From 94b6c2988a32da57246b2adc4b264bec27573fb3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 26 Jul 2024 23:11:40 +0200
Subject: [PATCH 01/28] plot: handle len_scale of 0

---
 src/gstools/covmodel/plot.py | 75 ++++++++++++++++++++++++++++--------
 1 file changed, 60 insertions(+), 15 deletions(-)

diff --git a/src/gstools/covmodel/plot.py b/src/gstools/covmodel/plot.py
index 32148c14..f7fa58db 100644
--- a/src/gstools/covmodel/plot.py
+++ b/src/gstools/covmodel/plot.py
@@ -68,7 +68,10 @@ def plot_vario_spatial(
 ):  # pragma: no cover
     """Plot spatial variogram of a given CovModel."""
     if x_max is None:
-        x_max = 3 * model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 * model.len_scale
     x_s = np.linspace(-x_max, x_max) + x_min
     pos = [x_s] * model.dim
     shp = tuple(len(p) for p in pos)
@@ -83,7 +86,10 @@ def plot_cov_spatial(
 ):  # pragma: no cover
     """Plot spatial covariance of a given CovModel."""
     if x_max is None:
-        x_max = 3 * model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 * model.len_scale
     x_s = np.linspace(-x_max, x_max) + x_min
     pos = [x_s] * model.dim
     shp = tuple(len(p) for p in pos)
@@ -98,7 +104,10 @@ def plot_cor_spatial(
 ):  # pragma: no cover
     """Plot spatial correlation of a given CovModel."""
     if x_max is None:
-        x_max = 3 * model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 * model.len_scale
     x_s = np.linspace(-x_max, x_max) + x_min
     pos = [x_s] * model.dim
     shp = tuple(len(p) for p in pos)
@@ -114,7 +123,10 @@ def plot_variogram(
     """Plot variogram of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = 3 * model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 * model.len_scale
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} variogram")
     ax.plot(x_s, model.variogram(x_s), **kwargs)
@@ -129,7 +141,10 @@ def plot_covariance(
     """Plot covariance of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = 3 * model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 * model.len_scale
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} covariance")
     ax.plot(x_s, model.covariance(x_s), **kwargs)
@@ -144,7 +159,10 @@ def plot_correlation(
     """Plot correlation function of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = 3 * model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 * model.len_scale
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} correlation")
     ax.plot(x_s, model.correlation(x_s), **kwargs)
@@ -159,7 +177,10 @@ def plot_vario_yadrenko(
     """Plot Yadrenko variogram of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = min(3 * model.len_scale, model.geo_scale * np.pi)
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = min(3 * model.len_scale, model.geo_scale * np.pi)
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} Yadrenko variogram")
     ax.plot(x_s, model.vario_yadrenko(x_s), **kwargs)
@@ -174,7 +195,10 @@ def plot_cov_yadrenko(
     """Plot Yadrenko covariance of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = min(3 * model.len_scale, model.geo_scale * np.pi)
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = min(3 * model.len_scale, model.geo_scale * np.pi)
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} Yadrenko covariance")
     ax.plot(x_s, model.cov_yadrenko(x_s), **kwargs)
@@ -189,7 +213,10 @@ def plot_cor_yadrenko(
     """Plot Yadrenko correlation function of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = min(3 * model.len_scale, model.geo_scale * np.pi)
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = min(3 * model.len_scale, model.geo_scale * np.pi)
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} Yadrenko correlation")
     ax.plot(x_s, model.cor_yadrenko(x_s), **kwargs)
@@ -204,7 +231,10 @@ def plot_vario_axis(
     """Plot variogram of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = 3 * model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 * model.len_scale
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} variogram on axis {axis}")
     ax.plot(x_s, model.vario_axis(x_s, axis), **kwargs)
@@ -219,7 +249,10 @@ def plot_cov_axis(
     """Plot variogram of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = 3 * model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 * model.len_scale
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} covariance on axis {axis}")
     ax.plot(x_s, model.cov_axis(x_s, axis), **kwargs)
@@ -234,7 +267,10 @@ def plot_cor_axis(
     """Plot variogram of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = 3 * model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 * model.len_scale
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} correlation on axis {axis}")
     ax.plot(x_s, model.cor_axis(x_s, axis), **kwargs)
@@ -249,7 +285,10 @@ def plot_spectrum(
     """Plot spectrum of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = 3 / model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 / model.len_scale
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} {model.dim}D spectrum")
     ax.plot(x_s, model.spectrum(x_s), **kwargs)
@@ -264,7 +303,10 @@ def plot_spectral_density(
     """Plot spectral density of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = 3 / model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 / model.len_scale
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} {model.dim}D spectral-density")
     ax.plot(x_s, model.spectral_density(x_s), **kwargs)
@@ -279,7 +321,10 @@ def plot_spectral_rad_pdf(
     """Plot radial spectral pdf of a given CovModel."""
     fig, ax = get_fig_ax(fig, ax)
     if x_max is None:
-        x_max = 3 / model.len_scale
+        if np.isclose(model.len_scale, 0):
+            x_max = 1.0
+        else:
+            x_max = 3 / model.len_scale
     x_s = np.linspace(x_min, x_max)
     kwargs.setdefault("label", f"{model.name} {model.dim}D spectral-rad-pdf")
     ax.plot(x_s, model.spectral_rad_pdf(x_s), **kwargs)

From abbb062cffff08391bf64e6c3ed96ffee5996a44 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 26 Jul 2024 23:12:34 +0200
Subject: [PATCH 02/28] covmodel: init len_scale with integral_scale if given;
 remove unused _integral_scale

---
 src/gstools/covmodel/base.py | 11 +++++------
 1 file changed, 5 insertions(+), 6 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index 23e19881..f5def43c 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -208,6 +208,8 @@ def __init__(
         self._nugget = float(nugget)
 
         # set anisotropy and len_scale, disable anisotropy for latlon models
+        if integral_scale is not None:
+            len_scale = integral_scale
         self._len_scale, self._anis = set_len_anis(
             self.dim, len_scale, anis, self.latlon
         )
@@ -221,7 +223,6 @@ def __init__(
             self.var = var
         else:
             self._var = float(var_raw)
-        self._integral_scale = None
         self.integral_scale = integral_scale
         # set var again, if int_scale affects var_factor
         if var_raw is None:
@@ -486,8 +487,7 @@ def default_rescale(self):
 
     def calc_integral_scale(self):
         """Calculate the integral scale of the isotrope model."""
-        self._integral_scale = integral(self.correlation, 0, np.inf)[0]
-        return self._integral_scale
+        return integral(self.correlation, 0, np.inf)[0]
 
     def percentile_scale(self, per=0.9):
         """Calculate the percentile scale of the isotrope model.
@@ -1043,8 +1043,7 @@ def integral_scale(self):
         ValueError
             If integral scale is not setable.
         """
-        self._integral_scale = self.calc_integral_scale()
-        return self._integral_scale
+        return self.calc_integral_scale()
 
     @integral_scale.setter
     def integral_scale(self, integral_scale):
@@ -1054,7 +1053,7 @@ def integral_scale(self, integral_scale):
             integral_scale = self.len_scale
             # reset len_scale
             self.len_scale = 1.0
-            int_tmp = self.calc_integral_scale()
+            int_tmp = self.integral_scale
             self.len_scale = integral_scale / int_tmp
             if not np.isclose(self.integral_scale, integral_scale, rtol=1e-3):
                 raise ValueError(

From c39866a90096a71db11092b746ca979e78c991a4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 26 Jul 2024 23:13:14 +0200
Subject: [PATCH 03/28] bounds: allow interval with equal bounds if closed

---
 src/gstools/covmodel/tools.py | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index dddeb441..cf310b94 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -297,11 +297,14 @@ def check_bounds(bounds):
                 * "oo" : open - open
                 * "oc" : open - close
                 * "co" : close - open
-                * "cc" : close - close
+                * "cc" : close - close (default)
     """
+    typ = bounds[2] if len(bounds) == 3 else "cc"
     if len(bounds) not in (2, 3):
         return False
-    if bounds[1] <= bounds[0]:
+    if (typ == "cc" and bounds[1] < bounds[0]) or (
+        typ != "cc" and bounds[1] <= bounds[0]
+    ):
         return False
     if len(bounds) == 3 and bounds[2] not in ("oo", "oc", "co", "cc"):
         return False

From df9f2baa949201a6f54f41a2473f074909365f38 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Sat, 27 Jul 2024 01:04:30 +0200
Subject: [PATCH 04/28] CovModel: add force_values logic

---
 src/gstools/covmodel/base.py  | 65 ++++++++++++++++++++++++-----------
 src/gstools/covmodel/fit.py   |  4 +++
 src/gstools/covmodel/tools.py | 10 +++---
 3 files changed, 55 insertions(+), 24 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index f5def43c..3a61e229 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -139,6 +139,8 @@ class CovModel:
         used for the spectrum calculation. Use with caution (Better: Don't!).
         ``None`` is equivalent to ``{"a": -1, "b": 1, "N": 1000, "h": 0.001}``.
         Default: :any:`None`
+    fixed: :class:`set` or :any:`None`, optional
+        Names of fixed arguments. Default: :any:`None`
     **opt_arg
         Optional arguments are covered by these keyword arguments.
         If present, they are described in the section `Other Parameters`.
@@ -161,6 +163,7 @@ def __init__(
         spatial_dim=None,
         var_raw=None,
         hankel_kw=None,
+        fixed=None,
         **opt_arg,
     ):
         # assert, that we use a subclass
@@ -169,6 +172,16 @@ def __init__(
         if not hasattr(self, "variogram"):
             raise TypeError("Don't instantiate 'CovModel' directly!")
 
+        # indicate that arguments are fixed (True after __init__)
+        self._fix = False
+        # force input values
+        forced = self.force_values()
+        var = forced.get("var", var)
+        len_scale = forced.get("len_scale", len_scale)
+        nugget = forced.get("nugget", nugget)
+        integral_scale = forced.get("integral_scale", integral_scale)
+        for opt in opt_arg:
+            opt_arg[opt] = forced.get(opt, opt_arg[opt])
         # prepare dim setting
         self._dim = None
         self._hankel_kw = None
@@ -198,6 +211,16 @@ def __init__(
         # optional arguments for the variogram-model
         set_opt_args(self, opt_arg)
 
+        # check fixed
+        fixed = set(fixed) if fixed is not None else set()
+        fixed = fixed | self.always_fixed()
+        valid_fixed = set(self.iso_arg)  # | set(["anis"])
+        if not fixed <= valid_fixed:
+            raise ValueError(
+                f"CovModel: unknown names in 'fixed': {fixed - valid_fixed}"
+            )
+        self._fixed = fixed
+
         # set standard boundaries for variance, len_scale, nugget and opt_arg
         bounds = self.default_arg_bounds()
         bounds.update(self.default_opt_arg_bounds())
@@ -234,6 +257,11 @@ def __init__(
         self.check_arg_bounds()
         # additional checks for the optional arguments (provided by user)
         self.check_opt_arg()
+        # set fixed bounds after checking original bounds
+        for arg in self.fixed:
+            val = getattr(self, arg)
+            self.set_arg_bounds(check_args=False, **{arg: (val, val, "cc")})
+        self._fix = True
         # precision for printing
         self._prec = 3
 
@@ -438,6 +466,14 @@ def pykrige_kwargs(self):
 
     # methods for optional/default arguments (can be overridden)
 
+    def always_fixed(self):
+        """Provide set of fixed arguments."""
+        return set()
+
+    def force_values(self):
+        """:class:`dict`: Forced values for arguments."""
+        return {}
+
     def default_opt_arg(self):
         """Provide default optional arguments by the user.
 
@@ -795,6 +831,11 @@ def check_arg_bounds(self):
 
     # bounds properties
 
+    @property
+    def fixed(self):
+        """:class:`set`: Set with names of fixed arguments."""
+        return self._fixed
+
     @property
     def var_bounds(self):
         """:class:`list`: Bounds for the variance.
@@ -809,11 +850,7 @@ def var_bounds(self):
 
     @var_bounds.setter
     def var_bounds(self, bounds):
-        if not check_bounds(bounds):
-            raise ValueError(
-                f"Given bounds for 'var' are not valid, got: {bounds}"
-            )
-        self._var_bounds = bounds
+        self.set_arg_bounds(var=bounds)
 
     @property
     def len_scale_bounds(self):
@@ -829,11 +866,7 @@ def len_scale_bounds(self):
 
     @len_scale_bounds.setter
     def len_scale_bounds(self, bounds):
-        if not check_bounds(bounds):
-            raise ValueError(
-                f"Given bounds for 'len_scale' are not valid, got: {bounds}"
-            )
-        self._len_scale_bounds = bounds
+        self.set_arg_bounds(len_scale=bounds)
 
     @property
     def nugget_bounds(self):
@@ -849,11 +882,7 @@ def nugget_bounds(self):
 
     @nugget_bounds.setter
     def nugget_bounds(self, bounds):
-        if not check_bounds(bounds):
-            raise ValueError(
-                f"Given bounds for 'nugget' are not valid, got: {bounds}"
-            )
-        self._nugget_bounds = bounds
+        self.set_arg_bounds(nugget=bounds)
 
     @property
     def anis_bounds(self):
@@ -869,11 +898,7 @@ def anis_bounds(self):
 
     @anis_bounds.setter
     def anis_bounds(self, bounds):
-        if not check_bounds(bounds):
-            raise ValueError(
-                f"Given bounds for 'anis' are not valid, got: {bounds}"
-            )
-        self._anis_bounds = bounds
+        self.set_arg_bounds(anis=bounds)
 
     @property
     def opt_arg_bounds(self):
diff --git a/src/gstools/covmodel/fit.py b/src/gstools/covmodel/fit.py
index 8b19f497..f19eaac3 100755
--- a/src/gstools/covmodel/fit.py
+++ b/src/gstools/covmodel/fit.py
@@ -165,10 +165,14 @@ def fit_variogram(
 
