def test_closed_form():
"gravmag.normal_gravity.gamma_closed_form compatible with somigliana"
lat = numpy.linspace(-90, 90, 200)
som = gamma_somigliana(lat, ellipsoid=WGS84)
closed = gamma_closed_form(lat, 0, ellipsoid=WGS84)
for i in xrange(len(lat)):
assert_almost_equal(closed[i], som[i], decimal=3,
err_msg='lat = {}'.format(lat[i]))
gradient = (gamma_closed_form(lat, 1, ellipsoid=WGS84)
- gamma_closed_form(lat, 0, ellipsoid=WGS84))
mean = numpy.mean(gradient)
assert_almost_equal(mean, -0.3086, decimal=4, err_msg='mean vs free-air')
gamma_a = gamma_closed_form(0, 0, ellipsoid=WGS84)
assert_almost_equal(gamma_a, utils.si2mgal(WGS84.gamma_a), decimal=5,
err_msg='equator vs gamma_a')
gamma_b = gamma_closed_form(90, 0, ellipsoid=WGS84)
assert_almost_equal(gamma_b, utils.si2mgal(WGS84.gamma_b), decimal=5,
err_msg='north pole vs gamma_b')
gamma_b = gamma_closed_form(-90, 0, ellipsoid=WGS84)
assert_almost_equal(gamma_b, utils.si2mgal(WGS84.gamma_b), decimal=5,
err_msg='south pole vs gamma_b')
def test_closed_form():
"gravmag.normal_gravity.gamma_closed_form compatible with somigliana"
lat = numpy.linspace(-90, 90, 200)
som = gamma_somigliana(lat, ellipsoid=WGS84)
closed = gamma_closed_form(lat, 0, ellipsoid=WGS84)
for i in xrange(len(lat)):
assert_almost_equal(closed[i],
som[i],
decimal=3,
err_msg='lat = {}'.format(lat[i]))
gradient = (gamma_closed_form(lat, 1, ellipsoid=WGS84) -
gamma_closed_form(lat, 0, ellipsoid=WGS84))
mean = numpy.mean(gradient)
assert_almost_equal(mean, -0.3086, decimal=4, err_msg='mean vs free-air')
gamma_a = gamma_closed_form(0, 0, ellipsoid=WGS84)
assert_almost_equal(gamma_a,
utils.si2mgal(WGS84.gamma_a),
decimal=5,
err_msg='equator vs gamma_a')
gamma_b = gamma_closed_form(90, 0, ellipsoid=WGS84)
assert_almost_equal(gamma_b,
utils.si2mgal(WGS84.gamma_b),
decimal=5,
err_msg='north pole vs gamma_b')
gamma_b = gamma_closed_form(-90, 0, ellipsoid=WGS84)
assert_almost_equal(gamma_b,
utils.si2mgal(WGS84.gamma_b),
decimal=5,
err_msg='south pole vs gamma_b')
def test_somigliana():
"gravmag.normal_gravity.gamma_somigliana computes consistent results"
res = gamma_somigliana(0, ellipsoid=WGS84)
assert res == utils.si2mgal(WGS84.gamma_a), \
"somigliana at equator != from gamma_a: {:.20f}".format(res)
res = gamma_somigliana(90, ellipsoid=WGS84)
assert res == utils.si2mgal(WGS84.gamma_b), \
"somigliana at north pole != from gamma_b: {:.20f}".format(res)
res = gamma_somigliana(-90, ellipsoid=WGS84)
assert res == utils.si2mgal(WGS84.gamma_b), \
"somigliana at south pole != from gamma_b: {:.20f}".format(res)
def test_somigliana():
"gravmag.normal_gravity.gamma_somigliana computes consistent results"
res = gamma_somigliana(0, ellipsoid=WGS84)
assert res == utils.si2mgal(WGS84.gamma_a), \
"somigliana at equator != from gamma_a: {:.20f}".format(res)
res = gamma_somigliana(90, ellipsoid=WGS84)
assert res == utils.si2mgal(WGS84.gamma_b), \
"somigliana at north pole != from gamma_b: {:.20f}".format(res)
res = gamma_somigliana(-90, ellipsoid=WGS84)
assert res == utils.si2mgal(WGS84.gamma_b), \
"somigliana at south pole != from gamma_b: {:.20f}".format(res)
def jacobian(self, p):
"""
Calculate the Jacobian matrix.
Will ignore the value of *p*.
The Jacobian will have 2*Pi*G*rho in the diagonal
if using Newton's method or Levemberg-Marquardt
and 1/(2*2*Pi*G*rho) if using Steepest Descent.
"""
method = getattr(self, 'fit_method', None)
step = utils.si2mgal(2*np.pi*constants.G*self.mesh.props['density'])
if method is not None and method == 'steepest':
step = 1/(2*step)
# Use a sparse matrix for the Jacobian in Compressed Sparse Row (CSR)
# format. See
# http://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csr_matrix.html
jac = scipy.sparse.diags([np.abs(step)], [0]).tocsr()
return jac
