def updatedata(self, A):
# Update b, c
try:
ALU = linalg.lu_factor(A)
BC = linalg.lu_solve(ALU, c_[linalg.lu_solve(ALU, self.data.b + 1e-8*self.data.Brand[:,:1]), \
self.data.c + 1e-8*self.data.Crand[:,:1]], trans=1)
C = linalg.lu_solve(ALU, BC[:,-1:])
B = BC[:,:1]
except:
if self.C.verbosity >= 1:
print 'Warning: Problem updating border vectors. Using svd...'
U, S, Vh = linalg.svd(A)
B = U[:,-1:]
C = transpose(Vh)[:,-1:]
bmult = cmult = 1
if matrixmultiply(transpose(self.data.b), B) < 0:
bmult = -1
if matrixmultiply(transpose(self.data.c), C) < 0:
cmult = -1
self.data.b = bmult*B*(linalg.norm(A,1)/linalg.norm(B))
self.data.c = cmult*C*(linalg.norm(A,Inf)/linalg.norm(C))
# Update
if self.update:
self.data.B[:,0] = self.data.b*(linalg.norm(A,1)/linalg.norm(self.data.b))
self.data.C[:,0] = self.data.c*(linalg.norm(A,Inf)/linalg.norm(self.data.c))
self.data.B[:,1] = self.data.w[:,2]*(linalg.norm(A,1)/linalg.norm(self.data.w,1))
self.data.C[:,1] = self.data.v[:,2]*(linalg.norm(A,Inf)/linalg.norm(self.data.v,1))
self.data.D[0,1] = self.data.g[0,1]
self.data.D[1,0] = self.data.g[1,0]
def intersect_line_ellipsoid(p1, p2, ec, radius_vectors):
"""Determine intersection points between line defined by p1 and p2,
and ellipsoid defined by centre ec and three radius vectors (tuple
of tuples, each inner tuple is a radius vector).
This requires numpy.
"""
# create transformation matrix that has the radius_vectors
# as its columns (hence the transpose)
rv = numpy.transpose(numpy.matrix(radius_vectors))
# calculate its inverse
rv_inv = numpy.linalg.pinv(rv)
# now transform the two points
# all points have to be relative to ellipsoid centre
# the [0] at the end and the numpy.array at the start is to make sure
# we pass a row vector (array) to the line_sphere_intersection
p1_e = numpy.array(numpy.matrixmultiply(rv_inv, numpy.array(p1) - numpy.array(ec)))[0]
p2_e = numpy.array(numpy.matrixmultiply(rv_inv, numpy.array(p2) - numpy.array(ec)))[0]
# now we only have to determine the intersection between the points
# (now transformed to ellipsoid space) with the unit sphere centred at 0
isects_e = intersect_line_sphere(p1_e, p2_e, (0.0,0.0,0.0), 1.0)
# transform intersections back to "normal" space
isects = []
for i in isects_e:
# numpy.array(...)[0] is for returning only row of matrix as array
itemp = numpy.array(numpy.matrixmultiply(rv, numpy.array(i)))[0]
isects.append(itemp + numpy.array(ec))
return isects
def glr_Uellipse(self, position, U, prob):
"""Renders the ellipsoid enclosing the given fractional probability
given the gaussian variance-covariance matrix U at the given position.
C=1.8724 = 68%
"""
## rotate U
R = self.matrix[:3,:3]
Ur = numpy.matrixmultiply(numpy.matrixmultiply(R, U), numpy.transpose(R))
Umax = max(linalg.eigenvalues(Ur))
try:
limit_radius = Gaussian.GAUSS3C[prob] * MARGIN * math.sqrt(Umax)
except ValueError:
limit_radius = 2.0
try:
Q = linalg.inverse(Ur)
except linalg.LinAlgError:
return
self.object_list.append(
(14,
matrixmultiply43(self.matrix, position),
limit_radius,
self.material_color_r,
self.material_color_g,
self.material_color_b,
Q,
-Gaussian.GAUSS3C[prob]**2))
def func(self, X, V):
k = self.C.TFdata.k
v1 = self.C.TFdata.v1
w1 = self.C.TFdata.w1
if k >=0:
J_coords = self.F.sysfunc.J_coords
w = sqrt(k)
q = v1 - (1j/w)*matrixmultiply(self.F.sysfunc.J_coords,v1)
p = w1 + (1j/w)*matrixmultiply(transpose(self.F.sysfunc.J_coords),w1)
p /= linalg.norm(p)
q /= linalg.norm(q)
p = reshape(p,(p.shape[0],))
q = reshape(q,(q.shape[0],))
direc = conjugate(1/matrixmultiply(transpose(conjugate(p)),q))
p = direc*p
l1 = firstlyapunov(X, self.F.sysfunc, w, J_coords=J_coords, p=p, q=q)
return array([l1])
else:
return array([1])
def process(self, X, V, C):
BifPoint.process(self, X, V, C)
J_coords = C.CorrFunc.sysfunc.jac(X, C.coords)
B = C.CorrFunc.sysfunc.hess(X, C.coords, C.coords)
W, VL, VR = linalg.eig(J_coords, left=1, right=1)
q = C.CorrFunc.testfunc.data.C / linalg.norm(
C.CorrFunc.testfunc.data.C)
p = C.CorrFunc.testfunc.data.B / matrixmultiply(
transpose(C.CorrFunc.testfunc.data.B), q)
self.found[-1].eigs = W
a = 0.5*matrixmultiply(transpose(p), reshape([bilinearform(B[i,:,:], q, q) \
for i in range(B.shape[0])],(B.shape[0],1)))[0][0]
if C.verbosity >= 2:
print('\nChecking...')
print(' |a| = %f' % a)
print('\n')
self.info(C, -1)
return True
def bCorrNumeric(X, Y, DX, beat_input, cut=0.001, app=0, path="./"):
R = np.transpose(beat_input.sensitivity_matrix)
b = beat_input.computevectorEXP(X, Y, DX) - beat_input.zerovector
corr = beat_input.varslist
m, n = np.shape(R)
if len(b) == m and len(corr) == n:
rms, ptop = calcRMSNumeric(b)
inva = generalized_inverse(R, cut)
print "initial {RMS, Peak}: { %e , %e } mm" % (rms, ptop)
print "finding best over", n, "correctors"
for i in range(n):
dStren = matrixmultiply(inva[i, :], b)
bvec = b - matrixmultiply(R[:, i], dStren)
rm, ptp = calcRMSNumeric(bvec)
if rm < rms:
rms = rm
rbest = i
rStren = dStren
if ptp < ptop:
ptop = ptp
pbest = i
pStren = dStren
print "final {RMS, Peak}: { %e , %e }" % (rms, ptop)
if rbest == pbest:
print "best corr:", corr[rbest], '%e' % (rStren), "1/m"
else:
print "--- warning: best corr for rms & peak are not same"
print "RMS best corr:", corr[rbest], '%e' % (rStren), "1/m"
print "Peak best corr:", corr[pbest], '%e' % (pStren), "1/m"
else:
print "dimensional mismatch in input variables"
def updatedata(self, A):
if self.update:
if self.corr:
B = self.data.w
C = self.data.v
else:
# Note: Problem when singular vectors switch smallest singular value (See NewLorenz).
# To overcome this, I have implemented a 1e-8 random nudge.
try:
ALU = linalg.lu_factor(A)
# BC = linalg.lu_solve(ALU, c_[linalg.lu_solve(ALU, self.data.B), self.data.C], trans=1)
# USE OF RANDOM NUDGE
BC = linalg.lu_solve(ALU, c_[linalg.lu_solve(ALU, self.data.B + 1e-8*self.data.Brand), \
self.data.C + 1e-8*self.data.Crand], trans=1)
C = linalg.lu_solve(ALU, BC[:,-1*self.data.q:])
B = BC[:,0:self.data.p]
except:
if self.C.verbosity >= 1:
print('Warning: Problem updating border vectors. Using svd...')
