def exercise_eigensystem():
s = eigensystem.real_symmetric(
m=flex.double(flex.grid(0,0)),
relative_epsilon=1e-6,
absolute_epsilon=1e-6)
s.values().all() == (0,)
assert s.vectors().all() == (0,0)
u = s.generalized_inverse_as_packed_u()
assert u.all() == (0,)
m = u.matrix_packed_u_as_symmetric()
assert m.all() == (0,0)
#
for n in xrange(1,10):
m = flex.double(flex.grid(n,n))
s = eigensystem.real_symmetric(m)
assert approx_equal(tuple(s.values()), [0]*n)
v = s.vectors()
for i in xrange(n):
for j in xrange(n):
x = 0
if (i == j): x = 1
assert approx_equal(v[(i,j)], x)
v = []
for i in xrange(n):
j = (i*13+17) % n
v.append(j)
m[i*(n+1)] = j
s = eigensystem.real_symmetric(m)
if (n == 3):
ss = eigensystem.real_symmetric((m[0],m[4],m[8],m[1],m[2],m[5]))
assert approx_equal(s.values(), ss.values())
assert approx_equal(s.vectors(), ss.vectors())
v.sort()
v.reverse()
assert approx_equal(s.values(), v)
if (n > 1):
assert approx_equal(flex.min(s.vectors()), 0)
assert approx_equal(flex.max(s.vectors()), 1)
assert approx_equal(flex.sum(s.vectors()), n)
for t in xrange(10):
for i in xrange(n):
for j in xrange(i,n):
m[i*n+j] = random.random() - 0.5
if (i != j):
m[j*n+i] = m[i*n+j]
s = eigensystem.real_symmetric(m)
if (n == 3):
ss = eigensystem.real_symmetric((m[0],m[4],m[8],m[1],m[2],m[5]))
assert approx_equal(s.values(), ss.values())
assert approx_equal(s.vectors(), ss.vectors())
v = list(s.values())
v.sort()
v.reverse()
assert list(s.values()) == v
for i in xrange(n):
l = s.values()[i]
x = s.vectors()[i*n:i*n+n]
mx = matrix_mul(m, n, n, x, n, 1)
lx = [e*l for e in x]
assert approx_equal(mx, lx)
#
m = (1.4573362052597449, 1.7361052947659894, 2.8065584999742659,
-0.5387293498219814, -0.018204949672480729, 0.44956507395617257)
n_repetitions = 10000
t0 = time.time()
v = time_eigensystem_real_symmetric(m, n_repetitions)
assert v == (0,0,0)
print "time_eigensystem_real_symmetric: %.3f micro seconds" % (
(time.time() - t0)/n_repetitions*1.e6)
from scitbx.linalg import time_lapack_dsyev
for use_fortran in [False, True]:
if (not use_fortran):
if (not scitbx.linalg.fem_is_available()): continue
impl_id = "fem"
else:
if (not scitbx.linalg.for_is_available()): continue
impl_id = "for"
v = time_lapack_dsyev(m, 2, use_fortran)
# to trigger one-time initialization of SAVE variables
t0 = time.time()
v = time_lapack_dsyev(m, n_repetitions, use_fortran)
assert v == (0,0,0)
print "time_lapack_dsyev %s: %.3f micro seconds" % (
impl_id, (time.time() - t0)/n_repetitions*1.e6)
#
s = eigensystem.real_symmetric(m=m)
assert s.min_abs_pivot() > 0
assert s.min_abs_pivot() < 1.e-10
assert approx_equal(s.generalized_inverse_as_packed_u(), [
0.77839538602575065, 0.25063185439711611, -0.03509803174624003,
0.68162798233326816, -0.10755998636596431, 0.37330996497431423])
s = eigensystem.real_symmetric(m=m, absolute_epsilon=10)
assert s.min_abs_pivot() == 10
assert approx_equal(s.vectors(), [0, 0, 1, 0, 1, 0, 1, 0, 0])
assert approx_equal(s.values(),
[2.8065584999742659, 1.7361052947659894, 1.4573362052597449])
s = eigensystem.real_symmetric(m=m, relative_epsilon=0)
assert s.min_abs_pivot() == 0
assert approx_equal(s.values(), [3,2,1])
def exercise_eigensystem():
s = eigensystem.real_symmetric(m=flex.double(flex.grid(0, 0)),
relative_epsilon=1e-6,
absolute_epsilon=1e-6)
s.values().all() == (0, )
assert s.vectors().all() == (0, 0)
u = s.generalized_inverse_as_packed_u()
assert u.all() == (0, )
m = u.matrix_packed_u_as_symmetric()
assert m.all() == (0, 0)
