matplotlib · timhoffm · Jun 28, 2025 · Jun 15, 2025 · Jun 24, 2025 · Jun 25, 2025
diff --git a/doc/api/colors_api.rst b/doc/api/colors_api.rst
@@ -21,6 +21,7 @@ Color norms
    :toctree: _as_gen/
    :template: autosummary.rst
 
+   Norm
    Normalize
    NoNorm
    AsinhNorm

diff --git a/lib/matplotlib/colorizer.py b/lib/matplotlib/colorizer.py
@@ -90,7 +90,7 @@ def norm(self):
 
     @norm.setter
     def norm(self, norm):
-        _api.check_isinstance((colors.Normalize, str, None), norm=norm)
+        _api.check_isinstance((colors.Norm, str, None), norm=norm)
         if norm is None:
             norm = colors.Normalize()
         elif isinstance(norm, str):

diff --git a/lib/matplotlib/colorizer.pyi b/lib/matplotlib/colorizer.pyi
@@ -10,12 +10,12 @@ class Colorizer:
     def __init__(
         self,
         cmap: str | colors.Colormap | None = ...,
-        norm: str | colors.Normalize | None = ...,
+        norm: str | colors.Norm | None = ...,
     ) -> None: ...
     @property
-    def norm(self) -> colors.Normalize: ...
+    def norm(self) -> colors.Norm: ...
     @norm.setter
-    def norm(self, norm: colors.Normalize | str | None) -> None: ...
+    def norm(self, norm: colors.Norm | str | None) -> None: ...
     def to_rgba(
         self,
         x: np.ndarray,
@@ -63,18 +63,18 @@ class _ColorizerInterface:
     def get_cmap(self) -> colors.Colormap: ...
     def set_cmap(self, cmap: str | colors.Colormap) -> None: ...
     @property
-    def norm(self) -> colors.Normalize: ...
+    def norm(self) -> colors.Norm: ...
     @norm.setter
-    def norm(self, norm: colors.Normalize | str | None) -> None: ...
-    def set_norm(self, norm: colors.Normalize | str | None) -> None: ...
+    def norm(self, norm: colors.Norm | str | None) -> None: ...
+    def set_norm(self, norm: colors.Norm | str | None) -> None: ...
     def autoscale(self) -> None: ...
     def autoscale_None(self) -> None: ...
 
 
 class _ScalarMappable(_ColorizerInterface):
     def __init__(
         self,
-        norm: colors.Normalize | None = ...,
+        norm: colors.Norm | None = ...,
         cmap: str | colors.Colormap | None = ...,
         *,
         colorizer: Colorizer | None = ...,

diff --git a/lib/matplotlib/colors.py b/lib/matplotlib/colors.py
@@ -41,6 +41,7 @@
 
 import base64
 from collections.abc import Sequence, Mapping
+from abc import ABC, abstractmethod
 import functools
 import importlib
 import inspect
@@ -2257,7 +2258,87 @@
         self._isinit = True
 
 
-class Normalize:
+class Norm(ABC):
+    """
+    Abstract base class for normalizations.
+
+    Subclasses include `Normalize` which maps from a scalar to
+    a scalar. However, this class makes no such requirement, and subclasses may
+    support the normalization of multiple variates simultaneously, with
+    separate normalization for each variate.
+    """
+
+    def __init__(self):
+        self.callbacks = cbook.CallbackRegistry(signals=["changed"])
+
+    @property
+    @abstractmethod
+    def vmin(self):
+        """Lower limit of the input data interval; maps to 0."""
+        pass
+
+    @property
+    @abstractmethod
+    def vmax(self):
+        """Upper limit of the input data interval; maps to 1."""
+        pass
+
+    @property
+    @abstractmethod
+    def clip(self):
+        """
+        Determines the behavior for mapping values outside the range ``[vmin, vmax]``.
+
+        See the *clip* parameter in `.Normalize`.
+        """
+        pass
+
+    @abstractmethod
+    def __call__(self, value, clip=None):
+        """
+        Normalize the data and return the normalized data.
+
+        Parameters
+        ----------
+        value
+            Data to normalize.
+        clip : bool, optional
+            See the description of the parameter *clip* in `.Normalize`.
+
+            If ``None``, defaults to ``self.clip`` (which defaults to
+            ``False``).
+
+        Notes
+        -----
+        If not already initialized, ``self.vmin`` and ``self.vmax`` are
+        initialized using ``self.autoscale_None(value)``.
+        """
+        pass
+
+    @abstractmethod
+    def autoscale(self, A):
+        """Set *vmin*, *vmax* to min, max of *A*."""
+        pass
+
+    @abstractmethod
+    def autoscale_None(self, A):
+        """If *vmin* or *vmax* are not set, use the min/max of *A* to set them."""
+        pass
+
+    @abstractmethod
+    def scaled(self):
+        """Return whether *vmin* and *vmax* are both set."""
+        pass
+
+    def _changed(self):
+        """
+        Call this whenever the norm is changed to notify all the
+        callback listeners to the 'changed' signal.
+        """
+        self.callbacks.process('changed')
+
+
+class Normalize(Norm):
     """
     A class which, when called, maps values within the interval
     ``[vmin, vmax]`` linearly to the interval ``[0.0, 1.0]``. The mapping of
@@ -2307,15 +2388,15 @@
         -----
         If ``vmin == vmax``, input data will be mapped to 0.
         """
+        super().__init__()
         self._vmin = _sanitize_extrema(vmin)
         self._vmax = _sanitize_extrema(vmax)
         self._clip = clip
         self._scale = None
-        self.callbacks = cbook.CallbackRegistry(signals=["changed"])
 