U, S, Vh = linalg.svd(A)
B = U[:,-1*self.data.p:]
C = transpose(Vh)[:,-1*self.data.q:]
bmult = cmult = 1
if matrixmultiply(transpose(self.data.B), B) < 0:
bmult = -1
if matrixmultiply(transpose(self.data.C), C) < 0:
cmult = -1
self.data.B = bmult*B*(linalg.norm(A,1)/linalg.norm(B))
self.data.C = cmult*C*(linalg.norm(A,Inf)/linalg.norm(C))
def bCorrNumeric(X, Y, DX, beat_input, cut=0.001, app=0, path="./"):
R = np.transpose(beat_input.sensitivity_matrix)
b = beat_input.computevectorEXP(X, Y, DX) - beat_input.zerovector
corr = beat_input.varslist
m, n = np.shape(R)
if len(b) == m and len(corr) == n:
rms, ptop = calcRMSNumeric(b)
inva = generalized_inverse(R, cut)
print "initial {RMS, Peak}: { %e , %e } mm" % (rms, ptop)
print "finding best over", n, "correctors"
for i in range(n):
dStren = matrixmultiply(inva[i, :], b)
bvec = b - matrixmultiply(R[:, i], dStren)
rm, ptp = calcRMSNumeric(bvec)
if rm < rms:
rms = rm
rbest = i
rStren = dStren
if ptp < ptop:
ptop = ptp
pbest = i
pStren = dStren
print "final {RMS, Peak}: { %e , %e }" % (rms, ptop)
if rbest == pbest:
print "best corr:", corr[rbest], '%e' % (rStren), "1/m"
else:
print "--- warning: best corr for rms & peak are not same"
print "RMS best corr:", corr[rbest], '%e' % (rStren), "1/m"
print "Peak best corr:", corr[pbest], '%e' % (pStren), "1/m"
else:
print "dimensional mismatch in input variables"
def itrSVD(X,
Y,
DX,
beat_input,
cut=0.001,
num_iter=1,
app=0,
tol=1e-9,
path="./"):
R = np.transpose(beat_input.sensitivity_matrix)
b = beat_input.computevectorEXP(X, Y, DX) - beat_input.zerovector
corr = beat_input.varslist
inva = generalized_inverse(R, cut)
rmss, ptopp = calcRMSNumeric(b)
RHO2 = {}
dStren = np.zeros(len(corr))
print 'Initial Phase-Beat:', '{RMS,PK2PK}', rmss, ptopp
for ITER in range(num_iter): # @UnusedVariable
dStren = dStren + matrixmultiply(inva, b)
bvec = b - matrixmultiply(R, dStren)
rm, ptp = calcRMSNumeric(bvec)
print 'ITER', num_iter, '{RMS,PK2PK}', rm, ptp
for j in range(len(corr)):
RHO2[corr[j]] = dStren[j]
wrtpar(corr, RHO2, app, path)
def __pade_approximation(self, nodeName, L, M, debug=0):
assert L == M - 1
num_moments = L+M+1
if debug: "DATA L=%s M=%s num_moments=%s" % (L, M, num_moments)
if debug: print "num_moments", num_moments
#scaling = 766423.0
node_index = self.TranslateNode(nodeName)
node_moments = []
# step 1: calculate the Moments
g_inverse = numpy.linalg.inverse(self.G)
if debug: print "g_inverse", g_inverse
last_moment = numpy.matrixmultiply(g_inverse, self.B)
if debug: print "last_moment", last_moment, node_index
node_moments.append(last_moment[node_index-1][0])
# test commit
for i in range(num_moments-1):
intermediate = -1 * numpy.matrixmultiply(g_inverse, self.C)
last_moment = numpy.matrixmultiply( intermediate, last_moment )
moment = self.Scaling * last_moment[node_index-1][0]
node_moments.append(moment)
last_moment = self.Scaling * last_moment
if debug: print "last_moment", last_moment
print "suggested scaling =", node_moments[0]/node_moments[1]
if debug: print "node_moments=", node_moments
# Call the general pade algorithm
a_coef, b_coef = MathHelpers.my_pade(node_moments, complex=False)
# Return results
return a_coef, b_coef, node_moments
def func(self, X, V):
H = self.F.sysfunc.hess(X, self.F.coords, self.F.coords)
q = self.F.testfunc.data.v/linalg.norm(self.F.testfunc.data.v)
p = self.F.testfunc.data.w/matrixmultiply(transpose(self.F.testfunc.data.w),q)
return array(0.5*matrixmultiply(transpose(p), reshape([bilinearform(H[i,:,:], q, q) \
for i in range(H.shape[0])],(H.shape[0],1)))[0])
def process(self, X, V, C):
BifPoint.process(self, X, V, C)
# Finds the new branch
J_coords = C.CorrFunc.jac(X, C.coords)
J_params = C.CorrFunc.jac(X, C.params)
A = r_[c_[J_coords, J_params], [V]]
W, VR = linalg.eig(A)
W0 = [ind for ind, eig in enumerate(W) if abs(eig) < 5e-5]
V1 = real(VR[:,W0[0]])
H = C.CorrFunc.hess(X, C.coords+C.params, C.coords+C.params)
c11 = matrixmultiply(self.data.psi,[bilinearform(H[i,:,:], V, V) for i in range(H.shape[0])])
c12 = matrixmultiply(self.data.psi,[bilinearform(H[i,:,:], V, V1) for i in range(H.shape[0])])
c22 = matrixmultiply(self.data.psi,[bilinearform(H[i,:,:], V1, V1) for i in range(H.shape[0])])
beta = 1
alpha = -1*c22/(2*c12)
V1 = alpha*V + beta*V1
V1 /= linalg.norm(V1)
self.found[-1].eigs = W
self.found[-1].branch = todict(C, V1)
self.info(C, -1)
return True
def glr_Uaxes(self, position, U, prob, color, line_width):
"""Draw the anisotropic axies of the atom at the given probability.
"""
## rotate U
R = self.matrix[:3,:3]
Ur = numpy.matrixmultiply(numpy.matrixmultiply(R, U), numpy.transpose(R))
evals, evecs = linalg.eigenvectors(Ur)
def calc_orth_symop(self, symop):
"""Calculates the orthogonal space symmetry operation (return SymOp)
given a fractional space symmetry operation (argument SymOp).
