def compare_times(max_n_power=8):
from scitbx.linalg import lapack_dsyev
mt = flex.mersenne_twister(seed=0)
show_tab_header = True
tfmt = "%5.2f"
for n_power in xrange(5,max_n_power+1):
n = 2**n_power
l = mt.random_double(size=n*(n+1)//2) * 2 - 1
a = l.matrix_packed_l_as_symmetric()
aes = a.deep_copy()
ala = [a.deep_copy(), a.deep_copy()]
wla = [flex.double(n, -1e100), flex.double(n, -1e100)]
t0 = time.time()
es = eigensystem.real_symmetric(aes)
tab = [n, tfmt % (time.time() - t0)]
for i,use_fortran in enumerate([False, True]):
t0 = time.time()
info = lapack_dsyev(
jobz="V", uplo="U", a=ala[i], w=wla[i], use_fortran=use_fortran)
if (info == 99):
tab.append(" --- ")
else:
assert info == 0
tab.append(tfmt % (time.time() - t0))
assert approx_equal(list(reversed(es.values())), wla[i])
if (show_tab_header):
print " time [s] eigenvalues"
print " n es fem for min max"
show_tab_header = False
tab.extend([es.values()[-1], es.values()[0]])
print "%3d %s %s %s [%6.2f %6.2f]" % tuple(tab)
def compare_times(max_n_power=8):
from scitbx.linalg import lapack_dsyev
mt = flex.mersenne_twister(seed=0)
show_tab_header = True
tfmt = "%5.2f"
for n_power in xrange(5, max_n_power + 1):
n = 2**n_power
l = mt.random_double(size=n * (n + 1) // 2) * 2 - 1
a = l.matrix_packed_l_as_symmetric()
aes = a.deep_copy()
ala = [a.deep_copy(), a.deep_copy()]
wla = [flex.double(n, -1e100), flex.double(n, -1e100)]
t0 = time.time()
es = eigensystem.real_symmetric(aes)
tab = [n, tfmt % (time.time() - t0)]
for i, use_fortran in enumerate([False, True]):
t0 = time.time()
info = lapack_dsyev(jobz="V",
uplo="U",
a=ala[i],
w=wla[i],
use_fortran=use_fortran)
if (info == 99):
tab.append(" --- ")
else:
assert info == 0
tab.append(tfmt % (time.time() - t0))
assert approx_equal(list(reversed(es.values())), wla[i])
if (show_tab_header):
print " time [s] eigenvalues"
print " n es fem for min max"
show_tab_header = False
tab.extend([es.values()[-1], es.values()[0]])
print "%3d %s %s %s [%6.2f %6.2f]" % tuple(tab)
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])
