r23 = 0.125 # avg correlation between predictors.
# random draws from trivariate normal distribution
x = multivariate_normal(NA.array([0,0,0]),NA.array([[1,r12,r13],[r12,1,r23],[r13,r23,1]]), nsamps)
x2 = multivariate_normal(NA.array([0,0,0]),NA.array([[1,r12,r13],[r12,1,r23],[r13,r23,1]]), nsamps)
print 'correlations (r12,r13,r23) = ',r12,r13,r23
print 'number of realizations = ',nsamps
# training data.
obs = x[:,0]
climprob = NA.sum((obs > 0).astype('f'))/nsamps
fcst = NA.transpose(x[:,1:]) # 2 predictors.
obs_binary = obs > 0.
# independent data for verification.
obs2 = x2[:,0]
fcst2 = NA.transpose(x2[:,1:])
# compute logistic regression.
beta,Jbar,llik = logistic_regression(fcst,obs_binary,verbose=True)
covmat = LA.inverse(Jbar)
stderr = NA.sqrt(mlab.diag(covmat))
print 'beta =' ,beta
print 'standard error =',stderr
# forecasts from independent data.
prob = calcprob(beta, fcst2)
# compute Brier Skill Score
verif = (obs2 > 0.).astype('f')
bs = mlab.mean((0.01*prob - verif)**2)
#!/usr/bin/python
## example2_8
from numarray import array, matrixmultiply, transpose
from choleski import *
a = array([[ 1.44, -0.36, 5.52, 0.0], \
[-0.36, 10.33, -7.78, 0.0], \
[ 5.52, -7.78, 28.40, 9.0], \
[ 0.0, 0.0, 9.0, 61.0]])
L = choleski(a)
print 'L =\n', L
print '\nCheck: L*L_transpose =\n', \
matrixmultiply(L,transpose(L))
raw_input("\nPress return to exit")
def get_evec(p, dim):
# extra call to array() to make it contiguous
v = array(transpose(p.v)[dim-1])
v.shape = (totdim, 3)
return v
def exportPointset(thepointset, infodict, separator=' ', linesep='\n',
precision=12, suppress_small=0, varvaldir='col',
ext='', append=False):
assert varvaldir in ['col', 'row'], \
"invalid variable value write direction"
# in order to avoid import cycles, cannot explicitly check that
# thepointset is of type Pointset, because Points.py imports this file
# (utils.py), so check an attribute instead.
try:
thepointset.coordnames
except AttributeError:
raise TypeError, "Must pass Pointset to this function: use arrayToPointset first!"
infodict_usedkeys = []
for key, info in infodict.iteritems():
if isinstance(info, str):
infodict_usedkeys += [info]
elif info == []:
infodict[key] = copy.copy(thepointset.coordnames)
infodict_usedkeys.extend(thepointset.coordnames)
else:
infodict_usedkeys += list(info)
allnames = copy.copy(thepointset.coordnames)
if thepointset._parameterized:
allnames.append(thepointset.indepvarname)
remlist = remain(infodict_usedkeys, allnames+range(len(allnames)))
if remlist != []:
print "Coords not found in pointset:", remlist
raise ValueError, \
"invalid keys in infodict - some not present in thepointset"
assert isinstance(ext, str), "'ext' extension argument must be a string"
if ext != '':
if ext[0] != '.':
ext = '.'+ext
if append:
assert varvaldir == 'col', ("append mode not supported for row"
"format of data ordering")
modestr = 'a'
else:
modestr = 'w'
totlen = len(thepointset)
if totlen == 0:
raise ValueError, ("Pointset is empty")
for fname, tup in infodict.iteritems():
try:
f = open(fname+ext, modestr)
except IOError:
print "There was a problem opening file "+fname+ext
raise
try:
if isinstance(tup, str):
try:
varray = thepointset[tup]
except TypeError:
raise ValueError, "Invalid specification of coordinates"
elif isinstance(tup, int):
try:
varray = thepointset[:,tup].toarray()
except TypeError:
raise ValueError, "Invalid specification of coordinates"
elif type(tup) in [list, tuple]:
if alltrue([type(ti)==str for ti in tup]):
thetup=list(tup)
if thepointset.indepvarname in tup:
tix = thetup.index(thepointset.indepvarname)
thetup.remove(thepointset.indepvarname)
try:
vlist = thepointset[thetup].toarray().tolist()
except TypeError:
raise ValueError, "Invalid specification of coordinates"
if len(thetup)==1:
vlist = [vlist]
if thepointset.indepvarname in tup:
vlist.insert(tix, thepointset.indepvararray.tolist())
varray = array(vlist)
elif alltrue([type(ti)==int for ti in tup]):
try:
varray = thepointset[:,tup].toarray()
except TypeError:
raise ValueError, "Invalid specification of coordinates"
else:
raise ValueError, "Invalid specification of coordinates"
else:
f.close()
raise TypeError, \
"infodict values must be singletons or tuples/lists of strings or integers"
except IOError:
f.close()
print "Problem writing to file"+fname+ext
raise
except KeyError:
f.close()
raise KeyError, ("Keys in infodict not found in pointset")
if varvaldir == 'row':
write_array(f, varray, separator, linesep,
precision, suppress_small, keep_open=0)
else:
write_array(f, transpose(varray), separator, linesep,
precision, suppress_small, keep_open=0)
def compute(self, trajname, dirn='f'):
continue_integ = ODEsystem.prepDirection(self, dirn)
if self._dircode == -1:
raise NotImplementedError, (
'Backwards integration is not implemented')
# validate spec if there exists a prior trajectory computation
if self.defined:
self.validateSpec()
self.validateICs()
self.clearWarnings()
self.clearErrors()
pnames = sortedDictKeys(self.pars)
xnames = self._var_ixmap # ensures correct order
# Check i.c.'s are well defined (finite)
self.checkInitialConditions()
if self._algparams['stiff']:
methstr = 'bdf'
methcode = 2
else:
methstr = 'adams'
methcode = 1
if self.haveJacobian():
haveJac = 1
else:
haveJac = 0
if isinstance(self._algparams['atol'], list):
if len(self._algparams['atol']) != self.dimension:
raise ValueError, 'atol list must have same length as phase dimension'
else:
atol = self._algparams['atol']
self._algparams['atol'] = [
atol for dimix in xrange(self.dimension)
]
indepdom0 = self.indepvariable.depdomain.get(0)
indepdom1 = self.indepvariable.depdomain.get(1)
if continue_integ:
if self._tdata[0] != self._solver.t:
print "Previous end time is %f" % self._solver.t
raise ValueError, \
"Start time not correctly updated for continuing orbit"
x0 = self._solver.y
indepdom0 = self._solver.t
else:
x0 = sortedDictValues(self.initialconditions, self.funcspec.vars)
if self._solver._integrator is None:
# Banded Jacobians not yet supported
#
# start a new integrator, because method may have been
# switched
self._solver.set_integrator(
'vode',
method=methstr,
rtol=self._algparams['rtol'],
atol=self._algparams['atol'],
nsteps=self._algparams['max_pts'],
max_step=self._algparams['max_step'],
min_step=self._algparams['min_step'],
first_step=self._algparams['init_step'],
with_jacobian=haveJac)
# speed up repeated access to solver by making a temp name for it
solver = self._solver
else:
# speed up repeated access to solver by making a temp name for it
solver = self._solver
solver.with_jacobian = haveJac
# self.mu = lband
# self.ml = uband
solver.rtol = self._algparams['rtol']
solver.atol = self._algparams['atol']
solver.method = methcode
# self.order = order
solver.nsteps = self._algparams['max_pts']
solver.max_step = self._algparams['max_step']
solver.min_step = self._algparams['min_step']
solver.first_step = self._algparams['init_step']
solver.set_initial_value(x0, indepdom0)
## if self._dircode == 1:
## solver.set_initial_value(x0, indepdom0)
## else:
## solver.set_initial_value(x0, indepdom1)
# wrap up each dictionary initial value as a singleton list
alltData = [indepdom0]
allxDataDict = dict(zip(xnames, map(listid, x0)))
plist = sortedDictValues(self.pars)
extralist = copy(plist)
if self.inputs:
# inputVarList is a list of Variables
inames = sortedDictKeys(self.inputs)
listend = self.numpars + len(self.inputs)
