def delta_icsd_forward_solution_matrix(depths, diameter, sigma_above):
""" Docstring found below """
num_depths, h, z, r_sq, it = utils.get_forward_solution_variables(depths, diameter, sigma_above)
result = numpy.matrix(numpy.empty((num_depths, num_depths), dtype=numpy.float64))
for i, j in itertools.product(range(num_depths), range(num_depths)):
result[j, i] = (h / 2.0) * (
(numpy.sqrt((z[j] - z[i]) ** 2 + r_sq) - abs(z[j] - z[i]))
+ it * (numpy.sqrt((z[j] + z[i]) ** 2 + r_sq) - abs(z[j] + z[i]))
)
return result
def step_icsd_forward_solution_matrix(depths, diameter, sigma_above):
''' Docstring found below '''
num_depths, h, z, r_sq, it = utils.get_forward_solution_variables(
depths, diameter, sigma_above)
result = numpy.matrix(numpy.empty((num_depths, num_depths),
dtype=numpy.float64))
for i, j in itertools.product(range(num_depths), range(num_depths)):
ub = z[i] + (h/2.0)
lb = z[i] - (h/2.0)
this_result = (1/4.0)*(
source_term_one(z[j], r_sq, z=ub) -
source_term_one(z[j], r_sq, z=lb) -
source_term_two(z[j], ub=ub, lb=lb) +
image_term(it=it, j=z[j], r_sq=r_sq, z=ub) -
image_term(it=it, j=z[j], r_sq=r_sq, z=lb))
result[j,i] = this_result
return result