mirror of
https://github.com/fjosw/pyerrors.git
synced 2025-03-15 14:50:25 +01:00
340 lines
13 KiB
Python
340 lines
13 KiB
Python
import numpy as np
|
|
import autograd.numpy as anp
|
|
import math
|
|
import pyerrors as pe
|
|
import pytest
|
|
|
|
np.random.seed(0)
|
|
|
|
|
|
def get_real_matrix(dimension):
|
|
base_matrix = np.empty((dimension, dimension), dtype=object)
|
|
for (n, m), entry in np.ndenumerate(base_matrix):
|
|
exponent_real = np.random.normal(0, 1)
|
|
exponent_imag = np.random.normal(0, 1)
|
|
base_matrix[n, m] = pe.Obs([np.random.normal(1.0, 0.1, 100)], ['t'])
|
|
|
|
|
|
return base_matrix
|
|
|
|
def get_complex_matrix(dimension):
|
|
base_matrix = np.empty((dimension, dimension), dtype=object)
|
|
for (n, m), entry in np.ndenumerate(base_matrix):
|
|
exponent_real = np.random.normal(0, 1)
|
|
exponent_imag = np.random.normal(0, 1)
|
|
base_matrix[n, m] = pe.CObs(pe.Obs([np.random.normal(1.0, 0.1, 100)], ['t']),
|
|
pe.Obs([np.random.normal(1.0, 0.1, 100)], ['t']))
|
|
|
|
return base_matrix
|
|
|
|
|
|
def test_matmul():
|
|
for dim in [4, 8]:
|
|
for const in [1, pe.cov_Obs(1.0, 0.002, 'cov')]:
|
|
my_list = []
|
|
length = 1000 + np.random.randint(200)
|
|
for i in range(dim ** 2):
|
|
my_list.append(pe.Obs([np.random.rand(length), np.random.rand(length + 1)], ['t1', 't2']))
|
|
my_array = const * np.array(my_list).reshape((dim, dim))
|
|
tt = pe.linalg.matmul(my_array, my_array) - my_array @ my_array
|
|
for t, e in np.ndenumerate(tt):
|
|
assert e.is_zero(), t
|
|
|
|
my_list = []
|
|
length = 1000 + np.random.randint(200)
|
|
for i in range(dim ** 2):
|
|
my_list.append(pe.CObs(pe.Obs([np.random.rand(length), np.random.rand(length + 1)], ['t1', 't2']),
|
|
pe.Obs([np.random.rand(length), np.random.rand(length + 1)], ['t1', 't2'])))
|
|
my_array = np.array(my_list).reshape((dim, dim)) * const
|
|
tt = pe.linalg.matmul(my_array, my_array) - my_array @ my_array
|
|
for t, e in np.ndenumerate(tt):
|
|
assert e.is_zero(), t
|
|
|
|
|
|
def test_jack_matmul():
|
|
tt = get_real_matrix(8)
|
|
check1 = pe.linalg.jack_matmul(tt, tt) - pe.linalg.matmul(tt, tt)
|
|
[o.gamma_method() for o in check1.ravel()]
|
|
assert np.all([o.is_zero_within_error(0.1) for o in check1.ravel()])
|
|
assert np.all([o.dvalue < 0.001 for o in check1.ravel()])
|
|
trace1 = np.trace(check1)
|
|
trace1.gamma_method()
|
|
assert trace1.dvalue < 0.001
|
|
|
|
tr = np.random.rand(8, 8)
|
|
check2 = pe.linalg.jack_matmul(tt, tr) - pe.linalg.matmul(tt, tr)
|
|
[o.gamma_method() for o in check2.ravel()]
|
|
assert np.all([o.is_zero_within_error(0.1) for o in check2.ravel()])
|
|
assert np.all([o.dvalue < 0.001 for o in check2.ravel()])
|
|
trace2 = np.trace(check2)
|
|
trace2.gamma_method()
|
|
assert trace2.dvalue < 0.001
|
|
|
|
tt2 = get_complex_matrix(8)
|
|
check3 = pe.linalg.jack_matmul(tt2, tt2) - pe.linalg.matmul(tt2, tt2)
|
|
[o.gamma_method() for o in check3.ravel()]
|
|
assert np.all([o.real.is_zero_within_error(0.1) for o in check3.ravel()])
|
|
assert np.all([o.imag.is_zero_within_error(0.1) for o in check3.ravel()])
|
|
assert np.all([o.real.dvalue < 0.001 for o in check3.ravel()])
|
|
assert np.all([o.imag.dvalue < 0.001 for o in check3.ravel()])
|
|
trace3 = np.trace(check3)
|
|
trace3.gamma_method()
|
|
assert trace3.real.dvalue < 0.001