#
for n in xrange(1, 10):
m = flex.double(flex.grid(n, n))
s = eigensystem.real_symmetric(m)
assert approx_equal(tuple(s.values()), [0] * n)
v = s.vectors()
for i in xrange(n):
for j in xrange(n):
x = 0
if (i == j): x = 1
assert approx_equal(v[(i, j)], x)
v = []
for i in xrange(n):
j = (i * 13 + 17) % n
v.append(j)
m[i * (n + 1)] = j
s = eigensystem.real_symmetric(m)
if (n == 3):
ss = eigensystem.real_symmetric(
(m[0], m[4], m[8], m[1], m[2], m[5]))
assert approx_equal(s.values(), ss.values())
assert approx_equal(s.vectors(), ss.vectors())
v.sort()
v.reverse()
assert approx_equal(s.values(), v)
if (n > 1):
assert approx_equal(flex.min(s.vectors()), 0)
assert approx_equal(flex.max(s.vectors()), 1)
assert approx_equal(flex.sum(s.vectors()), n)
for t in xrange(10):
for i in xrange(n):
for j in xrange(i, n):
m[i * n + j] = random.random() - 0.5
if (i != j):
m[j * n + i] = m[i * n + j]
s = eigensystem.real_symmetric(m)
if (n == 3):
ss = eigensystem.real_symmetric(
(m[0], m[4], m[8], m[1], m[2], m[5]))
assert approx_equal(s.values(), ss.values())
assert approx_equal(s.vectors(), ss.vectors())
v = list(s.values())
v.sort()
v.reverse()
assert list(s.values()) == v
for i in xrange(n):
l = s.values()[i]
x = s.vectors()[i * n:i * n + n]
mx = matrix_mul(m, n, n, x, n, 1)
lx = [e * l for e in x]
assert approx_equal(mx, lx)
#
m = (1.4573362052597449, 1.7361052947659894, 2.8065584999742659,
-0.5387293498219814, -0.018204949672480729, 0.44956507395617257)
n_repetitions = 10000
t0 = time.time()
v = time_eigensystem_real_symmetric(m, n_repetitions)
assert v == (0, 0, 0)
print "time_eigensystem_real_symmetric: %.3f micro seconds" % (
(time.time() - t0) / n_repetitions * 1.e6)
from scitbx.linalg import time_lapack_dsyev
for use_fortran in [False, True]:
if (not use_fortran):
if (not scitbx.linalg.fem_is_available()): continue
impl_id = "fem"
else:
if (not scitbx.linalg.for_is_available()): continue
impl_id = "for"
v = time_lapack_dsyev(m, 2, use_fortran)
# to trigger one-time initialization of SAVE variables
t0 = time.time()
v = time_lapack_dsyev(m, n_repetitions, use_fortran)
assert v == (0, 0, 0)
print "time_lapack_dsyev %s: %.3f micro seconds" % (
impl_id, (time.time() - t0) / n_repetitions * 1.e6)
#
s = eigensystem.real_symmetric(m=m)
assert s.min_abs_pivot() > 0
assert s.min_abs_pivot() < 1.e-10
assert approx_equal(s.generalized_inverse_as_packed_u(), [
0.77839538602575065, 0.25063185439711611, -0.03509803174624003,
0.68162798233326816, -0.10755998636596431, 0.37330996497431423
])
s = eigensystem.real_symmetric(m=m, absolute_epsilon=10)
assert s.min_abs_pivot() == 10
assert approx_equal(s.vectors(), [0, 0, 1, 0, 1, 0, 1, 0, 0])
assert approx_equal(
s.values(),
[2.8065584999742659, 1.7361052947659894, 1.4573362052597449])
s = eigensystem.real_symmetric(m=m, relative_epsilon=0)
assert s.min_abs_pivot() == 0
assert approx_equal(s.values(), [3, 2, 1])
def exercise(use_fortran):
from scitbx.linalg import lapack_dsyev
from scitbx.array_family import flex
from scitbx.math.tests.tst_math import matrix_mul
from libtbx.test_utils import approx_equal
import random
random.seed(0)
#
for diag in [0, 1]:
for n in range(1, 11):
for uplo in ["U", "L"]:
a = flex.double(flex.grid(n, n), 0)
for i in range(n):
a[(i, i)] = diag
w = flex.double(n, -1e100)
a_inp = a.deep_copy()
info = lapack_dsyev(jobz="V",
uplo=uplo,
a=a,
w=w,
use_fortran=use_fortran)
if (info == 99):
if (not use_fortran):
print("Skipping tests: lapack_dsyev not available.")
