diff --git a/examples/GLIsosurface.py b/examples/GLIsosurface.py
index 16045a78..1afe797c 100644
--- a/examples/GLIsosurface.py
+++ b/examples/GLIsosurface.py
@@ -7,7 +7,7 @@ This example uses the isosurface function to convert a scalar field
 ## Add path to library (just for examples; you do not need this)
 import initExample
 
-from pyqtgraph.Qt import QtCore, QtGui
+import numpy as np
 import pyqtgraph as pg
 import pyqtgraph.opengl as gl
 
@@ -22,23 +22,16 @@ g = gl.GLGridItem()
 g.scale(2,2,1)
 w.addItem(g)
 
-import numpy as np
-
 ## Define a scalar field from which we will generate an isosurface
 def psi(i, j, k, offset=(25, 25, 50)):
     x = i-offset[0]
     y = j-offset[1]
     z = k-offset[2]
-    th = np.arctan2(z, (x**2+y**2)**0.5)
-    phi = np.arctan2(y, x)
-    r = (x**2 + y**2 + z **2)**0.5
+    th = np.arctan2(z, np.hypot(x, y))
+    r = np.sqrt(x**2 + y**2 + z **2)
     a0 = 1
-    #ps = (1./81.) * (2./np.pi)**0.5 * (1./a0)**(3/2) * (6 - r/a0) * (r/a0) * np.exp(-r/(3*a0)) * np.cos(th)
     ps = (1./81.) * 1./(6.*np.pi)**0.5 * (1./a0)**(3/2) * (r/a0)**2 * np.exp(-r/(3*a0)) * (3 * np.cos(th)**2 - 1)
-    
     return ps
-    
-    #return ((1./81.) * (1./np.pi)**0.5 * (1./a0)**(3/2) * (r/a0)**2 * (r/a0) * np.exp(-r/(3*a0)) * np.sin(th) * np.cos(th) * np.exp(2 * 1j * phi))**2 
 
 
 print("Generating scalar field..")
diff --git a/examples/GLLinePlotItem.py b/examples/GLLinePlotItem.py
index b375c1c1..82e1f6fb 100644
--- a/examples/GLLinePlotItem.py
+++ b/examples/GLLinePlotItem.py
@@ -29,19 +29,16 @@ gz = gl.GLGridItem()
 gz.translate(0, 0, -10)
 w.addItem(gz)
 
-def fn(x, y):
-    return np.cos((x**2 + y**2)**0.5)
-
 n = 51
 y = np.linspace(-10,10,n)
 x = np.linspace(-10,10,100)
 for i in range(n):
-    yi = np.array([y[i]]*100)
-    d = (x**2 + yi**2)**0.5
+    yi = y[i]
+    d = np.hypot(x, yi)
     z = 10 * np.cos(d) / (d+1)
-    pts = np.vstack([x,yi,z]).transpose()
+    pts = np.column_stack([x, np.full_like(x, yi), z])
     plt = gl.GLLinePlotItem(pos=pts, color=pg.glColor((i,n*1.3)), width=(i+1)/10., antialias=True)
     w.addItem(plt)
-    
+
 if __name__ == '__main__':
     pg.mkQApp().exec_()
diff --git a/examples/GLScatterPlotItem.py b/examples/GLScatterPlotItem.py
index c279eadf..1d8d5e06 100644
--- a/examples/GLScatterPlotItem.py
+++ b/examples/GLScatterPlotItem.py
@@ -8,6 +8,7 @@ Demonstrates use of GLScatterPlotItem with rapidly-updating plots.
 import initExample
 
 import pyqtgraph as pg
+from pyqtgraph import functions as fn
 from pyqtgraph.Qt import QtCore, QtGui
 import pyqtgraph.opengl as gl
 import numpy as np
@@ -84,10 +85,10 @@ def update():
     global phase, sp2, d2
     s = -np.cos(d2*2+phase)
     color = np.empty((len(d2),4), dtype=np.float32)
-    color[:,3] = np.clip(s * 0.1, 0, 1)
-    color[:,0] = np.clip(s * 3.0, 0, 1)
-    color[:,1] = np.clip(s * 1.0, 0, 1)
-    color[:,2] = np.clip(s ** 3, 0, 1)
+    color[:,3] = fn.clip_array(s * 0.1, 0., 1.)
+    color[:,0] = fn.clip_array(s * 3.0, 0., 1.)
+    color[:,1] = fn.clip_array(s * 1.0, 0., 1.)
+    color[:,2] = fn.clip_array(s ** 3, 0., 1.)
     sp2.setData(color=color)
     phase -= 0.1
     
diff --git a/examples/GLVolumeItem.py b/examples/GLVolumeItem.py
index 5d7e6601..ba67514b 100644
--- a/examples/GLVolumeItem.py
+++ b/examples/GLVolumeItem.py
@@ -7,9 +7,10 @@ Demonstrates GLVolumeItem for displaying volumetric data.
 ## Add path to library (just for examples; you do not need this)
 import initExample
 
+import numpy as np
 import pyqtgraph as pg
-from pyqtgraph.Qt import QtCore, QtGui
 import pyqtgraph.opengl as gl
+from pyqtgraph import functions as fn
 
 app = pg.mkQApp("GLVolumeItem Example")
 w = gl.GLViewWidget()
@@ -23,27 +24,21 @@ g = gl.GLGridItem()
 g.scale(10, 10, 1)
 w.addItem(g)
 
-import numpy as np
 ## Hydrogen electron probability density
 def psi(i, j, k, offset=(50,50,100)):
     x = i-offset[0]
     y = j-offset[1]
     z = k-offset[2]
-    th = np.arctan2(z, (x**2+y**2)**0.5)
-    phi = np.arctan2(y, x)
-    r = (x**2 + y**2 + z **2)**0.5
+    th = np.arctan2(z, np.hypot(x, y))
+    r = np.sqrt(x**2 + y**2 + z **2)
     a0 = 2
-    #ps = (1./81.) * (2./np.pi)**0.5 * (1./a0)**(3/2) * (6 - r/a0) * (r/a0) * np.exp(-r/(3*a0)) * np.cos(th)
     ps = (1./81.) * 1./(6.*np.pi)**0.5 * (1./a0)**(3/2) * (r/a0)**2 * np.exp(-r/(3*a0)) * (3 * np.cos(th)**2 - 1)
-    
     return ps
-    
-    #return ((1./81.) * (1./np.pi)**0.5 * (1./a0)**(3/2) * (r/a0)**2 * (r/a0) * np.exp(-r/(3*a0)) * np.sin(th) * np.cos(th) * np.exp(2 * 1j * phi))**2 
 
 
 data = np.fromfunction(psi, (100,100,200))
-positive = np.log(np.clip(data, 0, data.max())**2)
-negative = np.log(np.clip(-data, 0, -data.min())**2)
+positive = np.log(fn.clip_array(data, np.finfo(data.dtype).eps, data.max())**2)
+negative = np.log(fn.clip_array(-data, -np.finfo(data.dtype).eps, -data.min())**2)
 
 d2 = np.empty(data.shape + (4,), dtype=np.ubyte)
 d2[..., 0] = positive * (255./positive.max())
diff --git a/examples/GLshaders.py b/examples/GLshaders.py
index 4e1acc51..38e6988d 100644
--- a/examples/GLshaders.py
+++ b/examples/GLshaders.py
@@ -9,6 +9,7 @@ used to affect the appearance of a surface.
 ## Add path to library (just for examples; you do not need this)
 import initExample
 
+import numpy as np
 from pyqtgraph.Qt import QtCore, QtGui
 import pyqtgraph as pg
 import pyqtgraph.opengl as gl
@@ -23,9 +24,6 @@ g = gl.GLGridItem()
 g.scale(2,2,1)
 w.addItem(g)
 
-import numpy as np
-
-
 md = gl.MeshData.sphere(rows=10, cols=20)
 x = np.linspace(-8, 8, 6)
 
diff --git a/examples/optics/pyoptic.py b/examples/optics/pyoptic.py
index f70edd2a..99221bd7 100644
--- a/examples/optics/pyoptic.py
+++ b/examples/optics/pyoptic.py
@@ -1,4 +1,5 @@
 # -*- coding: utf-8 -*-
+from math import atan2, asin, sin, cos, degrees, sqrt, hypot
 import pyqtgraph as pg
 from pyqtgraph.Qt import QtGui, QtCore
 import numpy as np
@@ -49,7 +50,7 @@ class GlassDB:
             B = list(map(float, [info['B1'], info['B2'], info['B3']]))
             C = list(map(float, [info['C1'], info['C2'], info['C3']]))
             w2 = (wl/1000.)**2
-            n = np.sqrt(1.0 + (B[0]*w2 / (w2-C[0])) + (B[1]*w2 / (w2-C[1])) + (B[2]*w2 / (w2-C[2])))
+            n = sqrt(1.0 + (B[0]*w2 / (w2-C[0])) + (B[1]*w2 / (w2-C[1])) + (B[2]*w2 / (w2-C[2])))
             cache[wl] = n
         return cache[wl]
         
