Cov (#130)

import numpy as np

import math

def compute_covariance(lat, lon, rad, latsigma=10., lonsigma=10., radsigma=15., semimajor_axis=1737400.0):

    """

    Given geospatial coordinates, desired accuracy sigmas, and an equitorial radius, compute a 2x3

    sigma covariange matrix.

    Parameters

    ----------

    lat : float

          A point's latitude in degrees

    lon : float

          A point's longitude in degrees

    rad : float

          The radius (z-value) of the point in meters

    latsigma : float

               The desired latitude accuracy in meters (Default 10.0)

    lonsigma : float

               The desired longitude accuracy in meters (Default 10.0)

    radsigma : float

               The desired radius accuracy in meters (Defualt: 15.0)

    semimajor_axis : float

                     The semi-major or equitorial radius in meters (Default: 1737400.0 - Moon)

    Returns

    -------

    rectcov : ndarray

              (2,3) covariance matrix

    """

    lat = math.radians(lat)

    lon = math.radians(lon)

    # SetSphericalSigmasDistance

    scaled_lat_sigma = latsigma / semimajor_axis

    # This is specific to each lon.

    scaled_lon_sigma = lonsigma * math.cos(lat) / semimajor_axis

    # SetSphericalSigmas

    cov = np.eye(3,3)

    cov[0,0] = scaled_lat_sigma ** 2

    cov[1,1] = scaled_lon_sigma ** 2

    cov[2,2] = radsigma ** 2

    # Approximate the Jacobian

    j = np.zeros((3,3))

    cosphi = math.cos(lat)

    sinphi = math.sin(lat)

    coslambda = math.cos(lon)

    sinlambda = math.sin(lon)

    rcosphi = rad * cosphi

    rsinphi = rad * sinphi

    j[0,0] = -rsinphi * coslambda

    j[0,1] = -rcosphi * sinlambda

    j[0,2] = cosphi * coslambda

    j[1,0] = -rsinphi * sinlambda

    j[1,1] = rcosphi * coslambda

    j[1,2] = cosphi * sinlambda

    j[2,0] = rcosphi

    j[2,1] = 0.

    j[2,2] = sinphi

    mat = j.dot(cov)

    mat = mat.dot(j.T)

    rectcov = np.zeros((2,3))

    rectcov[0,0] = mat[0,0]

    rectcov[0,1] = mat[0,1]

    rectcov[0,2] = mat[0,2]

    rectcov[1,0] = mat[1,1]

    rectcov[1,1] = mat[1,2]

    rectcov[1,2] = mat[2,2]

    return rectcov

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import numpy as np

import pytest

from plio.utils import covariance

def test_compute_covariance():

    # This test is using values from an ISIS control network

    lat = 86.235596

    lon = 140.006195

    rad = 1736777.625 

    sigmalat = 15.0

    sigmalon = 15.0

    sigmarad = 25.0

    semimajor_rad = 1737400.0

    cov = covariance.compute_covariance(lat, lon, rad, sigmalat, sigmalon, sigmarad, semimajor_rad)

    expected =  np.array([[132.97888775695, -111.55453178747, -20.08405416233],

                          [93.588991760138, 16.848822261184, 623.27512692323]])

    np.testing.assert_almost_equal(cov, expected)

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