def helper(self,T,prec=10):
Nvals = [10, 50, 100, 200]
for n in Nvals:
A = array(random.random((n,n)), dtype=T)
A = A/norm(A)
v = ones((n,1), dtype=T)
# C++ version
expA = zeros_like(A)
e.expm(A,expA)
# assertion
assert_almost_equal(expm(A),expA,prec)
def matrix_exp_pade_C(A, v, factor):
r"""Compute the solution of :math:`v' = A v` with a full
matrix exponential via Pade approximation.
Uses an efficient C++ implementation via the Eigen matrix library.
If the compiled module is not importable, it falls back to the scipy version.
: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`.
:return: The (approximate) value of :math:`\exp\left(-i \alpha A\right) v`
"""
import cpade
Anew = -1.0j*A*factor
expA = zeros_like(Anew)
cpade.expm(Anew,expA)
return dot(expA, v)
def runtiming(T, Nvals, Tc, reps):
"""runs timing with given type T"""
print "current type:", type_to_name[T]
Tc[T] = []
for n in Nvals:
print " n:", n,
A = array(random.random((n, n)), dtype=T)
ctime = inf
# time C++ version
for r in range(reps):
expA = zeros_like(A)
t = time.time()
e.expm(A, expA) # call C version with Eigen Pade approx.
ctime = min(ctime, time.time() - t)
print ctime
Tc[T].append(ctime)
del A, expA
for T in [float32, float64, complex64, complex128]:
thistime = time.time()
print "current type:", type_to_name[T]
Tc = []
Tp = []
Tp2= []
for n in Nvals:
print "n:",n,
A = array(random.random((n,n)), dtype=T)
ctime = inf; ptime = inf; p2time = inf
# time C++ version
for r in range(Creps):
expA = zeros_like(A)
t = time.time()
e.expm(A,expA) # call C version with Eigen Pade approx.
ctime = min(ctime, time.time()-t)
# time scipy version
for r in range(Preps):
t = time.time()
expA2 = expm(A)
ptime = min(ptime, time.time()-t)
# time new python version
for r in range(P2reps):
t = time.time()
expA3 = e2.expm(A)
p2time = min(p2time, time.time()-t)
Tc.append(ctime)