swarmpal.toolboxes.dsecs.aux_tools ================================== .. py:module:: swarmpal.toolboxes.dsecs.aux_tools Attributes ---------- .. autoapisummary:: swarmpal.toolboxes.dsecs.aux_tools.logger Functions --------- .. autoapisummary:: swarmpal.toolboxes.dsecs.aux_tools.sph2sph swarmpal.toolboxes.dsecs.aux_tools.sub_FindLongestNonZero swarmpal.toolboxes.dsecs.aux_tools.sub_inversion swarmpal.toolboxes.dsecs.aux_tools.sub_LonInterp swarmpal.toolboxes.dsecs.aux_tools.sub_Swarm_grids_1D swarmpal.toolboxes.dsecs.aux_tools.sub_Swarm_grids swarmpal.toolboxes.dsecs.aux_tools.get_eq swarmpal.toolboxes.dsecs.aux_tools._normalizev swarmpal.toolboxes.dsecs.aux_tools.sub_points_along_fieldline Module Contents --------------- .. py:data:: logger .. py:function:: sph2sph(latP, lonP, latOld, lonOld, VtOld, VpOld) Change coordinates and (horizontal part of) vectors from one spherical coordinate system to another. :param latP: Latitude and longitude of the new pole in the old coordinates, [deg] :type latP: float :param lonP: Latitude and longitude of the new pole in the old coordinates, [deg] :type lonP: float :param latOld: Latitudes and longitudes of the data points to be transformed in the old coordinate system, [deg] :type latOld: array :param lonOld: Latitudes and longitudes of the data points to be transformed in the old coordinate system, [deg] :type lonOld: array :param VtOld: Theta- and phi-components of a vector field at locations (latOld,lonOld). If you want to transform only coordinates make these empty arrays (np.array([])). :type VtOld: array :param VpOld: Theta- and phi-components of a vector field at locations (latOld,lonOld). If you want to transform only coordinates make these empty arrays (np.array([])). :type VpOld: array :returns: * **latNew, lonNew** (*array*) -- Coordinates of the points (latOld,lonOld) in the new system, [deg], same size as input parameters. Note that the old pole has longitude 0 and longitude is between 0 and 360. * **VtNew, VpNew** (*array*) -- Theta- and phi-components of the vector field in the new system. If no input vector field was given, these are empty vectors []. .. py:function:: sub_FindLongestNonZero(x) Find the longest sequence of consecutive non-zero elements in an array. Return the sequence and indices as y=x[ind]. :param x: Input array :type x: array :returns: * **y** (*array*) -- Longest sequence of consecutive non-zero elements * **ind** (*array*) -- Indices of the sequence .. py:function:: sub_inversion(secsMat, regMat, epsSVD, alpha, magVec) Solve matrix equation sysMat*resultVec = dataVec, using truncated singular value decomposition. :param secsMat: Matrix giving the magnetic field from SECS amplitudes :type secsMat: ndarray :param regMat: Regularization matrix for the SECS amplitudes :type regMat: ndarray :param epsSVD: Pre-defined truncation parameter so that all singular values smaller than epsSVD*(largest singular value) will be ignored :type epsSVD: float :param alpha: Parameter scaling the amount of regularization :type alpha: float :param magVec: Magnetic measurements to be fitted :type magVec: array :returns: **result_Vec** -- Vector of SECS amplitudes :rtype: array .. py:function:: sub_LonInterp(lat, lon, intLat, method, ekstra=np.nan) Robust interpolation of longitude by interpolating the sine and cosine of the angle. This way a 360 degree jump does not matter. :param lat: Original coordinates, [degree]. :type lat: ndarray :param lon: Original coordinates, [degree]. :type lon: ndarray :param intLat: Latitudes where original longitudes are interpolated to, [degree]. :type intLat: ndarray :param method: Interpolation method. Same as for scipy.interpolate.interp1d. :type method: str :returns: **intLon** -- Interpolated longitudes at latitudes intLat, [degree]. -180 <= intlon <= 180. :rtype: ndarray .. py:function:: sub_Swarm_grids_1D(lat1, lat2, Dlat1D, ExtLat1D) Creates 1D grid around the two Swarm satellite paths. :param lat1: Geographic latitudes of the satellites' paths, [degree]. :type lat1: ndarray :param lat2: Geographic latitudes of the satellites' paths, [degree]. :type lat2: ndarray :param Dlat1D: 1D grid spacing in latitudinal direction, [degree]. :type Dlat1D: int or float :param ExtLat1D: Number of points to extend the 1D grid outside the data area in latitudinal direction. :type ExtLat1D: int :returns: * **lat1D** (*ndarray*) -- Geographic latitudes of the 1D grid, [degree]. * **mat1Dsecond** (*ndarray*) -- Second gradient matrix. .. py:function:: sub_Swarm_grids(lat1, lon1, lat2, lon2, Dlat2D, LonRatio, ExtLat2D, ExtLon2D) Creates 2D grids around the two Swarm satellite paths. :param lat1: Geographic latitudes of the satellites' paths, [degree]. :type lat1: ndarray :param lat2: Geographic latitudes of the satellites' paths, [degree]. :type lat2: ndarray :param lon1: Geographic longitudes of the satellites' paths, [degree]. :type lon1: ndarray :param lon2: Geographic longitudes of the satellites' paths, [degree]. :type lon2: ndarray :param Dlat2D: 2D grid spacing in latitudinal direction, [degree]. :type Dlat2D: float :param LonRatio: Ratio between the satellite separation and longitudinal spacing of the 2D grid. :type LonRatio: float :param ExtLat2D: Number of points to extend the 2D grid outside the data area in latitudinal and longitudinal directions. :type ExtLat2D: int :param ExtLon2D: Number of points to extend the 2D grid outside the data area in latitudinal and longitudinal directions. :type ExtLon2D: int :returns: * **lat2D, lon2D** (*ndarray*) -- Geographic latitudes and longitudes of the 2D grid, [degree]. * **angle2D** (*ndarray*) -- Half-angle of such a spherical cap that has the same area as the 2D grid cell, [radian]. * **mat2DsecondLat** (*ndarray*) -- Second gradient matrix in latitude. .. py:function:: get_eq(ds, lat_filter_max=60, ovals=None) Splits data into a list of pieces suitable for DSECS analysis based on latitude. :param ds: Input dataset. :type ds: xarray :param lat_filter_max: Maximum geographic latitude (absolute value). All data above this limit is ignored. Default: 60 :type lat_filter_max: int, optional :param ovals: list of pre-calculated numpy slices with which to split the data. :type ovals: list :returns: **out** -- List of data segments split for DSECS analysis if they have been precalculated. :rtype: list of xarray, or None, None by default .. py:function:: _normalizev(v) Creates an unit vector. :param v: Input array. :type v: ndarray :returns: Normalized unit vector. :rtype: ndarray .. py:function:: sub_points_along_fieldline(thetaSECS, Rsecs, L, minD) Calculate points to be used in the Biot-Savart integral along field line in function SECS_2D_CurlFree_AntiSym_magnetic_lineintegral :param thetaSECS: Co-latitude of the CF SECS, [radian] :type thetaSECS: float :param Rsecs: Radius of the sphere where CF SECS is located, [km] :type Rsecs: float :param L: L-value of the field line starting from the CF SECS pole, [km NOTE: this is in kilometers, so really L*Rsecs; :type L: float :param minD: minimum horizontal distance between the CF SECS pole and footpoints of the points where magnetic field is needed, [km], SCALAR :type minD: float :returns: co-latitudes of the integration points (= end points of the current elements), [radian] :rtype: array