DOC: Update randn() to use rng.normal()

Updates all references to `randn` to use `normal` from Generator.
I left the matlib versions alone.
I remove all references to `seed=123` and left  `# may vary`.
Longer outputs were reformatted to use Jupyter style output.

[skip actions] [skip azp] [skip cirrus]

Author: bmwoodruff

numpy/polynomial/hermite.py

@@ -1460,11 +1460,11 @@ def hermfit(x, y, deg, rcond=None, full=False, w=None):
     --------
     >>> from numpy.polynomial.hermite import hermfit, hermval
     >>> x = np.linspace(-10, 10)
-    >>> rng = np.random.default_rng(seed=123)
+    >>> rng = np.random.default_rng()
     >>> err = rng.normal(scale=1./10,size=len(x))
     >>> y = hermval(x, [1, 2, 3]) + err
     >>> hermfit(x, y, 2)
-    array([1.02294967, 2.00016403, 2.99994614])
+    array([1.02294967, 2.00016403, 2.99994614]) # may vary
 
     """
     return pu._fit(hermvander, x, y, deg, rcond, full, w)

numpy/polynomial/hermite_e.py

@@ -1387,11 +1387,11 @@ def hermefit(x, y, deg, rcond=None, full=False, w=None):
     --------
     >>> from numpy.polynomial.hermite_e import hermefit, hermeval
     >>> x = np.linspace(-10, 10)
-    >>> rng = np.random.default_rng(seed=123)
+    >>> rng = np.random.default_rng()
     >>> err = rng.normal(scale=1./10,size=len(x))
     >>> y = hermeval(x, [1, 2, 3]) + err
     >>> hermefit(x, y, 2)
-    array([1.02284196, 2.00032805, 2.99978457])
+    array([1.02284196, 2.00032805, 2.99978457]) # may vary
 
     """
     return pu._fit(hermevander, x, y, deg, rcond, full, w)

numpy/polynomial/laguerre.py

@@ -1441,11 +1441,11 @@ def lagfit(x, y, deg, rcond=None, full=False, w=None):
     --------
     >>> from numpy.polynomial.laguerre import lagfit, lagval
     >>> x = np.linspace(0, 10)
-    >>> rng = np.random.default_rng(seed=123)
+    >>> rng = np.random.default_rng()
     >>> err = rng.normal(scale=1./10,size=len(x))
     >>> y = lagval(x, [1, 2, 3]) + err
     >>> lagfit(x, y, 2)
-    array([1.00578369, 1.99417356, 2.99827656])
+    array([1.00578369, 1.99417356, 2.99827656]) # may vary
 
     """
     return pu._fit(lagvander, x, y, deg, rcond, full, w)

numpy/polynomial/polynomial.py

@@ -1443,14 +1443,14 @@ def polyfit(x, y, deg, rcond=None, full=False, w=None):
     --------
     >>> from numpy.polynomial import polynomial as P
     >>> x = np.linspace(-1,1,51)  # x "data": [-1, -0.96, ..., 0.96, 1]
-    >>> rng = np.random.default_rng(seed=123)
+    >>> rng = np.random.default_rng()
     >>> err = rng.normal(size=len(x))
     >>> y = x**3 - x + err  # x^3 - x + Gaussian noise
     >>> c, stats = P.polyfit(x,y,3,full=True)
     >>> c # c[0], c[1] approx. -1, c[2] should be approx. 0, c[3] approx. 1
-    array([ 0.23111996, -1.02785049, -0.2241444 ,  1.08405657])
+    array([ 0.23111996, -1.02785049, -0.2241444 ,  1.08405657]) # may vary
     >>> stats # note the large SSR, explaining the rather poor results
-    [array([48.312088]),
+    [array([48.312088]),                                        # may vary
      4,
      array([1.38446749, 1.32119158, 0.50443316, 0.28853036]),
      1.1324274851176597e-14]