How to use the pykrige.core._initialize_variogram_model function in PyKrige

def test_core_initialize_variogram_model(validation_ref):

    data, _, _ = validation_ref

    # Note the variogram_function argument is not a string in real life...
    # core._initialize_variogram_model also checks the length of input
    # lists, which is redundant now because the same tests are done in
    # core._make_variogram_parameter_list
    with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1])).T,
            data[:, 2],
            "linear",
            [0.0],
            "linear",
            6,
            False,
            "euclidean",
        )
    with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1])).T,
            data[:, 2],
            "spherical",
            [0.0],
            "spherical",

# now because the same tests are done in
    # core._make_variogram_parameter_list
    with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1], data[:, 2])).T,
            data[:, 3],
            "linear",
            [0.0],
            "linear",
            6,
            False,
            "euclidean",
        )

    with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1], data[:, 2])).T,
            data[:, 3],
            "spherical",
            [0.0],
            "spherical",
            6,
            False,
            "euclidean",
        )

    with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1], data[:, 2])).T,
            data[:, 3],
            "linear",
            [0.0, 0.0],

with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1])).T,
            data[:, 2],
            "spherical",
            [0.0],
            "spherical",
            6,
            False,
            "euclidean",
        )

    # core._initialize_variogram_model does also check coordinate type,
    # this is NOT redundant
    with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1])).T,
            data[:, 2],
            "spherical",
            [0.0, 0.0, 0.0],
            "spherical",
            6,
            False,
            "tacos",
        )

    x = np.array([1.0 + n / np.sqrt(2) for n in range(4)])
    y = np.array([1.0 + n / np.sqrt(2) for n in range(4)])
    z = np.arange(1.0, 5.0, 1.0)
    lags, semivariance, variogram_model_parameters = core._initialize_variogram_model(
        np.vstack((x, y)).T, z, "linear", [0.0, 0.0], "linear", 6, False, "euclidean"
    )

with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1])).T,
            data[:, 2],
            "spherical",
            [0.0, 0.0, 0.0],
            "spherical",
            6,
            False,
            "tacos",
        )

    x = np.array([1.0 + n / np.sqrt(2) for n in range(4)])
    y = np.array([1.0 + n / np.sqrt(2) for n in range(4)])
    z = np.arange(1.0, 5.0, 1.0)
    lags, semivariance, variogram_model_parameters = core._initialize_variogram_model(
        np.vstack((x, y)).T, z, "linear", [0.0, 0.0], "linear", 6, False, "euclidean"
    )

    assert_allclose(lags, np.array([1.0, 2.0, 3.0]))
    assert_allclose(semivariance, np.array([0.5, 2.0, 4.5]))

def test_core_initialize_variogram_model_3d(sample_data_3d):

    data, _, _ = sample_data_3d

    # Note the variogram_function argument is not a string in real life...
    # again, these checks in core._initialize_variogram_model are redundant
    # now because the same tests are done in
    # core._make_variogram_parameter_list
    with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1], data[:, 2])).T,
            data[:, 3],
            "linear",
            [0.0],
            "linear",
            6,
            False,
            "euclidean",
        )

    with pytest.raises(ValueError):
        core._initialize_variogram_model(
            np.vstack((data[:, 0], data[:, 1], data[:, 2])).T,
            data[:, 3],
            "spherical",
            [0.0],

[self.XCENTER, self.YCENTER, self.ZCENTER],
            [self.anisotropy_scaling_y, self.anisotropy_scaling_z],
            [self.anisotropy_angle_x, self.anisotropy_angle_y, self.anisotropy_angle_z],
        ).T

        if self.verbose:
            print("Initializing variogram model...")

        vp_temp = _make_variogram_parameter_list(
            self.variogram_model, variogram_parameters
        )
        (
            self.lags,
            self.semivariance,
            self.variogram_model_parameters,
        ) = _initialize_variogram_model(
            np.vstack((self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED)).T,
            self.VALUES,
            self.variogram_model,
            vp_temp,
            self.variogram_function,
            nlags,
            weight,
            "euclidean",
        )

        if self.verbose:
            if self.variogram_model == "linear":
                print("Using '%s' Variogram Model" % "linear")
                print("Slope:", self.variogram_model_parameters[0])
                print("Nugget:", self.variogram_model_parameters[1], "\n")
            elif self.variogram_model == "power":