@@ -249,10 +250,14 @@ class Lens(Optic):
             p1 = surface.mapToItem(ray, p1)
             
             rd = ray['dir']
-            a1 = np.arctan2(rd[1], rd[0])
-            ar = a1 - ai + np.arcsin((np.sin(ai) * ray['ior'] / ior))
+
+            a1 = atan2(rd[1], rd[0])
+            try:
+                ar = a1 - ai + asin((sin(ai) * ray['ior'] / ior))
+            except ValueError:
+                ar = np.nan
             ray.setEnd(p1)
-            dp = Point(np.cos(ar), np.sin(ar))
+            dp = Point(cos(ar), sin(ar))
             ray = Ray(parent=ray, ior=ior, dir=dp)
         return [ray]
         
@@ -279,10 +284,10 @@ class Mirror(Optic):
         if p1 is not None:
             p1 = surface.mapToItem(ray, p1)
             rd = ray['dir']
-            a1 = np.arctan2(rd[1], rd[0])
-            ar = a1  + np.pi - 2*ai
+            a1 = atan2(rd[1], rd[0])
+            ar = a1 + np.pi - 2 * ai
             ray.setEnd(p1)
-            dp = Point(np.cos(ar), np.sin(ar))
+            dp = Point(cos(ar), sin(ar))
             ray = Ray(parent=ray, dir=dp)
         else:
             ray.setEnd(None)
@@ -374,7 +379,7 @@ class CircleSurface(pg.GraphicsObject):
             ## half-height of surface can't be larger than radius
             h2 = min(h2, abs(r))
             arc = QtCore.QRectF(0, -r, r*2, r*2)
-            a1 = np.arcsin(h2/r) * 180. / np.pi
+            a1 = degrees(asin(h2/r))
             a2 = -2*a1
             a1 += 180.
             self.path.arcMoveTo(arc, a1)
@@ -406,13 +411,13 @@ class CircleSurface(pg.GraphicsObject):
             if abs(y) > h:
                 return None, None
             else:
-                return (Point(0, y), np.arctan2(dir[1], dir[0]))
+                return (Point(0, y), atan2(dir[1], dir[0]))
         else:
             #print "  curve"
             ## find intersection of circle and line (quadratic formula)
             dx = dir[0]
             dy = dir[1]
-            dr = (dx**2 + dy**2) ** 0.5
+            dr = hypot(dx, dy)  # length
             D = p[0] * (p[1]+dy) - (p[0]+dx) * p[1]
             idr2 = 1.0 / dr**2
             disc = r**2 * dr**2 - D**2
@@ -423,8 +428,7 @@ class CircleSurface(pg.GraphicsObject):
                 sgn = -1
             else:
                 sgn = 1
-            
-        
+
             br = self.path.boundingRect()
             x1 = (D*dy + sgn*dx*disc2) * idr2
             y1 = (-D*dx + abs(dy)*disc2) * idr2
@@ -436,19 +440,12 @@ class CircleSurface(pg.GraphicsObject):
                 pt = Point(x2, y2)
                 if not br.contains(x2+r, y2):
                     return None, None
-                    raise Exception("No intersection!")
                 
-            norm = np.arctan2(pt[1], pt[0])
+            norm = atan2(pt[1], pt[0])
             if r < 0:
                 norm += np.pi
-            #print "  norm:", norm*180/3.1415
             dp = p - pt
-            #print "  dp:", dp
-            ang = np.arctan2(dp[1], dp[0]) 
-            #print "  ang:", ang*180/3.1415
-            #print "  ai:", (ang-norm)*180/3.1415
-            
-            #print "  intersection:", pt
+            ang = atan2(dp[1], dp[0]) 
             return pt + Point(r, 0), ang-norm
 
             
diff --git a/pyqtgraph/Point.py b/pyqtgraph/Point.py
index fea37dda..bdd8bc33 100644
--- a/pyqtgraph/Point.py
+++ b/pyqtgraph/Point.py
@@ -6,14 +6,8 @@ Distributed under MIT/X11 license. See license.txt for more information.
 """
 
 from .Qt import QtCore
-import numpy as np
+from math import atan2, hypot, degrees
 
-def clip(x, mn, mx):
-    if x > mx:
-        return mx
-    if x < mn:
-        return mn
-    return x
 
 class Point(QtCore.QPointF):
     """Extension of QPointF which adds a few missing methods."""
@@ -93,42 +87,21 @@ class Point(QtCore.QPointF):
         return self._math_('__pow__', a)
     
     def _math_(self, op, x):
-        #print "point math:", op
-        #try:
-            #fn  = getattr(QtCore.QPointF, op)
-            #pt = fn(self, x)
-            #print fn, pt, self, x
-            #return Point(pt)
-        #except AttributeError:
         x = Point(x)
         return Point(getattr(self[0], op)(x[0]), getattr(self[1], op)(x[1]))
     
     def length(self):
         """Returns the vector length of this Point."""
-        try:
-            return (self[0]**2 + self[1]**2) ** 0.5
-        except OverflowError:
-            try:
-                return self[1] / np.sin(np.arctan2(self[1], self[0]))
-            except OverflowError:
-                return np.inf
-    
+        return hypot(self[0], self[1])  # length
+
     def norm(self):
         """Returns a vector in the same direction with unit length."""
         return self / self.length()
     
     def angle(self, a):
         """Returns the angle in degrees between this vector and the vector a."""
-        n1 = self.length()
-        n2 = a.length()
-        if n1 == 0. or n2 == 0.:
-            return None
-        ## Probably this should be done with arctan2 instead..
-        ang = np.arccos(clip(self.dot(a) / (n1 * n2), -1.0, 1.0)) ### in radians
-        c = self.cross(a)
-        if c > 0:
-            ang *= -1.
-        return ang * 180. / np.pi
+        rads = atan2(self.y(), self.x()) - atan2(a.y(), a.x())
+        return degrees(rads)
     
     def dot(self, a):
         """Returns the dot product of a and this Point."""
@@ -146,8 +119,7 @@ class Point(QtCore.QPointF):
     
     def __repr__(self):
         return "Point(%f, %f)" % (self[0], self[1])
-    
-    
+
     def min(self):
         return min(self[0], self[1])
     
diff --git a/pyqtgraph/SRTTransform.py b/pyqtgraph/SRTTransform.py
index 35ec0625..a340f8b6 100644
--- a/pyqtgraph/SRTTransform.py
+++ b/pyqtgraph/SRTTransform.py
@@ -1,4 +1,5 @@
 # -*- coding: utf-8 -*-
+from math import atan2, degrees
 from .Qt import QtCore, QtGui
 from .Point import Point
 import numpy as np
@@ -76,7 +77,7 @@ class SRTTransform(QtGui.QTransform):
         self._state = {
             'pos': Point(p1),
             'scale': Point(dp2.length(), dp3.length() * sy),
-            'angle': (np.arctan2(dp2[1], dp2[0]) * 180. / np.pi) + da
+            'angle': degrees(atan2(dp2[1], dp2[0])) + da
         }
         self.update()
         
diff --git a/pyqtgraph/SRTTransform3D.py b/pyqtgraph/SRTTransform3D.py
index 7d458edd..2fd3ff87 100644
--- a/pyqtgraph/SRTTransform3D.py
+++ b/pyqtgraph/SRTTransform3D.py
@@ -1,4 +1,5 @@
 # -*- coding: utf-8 -*-
+from math import atan2, degrees
 from .Qt import QtCore, QtGui
 from .Vector import Vector
 from .Transform3D import Transform3D
@@ -164,7 +165,7 @@ class SRTTransform3D(Transform3D):
         sin = (r-r.T)[rInd] / (2. * sign * axis[axisInd])
         