     The fitted parameters will be instantly set in the model.
     """
+    for para in model.fixed:
+        para_select[para] = False
     # preprocess selected parameters
     para, sill, constrain_sill, anis = _pre_para(
         model, para_select, sill, anis
     )
+    if not any(para.values()):
+        raise ValueError("fit: no parameters selected for fitting.")
     # check curve_fit kwargs
     curve_fit_kwargs = {} if curve_fit_kwargs is None else curve_fit_kwargs
     # check method
diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index cf310b94..ad731aeb 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -458,6 +458,8 @@ def set_arg_bounds(model, check_args=True, **kwargs):
     # if variance needs to be resetted, do this at last
     var_bnds = []
     for arg, bounds in kwargs.items():
+        if model._fix and arg in model.fixed:
+            raise ValueError(f"Can't set bounds for fixed argument '{arg}'")
         if not check_bounds(bounds):
             raise ValueError(
                 f"Given bounds for '{arg}' are not valid, got: {bounds}"
@@ -468,11 +470,11 @@ def set_arg_bounds(model, check_args=True, **kwargs):
             var_bnds = bounds
             continue
         elif arg == "len_scale":
-            model.len_scale_bounds = bounds
+            model._len_scale_bounds = bounds
         elif arg == "nugget":
-            model.nugget_bounds = bounds
+            model._nugget_bounds = bounds
         elif arg == "anis":
-            model.anis_bounds = bounds
+            model._anis_bounds = bounds
         else:
             raise ValueError(f"set_arg_bounds: unknown argument '{arg}'")
         if check_args and check_arg_in_bounds(model, arg) > 0:
@@ -483,7 +485,7 @@ def set_arg_bounds(model, check_args=True, **kwargs):
                 setattr(model, arg, def_arg)
     # set var last like always
     if var_bnds:
-        model.var_bounds = var_bnds
+        model._var_bounds = var_bnds
         if check_args and check_arg_in_bounds(model, "var") > 0:
             model.var = default_arg_from_bounds(var_bnds)
 

From a3f1ec6d897ba161f93abd133db7480ee70fa5d5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Sat, 27 Jul 2024 23:05:10 +0200
Subject: [PATCH 05/28] generator: shortcut for 0 variance

---
 src/gstools/field/generator.py | 75 ++++++++++++++++++++++------------
 1 file changed, 50 insertions(+), 25 deletions(-)

diff --git a/src/gstools/field/generator.py b/src/gstools/field/generator.py
index d4cb0dea..89914785 100755
--- a/src/gstools/field/generator.py
+++ b/src/gstools/field/generator.py
@@ -152,6 +152,16 @@ def __call__(self, pos, add_nugget=True):
             the random modes
         """
 
+    @property
+    @abstractmethod
+    def model(self):
+        """:any:`CovModel`: Covariance model of the spatial random field."""
+
+    @property
+    def zero_var(self):
+        """:class:`bool`: Whether Covariance model has zero variance."""
+        return np.isclose(self.model.var, 0)
+
     @property
     @abstractmethod
     def value_type(self):
@@ -260,6 +270,10 @@ def __call__(self, pos, add_nugget=True):
             the random modes
         """
         pos = np.asarray(pos, dtype=np.double)
+        if self.zero_var:
+            shp = pos.shape[1:]
+            return self.get_nugget(shp) if add_nugget else np.full(shp, 0.0)
+        # generate if var is not 0
         summed_modes = _summate(
             self._cov_sample, self._z_1, self._z_2, pos, config.NUM_THREADS
         )
@@ -285,7 +299,7 @@ def get_nugget(self, shape):
                 size=shape
             )
         else:
-            nugget = 0.0
+            nugget = np.full(shape, 0.0) if self.zero_var else 0.0
         return nugget
 
     def update(self, model=None, seed=np.nan):
@@ -362,23 +376,26 @@ def reset_seed(self, seed=np.nan):
         self._z_1 = self._rng.random.normal(size=self._mode_no)
         self._z_2 = self._rng.random.normal(size=self._mode_no)
         # sample uniform on a sphere
-        sphere_coord = self._rng.sample_sphere(self.model.dim, self._mode_no)
-        # sample radii according to radial spectral density of the model
-        if self.sampling == "inversion" or (
-            self.sampling == "auto" and self.model.has_ppf
-        ):
-            pdf, cdf, ppf = self.model.dist_func
-            rad = self._rng.sample_dist(
-                size=self._mode_no, pdf=pdf, cdf=cdf, ppf=ppf, a=0
-            )
+        if self.zero_var:
+            self._cov_sample = np.full((self.model.dim, self._mode_no), 0.0)
         else:
-            rad = self._rng.sample_ln_pdf(
-                ln_pdf=self.model.ln_spectral_rad_pdf,
-                size=self._mode_no,
-                sample_around=1.0 / self.model.len_rescaled,
-            )
-        # get fully spatial samples by multiplying sphere samples and radii
-        self._cov_sample = rad * sphere_coord
+            sph_crd = self._rng.sample_sphere(self.model.dim, self._mode_no)
+            # sample radii according to radial spectral density of the model
+            if self.sampling == "inversion" or (
+                self.sampling == "auto" and self.model.has_ppf
+            ):
+                pdf, cdf, ppf = self.model.dist_func
+                rad = self._rng.sample_dist(
+                    size=self._mode_no, pdf=pdf, cdf=cdf, ppf=ppf, a=0
+                )
+            else:
+                rad = self._rng.sample_ln_pdf(
+                    ln_pdf=self.model.ln_spectral_rad_pdf,
+                    size=self._mode_no,
+                    sample_around=1.0 / self.model.len_rescaled,
+                )
+            # get spatial samples by multiplying sphere samples and radii
+            self._cov_sample = rad * sph_crd
 
     @property
     def sampling(self):
@@ -541,6 +558,10 @@ def __call__(self, pos, add_nugget=True):
             the random modes
         """
         pos = np.asarray(pos, dtype=np.double)
+        nugget = self.get_nugget(pos.shape) if add_nugget else 0.0
+        e1 = self._create_unit_vector(pos.shape)
+        if self.zero_var:
+            return self.mean_u * e1 + nugget
         summed_modes = _summate_incompr(
             self._cov_sample,
             self._z_1,
@@ -548,8 +569,6 @@ def __call__(self, pos, add_nugget=True):
             pos,
             config.NUM_THREADS,
         )
-        nugget = self.get_nugget(summed_modes.shape) if add_nugget else 0.0
-        e1 = self._create_unit_vector(summed_modes.shape)
         return (
             self.mean_u * e1
             + self.mean_u
@@ -667,7 +686,10 @@ def __call__(self, pos, add_nugget=True):
             the random modes
         """
         pos = np.asarray(pos, dtype=np.double)
-
+        if self.zero_var:
+            shp = pos.shape[1:]
+            return self.get_nugget(shp) if add_nugget else np.full(shp, 0.0)
+        # generate if var is not 0
         summed_modes = _summate_fourier(
             self._spectrum_factor,
             self._modes,
@@ -698,7 +720,7 @@ def get_nugget(self, shape):
                 size=shape
             )
         else:
-            nugget = 0.0
+            nugget = np.full(shape, 0.0) if self.zero_var else 0.0
         return nugget
 
     def update(self, model=None, seed=np.nan, period=None, mode_no=None):
@@ -800,10 +822,13 @@ def reset_seed(self, seed=np.nan):
         self._z_2 = self._rng.random.normal(size=np.prod(self._mode_no))
         # pre calc. the spectrum for all wave numbers they are handed over to
         # Cython, which doesn't have access to the CovModel
-        k_norm = np.linalg.norm(self._modes, axis=0)
-        self._spectrum_factor = np.sqrt(
-            self._model.spectrum(k_norm) * np.prod(self._delta_k)
-        )
+        if self.zero_var:
+            self._spectrum_factor = np.full(np.prod(self._mode_no), 0.0)
+        else:
+            k_norm = np.linalg.norm(self._modes, axis=0)
+            self._spectrum_factor = np.sqrt(
+                self._model.spectrum(k_norm) * np.prod(self._delta_k)
+            )
 
     def _fill_to_dim(
         self, values, dim, dtype=float, default_value=None

From 8b3ad819e3cf4431fa66f37bd11ace80d850db52 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 29 Jul 2024 00:42:25 +0200
Subject: [PATCH 06/28] CovModel: safer usage of privat attr; anis set bug fix;
 simpler int scale

---
 src/gstools/covmodel/base.py | 51 +++++++++++++++++-------------------
 1 file changed, 24 insertions(+), 27 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index 3a61e229..dcbffe57 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -173,7 +173,7 @@ def __init__(
             raise TypeError("Don't instantiate 'CovModel' directly!")
 
         # indicate that arguments are fixed (True after __init__)
-        self._fix = False
+        self._init = False
         # force input values
         forced = self.force_values()
         var = forced.get("var", var)
@@ -187,6 +187,7 @@ def __init__(
         self._hankel_kw = None
         self._sft = None
         # prepare parameters (they are checked in dim setting)
+        self._fixed = None
         self._rescale = None
         self._len_scale = None
         self._anis = None
@@ -246,7 +247,8 @@ def __init__(
             self.var = var
         else:
             self._var = float(var_raw)
-        self.integral_scale = integral_scale
+        if integral_scale is not None:
+            self.integral_scale = integral_scale
         # set var again, if int_scale affects var_factor
         if var_raw is None:
             self._var = None
@@ -261,7 +263,7 @@ def __init__(
         for arg in self.fixed:
             val = getattr(self, arg)
             self.set_arg_bounds(check_args=False, **{arg: (val, val, "cc")})
-        self._fix = True
+        self._init = True
         # precision for printing
         self._prec = 3
 
@@ -801,8 +803,8 @@ def default_arg_bounds(self):
         Given as a dictionary.
         """
         res = {
-            "var": (0.0, np.inf, "oo"),
-            "len_scale": (0.0, np.inf, "oo"),
+            "var": (0.0, np.inf, "co"),
+            "len_scale": (0.0, np.inf, "co"),
             "nugget": (0.0, np.inf, "co"),
             "anis": (0.0, np.inf, "oo"),
         }
@@ -1014,10 +1016,7 @@ def len_scale(self, len_scale):
         self._len_scale, anis = set_len_anis(
             self.dim, len_scale, self.anis, self.latlon
         )
-        if self.latlon:
-            self._anis = np.array((self.dim - 1) * [1], dtype=np.double)
-        else:
-            self._anis = anis
+        self._anis = anis
         self.check_arg_bounds()
 
     @property
@@ -1033,7 +1032,7 @@ def rescale(self, rescale):
     @property
     def len_rescaled(self):
         """:class:`float`: The rescaled main length scale of the model."""
-        return self._len_scale / self._rescale
+        return self.len_scale / self.rescale
 
     @property
     def anis(self):
@@ -1072,19 +1071,17 @@ def integral_scale(self):
 
     @integral_scale.setter
     def integral_scale(self, integral_scale):
-        if integral_scale is not None:
-            # format int-scale right
-            self.len_scale = integral_scale
-            integral_scale = self.len_scale
-            # reset len_scale
-            self.len_scale = 1.0
-            int_tmp = self.integral_scale
-            self.len_scale = integral_scale / int_tmp
-            if not np.isclose(self.integral_scale, integral_scale, rtol=1e-3):
-                raise ValueError(
-                    f"{self.name}: Integral scale could not be set correctly! "
-                    "Please just provide a 'len_scale'!"
-                )
+        int_scale, anis = set_len_anis(
+            self.dim, integral_scale, self.anis, self.latlon
+        )
+        old_scale = self.integral_scale
+        self.anis = anis
+        self.len_scale = self.len_scale * int_scale / old_scale
+        if not np.isclose(self.integral_scale, integral_scale, rtol=1e-3):
+            raise ValueError(
+                f"{self.name}: Integral scale could not be set correctly! "
+                "Please just provide a 'len_scale'!"
+            )
 
     @property
     def hankel_kw(self):
@@ -1139,7 +1136,7 @@ def sill(self):
     @property
     def arg(self):
         """:class:`list` of :class:`str`: Names of all arguments."""
-        return ["var", "len_scale", "nugget", "anis", "angles"] + self._opt_arg
+        return ["var", "len_scale", "nugget", "anis", "angles"] + self.opt_arg
 
     @property
     def arg_list(self):
@@ -1152,7 +1149,7 @@ def arg_list(self):
     @property
     def iso_arg(self):
         """:class:`list` of :class:`str`: Names of isotropic arguments."""
-        return ["var", "len_scale", "nugget"] + self._opt_arg
+        return ["var", "len_scale", "nugget"] + self.opt_arg
 
     @property
     def iso_arg_list(self):
@@ -1180,7 +1177,7 @@ def len_scale_vec(self):
         """
         res = np.zeros(self.dim, dtype=np.double)
         res[0] = self.len_scale
-        for i in range(1, self._dim):
+        for i in range(1, self.dim):
             res[i] = self.len_scale * self.anis[i - 1]
         return res
 
@@ -1226,7 +1223,7 @@ def __setattr__(self, name, value):
         """Set an attribute."""
         super().__setattr__(name, value)
         # if an optional variogram argument was given, check bounds
-        if hasattr(self, "_opt_arg") and name in self._opt_arg:
+        if getattr(self, "_init", False) and name in self.opt_arg:
             self.check_arg_bounds()
 
     def __repr__(self):

From a60b3d7e9e6066f986ea4baea60e0f78c7e1feb5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 29 Jul 2024 00:43:12 +0200
Subject: [PATCH 07/28] CovModel: check _init in bounds setter; also compare
 geo_scale; simpler repr