inputVarList = sortedDictValues(self.inputs)
ilist = _pollInputs(inputVarList, alltData[0] + self.globalt0,
self.checklevel)
else:
ilist = []
inames = []
listend = self.numpars
inputVarList = []
extralist.extend(ilist)
solver.set_f_params(extralist)
if haveJac:
solver.set_jac_params(extralist)
dt = self._algparams['init_step']
strict = self._algparams['strictdt']
# Make t mesh
if not all(isfinite(self.indepvariable.depdomain.get())):
print "Time domain was: ", self.indepvariable.depdomain.get()
raise ValueError, "Ensure time domain is finite"
if dt == indepdom1 - indepdom0:
# single-step integration required
tmesh = [indepdom0, indepdom1]
else:
notDone = True
repeatTol = 10
count = 0
while notDone and count <= repeatTol:
try:
tmesh = self.indepvariable.depdomain.uniformSample(
dt, strict=strict, avoidendpoints=self.checklevel > 2)
notDone = False
except AssertionError:
count += 1
dt = dt / 3.0
if count == repeatTol:
raise AssertionError, \
("supplied time step is too large for selected time"
" interval")
if len(tmesh) <= 2:
# safety net, in case too few points in mesh
# too few points unless we can add endpoint
if tmesh[-1] != indepdom1:
# dt too large for tmesh to have more than one point
tmesh.append(indepdom1)
if not strict: # get actual time step used
# don't use [0] in case avoided end points
dt = tmesh[2] - tmesh[1]
if self.eventstruct.query(['lowlevel']) != []:
raise ValueError, "Only high level events can be passed to VODE"
eventslist = self.eventstruct.query(
['highlevel', 'active', 'notvarlinked'])
termevents = self.eventstruct.query(['term'], eventslist)
# reverse time by reversing mesh doesn't work
## if self._dircode == -1:
## tmesh.reverse()
tmesh.pop(0) # get rid of first entry for initial condition
# per-iteration storage of variable data (initial values are irrelevant)
xDataDict = {}
xnames = self.funcspec.vars
# storage of all auxiliary variable data
allaDataDict = {}
anames = self.funcspec.auxvars
avals = apply(getattr(self, self.funcspec.auxspec[1]),
[indepdom0, x0, extralist])
for aix in range(len(anames)):
aname = anames[aix]
try:
allaDataDict[aname] = [avals[aix]]
except IndexError:
print "\nVODE generator: There was a problem evaluating " \
+ "an auxiliary variable"
print "Debug info: avals (length", len(avals), ") was ", avals
print "Index out of range was ", aix
print self.funcspec.auxspec[1]
print hasattr(self, self.funcspec.auxspec[1])
print "Args were:", [indepdom0, x0, extralist]
raise
# Initialize signs of event detection objects at IC
dataDict = copy(self.initialconditions)
dataDict.update(dict(zip(anames, avals)))
dataDict['t'] = indepdom0
self.setEventICs(self.initialconditions, self.globalt0)
if self.inputs:
parsinps = copy(self.pars)
parsinps.update(dict(zip(inames, ilist)))
else:
parsinps = self.pars
if eventslist != []:
evsflagged = self.eventstruct.pollHighLevelEvents(
None, dataDict, parsinps, eventslist)
if len(evsflagged) > 0:
raise RuntimeError, "Some events flagged at initial condition"
if continue_integ:
# revert to prevprevsign, since prevsign changed after call
self.eventstruct.resetHighLevelEvents(indepdom0, eventslist,
'prev')
else:
self.eventstruct.resetHighLevelEvents(indepdom0,
eventslist) #, 'off')
self.eventstruct.validateEvents(self.funcspec.vars + \
self.funcspec.auxvars + \
self.funcspec.inputs + \
['t'], eventslist)
# temp storage of first time at which terminal events found
# (this is used for keeping the correct end point of new mesh)
first_found_t = None
# list of precise non-terminal events to be resolved after integration
nontermprecevs = []
evnames = [ev[0] for ev in eventslist]
lastevtime = {}.fromkeys(evnames, None)
# initialize new event info dictionaries
Evtimes = {}
