def test_expm_multiply_interval_vector(self): np.random.seed(1234) interval = {'start': 0.1, 'stop': 3.2, 'endpoint': True} for num, n in product([14, 13, 2], [1, 2, 5, 20, 40]): A = scipy.linalg.inv(np.random.randn(n, n)) v = np.random.randn(n) samples = np.linspace(num=num, **interval) X = expm_multiply(A, v, num=num, **interval) for solution, t in zip(X, samples): assert_allclose(solution, sp_expm(t * A).dot(v)) # test for linear operator with unknown trace -> estimate trace Xguess = estimated(expm_multiply)(aslinearoperator(A), v, num=num, **interval) # test for linear operator with given trace Xgiven = expm_multiply(aslinearoperator(A), v, num=num, **interval, traceA=np.trace(A)) # test robustness for linear operator with wrong trace Xwrong = expm_multiply(aslinearoperator(A), v, num=num, **interval, traceA=np.trace(A) * 5) for sol_guess, sol_given, sol_wrong, t in zip( Xguess, Xgiven, Xwrong, samples): correct = sp_expm(t * A).dot(v) assert_allclose(sol_guess, correct) assert_allclose(sol_given, correct) assert_allclose(sol_wrong, correct)
def test_expm_multiply_interval_matrix(self): np.random.seed(1234) interval = {'start': 0.1, 'stop': 3.2, 'endpoint': True} for num, n, k in product([14, 13, 2], [1, 2, 5, 20, 40], [1, 2]): A = scipy.linalg.inv(np.random.randn(n, n)) B = np.random.randn(n, k) samples = np.linspace(num=num, **interval) X = expm_multiply(A, B, num=num, **interval) for solution, t in zip(X, samples): assert_allclose(solution, sp_expm(t*A).dot(B)) X = estimated(expm_multiply)(aslinearoperator(A), B, num=num, **interval) for solution, t in zip(X, samples): assert_allclose(solution, sp_expm(t*A).dot(B))
def test_sparse_expm_multiply_interval(self): np.random.seed(1234) start = 0.1 stop = 3.2 n = 40 k = 3 endpoint = True for num in (14, 13, 2): A = scipy.sparse.rand(n, n, density=0.05) B = np.random.randn(n, k) v = np.random.randn(n) for target in (B, v): X = expm_multiply(A, target, start=start, stop=stop, num=num, endpoint=endpoint) samples = np.linspace(start=start, stop=stop, num=num, endpoint=endpoint) with suppress_warnings() as sup: sup.filter(SparseEfficiencyWarning, "splu converted its input to CSC format") sup.filter( SparseEfficiencyWarning, "spsolve is more efficient when sparse b is in the CSC matrix format" ) for solution, t in zip(X, samples): assert_allclose(solution, sp_expm(t * A).dot(target))
def _help_test_specific_expm_interval_status(self, target_status): np.random.seed(1234) start = 0.1 stop = 3.2 num = 13 endpoint = True n = 5 k = 2 nrepeats = 10 nsuccesses = 0 for num in [14, 13, 2] * nrepeats: A = np.random.randn(n, n) B = np.random.randn(n, k) status = _expm_multiply_interval(A, B, start=start, stop=stop, num=num, endpoint=endpoint, status_only=True) if status == target_status: X, status = _expm_multiply_interval(A, B, start=start, stop=stop, num=num, endpoint=endpoint, status_only=False) assert_equal(X.shape, (num, n, k)) samples = np.linspace(start=start, stop=stop, num=num, endpoint=endpoint) for solution, t in zip(X, samples): assert_allclose(solution, sp_expm(t*A).dot(B)) nsuccesses += 1 if not nsuccesses: msg = 'failed to find a status-' + str(target_status) + ' interval' raise Exception(msg)
def test_scaled_expm_multiply_single_timepoint(self): np.random.seed(1234) t = 0.1 n = 5 k = 2 A = np.random.randn(n, n) B = np.random.randn(n, k) observed = _expm_multiply_simple(A, B, t=t) expected = sp_expm(t * A).dot(B) assert_allclose(observed, expected)
def test_matrix_vector_multiply(self): np.random.seed(1234) n = 40 nsamples = 10 for i in range(nsamples): A = scipy.linalg.inv(np.random.randn(n, n)) v = np.random.randn(n) observed = expm_multiply(A, v) expected = np.dot(sp_expm(A), v) assert_allclose(observed, expected)
def test_expm_multiply(self): np.random.seed(1234) n = 40 k = 3 nsamples = 10 for i in range(nsamples): A = scipy.linalg.inv(np.random.randn(n, n)) B = np.random.randn(n, k) observed = expm_multiply(A, B) expected = np.dot(sp_expm(A), B) assert_allclose(observed, expected)
