Use np.hypot whereever possible.

anntzer · anntzer · commit ca3c914f3bce · 2018-10-06T18:16:47.000+02:00
Except examples, where it may be too obscure? Also added -T to CI sphinx-build invocation, to help troubleshooting e.g. https://circleci.com/gh/anntzer/matplotlib/2505?utm_campaign=vcs-integration-link&utm_medium=referral&utm_source=github-build-link (show traceback on sphinx failure).
diff --git a/.circleci/config.yml b/.circleci/config.yml
@@ -74,7 +74,7 @@ mpl-run: &mpl-install
 
 doc-run: &doc-build
   name: Build documentation
-  command: make html
+  command: make html O=-T
   working_directory: doc
 
 doc-bundle-run: &doc-bundle
diff --git a/examples/event_handling/pick_event_demo.py b/examples/event_handling/pick_event_demo.py
@@ -126,7 +126,8 @@ def line_picker(line, mouseevent):
         xdata = line.get_xdata()
         ydata = line.get_ydata()
         maxd = 0.05
-        d = np.sqrt((xdata - mouseevent.xdata)**2. + (ydata - mouseevent.ydata)**2.)
+        d = np.sqrt(
+            (xdata - mouseevent.xdata)**2 + (ydata - mouseevent.ydata)**2)
 
         ind = np.nonzero(np.less_equal(d, maxd))
         if len(ind):
diff --git a/examples/images_contours_and_fields/barb_demo.py b/examples/images_contours_and_fields/barb_demo.py
@@ -28,12 +28,14 @@
 
 # Arbitrary set of vectors, make them longer and change the pivot point
 # (point around which they're rotated) to be the middle
-axs1[0, 1].barbs(data['x'], data['y'], data['u'], data['v'], length=8, pivot='middle')
+axs1[0, 1].barbs(
+    data['x'], data['y'], data['u'], data['v'], length=8, pivot='middle')
 
 # Showing colormapping with uniform grid.  Fill the circle for an empty barb,
 # don't round the values, and change some of the size parameters
-axs1[1, 0].barbs(X, Y, U, V, np.sqrt(U * U + V * V), fill_empty=True, rounding=False,
-                 sizes=dict(emptybarb=0.25, spacing=0.2, height=0.3))
+axs1[1, 0].barbs(
+    X, Y, U, V, np.sqrt(U ** 2 + V ** 2), fill_empty=True, rounding=False,
+    sizes=dict(emptybarb=0.25, spacing=0.2, height=0.3))
 
 # Change colors as well as the increments for parts of the barbs
 axs1[1, 1].barbs(data['x'], data['y'], data['u'], data['v'], flagcolor='r',
diff --git a/examples/images_contours_and_fields/contourf_demo.py b/examples/images_contours_and_fields/contourf_demo.py
@@ -30,7 +30,7 @@
 Z[:nr // 6, :nc // 6] = np.ma.masked
 
 # mask a circle in the middle:
-interior = np.sqrt((X**2) + (Y**2)) < 0.5
+interior = np.sqrt(X**2 + Y**2) < 0.5
 Z[interior] = np.ma.masked
 
 # We are using automatic selection of contour levels;
diff --git a/examples/images_contours_and_fields/plot_streamplot.py b/examples/images_contours_and_fields/plot_streamplot.py
@@ -20,7 +20,7 @@
 Y, X = np.mgrid[-w:w:100j, -w:w:100j]
 U = -1 - X**2 + Y
 V = 1 + X - Y**2
-speed = np.sqrt(U*U + V*V)
+speed = np.sqrt(U**2 + V**2)
 
