Example #1
0
def test_get_destination_data():
    m = flopy.modflow.Modflow.load('EXAMPLE.nam', model_ws=path)

    mg1 = m.modelgrid
    mg1.set_coord_info(xoff=mg1._xul_to_xll(0.0, 30.0),
                       yoff=mg1._yul_to_yll(0.0, 30.0),
                       angrot=30.0)

    mg = StructuredGrid(delc=m.dis.delc.array, delr=m.dis.delr.array)
    mg.set_coord_info(xoff=mg._xul_to_xll(1000.0, 30.0),
                      yoff=mg._yul_to_yll(1000.0, 30.0),
                      angrot=30.0)

    # test deprecation
    sr2 = SpatialReference(xll=mg.xoffset, yll=mg.yoffset, rotation=-30)
    if shapefile:
        m.dis.export(path + '/dis.shp')

    pthld = PathlineFile(os.path.join(path, 'EXAMPLE-3.pathline'))
    epd = EndpointFile(os.path.join(path, 'EXAMPLE-3.endpoint'))

    well_epd = epd.get_destination_endpoint_data(dest_cells=[(4, 12, 12)])
    well_pthld = pthld.get_destination_pathline_data(dest_cells=[(4, 12, 12)],
                                                     to_recarray=True)

    # same particle IDs should be in both endpoint data and pathline data
    tval = len(set(well_epd.particleid).difference(set(well_pthld.particleid)))
    msg = 'same particle IDs should be in both endpoint data and pathline data'
    assert tval == 0, msg

    # check that all starting locations are included in the pathline data
    # (pathline data slice not just endpoints)
    starting_locs = ra_slice(well_epd, ['k0', 'i0', 'j0'])
    pathline_locs = np.array(np.array(well_pthld)[['k', 'i', 'j']].tolist(),
                             dtype=starting_locs.dtype)
    assert np.all(np.in1d(starting_locs, pathline_locs))

    if shapefile is None:
        return  # skip remainder

    # test writing a shapefile of endpoints
    epd.write_shapefile(well_epd,
                        direction='starting',
                        shpname=os.path.join(path, 'starting_locs.shp'),
                        mg=m.modelgrid)

    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=True,
                          direction='starting',
                          mg=m.modelgrid,
                          shpname=fpth)
    fpth = os.path.join(path, 'pathlines_1per_end.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=True,
                          direction='ending',
                          mg=m.modelgrid,
                          shpname=fpth)
    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per2.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=True,
                          direction='starting',
                          mg=mg,
                          shpname=fpth)
    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per2_ll.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=True,
                          direction='starting',
                          mg=sr2,
                          shpname=fpth)
    fpth = os.path.join(path, 'pathlines.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=False,
                          mg=m.modelgrid,
                          shpname=fpth)

    # test that endpoints were rotated and written correctly
    from flopy.export.shapefile_utils import shp2recarray
    ra = shp2recarray(os.path.join(path, 'starting_locs.shp'))
    p3 = ra.geometry[ra.particleid == 4][0]
    xorig, yorig = m.modelgrid.get_coords(well_epd.x0[0], well_epd.y0[0])
    assert p3.x - xorig + p3.y - yorig < 1e-4
    xorig, yorig = mg1.xcellcenters[3, 4], mg1.ycellcenters[3, 4]
    assert np.abs(p3.x - xorig + p3.y -
                  yorig) < 1e-4  # this also checks for 1-based

    # test that particle attribute information is consistent with pathline file
    ra = shp2recarray(os.path.join(path, 'pathlines.shp'))
    inds = (ra.particleid == 8) & (ra.i == 12) & (ra.j == 12)
    assert ra.time[inds][0] - 20181.7 < .1
    assert ra.xloc[inds][0] - 0.933 < .01