---
 src/gstools/covmodel/tools.py | 50 +++++++++++++----------------------
 1 file changed, 18 insertions(+), 32 deletions(-)

diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index ad731aeb..9d53de58 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -458,7 +458,7 @@ def set_arg_bounds(model, check_args=True, **kwargs):
     # if variance needs to be resetted, do this at last
     var_bnds = []
     for arg, bounds in kwargs.items():
-        if model._fix and arg in model.fixed:
+        if model._init and arg in model.fixed:
             raise ValueError(f"Can't set bounds for fixed argument '{arg}'")
         if not check_bounds(bounds):
             raise ValueError(
@@ -598,6 +598,7 @@ def compare(this, that):
     equal &= np.all(np.isclose(this.anis, that.anis))
     equal &= np.all(np.isclose(this.angles, that.angles))
     equal &= np.isclose(this.rescale, that.rescale)
+    equal &= np.isclose(this.geo_scale, that.geo_scale)
     equal &= this.latlon == that.latlon
     equal &= this.temporal == that.temporal
     for opt in this.opt_arg:
@@ -614,39 +615,24 @@ def model_repr(model):  # pragma: no cover
     model : :any:`CovModel`
         The covariance model in use.
     """
-    m = model
-    p = model._prec
-    opt_str = ""
+    m, p = model, model._prec
+    ani_str, ang_str, o_str, r_str = "", "", "", ""
     t_str = ", temporal=True" if m.temporal else ""
+    d_str = f"latlon={m.latlon}" if m.latlon else f"dim={m.spatial_dim}"
+    p_str = f", var={m.var:.{p}}, len_scale={m.len_scale:.{p}}"
+    p_str += "" if np.isclose(m.nugget, 0) else f", nugget={m.nugget:.{p}}"
     if not np.isclose(m.rescale, m.default_rescale()):
-        opt_str += f", rescale={m.rescale:.{p}}"
+        o_str += f", rescale={m.rescale:.{p}}"
     for opt in m.opt_arg:
-        opt_str += f", {opt}={getattr(m, opt):.{p}}"
+        o_str += f", {opt}={getattr(m, opt):.{p}}"
     if m.latlon:
-        ani_str = (
-            ""
-            if m.is_isotropic or not m.temporal
-            else f", anis={m.anis[-1]:.{p}}"
-        )
-        r_str = (
-            ""
-            if np.isclose(m.geo_scale, 1)
-            else f", geo_scale={m.geo_scale:.{p}}"
-        )
-        repr_str = (
-            f"{m.name}(latlon={m.latlon}{t_str}, var={m.var:.{p}}, "
-            f"len_scale={m.len_scale:.{p}}, nugget={m.nugget:.{p}}"
-            f"{ani_str}{r_str}{opt_str})"
-        )
+        if not m.is_isotropic and m.temporal:
+            ani_str = f", anis={m.anis[-1]:.{p}}"
+        if not np.isclose(m.geo_scale, 1):
+            r_str = f", geo_scale={m.geo_scale:.{p}}"
     else:
-        # only print anis and angles if model is anisotropic or rotated
-        ani_str = "" if m.is_isotropic else f", anis={list_format(m.anis, p)}"
-        ang_str = (
-            f", angles={list_format(m.angles, p)}" if m.do_rotation else ""
-        )
-        repr_str = (
-            f"{m.name}(dim={m.spatial_dim}{t_str}, var={m.var:.{p}}, "
-            f"len_scale={m.len_scale:.{p}}, nugget={m.nugget:.{p}}"
-            f"{ani_str}{ang_str}{opt_str})"
-        )
-    return repr_str
+        if not m.is_isotropic:
+            ani_str = f", anis={list_format(m.anis, p)}"
+        if m.do_rotation:
+            ang_str = f", angles={list_format(m.angles, p)}"
+    return f"{m.name}({d_str}{t_str}{p_str}{ani_str}{ang_str}{r_str}{o_str})"

From 92210adabaae3c5052830d027d712bd71d1fce26 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 29 Jul 2024 00:45:59 +0200
Subject: [PATCH 08/28] CovModel: remove force arguments mechanic

---
 src/gstools/covmodel/base.py | 12 ------------
 1 file changed, 12 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index dcbffe57..d1d1cf0b 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -174,14 +174,6 @@ def __init__(
 
         # indicate that arguments are fixed (True after __init__)
         self._init = False
-        # force input values
-        forced = self.force_values()
-        var = forced.get("var", var)
-        len_scale = forced.get("len_scale", len_scale)
-        nugget = forced.get("nugget", nugget)
-        integral_scale = forced.get("integral_scale", integral_scale)
-        for opt in opt_arg:
-            opt_arg[opt] = forced.get(opt, opt_arg[opt])
         # prepare dim setting
         self._dim = None
         self._hankel_kw = None
@@ -472,10 +464,6 @@ def always_fixed(self):
         """Provide set of fixed arguments."""
         return set()
 
-    def force_values(self):
-        """:class:`dict`: Forced values for arguments."""
-        return {}
-
     def default_opt_arg(self):
         """Provide default optional arguments by the user.
 

From 8999bf98088446a91d728c4be376db474f7d06b8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 29 Jul 2024 00:50:43 +0200
Subject: [PATCH 09/28] pylint fixes

---
 pyproject.toml               | 2 +-
 src/gstools/covmodel/base.py | 1 -
 2 files changed, 1 insertion(+), 2 deletions(-)

diff --git a/pyproject.toml b/pyproject.toml
index 090c7c63..88185bf3 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -155,7 +155,7 @@ target-version = [
     max-locals = 50
     max-branches = 30
     max-statements = 85
-    max-attributes = 25
+    max-attributes = 30
     max-public-methods = 80
 
 [tool.cibuildwheel]
diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index d1d1cf0b..56f776af 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -21,7 +21,6 @@
 from gstools.covmodel.tools import (
     _init_subclass,
     check_arg_bounds,
-    check_bounds,
     compare,
     default_arg_from_bounds,
     model_repr,

From d643b450b86ff82f29f15c092c7d8fa271a1466d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Sun, 11 Aug 2024 12:16:13 +0200
Subject: [PATCH 10/28] TPL: remove var_raw and var_factor logic and only add
 intensity as property to TPL models

---
 src/gstools/covmodel/base.py       | 44 ++++--------------------------
 src/gstools/covmodel/fit.py        | 32 ++++------------------
 src/gstools/covmodel/tools.py      |  1 -
 src/gstools/covmodel/tpl_models.py | 26 +++++++++++-------
 4 files changed, 28 insertions(+), 75 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index 56f776af..fce1e64b 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -126,12 +126,6 @@ class CovModel:
         If given, the model dimension will be determined from this spatial dimension
         and the possible temporal dimension if temporal is ture.
         Default: None
-    var_raw : :class:`float` or :any:`None`, optional
-        raw variance of the model which will be multiplied with
-        :any:`CovModel.var_factor` to result in the actual variance.
-        If given, ``var`` will be ignored.
-        (This is just for models that override :any:`CovModel.var_factor`)
-        Default: :any:`None`
     hankel_kw: :class:`dict` or :any:`None`, optional
         Modify the init-arguments of
         :any:`hankel.SymmetricFourierTransform`
@@ -160,7 +154,6 @@ def __init__(
         geo_scale=RADIAN_SCALE,
         temporal=False,
         spatial_dim=None,
-        var_raw=None,
         hankel_kw=None,
         fixed=None,
         **opt_arg,
@@ -232,20 +225,12 @@ def __init__(
             self.dim, angles, self.latlon, self.temporal
         )
 
-        # set var at last, because of the var_factor (to be right initialized)
-        if var_raw is None:
-            self._var = None
-            self.var = var
-        else:
-            self._var = float(var_raw)
+        self._var = None
+        self.var = var
+
         if integral_scale is not None:
             self.integral_scale = integral_scale
-        # set var again, if int_scale affects var_factor
-        if var_raw is None:
-            self._var = None
-            self.var = var
-        else:
-            self._var = float(var_raw)
+
         # final check for parameter bounds
         self.check_arg_bounds()
         # additional checks for the optional arguments (provided by user)
@@ -500,10 +485,6 @@ def fix_dim(self):
         """Set a fix dimension for the model."""
         return None
 
-    def var_factor(self):
-        """Factor for the variance."""
-        return 1.0
-
     def default_rescale(self):
         """Provide default rescaling factor."""
         return 1.0
@@ -963,24 +944,11 @@ def dim(self, dim):
     @property
     def var(self):
         """:class:`float`: The variance of the model."""
-        return self._var * self.var_factor()
+        return self._var
 
     @var.setter
     def var(self, var):
-        self._var = float(var) / self.var_factor()
-        self.check_arg_bounds()
-
-    @property
-    def var_raw(self):
-        """:class:`float`: The raw variance of the model without factor.
-
-        (See. CovModel.var_factor)
-        """
-        return self._var
-
-    @var_raw.setter
-    def var_raw(self, var_raw):
-        self._var = float(var_raw)
+        self._var = float(var)
         self.check_arg_bounds()
 
     @property
diff --git a/src/gstools/covmodel/fit.py b/src/gstools/covmodel/fit.py
index f19eaac3..e6d6b03d 100755
--- a/src/gstools/covmodel/fit.py
+++ b/src/gstools/covmodel/fit.py
@@ -19,6 +19,7 @@
 __all__ = ["fit_variogram"]
 
 
+# this should be: set(mod.iso_arg) - set(mod.opt_arg)
 DEFAULT_PARA = ["var", "len_scale", "nugget"]
 
 
@@ -217,21 +218,13 @@ def fit_variogram(
 
 def _pre_para(model, para_select, sill, anis):
     """Preprocess selected parameters."""
-    var_last = False
-    var_tmp = 0.0  # init value
     for par in para_select:
         if par not in model.arg_bounds:
             raise ValueError(f"fit: unknown parameter in selection: {par}")
         if not isinstance(para_select[par], bool):
-            if par == "var":
-                var_last = True
-                var_tmp = float(para_select[par])
-            else:
-                setattr(model, par, float(para_select[par]))
+            setattr(model, par, float(para_select[par]))
             para_select[par] = False
-    # set variance last due to possible recalculations
-    if var_last:
-        model.var = var_tmp
+
     # remove those that were set to True
     para_select = {k: v for k, v in para_select.items() if not v}
     # handling the sill
@@ -426,9 +419,9 @@ def curve(x, arg1, *args):
         para_skip = 0
         opt_skip = 0
         if para["var"]:
-            var_tmp = args[para_skip]
+            model.var = args[para_skip]
             if constrain_sill:
-                nugget_tmp = sill - var_tmp
+                nugget_tmp = sill - model.var
                 # punishment, if resulting nugget out of range for fixed sill
                 if check_arg_in_bounds(model, "nugget", nugget_tmp) > 0:
                     return np.full_like(x, np.inf)
@@ -445,12 +438,6 @@ def curve(x, arg1, *args):
             if para[opt]:
                 setattr(model, opt, args[para_skip + opt_skip])
                 opt_skip += 1
-        # set var at last because of var_factor (other parameter needed)
-        if para["var"]:
-            model.var = var_tmp
-        # needs to be reset for TPL models when len_scale was changed
-        else:
-            model.var = var_save
         if is_dir_vario:
             if anis:
                 model.anis = args[1 - model.dim :]
@@ -469,13 +456,9 @@ def _post_fitting(model, para, popt, anis, is_dir_vario):
     fit_para = {}
     para_skip = 0
     opt_skip = 0
-    var_tmp = 0.0  # init value
     for par in DEFAULT_PARA:
         if para[par]:
-            if par == "var":  # set variance last
-                var_tmp = popt[para_skip]
-            else:
-                setattr(model, par, popt[para_skip])
+            setattr(model, par, popt[para_skip])
             fit_para[par] = popt[para_skip]
             para_skip += 1
         else:
@@ -491,9 +474,6 @@ def _post_fitting(model, para, popt, anis, is_dir_vario):
         if anis:
             model.anis = popt[1 - model.dim :]
         fit_para["anis"] = model.anis
-    # set var at last because of var_factor (other parameter needed)
-    if para["var"]:
-        model.var = var_tmp
     return fit_para
 
 
diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index 9d53de58..1c3c9ca0 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -592,7 +592,6 @@ def compare(this, that):
     equal = True
     equal &= this.name == that.name
     equal &= np.isclose(this.var, that.var)
-    equal &= np.isclose(this.var_raw, that.var_raw)  # ?! needless?
     equal &= np.isclose(this.nugget, that.nugget)
     equal &= np.isclose(this.len_scale, that.len_scale)
     equal &= np.all(np.isclose(this.anis, that.anis))
diff --git a/src/gstools/covmodel/tpl_models.py b/src/gstools/covmodel/tpl_models.py
index b728e7b9..40ed4ec8 100644
--- a/src/gstools/covmodel/tpl_models.py
+++ b/src/gstools/covmodel/tpl_models.py
@@ -31,6 +31,19 @@
 class TPLCovModel(CovModel):
     """Truncated-Power-Law Covariance Model base class for super-position."""
 
+    @property
+    def intensity(self):
+        """:class:`float`: Intensity of variation."""
+        return self.var / self.intensity_scaling
+
+    @property
+    def intensity_scaling(self):
+        """:class:`float`: Scaling of Intensity to result in variance."""
+        return (
+            self.len_up_rescaled ** (2 * self.hurst)
+            - self.len_low_rescaled ** (2 * self.hurst)
+        ) / (2 * self.hurst)
+
     @property
     def len_up(self):
         """:class:`float`: Upper length scale truncation of the model.
@@ -55,13 +68,6 @@ def len_low_rescaled(self):
         """
         return self.len_low / self.rescale
 
-    def var_factor(self):
-        """Factor for C (intensity of variation) to result in variance."""
-        return (
-            self.len_up_rescaled ** (2 * self.hurst)
-            - self.len_low_rescaled ** (2 * self.hurst)
-        ) / (2 * self.hurst)
-
     def cor(self, h):
         """TPL - normalized correlation function."""
 