 fig = plt.figure(figsize=(7, 9))
 gs = gridspec.GridSpec(nrows=3, ncols=2, height_ratios=[1, 1, 2])
diff --git a/examples/lines_bars_and_markers/scatter_masked.py b/examples/lines_bars_and_markers/scatter_masked.py
@@ -20,7 +20,7 @@
 y = 0.9 * np.random.rand(N)
 area = (20 * np.random.rand(N))**2  # 0 to 10 point radii
 c = np.sqrt(area)
-r = np.sqrt(x * x + y * y)
+r = np.sqrt(x ** 2 + y ** 2)
 area1 = np.ma.masked_where(r < r0, area)
 area2 = np.ma.masked_where(r >= r0, area)
 plt.scatter(x, y, s=area1, marker='^', c=c)
diff --git a/lib/matplotlib/contour.py b/lib/matplotlib/contour.py
@@ -230,11 +230,9 @@ def print_label(self, linecontour, labelwidth):
 
     def too_close(self, x, y, lw):
         "Return *True* if a label is already near this location."
-        for loc in self.labelXYs:
-            d = np.sqrt((x - loc[0]) ** 2 + (y - loc[1]) ** 2)
-            if d < 1.2 * lw:
-                return True
-        return False
+        thresh = (1.2 * lw) ** 2
+        return any((x - loc[0]) ** 2 + (y - loc[1]) ** 2 < thresh
+                   for loc in self.labelXYs)
 
     def get_label_coords(self, distances, XX, YY, ysize, lw):
         """
diff --git a/lib/matplotlib/lines.py b/lib/matplotlib/lines.py
@@ -477,17 +477,16 @@ def contains(self, mouseevent):
         else:
             pixels = self.figure.dpi / 72. * self.pickradius
 
-        # the math involved in checking for containment (here and inside of
-        # segment_hits) assumes that it is OK to overflow.  In case the
-        # application has set the error flags such that an exception is raised
-        # on overflow, we temporarily set the appropriate error flags here and
-        # set them back when we are finished.
+        # The math involved in checking for containment (here and inside of
+        # segment_hits) assumes that it is OK to overflow, so temporarily set
+        # the error flags accordingly.
         with np.errstate(all='ignore'):
             # Check for collision
             if self._linestyle in ['None', None]:
                 # If no line, return the nearby point(s)
-                d = (xt - mouseevent.x) ** 2 + (yt - mouseevent.y) ** 2
-                ind, = np.nonzero(np.less_equal(d, pixels ** 2))
+                ind, = np.nonzero(
+                    (xt - mouseevent.x) ** 2 + (yt - mouseevent.y) ** 2
+                    <= pixels ** 2)
             else:
                 # If line, return the nearby segment(s)
                 ind = segment_hits(mouseevent.x, mouseevent.y, xt, yt, pixels)
diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
@@ -1359,10 +1359,8 @@ def get_path(self):
         xb1, yb1, xb2, yb2 = self.getpoints(x1, y1, x2, y2, k1)
 
         # a point on the segment 20% of the distance from the tip to the base
-        theta = math.atan2(y2 - y1, x2 - x1)
-        r = math.sqrt((y2 - y1) ** 2. + (x2 - x1) ** 2.)
-        xm = x1 + self.frac * r * math.cos(theta)
-        ym = y1 + self.frac * r * math.sin(theta)
+        xm = x1 + self.frac * (x2 - x1)
+        ym = y1 + self.frac * (y2 - y1)
         xc1, yc1, xc2, yc2 = self.getpoints(x1, y1, xm, ym, k1)
         xd1, yd1, xd2, yd2 = self.getpoints(x1, y1, xm, ym, k2)
 
@@ -2915,10 +2913,10 @@ def connect(self, posA, posB):
                 codes.append(Path.LINETO)
             else:
                 dx1, dy1 = x1 - cx, y1 - cy
-                d1 = (dx1 ** 2 + dy1 ** 2) ** .5
+                d1 = np.hypot(dx1, dy1)
                 f1 = self.rad / d1
                 dx2, dy2 = x2 - cx, y2 - cy
-                d2 = (dx2 ** 2 + dy2 ** 2) ** .5
+                d2 = np.hypot(dx2, dy2)
                 f2 = self.rad / d2
                 vertices.extend([(cx + dx1 * f1, cy + dy1 * f1),
                                  (cx, cy),
@@ -3302,7 +3300,7 @@ def transmute(self, path, mutation_size, linewidth):
 
             head_length = self.head_length * mutation_size
             head_width = self.head_width * mutation_size
-            head_dist = math.sqrt(head_length ** 2 + head_width ** 2)
+            head_dist = np.hypot(head_length, head_width)
             cos_t, sin_t = head_length / head_dist, head_width / head_dist
 
