def __repr__(self):
"""Prints basic statistics about the multigrid hierarchy.
"""
from pyamg.util.linalg import condest
levels = self.levels[::-1]
output = 'multilevel_solver\n'
output += 'Conditioning Number of the matrix: %d\n' % condest(
self.A)
output += 'Number of Levels: %d\n' % len(levels)
output += 'Operator Complexity: %6.3f\n' % self.operator_complexity()
output += 'Grid Complexity: %6.3f\n' % self.grid_complexity()
# output += 'Coarse Solver: %s\n' % self.coarse_solver.name()
total_nnz = sum([level.A.nnz for level in levels])
output += ' level unknowns nonzeros\n'
for n, level in enumerate(levels):
A = level.A
output += ' %2d %10d %10d [%5.2f%%]\n' %\
(n, A.shape[1], A.nnz,\
(100 * float(A.nnz) / float(total_nnz)))
return output
def test_condest(self):
# make tests repeatable
np.random.seed(0)
# Should be exact for small matrices
cases = []
A = np.array([[2.14]])
cases.append(A)
A = np.array([[2.14j]])
cases.append(A)
A = np.array([[-1.2 + 2.14j]])
cases.append(A)
for i in range(1, 6):
A = np.random.rand(i, i)
A = 0.5 * (A.conj().T + A)
cases.append(A)
A = A + 1.0j*np.random.rand(i, i)
A = 0.5 * (A.conj().T + A)
cases.append(A)
for A in cases:
U, Sigma, Vh = svd(A)
exact = max(Sigma)/min(Sigma)
c = condest(A, symmetric=True)
assert_almost_equal(exact, c)
cases = []
for i in range(1, 6):
A = np.random.rand(i, i)
cases.append(A)
cases.append(1.0j*A)
A = A + 1.0j*np.random.rand(i, i)
cases.append(A)
for A in cases:
U, Sigma, Vh = svd(A)
exact = max(Sigma)/min(Sigma)
c = condest(A, symmetric=False)
assert_almost_equal(exact, c)
def test_condest(self):
# make tests repeatable
np.random.seed(0)
# Should be exact for small matrices
cases = []
A = np.array([[2.14]])
cases.append(A)
A = np.array([[2.14j]])
cases.append(A)
A = np.array([[-1.2 + 2.14j]])
cases.append(A)
for i in range(1, 6):
A = np.random.rand(i, i)
cases.append(A)
cases.append(1.0j*A)
A = A + 1.0j*np.random.rand(i, i)
cases.append(A)
for A in cases:
eigs = eigvals(A)
exact = max(np.abs(eigs))/min(np.abs(eigs))
c = condest(A)
assert_almost_equal(exact, c)
def test_condest(self):
# make tests repeatable
random.seed(0)
# Should be exact for small matrices
cases = []
A = mat(array([2.14]))
cases.append(A)
A = mat(array([2.14j]))
cases.append(A)
A = mat(array([-1.2 + 2.14j]))
cases.append(A)
for i in range(1, 6):
A = mat(rand(i, i))
cases.append(A)
cases.append(1.0j * A)
A = mat(A + 1.0j * rand(i, i))
cases.append(A)
for A in cases:
eigs = eigvals(A)
exact = max(abs(eigs)) / min(abs(eigs))
c = condest(A)
assert_almost_equal(exact, c)