     @property
     def vmin(self):
-        """Lower limit of the input data interval; maps to 0."""
+        # docstring inherited
         return self._vmin
 
     @vmin.setter
@@ -2327,7 +2408,7 @@
 
     @property
     def vmax(self):
-        """Upper limit of the input data interval; maps to 1."""
+        # docstring inherited
         return self._vmax
 
     @vmax.setter
@@ -2339,11 +2420,7 @@
 
     @property
     def clip(self):
-        """
-        Determines the behavior for mapping values outside the range ``[vmin, vmax]``.
-
-        See the *clip* parameter in `.Normalize`.
-        """
+        # docstring inherited
         return self._clip
 
     @clip.setter
@@ -2352,13 +2429,6 @@
             self._clip = value
             self._changed()
 
-    def _changed(self):
-        """
-        Call this whenever the norm is changed to notify all the
-        callback listeners to the 'changed' signal.
-        """
-        self.callbacks.process('changed')
-
     @staticmethod
     def process_value(value):
         """
@@ -2400,24 +2470,7 @@
         return result, is_scalar
 
     def __call__(self, value, clip=None):
-        """
-        Normalize the data and return the normalized data.
-
-        Parameters
-        ----------
-        value
-            Data to normalize.
-        clip : bool, optional
-            See the description of the parameter *clip* in `.Normalize`.
-
-            If ``None``, defaults to ``self.clip`` (which defaults to
-            ``False``).
-
-        Notes
-        -----
-        If not already initialized, ``self.vmin`` and ``self.vmax`` are
-        initialized using ``self.autoscale_None(value)``.
-        """
+        # docstring inherited
         if clip is None:
             clip = self.clip
 
@@ -2468,7 +2521,7 @@
             return vmin + value * (vmax - vmin)
 
     def autoscale(self, A):
-        """Set *vmin*, *vmax* to min, max of *A*."""
+        # docstring inherited
         with self.callbacks.blocked():
             # Pause callbacks while we are updating so we only get
             # a single update signal at the end
@@ -2477,7 +2530,7 @@
         self._changed()
 
     def autoscale_None(self, A):
-        """If *vmin* or *vmax* are not set, use the min/max of *A* to set them."""
+        # docstring inherited
         A = np.asanyarray(A)
 
         if isinstance(A, np.ma.MaskedArray):
@@ -2491,7 +2544,7 @@
             self.vmax = A.max()
 
     def scaled(self):
-        """Return whether *vmin* and *vmax* are both set."""
+        # docstring inherited
         return self.vmin is not None and self.vmax is not None
 
 
@@ -2775,7 +2828,7 @@
       unlike to arbitrary lambdas.
     """
 