"""
RF = numpy.matrixmultiply(symop.R, self.orth_to_frac)
ORF = numpy.matrixmultiply(self.frac_to_orth, RF)
Ot = numpy.matrixmultiply(self.frac_to_orth, symop.t)
return SpaceGroups.SymOp(ORF, Ot)
def pluecker_from_verts(A, B):
if len(A) == 3:
A = A[0], A[1], A[2], 1.0
if len(B) == 3:
B = B[0], B[1], B[2], 1.0
A = nx.reshape(A, (4, 1))
B = nx.reshape(B, (4, 1))
L = nx.matrixmultiply(A, nx.transpose(B)) - nx.matrixmultiply(
B, nx.transpose(A))
return Lmatrix2Lcoords(L)
def process(self, X, V, C):
BifPoint.process(self, X, V, C)
# Finds the new branch
J_coords = C.CorrFunc.jac(X, C.coords)
J_params = C.CorrFunc.jac(X, C.params)
singular = True
perpvec = r_[1, zeros(C.dim - 1)]
d = 1
while singular and d <= C.dim:
try:
v0 = linalg.solve(r_[c_[J_coords, J_params],
[perpvec]], \
r_[zeros(C.dim-1),1])
except:
perpvec = r_[0., perpvec[0:(C.dim - 1)]]
d += 1
else:
singular = False
if singular:
raise PyDSTool_ExistError(
"Problem in _compute: Failed to compute tangent vector.")
v0 /= linalg.norm(v0)
V = sign([x for x in v0 if abs(x) > 1e-8][0]) * v0
A = r_[c_[J_coords, J_params], [V]]
W, VR = linalg.eig(A)
W0 = [ind for ind, eig in enumerate(W) if abs(eig) < 5e-5]
V1 = real(VR[:, W0[0]])
H = C.CorrFunc.hess(X, C.coords + C.params, C.coords + C.params)
c11 = matrixmultiply(
self.data.psi,
[bilinearform(H[i, :, :], V, V) for i in range(H.shape[0])])
c12 = matrixmultiply(
self.data.psi,
[bilinearform(H[i, :, :], V, V1) for i in range(H.shape[0])])
c22 = matrixmultiply(
self.data.psi,
[bilinearform(H[i, :, :], V1, V1) for i in range(H.shape[0])])
beta = 1
alpha = -1 * c22 / (2 * c12)
V1 = alpha * V + beta * V1
V1 /= linalg.norm(V1)
self.found[-1].eigs = W
self.found[-1].branch = todict(C, V1)
self.info(C, -1)
return True
def __locate_newton(self, X, C):
"""x[0:self.dim] = (x,alpha)
x[self.dim] = beta
x[self.dim+1:2*self.dim] = p
"""
J_coords = C.CorrFunc.jac(X[0:C.dim], C.coords)
J_params = C.CorrFunc.jac(X[0:C.dim], C.params)
return r_[C.CorrFunc(X[0:C.dim]) + X[C.dim]*X[C.dim+1:], \
matrixmultiply(transpose(J_coords),X[C.dim+1:]), \
matrixmultiply(transpose(X[C.dim+1:]),J_params), \
matrixmultiply(transpose(X[C.dim+1:]),X[C.dim+1:]) - 1]
def __locate_newton(self, X, C):
"""x[0:self.dim] = (x,alpha)
x[self.dim] = beta
x[self.dim+1:2*self.dim] = p
"""
J_coords = C.CorrFunc.jac(X[0:C.dim], C.coords)
J_params = C.CorrFunc.jac(X[0:C.dim], C.params)
return r_[C.CorrFunc(X[0:C.dim]) + X[C.dim]*X[C.dim+1:], \
matrixmultiply(transpose(J_coords),X[C.dim+1:]), \
matrixmultiply(transpose(X[C.dim+1:]),J_params), \
matrixmultiply(transpose(X[C.dim+1:]),X[C.dim+1:]) - 1]
def firstlyapunov(X,
F,
w,
J_coords=None,
V=None,
W=None,
p=None,
q=None,
check=False):
if J_coords is None:
J_coords = F.jac(X, F.coords)
if p is None:
alpha = bilinearform(transpose(J_coords),V[:,0],V[:,1]) - \
1j*w*matrixmultiply(V[:,0],V[:,1])
beta = -1*bilinearform(transpose(J_coords),V[:,0],V[:,0]) + \
1j*w*matrixmultiply(V[:,0],V[:,0])
q = alpha * V[:, 0] + beta * V[:, 1]
alpha = bilinearform(J_coords,W[:,0],W[:,1]) + \
1j*w*matrixmultiply(W[:,0],W[:,1])
beta = -1*bilinearform(J_coords,W[:,0],W[:,0]) - \
1j*w*matrixmultiply(W[:,0],W[:,0])
p = alpha * W[:, 0] + beta * W[:, 1]
p /= linalg.norm(p)
q /= linalg.norm(q)
direc = conjugate(1 / matrixmultiply(conjugate(p), q))
p = direc * p
if check:
print('Checking...')
print(' |q| = %f' % linalg.norm(q))
temp = matrixmultiply(conjugate(p), q)
print(' |<p,q> - 1| = ', abs(temp - 1))
print(' |Aq - iwq| = %f' %
linalg.norm(matrixmultiply(J_coords, q) - 1j * w * q))
print(' |A*p + iwp| = %f\n' %
linalg.norm(matrixmultiply(transpose(J_coords), p) + 1j * w * p))
# Compute first lyapunov coefficient
B = F.hess(X, F.coords, F.coords)
D = hess3(F, X, F.coords)
b1 = array([bilinearform(B[i, :, :], q, q) for i in range(B.shape[0])])
b2 = array([bilinearform(B[i,:,:], conjugate(q),
linalg.solve(2*1j*w*eye(F.m) - J_coords, b1)) \
for i in range(B.shape[0])])
b3 = array([bilinearform(B[i,:,:], q, conjugate(q)) \
for i in range(B.shape[0])])
b4 = array([bilinearform(B[i,:,:], q, linalg.solve(J_coords, b3)) \
for i in range(B.shape[0])])
temp = array([trilinearform(D[i,:,:,:],q,q,conjugate(q)) \
for i in range(D.shape[0])]) + b2 - 2*b4
l1 = 0.5 * real(matrixmultiply(conjugate(p), temp))
return l1
def func(self, X, V):
F = self.C.CorrFunc
# print F.testfunc[0]
# print F.testfunc[0].data
F.testfunc[0](X,V)
# print F.testfunc[0].data
H = F.sysfunc.hess(X, self.F.coords, self.F.coords)
q = F.testfunc[0].data.v/linalg.norm(F.testfunc[0].data.v)
p = F.testfunc[0].data.w/matrixmultiply(transpose(F.testfunc[0].data.w),q)
return array(0.5*matrixmultiply(transpose(p), reshape([bilinearform(H[i,:,:], q, q) \
for i in range(H.shape[0])],(H.shape[0],1)))[0])
def Cmatrix(self):
'''
Calculate the C matrix
'''
self.C = []
self.gamma = []
self.f1001 = []
self.f1010 = []
S = getattr(self, "S")
R11 = getattr(self, "R11")
R12 = getattr(self, "R12")
R21 = getattr(self, "R21")
R22 = getattr(self, "R22")
BETX = getattr(self, "BETX")
BETY = getattr(self, "BETY")
ALFX = getattr(self, "ALFX")
ALFY = getattr(self, "ALFY")
J = numpy.reshape(numpy.array([0, 1, -1, 0]), (2, 2))
for j in range(0, len(S)):
R = numpy.array([[R11[j], R12[j]], [R21[j], R22[j]]])
C = matrixmultiply(-J, matrixmultiply(numpy.transpose(R), J))
C = (1 / numpy.sqrt(1 + determinant(R))) * C
g11 = 1 / numpy.sqrt(BETX[j])