             # begin arrow
diff --git a/lib/matplotlib/projections/geo.py b/lib/matplotlib/projections/geo.py
@@ -462,15 +462,12 @@ def transform_non_affine(self, ll):
             diff_long = longitude - clong
             cos_diff_long = np.cos(diff_long)
 
-            inner_k = (1.0 +
-                       np.sin(clat)*sin_lat +
-                       np.cos(clat)*cos_lat*cos_diff_long)
-            # Prevent divide-by-zero problems
-            inner_k = np.where(inner_k == 0.0, 1e-15, inner_k)
-            k = np.sqrt(2.0 / inner_k)
-            x = k*cos_lat*np.sin(diff_long)
-            y = k*(np.cos(clat)*sin_lat -
-                   np.sin(clat)*cos_lat*cos_diff_long)
+            inner_k = np.maximum(  # Prevent divide-by-zero problems
+                1 + np.sin(clat)*sin_lat + np.cos(clat)*cos_lat*cos_diff_long,
+                1e-15)
+            k = np.sqrt(2 / inner_k)
+            x = k * cos_lat*np.sin(diff_long)
+            y = k * (np.cos(clat)*sin_lat - np.sin(clat)*cos_lat*cos_diff_long)
 
             return np.concatenate((x, y), 1)
         transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
@@ -494,9 +491,8 @@ def transform_non_affine(self, xy):
             y = xy[:, 1:2]
             clong = self._center_longitude
             clat = self._center_latitude
-            p = np.sqrt(x*x + y*y)
-            p = np.where(p == 0.0, 1e-9, p)
-            c = 2.0 * np.arcsin(0.5 * p)
+            p = np.maximum(np.hypot(x, y), 1e-9)
+            c = 2 * np.arcsin(0.5 * p)
             sin_c = np.sin(c)
             cos_c = np.cos(c)
 
diff --git a/lib/matplotlib/projections/polar.py b/lib/matplotlib/projections/polar.py
@@ -149,15 +149,8 @@ def __str__(self):
     def transform_non_affine(self, xy):
         x = xy[:, 0:1]
         y = xy[:, 1:]
-        r = np.sqrt(x*x + y*y)
-        with np.errstate(invalid='ignore'):
-            # At x=y=r=0 this will raise an
-            # invalid value warning when doing 0/0
-            # Divide by zero warnings are only raised when
-            # the numerator is different from 0. That
-            # should not happen here.
-            theta = np.arccos(x / r)
-        theta = np.where(y < 0, 2 * np.pi - theta, theta)
+        r = np.hypot(x, y)
+        theta = (np.arctan2(y, x) + 2 * np.pi) % (2 * np.pi)
 
         # PolarAxes does not use the theta transforms here, but apply them for
         # backwards-compatibility if not being used by it.
diff --git a/lib/matplotlib/streamplot.py b/lib/matplotlib/streamplot.py
@@ -190,7 +190,7 @@ def streamplot(axes, x, y, u, v, density=1, linewidth=None, color=None,
         streamlines.extend(np.hstack([points[:-1], points[1:]]))
 