         ## finally, we get the complete angle from arctan(sin/cos)
-        self._state['angle'] = np.arctan2(sin, cos) * 180 / np.pi
+        self._state['angle'] = degrees(atan2(sin, cos))
         if self._state['angle'] == 0:
             self._state['axis'] = (0,0,1)
         
diff --git a/pyqtgraph/Vector.py b/pyqtgraph/Vector.py
index a9d28e41..a64e8968 100644
--- a/pyqtgraph/Vector.py
+++ b/pyqtgraph/Vector.py
@@ -4,9 +4,9 @@ Vector.py -  Extension of QVector3D which adds a few missing methods.
 Copyright 2010  Luke Campagnola
 Distributed under MIT/X11 license. See license.txt for more information.
 """
-
+from math import acos, degrees
 from .Qt import QtGui, QtCore, QT_LIB
-import numpy as np
+from . import functions as fn
 
 class Vector(QtGui.QVector3D):
     """Extension of QVector3D which adds a few helpful methods."""
@@ -88,11 +88,11 @@ class Vector(QtGui.QVector3D):
         if n1 == 0. or n2 == 0.:
             return None
         ## Probably this should be done with arctan2 instead..
-        ang = np.arccos(np.clip(QtGui.QVector3D.dotProduct(self, a) / (n1 * n2), -1.0, 1.0)) ### in radians
+        rads = acos(fn.clip_scalar(QtGui.QVector3D.dotProduct(self, a) / (n1 * n2), -1.0, 1.0)) ### in radians
 #        c = self.crossProduct(a)
 #        if c > 0:
 #            ang *= -1.
-        return ang * 180. / np.pi
+        return degrees(rads)
 
     def __abs__(self):
         return Vector(abs(self.x()), abs(self.y()), abs(self.z()))
diff --git a/pyqtgraph/canvas/CanvasItem.py b/pyqtgraph/canvas/CanvasItem.py
index 88612055..3883919e 100644
--- a/pyqtgraph/canvas/CanvasItem.py
+++ b/pyqtgraph/canvas/CanvasItem.py
@@ -1,6 +1,6 @@
 # -*- coding: utf-8 -*-
-import numpy as np
-from ..Qt import QtGui, QtCore, QtSvg, QT_LIB
+from ..Qt import QtGui, QtCore, QT_LIB
+from .. import functions as fn
 from ..graphicsItems.ROI import ROI
 from .. import SRTTransform, ItemGroup
 import importlib
@@ -240,7 +240,7 @@ class CanvasItem(QtCore.QObject):
         self._graphicsItem.setOpacity(alpha)
         
     def setAlpha(self, alpha):
-        self.alphaSlider.setValue(int(np.clip(alpha * 1023, 0, 1023)))
+        self.alphaSlider.setValue(int(fn.clip_scalar(alpha * 1023, 0, 1023)))
         
     def alpha(self):
         return self.alphaSlider.value() / 1023.
diff --git a/pyqtgraph/debug.py b/pyqtgraph/debug.py
index 15d1fb3c..37b612cd 100644
--- a/pyqtgraph/debug.py
+++ b/pyqtgraph/debug.py
@@ -202,7 +202,7 @@ def findRefPath(startObj, endObj, maxLen=8, restart=True, seen={}, path=None, ig
             #print prefix+"  FRAME"
             continue
         try:
-            if any([r is x for x in  path]):
+            if any(r is x for x in  path):
                 #print prefix+"  LOOP", objChainString([r]+path)
                 continue
         except:
@@ -282,7 +282,7 @@ def refPathString(chain):
         o2 = chain[i]
         cont = False
         if isinstance(o1, list) or isinstance(o1, tuple):
-            if any([o2 is x for x in o1]):
+            if any(o2 is x for x in o1):
                 s += "[%d]" % o1.index(o2)
                 continue
         #print "  not list"
diff --git a/pyqtgraph/dockarea/Container.py b/pyqtgraph/dockarea/Container.py
index 04b775f9..34f16288 100644
--- a/pyqtgraph/dockarea/Container.py
+++ b/pyqtgraph/dockarea/Container.py
@@ -126,7 +126,7 @@ class SplitContainer(Container, QtGui.QSplitter):
         
     def saveState(self):
         sizes = self.sizes()
-        if all([x == 0 for x in sizes]):
+        if all(x == 0 for x in sizes):
             sizes = [10] * len(sizes)
         return {'sizes': sizes}
         
diff --git a/pyqtgraph/functions.py b/pyqtgraph/functions.py
index 6b9916c1..45043a4c 100644
--- a/pyqtgraph/functions.py
+++ b/pyqtgraph/functions.py
@@ -60,19 +60,15 @@ def siScale(x, minVal=1e-25, allowUnicode=True):
     
     if isinstance(x, decimal.Decimal):
         x = float(x)
-        
     try:
-        if np.isnan(x) or np.isinf(x):
+        if not math.isfinite(x):
             return(1, '')
     except:
-        print(x, type(x))
         raise
     if abs(x) < minVal:
         m = 0
-        x = 0
     else:
-        m = int(np.clip(np.floor(np.log(abs(x))/np.log(1000)), -9.0, 9.0))
-    
+        m = int(clip_scalar(math.floor(math.log(abs(x))/math.log(1000)), -9.0, 9.0))
     if m == 0:
         pref = ''
     elif m < -8 or m > 8:
@@ -84,7 +80,6 @@ def siScale(x, minVal=1e-25, allowUnicode=True):
             pref = SI_PREFIXES_ASCII[m+8]
     m1 = -3*m
     p = 10.**m1
-    
     return (p, pref)
 
 
@@ -268,6 +263,8 @@ def mkColor(*args):
                 g = int(c[2:4], 16)
                 b = int(c[4:6], 16)
                 a = int(c[6:8], 16)
+            else:
+                raise ValueError(f"Unknown how to convert string {c} to color")
         elif isinstance(args[0], QtGui.QColor):
             return QtGui.QColor(args[0])
         elif np.issubdtype(type(args[0]), np.floating):
@@ -275,10 +272,10 @@ def mkColor(*args):
             a = 255
         elif hasattr(args[0], '__len__'):
             if len(args[0]) == 3:
-                (r, g, b) = args[0]
+                r, g, b = args[0]
                 a = 255
             elif len(args[0]) == 4:
-                (r, g, b, a) = args[0]
+                r, g, b, a = args[0]
             elif len(args[0]) == 2:
                 return intColor(*args[0])
             else:
@@ -288,16 +285,13 @@ def mkColor(*args):
         else:
             raise TypeError(err)
     elif len(args) == 3:
-        (r, g, b) = args
+        r, g, b = args
         a = 255
     elif len(args) == 4:
-        (r, g, b, a) = args
+        r, g, b, a = args
     else:
         raise TypeError(err)
-    
-    args = [r,g,b,a]
-    args = [0 if np.isnan(a) or np.isinf(a) else a for a in args]
-    args = list(map(int, args))
+    args = [int(a) if np.isfinite(a) else 0 for a in (r, g, b, a)]
     return QtGui.QColor(*args)
 
 
@@ -432,16 +426,16 @@ def makeArrowPath(headLen=20, headWidth=None, tipAngle=20, tailLen=20, tailWidth
     If *tailLen* is None, no tail will be drawn.
     """
     if headWidth is None:
-        headWidth = headLen * np.tan(tipAngle * 0.5 * np.pi/180.)
+        headWidth = headLen * math.tan(math.radians(tipAngle * 0.5))
     path = QtGui.QPainterPath()
     path.moveTo(0,0)
     path.lineTo(headLen, -headWidth)
     if tailLen is None:
-        innerY = headLen - headWidth * np.tan(baseAngle*np.pi/180.)
+        innerY = headLen - headWidth * math.tan(math.radians(baseAngle))
         path.lineTo(innerY, 0)
     else:
         tailWidth *= 0.5
-        innerY = headLen - (headWidth-tailWidth) * np.tan(baseAngle*np.pi/180.)
+        innerY = headLen - (headWidth-tailWidth) * math.tan(math.radians(baseAngle))
         path.lineTo(innerY, -tailWidth)
         path.lineTo(headLen + tailLen, -tailWidth)
         path.lineTo(headLen + tailLen, tailWidth)
@@ -458,7 +452,7 @@ def eq(a, b):
     
     1. Returns True if a IS b, even if a==b still evaluates to False.
     2. While a is b will catch the case with np.nan values, special handling is done for distinct
-       float('nan') instances using np.isnan.
+       float('nan') instances using math.isnan.
     3. Tests for equivalence using ==, but silently ignores some common exceptions that can occur
        (AtrtibuteError, ValueError).
     4. When comparing arrays, returns False if the array shapes are not the same.
@@ -472,7 +466,7 @@ def eq(a, b):
 
     # The above catches np.nan, but not float('nan')
     if isinstance(a, float) and isinstance(b, float):
-        if np.isnan(a) and np.isnan(b):
+        if math.isnan(a) and math.isnan(b):
             return True
 
     # Avoid comparing large arrays against scalars; this is expensive and we know it should return False.
diff --git a/pyqtgraph/graphicsItems/ArrowItem.py b/pyqtgraph/graphicsItems/ArrowItem.py
index 77b6c44c..2d79d360 100644
--- a/pyqtgraph/graphicsItems/ArrowItem.py
+++ b/pyqtgraph/graphicsItems/ArrowItem.py
@@ -1,3 +1,4 @@
+from math import hypot
 from ..Qt import QtGui, QtCore
 from .. import functions as fn
 import numpy as np
@@ -135,7 +136,7 @@ class ArrowItem(QtGui.QGraphicsPathItem):
         pad = 0
         if self.opts['pxMode']:
             br = self.boundingRect()
-            pad += (br.width()**2 + br.height()**2) ** 0.5
+            pad += hypot(br.width(), br.height())
         pen = self.pen()
         if pen.isCosmetic():
             pad += max(1, pen.width()) * 0.7072
diff --git a/pyqtgraph/graphicsItems/AxisItem.py b/pyqtgraph/graphicsItems/AxisItem.py
index 37490d9d..28459923 100644
--- a/pyqtgraph/graphicsItems/AxisItem.py
+++ b/pyqtgraph/graphicsItems/AxisItem.py
@@ -4,6 +4,7 @@ from ..python2_3 import asUnicode
 import numpy as np
 from ..Point import Point
 from .. import debug as debug
+from math import ceil, floor, log, log10, isfinite
 import sys
 import weakref
 from .. import functions as fn
@@ -511,7 +512,7 @@ class AxisItem(GraphicsWidget):
     def setRange(self, mn, mx):
         """Set the range of values displayed by the axis.
         Usually this is handled automatically by linking the axis to a ViewBox with :func:`linkToView <pyqtgraph.AxisItem.linkToView>`"""
-        if any(np.isinf((mn, mx))) or any(np.isnan((mn, mx))):
+        if not isfinite(mn) or not isfinite(mx):
             raise Exception("Not setting range to [%s, %s]" % (str(mn), str(mx)))
         self.range = [mn, mx]
         if self.autoSIPrefix:
@@ -680,13 +681,13 @@ class AxisItem(GraphicsWidget):
             return []
 
