IlluminationModel.compute_photoclinometry_jacobian

giant.ray_tracer.illumination:

abstractmethod IlluminationModel.compute_photoclinometry_jacobian(observations, rotation_to_inertial, max_inc=1.2217304763960306, max_emi=1.2217304763960306, max_phase=2.443460952792061, update=False, update_weight=0.005)[source]

This computes the Jacobian matrix of the change in the illumination values given a change in the surface normal (represented by a change in the surface slope) and a change in the local albedo values.

Mathematically the jacobian is

\[\mathbf{J}=\frac{\partial I}{\partial\left[\begin{array} {ccc} h_x & h_y & \alpha \end{array}\right]} \]

where \(h_x\) is the slope in the x direction, \(h_y\) is the slope in the y direction, and \(\alpha\) is the local albedo.

Parameters:

  • observations (ndarray) – The observations as a numpy array with type ILLUM_DTYPE.

  • rotation_to_inertial (ndarray) – The rotation that takes the frame the observations are expressed in into the the local frame for the surface (usually the local east north up frame)

  • max_inc (float) – the maximum incidence angle to consider valid in radians

  • max_emi (float) – the maximum emission angle to consider valid in radians

  • max_phase (float) – the maximum phase angle to consider valid in radians

  • update (bool) – A flag specifying whether to form an update Jacobian

  • update_weight (float) – The weight of the prior values if doing an update

Returns:

the jacobian matrix as a n(+3)x3 array (where n is the number of observations) and a boolean array of length n specifying which rows of the jacobian matrix are valid

Return type:

Tuple[ndarray, ndarray]