-    class Norm(base_norm_cls):
+    class ScaleNorm(base_norm_cls):
         def __reduce__(self):
             cls = type(self)
             # If the class is toplevel-accessible, it is possible to directly
@@ -2855,15 +2908,15 @@
             return super().autoscale_None(in_trf_domain)
 
     if base_norm_cls is Normalize:
-        Norm.__name__ = f"{scale_cls.__name__}Norm"
-        Norm.__qualname__ = f"{scale_cls.__qualname__}Norm"
+        ScaleNorm.__name__ = f"{scale_cls.__name__}Norm"
+        ScaleNorm.__qualname__ = f"{scale_cls.__qualname__}Norm"
     else:
-        Norm.__name__ = base_norm_cls.__name__
-        Norm.__qualname__ = base_norm_cls.__qualname__
-    Norm.__module__ = base_norm_cls.__module__
-    Norm.__doc__ = base_norm_cls.__doc__
+        ScaleNorm.__name__ = base_norm_cls.__name__
+        ScaleNorm.__qualname__ = base_norm_cls.__qualname__
+    ScaleNorm.__module__ = base_norm_cls.__module__
+    ScaleNorm.__doc__ = base_norm_cls.__doc__
 
-    return Norm
+    return ScaleNorm
 
 
 def _create_empty_object_of_class(cls):

diff --git a/lib/matplotlib/colors.pyi b/lib/matplotlib/colors.pyi
@@ -1,4 +1,5 @@
 from collections.abc import Callable, Iterable, Iterator, Mapping, Sequence
+from abc import ABC, abstractmethod
 from matplotlib import cbook, scale
 import re
 
@@ -249,8 +250,29 @@ class BivarColormapFromImage(BivarColormap):
         origin: Sequence[float] = ..., name: str = ...
     ) -> None: ...
 
-class Normalize:
+class Norm(ABC):
     callbacks: cbook.CallbackRegistry
+    def __init__(self) -> None: ...
+    @property
+    @abstractmethod
+    def vmin(self) -> float | tuple[float] | None: ...
+    @property
+    @abstractmethod
+    def vmax(self) -> float | tuple[float] | None: ...
+    @property
+    @abstractmethod
+    def clip(self) -> bool | tuple[bool]: ...
+    @abstractmethod
+    def __call__(self, value: np.ndarray, clip: bool | None = ...) -> ArrayLike: ...
+    @abstractmethod
+    def autoscale(self, A: ArrayLike) -> None: ...
+    @abstractmethod
+    def autoscale_None(self, A: ArrayLike) -> None: ...
+    @abstractmethod
+    def scaled(self) -> bool: ...
+
+
+class Normalize(Norm):
     def __init__(
         self, vmin: float | None = ..., vmax: float | None = ..., clip: bool = ...
     ) -> None: ...

diff --git a/lib/matplotlib/tests/baseline_images/test_colors/test_norm_abc.png b/lib/matplotlib/tests/baseline_images/test_colors/test_norm_abc.png
diff --git a/lib/matplotlib/tests/test_colors.py b/lib/matplotlib/tests/test_colors.py
@@ -7,6 +7,7 @@
 from PIL import Image
 import pytest
 import base64
+import platform
 
 from numpy.testing import assert_array_equal, assert_array_almost_equal
 
@@ -1829,3 +1830,49 @@
         cmap([value for value, _ in value_color_tuples]),
         to_rgba_array([color for _, color in value_color_tuples]),
     )
+
+
+@image_comparison(['test_norm_abc.png'], remove_text=True,
+                   tol=0 if platform.machine() == 'x86_64' else 0.05)
+def test_norm_abc():
+
+    class CustomHalfNorm(mcolors.Norm):
+        def __init__(self):
+            super().__init__()
+
+        @property
+        def vmin(self):
+            return 0
+
+        @property
+        def vmax(self):
+            return 1
+
+        @property
+        def clip(self):
+            return False
+
+        def __call__(self, value, clip=None):
+            return value / 2
+
+        def inverse(self, value):
+            return 2 * value
+
+        def autoscale(self, A):
+            pass
+
+        def autoscale_None(self, A):
+            pass
+
+        def scaled(self):
+            return True
+
+    fig, axes = plt.subplots(2,2)
+
+    r = np.linspace(-1, 3, 16*16).reshape((16,16))
+    norm = CustomHalfNorm()
+    colorizer = mpl.colorizer.Colorizer(cmap='viridis', norm=norm)
+    c = axes[0,0].imshow(r, colorizer=colorizer)
+    axes[0,1].pcolor(r, colorizer=colorizer)
+    axes[1,0].contour(r, colorizer=colorizer)
+    axes[1,1].contourf(r, colorizer=colorizer)