g12 = 0
g21 = ALFX[j] / numpy.sqrt(BETX[j])
g22 = numpy.sqrt(BETX[j])
Ga = numpy.reshape(numpy.array([g11, g12, g21, g22]), (2, 2))
g11 = 1 / numpy.sqrt(BETY[j])
g12 = 0
g21 = ALFY[j] / numpy.sqrt(BETY[j])
g22 = numpy.sqrt(BETY[j])
Gb = numpy.reshape(numpy.array([g11, g12, g21, g22]), (2, 2))
C = matrixmultiply(Ga, matrixmultiply(C, inverse(Gb)))
gamma = 1 - determinant(C)
self.gamma.append(gamma)
C = numpy.ravel(C)
self.C.append(C)
self.f1001.append(((C[0] + C[3]) * 1j + (C[1] - C[2])) / 4 / gamma)
self.f1010.append(
((C[0] - C[3]) * 1j + (-C[1] - C[2])) / 4 / gamma)
self.F1001R = numpy.array(self.f1001).real
self.F1001I = numpy.array(self.f1001).imag
self.F1010R = numpy.array(self.f1010).real
self.F1010I = numpy.array(self.f1010).imag
self.F1001W = numpy.sqrt(self.F1001R**2 + self.F1001I**2)
self.F1010W = numpy.sqrt(self.F1010R**2 + self.F1010I**2)
self.GAMMAC = numpy.array(self.gamma)
def bNCorrNumeric(X,
Y,
DX,
beat_input,
cut=0.001,
ncorr=3,
app=0,
tol=1e-9,
path="./",
beta_x=None,
beta_y=None):
R = np.transpose(beat_input.sensitivity_matrix)
n = np.shape(R)[1]
b = beat_input.computevectorEXP(X, Y, DX, beta_x,
beta_y) - beat_input.zerovector
corr = beat_input.varslist
inva = generalized_inverse(R, cut)
RHO2 = {}
rmss, ptopp = calcRMSNumeric(b)
print 'Initial Phase-beat {RMS,PK2PK}:', rmss, ptopp
for ITER in range(ncorr):
for j in range(n):
if j not in RHO2:
RHO = [k for k in RHO2.keys()]
RHO.append(j)
RR = np.take(R, RHO, 1)
invaa = np.take(inva, RHO, 0)
dStren = matrixmultiply(invaa, b)
#--- calculate residual due to 1..nth corrector
bvec = b - matrixmultiply(RR, dStren)
rm, ptp = calcRMSNumeric(bvec)
if rm < rmss:
rmss = rm
ptopp = ptp
rbest = j
rStren = dStren
print 'ITER:', ITER + 1, ' RMS,PK2PK:', rmss, ptopp
RHO2[rbest] = (rmss, ptopp)
if (rm < tol):
print "RMS converged with", ITER, "correctors"
break
if (rm < rmss):
print "stopped after", ITER, "correctors"
break
itr = 0
RHO3 = {} #-- make dict RHO3={corr:strength,...}
for j in RHO2:
RHO3[corr[j]] = rStren[itr]
itr += 1
print '\n', sortDict(RHO3)
wrtpar(corr, RHO3, app, path)
return RHO3
def do_svd_clean(self, plane):
"""Does a SVD clean on the given plane"""
time_start = time.time()
print "(plane {0}) removing noise floor with SVD".format(plane)
A = numpy.array(self.sddsfile.dictionary_plane_to_bpms[plane].bpm_data)
number_of_bpms = A.shape[0]
if number_of_bpms <= 10:
sys.exit("Number of bpms <= 10")
# normalise the matrix
sqrt_number_of_turns = numpy.sqrt(A.shape[1])
A_mean = numpy.mean(A)
A = (A - A_mean) / sqrt_number_of_turns
if PRINT_TIMES:
print ">> Time for svdClean (before SVD call): {0}s".format(time.time() - time_start)
USV = self.get_singular_value_decomposition(A)
if PRINT_TIMES:
print ">> Time for svdClean (after SVD call): {0}s".format(time.time() - time_start)
# remove bad BPM by SVD -tbach
good_bpm_indices = self.remove_bad_bpms_and_get_good_bpm_indices(USV, plane)
USV = (USV[0][good_bpm_indices], USV[1], USV[2])
number_of_bpms = len(good_bpm_indices)
print ">> Values in GOOD BPMs: "
print number_of_bpms
# ----SVD cut for noise floor
if _InputData.singular_values_amount_to_keep < number_of_bpms:
print "(plane {0}) amount of singular values to keep: {1}".format(
plane, _InputData.singular_values_amount_to_keep
)
USV[1][_InputData.singular_values_amount_to_keep :] = 0
else:
print "requested more singular values than available(={0})".format(number_of_bpms)
A = matrixmultiply(USV[0], matrixmultiply(numpy.diag(USV[1]), USV[2]))
# A0 * (A1 * A2) should require less operations than (A0 * A1) * A2,
# because of the different sizes
# A0 has (M, K), A1 has (K, K) and A2 has (K, N) with K=min(M,N)
# Most of the time, the number of turns is greater then
# the number of BPM, so M > N
# --tbach
A = (A * sqrt_number_of_turns) + A_mean
bpmres = numpy.mean(numpy.std(A - self.sddsfile.dictionary_plane_to_bpms[plane].bpm_data, axis=1))
print "(plane {0}) Average BPM resolution: ".format(plane) + str(bpmres)
self.sddsfile.dictionary_plane_to_bpms[plane].bpm_data = A
if PRINT_TIMES:
print ">> Time for do_svd_clean: {0}s".format(time.time() - time_start)
def test_module():
import random
import AtomMath
import FileIO
import Structure
R = AtomMath.rmatrixu(numpy.array((0.0, 0.0, 1.0), float), math.pi / 2.0)
struct1 = FileIO.LoadStructure(fil="/home/jpaint/8rxn/8rxn.pdb")
struct2 = FileIO.LoadStructure(fil="/home/jpaint/8rxn/8rxn.pdb")
chn1 = struct1.get_chain("A")
chn2 = struct2.get_chain("A")
rc = lambda: 0.1 * (random.random() - 1.0)
for atm in chn2.iter_atoms():
atm.position = numpy.matrixmultiply(R, atm.position) + numpy.array(
(rc(), rc(), rc()), float)
alist = []
for atm1 in chn1.iter_atoms():
if atm1.name != "CA":
continue
atm2 = chn2.get_equivalent_atom(atm1)
if atm2 == None: continue
alist.append((atm1, atm2))
sup = SuperimposeAtoms(alist)
R = sup.R
Q = sup.Q
print Q
print R
so = sup.src_origin
do = sup.dst_origin
sup1 = Structure.Structure(structure_id="JMP1")
for atm in chn1.iter_atoms():
atm.position = numpy.matrixmultiply(R, atm.position - so)
sup1.add_atom(atm)
FileIO.SaveStructure(fil="super1.pdb", struct=sup1)
sup2 = Structure.Structure(structure_id="JMP2")
for atm in chn2.iter_atoms():
atm.position = atm.position - do
sup2.add_atom(atm)
FileIO.SaveStructure(fil="super2.pdb", struct=sup2)
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) # COMEBACKTO!!!