@@ -125,7 +131,7 @@ class TPLGaussian(TPLCovModel):
         * :math:`C>0` :
           scaling factor from the Power-Law (intensity of variation)
           This parameter will be calculated internally by the given variance.
-          You can access C directly by ``model.var_raw``
+          You can access C by ``model.intensity``
         * :math:`0<H<1` : hurst coefficient (``model.hurst``)
         * :math:`\ell_{\mathrm{low}}\geq 0` : lower length scale truncation
           of the model (``model.len_low``)
@@ -258,7 +264,7 @@ class TPLExponential(TPLCovModel):
         * :math:`C>0` :
           scaling factor from the Power-Law (intensity of variation)
           This parameter will be calculated internally by the given variance.
-          You can access C directly by ``model.var_raw``
+          You can access C by ``model.intensity``
         * :math:`0<H<\frac{1}{2}` : hurst coefficient (``model.hurst``)
         * :math:`\ell_{\mathrm{low}}\geq 0` : lower length scale truncation
           of the model (``model.len_low``)
@@ -398,7 +404,7 @@ class TPLStable(TPLCovModel):
         * :math:`C>0` :
           scaling factor from the Power-Law (intensity of variation)
           This parameter will be calculated internally by the given variance.
-          You can access C directly by ``model.var_raw``
+          You can access C by ``model.intensity``
         * :math:`0<H<\frac{\alpha}{2}` : hurst coefficient (``model.hurst``)
         * :math:`\ell_{\mathrm{low}}\geq 0` : lower length scale truncation
           of the model (``model.len_low``)

From 81e5421ff3f0e9f1a5b81f0f78d193091be655f0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Sun, 11 Aug 2024 12:16:38 +0200
Subject: [PATCH 11/28] tests: remove tests for var_raw

---
 tests/test_covmodel.py | 8 +-------
 1 file changed, 1 insertion(+), 7 deletions(-)

diff --git a/tests/test_covmodel.py b/tests/test_covmodel.py
index a2729dd6..c42e4774 100644
--- a/tests/test_covmodel.py
+++ b/tests/test_covmodel.py
@@ -201,15 +201,9 @@ def test_tpl_models(self):
                     self.gamma_x, self.gamma_y, sill=1.1, nugget=False
                 )
                 self.assertAlmostEqual(model.var, 1.1, delta=1e-5)
-                # check var_raw handling
-                model = Model(var_raw=1, len_low=0, integral_scale=10)
-                var_save = model.var
-                model.var_raw = 1.1
-                self.assertAlmostEqual(model.var, var_save * 1.1)
-                self.assertAlmostEqual(model.integral_scale, 10)
                 # integral scale is not setable when len_low is not 0
                 with self.assertRaises(ValueError):
-                    Model(var_raw=1, len_low=5, integral_scale=10)
+                    Model(len_low=5, integral_scale=10)
 
     def test_fitting(self):
         for Model in self.std_cov_models:

From 669e9a203a5d40d7b35f11896e64674f3c57e0b2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Sun, 11 Aug 2024 16:58:40 +0200
Subject: [PATCH 12/28] CovModel: remove mechanism for fixed args again

---
 src/gstools/covmodel/base.py  | 36 ++++-------------------------------
 src/gstools/covmodel/fit.py   |  2 --
 src/gstools/covmodel/tools.py |  2 --
 3 files changed, 4 insertions(+), 36 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index fce1e64b..4a1ee76c 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -132,8 +132,6 @@ class CovModel:
         used for the spectrum calculation. Use with caution (Better: Don't!).
         ``None`` is equivalent to ``{"a": -1, "b": 1, "N": 1000, "h": 0.001}``.
         Default: :any:`None`
-    fixed: :class:`set` or :any:`None`, optional
-        Names of fixed arguments. Default: :any:`None`
     **opt_arg
         Optional arguments are covered by these keyword arguments.
         If present, they are described in the section `Other Parameters`.
@@ -155,7 +153,6 @@ def __init__(
         temporal=False,
         spatial_dim=None,
         hankel_kw=None,
-        fixed=None,
         **opt_arg,
     ):
         # assert, that we use a subclass
@@ -164,14 +161,13 @@ def __init__(
         if not hasattr(self, "variogram"):
             raise TypeError("Don't instantiate 'CovModel' directly!")
 
-        # indicate that arguments are fixed (True after __init__)
+        # indicator for initialization status (True after __init__)
         self._init = False
         # prepare dim setting
         self._dim = None
         self._hankel_kw = None
         self._sft = None
         # prepare parameters (they are checked in dim setting)
-        self._fixed = None
         self._rescale = None
         self._len_scale = None
         self._anis = None
@@ -196,16 +192,6 @@ def __init__(
         # optional arguments for the variogram-model
         set_opt_args(self, opt_arg)
 
-        # check fixed
-        fixed = set(fixed) if fixed is not None else set()
-        fixed = fixed | self.always_fixed()
-        valid_fixed = set(self.iso_arg)  # | set(["anis"])
-        if not fixed <= valid_fixed:
-            raise ValueError(
-                f"CovModel: unknown names in 'fixed': {fixed - valid_fixed}"
-            )
-        self._fixed = fixed
-
         # set standard boundaries for variance, len_scale, nugget and opt_arg
         bounds = self.default_arg_bounds()
         bounds.update(self.default_opt_arg_bounds())
@@ -213,6 +199,7 @@ def __init__(
 
         # set parameters
         self.rescale = rescale
+        self._var = float(var)
         self._nugget = float(nugget)
 
         # set anisotropy and len_scale, disable anisotropy for latlon models
@@ -225,9 +212,6 @@ def __init__(
             self.dim, angles, self.latlon, self.temporal
         )
 
-        self._var = None
-        self.var = var
-
         if integral_scale is not None:
             self.integral_scale = integral_scale
 
@@ -235,13 +219,10 @@ def __init__(
         self.check_arg_bounds()
         # additional checks for the optional arguments (provided by user)
         self.check_opt_arg()
-        # set fixed bounds after checking original bounds
-        for arg in self.fixed:
-            val = getattr(self, arg)
-            self.set_arg_bounds(check_args=False, **{arg: (val, val, "cc")})
-        self._init = True
         # precision for printing
         self._prec = 3
+        # initialized
+        self._init = True
 
     # one of these functions needs to be overridden
     def __init_subclass__(cls):
@@ -444,10 +425,6 @@ def pykrige_kwargs(self):
 
     # methods for optional/default arguments (can be overridden)
 
-    def always_fixed(self):
-        """Provide set of fixed arguments."""
-        return set()
-
     def default_opt_arg(self):
         """Provide default optional arguments by the user.
 
@@ -801,11 +778,6 @@ def check_arg_bounds(self):
 
     # bounds properties
 
-    @property
-    def fixed(self):
-        """:class:`set`: Set with names of fixed arguments."""
-        return self._fixed
-
     @property
     def var_bounds(self):
         """:class:`list`: Bounds for the variance.
diff --git a/src/gstools/covmodel/fit.py b/src/gstools/covmodel/fit.py
index e6d6b03d..b40fc845 100755
--- a/src/gstools/covmodel/fit.py
+++ b/src/gstools/covmodel/fit.py
@@ -166,8 +166,6 @@ def fit_variogram(
 
     The fitted parameters will be instantly set in the model.
     """
-    for para in model.fixed:
-        para_select[para] = False
     # preprocess selected parameters
     para, sill, constrain_sill, anis = _pre_para(
         model, para_select, sill, anis
diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index 1c3c9ca0..78a90a7b 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -458,8 +458,6 @@ def set_arg_bounds(model, check_args=True, **kwargs):
     # if variance needs to be resetted, do this at last
     var_bnds = []
     for arg, bounds in kwargs.items():
-        if model._init and arg in model.fixed:
-            raise ValueError(f"Can't set bounds for fixed argument '{arg}'")
         if not check_bounds(bounds):
             raise ValueError(
                 f"Given bounds for '{arg}' are not valid, got: {bounds}"

From 01d1d8233ae44fe63ad84e170a0e68d1b296592b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 12 Aug 2024 00:34:57 +0200
Subject: [PATCH 13/28] CovModel: simplify fitting routines

---
 src/gstools/covmodel/fit.py | 62 +++++++++----------------------------
 1 file changed, 14 insertions(+), 48 deletions(-)

diff --git a/src/gstools/covmodel/fit.py b/src/gstools/covmodel/fit.py
index b40fc845..b5836c0d 100755
--- a/src/gstools/covmodel/fit.py
+++ b/src/gstools/covmodel/fit.py
@@ -19,10 +19,6 @@
 __all__ = ["fit_variogram"]
 
 
-# this should be: set(mod.iso_arg) - set(mod.opt_arg)
-DEFAULT_PARA = ["var", "len_scale", "nugget"]
-
-
 def fit_variogram(
     model,
     x_data,
@@ -263,8 +259,7 @@ def _pre_para(model, para_select, sill, anis):
     else:
         constrain_sill = False
     # select all parameters to be fitted
-    para = {par: True for par in DEFAULT_PARA}
-    para.update({opt: True for opt in model.opt_arg})
+    para = {par: True for par in model.iso_arg}
     # now deselect unwanted parameters
     para.update(para_select)
     # check if anisotropy should be fitted or set
@@ -363,7 +358,7 @@ def _init_curve_fit_para(model, para, init_guess, constrain_sill, sill, anis):
     low_bounds = []
     top_bounds = []
     init_guess_list = []
-    for par in DEFAULT_PARA:
+    for par in model.iso_arg:
         if para[par]:
             low_bounds.append(model.arg_bounds[par][0])
             if par == "var" and constrain_sill:  # var <= sill in this case
@@ -376,16 +371,6 @@ def _init_curve_fit_para(model, para, init_guess, constrain_sill, sill, anis):
                     default=init_guess[par],
                 )
             )
-    for opt in model.opt_arg:
-        if para[opt]:
-            low_bounds.append(model.arg_bounds[opt][0])
-            top_bounds.append(model.arg_bounds[opt][1])
-            init_guess_list.append(
-                _init_guess(
-                    bounds=[low_bounds[-1], top_bounds[-1]],
-                    default=init_guess[opt],
-                )
-            )
     if anis:
         for i in range(model.dim - 1):
             low_bounds.append(model.anis_bounds[0])
@@ -408,34 +393,23 @@ def _init_guess(bounds, default):
 
 def _get_curve(model, para, constrain_sill, sill, anis, is_dir_vario):
     """Create the curve for scipys curve_fit."""
-    var_save = model.var
 
     # we need arg1, otherwise curve_fit throws an error (bug?!)
     def curve(x, arg1, *args):
         """Adapted Variogram function."""
         args = (arg1,) + args
         para_skip = 0
-        opt_skip = 0
-        if para["var"]:
-            model.var = args[para_skip]
-            if constrain_sill:
-                nugget_tmp = sill - model.var
-                # punishment, if resulting nugget out of range for fixed sill
-                if check_arg_in_bounds(model, "nugget", nugget_tmp) > 0:
-                    return np.full_like(x, np.inf)
-                # nugget estimation deselected in this case
-                model.nugget = nugget_tmp
-            para_skip += 1
-        if para["len_scale"]:
-            model.len_scale = args[para_skip]
-            para_skip += 1
-        if para["nugget"]:
-            model.nugget = args[para_skip]
-            para_skip += 1
-        for opt in model.opt_arg:
-            if para[opt]:
-                setattr(model, opt, args[para_skip + opt_skip])
-                opt_skip += 1
+        for par in model.iso_arg:
+            if para[par]:
+                setattr(model, par, args[para_skip])
+                para_skip += 1
+        if constrain_sill:
+            nugget_tmp = sill - model.var
+            # punishment, if resulting nugget out of range for fixed sill
+            if check_arg_in_bounds(model, "nugget", nugget_tmp) > 0:
+                return np.full_like(x, np.inf)
+            # nugget estimation deselected in this case
+            model.nugget = nugget_tmp
         if is_dir_vario:
             if anis:
                 model.anis = args[1 - model.dim :]
@@ -453,21 +427,13 @@ def _post_fitting(model, para, popt, anis, is_dir_vario):
     """Postprocess fitting results and application to model."""
     fit_para = {}
     para_skip = 0
-    opt_skip = 0
-    for par in DEFAULT_PARA:
+    for par in model.iso_arg:
         if para[par]:
             setattr(model, par, popt[para_skip])
             fit_para[par] = popt[para_skip]
             para_skip += 1
         else:
             fit_para[par] = getattr(model, par)
-    for opt in model.opt_arg:
-        if para[opt]:
-            setattr(model, opt, popt[para_skip + opt_skip])
-            fit_para[opt] = popt[para_skip + opt_skip]
-            opt_skip += 1
-        else:
-            fit_para[opt] = getattr(model, opt)
     if is_dir_vario:
         if anis:
             model.anis = popt[1 - model.dim :]

From 418038f521a4f566b8016990db67547be1f39b69 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 12 Aug 2024 11:34:51 +0200
Subject: [PATCH 14/28] CovModel: fix setting integral scale as list of values

---
 src/gstools/covmodel/base.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index 4a1ee76c..a02a4651 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -1004,7 +1004,7 @@ def integral_scale(self, integral_scale):
         old_scale = self.integral_scale
         self.anis = anis
         self.len_scale = self.len_scale * int_scale / old_scale
-        if not np.isclose(self.integral_scale, integral_scale, rtol=1e-3):
+        if not np.isclose(self.integral_scale, int_scale, rtol=1e-3):
             raise ValueError(
                 f"{self.name}: Integral scale could not be set correctly! "
                 "Please just provide a 'len_scale'!"

From d8b037fe994c422fc29c147d3b01ef152e927df5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 12 Aug 2024 12:38:40 +0200
Subject: [PATCH 15/28] no need to set var last anymore

---
 src/gstools/covmodel/tools.py | 15 +++------------
 1 file changed, 3 insertions(+), 12 deletions(-)

diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index 78a90a7b..448dc6c1 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -455,18 +455,14 @@ def set_arg_bounds(model, check_args=True, **kwargs):
         <type> is one of ``"oo"``, ``"cc"``, ``"oc"`` or ``"co"``
         to define if the bounds are open ("o") or closed ("c").
     """
-    # if variance needs to be resetted, do this at last
-    var_bnds = []
     for arg, bounds in kwargs.items():
         if not check_bounds(bounds):
-            raise ValueError(
-                f"Given bounds for '{arg}' are not valid, got: {bounds}"
-            )
+            msg = f"Given bounds for '{arg}' are not valid, got: {bounds}"
+            raise ValueError(msg)
         if arg in model.opt_arg:
             model._opt_arg_bounds[arg] = bounds
         elif arg == "var":
-            var_bnds = bounds
-            continue
+            model._var_bounds = bounds
         elif arg == "len_scale":
             model._len_scale_bounds = bounds
         elif arg == "nugget":
@@ -481,11 +477,6 @@ def set_arg_bounds(model, check_args=True, **kwargs):
                 setattr(model, arg, [def_arg] * (model.dim - 1))
             else:
                 setattr(model, arg, def_arg)
-    # set var last like always
-    if var_bnds:
-        model._var_bounds = var_bnds
-        if check_args and check_arg_in_bounds(model, "var") > 0:
-            model.var = default_arg_from_bounds(var_bnds)
 
 
 def check_arg_bounds(model):

From 0b632253efcb6a1b69f76bf72b393ff2b1e94fe1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 12 Aug 2024 12:38:57 +0200
Subject: [PATCH 16/28] fit: add comment

---
 src/gstools/covmodel/fit.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/gstools/covmodel/fit.py b/src/gstools/covmodel/fit.py
index b5836c0d..5ba398ef 100755
--- a/src/gstools/covmodel/fit.py
+++ b/src/gstools/covmodel/fit.py
@@ -169,7 +169,7 @@ def fit_variogram(
     if not any(para.values()):
         raise ValueError("fit: no parameters selected for fitting.")
     # check curve_fit kwargs
-    curve_fit_kwargs = {} if curve_fit_kwargs is None else curve_fit_kwargs
+    curve_fit_kwargs = curve_fit_kwargs or {}
     # check method
     if method not in ["trf", "dogbox"]:
         raise ValueError("fit: method needs to be either 'trf' or 'dogbox'")
@@ -212,13 +212,13 @@ def fit_variogram(
 
 def _pre_para(model, para_select, sill, anis):
     """Preprocess selected parameters."""
+    # if values given, set them in the model, afterwards all entries are bool
     for par in para_select:
         if par not in model.arg_bounds:
             raise ValueError(f"fit: unknown parameter in selection: {par}")
         if not isinstance(para_select[par], bool):
             setattr(model, par, float(para_select[par]))
             para_select[par] = False
-
     # remove those that were set to True
     para_select = {k: v for k, v in para_select.items() if not v}
     # handling the sill

From 21d0e4a27d8b3dce26a8c2956ea398c0db601c50 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Wed, 14 Aug 2024 12:12:45 +0200
Subject: [PATCH 17/28] add ratio error class; better arg checking routines

---
 src/gstools/covmodel/tools.py | 30 ++++++++++++++++++------------
 1 file changed, 18 insertions(+), 12 deletions(-)

diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index 448dc6c1..50ef04dd 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -6,6 +6,7 @@
 The following classes and functions are provided
 
 .. autosummary::
+   RatioError
    AttributeWarning
    rad_fac
    set_opt_args
@@ -34,6 +35,7 @@
 from gstools.tools.misc import list_format
 
 __all__ = [
+    "RatioError",
     "AttributeWarning",
     "rad_fac",
     "set_opt_args",
@@ -52,6 +54,10 @@
 ]
 
 
+class RatioError(Exception):
+    """Error for invalid ratios in SumModel."""
+
+
 class AttributeWarning(UserWarning):
     """Attribute warning for CovModel class."""
 