def test_scaled_expm_multiply(self): np.random.seed(1234) n = 40 k = 3 nsamples = 10 for i in range(nsamples): for t in (0.2, 1.0, 1.5): with np.errstate(invalid='ignore'): A = scipy.linalg.inv(np.random.randn(n, n)) B = np.random.randn(n, k) observed = _expm_multiply_simple(A, B, t=t) expected = np.dot(sp_expm(t * A), B) assert_allclose(observed, expected)
def test_expm_multiply_dtype(dtype_a, dtype_b, b_is_matrix): """Make sure `expm_multiply` handles all numerical dtypes correctly.""" assert_allclose_ = (partial(assert_allclose, rtol=1e-3, atol=1e-5) if {dtype_a, dtype_b} & IMPRECISE else assert_allclose) rng = np.random.default_rng(1234) # test data n = 7 b_shape = (n, 3) if b_is_matrix else (n, ) if dtype_a in REAL_DTYPES: A = scipy.linalg.inv(rng.random([n, n])).astype(dtype_a) else: A = scipy.linalg.inv( rng.random([n, n]) + 1j*rng.random([n, n]) ).astype(dtype_a) if dtype_b in REAL_DTYPES: B = (2*rng.random(b_shape)).astype(dtype_b) else: B = (rng.random(b_shape) + 1j*rng.random(b_shape)).astype(dtype_b) # single application sol_mat = expm_multiply(A, B) sol_op = estimated(expm_multiply)(aslinearoperator(A), B) direct_sol = np.dot(sp_expm(A), B) assert_allclose_(sol_mat, direct_sol) assert_allclose_(sol_op, direct_sol) sol_op = expm_multiply(aslinearoperator(A), B, traceA=np.trace(A)) assert_allclose_(sol_op, direct_sol) # for time points interval = {'start': 0.1, 'stop': 3.2, 'num': 13, 'endpoint': True} samples = np.linspace(**interval) X_mat = expm_multiply(A, B, **interval) X_op = estimated(expm_multiply)(aslinearoperator(A), B, **interval) for sol_mat, sol_op, t in zip(X_mat, X_op, samples): direct_sol = sp_expm(t*A).dot(B) assert_allclose_(sol_mat, direct_sol) assert_allclose_(sol_op, direct_sol)
def test_expm_multiply_interval_vector(self): np.random.seed(1234) start = 0.1 stop = 3.2 endpoint = True for num in (14, 13, 2): for n in (1, 2, 5, 20, 40): A = scipy.linalg.inv(np.random.randn(n, n)) v = np.random.randn(n) X = expm_multiply(A, v, start=start, stop=stop, num=num, endpoint=endpoint) samples = np.linspace(start=start, stop=stop, num=num, endpoint=endpoint) for solution, t in zip(X, samples): assert_allclose(solution, sp_expm(t*A).dot(v))
def test_scaled_expm_multiply(self): np.random.seed(1234) n = 40 k = 3 nsamples = 10 for i, t in product(range(nsamples), [0.2, 1.0, 1.5]): with np.errstate(invalid='ignore'): A = scipy.linalg.inv(np.random.randn(n, n)) B = np.random.randn(n, k) observed = _expm_multiply_simple(A, B, t=t) expected = np.dot(sp_expm(t * A), B) assert_allclose(observed, expected) observed = estimated(_expm_multiply_simple)( aslinearoperator(A), B, t=t) assert_allclose(observed, expected)
def test_expm_multiply(self): np.random.seed(1234) n = 40 k = 3 nsamples = 10 for i in range(nsamples): A = scipy.linalg.inv(np.random.randn(n, n)) B = np.random.randn(n, k) observed = expm_multiply(A, B) expected = np.dot(sp_expm(A), B) assert_allclose(observed, expected) observed = estimated(expm_multiply)(aslinearoperator(A), B) assert_allclose(observed, expected) traceA = np.trace(A) observed = expm_multiply(aslinearoperator(A), B, traceA=traceA) assert_allclose(observed, expected)
def test_sparse_expm_multiply(self): np.random.seed(1234) n = 40 k = 3 nsamples = 10 for i in range(nsamples): A = scipy.sparse.rand(n, n, density=0.05) B = np.random.randn(n, k) observed = expm_multiply(A, B) with suppress_warnings() as sup: sup.filter(SparseEfficiencyWarning, "splu requires CSC matrix format") sup.filter(SparseEfficiencyWarning, "spsolve is more efficient when sparse b is in the" " CSC matrix format") expected = sp_expm(A).dot(B) assert_allclose(observed, expected)
def time_expm(self, n, format): if format == 'sparse': sp_expm(self.A_sparse) elif format == 'dense': scipy.linalg.expm(self.A_dense)