invert(L)
h = matrixmultiply(b, matrixmultiply(a, transpose(L)))
return h, transpose(L)
def Cmatrix(self):
'''
Calculate the C matrix
'''
self.C = []
self.gamma = []
self.f1001 = []
self.f1010 = []
S = getattr(self, "S")
R11 = getattr(self, "R11")
R12 = getattr(self, "R12")
R21 = getattr(self, "R21")
R22 = getattr(self, "R22")
BETX = getattr(self, "BETX")
BETY = getattr(self, "BETY")
ALFX = getattr(self, "ALFX")
ALFY = getattr(self, "ALFY")
J = numpy.reshape(numpy.array([0, 1, -1, 0]), (2, 2))
for j in range(0, len(S)):
R = numpy.array([[R11[j], R12[j]], [R21[j], R22[j]]])
C = matrixmultiply(-J, matrixmultiply(numpy.transpose(R), J))
C = (1 / numpy.sqrt(1 + determinant(R))) * C
g11 = 1 / numpy.sqrt(BETX[j])
g12 = 0
g21 = ALFX[j] / numpy.sqrt(BETX[j])
g22 = numpy.sqrt(BETX[j])
Ga = numpy.reshape(numpy.array([g11, g12, g21, g22]), (2, 2))
g11 = 1 / numpy.sqrt(BETY[j])
g12 = 0
g21 = ALFY[j] / numpy.sqrt(BETY[j])
g22 = numpy.sqrt(BETY[j])
Gb = numpy.reshape(numpy.array([g11, g12, g21, g22]), (2, 2))
C = matrixmultiply(Ga, matrixmultiply(C, inverse(Gb)))
gamma = 1 - determinant(C)
self.gamma.append(gamma)
C = numpy.ravel(C)
self.C.append(C)
self.f1001.append(((C[0] + C[3]) * 1j + (C[1] - C[2])) / 4 / gamma)
self.f1010.append(((C[0] - C[3]) * 1j + (-C[1] - C[2])) / 4 / gamma)
self.F1001R = numpy.array(self.f1001).real
self.F1001I = numpy.array(self.f1001).imag
self.F1010R = numpy.array(self.f1010).real
self.F1010I = numpy.array(self.f1010).imag
self.F1001W = numpy.sqrt(self.F1001R ** 2 + self.F1001I ** 2)
self.F1010W = numpy.sqrt(self.F1010R ** 2 + self.F1010I ** 2)
def __locate_newton(self, X, C):
"""Note: This is redundant!! B is a column of A!!! Works for now, though..."""
pind = self.testfuncs[0].pind
J_coords = C.CorrFunc.jac(X[0:C.dim], C.coords)
J_params = C.CorrFunc.jac(X[0:C.dim], C.params)
A = c_[J_coords, J_params[:,pind]]
B = J_params[:,pind]
return r_[C.CorrFunc(X[0:C.dim]) + X[C.dim]*X[C.dim+1:], \
matrixmultiply(transpose(A),X[C.dim+1:]), \
matrixmultiply(transpose(X[C.dim+1:]),B), \
matrixmultiply(transpose(X[C.dim+1:]),X[C.dim+1:]) - 1]
def test_module():
import random
import AtomMath
import FileIO
import Structure
R = AtomMath.rmatrixu(numpy.array((0.0, 0.0, 1.0), float), math.pi/2.0)
struct1 = FileIO.LoadStructure(fil="/home/jpaint/8rxn/8rxn.pdb")
struct2 = FileIO.LoadStructure(fil="/home/jpaint/8rxn/8rxn.pdb")
chn1 = struct1.get_chain("A")
chn2 = struct2.get_chain("A")
rc = lambda: 0.1 * (random.random() - 1.0)
for atm in chn2.iter_atoms():
atm.position = numpy.matrixmultiply(R, atm.position) + numpy.array((rc(),rc(),rc()),float)
alist = []
for atm1 in chn1.iter_atoms():
if atm1.name != "CA":
continue
atm2 = chn2.get_equivalent_atom(atm1)
if atm2 == None: continue
alist.append((atm1, atm2))
sup = SuperimposeAtoms(alist)
R = sup.R
Q = sup.Q
print Q
print R
so = sup.src_origin
do = sup.dst_origin
sup1 = Structure.Structure(structure_id = "JMP1")
for atm in chn1.iter_atoms():
atm.position = numpy.matrixmultiply(R, atm.position - so)
sup1.add_atom(atm)
FileIO.SaveStructure(fil="super1.pdb", struct=sup1)
sup2 = Structure.Structure(structure_id = "JMP2")
for atm in chn2.iter_atoms():
atm.position = atm.position - do
sup2.add_atom(atm)
FileIO.SaveStructure(fil="super2.pdb", struct=sup2)
def __locate_newton(self, X, C):
"""Note: This is redundant!! B is a column of A!!! Works for now, though..."""
pind = self.testfuncs[0].pind
J_coords = C.CorrFunc.jac(X[0:C.dim], C.coords)
J_params = C.CorrFunc.jac(X[0:C.dim], C.params)
A = c_[J_coords, J_params[:,pind]]
B = J_params[:,pind]
return r_[C.CorrFunc(X[0:C.dim]) + X[C.dim]*X[C.dim+1:], \
matrixmultiply(transpose(A),X[C.dim+1:]), \
matrixmultiply(transpose(X[C.dim+1:]),B), \
matrixmultiply(transpose(X[C.dim+1:]),X[C.dim+1:]) - 1]
def svdClean(self, plane):
global nturns, tx, ty
print 'removing noise floor',plane
if plane == 'x':
b = tx[turn:,:] #truncate by the first 5 turns
n_turns = shape(b)[0]
elif plane == 'y':
b = ty[turn:,:] #truncate by the first 5 turns
n_turns = shape(b)[0]
else:
print "no tbt data acquired"
b_mean = mean(b)
b = (b-b_mean)/sqrt(n_turns)
n_bpms = shape(b)[1]
#----svd for matrix with bpms >10
if n_bpms > 10:
A = singular_value_decomposition(b,full_matrices=0)
#print "Singular values:",A[1]
else:
sys.exit('Exit, # of bpms < 10')
#----SVD cut for noise floor
if sing_val > n_bpms:
svdcut = n_bpms
print 'requested more singular values than available'
print '# of sing_val used for', plane, '=', n_bpms
else:
svdcut = int(sing_val)
print '# of sing_val used for', plane, '=', svdcut
#print A[1][0]
A[1][svdcut:] = 0.
#temp=matrixmultiply(identity(len(A[1]))*A[1], A[2])
temp=matrixmultiply(diag(A[1]), A[2])
b = matrixmultiply(A[0],temp) ### check
b = (b *sqrt(n_turns))+b_mean
#b = b*sqrt(n_turns)
if plane == 'x':
tx[turn:,:] = b
elif plane == 'y':
ty[turn:,:] = b
else:
print "no tbt data to analyze"
nturns = shape(tx)[0]
def bialttoeig(q, p, n, A):
v1, v2 = invwedge(q, n)
w1, w2 = invwedge(p, n)
A11 = bilinearform(A,v1,v1)
A22 = bilinearform(A,v2,v2)
A12 = bilinearform(A,v1,v2)
A21 = bilinearform(A,v2,v1)
v11 = matrixmultiply(transpose(v1),v1)
v22 = matrixmultiply(transpose(v2),v2)
v12 = matrixmultiply(transpose(v1),v2)
D = v11*v22 - v12*v12
k = (A11*A22 - A12*A21)/D
return k[0][0], v1, w1
def bialttoeig(q, p, n, A):
v1, v2 = invwedge(q, n)
w1, w2 = invwedge(p, n)
A11 = bilinearform(A, v1, v1)
A22 = bilinearform(A, v2, v2)
A12 = bilinearform(A, v1, v2)
A21 = bilinearform(A, v2, v1)
v11 = matrixmultiply(transpose(v1), v1)
v22 = matrixmultiply(transpose(v2), v2)
v12 = matrixmultiply(transpose(v1), v2)
D = v11 * v22 - v12 * v12
k = (A11 * A22 - A12 * A21) / D
return k[0][0], v1, w1
def process(self, X, V, C):
BifPoint.process(self, X, V, C)
# Finds the new branch
J_coords = C.CorrFunc.jac(X, C.coords)
J_params = C.CorrFunc.jac(X, C.params)
singular = True
perpvec = r_[1,zeros(C.dim-1)]
d = 1
while singular and d <= C.dim:
try:
v0 = linalg.solve(r_[c_[J_coords, J_params],
[perpvec]], \
r_[zeros(C.dim-1),1])
except:
perpvec = r_[0., perpvec[0:(C.dim-1)]]
d += 1
else:
singular = False
if singular:
raise PyDSTool_ExistError("Problem in _compute: Failed to compute tangent vector.")