@@ -311,7 +317,7 @@ def check_bounds(bounds):
     return True
 
 
-def check_arg_in_bounds(model, arg, val=None):
+def check_arg_in_bounds(model, arg, val=None, error=False):
     """Check if given argument value is in bounds of the given model."""
     if arg not in model.arg_bounds:
         raise ValueError(f"check bounds: unknown argument: {arg}")
@@ -320,6 +326,7 @@ def check_arg_in_bounds(model, arg, val=None):
     val = np.asarray(val)
     error_case = 0
     if len(bnd) == 2:
+        bnd = list(bnd)
         bnd.append("cc")  # use closed intervals by default
     if bnd[2][0] == "c":
         if np.any(val < bnd[0]):
@@ -333,6 +340,15 @@ def check_arg_in_bounds(model, arg, val=None):
     else:
         if np.any(val >= bnd[1]):
             error_case = 4
+    if error:
+        if error_case == 1:
+            raise ValueError(f"{arg} needs to be >= {bnd[0]}, got: {val}")
+        if error_case == 2:
+            raise ValueError(f"{arg} needs to be > {bnd[0]}, got: {val}")
+        if error_case == 3:
+            raise ValueError(f"{arg} needs to be <= {bnd[1]}, got: {val}")
+        if error_case == 4:
+            raise ValueError(f"{arg} needs to be < {bnd[1]}, got: {val}")
     return error_case
 
 
@@ -497,17 +513,7 @@ def check_arg_bounds(model):
     for arg in model.arg_bounds:
         if not model.arg_bounds[arg]:
             continue  # no bounds given during init (called from self.dim)
-        bnd = list(model.arg_bounds[arg])
-        val = getattr(model, arg)
-        error_case = check_arg_in_bounds(model, arg)
-        if error_case == 1:
-            raise ValueError(f"{arg} needs to be >= {bnd[0]}, got: {val}")
-        if error_case == 2:
-            raise ValueError(f"{arg} needs to be > {bnd[0]}, got: {val}")
-        if error_case == 3:
-            raise ValueError(f"{arg} needs to be <= {bnd[1]}, got: {val}")
-        if error_case == 4:
-            raise ValueError(f"{arg} needs to be < {bnd[1]}, got: {val}")
+        check_arg_in_bounds(model, arg, error=True)
 
 
 def set_dim(model, dim):

From e6374db261076351920c3fb1857690c558a57b90 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Thu, 15 Aug 2024 23:26:21 +0200
Subject: [PATCH 18/28] CovModel: better dim setting

---
 src/gstools/covmodel/tools.py | 17 +++++++----------
 1 file changed, 7 insertions(+), 10 deletions(-)

diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index 50ef04dd..a70c8118 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -511,8 +511,6 @@ def check_arg_bounds(model):
     """
     # check var, len_scale, nugget and optional-arguments
     for arg in model.arg_bounds:
-        if not model.arg_bounds[arg]:
-            continue  # no bounds given during init (called from self.dim)
         check_arg_in_bounds(model, arg, error=True)
 
 
@@ -557,16 +555,15 @@ def set_dim(model, dim):
     model._dim = int(dim)
     # create fourier transform just once (recreate for dim change)
     model._sft = SFT(ndim=model.dim, **model.hankel_kw)
-    # recalculate dimension related parameters
-    if model._anis is not None:
-        model._len_scale, model._anis = set_len_anis(
-            model.dim, model._len_scale, model._anis
+    # recalculate dimension related parameters (if model initialized)
+    if model._init:
+        model.len_scale, model.anis = set_len_anis(
+            model.dim, model.len_scale, model.anis
         )
-    if model._angles is not None:
-        model._angles = set_model_angles(
-            model.dim, model._angles, model.latlon, model.temporal
+        model.angles = set_model_angles(
+            model.dim, model.angles, model.latlon, model.temporal
         )
-    model.check_arg_bounds()
+        model.check_arg_bounds()
 
 
 def compare(this, that):

From dcb003bffec9fa2f4e0c1ebf0e174620a0183bd7 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 16 Aug 2024 00:04:00 +0200
Subject: [PATCH 19/28] add sum_tools submodule

---
 src/gstools/covmodel/sum_tools.py | 245 ++++++++++++++++++++++++++++++
 src/gstools/covmodel/tools.py     |   5 -
 2 files changed, 245 insertions(+), 5 deletions(-)
 create mode 100644 src/gstools/covmodel/sum_tools.py

diff --git a/src/gstools/covmodel/sum_tools.py b/src/gstools/covmodel/sum_tools.py
new file mode 100644
index 00000000..a4a1647a
--- /dev/null
+++ b/src/gstools/covmodel/sum_tools.py
@@ -0,0 +1,245 @@
+"""
+GStools subpackage providing tools for sum-models.
+
+.. currentmodule:: gstools.covmodel.sum_tools
+
+The following classes and functions are provided
+
+.. autosummary::
+   RatioError
+   ARG_DEF
+   default_mod_kwargs
+   sum_check
+   sum_default_arg_bounds
+   sum_default_opt_arg_bounds
+   sum_set_norm_var_ratios
+   sum_set_norm_len_ratios
+   sum_model_repr
+"""
+
+import numpy as np
+
+from gstools.covmodel.tools import check_arg_in_bounds
+from gstools.tools import RADIAN_SCALE
+from gstools.tools.misc import list_format
+
+__all__ = [
+    "RatioError",
+    "ARG_DEF",
+    "default_mod_kwargs",
+    "sum_check",
+    "sum_default_arg_bounds",
+    "sum_default_opt_arg_bounds",
+    "sum_set_norm_var_ratios",
+    "sum_set_norm_len_ratios",
+    "sum_model_repr",
+]
+
+
+class RatioError(Exception):
+    """Error for invalid ratios in SumModel."""
+
+
+ARG_DEF = {
+    "dim": 3,
+    "latlon": False,
+    "temporal": False,
+    "geo_scale": RADIAN_SCALE,
+    "spatial_dim": None,
+    "hankel_kw": None,
+}
+"""dict: default model arguments"""
+
+
+def default_mod_kwargs(kwargs):
+    """Generate default model keyword arguments."""
+    mod_kw = {}
+    for arg, default in ARG_DEF.items():
+        mod_kw[arg] = kwargs.get(arg, default)
+    return mod_kw
+
+
+def sum_check(summod):
+    """Check consistency of contained models."""
+    # prevent dim error in anis and angles
+    if any(mod.dim != summod.dim for mod in summod):
+        msg = "SumModel: models need to have same dimension."
+        raise ValueError(msg)
+    if any(mod.latlon != summod.latlon for mod in summod):
+        msg = "SumModel: models need to have same latlon config."
+        raise ValueError(msg)
+    if any(mod.temporal != summod.temporal for mod in summod):
+        msg = "SumModel: models need to have same temporal config."
+        raise ValueError(msg)
+    if not all(np.isclose(mod.nugget, 0) for mod in summod):
+        msg = "SumModel: models need to have 0 nugget."
+        raise ValueError(msg)
+    if not np.allclose([mod.geo_scale for mod in summod], summod.geo_scale):
+        msg = "SumModel: models need to have same geo_scale."
+        raise ValueError(msg)
+    if not all(np.allclose(mod.anis, summod.anis) for mod in summod):
+        msg = "SumModel: models need to have same anisotropy ratios."
+        raise ValueError(msg)
+    if not all(np.allclose(mod.angles, summod.angles) for mod in summod):
+        msg = "SumModel: models need to have same rotation angles."
+        raise ValueError(msg)
+
+
+def sum_default_arg_bounds(summod):
+    """Default boundaries for arguments as dict."""
+    var_bnds = [mod.var_bounds for mod in summod.models]
+    len_bnds = [mod.len_scale_bounds for mod in summod.models]
+    var_lo = sum([bnd[0] for bnd in var_bnds], start=0.0)
+    var_hi = sum([bnd[1] for bnd in var_bnds], start=0.0)
+    len_lo = min([bnd[0] for bnd in len_bnds], default=0.0)
+    len_hi = max([bnd[1] for bnd in len_bnds], default=0.0)
+    res = {
+        "var": (var_lo, var_hi),
+        "len_scale": (len_lo, len_hi),
+        "nugget": (0.0, np.inf, "co"),
+        "anis": (0.0, np.inf, "oo"),
+    }
+    return res
+
+
+def sum_default_opt_arg_bounds(summod):
+    """Defaults boundaries for optional arguments as dict."""
+    bounds = {}
+    for i, mod in enumerate(summod.models):
+        bounds.update(
+            {f"{opt}_{i}": bnd for opt, bnd in mod.opt_arg_bounds.items()}
+        )
+    return bounds
+
+
+def sum_set_norm_var_ratios(summod, ratios, skip=None, var=None):
+    """
+    Set variances of contained models by normalized ratios in [0, 1].
+
+    Ratios are given as normalized ratios in [0, 1] as relative ratio of
+    variance to remaining difference to total variance of the Sum-Model.
+
+    Parameters
+    ----------
+    ratios : iterable
+        Ratios to set. Should have a length of len(models) - len(exclude) - 1
+    skip : iterable, optional
+        Model indices to skip. Should have compatible lenth, by default None
+    var : float, optional
+        Desired variance, by default current variance
+
+    Raises
+    ------
+    ValueError
+        If number of ratios is not matching.
+    """
+    skip = skip or set()
+    if len(summod) != len(ratios) + len(skip) + 1:
+        msg = "SumModel.set_norm_ratios: number of ratios not matching."
+        raise ValueError(msg)
+    ids = range(len(summod))
+    if fail := set(skip) - set(ids):
+        msg = f"SumModel.set_norm_var_ratios: skip ids not valid: {fail}"
+        raise ValueError(msg)
+    var = summod.var if var is None else float(var)
+    check_arg_in_bounds(summod, "var", var, error=True)
+    var_sum = sum(summod.models[i].var for i in skip)
+    if var_sum > var:
+        msg = "SumModel.set_norm_var_ratios: skiped variances to big."
+        raise RatioError(msg)
+    j = 0
+    for i in ids:
+        if i in skip:
+            continue
+        var_diff = var - var_sum
+        # last model gets remaining diff
+        var_set = var_diff * ratios[j] if j < len(ratios) else var_diff
+        summod[i].var = var_set
+        var_sum += var_set
+        j += 1
+
+
+def sum_set_norm_len_ratios(summod, ratios, skip=None, len_scale=None):
+    """
+    Set length scales of contained models by normalized ratios in [0, 1].
+
+    Ratios are given as normalized ratios in [0, 1] as relative ratio of
+    len_scale * var / total_var to remaining difference to
+    total len_scale of the Sum-Model.
+
+    Parameters
+    ----------
+    ratios : iterable
+        Ratios to set. Should have a length of len(models) - len(exclude) - 1
+    skip : iterable, optional
+        Model indices to skip. Should have compatible lenth, by default None
+    len_scale : float, optional
+        Desired len_scale, by default current len_scale
+
+    Raises
+    ------
+    ValueError
+        If number of ratios is not matching.
+    """
+    skip = skip or set()
+    if len(summod) != len(ratios) + len(skip) + 1:
+        msg = "SumModel.set_norm_len_ratios: number of ratios not matching."
+        raise ValueError(msg)
+    ids = range(len(summod))
+    if fail := set(skip) - set(ids):
+        msg = f"SumModel.set_norm_len_ratios: skip ids not valid: {fail}"
+        raise ValueError(msg)
+    len_scale = summod.len_scale if len_scale is None else float(len_scale)
+    check_arg_in_bounds(summod, "len_scale", len_scale, error=True)
+    len_sum = sum(summod[i].len_scale * summod.ratios[i] for i in skip)
+    if len_sum > len_scale:
+        msg = "SumModel.set_norm_len_ratios: skiped length scales to big."
+        raise RatioError(msg)
+    j = 0
+    for i in ids:
+        if i in skip:
+            continue
+        len_diff = len_scale - len_sum
+        # last model gets remaining diff
+        len_set = len_diff * ratios[j] if j < len(ratios) else len_diff
+        summod[i].len_scale = (
+            0.0
+            if np.isclose(summod.ratios[j], 0)
+            else len_set / summod.ratios[j]
+        )
+        len_sum += len_set
+        j += 1
+
+
+def sum_model_repr(summod):  # pragma: no cover
+    """
+    Generate the sum-model string representation.
+
+    Parameters
+    ----------
+    model : :any:`SumModel`
+        The sum-model in use.
+    """
+    m, p = summod, summod._prec
+    ani_str, ang_str, o_str, r_str, p_str = "", "", "", "", ""
+    m_str = ", ".join([mod.name for mod in m.models])
+    t_str = ", temporal=True" if m.temporal else ""
+    d_str = f"latlon={m.latlon}" if m.latlon else f"dim={m.spatial_dim}"
+    if len(m) > 0:
+        m_str += ", "
+        p_str += f", vars={list_format(m.vars, p)}"
+        p_str += f", len_scales={list_format(m.len_scales, p)}"
+    p_str += "" if np.isclose(m.nugget, 0) else f", nugget={m.nugget:.{p}}"
+    for opt in m.opt_arg:
+        o_str += f", {opt}={getattr(m, opt):.{p}}"
+    if m.latlon:
+        if not m.is_isotropic and m.temporal:
+            ani_str = f", anis={m.anis[-1]:.{p}}"
+        if not np.isclose(m.geo_scale, 1):
+            r_str = f", geo_scale={m.geo_scale:.{p}}"
+    else:
+        if not m.is_isotropic:
+            ani_str = f", anis={list_format(m.anis, p)}"
+        if m.do_rotation:
+            ang_str = f", angles={list_format(m.angles, p)}"
+    return f"{m.name}({m_str}{d_str}{t_str}{p_str}{ani_str}{ang_str}{r_str}{o_str})"
diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index a70c8118..52a6e64c 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -6,7 +6,6 @@
 The following classes and functions are provided
 
 .. autosummary::
-   RatioError
    AttributeWarning
    rad_fac
    set_opt_args
@@ -54,10 +53,6 @@
 ]
 
 
-class RatioError(Exception):
-    """Error for invalid ratios in SumModel."""
-
-
 class AttributeWarning(UserWarning):
     """Attribute warning for CovModel class."""
 

