Merge branch 'main' into never_copy

8 files changed, 41 insertions, 32 deletions

diff --git a/numpy/lib/polynomial.py b/numpy/lib/polynomial.py
index 56fcce621..23021cafa 100644
--- a/numpy/lib/polynomial.py
+++ b/numpy/lib/polynomial.py
@@ -489,8 +489,11 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False):
         default) just the coefficients are returned, when True diagnostic
         information from the singular value decomposition is also returned.
     w : array_like, shape (M,), optional
-        Weights to apply to the y-coordinates of the sample points. For
-        gaussian uncertainties, use 1/sigma (not 1/sigma**2).
+        Weights. If not None, the weight ``w[i]`` applies to the unsquared
+        residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
+        chosen so that the errors of the products ``w[i]*y[i]`` all have the
+        same variance.  When using inverse-variance weighting, use
+        ``w[i] = 1/sigma(y[i])``.  The default value is None.
     cov : bool or str, optional
         If given and not `False`, return not just the estimate but also its
         covariance matrix. By default, the covariance are scaled by
@@ -498,7 +501,7 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None, cov=False):
         to be unreliable except in a relative sense and everything is scaled
         such that the reduced chi2 is unity. This scaling is omitted if
         ``cov='unscaled'``, as is relevant for the case that the weights are
-        1/sigma**2, with sigma known to be a reliable estimate of the
+        w = 1/sigma, with sigma known to be a reliable estimate of the
         uncertainty.
 
     Returns
diff --git a/numpy/polynomial/_polybase.py b/numpy/polynomial/_polybase.py
index b04b8e66b..5525b232b 100644
--- a/numpy/polynomial/_polybase.py
+++ b/numpy/polynomial/_polybase.py
@@ -936,11 +936,11 @@ class ABCPolyBase(abc.ABC):
             diagnostic information from the singular value decomposition is
             also returned.
         w : array_like, shape (M,), optional
-            Weights. If not None the contribution of each point
-            ``(x[i],y[i])`` to the fit is weighted by ``w[i]``. Ideally the
-            weights are chosen so that the errors of the products
-            ``w[i]*y[i]`` all have the same variance.  The default value is
-            None.
+            Weights. If not None, the weight ``w[i]`` applies to the unsquared
+            residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
+            chosen so that the errors of the products ``w[i]*y[i]`` all have
+            the same variance.  When using inverse-variance weighting, use
+            ``w[i] = 1/sigma(y[i])``.  The default value is None.
 
             .. versionadded:: 1.5.0
         window : {[beg, end]}, optional
diff --git a/numpy/polynomial/chebyshev.py b/numpy/polynomial/chebyshev.py
index d24fc738f..210000ec4 100644
--- a/numpy/polynomial/chebyshev.py
+++ b/numpy/polynomial/chebyshev.py
@@ -1582,10 +1582,11 @@ def chebfit(x, y, deg, rcond=None, full=False, w=None):
         default) just the coefficients are returned, when True diagnostic
         information from the singular value decomposition is also returned.
     w : array_like, shape (`M`,), optional
-        Weights. If not None, the contribution of each point
-        ``(x[i],y[i])`` to the fit is weighted by ``w[i]``. Ideally the
-        weights are chosen so that the errors of the products ``w[i]*y[i]``
-        all have the same variance.  The default value is None.
+        Weights. If not None, the weight ``w[i]`` applies to the unsquared
+        residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
+        chosen so that the errors of the products ``w[i]*y[i]`` all have the
+        same variance.  When using inverse-variance weighting, use
+        ``w[i] = 1/sigma(y[i])``.  The default value is None.
 
         .. versionadded:: 1.5.0
 
diff --git a/numpy/polynomial/hermite.py b/numpy/polynomial/hermite.py
index eef5c25b2..c1b9f71c0 100644
--- a/numpy/polynomial/hermite.py
+++ b/numpy/polynomial/hermite.py
@@ -1310,10 +1310,11 @@ def hermfit(x, y, deg, rcond=None, full=False, w=None):
         default) just the coefficients are returned, when True diagnostic
         information from the singular value decomposition is also returned.
     w : array_like, shape (`M`,), optional
-        Weights. If not None, the contribution of each point
-        ``(x[i],y[i])`` to the fit is weighted by ``w[i]``. Ideally the
-        weights are chosen so that the errors of the products ``w[i]*y[i]``
-        all have the same variance.  The default value is None.
+        Weights. If not None, the weight ``w[i]`` applies to the unsquared
+        residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
+        chosen so that the errors of the products ``w[i]*y[i]`` all have the
+        same variance.  When using inverse-variance weighting, use
+        ``w[i] = 1/sigma(y[i])``.  The default value is None.
 