         ## decide optimal minor tick spacing in pixels (this is just aesthetics)
-        optimalTickCount = max(2., np.log(size))
+        optimalTickCount = max(2., log(size))
 
         ## optimal minor tick spacing
         optimalSpacing = dif / optimalTickCount
 
         ## the largest power-of-10 spacing which is smaller than optimal
-        p10unit = 10 ** np.floor(np.log10(optimalSpacing))
+        p10unit = 10 ** floor(log10(optimalSpacing))
 
         ## Determine major/minor tick spacings which flank the optimal spacing.
         intervals = np.array([1., 2., 10., 20., 100.]) * p10unit
@@ -758,7 +759,7 @@ class AxisItem(GraphicsWidget):
             spacing, offset = tickLevels[i]
 
             ## determine starting tick
-            start = (np.ceil((minVal-offset) / spacing) * spacing) + offset
+            start = (ceil((minVal-offset) / spacing) * spacing) + offset
 
             ## determine number of ticks
             num = int((maxVal-start) / spacing) + 1
@@ -766,7 +767,7 @@ class AxisItem(GraphicsWidget):
             ## remove any ticks that were present in higher levels
             ## we assume here that if the difference between a tick value and a previously seen tick value
             ## is less than spacing/100, then they are 'equal' and we can ignore the new tick.
-            values = list(filter(lambda x: all(np.abs(allValues-x) > spacing/self.scale*0.01), values))
+            values = list(filter(lambda x: np.all(np.abs(allValues-x) > spacing/self.scale*0.01), values))
             allValues = np.concatenate([allValues, values])
             ticks.append((spacing/self.scale, values))
 
@@ -795,8 +796,8 @@ class AxisItem(GraphicsWidget):
                 ticks.append((spacing, t))
 
         if len(ticks) < 3:
-            v1 = int(np.floor(minVal))
-            v2 = int(np.ceil(maxVal))
+            v1 = int(floor(minVal))
+            v2 = int(ceil(maxVal))
             #major = list(range(v1+1, v2))
 
             minor = []
@@ -822,7 +823,7 @@ class AxisItem(GraphicsWidget):
         if self.logMode:
             return self.logTickStrings(values, scale, spacing)
 
-        places = max(0, np.ceil(-np.log10(spacing*scale)))
+        places = max(0, ceil(-log10(spacing*scale)))
         strings = []
         for v in values:
             vs = v * scale
@@ -969,7 +970,7 @@ class AxisItem(GraphicsWidget):
             if lineAlpha is None:
                 lineAlpha = 255 / (i+1)
                 if self.grid is not False:
-                    lineAlpha *= self.grid/255. * np.clip((0.05  * lengthInPixels / (len(ticks)+1)), 0., 1.)
+                    lineAlpha *= self.grid/255. * fn.clip_scalar((0.05  * lengthInPixels / (len(ticks)+1)), 0., 1.)
             elif isinstance(lineAlpha, float):
                 lineAlpha *= 255
                 lineAlpha = max(0, int(round(lineAlpha)))
diff --git a/pyqtgraph/graphicsItems/CurvePoint.py b/pyqtgraph/graphicsItems/CurvePoint.py
index 368a0a82..c7052ddb 100644
--- a/pyqtgraph/graphicsItems/CurvePoint.py
+++ b/pyqtgraph/graphicsItems/CurvePoint.py
@@ -1,6 +1,7 @@
+from math import atan2, degrees
 from ..Qt import QtGui, QtCore
 from . import ArrowItem
-import numpy as np
+from ..functions import clip_scalar
 from ..Point import Point
 import weakref
 from .GraphicsObject import GraphicsObject
@@ -61,26 +62,26 @@ class CurvePoint(GraphicsObject):
             pos = self.property('position')
             if 'QVariant' in repr(pos):   ## need to support 2 APIs  :(
                 pos = pos.toDouble()[0]
-            index = (len(x)-1) * np.clip(pos, 0.0, 1.0)
+            index = (len(x)-1) * clip_scalar(pos, 0.0, 1.0)
             
         if index != int(index):  ## interpolate floating-point values
             i1 = int(index)
-            i2 = np.clip(i1+1, 0, len(x)-1)
+            i2 = clip_scalar(i1+1, 0, len(x)-1)
             s2 = index-i1
             s1 = 1.0-s2
             newPos = (x[i1]*s1+x[i2]*s2, y[i1]*s1+y[i2]*s2)
         else:
             index = int(index)
-            i1 = np.clip(index-1, 0, len(x)-1)
-            i2 = np.clip(index+1, 0, len(x)-1)
+            i1 = clip_scalar(index-1, 0, len(x)-1)
+            i2 = clip_scalar(index+1, 0, len(x)-1)
             newPos = (x[index], y[index])
             
         p1 = self.parentItem().mapToScene(QtCore.QPointF(x[i1], y[i1]))
         p2 = self.parentItem().mapToScene(QtCore.QPointF(x[i2], y[i2]))
-        ang = np.arctan2(p2.y()-p1.y(), p2.x()-p1.x()) ## returns radians
+        rads = atan2(p2.y()-p1.y(), p2.x()-p1.x()) ## returns radians
         self.resetTransform()
         if self._rotate:
-            self.setRotation(180 + np.rad2deg(ang)) ## takes degrees
+            self.setRotation(180 + degrees(rads))
         QtGui.QGraphicsItem.setPos(self, *newPos)
         return True
         
diff --git a/pyqtgraph/graphicsItems/GraphicsItem.py b/pyqtgraph/graphicsItems/GraphicsItem.py
index 61f48a45..273d419f 100644
--- a/pyqtgraph/graphicsItems/GraphicsItem.py
+++ b/pyqtgraph/graphicsItems/GraphicsItem.py
@@ -1,4 +1,5 @@
 import warnings
+from math import hypot
 from collections import OrderedDict
 from functools import reduce
 from ..Qt import QtGui, QtCore, isQObjectAlive
@@ -308,7 +309,7 @@ class GraphicsItem(object):
         v = self.pixelVectors()
         if v == (None, None):
             return None, None
-        return (v[0].x()**2+v[0].y()**2)**0.5, (v[1].x()**2+v[1].y()**2)**0.5
+        return (hypot(v[0].x(), v[0].y()), hypot(v[1].x(), v[1].y()))  # lengths
 
     def pixelWidth(self):
         ## deprecated
diff --git a/pyqtgraph/graphicsItems/GridItem.py b/pyqtgraph/graphicsItems/GridItem.py
index 4cb30bf8..312d7b62 100644
--- a/pyqtgraph/graphicsItems/GridItem.py
+++ b/pyqtgraph/graphicsItems/GridItem.py
@@ -126,8 +126,7 @@ class GridItem(UIGraphicsItem):
         for i in range(self.grid_depth - 1, -1, -1):
             dist = br-ul
             nlTarget = 10.**i
-
-            d = 10. ** np.floor(np.log10(abs(dist/nlTarget))+0.5)
+            d = 10. ** np.floor(np.log10(np.abs(dist/nlTarget))+0.5)
             for ax in range(0,2):
                 ts = self.opts['tickSpacing'][ax]
                 try:
@@ -141,11 +140,6 @@ class GridItem(UIGraphicsItem):
             br1 = np.ceil(br / d) * d
             dist = br1-ul1
             nl = (dist / d) + 0.5
-            #print "level", i
-            #print "  dim", dim
-            #print "  dist", dist
-            #print "  d", d
-            #print "  nl", nl
             for ax in range(0,2):  ## Draw grid for both axes
                 if i >= len(self.opts['tickSpacing'][ax]):
                     continue
@@ -153,7 +147,7 @@ class GridItem(UIGraphicsItem):
                     continue
 
                 ppl = dim[ax] / nl[ax]
-                c = np.clip(5 * (ppl-3), 0., 50.).astype(int)
+                c = int(fn.clip_scalar(5 * (ppl-3), 0, 50))
 