    # test that k, i, j are correct for single geometry pathlines, forwards
    # and backwards
    ra = shp2recarray(os.path.join(path, 'pathlines_1per.shp'))
    assert ra.i[0] == 4, ra.j[0] == 5
    ra = shp2recarray(os.path.join(path, 'pathlines_1per_end.shp'))
    assert ra.i[0] == 13, ra.j[0] == 13

    # test use of arbitrary spatial reference and offset
    mg1.set_coord_info(xoff=mg.xoffset,
                       yoff=mg.yoffset,
                       angrot=mg.angrot,
                       epsg=mg.epsg,
                       proj4=mg.proj4)
    ra = shp2recarray(os.path.join(path, 'pathlines_1per2.shp'))
    p3_2 = ra.geometry[ra.particleid == 4][0]
    test1 = mg1.xcellcenters[3, 4]
    test2 = mg1.ycellcenters[3, 4]
    assert np.abs(p3_2.x[0] - mg1.xcellcenters[3, 4] + p3_2.y[0] -
                  mg1.ycellcenters[3, 4]) < 1e-4

    # arbitrary spatial reference with ll specified instead of ul
    ra = shp2recarray(os.path.join(path, 'pathlines_1per2_ll.shp'))
    p3_2 = ra.geometry[ra.particleid == 4][0]
    #sr3 = SpatialReference(xll=sr.xll, yll=sr.yll, rotation=-30,
    #                       delc=list(m.dis.delc))
    mg.set_coord_info(xoff=mg.xoffset, yoff=mg.yoffset, angrot=-30.0)
    assert np.abs(p3_2.x[0] - mg.xcellcenters[3, 4] + p3_2.y[0] -
                  mg.ycellcenters[3, 4]) < 1e-4

    xul = 3628793
    yul = 21940389

    m = flopy.modflow.Modflow.load('EXAMPLE.nam', model_ws=path)

    mg4 = m.modelgrid
    mg4.set_coord_info(xoff=mg4._xul_to_xll(xul, 0.0),
                       yoff=mg4._yul_to_yll(yul, 0.0),
                       angrot=0.0,
                       epsg=mg4.epsg,
                       proj4=mg4.proj4)

    fpth = os.path.join(path, 'dis2.shp')
    m.dis.export(fpth)
    pthobj = flopy.utils.PathlineFile(os.path.join(path, 'EXAMPLE-3.pathline'))
    fpth = os.path.join(path, 'pathlines_1per3.shp')
    pthobj.write_shapefile(shpname=fpth, direction='ending', mg=mg4)
Example #2
0
def test_get_destination_data():
    m = flopy.modflow.Modflow.load('EXAMPLE.nam', model_ws=path)

    m.sr = SpatialReference(delr=m.dis.delr, delc=m.dis.delc, xul=0, yul=0,
                            rotation=30)
    sr = SpatialReference(delr=list(m.dis.delr), delc=list(m.dis.delc),
                          xul=1000, yul=1000, rotation=30)
    sr2 = SpatialReference(xll=sr.xll, yll=sr.yll, rotation=-30)
    m.dis.export(path + '/dis.shp')

    pthld = PathlineFile(os.path.join(path, 'EXAMPLE-3.pathline'))
    epd = EndpointFile(os.path.join(path, 'EXAMPLE-3.endpoint'))

    well_epd = epd.get_destination_endpoint_data(dest_cells=[(4, 12, 12)])
    well_pthld = pthld.get_destination_pathline_data(dest_cells=[(4, 12, 12)])

    # same particle IDs should be in both endpoing data and pathline data
    assert len(
        set(well_epd.particleid).difference(set(well_pthld.particleid))) == 0

    # check that all starting locations are included in the pathline data
    # (pathline data slice not just endpoints)
    starting_locs = ra_slice(well_epd, ['k0', 'i0', 'j0'])
    pathline_locs = np.array(well_pthld[['k', 'i', 'j']].tolist(),
                             dtype=starting_locs.dtype)
    assert np.all(np.in1d(starting_locs, pathline_locs))

