def __init__(self,F,Ne,S,**kwargs):
self.tol = kwargs.get('tol',settings.DMPTolerance)
self.maxit = kwargs.get('maxit',settings.DMPIterations)
self.S = S
self.N = F.shape[0]
self.I = identity(self.N,'d')
self.Ne = Ne
self.F = F
self.emin, self.emax = lanczos_minmax(self.F,self.S)
self.initialize()
self.print_init_info()
return
def __init__(self,F,Ne,S,**opts):
self.tol = opts.get('tol',1e-7)
self.maxit = opts.get('maxit',50)
self.S = S
self.N = F.shape[0]
self.I = identity(self.N,'d')
self.Ne = Ne
self.F = F
self.emin, self.emax = lanczos_minmax(self.F,self.S)
self.initialize()
self.print_init_info()
return
def __init__(self, F, Ne, S, **kwargs):
self.tol = kwargs.get('tol', settings.DMPTolerance)
self.maxit = kwargs.get('maxit', settings.DMPIterations)
self.S = S
self.N = F.shape[0]
self.I = identity(self.N, 'd')
self.Ne = Ne
self.F = F
self.emin, self.emax = lanczos_minmax(self.F, self.S)
self.initialize()
self.print_init_info()
return
def __init__(self, F, Ne, S, **opts):
self.tol = opts.get('tol', 1e-7)
self.maxit = opts.get('maxit', 50)
self.S = S
self.N = F.shape[0]
self.I = identity(self.N, 'd')
self.Ne = Ne
self.F = F
self.emin, self.emax = lanczos_minmax(self.F, self.S)
self.initialize()
self.print_init_info()
return
def expmat(A,**kwargs):
nmax = kwargs.get('nmax',12)
cut = kwargs.get('cut',1e-8)
E = identity(A.shape[0],'d')
D = E
for i in xrange(1,nmax):
D = matrixmultiply(D,A)/i
E += D
maxel = D.max()
if abs(maxel) < cut:
break
else:
print "Warning: expmat unconverged after %d iters: %g" % (nmax,maxel)
return E
def __init__(self,F,Ne,S=None,**opts):
self.tol = opts.get('tol',1e-7)
self.maxit = opts.get('maxit',100)
self.do_orth = S is not None
self.N = F.shape[0]
self.I = identity(self.N,'d')
self.Ne = Ne
if self.do_orth:
self.X = SymOrth(S)
self.F = simx(F,self.X)
self.emin, self.emax = gershgorin_minmax(self.F)
self.initialize()
self.print_init_info()
return
def __init__(self,F,Ne,S=None,**kwargs):
self.tol = kwargs.get('tol',settings.DMPTolerance)
self.maxit = kwargs.get('maxit',settings.DMPIterations)
self.do_orth = S is not None
self.N = F.shape[0]
self.I = identity(self.N,'d')
self.Ne = Ne
if self.do_orth:
self.X = SymOrth(S)
self.F = simx(F,self.X)
self.emin, self.emax = gershgorin_minmax(self.F)
self.initialize()
self.print_init_info()
return
def __init__(self, F, Ne, S=None, **kwargs):
self.tol = kwargs.get('tol', settings.DMPTolerance)
self.maxit = kwargs.get('maxit', settings.DMPIterations)
self.do_orth = S is not None
self.N = F.shape[0]
self.I = identity(self.N, 'd')
self.Ne = Ne
if self.do_orth:
self.X = SymOrth(S)
self.F = simx(F, self.X)
self.emin, self.emax = gershgorin_minmax(self.F)
self.initialize()
self.print_init_info()
return
def __init__(self, F, Ne, S=None, **opts):
self.tol = opts.get('tol', 1e-7)
self.maxit = opts.get('maxit', 100)
self.do_orth = S is not None
self.N = F.shape[0]
self.I = identity(self.N, 'd')
self.Ne = Ne
if self.do_orth:
self.X = SymOrth(S)
self.F = simx(F, self.X)
self.emin, self.emax = gershgorin_minmax(self.F)
self.initialize()
self.print_init_info()
return
def jacobi(A,**kwargs):
"""\
E,V = jacobi(A,**kwargs) - Solve the eigenvalues/vectors of matrix
A using Jacobi's method.