|
|
assert trace3.imag.dvalue < 0.001
|
|
|
|
tr2 = np.random.rand(8, 8) + 1j * np.random.rand(8, 8)
|
|
check4 = pe.linalg.jack_matmul(tt2, tr2) - pe.linalg.matmul(tt2, tr2)
|
|
[o.gamma_method() for o in check4.ravel()]
|
|
assert np.all([o.real.is_zero_within_error(0.1) for o in check4.ravel()])
|
|
assert np.all([o.imag.is_zero_within_error(0.1) for o in check4.ravel()])
|
|
assert np.all([o.real.dvalue < 0.001 for o in check4.ravel()])
|
|
assert np.all([o.imag.dvalue < 0.001 for o in check4.ravel()])
|
|
trace4 = np.trace(check4)
|
|
trace4.gamma_method()
|
|
assert trace4.real.dvalue < 0.001
|
|
assert trace4.imag.dvalue < 0.001
|
|
|
|
|
|
def test_einsum():
|
|
|
|
def _perform_real_check(arr):
|
|
[o.gamma_method() for o in arr]
|
|
assert np.all([o.is_zero_within_error(0.001) for o in arr])
|
|
assert np.all([o.dvalue < 0.001 for o in arr])
|
|
|
|
def _perform_complex_check(arr):
|
|
[o.gamma_method() for o in arr]
|
|
assert np.all([o.real.is_zero_within_error(0.001) for o in arr])
|
|
assert np.all([o.real.dvalue < 0.001 for o in arr])
|
|
assert np.all([o.imag.is_zero_within_error(0.001) for o in arr])
|
|
assert np.all([o.imag.dvalue < 0.001 for o in arr])
|
|
|
|
|
|
tt = [get_real_matrix(4), get_real_matrix(3)]
|
|
q = np.tensordot(tt[0], tt[1], 0)
|
|
c1 = tt[1] @ q
|
|
c2 = pe.linalg.einsum('ij,abjd->abid', tt[1], q)
|
|
check1 = c1 - c2
|
|
_perform_real_check(check1.ravel())
|
|
check2 = np.trace(tt[0]) - pe.linalg.einsum('ii', tt[0])
|
|
_perform_real_check([check2])
|
|
check3 = np.trace(tt[1]) - pe.linalg.einsum('ii', tt[1])
|
|
_perform_real_check([check3])
|
|
|
|
tt = [get_real_matrix(4), np.random.random((3, 3))]
|
|
q = np.tensordot(tt[0], tt[1], 0)
|
|
c1 = tt[1] @ q
|
|
c2 = pe.linalg.einsum('ij,abjd->abid', tt[1], q)
|
|
check1 = c1 - c2
|
|
_perform_real_check(check1.ravel())
|
|
|
|
tt = [get_complex_matrix(4), get_complex_matrix(3)]
|
|
q = np.tensordot(tt[0], tt[1], 0)
|
|
c1 = tt[1] @ q
|
|
c2 = pe.linalg.einsum('ij,abjd->abid', tt[1], q)
|
|
check1 = c1 - c2
|
|
_perform_complex_check(check1.ravel())
|
|
check2 = np.trace(tt[0]) - pe.linalg.einsum('ii', tt[0])
|
|
_perform_complex_check([check2])
|
|
check3 = np.trace(tt[1]) - pe.linalg.einsum('ii', tt[1])
|
|
_perform_complex_check([check3])
|
|
|
|
tt = [get_complex_matrix(4), np.random.random((3, 3))]
|
|
q = np.tensordot(tt[0], tt[1], 0)
|
|
c1 = tt[1] @ q
|
|
c2 = pe.linalg.einsum('ij,abjd->abid', tt[1], q)
|
|
check1 = c1 - c2
|
|
_perform_complex_check(check1.ravel())
|
|
|
|
|
|
def test_multi_dot():
|
|
for dim in [4, 6]:
|
|
my_list = []
|
|
length = 1000 + np.random.randint(200)
|
|
for i in range(dim ** 2):
|
|
my_list.append(pe.Obs([np.random.rand(length), np.random.rand(length + 1)], ['t1', 't2']))
|
|
my_array = pe.cov_Obs(1.0, 0.002, 'cov') * np.array(my_list).reshape((dim, dim))
|
|
tt = pe.linalg.matmul(my_array, my_array, my_array, my_array) - my_array @ my_array @ my_array @ my_array
|
|
for t, e in np.ndenumerate(tt):
|
|
assert e.is_zero(), t
|
|
|
|
my_list = []
|
|
length = 1000 + np.random.randint(200)
|
|
for i in range(dim ** 2):
|
|
my_list.append(pe.CObs(pe.Obs([np.random.rand(length), np.random.rand(length + 1)], ['t1', 't2']),
|
|
pe.Obs([np.random.rand(length), np.random.rand(length + 1)], ['t1', 't2'])))
|