    # test writing a shapefile of endpoints
    epd.write_shapefile(well_epd, direction='starting',
                        shpname=os.path.join(path, 'starting_locs.shp'),
                        sr=m.sr)

    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=True,
                          direction='starting', sr=m.sr,
                          shpname=fpth)
    fpth = os.path.join(path, 'pathlines_1per_end.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=True,
                          direction='ending', sr=m.sr,
                          shpname=fpth)
    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per2.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=True,
                          direction='starting', sr=sr,
                          shpname=fpth)
    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per2_ll.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=True,
                          direction='starting', sr=sr2,
                          shpname=fpth)
    fpth = os.path.join(path, 'pathlines.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=False,
                          sr=m.sr,
                          shpname=fpth)

    # test that endpoints were rotated and written correctly
    from flopy.export.shapefile_utils import shp2recarray
    ra = shp2recarray(os.path.join(path, 'starting_locs.shp'))
    p3 = ra.geometry[ra.particleid == 4][0]
    xorig, yorig = m.sr.transform(well_epd.x0[0], well_epd.y0[0])
    assert p3.x - xorig + p3.y - yorig < 1e-4
    xorig, yorig = m.sr.xcentergrid[3, 4], m.sr.ycentergrid[3, 4]
    assert np.abs(
        p3.x - xorig + p3.y - yorig) < 1e-4  # this also checks for 1-based

    # test that particle attribute information is consistent with pathline file
    ra = shp2recarray(os.path.join(path, 'pathlines.shp'))
    inds = (ra.particleid == 8) & (ra.i == 12) & (ra.j == 12)
    assert ra.time[inds][0] - 20181.7 < .1
    assert ra.xloc[inds][0] - 0.933 < .01

    # test that k, i, j are correct for single geometry pathlines, forwards and backwards
    ra = shp2recarray(os.path.join(path, 'pathlines_1per.shp'))
    assert ra.i[0] == 4, ra.j[0] == 5
    ra = shp2recarray(os.path.join(path, 'pathlines_1per_end.shp'))
    assert ra.i[0] == 13, ra.j[0] == 13

    # test use of arbitrary spatial reference and offset
    ra = shp2recarray(os.path.join(path, 'pathlines_1per2.shp'))
    p3_2 = ra.geometry[ra.particleid == 4][0]
    assert np.abs(
        p3_2.x[0] - sr.xcentergrid[3, 4] + p3_2.y[0] - sr.ycentergrid[
            3, 4]) < 1e-4

    # arbitrary spatial reference with ll specified instead of ul
    ra = shp2recarray(os.path.join(path, 'pathlines_1per2_ll.shp'))
    p3_2 = ra.geometry[ra.particleid == 4][0]
    sr3 = SpatialReference(xll=sr.xll, yll=sr.yll, rotation=-30,
                           delr=list(m.dis.delr), delc=list(m.dis.delc))
    assert np.abs(
        p3_2.x[0] - sr3.xcentergrid[3, 4] + p3_2.y[0] - sr3.ycentergrid[
            3, 4]) < 1e-4

    xul = 3628793
    yul = 21940389

    m = flopy.modflow.Modflow.load('EXAMPLE.nam', model_ws=path)

    m.sr = flopy.utils.reference.SpatialReference(delr=m.dis.delr,
                                                  delc=m.dis.delc, lenuni=1,
                                                  xul=xul, yul=yul,
                                                  rotation=0.0)
    fpth = os.path.join(path, 'dis2.shp')
    m.dis.export(fpth)
    pthobj = flopy.utils.PathlineFile(os.path.join(path, 'EXAMPLE-3.pathline'))
    fpth = os.path.join(path, 'pathlines_1per3.shp')
    pthobj.write_shapefile(shpname=fpth,
                           direction='ending',
                           sr=m.sr)
Example #3
0
def test_get_destination_data():
    m = flopy.modflow.Modflow.load('EXAMPLE.nam', model_ws=path)