         # Add arrows half way along each trajectory.
-        s = np.cumsum(np.sqrt(np.diff(tx) ** 2 + np.diff(ty) ** 2))
+        s = np.cumsum(np.hypot(np.diff(tx), np.diff(ty)))
         n = np.searchsorted(s, s[-1] / 2.)
         arrow_tail = (tx[n], ty[n])
         arrow_head = (np.mean(tx[n:n + 2]), np.mean(ty[n:n + 2]))
@@ -413,7 +413,7 @@ def get_integrator(u, v, dmap, minlength, maxlength, integration_direction):
     # speed (path length) will be in axes-coordinates
     u_ax = u / dmap.grid.nx
     v_ax = v / dmap.grid.ny
-    speed = np.ma.sqrt(u_ax ** 2 + v_ax ** 2)
+    speed = np.ma.hypot(u_ax, v_ax)
 
     def forward_time(xi, yi):
         ds_dt = interpgrid(speed, xi, yi)
@@ -536,7 +536,7 @@ def _integrate_rk12(x0, y0, dmap, f, maxlength):
 
         nx, ny = dmap.grid.shape
         # Error is normalized to the axes coordinates
-        error = np.sqrt(((dx2 - dx1) / nx) ** 2 + ((dy2 - dy1) / ny) ** 2)
+        error = np.hypot((dx2 - dx1) / nx, (dy2 - dy1) / ny)
 
         # Only save step if within error tolerance
         if error < maxerror:
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
@@ -1173,7 +1173,7 @@ def test_pcolorargs():
     x = np.linspace(-1.5, 1.5, n)
     y = np.linspace(-1.5, 1.5, n*2)
     X, Y = np.meshgrid(x, y)
-    Z = np.sqrt(X**2 + Y**2)/5
+    Z = np.hypot(X, Y) / 5
 
     _, ax = plt.subplots()
     with pytest.raises(TypeError):
diff --git a/lib/matplotlib/tests/test_contour.py b/lib/matplotlib/tests/test_contour.py
@@ -291,7 +291,7 @@ def test_corner_mask():
     np.random.seed([1])
     x, y = np.meshgrid(np.linspace(0, 2.0, n), np.linspace(0, 2.0, n))
     z = np.cos(7*x)*np.sin(8*y) + noise_amp*np.random.rand(n, n)
-    mask = np.where(np.random.rand(n, n) >= mask_level, True, False)
+    mask = np.random.rand(n, n) >= mask_level
     z = np.ma.array(z, mask=mask)
 
     for corner_mask in [False, True]:
@@ -362,7 +362,7 @@ def test_circular_contour_warning():
     # Check that almost circular contours don't throw a warning
     with pytest.warns(None) as record:
         x, y = np.meshgrid(np.linspace(-2, 2, 4), np.linspace(-2, 2, 4))
-        r = np.sqrt(x ** 2 + y ** 2)
+        r = np.hypot(x, y)
 
         plt.figure()
         cs = plt.contour(x, y, r)
diff --git a/lib/matplotlib/tests/test_image.py b/lib/matplotlib/tests/test_image.py
@@ -745,12 +745,11 @@ def test_mask_image():
 def test_imshow_endianess():
     x = np.arange(10)
     X, Y = np.meshgrid(x, x)
-    Z = ((X-5)**2 + (Y-5)**2)**0.5
+    Z = np.hypot(X - 5, Y - 5)
 
     fig, (ax1, ax2) = plt.subplots(1, 2)
 
-    kwargs = dict(origin="lower", interpolation='nearest',
-                  cmap='viridis')
+    kwargs = dict(origin="lower", interpolation='nearest', cmap='viridis')
 
     ax1.imshow(Z.astype('<f8'), **kwargs)
     ax2.imshow(Z.astype('>f8'), **kwargs)
diff --git a/lib/matplotlib/tests/test_quiver.py b/lib/matplotlib/tests/test_quiver.py
@@ -136,7 +136,7 @@ def test_barbs():
     X, Y = np.meshgrid(x, x)
     U, V = 12*X, 12*Y
     fig, ax = plt.subplots()
-    ax.barbs(X, Y, U, V, np.sqrt(U*U + V*V), fill_empty=True, rounding=False,
+    ax.barbs(X, Y, U, V, np.hypot(U, V), fill_empty=True, rounding=False,
              sizes=dict(emptybarb=0.25, spacing=0.2, height=0.3),
              cmap='viridis')
 