v0 /= linalg.norm(v0)
V = sign([x for x in v0 if abs(x) > 1e-8][0])*v0
A = r_[c_[J_coords, J_params], [V]]
W, VR = linalg.eig(A)
W0 = [ind for ind, eig in enumerate(W) if abs(eig) < 5e-5]
V1 = real(VR[:,W0[0]])
H = C.CorrFunc.hess(X, C.coords+C.params, C.coords+C.params)
c11 = matrixmultiply(self.data.psi,[bilinearform(H[i,:,:], V, V) for i in range(H.shape[0])])
c12 = matrixmultiply(self.data.psi,[bilinearform(H[i,:,:], V, V1) for i in range(H.shape[0])])
c22 = matrixmultiply(self.data.psi,[bilinearform(H[i,:,:], V1, V1) for i in range(H.shape[0])])
beta = 1
alpha = -1*c22/(2*c12)
V1 = alpha*V + beta*V1
V1 /= linalg.norm(V1)
self.found[-1].eigs = W
self.found[-1].branch = todict(C, V1)
self.info(C, -1)
return True
def mulXY(self, x, y):
"""Muliplies the matrix with each x/y element
Arguments:
x -- a sequence with x elements
y -- a sequence with y elements
"""
start = time.time()
length = min(len(x), len(y))
w = numpy.ones(length, Float)
#print x, y
#for i in xrange(length):
# point = numpy.matrixmultiply(self.matrix, points[i])
# newx[i] = point[0] / point[2]
# newy[i] = point[1] / point[2]
#end = time.time()
#if end - start > 1.0:
# set_trace()
x = numpy.array(x, numpy.Float)
y = numpy.array(y, numpy.Float)
points = numpy.matrixmultiply(self.matrix, array([x, y, w]))
newx = points[0] / points[2]
newy = points[1] / points[2]
return newx, newy
def correctbeatEXP2(x,
x2,
y,
y2,
dx,
dx2,
beat_input2,
cut=0.01,
app=0,
path="./"):
###########################################################
R = transpose(beat_input2.sensitivity_matrix)
vector = beat_input2.computevectorEXP2(x, x2, y, y2, dx, dx2)
wg = beat_input2.wg
weisvec = array(
concatenate([
sqrt(wg[0]) *
ones(len(beat_input2.phasexlist) + len(beat_input2.phasexlist2)),
sqrt(wg[1]) *
ones(len(beat_input2.phaseylist) + len(beat_input2.phaseylist2)),
sqrt(wg[2]) *
ones(len(beat_input2.betaxlist) + len(beat_input2.betaxlist2)),
sqrt(wg[3]) *
ones(len(beat_input2.betaylist) + len(beat_input2.betaylist2)),
sqrt(wg[4]) *
ones(len(beat_input2.displist) + len(beat_input2.displist2)),
sqrt(wg[5]) * ones(4)
]))
Rnew = transpose(transpose(R) * weisvec)
#print (vector-beat_input.zerovector) # Good line to debug big correction strs
delta = -matrixmultiply(generalized_inverse(
Rnew, cut), (vector - beat_input2.zerovector) / beat_input2.normvector)
writeparams(delta, beat_input2.varslist, app, path)
return [delta, beat_input2.varslist]
def numeric_gemm_var1_flat(A, B, C, mc, kc, nc, mr=1, nr=1):
M, N = C.shape
K = A.shape[0]
mc = min(mc, M)
kc = min(kc, K)
nc = min(nc, N)
tA = numpy.zeros((mc, kc), dtype=numpy.float)
tB = numpy.zeros((kc, N), dtype=numpy.float)
for k in range(0, K, kc):
# Pack B into tB
tB[:, :] = B[k:k + kc:, :]
for i in range(0, M, mc):
imc = i + mc
# Pack A into tA
tA[:, :] = A[i:imc, k:k + kc]
for j in range(0, N): # , nc):
# Cj += ABj + Cj
# jnc = j+nc
ABj = numpy.matrixmultiply(tA, tB[:, j])
numpy.add(C[i:imc:, j], ABj, C[i:imc:, j])
# Store Caux into memory
return
def transform(self, position):
"""Transforms a source position to its aligned position.
"""
position = position - self.src_origin
position = numpy.matrixmultiply(self.R, position)
position = position + self.dst_origin
return position
def correctcouple(a, dispy, couple_input, cut=0.01, app=0, path="./"):
sm = couple_input.sensitivity_matrix
if np.count_nonzero(sm) < 1:
raise ValueError('Sensitivity matrix has only zeros')
R = np.transpose(sm)
vector=couple_input.computevector(a,dispy)
wg=couple_input.wg
weisvec = np.array(np.concatenate([
np.sqrt(wg[0])*np.ones(len(couple_input.couplelist)),
np.sqrt(wg[1])*np.ones(len(couple_input.couplelist)),
np.sqrt(wg[2])*np.ones(len(couple_input.couplelist)),
np.sqrt(wg[3])*np.ones(len(couple_input.couplelist)),
np.sqrt(wg[4])*np.ones(len(couple_input.dispylist))
])
)
Rnew = np.transpose(np.transpose(R)*weisvec)
delta = -matrixmultiply(generalized_inverse(Rnew,cut), (vector-couple_input.zerovector)/couple_input.normvector)
write_params(delta, couple_input.varslist, app, path=path)
return [delta, couple_input.varslist]
def rmatrixz(vec):
"""Return a rotation matrix which transforms the coordinate system
such that the vector vec is aligned along the z axis.
"""
u, v, w = normalize(vec)
d = math.sqrt(u * u + v * v)
if d != 0.0:
Rxz = numpy.array(
[[u / d, v / d, 0.0], [-v / d, u / d, 0.0], [0.0, 0.0, 1.0]],
float)
else:
Rxz = numpy.identity(3, float)
Rxz2z = numpy.array([[w, 0.0, -d], [0.0, 1.0, 0.0], [d, 0.0, w]], float)
R = numpy.matrixmultiply(Rxz2z, Rxz)
try:
assert numpy.allclose(linalg.determinant(R), 1.0)
except AssertionError:
print "rmatrixz(%s) determinant(R)=%f" % (vec, linalg.determinant(R))
raise
return R
def classify(self, vector):
if self._should_normalise:
vector = self._normalise(vector)
if self._Tt != None:
vector = numpy.matrixmultiply(self._Tt, vector)
cluster = self.classify_vectorspace(vector)
return self.cluster_name(cluster)
def correctcouple2(couple,
couple2,
dispy,
dispy2,
couple_input2,
cut=0.01,
app=0,
path="./"):
################################################
R = transpose(couple_input.sensitivity_matrix2)
vector = couple_input2.computevector2(couple, couple2, dispy, dispy2)
wg = couple_input2.wg
weisvec = array(
concatenate([
sqrt(wg[0]) * ones(len(couple_input2.couplelist)),
sqrt(wg[0]) * ones(len(couple_input2.couplelist2)),
sqrt(wg[1]) * ones(len(couple_input2.couplelist)),
sqrt(wg[1]) * ones(len(couple_input2.couplelist2)),
sqrt(wg[2]) * ones(len(couple_input2.couplelist)),
sqrt(wg[2]) * ones(len(couple_input2.couplelist2)),
sqrt(wg[3]) * ones(len(couple_input2.couplelist)),
sqrt(wg[3]) * ones(len(couple_input2.couplelist2)),
sqrt(wg[4]) * ones(len(couple_input2.dispylist)),
sqrt(wg[4]) * ones(len(couple_input2.dispylist2))
]))
Rnew = transpose(transpose(R) * weisvec)
delta = -matrixmultiply(
generalized_inverse(Rnew, cut),
(vector - couple_input2.zerovector) / couple_input2.normvector)
writeparams(delta, couple_input2.varslist, app, path=path)
return [delta, couple_input2.varslist]
def transform(self, position):
"""Transforms a source position to its aligned position.