                 linePen = self.opts['pen']
                 lineColor = self.opts['pen'].color()
diff --git a/pyqtgraph/graphicsItems/InfiniteLine.py b/pyqtgraph/graphicsItems/InfiniteLine.py
index 74a8da95..c64a4684 100644
--- a/pyqtgraph/graphicsItems/InfiniteLine.py
+++ b/pyqtgraph/graphicsItems/InfiniteLine.py
@@ -1,4 +1,5 @@
 # -*- coding: utf-8 -*-
+from math import atan2, degrees
 from ..Qt import QtGui, QtCore
 from ..Point import Point
 from .GraphicsObject import GraphicsObject
@@ -359,7 +360,7 @@ class InfiniteLine(GraphicsObject):
         up = tr.map(Point(left, 1))
         dif = end - start
         length = Point(dif).length()
-        angle = np.arctan2(dif.y(), dif.x()) * 180 / np.pi
+        angle = degrees(atan2(dif.y(), dif.x()))
         
         p.translate(start)
         p.rotate(angle)
@@ -592,7 +593,7 @@ class InfLineLabel(TextItem):
                 return
 
             rel = self._posToRel(ev.pos())
-            self.orthoPos = np.clip(self._startPosition + rel - self._cursorOffset, 0, 1)
+            self.orthoPos = fn.clip_scalar(self._startPosition + rel - self._cursorOffset, 0., 1.)
             self.updatePosition()
             if ev.isFinish():
                 self._moving = False
diff --git a/pyqtgraph/graphicsItems/NonUniformImage.py b/pyqtgraph/graphicsItems/NonUniformImage.py
index 2b697767..fc42bf27 100644
--- a/pyqtgraph/graphicsItems/NonUniformImage.py
+++ b/pyqtgraph/graphicsItems/NonUniformImage.py
@@ -1,4 +1,5 @@
 from ..Qt import QtGui, QtCore
+import math
 import numpy as np
 from ..colormap import ColorMap
 from .GraphicsObject import GraphicsObject
@@ -94,7 +95,7 @@ class NonUniformImage(GraphicsObject):
                     value = 0.0
                 elif np.isposinf(value):
                     value = 1.0
-                elif np.isnan(value):
+                elif math.isnan(value):
                     continue  # ignore NaN
                 else:
                     value = (value - mn) / (mx - mn)  # normalize
diff --git a/pyqtgraph/graphicsItems/PlotCurveItem.py b/pyqtgraph/graphicsItems/PlotCurveItem.py
index 39003813..06f9bdee 100644
--- a/pyqtgraph/graphicsItems/PlotCurveItem.py
+++ b/pyqtgraph/graphicsItems/PlotCurveItem.py
@@ -1,7 +1,7 @@
 # -*- coding: utf-8 -*-
 from ..Qt import QtCore, QtGui, QtWidgets
 HAVE_OPENGL = hasattr(QtWidgets, 'QOpenGLWidget')
-
+import math
 import warnings
 import numpy as np
 from .GraphicsObject import GraphicsObject
@@ -131,6 +131,8 @@ class PlotCurveItem(GraphicsObject):
         elif ax == 1:
             d = y
             d2 = x
+        else:
+            raise ValueError("Invalid axis value")
 
         ## If an orthogonal range is specified, mask the data now
         if orthoRange is not None:
@@ -149,7 +151,7 @@ class PlotCurveItem(GraphicsObject):
                 # All-NaN data is acceptable; Explicit numpy warning is not needed.
                 warnings.simplefilter("ignore")
                 b = (np.nanmin(d), np.nanmax(d))
-            if any(np.isinf(b)):
+            if math.isinf(b[0]) or math.isinf(b[1]):
                 mask = np.isfinite(d)
                 d = d[mask]
                 if len(d) == 0:
diff --git a/pyqtgraph/graphicsItems/PlotDataItem.py b/pyqtgraph/graphicsItems/PlotDataItem.py
index 2c07798b..49d8ef61 100644
--- a/pyqtgraph/graphicsItems/PlotDataItem.py
+++ b/pyqtgraph/graphicsItems/PlotDataItem.py
@@ -1,5 +1,6 @@
 # -*- coding: utf-8 -*-
 import warnings
+import math
 import numpy as np
 from .. import metaarray as metaarray
 from ..Qt import QtCore
@@ -660,7 +661,7 @@ class PlotDataItem(GraphicsObject):
                         eps = np.finfo(y.dtype).eps
                     else:
                         eps = 1
-                    y = np.sign(y) * np.log10(np.abs(y)+eps)
+                    y = np.copysign(np.log10(np.abs(y)+eps), y)
 
             ds = self.opts['downsample']
             if not isinstance(ds, int):
@@ -799,10 +800,10 @@ class PlotDataItem(GraphicsObject):
             # All-NaN data is handled by returning None; Explicit numpy warning is not needed.
             warnings.simplefilter("ignore")
             ymin = np.nanmin(self.yData)
-            if np.isnan( ymin ):
+            if math.isnan( ymin ):
                 return None # most likely case for all-NaN data
             xmin = np.nanmin(self.xData)
-            if np.isnan( xmin ):
+            if math.isnan( xmin ):
                 return None # less likely case for all-NaN data
             ymax = np.nanmax(self.yData)
             xmax = np.nanmax(self.xData)
diff --git a/pyqtgraph/graphicsItems/PlotItem/PlotItem.py b/pyqtgraph/graphicsItems/PlotItem/PlotItem.py
index a2affcf7..8da9ba39 100644
--- a/pyqtgraph/graphicsItems/PlotItem/PlotItem.py
+++ b/pyqtgraph/graphicsItems/PlotItem/PlotItem.py
@@ -372,7 +372,7 @@ class PlotItem(GraphicsWidget):
         if y is not None:
             self.ctrl.yGridCheck.setChecked(y)
         if alpha is not None:
-            v = np.clip(alpha, 0, 1)*self.ctrl.gridAlphaSlider.maximum()
+            v = fn.clip_scalar(alpha, 0., 1.)*self.ctrl.gridAlphaSlider.maximum()
             self.ctrl.gridAlphaSlider.setValue(v)
         
     def close(self):
diff --git a/pyqtgraph/graphicsItems/ROI.py b/pyqtgraph/graphicsItems/ROI.py
index c2cb49ed..6c5f8418 100644
--- a/pyqtgraph/graphicsItems/ROI.py
+++ b/pyqtgraph/graphicsItems/ROI.py
@@ -15,9 +15,9 @@ of how to build an ROI at the bottom of the file.
 from ..Qt import QtCore, QtGui
 import numpy as np
 #from numpy.linalg import norm
-from ..Point import *
+from ..Point import Point
 from ..SRTTransform import SRTTransform
-from math import cos, sin
+from math import atan2, cos, sin, hypot, radians
 from .. import functions as fn
 from .GraphicsObject import GraphicsObject
 from .UIGraphicsItem import UIGraphicsItem
@@ -141,12 +141,13 @@ class ROI(GraphicsObject):
                  maxBounds=None, snapSize=1.0, scaleSnap=False,
                  translateSnap=False, rotateSnap=False, parent=None, pen=None,
                  hoverPen=None, handlePen=None, handleHoverPen=None,
-                 movable=True, rotatable=True, resizable=True, removable=False):
+                 movable=True, rotatable=True, resizable=True, removable=False,
+                 aspectLocked=False):
         GraphicsObject.__init__(self, parent)
         self.setAcceptedMouseButtons(QtCore.Qt.NoButton)
         pos = Point(pos)
         size = Point(size)
-        self.aspectLocked = False
+        self.aspectLocked = aspectLocked
         self.translatable = movable
         self.rotatable = rotatable
         self.resizable = resizable
@@ -678,7 +679,7 @@ class ROI(GraphicsObject):
         
         The format returned is a list of (name, pos) tuples.
         """
-        if index == None:
+        if index is None:
             positions = []
             for h in self.handles:
                 positions.append((h['name'], h['pos']))
@@ -691,7 +692,7 @@ class ROI(GraphicsObject):
         
         The format returned is a list of (name, pos) tuples.
         """
-        if index == None:
+        if index is None:
             positions = []
             for h in self.handles:
                 positions.append((h['name'], h['item'].scenePos()))
@@ -1247,8 +1248,8 @@ class ROI(GraphicsObject):
         vx = img.mapToData(self.mapToItem(img, QtCore.QPointF(1, 0))) - origin
         vy = img.mapToData(self.mapToItem(img, QtCore.QPointF(0, 1))) - origin
         
-        lvx = np.sqrt(vx.x()**2 + vx.y()**2)
-        lvy = np.sqrt(vy.x()**2 + vy.y()**2)
+        lvx = hypot(vx.x(), vx.y())  # length
+        lvy = hypot(vy.x(), vy.y())  # length
         ##img.width is number of pixels, not width of item.
         ##need pxWidth and pxHeight instead of pxLen ?
         sx = 1.0 / lvx
@@ -1298,7 +1299,7 @@ class ROI(GraphicsObject):
         """Return global transformation (rotation angle+translation) required to move 
         from relative state to current state. If relative state isn't specified,
         then we use the state of the ROI when mouse is pressed."""
-        if relativeTo == None:
+        if relativeTo is None:
             relativeTo = self.preMoveState
         st = self.getState()
         