From 057c8884791059fdf06de95108f8c12d7c3ebd8a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 16 Aug 2024 00:04:21 +0200
Subject: [PATCH 20/28] add SumModel class

---
 src/gstools/covmodel/base.py | 503 +++++++++++++++++++++++++++++++++++
 1 file changed, 503 insertions(+)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index a02a4651..8e694b26 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -18,9 +18,19 @@
 
 from gstools.covmodel import plot
 from gstools.covmodel.fit import fit_variogram
+from gstools.covmodel.sum_tools import (
+    default_mod_kwargs,
+    sum_check,
+    sum_default_arg_bounds,
+    sum_default_opt_arg_bounds,
+    sum_model_repr,
+    sum_set_norm_len_ratios,
+    sum_set_norm_var_ratios,
+)
 from gstools.covmodel.tools import (
     _init_subclass,
     check_arg_bounds,
+    check_arg_in_bounds,
     compare,
     default_arg_from_bounds,
     model_repr,
@@ -1156,3 +1166,496 @@ def __setattr__(self, name, value):
     def __repr__(self):
         """Return String representation."""
         return model_repr(self)
+
+
+class SumModel(CovModel):
+    r"""Class for sums of covariance models.
+
+    Parameters
+    ----------
+    *models
+        tuple of :any:`CovModel` instances of subclasses to sum.
+    dim : :class:`int`, optional
+        dimension of the model.
+        Includes the temporal dimension if temporal is true.
+        To specify only the spatial dimension in that case, use `spatial_dim`.
+        Default: ``3``
+    vars : :class:`list` of :class:`float`, optional
+        variances of the models. Will reset present variances.
+    len_scales : :class:`list` of :class:`float`, optional
+        length scale of the models. Will reset present length scales.
+    nugget : :class:`float`, optional
+        nugget of the sum-model. All summed models will a nugget of zero.
+        Default: ``0.0``
+    anis : :class:`float` or :class:`list`, optional
+        anisotropy ratios in the transversal directions [e_y, e_z].
+
+            * e_y = l_y / l_x
+            * e_z = l_z / l_x
+
+        If only one value is given in 3D, e_y will be set to 1.
+        This value will be ignored, if multiple len_scales are given.
+        Default: ``1.0``
+    angles : :class:`float` or :class:`list`, optional
+        angles of rotation (given in rad):
+
+            * in 2D: given as rotation around z-axis
+            * in 3D: given by yaw, pitch, and roll (known as Tait–Bryan angles)
+
+         Default: ``0.0``
+    integral_scale : :class:`float` or :class:`list` or :any:`None`, optional
+        If given, ``len_scale`` will be ignored and recalculated,
+        so that the integral scale of the model matches the given one.
+        Default: :any:`None`
+    rescale : :class:`float` or :any:`None`, optional
+        Optional rescaling factor to divide the length scale with.
+        This could be used for unit conversion or rescaling the length scale
+        to coincide with e.g. the integral scale.
+        Will be set by each model individually.
+        Default: :any:`None`
+    latlon : :class:`bool`, optional
+        Whether the model is describing 2D fields on earths surface described
+        by latitude and longitude. When using this, the model will internally
+        use the associated 'Yadrenko' model to represent a valid model.
+        This means, the spatial distance :math:`r` will be replaced by
+        :math:`2\sin(\alpha/2)`, where :math:`\alpha` is the great-circle
+        distance, which is equal to the spatial distance of two points in 3D.
+        As a consequence, `dim` will be set to `3` and anisotropy will be
+        disabled. `geo_scale` can be set to e.g. earth's radius,
+        to have a meaningful `len_scale` parameter.
+        Default: False
+    geo_scale : :class:`float`, optional
+        Geographic unit scaling in case of latlon coordinates to get a
+        meaningful length scale unit.
+        By default, len_scale is assumed to be in radians with latlon=True.
+        Can be set to :any:`KM_SCALE` to have len_scale in km or
+        :any:`DEGREE_SCALE` to have len_scale in degrees.
+        Default: :any:`RADIAN_SCALE`
+    temporal : :class:`bool`, optional
+        Create a metric spatio-temporal covariance model.
+        Setting this to true will increase `dim` and `field_dim` by 1.
+        `spatial_dim` will be `field_dim - 1`.
+        The time-dimension is appended, meaning the pos tuple is (x,y,z,...,t).
+        Default: False
+    spatial_dim : :class:`int`, optional
+        spatial dimension of the model.
+        If given, the model dimension will be determined from this spatial dimension
+        and the possible temporal dimension if temporal is ture.
+        Default: None
+    var : :class:`float`, optional
+        Total variance of the sum-model. Will evenly scale present variances.
+    len_scale : :class:`float` or :class:`list`, optional
+        Total length scale of the sum-model. Will evenly scale present length scales.
+    **opt_arg
+        Optional arguments of the sub-models will have and added index of the sub-model.
+        Also covers ``var_<i>`` and ``length_scale_<i>``.
+    """
+
+    def __init__(self, *models, **kwargs):
+        self._init = False
+        self._models = []
+        add_nug = 0.0
+        for mod in models:
+            if isinstance(mod, type) and issubclass(mod, SumModel):
+                continue  # treat un-init sum-model as nugget model with 0 nugget
+            if isinstance(mod, SumModel):
+                self._models += mod.models
+                add_nug += mod.nugget
+            elif isinstance(mod, CovModel):
+                self._models.append(mod)
+            elif isinstance(mod, type) and issubclass(mod, CovModel):
+                self._models.append(mod(**default_mod_kwargs(kwargs)))
+            else:
+                msg = "SumModel: models need to be instances or subclasses of CovModel."
+                raise ValueError(msg)
+        # handle parameters when only Nugget models given
+        if models and not self.models:
+            for mod in models:
+                if not isinstance(mod, type):
+                    kwargs.setdefault("dim", mod.dim)
+                    kwargs.setdefault("latlon", mod.latlon)
+                    kwargs.setdefault("temporal", mod.temporal)
+                    kwargs.setdefault("geo_scale", mod.geo_scale)
+                    kwargs.setdefault("anis", mod.anis)
+                    kwargs.setdefault("angles", mod.angles)
+                    break
+        # pop entries that can't be re-set
+        self._latlon = bool(
+            kwargs.pop(
+                "latlon", self.models[0].latlon if self.models else False
+            )
+        )
+        self._temporal = bool(
+            kwargs.pop(
+                "temporal", self.models[0].temporal if self.models else False
+            )
+        )
+        self._geo_scale = float(
+            kwargs.pop(
+                "geo_scale",
+                self.models[0].geo_scale if self.models else RADIAN_SCALE,
+            )
+        )
+        var_set = kwargs.pop("var", None)
+        len_set = kwargs.pop("len_scale", None)
+        # convert nugget
+        self._nugget = float(
+            kwargs.pop(
+                "nugget",
+                sum((mod.nugget for mod in self.models), 0.0) + add_nug,
+            )
+        )
+        for mod in self.models:
+            mod._nugget = 0.0
+        # prepare dim setting
+        if "spatial_dim" in kwargs:
+            spatial_dim = kwargs.pop("spatial_dim")
+            if spatial_dim is not None:
+                kwargs["dim"] = spatial_dim + int(self.temporal)
+        self._dim = None
+        self._hankel_kw = {}
+        self._sft = None
+        self.dim = kwargs.get("dim", self.models[0].dim if self.models else 3)
+        # prepare parameters (they are checked in dim setting)
+        self._rescale = 1.0
+        anis = kwargs.get("anis", self.models[0].anis if self.models else 1)
+        angles = kwargs.get(
+            "angles", self.models[0].angles if self.models else 0
+        )
+        _, self._anis = set_len_anis(self.dim, 1.0, anis, self.latlon)
+        self._angles = set_model_angles(
+            self.dim, angles, self.latlon, self.temporal
+        )
+        # prepare parameters boundaries
+        self._var_bounds = None
+        self._len_scale_bounds = None
+        self._nugget_bounds = None
+        self._anis_bounds = None
+        self._opt_arg_bounds = {}
+        bounds = self.default_arg_bounds()
+        bounds.update(self.default_opt_arg_bounds())
+        self.set_arg_bounds(check_args=False, **bounds)
+        # opt arg determining
+        self._prec = 3
+        self._init = True
+        # set remaining args
+        for arg, val in kwargs.items():
+            setattr(self, arg, val)
+        if var_set is not None:
+            self.var = var_set
+        if len_set is not None:
+            self.len_scale = len_set
+        # check for consistency
+        self.check()
+
+    def __iter__(self):
+        return iter(self.models)
+
+    def __len__(self):
+        return len(self.models)
+
+    def __contains__(self, item):
+        return item in self.models
+
+    def __getitem__(self, key):
+        return self.models[key]
+
+    def check(self):
+        """Check consistency of contained models."""
+        sum_check(self)
+
+    def default_arg_bounds(self):
+        """Default boundaries for arguments as dict."""
+        return sum_default_arg_bounds(self)
+
+    def default_opt_arg_bounds(self):
+        """Defaults boundaries for optional arguments as dict."""
+        return sum_default_opt_arg_bounds(self)
+
+    def set_norm_var_ratios(self, ratios, skip=None, var=None):
+        """
+        Set variances of contained models by normalized ratios in [0, 1].
+
+        Ratios are given as normalized ratios in [0, 1] as relative ratio of
+        variance to remaining difference to total variance of the Sum-Model.
+
+        Parameters
+        ----------
+        ratios : iterable
+            Ratios to set. Should have a length of len(models) - len(exclude) - 1
+        skip : iterable, optional
+            Model indices to skip. Should have compatible lenth, by default None
+        var : float, optional
+            Desired variance, by default current variance
+
+        Raises
+        ------
+        ValueError
+            If number of ratios is not matching.
+        """
+        sum_set_norm_var_ratios(self, ratios, skip, var)
+
+    def set_norm_len_ratios(self, ratios, skip=None, len_scale=None):
+        """
+        Set length scales of contained models by normalized ratios in [0, 1].
+
+        Ratios are given as normalized ratios in [0, 1] as relative ratio of
+        len_scale * var / total_var to remaining difference to
+        total len_scale of the Sum-Model.
+
+        Parameters
+        ----------
+        ratios : iterable
+            Ratios to set. Should have a length of len(models) - len(exclude) - 1
+        skip : iterable, optional
+            Model indices to skip. Should have compatible lenth, by default None
+        len_scale : float, optional
+            Desired len_scale, by default current len_scale
+
+        Raises
+        ------
+        ValueError
+            If number of ratios is not matching.
+        """
+        sum_set_norm_len_ratios(self, ratios, skip, len_scale)
+
+    @property
+    def hankel_kw(self):
+        """:class:`dict`: :any:`hankel.SymmetricFourierTransform` kwargs."""
+        return self._hankel_kw
+
+    @property
+    def models(self):
+        """:class:`tuple`: The summed models."""
+        return self._models
+
+    @property
+    def geo_scale(self):
+        """:class:`float`: Geographic scaling for geographical coords."""
+        return self._geo_scale
+
+    @geo_scale.setter
+    def geo_scale(self, geo_scale):
+        self._geo_scale = abs(float(geo_scale))
+        for mod in self.models:
+            mod.geo_scale = geo_scale
+
+    @property
+    def dim(self):
+        """:class:`int`: The dimension of the model."""
+        return self._dim
+
+    @dim.setter
+    def dim(self, dim):
+        set_dim(self, dim)
+        for mod in self.models:
+            mod.dim = dim
+
+    @property
+    def var(self):
+        """:class:`float`: The variance of the model."""
+        return sum((var for var in self.vars), 0.0)
+
+    @var.setter
+    def var(self, var):
+        for mod, rat in zip(self.models, self.ratios):
+            mod.var = rat * var
+        if not self.models and not np.isclose(var, 0):
+            msg = f"{self.name}: variance needs to be 0."
+            raise ValueError(msg)
+        check_arg_in_bounds(self, "var", error=True)
+        check_arg_in_bounds(self, "len_scale", error=True)
+
+    @property
+    def vars(self):
+        """:class:`list`: The variances of the models."""
+        return [mod.var for mod in self.models]
+
+    @vars.setter
+    def vars(self, vars):
+        if len(vars) != len(self):
+            msg = "SumModel: number of given variances not matching"
+            raise ValueError(msg)
+        for mod, var in zip(self.models, vars):
+            mod.var = var
+        check_arg_in_bounds(self, "var", error=True)
+        check_arg_in_bounds(self, "len_scale", error=True)
+
+    @property
+    def len_scale(self):
+        """:class:`float`: The main length scale of the model."""
+        return sum(
+            (
+                mod.len_scale * rat
+                for mod, rat in zip(self.models, self.ratios)
+            ),
+            0.0,
+        )
+
+    @len_scale.setter
+    def len_scale(self, len_scale):
+        len_scale, anis = set_len_anis(
+            self.dim, len_scale, self.anis, self.latlon
+        )
+        old_scale = self.len_scale
+        self.anis = anis
+        for mod in self.models:
+            mod.len_scale = mod.len_scale * len_scale / old_scale
+        if not self.models and not np.isclose(len_scale, 0):
+            msg = f"{self.name}: length scale needs to be 0."
+            raise ValueError(msg)
+        check_arg_in_bounds(self, "len_scale", error=True)
+
+    @property
+    def len_scales(self):
+        """:class:`list`: The main length scales of the models."""
+        return [mod.len_scale for mod in self.models]
+
+    @len_scales.setter
+    def len_scales(self, len_scales):
+        if len(len_scales) != len(self):
+            msg = "SumModel: number of given length scales not matching"
+            raise ValueError(msg)
+        for mod, len_scale in zip(self.models, len_scales):
+            mod.len_scale = len_scale
+        check_arg_in_bounds(self, "len_scale", error=True)
+
+    @property
+    def anis(self):
+        """:class:`numpy.ndarray`: The anisotropy factors of the model."""
+        return self._anis
+
+    @anis.setter
+    def anis(self, anis):
+        _, self._anis = set_len_anis(self.dim, 1.0, anis, self.latlon)
+        for mod in self.models:
+            mod.anis = anis
+        check_arg_in_bounds(self, "anis", error=True)
+
+    @property
+    def angles(self):
+        """:class:`numpy.ndarray`: Rotation angles (in rad) of the model."""
+        return self._angles
+
+    @angles.setter
+    def angles(self, angles):
+        self._angles = set_model_angles(
+            self.dim, angles, self.latlon, self.temporal
+        )
+        for mod in self.models:
+            mod.angles = angles
+
+    @property
+    def ratios(self):
+        var = self.var
+        if np.isclose(var, 0) and len(self) > 0:
+            return np.full(len(self), 1 / len(self))
+        return np.array([mod.var / var for mod in self.models])
+
+    @ratios.setter
+    def ratios(self, ratios):
+        if len(ratios) != len(self):
+            msg = "SumModel.ratios: wrong number of given ratios."
+            raise ValueError(msg)
+        if ratios and not np.isclose(np.sum(ratios), 1):
+            msg = "SumModel.ratios: given ratios do not sum to 1."
+            raise ValueError(msg)
+        var = self.var
+        for mod, rat in zip(self.models, ratios):
+            mod.var = var * rat
+        check_arg_in_bounds(self, "var", error=True)
+        check_arg_in_bounds(self, "len_scale", error=True)
+
+    def calc_integral_scale(self):
+        return sum(
+            (
+                mod.integral_scale * rat
+                for mod, rat in zip(self.models, self.ratios)
+            ),
+            0.0,
+        )
+
+    def spectral_density(self, k):
+        return sum(
+            (
+                mod.spectral_density(k) * rat
+                for mod, rat in zip(self.models, self.ratios)
+            ),
+            np.zeros_like(k, dtype=np.double),
+        )
+
+    def correlation(self, r):
+        return sum(
+            (
+                mod.correlation(r) * rat
+                for mod, rat in zip(self.models, self.ratios)
+            ),
+            np.zeros_like(r, dtype=np.double),
+        )
+
+    @property
+    def opt_arg(self):
+        """:class:`list` of :class:`str`: Names of the optional arguments."""
+        return sum(
+            [
+                [f"{opt}_{i}" for opt in mod.opt_arg]
+                for i, mod in enumerate(self.models)
+            ],
+            [],
+        )
+
+    @property
+    def sub_arg(self):
+        """:class:`list` of :class:`str`: Names of the sub-arguments for var and len_scale."""
+        return sum(
+            [
+                [f"{o}_{i}" for o in ["var", "len_scale"]]
+                for i, mod in enumerate(self.models)
+            ],
+            [],
+        )
+
+    def __setattr__(self, name, value):
+        """Set an attribute."""
+        sub_arg = False
+        if getattr(self, "_init", False):
+            for i, mod in enumerate(self.models):
+                if name == f"var_{i}":
+                    mod.var = value
+                    sub_arg = True
+                if name == f"len_scale_{i}":
+                    mod.len_scale = value
+                    sub_arg = True
+                if name == f"integral_scale_{i}":
+                    mod.integral_scale = value
+                    sub_arg = True
+                for opt in mod.opt_arg:
+                    if name == f"{opt}_{i}":
+                        setattr(mod, opt, value)
+                        sub_arg = True
+                if sub_arg:
+                    break
+        if sub_arg:
+            self.check_arg_bounds()
+        else:
+            super().__setattr__(name, value)
+
+    def __getattr__(self, name):
+        """Get an attribute."""
+        # __getattr__ is only called when an attribute is not found in the usual places
+        if name != "_init" and getattr(self, "_init", False):
+            for i, mod in enumerate(self.models):
+                if name == f"var_{i}":
+                    return mod.var
+                if name == f"len_scale_{i}":
+                    return mod.len_scale
+                if name == f"integral_scale_{i}":
+                    return mod.integral_scale
+                for opt in mod.opt_arg:
+                    if name == f"{opt}_{i}":
+                        return getattr(mod, opt)
+        raise AttributeError(f"'{self.name}' object has no attribute '{name}'")
+
+    def __repr__(self):
+        """Return String representation."""
+        return sum_model_repr(self)