    m.sr = SpatialReference(delr=m.dis.delr,
                            delc=m.dis.delc,
                            xul=0,
                            yul=0,
                            rotation=30)
    sr = SpatialReference(delr=list(m.dis.delr),
                          delc=list(m.dis.delc),
                          xul=1000,
                          yul=1000,
                          rotation=30)
    sr2 = SpatialReference(xll=sr.xll, yll=sr.yll, rotation=-30)
    m.dis.export(path + '/dis.shp')

    pthld = PathlineFile(os.path.join(path, 'EXAMPLE-3.pathline'))
    epd = EndpointFile(os.path.join(path, 'EXAMPLE-3.endpoint'))

    well_epd = epd.get_destination_endpoint_data(dest_cells=[(4, 12, 12)])
    well_pthld = pthld.get_destination_pathline_data(dest_cells=[(4, 12, 12)],
                                                     to_recarray=True)

    # same particle IDs should be in both endpoint data and pathline data
    tval = len(set(well_epd.particleid).difference(set(well_pthld.particleid)))
    msg = 'same particle IDs should be in both endpoint data and pathline data'
    assert tval == 0, msg

    # check that all starting locations are included in the pathline data
    # (pathline data slice not just endpoints)
    starting_locs = ra_slice(well_epd, ['k0', 'i0', 'j0'])
    pathline_locs = np.array(np.array(well_pthld)[['k', 'i', 'j']].tolist(),
                             dtype=starting_locs.dtype)
    assert np.all(np.in1d(starting_locs, pathline_locs))

    # test writing a shapefile of endpoints
    epd.write_shapefile(well_epd,
                        direction='starting',
                        shpname=os.path.join(path, 'starting_locs.shp'),
                        sr=m.sr)

    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=True,
                          direction='starting',
                          sr=m.sr,
                          shpname=fpth)
    fpth = os.path.join(path, 'pathlines_1per_end.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=True,
                          direction='ending',
                          sr=m.sr,
                          shpname=fpth)
    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per2.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=True,
                          direction='starting',
                          sr=sr,
                          shpname=fpth)
    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per2_ll.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=True,
                          direction='starting',
                          sr=sr2,
                          shpname=fpth)
    fpth = os.path.join(path, 'pathlines.shp')
    pthld.write_shapefile(well_pthld,
                          one_per_particle=False,
                          sr=m.sr,
                          shpname=fpth)

    # test that endpoints were rotated and written correctly
    from flopy.export.shapefile_utils import shp2recarray
    ra = shp2recarray(os.path.join(path, 'starting_locs.shp'))
    p3 = ra.geometry[ra.particleid == 4][0]
    xorig, yorig = m.sr.transform(well_epd.x0[0], well_epd.y0[0])
    assert p3.x - xorig + p3.y - yorig < 1e-4
    xorig, yorig = m.sr.xcentergrid[3, 4], m.sr.ycentergrid[3, 4]
    assert np.abs(p3.x - xorig + p3.y -
                  yorig) < 1e-4  # this also checks for 1-based

    # test that particle attribute information is consistent with pathline file
    ra = shp2recarray(os.path.join(path, 'pathlines.shp'))
    inds = (ra.particleid == 8) & (ra.i == 12) & (ra.j == 12)
    assert ra.time[inds][0] - 20181.7 < .1
    assert ra.xloc[inds][0] - 0.933 < .01

    # test that k, i, j are correct for single geometry pathlines, forwards
    # and backwards
    ra = shp2recarray(os.path.join(path, 'pathlines_1per.shp'))
    assert ra.i[0] == 4, ra.j[0] == 5
    ra = shp2recarray(os.path.join(path, 'pathlines_1per_end.shp'))
    assert ra.i[0] == 13, ra.j[0] == 13

    # test use of arbitrary spatial reference and offset
    ra = shp2recarray(os.path.join(path, 'pathlines_1per2.shp'))
    p3_2 = ra.geometry[ra.particleid == 4][0]
    assert np.abs(p3_2.x[0] - sr.xcentergrid[3, 4] + p3_2.y[0] -
                  sr.ycentergrid[3, 4]) < 1e-4