Evpoints = {}
if continue_integ:
for evname in evnames:
try:
# these are in global time, so convert to local time
lastevtime[evname] = self.eventstruct.Evtimes[evname][
-1] - self.globalt0
except (IndexError, KeyError):
# IndexError: Evtimes[evname] was None
# KeyError: Evtimes does not have key evname
pass
for evname in evnames:
Evtimes[evname] = []
Evpoints[evname] = []
# temp storage for repeatedly used object attributes (for lookup efficiency)
depdomains = {}
for xi in xrange(self.dimension):
depdomains[xi] = self.variables[xnames[xi]].depdomain
# Main integration loop
num_points = 0
breakwhile = False
while not breakwhile:
try:
new_t = tmesh.pop(0) # this destroys tmesh for future use
except IndexError:
break
try:
errcode = solver.integrate(new_t)
except:
print "Error calling right hand side function:"
self.showSpec()
print "Numerical traceback information (current state, " \
+ "parameters, etc.)"
print "in generator dictionary 'traceback'"
self.traceback = {
'vars': dict(zip(xnames, solver.y)),
'pars': dict(zip(pnames, plist)),
'inputs': dict(zip(inames, ilist)),
self.indepvariable.name: new_t
}
raise
for xi in xrange(self.dimension):
xDataDict[xnames[xi]] = solver.y[xi]
if not self.contains(depdomains[xi], solver.y[xi],
self.checklevel):
self.warnings.append(
(W_TERMSTATEBD, (solver.t, xnames[xi], solver.y[xi],
depdomains[xi].get())))
breakwhile = True
break # for loop
if breakwhile:
break
avals = apply(
getattr(self, self.funcspec.auxspec[1]),
[new_t, sortedDictValues(xDataDict), extralist])
# Uncomment the following assertion for debugging
# assert all([isfinite(a) for a in avals]), \
# "Some auxiliary variable values not finite"
aDataDict = dict(zip(anames, avals))
if eventslist != []:
dataDict = copy(xDataDict)
dataDict.update(aDataDict)
dataDict['t'] = new_t
if self.inputs:
parsinps = copy(self.pars)
parsinps.update(
dict(
zip(
inames,
## extralist[self.numpars:listend])))
_pollInputs(inputVarList,
new_t + self.globalt0,
self.checklevel))))
else:
parsinps = self.pars
evsflagged = self.eventstruct.pollHighLevelEvents(
None, dataDict, parsinps, eventslist)
## print new_t, evsflagged
# evsflagged = [ev for ev in evsflagged if solver.t-indepdom0 > ev[1].eventinterval]
termevsflagged = filter(lambda e: e in evsflagged, termevents)
nontermevsflagged = filter(lambda e: e not in termevsflagged,
evsflagged)
# register any non-terminating events in the warnings
# list, unless they are 'precise' in which case flag
# them to be resolved after integration completes
if len(nontermevsflagged) > 0:
evnames = [ev[0] for ev in nontermevsflagged]
precEvts = self.eventstruct.query(['precise'],
nontermevsflagged)
prec_evnames = [e[0] for e in precEvts]
# first register non-precise events
nonprec_evnames = remain(evnames, prec_evnames)
# only record events if they have not been previously
# flagged within their event interval
if nonprec_evnames != []:
temp_names = []
for evname in nonprec_evnames:
prevevt_time = lastevtime[evname]
if prevevt_time is None:
ignore_ev = False
else:
if solver.t - prevevt_time < e[1].eventinterval:
ignore_ev = True
else:
ignore_ev = False
if not ignore_ev:
temp_names.append(evname)
lastevtime[evname] = solver.t
self.warnings.append(
(W_NONTERMEVENT, (solver.t, temp_names)))
for evname in temp_names:
Evtimes[evname].append(solver.t)
Evpoints[evname].append(solver.y)
for e in precEvts:
# only record events if they have not been previously
# flagged within their event interval
prevevt_time = lastevtime[e[0]]
if prevevt_time is None:
ignore_ev = False
else:
if solver.t - dt - prevevt_time < e[
1].eventinterval:
ignore_ev = True
else:
ignore_ev = False
if not ignore_ev:
nontermprecevs.append((solver.t - dt, solver.t, e))