|
my_array = np.array(my_list).reshape((dim, dim)) * pe.cov_Obs(1.0, 0.002, 'cov')
|
|
tt = pe.linalg.matmul(my_array, my_array, my_array, my_array) - my_array @ my_array @ my_array @ my_array
|
|
for t, e in np.ndenumerate(tt):
|
|
assert e.is_zero(), t
|
|
|
|
|
|
def test_jack_multi_dot():
|
|
for dim in [2, 4, 8]:
|
|
my_array = get_real_matrix(dim)
|
|
|
|
tt = pe.linalg.jack_matmul(my_array, my_array, my_array) - pe.linalg.matmul(my_array, my_array, my_array)
|
|
|
|
for t, e in np.ndenumerate(tt):
|
|
e.gamma_method()
|
|
assert e.is_zero_within_error(0.01)
|
|
assert e.is_zero(atol=1e-1), t
|
|
assert np.isclose(e.value, 0.0)
|
|
|
|
|
|
def test_matmul_irregular_histories():
|
|
dim = 2
|
|
length = 500
|
|
|
|
standard_array = []
|
|
for i in range(dim ** 2):
|
|
standard_array.append(pe.Obs([np.random.normal(1.1, 0.2, length)], ['ens1']))
|
|
standard_matrix = np.array(standard_array).reshape((dim, dim)) * pe.pseudo_Obs(0.1, 0.002, 'qr')
|
|
|
|
for idl in [range(1, 501, 2), range(250, 273), [2, 8, 19, 20, 78]]:
|
|
irregular_array = []
|
|
for i in range(dim ** 2):
|
|
irregular_array.append(pe.Obs([np.random.normal(1.1, 0.2, len(idl))], ['ens1'], idl=[idl]))
|
|
irregular_matrix = np.array(irregular_array).reshape((dim, dim))
|
|
|
|
t1 = standard_matrix @ irregular_matrix
|
|
t2 = pe.linalg.matmul(standard_matrix, irregular_matrix)
|
|
|
|
assert np.all([o.is_zero() for o in (t1 - t2).ravel()])
|
|
assert np.all([o.is_merged for o in t1.ravel()])
|
|
assert np.all([o.is_merged for o in t2.ravel()])
|
|
|
|
|
|
def test_irregular_matrix_inverse():
|
|
dim = 3
|
|
length = 500
|
|
|
|
for idl in [range(8, 508, 10), range(250, 273), [2, 8, 19, 20, 78, 99, 828, 10548979]]:
|
|
irregular_array = []
|
|
for i in range(dim ** 2):
|
|
irregular_array.append(pe.Obs([np.random.normal(1.1, 0.2, len(idl)), np.random.normal(0.25, 0.1, 10)], ['ens1', 'ens2'], idl=[idl, range(1, 11)]))
|
|
irregular_matrix = np.array(irregular_array).reshape((dim, dim))
|
|
|
|
invertible_irregular_matrix = np.identity(dim) + irregular_matrix @ irregular_matrix.T
|
|
|
|
inverse = pe.linalg.inv(invertible_irregular_matrix)
|
|
|
|
assert np.allclose(np.linalg.inv(np.vectorize(lambda x: x.value)(invertible_irregular_matrix)) - np.vectorize(lambda x: x.value)(inverse), 0.0)
|
|
|
|
check1 = pe.linalg.matmul(invertible_irregular_matrix, inverse)
|
|
assert np.all([o.is_zero() for o in (check1 - np.identity(dim)).ravel()])
|
|
check2 = invertible_irregular_matrix @ inverse
|
|
assert np.all([o.is_zero() for o in (check2 - np.identity(dim)).ravel()])
|
|
|
|
|
|
def test_matrix_inverse():
|
|
content = []
|
|
for t in range(9):
|
|
exponent = np.random.normal(3, 5)
|
|
content.append(pe.pseudo_Obs(2 + 10 ** exponent, 10 ** (exponent - 1), 't'))
|
|
|
|
content.append(1.0) # Add 1.0 as a float
|
|
matrix = np.diag(content)
|
|
inverse_matrix = pe.linalg.inv(matrix)
|
|
assert all([o.is_zero() for o in np.diag(matrix) * np.diag(inverse_matrix) - 1])
|
|
|
|
|
|
def test_complex_matrix_inverse():
|
|
dimension = 4
|
|
base_matrix = np.empty((dimension, dimension), dtype=object)
|
|
matrix = np.empty((dimension, dimension), dtype=complex)
|
|
for (n, m), entry in np.ndenumerate(base_matrix):
|
|
exponent_real = np.random.normal(2, 3)
|
|
exponent_imag = np.random.normal(2, 3)