    # arbitrary spatial reference with ll specified instead of ul
    ra = shp2recarray(os.path.join(path, 'pathlines_1per2_ll.shp'))
    p3_2 = ra.geometry[ra.particleid == 4][0]
    sr3 = SpatialReference(xll=sr.xll,
                           yll=sr.yll,
                           rotation=-30,
                           delr=list(m.dis.delr),
                           delc=list(m.dis.delc))
    assert np.abs(p3_2.x[0] - sr3.xcentergrid[3, 4] + p3_2.y[0] -
                  sr3.ycentergrid[3, 4]) < 1e-4

    xul = 3628793
    yul = 21940389

    m = flopy.modflow.Modflow.load('EXAMPLE.nam', model_ws=path)

    m.sr = flopy.utils.reference.SpatialReference(delr=m.dis.delr,
                                                  delc=m.dis.delc,
                                                  lenuni=1,
                                                  xul=xul,
                                                  yul=yul,
                                                  rotation=0.0)
    fpth = os.path.join(path, 'dis2.shp')
    m.dis.export(fpth)
    pthobj = flopy.utils.PathlineFile(os.path.join(path, 'EXAMPLE-3.pathline'))
    fpth = os.path.join(path, 'pathlines_1per3.shp')
    pthobj.write_shapefile(shpname=fpth, direction='ending', sr=m.sr)
Example #4
0
def test_get_destination_data():
    m = flopy.modflow.Modflow.load('EXAMPLE.nam', model_ws=path)

    mg1 = m.modelgrid
    mg1.set_coord_info(xoff=mg1._xul_to_xll(0.0, 30.0),
                       yoff=mg1._yul_to_yll(0.0, 30.0),
                       angrot=30.0)

    mg = StructuredGrid(delc=m.dis.delc.array,
                        delr=m.dis.delr.array)
    mg.set_coord_info(xoff=mg._xul_to_xll(1000.0, 30.0),
                      yoff=mg._yul_to_yll(1000.0, 30.0),
                      angrot=30.0)

    # test deprecation
    sr2 = SpatialReference(xll=mg.xoffset, yll=mg.yoffset, rotation=-30)
    m.dis.export(path + '/dis.shp')

    pthld = PathlineFile(os.path.join(path, 'EXAMPLE-3.pathline'))
    epd = EndpointFile(os.path.join(path, 'EXAMPLE-3.endpoint'))

    well_epd = epd.get_destination_endpoint_data(dest_cells=[(4, 12, 12)])
    well_pthld = pthld.get_destination_pathline_data(dest_cells=[(4, 12, 12)],
                                                     to_recarray=True)

    # same particle IDs should be in both endpoint data and pathline data
    tval = len(set(well_epd.particleid).difference(set(well_pthld.particleid)))
    msg = 'same particle IDs should be in both endpoint data and pathline data'
    assert tval == 0, msg

    # check that all starting locations are included in the pathline data
    # (pathline data slice not just endpoints)
    starting_locs = ra_slice(well_epd, ['k0', 'i0', 'j0'])
    pathline_locs = np.array(np.array(well_pthld)[['k', 'i', 'j']].tolist(),
                             dtype=starting_locs.dtype)
    assert np.all(np.in1d(starting_locs, pathline_locs))

    # test writing a shapefile of endpoints
    epd.write_shapefile(well_epd, direction='starting',
                        shpname=os.path.join(path, 'starting_locs.shp'),
                        mg=m.modelgrid)

