def helper(self,T,prec=10):
k = 7
Nvals = [10, 50, 100, 1000, 5000]
for n in Nvals:
A = array(random.random((n,n)), dtype=T)
v = ones((n,1), dtype=T)
# C++ version
V = zeros((n,k), dtype=T)
H = zeros((k+1,k), dtype=T)
a.arnoldi(A,v,k,V,H)
# Python version
Vloc,Hloc = arnoldi(A,v,k)
# assertion
assert_almost_equal(norm(H)/n,norm(Hloc)/n,prec)
def matrix_exp_arnoldi_C(A, v, factor, k):
r"""Compute the solution of :math:`v' = A v` via :math:`k`
steps of a the Arnoldi krylov method. Uses a C++ implementation.
:param A: The matrix :math:`A` of shape :math:`N \times N`.
:param v: The vector :math:`v` of length :math:`N`.
:param factor: An additional scalar factor :math:`\alpha`.
:param k: The number :math:`k` of Krylov steps performed.
:return: The (approximate) value of :math:`\exp\left(-i \alpha A\right) v`.
"""
# try to import compiled module
from carnoldi import arnoldi
k = min(min(A.shape), k)
V = zeros((A.shape[0],k),dtype=A.dtype)
H = zeros((k+1,k),dtype=A.dtype)
arnoldi(A, v, k, V, H)
eH = mat(expm(-1.0j*factor*H[:-1,:]))
r = V * eH[:,0]
return asarray(r * norm(v))
def matrix_exp_arnoldi(A, v, factor, k):
r"""Compute the solution of :math:`v' = A v` via :math:`k`
steps of a the Arnoldi krylov method.
:param A: The matrix :math:`A` of shape :math:`N \times N`.
:param v: The vector :math:`v` of length :math:`N`.
:param factor: An additional scalar factor :math:`\alpha`.
:param k: The number :math:`k` of Krylov steps performed.
:return: The (approximate) value of :math:`\exp\left(-i \alpha A\right) v`.
"""
V, H = arnoldi(A, v, min(min(A.shape), k))
eH = mat(expm(-1.0j*factor*H[:-1,:]))
r = V[:,:-1] * eH[:,0]
return asarray(r * norm(v))
print "current type:", type_to_name[T]
Tc = []
Tp = []
for n in Nvals:
print "n:", n
#A = array(diag(2*ones(n)) - diag(ones(n-1),1) - diag(ones(n-1),-1), dtype=t)
A = array(random.random((n, n)), dtype=T)
v = ones((n, 1), dtype=T)
ctime = inf
ptime = inf
for r in range(Creps):
# time C++ version
V = zeros((n, k), dtype=T)
H = zeros((k + 1, k), dtype=T)
t = time.time()
a.arnoldi(A, v, k, V, H)
ctime = min(ctime, time.time() - t)
for r in range(Preps): # time python version
t = time.time()
Vloc, Hloc = arnoldi(A, v, k)
ptime = min(ptime, time.time() - t)
Tc.append(ctime)
Tp.append(ptime)
normHH = norm(H - Hloc) / norm(H) # "relative" norm
epsilon = 1e-5
if normHH > epsilon:
print "H-Hloc is not small (%f>%f)!" % (normHH, epsilon)
del A, v, V, H, Vloc, Hloc
plt.loglog(Nvals, Tp, '-o', label="Python")
for T in [float32, float64, complex64, complex128]:
print "current type:", type_to_name[T]
Tc = []
Tp = []
for n in Nvals:
print "n:",n
#A = array(diag(2*ones(n)) - diag(ones(n-1),1) - diag(ones(n-1),-1), dtype=t)
A = array(random.random((n,n)), dtype=T)
v = ones((n,1), dtype=T)
ctime = inf; ptime = inf
for r in range(Creps):
# time C++ version
V = zeros((n,k), dtype=T)
H = zeros((k+1,k), dtype=T)
t = time.time()
a.arnoldi(A,v,k,V,H)
ctime = min(ctime, time.time()-t)
for r in range(Preps):# time python version
t = time.time()
Vloc,Hloc = arnoldi(A,v,k)
ptime = min(ptime, time.time()-t)
Tc.append(ctime)
Tp.append(ptime)
normHH = norm(H-Hloc)/norm(H) # "relative" norm
epsilon = 1e-5
if normHH > epsilon:
print "H-Hloc is not small (%f>%f)!"%(normHH,epsilon)
del A, v, V, H, Vloc, Hloc
plt.loglog(Nvals, Tp, '-o', label="Python")