     Returns
     -------
diff --git a/numpy/polynomial/hermite_e.py b/numpy/polynomial/hermite_e.py
index 05d1337b0..b7095c910 100644
--- a/numpy/polynomial/hermite_e.py
+++ b/numpy/polynomial/hermite_e.py
@@ -1301,10 +1301,11 @@ def hermefit(x, y, deg, rcond=None, full=False, w=None):
         default) just the coefficients are returned, when True diagnostic
         information from the singular value decomposition is also returned.
     w : array_like, shape (`M`,), optional
-        Weights. If not None, the contribution of each point
-        ``(x[i],y[i])`` to the fit is weighted by ``w[i]``. Ideally the
-        weights are chosen so that the errors of the products ``w[i]*y[i]``
-        all have the same variance.  The default value is None.
+        Weights. If not None, the weight ``w[i]`` applies to the unsquared
+        residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
+        chosen so that the errors of the products ``w[i]*y[i]`` all have the
+        same variance.  When using inverse-variance weighting, use
+        ``w[i] = 1/sigma(y[i])``.  The default value is None.
 
     Returns
     -------
diff --git a/numpy/polynomial/laguerre.py b/numpy/polynomial/laguerre.py
index 69d557510..d3b6432dc 100644
--- a/numpy/polynomial/laguerre.py
+++ b/numpy/polynomial/laguerre.py
@@ -1307,10 +1307,11 @@ def lagfit(x, y, deg, rcond=None, full=False, w=None):
         default) just the coefficients are returned, when True diagnostic
         information from the singular value decomposition is also returned.
     w : array_like, shape (`M`,), optional
-        Weights. If not None, the contribution of each point
-        ``(x[i],y[i])`` to the fit is weighted by ``w[i]``. Ideally the
-        weights are chosen so that the errors of the products ``w[i]*y[i]``
-        all have the same variance.  The default value is None.
+        Weights. If not None, the weight ``w[i]`` applies to the unsquared
+        residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
+        chosen so that the errors of the products ``w[i]*y[i]`` all have the
+        same variance.  When using inverse-variance weighting, use
+        ``w[i] = 1/sigma(y[i])``.  The default value is None.
 
     Returns
     -------
diff --git a/numpy/polynomial/legendre.py b/numpy/polynomial/legendre.py
index cd4da2a79..d4cf4accf 100644
--- a/numpy/polynomial/legendre.py
+++ b/numpy/polynomial/legendre.py
@@ -1321,10 +1321,11 @@ def legfit(x, y, deg, rcond=None, full=False, w=None):
         default) just the coefficients are returned, when True diagnostic
         information from the singular value decomposition is also returned.
     w : array_like, shape (`M`,), optional
-        Weights. If not None, the contribution of each point
-        ``(x[i],y[i])`` to the fit is weighted by ``w[i]``. Ideally the
-        weights are chosen so that the errors of the products ``w[i]*y[i]``
-        all have the same variance.  The default value is None.
+        Weights. If not None, the weight ``w[i]`` applies to the unsquared
+        residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
+        chosen so that the errors of the products ``w[i]*y[i]`` all have the
+        same variance.  When using inverse-variance weighting, use
+        ``w[i] = 1/sigma(y[i])``.  The default value is None.
 
         .. versionadded:: 1.5.0
 
diff --git a/numpy/polynomial/polynomial.py b/numpy/polynomial/polynomial.py
index 940eed5e3..d8a032068 100644
--- a/numpy/polynomial/polynomial.py
+++ b/numpy/polynomial/polynomial.py
@@ -1252,10 +1252,11 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None):
         diagnostic information from the singular value decomposition (used
         to solve the fit's matrix equation) is also returned.
     w : array_like, shape (`M`,), optional
-        Weights. If not None, the contribution of each point
-        ``(x[i],y[i])`` to the fit is weighted by ``w[i]``. Ideally the
-        weights are chosen so that the errors of the products ``w[i]*y[i]``
-        all have the same variance.  The default value is None.
+        Weights. If not None, the weight ``w[i]`` applies to the unsquared
+        residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
+        chosen so that the errors of the products ``w[i]*y[i]`` all have the
+        same variance.  When using inverse-variance weighting, use
+        ``w[i] = 1/sigma(y[i])``.  The default value is None.
 
         .. versionadded:: 1.5.0