Options:
Name Default Definition
tol 1e-10 The tolerance for an element to be declared zero
max_sweeps 200 Maximum number of sweeps through the matrix
"""
max_sweeps = kwargs.get('max_sweeps',settings.JacobiSweeps)
tol = kwargs.get('tol',settings.JacobiTolerance)
n = len(A)
V = identity(n,'d')
b = diagonal(A)
d = diagonal(A)
z = zeros(n,'d')
nrot = 0
for irot in xrange(max_sweeps):
sm = 0
for ip in xrange(n-1):
for iq in xrange(ip+1,n):
sm += abs(A[ip,iq])
if sm < tol:
# Normal return
return evsort(b,V)
thresh = 0
if irot < 3: thresh = 0.2*sm/n/n
for ip in xrange(n-1):
for iq in xrange(ip+1,n):
g = 100*abs(A[ip,iq])
if irot > 3 and g < tol:
A[ip,iq] = 0
elif abs(A[ip,iq]) > thresh:
h = d[iq]-d[ip]
if g < tol:
t = A[ip,iq]/h # t = 1/(2\theta)
else:
theta = 0.5*h/A[ip,iq] # eq 11.1.10
t = 1./(abs(theta)+sqrt(1.+theta*theta))
if theta < 0: t = -t
c = 1.0/sqrt(1+t*t)
s = t*c
tau = s/(1.0+c)
h = t*A[ip,iq]
z[ip] -= h
z[iq] += h
d[ip] -= h
d[iq] += h
A[ip,iq] = 0
for j in xrange(ip):
A[j,ip],A[j,iq] = rotate(A[j,ip],A[j,iq],s,tau)
for j in xrange(ip+1,iq):
A[ip,j],A[j,iq] = rotate(A[ip,j],A[j,iq],s,tau)
for j in xrange(iq+1,n):
A[ip,j],A[iq,j] = rotate(A[ip,j],A[iq,j],s,tau)
for j in xrange(n):
V[j,ip],V[j,iq] = rotate(V[j,ip],V[j,iq],s,tau)
nrot += 1
for ip in xrange(n):
b[ip] += z[ip]
d[ip] = b[ip]
z[ip] = 0
else:
print "Too many iterations"
return None
def jacobi(A, **kwargs):
"""\
E,V = jacobi(A,**kwargs) - Solve the eigenvalues/vectors of matrix
A using Jacobi's method.
Options:
Name Default Definition
tol 1e-10 The tolerance for an element to be declared zero
max_sweeps 200 Maximum number of sweeps through the matrix
"""
max_sweeps = kwargs.get('max_sweeps', settings.JacobiSweeps)
tol = kwargs.get('tol', settings.JacobiTolerance)
n = len(A)
V = identity(n, 'd')
b = diagonal(A)
d = diagonal(A)
z = zeros(n, 'd')
nrot = 0
for irot in xrange(max_sweeps):
sm = 0
for ip in xrange(n - 1):
for iq in xrange(ip + 1, n):
sm += abs(A[ip, iq])
if sm < tol:
# Normal return
return evsort(b, V)
thresh = 0
if irot < 3: thresh = 0.2 * sm / n / n
for ip in xrange(n - 1):
for iq in xrange(ip + 1, n):
g = 100 * abs(A[ip, iq])
if irot > 3 and g < tol:
A[ip, iq] = 0
elif abs(A[ip, iq]) > thresh:
h = d[iq] - d[ip]
if g < tol:
t = A[ip, iq] / h # t = 1/(2\theta)
else:
theta = 0.5 * h / A[ip, iq] # eq 11.1.10
t = 1. / (abs(theta) + sqrt(1. + theta * theta))
if theta < 0: t = -t
c = 1.0 / sqrt(1 + t * t)
s = t * c
tau = s / (1.0 + c)
h = t * A[ip, iq]
z[ip] -= h
z[iq] += h
d[ip] -= h
d[iq] += h
A[ip, iq] = 0
for j in xrange(ip):
A[j, ip], A[j, iq] = rotate(A[j, ip], A[j, iq], s, tau)
for j in xrange(ip + 1, iq):
A[ip, j], A[j, iq] = rotate(A[ip, j], A[j, iq], s, tau)
for j in xrange(iq + 1, n):
A[ip, j], A[iq, j] = rotate(A[ip, j], A[iq, j], s, tau)
for j in xrange(n):
V[j, ip], V[j, iq] = rotate(V[j, ip], V[j, iq], s, tau)
nrot += 1
for ip in xrange(n):
b[ip] += z[ip]
d[ip] = b[ip]
z[ip] = 0
else:
print "Too many iterations"
return None
