def test_transform_data4(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
if not hasattr(nm, 'einsum'):
self.report('no numpy.einsum(), skipping!')
return ok
expected = nm.zeros((6, 6), dtype=nm.float64)
expected[0, 0] = expected[1, 1] = 1.0
phi = nm.deg2rad(30.)
dr, v1, v2, om1, om2 = get_ortho_d(phi, phi + nm.deg2rad(90.))
# Rotate coordinate system by phi.
mtx = tn.make_axis_rotation_matrix([0., 0., 1.], phi)
do = tn.transform_data(dr[None, ...], mtx=mtx[None, ...])
_ok = nm.allclose(do, expected, rtol=0.0, atol=1e-14)
self.report('sym. 4th-th order tensor rotation: %s' % _ok)
ok = ok and _ok
dt, vt1, vt2, omt1, omt2 = get_ortho_d(0, nm.deg2rad(90.))
expected1 = nm.zeros((3, 3), dtype=nm.float64)
expected1[0, 0] = 1.0
expected2 = nm.zeros((3, 3), dtype=nm.float64)
expected2[1, 1] = 1.0
omr1 = nm.einsum('pq,ip,jq->ij', om1, mtx, mtx)
omr2 = nm.einsum('pq,ip,jq->ij', om2, mtx, mtx)
ii = tn.get_sym_indices(3)
jj = tn.get_full_indices(3)
o1 = om1.flat[ii]
o2 = om2.flat[ii]
omr12 = tn.transform_data(o1[None,...], mtx=mtx[None, ...])[0, jj]
omr22 = tn.transform_data(o2[None,...], mtx=mtx[None, ...])[0, jj]
_ok1 = nm.allclose(omr1, expected1, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr12, expected1, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 1: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
_ok1 = nm.allclose(omr2, expected2, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr22, expected2, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 2: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
return ok
def test_transform_data4(self):
import numpy as nm
import sfepy.mechanics.tensors as tn
ok = True
if not hasattr(nm, 'einsum'):
self.report('no numpy.einsum(), skipping!')
return ok
expected = nm.zeros((6, 6), dtype=nm.float64)
expected[0, 0] = expected[1, 1] = 1.0
phi = nm.deg2rad(30.)
dr, v1, v2, om1, om2 = get_ortho_d(phi, phi + nm.deg2rad(90.))
# Rotate coordinate system by phi.
mtx = tn.make_axis_rotation_matrix([0., 0., 1.], phi)
do = tn.transform_data(dr[None, ...], mtx=mtx[None, ...])
_ok = nm.allclose(do, expected, rtol=0.0, atol=1e-14)
self.report('sym. 4th-th order tensor rotation: %s' % _ok)
ok = ok and _ok
dt, vt1, vt2, omt1, omt2 = get_ortho_d(0, nm.deg2rad(90.))
expected1 = nm.zeros((3, 3), dtype=nm.float64)
expected1[0, 0] = 1.0
expected2 = nm.zeros((3, 3), dtype=nm.float64)
expected2[1, 1] = 1.0
omr1 = nm.einsum('pq,ip,jq->ij', om1, mtx, mtx)
omr2 = nm.einsum('pq,ip,jq->ij', om2, mtx, mtx)
ii = tn.get_sym_indices(3)
jj = tn.get_full_indices(3)
o1 = om1.flat[ii]
o2 = om2.flat[ii]
omr12 = tn.transform_data(o1[None,...], mtx=mtx[None, ...])[0, jj]
omr22 = tn.transform_data(o2[None,...], mtx=mtx[None, ...])[0, jj]
_ok1 = nm.allclose(omr1, expected1, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr12, expected1, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 1: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
_ok1 = nm.allclose(omr2, expected2, rtol=0.0, atol=1e-14)
_ok2 = nm.allclose(omr22, expected2, rtol=0.0, atol=1e-14)
self.report('einsum-transform_data compatibility 2: %s %s'
% (_ok1, _ok2))
ok = ok and _ok1 and _ok2
return ok
def get_ortho_d(phi1, phi2):
import numpy as nm
import sfepy.mechanics.tensors as tn
v1 = nm.array([nm.cos(phi1), nm.sin(phi1), 0])
v2 = nm.array([nm.cos(phi2), nm.sin(phi2), 0])
om1 = nm.outer(v1, v1)
om2 = nm.outer(v2, v2)
ii = tn.get_sym_indices(3)
o1 = om1.flat[ii]
o2 = om2.flat[ii]
dr = nm.outer(o1, o1) + nm.outer(o2, o2)
return dr, v1, v2, om1, om2
def get_ortho_d(phi1, phi2):
import numpy as nm
import sfepy.mechanics.tensors as tn
v1 = nm.array([nm.cos(phi1), nm.sin(phi1), 0])
v2 = nm.array([nm.cos(phi2), nm.sin(phi2), 0])
om1 = nm.outer(v1, v1)
om2 = nm.outer(v2, v2)
ii = tn.get_sym_indices(3)
o1 = om1.flat[ii]
o2 = om2.flat[ii]
dr = nm.outer(o1, o1) + nm.outer(o2, o2)
return dr, v1, v2, om1, om2