@@ -1425,7 +1426,7 @@ class Handle(UIGraphicsItem):
         menu = self.scene().addParentContextMenus(self, self.getMenu(), ev)
         
         ## Make sure it is still ok to remove this handle
-        removeAllowed = all([r.checkRemoveHandle(self) for r in self.rois])
+        removeAllowed = all(r.checkRemoveHandle(self) for r in self.rois)
         self.removeAction.setEnabled(removeAllowed)
         pos = ev.screenPos()
         menu.popup(QtCore.QPoint(pos.x(), pos.y()))    
@@ -1481,7 +1482,7 @@ class Handle(UIGraphicsItem):
         size = self.radius
         self.path = QtGui.QPainterPath()
         ang = self.startAng
-        dt = 2*np.pi / self.sides
+        dt = 2 * np.pi / self.sides
         for i in range(0, self.sides+1):
             x = size * cos(ang)
             y = size * sin(ang)
@@ -1518,13 +1519,13 @@ class Handle(UIGraphicsItem):
             return None
         
         v = dt.map(QtCore.QPointF(1, 0)) - dt.map(QtCore.QPointF(0, 0))
-        va = np.arctan2(v.y(), v.x())
+        va = atan2(v.y(), v.x())
         
         dti = fn.invertQTransform(dt)
         devPos = dt.map(QtCore.QPointF(0,0))
         tr = QtGui.QTransform()
         tr.translate(devPos.x(), devPos.y())
-        tr.rotate(va * 180. / 3.1415926)
+        tr.rotateRadians(va)
         
         return dti.map(tr.map(self.path))
         
@@ -1663,7 +1664,7 @@ class LineROI(ROI):
         d = pos2-pos1
         l = d.length()
         ang = Point(1, 0).angle(d)
-        ra = ang * np.pi / 180.
+        ra = radians(ang if ang is not None else 0.)
         c = Point(-width/2. * sin(ra), -width/2. * cos(ra))
         pos1 = pos1 + c
         
@@ -1671,9 +1672,6 @@ class LineROI(ROI):
         self.addScaleRotateHandle([0, 0.5], [1, 0.5])
         self.addScaleRotateHandle([1, 0.5], [0, 0.5])
         self.addScaleHandle([0.5, 1], [0.5, 0.5])
-        
-
-        
 
 
 class MultiRectROI(QtGui.QGraphicsObject):
@@ -1887,7 +1885,7 @@ class EllipseROI(ROI):
         h = arr.shape[axes[1]]
 
         ## generate an ellipsoidal mask
-        mask = np.fromfunction(lambda x,y: (((x+0.5)/(w/2.)-1)**2+ ((y+0.5)/(h/2.)-1)**2)**0.5 < 1, (w, h))
+        mask = np.fromfunction(lambda x,y: np.hypot(((x+0.5)/(w/2.)-1), ((y+0.5)/(h/2.)-1)) < 1, (w, h))
         
         # reshape to match array axes
         if axes[0] > axes[1]:
@@ -1914,7 +1912,7 @@ class EllipseROI(ROI):
             center = br.center()
             r1 = br.width() / 2.
             r2 = br.height() / 2.
-            theta = np.linspace(0, 2*np.pi, 24)
+            theta = np.linspace(0, 2 * np.pi, 24)
             x = center.x() + r1 * np.cos(theta)
             y = center.y() + r2 * np.sin(theta)
             path.moveTo(x[0], y[0])
@@ -1944,8 +1942,7 @@ class CircleROI(EllipseROI):
             if radius is None:
                 raise TypeError("Must provide either size or radius.")
             size = (radius*2, radius*2)
-        EllipseROI.__init__(self, pos, size, **args)
-        self.aspectLocked = True
+        EllipseROI.__init__(self, pos, size, aspectLocked=True, **args)
         
     def _addHandles(self):
         self.addScaleHandle([0.5*2.**-0.5 + 0.5, 0.5*2.**-0.5 + 0.5], [0.5, 0.5])
@@ -2310,16 +2307,15 @@ class CrosshairROI(ROI):
     """A crosshair ROI whose position is at the center of the crosshairs. By default, it is scalable, rotatable and translatable."""
     
     def __init__(self, pos=None, size=None, **kargs):
-        if size == None:
+        if size is None:
             size=[1,1]
-        if pos == None:
+        if pos is None:
             pos = [0,0]
         self._shape = None
-        ROI.__init__(self, pos, size, **kargs)
+        ROI.__init__(self, pos, size, aspectLocked=True, **kargs)
         
         self.sigRegionChanged.connect(self.invalidate)
         self.addScaleRotateHandle(Point(1, 0), Point(0, 0))
-        self.aspectLocked = True
 
     def invalidate(self):
         self._shape = None
@@ -2394,8 +2390,7 @@ class TriangleROI(ROI):
     """
 
     def __init__(self, pos, size, **args):
-        ROI.__init__(self, pos, [size, size], **args)
-        self.aspectLocked = True
+        ROI.__init__(self, pos, [size, size], aspectLocked=True, **args)
         angles = np.linspace(0, np.pi * 4 / 3, 3)
         verticies = (np.array((np.sin(angles), np.cos(angles))).T + 1.0) / 2.0
         self.poly = QtGui.QPolygonF()
diff --git a/pyqtgraph/graphicsItems/ScatterPlotItem.py b/pyqtgraph/graphicsItems/ScatterPlotItem.py
index 3d35f8fc..080a8b24 100644
--- a/pyqtgraph/graphicsItems/ScatterPlotItem.py
+++ b/pyqtgraph/graphicsItems/ScatterPlotItem.py
@@ -6,6 +6,7 @@ try:
 except ImportError:
     imap = map
 import itertools
+import math
 import numpy as np
 import weakref
 from ..Qt import QtGui, QtCore, QT_LIB
@@ -116,7 +117,7 @@ def renderSymbol(symbol, size, pen, brush, device=None):
     for more information).
     """
     ## Render a spot with the given parameters to a pixmap
-    penPxWidth = max(np.ceil(pen.widthF()), 1)
+    penPxWidth = max(math.ceil(pen.widthF()), 1)
     if device is None:
         device = QtGui.QImage(int(size+penPxWidth), int(size+penPxWidth), QtGui.QImage.Format_ARGB32)
         device.fill(0)
@@ -950,6 +951,8 @@ class ScatterPlotItem(GraphicsObject):
         elif ax == 1:
             d = self.data['y']
             d2 = self.data['x']
+        else:
+            raise ValueError("Invalid axis value")
 
         if orthoRange is not None:
             mask = (d2 >= orthoRange[0]) * (d2 <= orthoRange[1])
@@ -1073,7 +1076,7 @@ class ScatterPlotItem(GraphicsObject):
             # Map points using painter's world transform so they are drawn with pixel-valued sizes
             pts = np.vstack([self.data['x'], self.data['y']])
             pts = fn.transformCoordinates(p.transform(), pts)
-            pts = np.clip(pts, -2 ** 30, 2 ** 30)  # prevent Qt segmentation fault.
+            pts = fn.clip_array(pts, -2 ** 30, 2 ** 30)  # prevent Qt segmentation fault.
             p.resetTransform()
 
             if self.opts['useCache'] and self._exportOpts is False:
diff --git a/pyqtgraph/graphicsItems/TargetItem.py b/pyqtgraph/graphicsItems/TargetItem.py
index 26f40b9b..1a4d5144 100644
--- a/pyqtgraph/graphicsItems/TargetItem.py
+++ b/pyqtgraph/graphicsItems/TargetItem.py
@@ -1,5 +1,4 @@
-from math import atan2, pi
-
+from math import atan2
 from ..Qt import QtGui, QtCore
 from ..Point import Point
 from .. import functions as fn
@@ -243,7 +242,7 @@ class TargetItem(UIGraphicsItem):
         tr = QtGui.QTransform()
         tr.translate(devPos.x(), devPos.y())
         va = atan2(v.y(), v.x())
-        tr.rotate(va * 180.0 / pi)
+        tr.rotateRadians(va)
         tr.scale(self.scale, self.scale)
         return dti.map(tr.map(self._path))
 
diff --git a/pyqtgraph/graphicsItems/TextItem.py b/pyqtgraph/graphicsItems/TextItem.py
index 8dcb04f6..2af87d5d 100644
--- a/pyqtgraph/graphicsItems/TextItem.py
+++ b/pyqtgraph/graphicsItems/TextItem.py
@@ -1,4 +1,4 @@
-import numpy as np
+from math import atan2, degrees
 from ..Qt import QtCore, QtGui
 from ..Point import Point
 from .. import functions as fn
@@ -208,7 +208,7 @@ class TextItem(GraphicsObject):
         angle = -self.angle
         if self.rotateAxis is not None:
             d = pt.map(self.rotateAxis) - pt.map(Point(0, 0))
-            a = np.arctan2(d.y(), d.x()) * 180 / np.pi
+            a = degrees(atan2(d.y(), d.x()))
             angle += a
         t.rotate(angle)  
         self.setTransform(t)
diff --git a/pyqtgraph/graphicsItems/ViewBox/ViewBox.py b/pyqtgraph/graphicsItems/ViewBox/ViewBox.py
index 6725d78b..8d60c577 100644
--- a/pyqtgraph/graphicsItems/ViewBox/ViewBox.py
+++ b/pyqtgraph/graphicsItems/ViewBox/ViewBox.py
@@ -1,6 +1,7 @@
 # -*- coding: utf-8 -*-
 import weakref
 import sys
+import math
 from copy import deepcopy
 import numpy as np
 from ...Qt import QtGui, QtCore
@@ -549,10 +550,9 @@ class ViewBox(GraphicsWidget):
                     dy = 1
                 mn -= dy*0.5
                 mx += dy*0.5
-                xpad = 0.0
 