# be conservative as to where the event is, so
# that don't miss any events.
lastevtime[e[0]] = solver.t - dt
e[1].reset() #e[1].prevsign = None #
do_termevs = []
if termevsflagged != []:
# only record events if they have not been previously
# flagged within their event interval
for e in termevsflagged:
prevevt_time = lastevtime[e[0]]
## print "Event %s flagged."%e[0]
## print " ... last time was ", prevevt_time
## print " ... event interval = ", e[1].eventinterval
## print " ... t = %f, dt = %f"%(solver.t, dt)
if prevevt_time is None:
ignore_ev = False
else:
## print " ... comparison = %f < %f"%(solver.t-dt-prevevt_time, e[1].eventinterval)
if solver.t - dt - prevevt_time < e[
1].eventinterval:
ignore_ev = True
## print "VODE ignore ev"
else:
ignore_ev = False
if not ignore_ev:
do_termevs.append(e)
if len(do_termevs) > 0:
# >= 1 active terminal event flagged at this time point
if all([not ev[1].preciseFlag for ev in do_termevs]):
# then none of the events specify greater accuracy
# register the event in the warnings
evnames = [ev[0] for ev in do_termevs]
self.warnings.append((W_TERMEVENT, \
(solver.t, evnames)))
for evname in evnames:
Evtimes[evname].append(solver.t)
Evpoints[evname].append(solver.y)
breakwhile = True # break while loop after appending t, x
else:
# find which are the 'precise' events that flagged
precEvts = self.eventstruct.query(['precise'],
do_termevs)
# these events have flagged once so eventdelay has
# been used. now switch it off while finding event
# precisely (should be redundant after change to
# eventinterval and eventdelay parameters)
evnames = [ev[0] for ev in precEvts]
if first_found_t is None:
## print "first time round at", solver.t
numtries = 0
first_found_t = solver.t
restore_evts = deepcopy(precEvts)
minbisectlimit = min(
[ev[1].bisectlimit for ev in precEvts])
for ev in precEvts:
ev[1].eventdelay = 0.
else:
numtries += 1
## print "time round: ", numtries
if numtries > minbisectlimit:
self.warnings.append(
(W_BISECTLIMIT, (solver.t, evnames)))
breakwhile = True
# find minimum eventtol in precEvts
dt_min = min([e[1].eventtol for e in precEvts])
# get previous time point
if len(alltData) >= 1:
# take one step back -> told, which will
# get dt added back to first new meshpoint
# (solver.t is the step *after* the event was
# detected)
told = solver.t - dt
else:
raise ValueError("Event %s found too "%evnames[0]+\
"close to local start time: try decreasing "
"initial step size (current size is "
"%f @ t=%f)"%(dt,solver.t+self.globalt0))
if dt_min >= dt:
## print "Registering event:", dt_min, dt
# register the event in the warnings
self.warnings.append(
(W_TERMEVENT, (solver.t, evnames)))
for evname in evnames:
Evtimes[evname].append(solver.t)
Evpoints[evname].append(solver.y)
