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flow_conversion

This module deals with the conversion of flow velocity vectors from cartesian to geographic vector. Taken from Andrew Walker's package pyflowng (private repository).

get_rotmat_to_geographical(lon, lat)

Return the rotation matrix at a longitude/latitude to convert the cartesian flow vector into geographical coordinates.

Parameters:

Name Type Description Default
lon float

longitude

 required
lat float

latitude

 required

Returns:

Type Description
2D numpy array

transformation matrix
Source code in terratools/flow_conversion.py 
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def get_rotmat_to_geographical(lon, lat):
    """
    Return the rotation matrix at a longitude/latitude
    to convert the cartesian flow vector into
    geographical coordinates.

    :param lon: longitude
    :type lon: float
    :param lat: latitude
    :type lat: float
    :return trans: transformation matrix
    :rtype trans: 2D numpy array
    """

    # check longitude and latitude are integers or floats

    if isinstance(lat, np.ndarray):
        if lon.dtype.kind != "f" and lon.dtype.kind == "i":
            raise AssertionError("longitude needs to be integer or float")
    elif np.isscalar(lon):
        if not isinstance(lon, (int, float, np.floating, np.integer)):
            raise AssertionError("longitude needs to be integer or float")
    else:
        raise AssertionError("longitude type not acceptable")

    if isinstance(lat, np.ndarray):
        if lat.dtype.kind != "f" and lat.dtype.kind == "i":
            raise AssertionError("latitude needs to be integer or float")
    elif np.isscalar(lat):
        if not isinstance(lat, (int, float, np.floating, np.integer)):
            raise AssertionError("latitude needs to be integer or float")
    else:
        raise AssertionError("latitude type not acceptable")

    # Unit vectors on global system
    x_hat = np.array([1.0, 0.0, 0.0])
    y_hat = np.array([0.0, 1.0, 0.0])
    z_hat = np.array([0.0, 0.0, 1.0])

    # Find unit vector pointing to location in cart space
    (x0, y0, z0) = gt.geog2cart(lon, lat, 1.0)

    u_hat = np.array([x0, y0, z0])
    u_hat = u_hat / np.sqrt(np.sum(np.power(u_hat, 2.0)))

    # Local West and East unit vector(s)
    e_hat = np.cross(z_hat, u_hat)
    e_hat = e_hat / np.sqrt(np.sum(np.power(e_hat, 2.0)))
    w_hat = np.cross(u_hat, z_hat)
    w_hat = w_hat / np.sqrt(np.sum(np.power(w_hat, 2.0)))

    # Local North unit vector
    n_hat = np.cross(u_hat, e_hat)
    # No need to normalise, p and e are already orthoganol.

    # http://www.kwon3d.com/theory/transform/transform.html

    trans = np.array(
        [
            [np.dot(x_hat, e_hat), np.dot(y_hat, e_hat), np.dot(z_hat, e_hat)],
            [np.dot(x_hat, n_hat), np.dot(y_hat, n_hat), np.dot(z_hat, n_hat)],
            [np.dot(x_hat, u_hat), np.dot(y_hat, u_hat), np.dot(z_hat, u_hat)],
        ]
    )

    return trans

rotate_vector(vec, lon, lat)

Convert the cartesian flow vector into geographical vector.

Parameters:

Name Type Description Default
vec 1D numpy array of floats

cartesian flow vector in [vx,vy,vz]

 required
lon float

longitude

 required
lat float

latitude

 required

Returns:

Type Description
1D numpy array of floats

geographical flow vector in [east, north, up] ('up' is radial +ve outwards)
Source code in terratools/flow_conversion.py 
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def rotate_vector(vec, lon, lat):
    """
    Convert the cartesian flow vector into
    geographical vector.

    :param vec: cartesian flow vector in [vx,vy,vz]
    :type vec: 1D numpy array of floats
    :param lon: longitude
    :type lon: float
    :param lat: latitude
    :type lat: float
    :return vec: geographical flow vector in [east, north, up] ('up' is radial +ve outwards)
    :rtype vec: 1D numpy array of floats
    """

    # convert to array if vec is a list
    vec = np.array(vec)

    if isinstance(vec, np.ndarray):
        if vec.dtype.kind != "f" and vec.dtype.kind != "i":
            raise AssertionError("flow vector needs to hold integers or floats.")
    else:
        raise AssertionError("flow vector needs to be a numpy array.")

    # get transformation matrix
    trans = get_rotmat_to_geographical(lon, lat)
    # apply transform to cartesian vector
    vec = np.matmul(vec, np.transpose(trans))
    return vec