             # Make sure no nan/inf get through
-            if not all(np.isfinite([mn, mx])):
+            if not math.isfinite(mn) or not math.isfinite(mx):
                 raise Exception("Cannot set range [%s, %s]" % (str(mn), str(mx)))
 
             # Apply padding
@@ -666,7 +666,7 @@ class ViewBox(GraphicsWidget):
     def suggestPadding(self, axis):
         l = self.width() if axis==0 else self.height()
         if l > 0:
-            padding = np.clip(1./(l**0.5), 0.02, 0.1)
+            padding = fn.clip_scalar(1./(l**0.5), 0.02, 0.1)
         else:
             padding = 0.02
         return padding
@@ -903,11 +903,11 @@ class ViewBox(GraphicsWidget):
                     targetRect[ax] = childRange[ax]
                     args['xRange' if ax == 0 else 'yRange'] = targetRect[ax]
 
-             # check for and ignore bad ranges
+            # check for and ignore bad ranges
             for k in ['xRange', 'yRange']:
                 if k in args:
-                    if not np.all(np.isfinite(args[k])):
-                        r = args.pop(k)
+                    if not math.isfinite(args[k][0]) or not math.isfinite(args[k][1]):
+                        _ = args.pop(k)
                         #print("Warning: %s is invalid: %s" % (k, str(r))
 
             if len(args) == 0:
@@ -1369,10 +1369,20 @@ class ViewBox(GraphicsWidget):
                 xr = item.dataBounds(0, frac=frac[0], orthoRange=orthoRange[0])
                 yr = item.dataBounds(1, frac=frac[1], orthoRange=orthoRange[1])
                 pxPad = 0 if not hasattr(item, 'pixelPadding') else item.pixelPadding()
-                if xr is None or (xr[0] is None and xr[1] is None) or np.isnan(xr).any() or np.isinf(xr).any():
+                if (
+                    xr is None or
+                    (xr[0] is None and xr[1] is None) or
+                    not math.isfinite(xr[0]) or
+                    not math.isfinite(xr[1])
+                ):
                     useX = False
                     xr = (0,0)
-                if yr is None or (yr[0] is None and yr[1] is None) or np.isnan(yr).any() or np.isinf(yr).any():
+                if (
+                    yr is None or
+                    (yr[0] is None and yr[1] is None) or
+                    not math.isfinite(yr[0]) or
+                    not math.isfinite(yr[1])
+                ):
                     useY = False
                     yr = (0,0)
 
diff --git a/pyqtgraph/imageview/ImageView.py b/pyqtgraph/imageview/ImageView.py
index 62c030a4..f934b36d 100644
--- a/pyqtgraph/imageview/ImageView.py
+++ b/pyqtgraph/imageview/ImageView.py
@@ -12,14 +12,16 @@ Widget used for displaying 2D or 3D data. Features:
   - ROI plotting
   - Image normalization through a variety of methods
 """
-import os, sys
+import os
+from math import log10
 import numpy as np
 
 from ..Qt import QtCore, QtGui, QT_LIB
+from .. import functions as fn
 import importlib
 ui_template = importlib.import_module(
     f'.ImageViewTemplate_{QT_LIB.lower()}', package=__package__)
-    
+
 from ..graphicsItems.ImageItem import *
 from ..graphicsItems.ROI import *
 from ..graphicsItems.LinearRegionItem import *
@@ -272,7 +274,7 @@ class ImageView(QtGui.QWidget):
         
         if not isinstance(img, np.ndarray):
             required = ['dtype', 'max', 'min', 'ndim', 'shape', 'size']
-            if not all([hasattr(img, attr) for attr in required]):
+            if not all(hasattr(img, attr) for attr in required):
                 raise TypeError("Image must be NumPy array or any object "
                                 "that provides compatible attributes/methods:\n"
                                 "  %s" % str(required))
@@ -512,7 +514,7 @@ class ImageView(QtGui.QWidget):
         
     def setCurrentIndex(self, ind):
         """Set the currently displayed frame index."""
-        index = np.clip(ind, 0, self.getProcessedImage().shape[self.axes['t']]-1)
+        index = fn.clip_scalar(ind, 0, self.getProcessedImage().shape[self.axes['t']]-1)
         self.ignorePlaying = True
         # Implicitly call timeLineChanged
         self.timeLine.setValue(self.tVals[index])
@@ -807,7 +809,7 @@ class ImageView(QtGui.QWidget):
         img = self.getProcessedImage()
         if self.hasTimeAxis():
             base, ext = os.path.splitext(fileName)
-            fmt = "%%s%%0%dd%%s" % int(np.log10(img.shape[0])+1)
+            fmt = "%%s%%0%dd%%s" % int(log10(img.shape[0])+1)
             for i in range(img.shape[0]):
                 self.imageItem.setImage(img[i], autoLevels=False)
                 self.imageItem.save(fmt % (base, i, ext))
diff --git a/pyqtgraph/metaarray/MetaArray.py b/pyqtgraph/metaarray/MetaArray.py
index 169ff43c..b07f66ab 100644
--- a/pyqtgraph/metaarray/MetaArray.py
+++ b/pyqtgraph/metaarray/MetaArray.py
@@ -124,7 +124,7 @@ class MetaArray(object):
     nameTypes = [basestring, tuple]
     @staticmethod
     def isNameType(var):
-        return any([isinstance(var, t) for t in MetaArray.nameTypes])
+        return any(isinstance(var, t) for t in MetaArray.nameTypes)
         
         
     ## methods to wrap from embedded ndarray / HDF5 
diff --git a/pyqtgraph/opengl/GLViewWidget.py b/pyqtgraph/opengl/GLViewWidget.py
index 2dace1fa..098d7ce9 100644
--- a/pyqtgraph/opengl/GLViewWidget.py
+++ b/pyqtgraph/opengl/GLViewWidget.py
@@ -5,6 +5,7 @@ import numpy as np
 from .. import Vector
 from .. import functions as fn
 import warnings
+from math import cos, sin, tan, radians
 ##Vector = QtGui.QVector3D
 
 ShareWidget = None
@@ -174,7 +175,7 @@ class GLViewWidget(QtWidgets.QOpenGLWidget):
         nearClip = dist * 0.001
         farClip = dist * 1000.
 
-        r = nearClip * np.tan(fov * 0.5 * np.pi / 180.)
+        r = nearClip * tan(0.5 * radians(fov))
         t = r * h / w
 
         ## Note that X0 and width in these equations must be the values used in viewport
@@ -316,12 +317,12 @@ class GLViewWidget(QtWidgets.QOpenGLWidget):
             pos = center - self.opts['rotation'].rotatedVector( Vector(0,0,dist) )
         else:
             # using 'euler' rotation method
-            elev = self.opts['elevation'] * np.pi / 180
-            azim = self.opts['azimuth'] * np.pi / 180
+            elev = radians(self.opts['elevation'])
+            azim = radians(self.opts['azimuth'])
             pos = Vector(
-                center.x() + dist * np.cos(elev) * np.cos(azim),
-                center.y() + dist * np.cos(elev) * np.sin(azim),
-                center.z() + dist * np.sin(elev)
+                center.x() + dist * cos(elev) * cos(azim),
+                center.y() + dist * cos(elev) * sin(azim),
+                center.z() + dist * sin(elev)
             )
         return pos
 