From 656125a4c37345b7bd4cea12639e52bb538f31ad Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 16 Aug 2024 00:09:43 +0200
Subject: [PATCH 21/28] add pure Nugget model

---
 src/gstools/__init__.py          |  6 +++
 src/gstools/covmodel/__init__.py |  7 +++-
 src/gstools/covmodel/models.py   | 67 +++++++++++++++++++++++++++++++-
 3 files changed, 78 insertions(+), 2 deletions(-)

diff --git a/src/gstools/__init__.py b/src/gstools/__init__.py
index 11e63a2b..7488dc9c 100644
--- a/src/gstools/__init__.py
+++ b/src/gstools/__init__.py
@@ -54,6 +54,7 @@
 
 .. autosummary::
    CovModel
+   SumModel
 
 Covariance Models
 ^^^^^^^^^^^^^^^^^
@@ -62,6 +63,7 @@
 ~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 .. autosummary::
+   Nugget
    Gaussian
    Exponential
    Matern
@@ -153,9 +155,11 @@
     JBessel,
     Linear,
     Matern,
+    Nugget,
     Rational,
     Spherical,
     Stable,
+    SumModel,
     SuperSpherical,
     TPLExponential,
     TPLGaussian,
@@ -198,6 +202,8 @@
 __all__ += ["transform", "normalizer", "config"]
 __all__ += [
     "CovModel",
+    "SumModel",
+    "Nugget",
     "Gaussian",
     "Exponential",
     "Matern",
diff --git a/src/gstools/covmodel/__init__.py b/src/gstools/covmodel/__init__.py
index 28ab81f2..76920c61 100644
--- a/src/gstools/covmodel/__init__.py
+++ b/src/gstools/covmodel/__init__.py
@@ -19,6 +19,7 @@
    :toctree:
 
    CovModel
+   SumModel
 
 Covariance Models
 ^^^^^^^^^^^^^^^^^
@@ -27,6 +28,7 @@
 .. autosummary::
    :toctree:
 
+   Nugget
    Gaussian
    Exponential
    Matern
@@ -53,7 +55,7 @@
    TPLSimple
 """
 
-from gstools.covmodel.base import CovModel
+from gstools.covmodel.base import CovModel, SumModel
 from gstools.covmodel.models import (
     Circular,
     Cubic,
@@ -64,6 +66,7 @@
     JBessel,
     Linear,
     Matern,
+    Nugget,
     Rational,
     Spherical,
     Stable,
@@ -78,6 +81,8 @@
 
 __all__ = [
     "CovModel",
+    "SumModel",
+    "Nugget",
     "Gaussian",
     "Exponential",
     "Matern",
diff --git a/src/gstools/covmodel/models.py b/src/gstools/covmodel/models.py
index b1a9d68e..80dbd705 100644
--- a/src/gstools/covmodel/models.py
+++ b/src/gstools/covmodel/models.py
@@ -6,6 +6,7 @@
 The following classes are provided
 
 .. autosummary::
+   Nugget
    Gaussian
    Exponential
    Matern
@@ -27,11 +28,12 @@
 import numpy as np
 from scipy import special as sps
 
-from gstools.covmodel.base import CovModel
+from gstools.covmodel.base import CovModel, SumModel
 from gstools.covmodel.tools import AttributeWarning
 from gstools.tools.special import exp_int, inc_gamma_low
 
 __all__ = [
+    "Nugget",
     "Gaussian",
     "Exponential",
     "Matern",
@@ -48,6 +50,69 @@
 ]
 
 
+class Nugget(SumModel):
+    r"""Pure nugget model.
+
+    Parameters
+    ----------
+    dim : :class:`int`, optional
+        dimension of the model.
+        Includes the temporal dimension if temporal is true.
+        To specify only the spatial dimension in that case, use `spatial_dim`.
+        Default: ``3``
+    nugget : :class:`float`, optional
+        nugget of the model. Default: ``0.0``
+    anis : :class:`float` or :class:`list`, optional
+        anisotropy ratios in the transversal directions [e_y, e_z].
+
+            * e_y = l_y / l_x
+            * e_z = l_z / l_x
+
+        If only one value is given in 3D, e_y will be set to 1.
+        This value will be ignored, if multiple len_scales are given.
+        Default: ``1.0``
+    angles : :class:`float` or :class:`list`, optional
+        angles of rotation (given in rad):
+
+            * in 2D: given as rotation around z-axis
+            * in 3D: given by yaw, pitch, and roll (known as Tait–Bryan angles)
+
+         Default: ``0.0``
+    latlon : :class:`bool`, optional
+        Whether the model is describing 2D fields on earths surface described
+        by latitude and longitude. When using this, the model will internally
+        use the associated 'Yadrenko' model to represent a valid model.
+        This means, the spatial distance :math:`r` will be replaced by
+        :math:`2\sin(\alpha/2)`, where :math:`\alpha` is the great-circle
+        distance, which is equal to the spatial distance of two points in 3D.
+        As a consequence, `dim` will be set to `3` and anisotropy will be
+        disabled. `geo_scale` can be set to e.g. earth's radius,
+        to have a meaningful `len_scale` parameter.
+        Default: False
+    geo_scale : :class:`float`, optional
+        Geographic unit scaling in case of latlon coordinates to get a
+        meaningful length scale unit.
+        By default, len_scale is assumed to be in radians with latlon=True.
+        Can be set to :any:`KM_SCALE` to have len_scale in km or
+        :any:`DEGREE_SCALE` to have len_scale in degrees.
+        Default: :any:`RADIAN_SCALE`
+    temporal : :class:`bool`, optional
+        Create a metric spatio-temporal covariance model.
+        Setting this to true will increase `dim` and `field_dim` by 1.
+        `spatial_dim` will be `field_dim - 1`.
+        The time-dimension is appended, meaning the pos tuple is (x,y,z,...,t).
+        Default: False
+    spatial_dim : :class:`int`, optional
+        spatial dimension of the model.
+        If given, the model dimension will be determined from this spatial dimension
+        and the possible temporal dimension if temporal is ture.
+        Default: None
+    """
+
+    def __init__(self, **kwargs):
+        super().__init__(**kwargs)
+
+
 class Gaussian(CovModel):
     r"""The Gaussian covariance model.
 

From dbdfa27fabcf5eb072ac0c43085c77d6bd008d74 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 16 Aug 2024 00:26:32 +0200
Subject: [PATCH 22/28] CovModel: let the sum magic happen

---
 src/gstools/covmodel/base.py | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index 8e694b26..68af58d0 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -1163,6 +1163,14 @@ def __setattr__(self, name, value):
         if getattr(self, "_init", False) and name in self.opt_arg:
             self.check_arg_bounds()
 
+    def __add__(self, other):
+        """Add two covariance models and return a SumModel."""
+        return SumModel(self, other)
+
+    def __radd__(self, other):
+        """Add two covariance models and return a SumModel."""
+        return SumModel(self, other)
+
     def __repr__(self):
         """Return String representation."""
         return model_repr(self)

From 2858f063665ffb2b1d7b5a921ac25609f47c7835 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 16 Aug 2024 00:35:53 +0200
Subject: [PATCH 23/28] pylint fixes

---
 src/gstools/covmodel/base.py      | 10 ++++++----
 src/gstools/covmodel/models.py    |  2 +-
 src/gstools/covmodel/sum_tools.py |  9 +++++----
 src/gstools/covmodel/tools.py     |  1 -
 4 files changed, 12 insertions(+), 10 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index 68af58d0..a495d80b 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -9,7 +9,7 @@
    CovModel
 """
 
-# pylint: disable=C0103, R0201, E1101, C0302, W0613
+# pylint: disable=C0103, R0201, E1101, C0302, W0613, W0231
 import copy
 
 import numpy as np
@@ -1480,11 +1480,11 @@ def vars(self):
         return [mod.var for mod in self.models]
 
     @vars.setter
-    def vars(self, vars):
-        if len(vars) != len(self):
+    def vars(self, variances):
+        if len(variances) != len(self):
             msg = "SumModel: number of given variances not matching"
             raise ValueError(msg)
-        for mod, var in zip(self.models, vars):
+        for mod, var in zip(self.models, variances):
             mod.var = var
         check_arg_in_bounds(self, "var", error=True)
         check_arg_in_bounds(self, "len_scale", error=True)
@@ -1555,6 +1555,7 @@ def angles(self, angles):
 
     @property
     def ratios(self):
+        """:class:`numpy.ndarray`: Variance ratios of the sub-models."""
         var = self.var
         if np.isclose(var, 0) and len(self) > 0:
             return np.full(len(self), 1 / len(self))
@@ -1593,6 +1594,7 @@ def spectral_density(self, k):
         )
 
     def correlation(self, r):
+        """SumModel correlation function."""
         return sum(
             (
                 mod.correlation(r) * rat
diff --git a/src/gstools/covmodel/models.py b/src/gstools/covmodel/models.py
index 80dbd705..7c1cd836 100644
--- a/src/gstools/covmodel/models.py
+++ b/src/gstools/covmodel/models.py
@@ -22,7 +22,7 @@
    JBessel
 """
 
-# pylint: disable=C0103, E1101, R0201
+# pylint: disable=C0103, C0302, E1101, R0201
 import warnings
 
 import numpy as np
diff --git a/src/gstools/covmodel/sum_tools.py b/src/gstools/covmodel/sum_tools.py
index a4a1647a..c4b9a90e 100644
--- a/src/gstools/covmodel/sum_tools.py
+++ b/src/gstools/covmodel/sum_tools.py
@@ -17,6 +17,7 @@
    sum_model_repr
 """
 