diff --git a/lib/matplotlib/tests/test_streamplot.py b/lib/matplotlib/tests/test_streamplot.py
@@ -53,9 +53,9 @@ def test_colormap():
                   remove_text=True, style='mpl20')
 def test_linewidth():
     X, Y, U, V = velocity_field()
-    speed = np.sqrt(U*U + V*V)
-    lw = 5*speed/speed.max()
-    df = 25. / 30.   # Compatibility factor for old test image
+    speed = np.hypot(U, V)
+    lw = 5 * speed / speed.max()
+    df = 25 / 30   # Compatibility factor for old test image
     plt.streamplot(X, Y, U, V, density=[0.5 * df, 1. * df], color='k',
                    linewidth=lw)
 
diff --git a/lib/matplotlib/tests/test_triangulation.py b/lib/matplotlib/tests/test_triangulation.py
@@ -662,10 +662,10 @@ def test_triinterp_transformations():
     min_radius = 0.15
 
     def z(x, y):
-        r1 = np.sqrt((0.5-x)**2 + (0.5-y)**2)
-        theta1 = np.arctan2(0.5-x, 0.5-y)
-        r2 = np.sqrt((-x-0.2)**2 + (-y-0.2)**2)
-        theta2 = np.arctan2(-x-0.2, -y-0.2)
+        r1 = np.hypot(0.5 - x, 0.5 - y)
+        theta1 = np.arctan2(0.5 - x, 0.5 - y)
+        r2 = np.hypot(-x - 0.2, -y - 0.2)
+        theta2 = np.arctan2(-x - 0.2, -y - 0.2)
         z = -(2*(np.exp((r1/10)**2)-1)*30. * np.cos(7.*theta1) +
               (np.exp((r2/10)**2)-1)*30. * np.cos(11.*theta2) +
               0.7*(x**2 + y**2))
@@ -750,10 +750,10 @@ def test_tri_smooth_contouring():
     min_radius = 0.15
 
     def z(x, y):
-        r1 = np.sqrt((0.5-x)**2 + (0.5-y)**2)
-        theta1 = np.arctan2(0.5-x, 0.5-y)
-        r2 = np.sqrt((-x-0.2)**2 + (-y-0.2)**2)
-        theta2 = np.arctan2(-x-0.2, -y-0.2)
+        r1 = np.hypot(0.5 - x, 0.5 - y)
+        theta1 = np.arctan2(0.5 - x, 0.5 - y)
+        r2 = np.hypot(-x - 0.2, -y - 0.2)
+        theta2 = np.arctan2(-x - 0.2, -y - 0.2)
         z = -(2*(np.exp((r1/10)**2)-1)*30. * np.cos(7.*theta1) +
               (np.exp((r2/10)**2)-1)*30. * np.cos(11.*theta2) +
               0.7*(x**2 + y**2))
@@ -815,8 +815,8 @@ def dipole_potential(x, y):
 
     # Computes the electrical field (Ex, Ey) as gradient of -V
     tci = mtri.CubicTriInterpolator(triang, -V)
-    (Ex, Ey) = tci.gradient(triang.x, triang.y)
-    E_norm = np.sqrt(Ex**2 + Ey**2)
+    Ex, Ey = tci.gradient(triang.x, triang.y)
+    E_norm = np.hypot(Ex, Ey)
 