# Cannot continue -- dt_min no smaller than
# previous dt. If this is more than the first time
# in this code then have found the event to within
# the minimum 'precise' event's eventtol, o/w need
# to set eventtol smaller.
breakwhile = True # while loop
if not breakwhile:
dt_new = dt / 5.0
# calc new tmesh
trangewidth = 2 * dt #first_found_t - told
numpoints = int(math.ceil(trangewidth / dt_new))
# choose slightly smaller dt to fit trange exactly
dt = trangewidth / numpoints
tmesh = [
told + i * dt
for i in xrange(1, numpoints + 1)
]
# reset events according to new time mesh,
# setting known previous event state to be their
# "no event found" state
self.eventstruct.resetHighLevelEvents(told,
precEvts,
state='off')
# build new ic with last good values (at t=told)
if len(alltData) > 1:
new_ic = [allxDataDict[xname][-1] \
for xname in xnames]
else:
new_ic = x0
# reset integrator
solver.set_initial_value(new_ic, told)
extralist[self.numpars:listend] = \
[apply(f, [told+self.globalt0,
self.checklevel]) \
for f in inputVarList]
solver.set_f_params(extralist)
# continue integrating over new mesh
continue # while
alltData.append(solver.t)
for xi in xrange(self.dimension):
allxDataDict[xnames[xi]].append(solver.y[xi])
for aix in xrange(len(anames)):
aname = anames[aix]
allaDataDict[aname].append(avals[aix])
num_points += 1
if not breakwhile:
try:
extralist[self.numpars:listend] = [apply(f, \
[solver.t+self.globalt0,
self.checklevel]) \
for f in inputVarList]
except ValueError:
print 'External input call caused value out of range error:',\
't = ', solver.t
for f in inputVarList:
if len(f.warnings):
print 'External input variable %s out of range:' % f.name
print ' t = ', repr(f.warnings[-1][0]), ', ', \
f.name, ' = ', repr(f.warnings[-1][1])
raise
except AssertionError:
print 'External input call caused t out of range error: t = ', \
solver.t
raise
solver.set_f_params(extralist)
breakwhile = not solver.successful()
# Check that any terminal events found terminated the code correctly
if first_found_t is not None:
# ... then terminal events were found. Those that were 'precise' had
# their 'eventdelay' attribute temporarily set to 0. It now should
# be restored.
for evname1, ev1 in termevents:
# restore_evts are copies of the originally flagged 'precise'
# events
for evname2, ev2 in restore_evts:
if evname2 == evname1:
ev1.eventdelay = ev2.eventdelay
try:
if self.warnings[-1][0] not in [W_TERMEVENT, W_TERMSTATEBD]:
raise RuntimeError("Event finding code for terminal event "
"failed in Generator " + self.name + \
": try decreasing eventdelay or "
"eventinterval below eventtol")
except IndexError:
print "Output stats: ", self.outputstats
raise RuntimeError("Event finding failed in Generator " + \
self.name + ": try decreasing eventdelay "
"or eventinterval below eventtol")
# Package up computed trajectory in Variable variables
# Add external inputs warnings to self.warnings, if any
for f in inputVarList:
for winfo in f.warnings:
self.warnings.append(
(W_NONTERMSTATEBD, (winfo[0], f.name, winfo[1],
f.depdomain.get())))
# check for non-unique terminal event
termcount = 0
for (w, i) in self.warnings:
if w == W_TERMEVENT or w == W_TERMSTATEBD:
termcount += 1
if termcount > 1:
self.errors.append((E_NONUNIQUETERM, (alltData[-1], i[1])))