    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=True,
                          direction='starting', mg=m.modelgrid,
                          shpname=fpth)
    fpth = os.path.join(path, 'pathlines_1per_end.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=True,
                          direction='ending', mg=m.modelgrid,
                          shpname=fpth)
    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per2.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=True,
                          direction='starting', mg=mg,
                          shpname=fpth)
    # test writing shapefile of pathlines
    fpth = os.path.join(path, 'pathlines_1per2_ll.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=True,
                          direction='starting', mg=sr2,
                          shpname=fpth)
    fpth = os.path.join(path, 'pathlines.shp')
    pthld.write_shapefile(well_pthld, one_per_particle=False,
                          mg=m.modelgrid,
                          shpname=fpth)

    # test that endpoints were rotated and written correctly
    from flopy.export.shapefile_utils import shp2recarray
    ra = shp2recarray(os.path.join(path, 'starting_locs.shp'))
    p3 = ra.geometry[ra.particleid == 4][0]
    xorig, yorig = m.modelgrid.get_coords(well_epd.x0[0], well_epd.y0[0])
    assert p3.x - xorig + p3.y - yorig < 1e-4
    xorig, yorig = mg1.xcellcenters[3, 4], mg1.ycellcenters[3, 4]
    assert np.abs(
        p3.x - xorig + p3.y - yorig) < 1e-4  # this also checks for 1-based

    # test that particle attribute information is consistent with pathline file
    ra = shp2recarray(os.path.join(path, 'pathlines.shp'))
    inds = (ra.particleid == 8) & (ra.i == 12) & (ra.j == 12)
    assert ra.time[inds][0] - 20181.7 < .1
    assert ra.xloc[inds][0] - 0.933 < .01

    # test that k, i, j are correct for single geometry pathlines, forwards
    # and backwards
    ra = shp2recarray(os.path.join(path, 'pathlines_1per.shp'))
    assert ra.i[0] == 4, ra.j[0] == 5
    ra = shp2recarray(os.path.join(path, 'pathlines_1per_end.shp'))
    assert ra.i[0] == 13, ra.j[0] == 13

    # test use of arbitrary spatial reference and offset
    mg1.set_coord_info(xoff=mg.xoffset, yoff=mg.yoffset, angrot=mg.angrot,
                       epsg=mg.epsg, proj4=mg.proj4)
    ra = shp2recarray(os.path.join(path, 'pathlines_1per2.shp'))
    p3_2 = ra.geometry[ra.particleid == 4][0]
    test1 = mg1.xcellcenters[3, 4]
    test2 = mg1.ycellcenters[3, 4]
    assert np.abs(
        p3_2.x[0] - mg1.xcellcenters[3, 4] + p3_2.y[0] - mg1.ycellcenters[
            3, 4]) < 1e-4

    # arbitrary spatial reference with ll specified instead of ul
    ra = shp2recarray(os.path.join(path, 'pathlines_1per2_ll.shp'))
    p3_2 = ra.geometry[ra.particleid == 4][0]
    #sr3 = SpatialReference(xll=sr.xll, yll=sr.yll, rotation=-30,
    #                       delc=list(m.dis.delc))
    mg.set_coord_info(xoff=mg.xoffset, yoff=mg.yoffset, angrot=-30.0)
    assert np.abs(
        p3_2.x[0] - mg.xcellcenters[3, 4] + p3_2.y[0] - mg.ycellcenters[
            3, 4]) < 1e-4

    xul = 3628793
    yul = 21940389

    m = flopy.modflow.Modflow.load('EXAMPLE.nam', model_ws=path)

    mg4 = m.modelgrid
    mg4.set_coord_info(xoff=mg4._xul_to_xll(xul, 0.0),
                       yoff=mg4._yul_to_yll(yul, 0.0),
                       angrot=0.0, epsg=mg4.epsg, proj4=mg4.proj4)

    fpth = os.path.join(path, 'dis2.shp')
    m.dis.export(fpth)
    pthobj = flopy.utils.PathlineFile(os.path.join(path, 'EXAMPLE-3.pathline'))
    fpth = os.path.join(path, 'pathlines_1per3.shp')
    pthobj.write_shapefile(shpname=fpth,
                           direction='ending',
                           mg=mg4)