"""
position = position - self.src_origin
position = numpy.matrixmultiply(self.R, position)
position = position + self.dst_origin
return position
def eigenvector_for_largest_eigenvalue(matrix):
"""Returns eigenvector corresponding to largest eigenvalue of matrix.
Implements a numerical method for finding an eigenvector by repeated
application of the matrix to a starting vector. For a matrix A the
process w(k) <-- A*w(k-1) converges to eigenvector w with the largest
eigenvalue. Because distance matrix D has all entries >= 0, a theorem
due to Perron and Frobenius on nonnegative matrices guarantees good
behavior of this method, excepting degenerate cases where the
iteration oscillates. For distance matrices a remedy is to add the
identity matrix to A, permitting the iteration to converge to the
eigenvector. (From Sander and Schneider (1991), and Vingron and
Sibbald (1993))
Note: Only works on square matrices.
"""
#always add the identity matrix to avoid oscillating behavior
matrix = matrix + identity(len(matrix))
#v is a random vector (chosen as the normalized vector of ones)
v = ones(len(matrix))/len(matrix)
#iterate until convergence
for i in range(1000):
new_v = matrixmultiply(matrix,v)
new_v = new_v/sum(new_v, 0) #normalize
if sum(list(map(abs,new_v-v)), 0) > 1e-9:
v = new_v #not converged yet
continue
else: #converged
break
return new_v
def func(self, X, V):
H = self.F.sysfunc.hess(X, self.F.coords, self.F.coords)
v = self.F.testfunc.data.v
w = self.F.testfunc.data.w
return array(matrixmultiply(transpose(w), reshape([bilinearform(H[i,:,:], v, v) \
for i in range(H.shape[0])],(H.shape[0],1)))[0])
"""This commented text is normal form information (I think). It's a temporary commment. Delete when comfortable."""
def correctcouple(a, dispy, couple_input, cut=0.01, app=0, path="./"):
sm = couple_input.sensitivity_matrix
if np.count_nonzero(sm) < 1:
raise ValueError('Sensitivity matrix has only zeros')
R = np.transpose(sm)
vector = couple_input.computevector(a, dispy)
wg = couple_input.wg
weisvec = np.array(
np.concatenate([
np.sqrt(wg[0]) * np.ones(len(couple_input.couplelist)),
np.sqrt(wg[1]) * np.ones(len(couple_input.couplelist)),
np.sqrt(wg[2]) * np.ones(len(couple_input.couplelist)),
np.sqrt(wg[3]) * np.ones(len(couple_input.couplelist)),
np.sqrt(wg[4]) * np.ones(len(couple_input.dispylist))
]))
Rnew = np.transpose(np.transpose(R) * weisvec)
delta = -matrixmultiply(
generalized_inverse(Rnew, cut),
(vector - couple_input.zerovector) / couple_input.normvector)
write_params(delta, couple_input.varslist, app, path=path)
return [delta, couple_input.varslist]
def classify(self, vector):
if self._should_normalise:
vector = self._normalise(vector)
if self._Tt != None:
vector = numpy.matrixmultiply(self._Tt, vector)
cluster = self.classify_vectorspace(vector)
return self.cluster_name(cluster)
def eigenvector_for_largest_eigenvalue(matrix):
"""Returns eigenvector corresponding to largest eigenvalue of matrix.
Implements a numerical method for finding an eigenvector by repeated
application of the matrix to a starting vector. For a matrix A the
process w(k) <-- A*w(k-1) converges to eigenvector w with the largest
eigenvalue. Because distance matrix D has all entries >= 0, a theorem
due to Perron and Frobenius on nonnegative matrices guarantees good
behavior of this method, excepting degenerate cases where the
iteration oscillates. For distance matrices a remedy is to add the
identity matrix to A, permitting the iteration to converge to the
eigenvector. (From Sander and Schneider (1991), and Vingron and
Sibbald (1993))
Note: Only works on square matrices.
"""
#always add the identity matrix to avoid oscillating behavior
matrix = matrix + identity(len(matrix))
#v is a random vector (chosen as the normalized vector of ones)
v = ones(len(matrix)) / len(matrix)
#iterate until convergence
for i in range(1000):
new_v = matrixmultiply(matrix, v)
new_v = new_v / sum(new_v, 0) #normalize
if sum(map(abs, new_v - v), 0) > 1e-9:
v = new_v #not converged yet
continue
else: #converged
break
return new_v
def numeric_gemm_var1_flat(A, B, C, mc, kc, nc, mr=1, nr=1):
M, N = C.shape
K = A.shape[0]
mc = min(mc, M)
kc = min(kc, K)
nc = min(nc, N)
tA = numpy.zeros((mc, kc), dtype = numpy.float)
tB = numpy.zeros((kc, N), dtype = numpy.float)
for k in range(0, K, kc):
# Pack B into tB
tB[:,:] = B[k:k+kc:,:]
for i in range(0, M, mc):
imc = i+mc
# Pack A into tA
tA[:,:] = A[i:imc,k:k+kc]
for j in range(0, N): # , nc):
# Cj += ABj + Cj
# jnc = j+nc
ABj = numpy.matrixmultiply(tA, tB[:,j])
numpy.add(C[i:imc:,j], ABj, C[i:imc:,j])
# Store Caux into memory
return
def correctbeatEXP(x,
y,
dx,
beat_input,
cut=0.01,
app=0,
path="./",
xbet=[],
ybet=[]):
R = np.transpose(beat_input.sensitivity_matrix)
vector = beat_input.computevectorEXP(x, y, dx, xbet, ybet)
wg = beat_input.wg
weisvec = np.array(
np.concatenate([
np.sqrt(wg[0]) * np.ones(len(beat_input.phasexlist)),
np.sqrt(wg[1]) * np.ones(len(beat_input.phaseylist)),
np.sqrt(wg[2]) * np.ones(len(beat_input.betaxlist)),
np.sqrt(wg[3]) * np.ones(len(beat_input.betaylist)),
np.sqrt(wg[4]) * np.ones(len(beat_input.displist)),
np.sqrt(wg[5]) * np.ones(2)
]))
Rnew = np.transpose(np.transpose(R) * weisvec)
delta = -matrixmultiply(generalized_inverse(
Rnew, cut), (vector - beat_input.zerovector) / beat_input.normvector)
writeparams(delta, beat_input.varslist, app, path)
return [delta, beat_input.varslist]
def itrSVD(X, Y, DX, beat_input, cut=0.001, num_iter=1, app=0, tol=1e-9, path="./"):
R = np.transpose(beat_input.sensitivity_matrix)
b = beat_input.computevectorEXP(X, Y, DX) - beat_input.zerovector
corr = beat_input.varslist
inva = generalized_inverse(R, cut)
rmss, ptopp = calcRMSNumeric(b)
RHO2 = {}
dStren = np.zeros(len(corr))
print 'Initial Phase-Beat:', '{RMS,PK2PK}', rmss, ptopp
for ITER in range(num_iter): # @UnusedVariable
dStren = dStren + matrixmultiply(inva, b)
bvec = b - matrixmultiply(R, dStren)
rm, ptp = calcRMSNumeric(bvec)
print 'ITER', num_iter, '{RMS,PK2PK}', rm, ptp
for j in range(len(corr)):
RHO2[corr[j]] = dStren[j]
wrtpar(corr, RHO2, app, path)
def func(self, X, V):
H = self.F.sysfunc.hess(X, self.F.coords, self.F.coords)
v = self.F.testfunc.data.v
w = self.F.testfunc.data.w
return array(matrixmultiply(transpose(w), reshape([bilinearform(H[i,:,:], v, v) \
for i in range(H.shape[0])],(H.shape[0],1)))[0])
"""This commented text is normal form information (I think). It's a temporary commment. Delete when comfortable."""