# uncomment the following lines for debugging
# assert len(alltData) == len(allxDataDict.values()[0]) \
# == len(allaDataDict.values()[0]), "Output data size mismatch"
# for val_list in allaDataDict.values():
# assert all([isfinite(x) for x in val_list])
# Create variables (self.variables contains no actual data)
# These versions of the variables are only final if no non-terminal
# events need to be inserted.
variables = copyVarDict(self.variables)
for x in xnames:
if len(alltData) > 1:
variables[x] = Variable(interp1d(alltData, allxDataDict[x]),
't', x, x)
else:
print "Error in Generator:", self.name
print "t = ", alltData
print "x = ", allxDataDict
raise PyDSTool_ValueError, "Fewer than 2 data points computed"
for a in anames:
if len(alltData) > 1:
variables[a] = Variable(interp1d(alltData, allaDataDict[a]),
't', a, a)
else:
print "Error in Generator:", self.name
print "t = ", alltData
print "x = ", allxDataDict
raise PyDSTool_ValueError, "Fewer than 2 data points computed"
# Resolve non-terminal 'precise' events that were flagged, using the
# variables created. Then, add them to a new version of the variables.
ntpe_tdict = {}
for (et0, et1, e) in nontermprecevs:
lost_evt = False
search_dt = max((et1 - et0) / 5, e[1].eventinterval)
et_precise_list = e[1].searchForEvents(trange=[et0, et1],
dt=search_dt,
checklevel=self.checklevel,
parDict=self.pars,
vars=variables,
inputs=self.inputs,
abseps=self._abseps,
eventdelay=False,
globalt0=self.globalt0)
if et_precise_list == []:
lost_evt = True
for et_precise in et_precise_list:
if et_precise[0] is not None:
if et_precise[0] in ntpe_tdict:
# add event name at this time (that already exists in the dict)
ntpe_tdict[et_precise[0]].append(e[0])
else:
# add event name at this time (when time is not already in dict)
ntpe_tdict[et_precise[0]] = [e[0]]
else:
lost_evt = True
if lost_evt:
raise PyDSTool_ExistError, \
("Internal error: A non-terminal, 'precise' event '"
+e[0]+"' was lost after integration!")
# add non-terminal event points to variables
if ntpe_tdict != {}:
# find indices of times at which event times will be inserted
tix = 0
evts = ntpe_tdict.keys()
evts.sort()
for evix in xrange(len(evts)):
evt = evts[evix]
evnames = ntpe_tdict[evt]
self.warnings.append((W_NONTERMEVENT, (evt, evnames)))
xval = [variables[x](evt) for x in xnames]
for evname in evnames:
Evtimes[evname].append(evt)
Evpoints[evname].append(array(xval))
tcond = less_equal(alltData[tix:], evt).tolist()
try:
tix = tcond.index(0) + tix # lowest index for t > evt
do_insert = (alltData[tix - 1] != evt)
except ValueError:
# evt = last t value so no need to add it
do_insert = False
if do_insert:
alltData.insert(tix, evt)
xvaldict = dict(zip(xnames, xval))
for x in xnames:
allxDataDict[x].insert(tix, xvaldict[x])
for a in anames:
allaDataDict[a].insert(tix, variables[a](evt))
for x in xnames:
variables[x] = Variable(interp1d(alltData, allxDataDict[x]),
't', x, x)
for a in anames:
variables[a] = Variable(interp1d(alltData, allaDataDict[a]),
't', a, a)
self.outputstats = {
'last_step': dt,
'num_fcns': num_points,
'num_steps': num_points,
'errorStatus': errcode
}
if solver.successful():
self.validateSpec()
for evname, evtlist in Evtimes.iteritems():
try:
self.eventstruct.Evtimes[evname].extend([et+self.globalt0 \
for et in evtlist])
except KeyError:
self.eventstruct.Evtimes[evname] = [et+self.globalt0 \
for et in evtlist]
# build event pointset information (reset previous trajectory's)
self.trajevents = {}
for (evname, ev) in eventslist:
evpt = Evpoints[evname]
if evpt == []:
self.trajevents[evname] = None
else:
evpt = transpose(array(evpt))
self.trajevents[evname] = Pointset({
'coordnames':
xnames,
'indepvarname':
't',
'coordarray':
evpt,
'indepvararray':
Evtimes[evname],
'indepvartype':
Float
})
self.defined = True
return Trajectory(trajname, variables.values(), self.globalt0,
self.checklevel)
else:
try:
self.errors.append(
(E_COMPUTFAIL, (solver.t, self._errorcodes[errcode])))
except TypeError:
# e.g. when errcode has been used to return info list
print "Error information: ", errcode
self.errors.append(
(E_COMPUTFAIL, (solver.t, self._errorcodes[0])))
self.defined = False