+# pylint: disable=W0212
 import numpy as np
 
 from gstools.covmodel.tools import check_arg_in_bounds
@@ -89,10 +90,10 @@ def sum_default_arg_bounds(summod):
     """Default boundaries for arguments as dict."""
     var_bnds = [mod.var_bounds for mod in summod.models]
     len_bnds = [mod.len_scale_bounds for mod in summod.models]
-    var_lo = sum([bnd[0] for bnd in var_bnds], start=0.0)
-    var_hi = sum([bnd[1] for bnd in var_bnds], start=0.0)
-    len_lo = min([bnd[0] for bnd in len_bnds], default=0.0)
-    len_hi = max([bnd[1] for bnd in len_bnds], default=0.0)
+    var_lo = sum((bnd[0] for bnd in var_bnds), start=0.0)
+    var_hi = sum((bnd[1] for bnd in var_bnds), start=0.0)
+    len_lo = min((bnd[0] for bnd in len_bnds), default=0.0)
+    len_hi = max((bnd[1] for bnd in len_bnds), default=0.0)
     res = {
         "var": (var_lo, var_hi),
         "len_scale": (len_lo, len_hi),
diff --git a/src/gstools/covmodel/tools.py b/src/gstools/covmodel/tools.py
index 52a6e64c..69bf963b 100644
--- a/src/gstools/covmodel/tools.py
+++ b/src/gstools/covmodel/tools.py
@@ -34,7 +34,6 @@
 from gstools.tools.misc import list_format
 
 __all__ = [
-    "RatioError",
     "AttributeWarning",
     "rad_fac",
     "set_opt_args",

From 947619a0428e716e7b3ee78952b631be3c24824d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 16 Aug 2024 00:40:47 +0200
Subject: [PATCH 24/28] fix doc-string of SumModel for docs

---
 src/gstools/covmodel/base.py | 12 ++++++++++++
 1 file changed, 12 insertions(+)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index a495d80b..252bdeb3 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -1356,6 +1356,18 @@ def __init__(self, *models, **kwargs):
         # check for consistency
         self.check()
 
+    def __init_subclass__(cls):
+        """Initialize gstools sum-model."""
+        _init_subclass(cls)
+        # overridden functions get standard doc if no new doc was created
+        ign = ["__", "variogram", "covariance", "cor"]
+        for att, attr_cls in cls.__dict__.items():
+            if any(att.startswith(i) for i in ign) or att not in dir(CovModel):
+                continue
+            attr_doc = getattr(CovModel, att).__doc__
+            if attr_cls.__doc__ is None:
+                attr_cls.__doc__ = attr_doc
+
     def __iter__(self):
         return iter(self.models)
 

From 480fa32e8d6d227ac9e8039e4dabc222951adea0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 16 Aug 2024 00:57:54 +0200
Subject: [PATCH 25/28] CovModel: add switch to add doc string

---
 src/gstools/covmodel/base.py | 19 ++++++-------------
 1 file changed, 6 insertions(+), 13 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index 252bdeb3..e080ba20 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -147,6 +147,8 @@ class CovModel:
         If present, they are described in the section `Other Parameters`.
     """
 
+    _add_doc = True
+
     def __init__(
         self,
         dim=3,
@@ -242,7 +244,8 @@ def __init_subclass__(cls):
         # modify the docstrings: class docstring gets attributes added
         if cls.__doc__ is None:
             cls.__doc__ = "User defined GSTools Covariance-Model."
-        cls.__doc__ += CovModel.__doc__[45:]
+        if cls._add_doc:
+            cls.__doc__ += CovModel.__doc__[45:]
         # overridden functions get standard doc if no new doc was created
         ign = ["__", "variogram", "covariance", "cor"]
         for att, attr_cls in cls.__dict__.items():
@@ -1259,6 +1262,8 @@ class SumModel(CovModel):
         Also covers ``var_<i>`` and ``length_scale_<i>``.
     """
 
+    _add_doc = False
+
     def __init__(self, *models, **kwargs):
         self._init = False
         self._models = []
@@ -1356,18 +1361,6 @@ def __init__(self, *models, **kwargs):
         # check for consistency
         self.check()
 
-    def __init_subclass__(cls):
-        """Initialize gstools sum-model."""
-        _init_subclass(cls)
-        # overridden functions get standard doc if no new doc was created
-        ign = ["__", "variogram", "covariance", "cor"]
-        for att, attr_cls in cls.__dict__.items():
-            if any(att.startswith(i) for i in ign) or att not in dir(CovModel):
-                continue
-            attr_doc = getattr(CovModel, att).__doc__
-            if attr_cls.__doc__ is None:
-                attr_cls.__doc__ = attr_doc
-
     def __iter__(self):
         return iter(self.models)
 

From 171efbad0cbb1f55523be315b6db053ba8414a44 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Fri, 16 Aug 2024 00:58:09 +0200
Subject: [PATCH 26/28] Fourier: fix doc

---
 src/gstools/field/generator.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/gstools/field/generator.py b/src/gstools/field/generator.py
index 89914785..83d13816 100755
--- a/src/gstools/field/generator.py
+++ b/src/gstools/field/generator.py
@@ -736,7 +736,7 @@ def update(self, model=None, seed=np.nan, period=None, mode_no=None):
             the seed of the random number generator.
             If :any:`None`, a random seed is used. If :any:`numpy.nan`,
             the actual seed will be kept. Default: :any:`numpy.nan`
-        period : :class:`list` or :any:`None, optional
+        period : :class:`list` or :any:`None`, optional
             The spatial periodicity of the field, is often the domain size.
         mode_no : :class:`list` or :any:`None`, optional
             Number of Fourier modes per dimension.

From e7838cf023ceff961054426e7b6eb0a169d32601 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 19 Aug 2024 11:30:24 +0200
Subject: [PATCH 27/28] SumModel: models need to either be all instances or all
 subclasses of CovModel

---
 src/gstools/covmodel/base.py | 57 +++++++++++++++++++++++++++++-------
 1 file changed, 46 insertions(+), 11 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index e080ba20..dd7ab2ee 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -1182,15 +1182,32 @@ def __repr__(self):
 class SumModel(CovModel):
     r"""Class for sums of covariance models.
 
+    This class represents sums of covariance models. The nugget of
+    each contained model will be set to zero and the sum model will
+    have its own nugget.
+    The variance of the sum model is the sum of the sub model variances
+    and the length scale of the sum model is the variance-weighted sum
+    of the length scales of the sub models. This is motivated by the fact,
+    that the integral scale of the sum model is equal to the variance-weighted
+    sum of the integral scales of the sub models.
+    An empty sum represents a pure Nugget model.
+    Resetting the total variance or the total length scale will evenly
+    scale the variances or length scales of the sub models.
+
     Parameters
     ----------
     *models
         tuple of :any:`CovModel` instances of subclasses to sum.
+        All models will get a nugget of zero and the nugget will
+        be set in the SumModel directly.
+        Models need to have matching temporal setting,
+        latlon setting, anis, angles and geo_scale.
+        The model dimension will be specified by the first given model.
     dim : :class:`int`, optional
         dimension of the model.
         Includes the temporal dimension if temporal is true.
         To specify only the spatial dimension in that case, use `spatial_dim`.
-        Default: ``3``
+        Default: ``3`` or dimension of the first given model (if instance).
     vars : :class:`list` of :class:`float`, optional
         variances of the models. Will reset present variances.
     len_scales : :class:`list` of :class:`float`, optional
@@ -1206,14 +1223,14 @@ class SumModel(CovModel):
 
         If only one value is given in 3D, e_y will be set to 1.
         This value will be ignored, if multiple len_scales are given.
-        Default: ``1.0``
+        Default: ``1.0`` or anis of the first given model (if instance).
     angles : :class:`float` or :class:`list`, optional
         angles of rotation (given in rad):
 
             * in 2D: given as rotation around z-axis
             * in 3D: given by yaw, pitch, and roll (known as Tait–Bryan angles)
 
-         Default: ``0.0``
+         Default: ``0.0`` or angles of the first given model (if instance).
     integral_scale : :class:`float` or :class:`list` or :any:`None`, optional
         If given, ``len_scale`` will be ignored and recalculated,
         so that the integral scale of the model matches the given one.
@@ -1234,20 +1251,20 @@ class SumModel(CovModel):
         As a consequence, `dim` will be set to `3` and anisotropy will be
         disabled. `geo_scale` can be set to e.g. earth's radius,
         to have a meaningful `len_scale` parameter.
-        Default: False
+        Default: False or latlon config of the first given model (if instance).
     geo_scale : :class:`float`, optional
         Geographic unit scaling in case of latlon coordinates to get a
         meaningful length scale unit.
         By default, len_scale is assumed to be in radians with latlon=True.
         Can be set to :any:`KM_SCALE` to have len_scale in km or
         :any:`DEGREE_SCALE` to have len_scale in degrees.
-        Default: :any:`RADIAN_SCALE`
+        Default: :any:`RADIAN_SCALE` or geo_scale of the first given model (if instance).
     temporal : :class:`bool`, optional
         Create a metric spatio-temporal covariance model.
         Setting this to true will increase `dim` and `field_dim` by 1.
         `spatial_dim` will be `field_dim - 1`.
         The time-dimension is appended, meaning the pos tuple is (x,y,z,...,t).
-        Default: False
+        Default: False or temporal config of the first given model (if instance).
     spatial_dim : :class:`int`, optional
         spatial dimension of the model.
         If given, the model dimension will be determined from this spatial dimension
@@ -1259,7 +1276,8 @@ class SumModel(CovModel):
         Total length scale of the sum-model. Will evenly scale present length scales.
     **opt_arg
         Optional arguments of the sub-models will have and added index of the sub-model.
-        Also covers ``var_<i>`` and ``length_scale_<i>``.
+        Also covers ``var_<i>`` and ``length_scale_<i>`` but they should preferably be
+        set by ``vars`` and ``length_scales``.
     """
 
     _add_doc = False
@@ -1268,15 +1286,31 @@ def __init__(self, *models, **kwargs):
         self._init = False
         self._models = []
         add_nug = 0.0
+        to_init = None
+        imsg = (
+            "SumModel: either all models are CovModel instances or subclasses."
+        )
         for mod in models:
             if isinstance(mod, type) and issubclass(mod, SumModel):
+                if to_init is not None and not to_init:
+                    raise ValueError(imsg)
+                to_init = True
                 continue  # treat un-init sum-model as nugget model with 0 nugget
             if isinstance(mod, SumModel):
+                if to_init is not None and to_init:
+                    raise ValueError(imsg)
+                to_init = False
                 self._models += mod.models
                 add_nug += mod.nugget
             elif isinstance(mod, CovModel):
+                if to_init is not None and to_init:
+                    raise ValueError(imsg)
+                to_init = False
                 self._models.append(mod)
             elif isinstance(mod, type) and issubclass(mod, CovModel):
+                if to_init is not None and not to_init:
+                    raise ValueError(imsg)
+                to_init = True
                 self._models.append(mod(**default_mod_kwargs(kwargs)))
             else:
                 msg = "SumModel: models need to be instances or subclasses of CovModel."
@@ -1315,7 +1349,7 @@ def __init__(self, *models, **kwargs):
         self._nugget = float(
             kwargs.pop(
                 "nugget",
-                sum((mod.nugget for mod in self.models), 0.0) + add_nug,
+                sum((mod.nugget for mod in self.models), 0) + add_nug,
             )
         )
         for mod in self.models:
@@ -1339,7 +1373,7 @@ def __init__(self, *models, **kwargs):
         self._angles = set_model_angles(
             self.dim, angles, self.latlon, self.temporal
         )
-        # prepare parameters boundaries
+        # prepare parameter boundaries
         self._var_bounds = None
         self._len_scale_bounds = None
         self._nugget_bounds = None
@@ -1348,17 +1382,18 @@ def __init__(self, *models, **kwargs):
         bounds = self.default_arg_bounds()
         bounds.update(self.default_opt_arg_bounds())
         self.set_arg_bounds(check_args=False, **bounds)
-        # opt arg determining
+        # finalize init
         self._prec = 3
         self._init = True
         # set remaining args
         for arg, val in kwargs.items():
             setattr(self, arg, val)
+        # reset total variance and length scale last
         if var_set is not None:
             self.var = var_set
         if len_set is not None:
             self.len_scale = len_set
-        # check for consistency
+        # check consistency of sub models
         self.check()
 
     def __iter__(self):

From 0e35a222ef110af52f59ec2048b0be0d4c3cf2de Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sebastian=20M=C3=BCller?= <mueller.seb@posteo.de>
Date: Mon, 19 Aug 2024 11:40:08 +0200
Subject: [PATCH 28/28] SumModel: sum models have a constant rescale factor of
 1 since they are derived from correlation not cor

---
 src/gstools/covmodel/base.py | 13 ++++++-------
 1 file changed, 6 insertions(+), 7 deletions(-)

diff --git a/src/gstools/covmodel/base.py b/src/gstools/covmodel/base.py
index dd7ab2ee..38a47491 100644
--- a/src/gstools/covmodel/base.py
+++ b/src/gstools/covmodel/base.py
@@ -1193,6 +1193,7 @@ class SumModel(CovModel):
     An empty sum represents a pure Nugget model.
     Resetting the total variance or the total length scale will evenly
     scale the variances or length scales of the sub models.
+    Sum models will have a constant rescale factor of one.
 
     Parameters
     ----------
@@ -1235,12 +1236,6 @@ class SumModel(CovModel):
         If given, ``len_scale`` will be ignored and recalculated,
         so that the integral scale of the model matches the given one.
         Default: :any:`None`
-    rescale : :class:`float` or :any:`None`, optional
-        Optional rescaling factor to divide the length scale with.
-        This could be used for unit conversion or rescaling the length scale
-        to coincide with e.g. the integral scale.
-        Will be set by each model individually.
-        Default: :any:`None`
     latlon : :class:`bool`, optional
         Whether the model is describing 2D fields on earths surface described
         by latitude and longitude. When using this, the model will internally
@@ -1364,7 +1359,6 @@ def __init__(self, *models, **kwargs):
         self._sft = None
         self.dim = kwargs.get("dim", self.models[0].dim if self.models else 3)
         # prepare parameters (they are checked in dim setting)
-        self._rescale = 1.0
         anis = kwargs.get("anis", self.models[0].anis if self.models else 1)
         angles = kwargs.get(
             "angles", self.models[0].angles if self.models else 0
@@ -1477,6 +1471,11 @@ def models(self):
         """:class:`tuple`: The summed models."""
         return self._models
 
+    @property
+    def rescale(self):
+        """:class:`float`: SumModel has a constant rescale factor of one."""
+        return 1.0
+
     @property
     def geo_scale(self):
         """:class:`float`: Geographic scaling for geographical coords."""