def do_svd_clean(self, plane):
"""Does a SVD clean on the given plane"""
time_start = time.time()
print "(plane", plane, ") removing noise floor with SVD"
A = numpy.array(self.sddsfile.dictionary_plane_to_bpms[plane].bpm_data)
number_of_bpms = A.shape[0]
if number_of_bpms <= 10:
sys.exit("Number of bpms <= 10")
# normalise the matrix
sqrt_number_of_turns = numpy.sqrt(A.shape[1])
A_mean = numpy.mean(A)
A = (A - A_mean) / sqrt_number_of_turns
if PRINT_TIMES:
print ">>Time for svdClean (before SVD call):", time.time() - time_start, "s"
USV = self.get_singular_value_decomposition(A)
if PRINT_TIMES:
print ">>Time for svdClean (after SVD call): ", time.time() - time_start, "s"
# remove bad BPM by SVD (tbach)
goodbpm_indices = self.get_badbpm_indices(USV, plane)
USV = (USV[0][goodbpm_indices], USV[1], USV[2])
number_of_bpms = len(goodbpm_indices)
#----SVD cut for noise floor
if _InputData.sing_val < number_of_bpms:
print "(plane", plane, ") svdcut:", _InputData.sing_val
USV[1][_InputData.sing_val:] = 0
else:
print "requested more singular values than available"
A = matrixmultiply(USV[0], matrixmultiply(numpy.diag(USV[1]), USV[2]))
# A0 * (A1 * A2) should require less operations than (A0 * A1) * A2,
# because of the different sizes
# A0 has (M, K), A1 has (K, K) and A2 has (K, N) with K=min(M,N)
# Most of the time, the number of turns is greater then
# the number of BPM, so M > N
# --tbach
A = (A * sqrt_number_of_turns) + A_mean
self.sddsfile.dictionary_plane_to_bpms[plane].bpm_data = A
if PRINT_TIMES:
print ">>Time for do_svd_clean:", time.time() - time_start, "s"
def vector(self, vector):
"""
Returns the vector after normalisation and dimensionality reduction
"""
if self._should_normalise:
vector = self._normalise(vector)
if self._Tt != None:
vector = numpy.matrixmultiply(self._Tt, vector)
return vector
def firstlyapunov(X, F, w, J_coords=None, V=None, W=None, p=None, q=None,
check=False):
if J_coords is None:
J_coords = F.jac(X, F.coords)
if p is None:
alpha = bilinearform(transpose(J_coords),V[:,0],V[:,1]) - \
1j*w*matrixmultiply(V[:,0],V[:,1])
beta = -1*bilinearform(transpose(J_coords),V[:,0],V[:,0]) + \
1j*w*matrixmultiply(V[:,0],V[:,0])
q = alpha*V[:,0] + beta*V[:,1]
alpha = bilinearform(J_coords,W[:,0],W[:,1]) + \
1j*w*matrixmultiply(W[:,0],W[:,1])
beta = -1*bilinearform(J_coords,W[:,0],W[:,0]) - \
1j*w*matrixmultiply(W[:,0],W[:,0])
p = alpha*W[:,0] + beta*W[:,1]
p /= linalg.norm(p)
q /= linalg.norm(q)
direc = conjugate(1/matrixmultiply(conjugate(p),q))
p = direc*p
if check:
print('Checking...')
print(' |q| = %f' % linalg.norm(q))
temp = matrixmultiply(conjugate(p),q)
print(' |<p,q> - 1| = ', abs(temp-1))
print(' |Aq - iwq| = %f' % linalg.norm(matrixmultiply(J_coords,q) - 1j*w*q))
print(' |A*p + iwp| = %f\n' % linalg.norm(matrixmultiply(transpose(J_coords),p) + 1j*w*p))
# Compute first lyapunov coefficient
B = F.hess(X, F.coords, F.coords)
D = hess3(F, X, F.coords)
b1 = array([bilinearform(B[i,:,:], q, q) for i in range(B.shape[0])])
b2 = array([bilinearform(B[i,:,:], conjugate(q),
linalg.solve(2*1j*w*eye(F.m) - J_coords, b1)) \
for i in range(B.shape[0])])
b3 = array([bilinearform(B[i,:,:], q, conjugate(q)) \
for i in range(B.shape[0])])
b4 = array([bilinearform(B[i,:,:], q, linalg.solve(J_coords, b3)) \
for i in range(B.shape[0])])
temp = array([trilinearform(D[i,:,:,:],q,q,conjugate(q)) \
for i in range(D.shape[0])]) + b2 - 2*b4
l1 = 0.5*real(matrixmultiply(conjugate(p), temp))
return l1
def test(algs, niters = 5, validate = False):
"""
Test a numcer of algorithms and return the results.
"""
if type(algs) is not list:
algs = [algs]
results = []
m,n,k = (64,64,64)
# Cache effects show up between 2048 and 4096 on a G4
tests = [8, 16, 32, 64] # , 128, 256, 512, 768, 1024, 2048, 4096]: [2048, 4096]: #
tests = [128, 256, 512, 1024, 2048, 4096]
# tests = [4096]
# tests = [2048]
# tests = [512]
for size in tests:
m,n,k = (size, size, size)
A, B, C = create_matrices(m, k, n)
if validate:
C_valid = numpy.matrixmultiply(A, B)
for alg in algs:
print alg.func_name, size
if validate:
alg(A, B, C)
_validate(alg.func_name, m, n, k, C, C_valid)
# KC = [32, 64, 128, 256] # , 512]
KC = [32, 64, 128, 256] # , 256] # , 512]
# KC = [64]
KC = [128, 256]
KC = [256]
NC = [32, 64, 128, 256] # , 512]
# NC = [32, 32, 32]
# NC = [256, 256, 256]
# NC = [128, 128, 128]
NC = [128, 256]
NC = [128]
for mc in [32]: # , 64, 128, 256]:
for kc in KC:
for nc in NC:
# print ' ', mc, kc, nc
# try:
if True:
times = run_alg(alg, A, B, C, mc, kc, nc, 4, 4, niters)
result = _result(alg.func_name, m, k, n, mc, kc, nc, times)
results.append(result)
print result
# except:
# print 'Failed: ', alg.func_name, m, k, n, mc, kc, nc, times
return results