[self.XCENTER, self.YCENTER, self.ZCENTER],
            [self.anisotropy_scaling_y, self.anisotropy_scaling_z],
            [self.anisotropy_angle_x, self.anisotropy_angle_y, self.anisotropy_angle_z],
        ).T

        if self.verbose:
            print("Initializing variogram model...")

        vp_temp = _make_variogram_parameter_list(
            self.variogram_model, variogram_parameters
        )
        (
            self.lags,
            self.semivariance,
            self.variogram_model_parameters,
        ) = _initialize_variogram_model(
            np.vstack((self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED)).T,
            self.VALUES,
            self.variogram_model,
            vp_temp,
            self.variogram_function,
            nlags,
            weight,
            "euclidean",
        )

        if self.verbose:
            if self.variogram_model == "linear":
                print("Using '%s' Variogram Model" % "linear")
                print("Slope:", self.variogram_model_parameters[0])
                print("Nugget:", self.variogram_model_parameters[1], "\n")
            elif self.variogram_model == "power":

self.anisotropy_scaling = 1.0
                self.anisotropy_angle = 0.0
                self.X_ADJUSTED = self.X_ORIG
                self.Y_ADJUSTED = self.Y_ORIG
        if self.verbose:
            print("Updating variogram mode...")

        # See note above about the 'use_psill' kwarg...
        vp_temp = _make_variogram_parameter_list(
            self.variogram_model, variogram_parameters
        )
        (
            self.lags,
            self.semivariance,
            self.variogram_model_parameters,
        ) = _initialize_variogram_model(
            np.vstack((self.X_ADJUSTED, self.Y_ADJUSTED)).T,
            self.Z,
            self.variogram_model,
            vp_temp,
            self.variogram_function,
            nlags,
            weight,
            self.coordinates_type,
        )

        if self.verbose:
            print("Coordinates type: '%s'" % self.coordinates_type, "\n")
            if self.variogram_model == "linear":
                print("Using '%s' Variogram Model" % "linear")
                print("Slope:", self.variogram_model_parameters[0])
                print("Nugget:", self.variogram_model_parameters[1], "\n")

self.anisotropy_angle_y,
                    self.anisotropy_angle_z,
                ],
            ).T

        if self.verbose:
            print("Updating variogram mode...")

        vp_temp = _make_variogram_parameter_list(
            self.variogram_model, variogram_parameters
        )
        (
            self.lags,
            self.semivariance,
            self.variogram_model_parameters,
        ) = _initialize_variogram_model(
            np.vstack((self.X_ADJUSTED, self.Y_ADJUSTED, self.Z_ADJUSTED)).T,
            self.VALUES,
            self.variogram_model,
            vp_temp,
            self.variogram_function,
            nlags,
            weight,
            "euclidean",
        )

        if self.verbose:
            if self.variogram_model == "linear":
                print("Using '%s' Variogram Model" % "linear")
                print("Slope:", self.variogram_model_parameters[0])
                print("Nugget:", self.variogram_model_parameters[1], "\n")
            elif self.variogram_model == "power":

[self.anisotropy_scaling],
            [self.anisotropy_angle],
        ).T

        if self.verbose:
            print("Initializing variogram model...")

        # see comment in ok.py about 'use_psill' kwarg...
        vp_temp = _make_variogram_parameter_list(
            self.variogram_model, variogram_parameters
        )
        (
            self.lags,
            self.semivariance,
            self.variogram_model_parameters,
        ) = _initialize_variogram_model(
            np.vstack((self.X_ADJUSTED, self.Y_ADJUSTED)).T,
            self.Z,
            self.variogram_model,
            vp_temp,
            self.variogram_function,
            nlags,
            weight,
            "euclidean",
        )
        # TODO extend geographic capabilities to UK...

        if self.verbose:
            if self.variogram_model == "linear":
                print("Using '%s' Variogram Model" % "linear")
                print("Slope:", self.variogram_model_parameters[0])
                print("Nugget:", self.variogram_model_parameters[1], "\n")