     # Plot the triangulation, the potential iso-contours and the vector field
     plt.figure()
@@ -936,7 +936,7 @@ def test_trirefine():
     y = np.asarray([0.0, 0.0, 1.0, 1.0])
     triang = [mtri.Triangulation(x, y, [[0, 1, 3], [3, 2, 0]]),
               mtri.Triangulation(x, y, [[0, 1, 3], [2, 0, 3]])]
-    z = np.sqrt((x-0.3)*(x-0.3) + (y-0.4)*(y-0.4))
+    z = np.hypot(x - 0.3, y - 0.4)
     # Refining the 2 triangulations and reordering the points
     xyz_data = []
     for i in range(2):
diff --git a/lib/matplotlib/tri/tritools.py b/lib/matplotlib/tri/tritools.py
@@ -92,9 +92,9 @@ def circle_ratios(self, rescale=True):
         a = tri_pts[:, 1, :] - tri_pts[:, 0, :]
         b = tri_pts[:, 2, :] - tri_pts[:, 1, :]
         c = tri_pts[:, 0, :] - tri_pts[:, 2, :]
-        a = np.sqrt(a[:, 0]**2 + a[:, 1]**2)
-        b = np.sqrt(b[:, 0]**2 + b[:, 1]**2)
-        c = np.sqrt(c[:, 0]**2 + c[:, 1]**2)
+        a = np.hypot(a[:, 0], a[:, 1])
+        b = np.hypot(b[:, 0], b[:, 1])
+        c = np.hypot(c[:, 0], c[:, 1])
         # circumcircle and incircle radii
         s = (a+b+c)*0.5
         prod = s*(a+b-s)*(a+c-s)*(b+c-s)
diff --git a/lib/matplotlib/widgets.py b/lib/matplotlib/widgets.py
@@ -2685,7 +2685,7 @@ def _onmove(self, event):
             # Calculate distance to the start vertex.
             x0, y0 = self.line.get_transform().transform((self._xs[0],
                                                           self._ys[0]))
-            v0_dist = np.sqrt((x0 - event.x) ** 2 + (y0 - event.y) ** 2)
+            v0_dist = np.hypot(x0 - event.x, y0 - event.y)
             # Lock on to the start vertex if near it and ready to complete.
             if len(self._xs) > 3 and v0_dist < self.vertex_select_radius:
                 self._xs[-1], self._ys[-1] = self._xs[0], self._ys[0]
diff --git a/lib/mpl_toolkits/mplot3d/proj3d.py b/lib/mpl_toolkits/mplot3d/proj3d.py
@@ -37,7 +37,7 @@ def line2d_dist(l, p):
     """
     a, b, c = l
     x0, y0 = p
-    return abs((a*x0 + b*y0 + c) / np.sqrt(a**2+b**2))
+    return abs((a*x0 + b*y0 + c) / np.hypot(a, b))
 
 
 def line2d_seg_dist(p1, p2, p0):
@@ -57,7 +57,7 @@ def line2d_seg_dist(p1, p2, p0):
 
     u = (x01*x21 + y01*y21) / (x21**2 + y21**2)
     u = np.clip(u, 0, 1)
-    d = np.sqrt((x01 - u*x21)**2 + (y01 - u*y21)**2)
+    d = np.hypot(x01 - u*x21, y01 - u*y21)
 
     return d
 
diff --git a/lib/mpl_toolkits/tests/test_mplot3d.py b/lib/mpl_toolkits/tests/test_mplot3d.py
@@ -154,7 +154,7 @@ def f(t):
 
     ax = fig.add_subplot(2, 1, 2, projection='3d')
     X, Y = np.meshgrid(np.arange(-5, 5, 0.25), np.arange(-5, 5, 0.25))
-    R = np.sqrt(X ** 2 + Y ** 2)
+    R = np.hypot(X, Y)
     Z = np.sin(R)
 
     surf = ax.plot_surface(X, Y, Z, rcount=40, ccount=40,
@@ -202,7 +202,7 @@ def test_surface3d():
     X = np.arange(-5, 5, 0.25)
     Y = np.arange(-5, 5, 0.25)
     X, Y = np.meshgrid(X, Y)
-    R = np.sqrt(X ** 2 + Y ** 2)
+    R = np.hypot(X, Y)
     Z = np.sin(R)
     surf = ax.plot_surface(X, Y, Z, rcount=40, ccount=40, cmap=cm.coolwarm,
                            lw=0, antialiased=False)