|
|
base_matrix[n, m] = pe.CObs(pe.pseudo_Obs(2 + 10 ** exponent_real, 10 ** (exponent_real - 1), 't'),
|
|
pe.pseudo_Obs(2 + 10 ** exponent_imag, 10 ** (exponent_imag - 1), 't'))
|
|
|
|
# Construct invertible matrix
|
|
obs_matrix = np.identity(dimension) + base_matrix @ base_matrix.T
|
|
|
|
for (n, m), entry in np.ndenumerate(obs_matrix):
|
|
matrix[n, m] = entry.real.value + 1j * entry.imag.value
|
|
|
|
inverse_matrix = np.linalg.inv(matrix)
|
|
inverse_obs_matrix = pe.linalg.inv(obs_matrix)
|
|
for (n, m), entry in np.ndenumerate(inverse_matrix):
|
|
assert np.isclose(inverse_matrix[n, m].real, inverse_obs_matrix[n, m].real.value)
|
|
assert np.isclose(inverse_matrix[n, m].imag, inverse_obs_matrix[n, m].imag.value)
|
|
|
|
|
|
def test_matrix_functions():
|
|
dim = 4
|
|
matrix = []
|
|
for i in range(dim):
|
|
row = []
|
|
for j in range(dim):
|
|
row.append(pe.pseudo_Obs(np.random.rand(), 0.2 + 0.1 * np.random.rand(), 'e1'))
|
|
matrix.append(row)
|
|
matrix = np.array(matrix) @ np.identity(dim)
|
|
|
|
# Check inverse of matrix
|
|
inv = pe.linalg.inv(matrix)
|
|
check_inv = matrix @ inv
|
|
|
|
for (i, j), entry in np.ndenumerate(check_inv):
|
|
entry.gamma_method()
|
|
if(i == j):
|
|
assert math.isclose(entry.value, 1.0, abs_tol=1e-9), 'value ' + str(i) + ',' + str(j) + ' ' + str(entry.value)
|
|
else:
|
|
assert math.isclose(entry.value, 0.0, abs_tol=1e-9), 'value ' + str(i) + ',' + str(j) + ' ' + str(entry.value)
|
|
assert math.isclose(entry.dvalue, 0.0, abs_tol=1e-9), 'dvalue ' + str(i) + ',' + str(j) + ' ' + str(entry.dvalue)
|
|
|
|
# Check Cholesky decomposition
|
|
sym = np.dot(matrix, matrix.T)
|
|
cholesky = pe.linalg.cholesky(sym)
|
|
check = cholesky @ cholesky.T
|
|
|
|
for (i, j), entry in np.ndenumerate(check):
|
|
diff = entry - sym[i, j]
|
|
assert diff.is_zero()
|
|
|
|
# Check eigh
|
|
e, v = pe.linalg.eigh(sym)
|
|
for i in range(dim):
|
|
tmp = sym @ v[:, i] - v[:, i] * e[i]
|
|
for j in range(dim):
|
|
assert tmp[j].is_zero()
|
|
|
|
# Check svd
|
|
u, v, vh = pe.linalg.svd(sym)
|
|
diff = sym - u @ np.diag(v) @ vh
|
|
|
|
for (i, j), entry in np.ndenumerate(diff):
|
|
assert entry.is_zero()
|
|
|
|
|
|
def test_complex_matrix_operations():
|
|
dimension = 4
|
|
base_matrix = np.empty((dimension, dimension), dtype=object)
|
|
for (n, m), entry in np.ndenumerate(base_matrix):
|
|
exponent_real = np.random.normal(3, 5)
|
|
exponent_imag = np.random.normal(3, 5)
|
|
base_matrix[n, m] = pe.CObs(pe.pseudo_Obs(2 + 10 ** exponent_real, 10 ** (exponent_real - 1), 't'),
|
|
pe.pseudo_Obs(2 + 10 ** exponent_imag, 10 ** (exponent_imag - 1), 't'))
|
|
|
|
for other in [2, 2.3, (1 - 0.1j), (0 + 2.1j)]:
|
|
ta = base_matrix * other
|
|
tb = other * base_matrix
|
|
diff = ta - tb
|
|
for (i, j), entry in np.ndenumerate(diff):
|
|
assert entry.is_zero()
|
|
ta = base_matrix + other
|
|
tb = other + base_matrix
|
|
diff = ta - tb
|
|
for (i, j), entry in np.ndenumerate(diff):
|
|
assert entry.is_zero()
|
|
ta = base_matrix - other
|
|
tb = other - base_matrix
|
|
diff = ta + tb
|
|
for (i, j), entry in np.ndenumerate(diff):
|
|
assert entry.is_zero()
|
|
ta = base_matrix / other
|
|
tb = other / base_matrix
|
|
diff = ta * tb - 1
|
|
for (i, j), entry in np.ndenumerate(diff):
|
|
assert entry.is_zero()
|