return
assert info == 0
assert approx_equal(w, [diag] * n)
if (diag != 0):
assert approx_equal(a, a_inp)
#
for i_trial in range(10):
for n in range(1, 11):
for uplo in ["U", "L"]:
a = flex.double(flex.grid(n, n))
for i in range(n):
for j in range(i, n):
a[i * n + j] = random.random() - 0.5
if (i != j):
a[j * n + i] = a[i * n + j]
w = flex.double(n, -1e100)
a_inp = a.deep_copy()
info = lapack_dsyev(jobz="V",
uplo=uplo,
a=a,
w=w,
use_fortran=use_fortran)
assert info == 0
for i in range(1, n):
assert w[i - 1] <= w[i]
for i in range(n):
l = w[i]
x = a[i * n:i * n + n]
ax = matrix_mul(a_inp, n, n, x, n, 1)
lx = [e * l for e in x]
assert approx_equal(ax, lx)
#
a = flex.double([0.47, 0.10, -0.21, 0.10, 0.01, -0.03, -0.21, -0.03, 0.35])
a.reshape(flex.grid(3, 3))
w = flex.double(3, -1e100)
info = lapack_dsyev(jobz="V", uplo=uplo, a=a, w=w, use_fortran=use_fortran)
assert info == 0
assert approx_equal(w, [-0.0114574, 0.1978572, 0.6436002])
assert approx_equal(a, [
-0.2236115, 0.9734398, -0.0491212, -0.5621211, -0.1699700, -0.8094010,
-0.7962523, -0.1533793, 0.5851983
])
def exercise(use_fortran):
from scitbx.linalg import lapack_dsyev
from scitbx.array_family import flex
from scitbx.math.tests.tst_math import matrix_mul
from libtbx.test_utils import approx_equal
import random
random.seed(0)
#
for diag in [0, 1]:
for n in xrange(1, 11):
for uplo in ["U", "L"]:
a = flex.double(flex.grid(n,n), 0)
for i in xrange(n):
a[(i,i)] = diag
w = flex.double(n, -1e100)
a_inp = a.deep_copy()
info = lapack_dsyev(
jobz="V", uplo=uplo, a=a, w=w, use_fortran=use_fortran)
if (info == 99):
if (not use_fortran):
print "Skipping tests: lapack_dsyev not available."
return
assert info == 0
assert approx_equal(w, [diag]*n)
if (diag != 0):
assert approx_equal(a, a_inp)
#
for i_trial in xrange(10):
for n in xrange(1, 11):
for uplo in ["U", "L"]:
a = flex.double(flex.grid(n,n))
for i in xrange(n):
for j in xrange(i,n):
a[i*n+j] = random.random() - 0.5
if (i != j):
a[j*n+i] = a[i*n+j]
w = flex.double(n, -1e100)
a_inp = a.deep_copy()
info = lapack_dsyev(
jobz="V", uplo=uplo, a=a, w=w, use_fortran=use_fortran)
assert info == 0
for i in xrange(1,n):
assert w[i-1] <= w[i]
for i in xrange(n):
l = w[i]
x = a[i*n:i*n+n]
ax = matrix_mul(a_inp, n, n, x, n, 1)
lx = [e*l for e in x]
assert approx_equal(ax, lx)
#
a = flex.double([
0.47, 0.10, -0.21,
0.10, 0.01, -0.03,
-0.21, -0.03, 0.35])
a.reshape(flex.grid(3,3))
w = flex.double(3, -1e100)
info = lapack_dsyev(jobz="V", uplo=uplo, a=a, w=w, use_fortran=use_fortran)
assert info == 0
assert approx_equal(w, [-0.0114574, 0.1978572, 0.6436002])
assert approx_equal(a, [
-0.2236115, 0.9734398, -0.0491212,
-0.5621211, -0.1699700, -0.8094010,
-0.7962523, -0.1533793, 0.5851983])
