def phiv(self, h, v):
"""
Computes phi(h*Hm)*v and two other vectors
:param h: factor
:param v: vector to apply phi(h*Hm) to
:returns: 3-tuple of vectors ``( phi(h/3*Hm)*v, phi(2h/3*Hm)*v, phi(h*Hm)*v )``
"""
# if Df is nearly singular, Df^-1 * (exp(Df)-1)*v is numerically ill-conditioned, but should give v
# check norm of Jacobian:
if self.rhs.normDf(self.y[-1]) < np.finfo(np.double).eps:
return (v,v,v)
# if v is too small, phi*v is also almost zero.
# must check for this since arnoldi iterations needs v != 0
if norm(v) < np.finfo(np.double).eps:
res = np.zeros_like(v)
return (res,res,res)
# use flag argument to find correct KrylovPhi instance
pk = KrylovPhi(self.rhs, exp4=self, tau=h)
# compute Krylov subspace approximation of phi(h*A)*v
pk.compute(v)
p1,p2,p3 = pk.phi3()
if self.stats:
self.stats["RHSevals"] += pk.m-1 # dimension of Krylov space minus 1 corresponds to number of applyA calls
return (p1, p2, p3)
def phiv(self, h, v, flag=-1, reuse=False):
"""
Computes phi(h*Hm)*v and two other vectors
:param h: factor
:param v: vector to apply phi(h*Hm) to
:param flag: if it is in (0,1,2), use corresponding instance of ``PhiKrylov``
:param reuse: if True, attempt to reuse the old Krylov space
:returns: 3-tuple of vectors ``( phi(h/3*Hm)*v, phi(2h/3*Hm)*v, phi(h*Hm)*v )``
"""
# if Df is nearly singular, Df^-1 * (exp(Df)-1)*v is numerically ill-conditioned, but should give v
# check norm of Jacobian:
if self.rhs.normDf(self.y[-1]) < np.finfo(np.double).eps:
return (v,v,v)
# if v is too small, phi*v is also almost zero.
# must check for this since arnoldi iterations needs v != 0
if norm(v) < np.finfo(np.double).eps:
res = np.zeros_like(v)
return (res,res,res)
# use flag argument to find correct KrylovPhi instance
if not flag in [0,1,2]:
pk = KrylovPhi(self.rhs, exp4=self, tau=h)
reuse = False
else:
pk = self.krylov[flag]
pk.tau = h
if np.isscalar(v) or len(v) <= pk.m_max:
reuse = False
# reuse already computed krylov space
if reuse:
p1,p2,p3 = pk.phi3()
else:
# compute Krylov subspace approximation of phi(h*A)*v
pk.compute(v)
if self.stats:
# dimension of Krylov space minus 1 corresponds to number of applyA calls
self.stats["RHSevals"] += pk.m-1
p1,p2,p3 = pk.phi3()
return (p1, p2, p3)