@@ -335,7 +336,7 @@ class GLViewWidget(QtWidgets.QOpenGLWidget):
             self.opts['rotation'] = q
         else: # default euler rotation method
             self.opts['azimuth'] += azim
-            self.opts['elevation'] = np.clip(self.opts['elevation'] + elev, -90, 90)
+            self.opts['elevation'] = fn.clip_scalar(self.opts['elevation'] + elev, -90., 90.)
         self.update()
         
     def pan(self, dx, dy, dz, relative='global'):
@@ -378,7 +379,7 @@ class GLViewWidget(QtWidgets.QOpenGLWidget):
             cPos = self.cameraPosition()
             cVec = self.opts['center'] - cPos
             dist = cVec.length()  ## distance from camera to center
-            xDist = dist * 2. * np.tan(0.5 * self.opts['fov'] * np.pi / 180.)  ## approx. width of view at distance of center point
+            xDist = dist * 2. * tan(0.5 * radians(self.opts['fov']))  ## approx. width of view at distance of center point
             xScale = xDist / self.width()
             zVec = QtGui.QVector3D(0,0,1)
             xVec = QtGui.QVector3D.crossProduct(zVec, cVec).normalized()
@@ -399,15 +400,15 @@ class GLViewWidget(QtWidgets.QOpenGLWidget):
                 # apply translation
                 self.opts['center'] += scale_factor * (xv*-dx + yv*dy + zv*dz)
             else: # use default euler rotation method
-                elev = np.radians(self.opts['elevation'])
-                azim = np.radians(self.opts['azimuth'])
-                fov = np.radians(self.opts['fov'])
+                elev = radians(self.opts['elevation'])
+                azim = radians(self.opts['azimuth'])
+                fov = radians(self.opts['fov'])
                 dist = (self.opts['center'] - self.cameraPosition()).length()
-                fov_factor = np.tan(fov / 2) * 2
+                fov_factor = tan(fov / 2) * 2
                 scale_factor = dist * fov_factor / self.width()
-                z = scale_factor * np.cos(elev) * dy
-                x = scale_factor * (np.sin(azim) * dx - np.sin(elev) * np.cos(azim) * dy)
-                y = scale_factor * (np.cos(azim) * dx + np.sin(elev) * np.sin(azim) * dy)
+                z = scale_factor * cos(elev) * dy
+                x = scale_factor * (sin(azim) * dx - sin(elev) * cos(azim) * dy)
+                y = scale_factor * (cos(azim) * dx + sin(elev) * sin(azim) * dy)
                 self.opts['center'] += QtGui.QVector3D(x, -y, z)
         else:
             raise ValueError("relative argument must be global, view, or view-upright")
@@ -425,7 +426,7 @@ class GLViewWidget(QtWidgets.QOpenGLWidget):
             dist = ((pos-cam)**2).sum(axis=-1)**0.5
         else:
             dist = (pos-cam).length()
-        xDist = dist * 2. * np.tan(0.5 * self.opts['fov'] * np.pi / 180.)
+        xDist = dist * 2. * tan(0.5 * radians(self.opts['fov']))
         return xDist / self.width()
         
     def mousePressEvent(self, ev):
diff --git a/pyqtgraph/opengl/items/GLScatterPlotItem.py b/pyqtgraph/opengl/items/GLScatterPlotItem.py
index 5d81515b..834ede0b 100644
--- a/pyqtgraph/opengl/items/GLScatterPlotItem.py
+++ b/pyqtgraph/opengl/items/GLScatterPlotItem.py
@@ -3,7 +3,8 @@ from OpenGL.GL import *
 from OpenGL.arrays import vbo
 from .. GLGraphicsItem import GLGraphicsItem
 from .. import shaders
-from ... import QtGui
+from ... import functions as fn
+from ...Qt import QtGui
 import numpy as np
 
 __all__ = ['GLScatterPlotItem']
@@ -61,13 +62,12 @@ class GLScatterPlotItem(GLGraphicsItem):
         
         ## Generate texture for rendering points
         w = 64
-        def fn(x,y):
-            r = ((x-(w-1)/2.)**2 + (y-(w-1)/2.)**2) ** 0.5
-            return 255 * (w/2. - np.clip(r, w/2.-1.0, w/2.))
+        def genTexture(x,y):
+            r = np.hypot((x-(w-1)/2.), (y-(w-1)/2.))
+            return 255 * (w / 2 - fn.clip_array(r, w / 2 - 1, w / 2))
         pData = np.empty((w, w, 4))
         pData[:] = 255
-        pData[:,:,3] = np.fromfunction(fn, pData.shape[:2])
-        #print pData.shape, pData.min(), pData.max()
+        pData[:,:,3] = np.fromfunction(genTexture, pData.shape[:2])
         pData = pData.astype(np.ubyte)
         
         if getattr(self, "pointTexture", None) is None:
diff --git a/pyqtgraph/parametertree/SystemSolver.py b/pyqtgraph/parametertree/SystemSolver.py
index cac42483..d7b6bef8 100644
--- a/pyqtgraph/parametertree/SystemSolver.py
+++ b/pyqtgraph/parametertree/SystemSolver.py
@@ -1,6 +1,8 @@
 from collections import OrderedDict
 import numpy as np
 import copy
+from math import log2
+from .. import functions as fn
 
 
 class SystemSolver(object):
@@ -390,15 +392,12 @@ if __name__ == '__main__':
                 sh = self.shutter   # this raises RuntimeError if shutter has not
                                    # been specified
                 ap = 4.0 * (sh / (1./60.)) * (iso / 100.) * (2 ** exp) * (2 ** light)
-                ap = np.clip(ap, 2.0, 16.0)
+                ap = fn.clip_scalar(ap, 2.0, 16.0)
             except RuntimeError:
                 # program mode; we can select a suitable shutter
                 # value at the same time.
                 sh = (1./60.)
                 raise
-            
-            
-            
             return ap
 
         def _balance(self):
@@ -406,10 +405,8 @@ if __name__ == '__main__':
             light = self.lightMeter
             sh = self.shutter
             ap = self.aperture
-            fl = self.flash
-            
             bal = (4.0 / ap) * (sh / (1./60.)) * (iso / 100.) * (2 ** light)
-            return np.log2(bal)
+            return log2(bal)
     
     camera = Camera()
     
diff --git a/pyqtgraph/widgets/ColorMapWidget.py b/pyqtgraph/widgets/ColorMapWidget.py
index 5d1e5681..9f2fafe8 100644
--- a/pyqtgraph/widgets/ColorMapWidget.py
+++ b/pyqtgraph/widgets/ColorMapWidget.py
@@ -161,7 +161,7 @@ class ColorMapParameter(ptree.types.GroupParameter):
             elif op == 'Set':
                 colors[mask] = colors2[mask]            
                 
-        colors = np.clip(colors, 0, 1)
+        colors = fn.clip_array(colors, 0., 1.)
         if mode == 'byte':
             colors = (colors * 255).astype(np.ubyte)
         
@@ -210,11 +210,11 @@ class RangeColorMapItem(ptree.types.SimpleParameter):
     def map(self, data):
         data = data[self.fieldName]
         
-        scaled = np.clip((data-self['Min']) / (self['Max']-self['Min']), 0, 1)
+        scaled = fn.clip_array((data-self['Min']) / (self['Max']-self['Min']), 0, 1)
         cmap = self.value()
         colors = cmap.map(scaled, mode='float')
         
-        mask = np.isnan(data) | np.isinf(data)
+        mask = np.invert(np.isfinite(data))
         nanColor = self['NaN']
         nanColor = (nanColor.red()/255., nanColor.green()/255., nanColor.blue()/255., nanColor.alpha()/255.)
         colors[mask] = nanColor
diff --git a/pyqtgraph/widgets/GraphicsView.py b/pyqtgraph/widgets/GraphicsView.py
index 3054f0e7..d2b0f553 100644
--- a/pyqtgraph/widgets/GraphicsView.py
+++ b/pyqtgraph/widgets/GraphicsView.py
@@ -7,10 +7,7 @@ Distributed under MIT/X11 license. See license.txt for more information.
 
 from ..Qt import QtCore, QtGui, QtWidgets, QT_LIB
 from ..Point import Point
-import sys, os
-from .FileDialog import FileDialog
 from ..GraphicsScene import GraphicsScene
-import numpy as np
 from .. import functions as fn
 from .. import debug as debug
 from .. import getConfigOption
@@ -378,7 +375,7 @@ class GraphicsView(QtGui.QGraphicsView):
             return
         
         if ev.buttons() == QtCore.Qt.RightButton:
-            delta = Point(np.clip(delta[0], -50, 50), np.clip(-delta[1], -50, 50))
+            delta = Point(fn.clip_scalar(delta[0], -50, 50), fn.clip_scalar(-delta[1], -50, 50))
             scale = 1.01 ** delta
             self.scale(scale[0], scale[1], center=self.mapToScene(self.mousePressPos))
             self.sigDeviceRangeChanged.emit(self, self.range)
diff --git a/pyqtgraph/widgets/JoystickButton.py b/pyqtgraph/widgets/JoystickButton.py
index 4e4a335f..53674df2 100644
--- a/pyqtgraph/widgets/JoystickButton.py
+++ b/pyqtgraph/widgets/JoystickButton.py
@@ -1,4 +1,5 @@
-from ..Qt import QtGui, QtCore
+from math import hypot
+from ..Qt import QtGui, QtCore, mkQApp
 
 
 __all__ = ['JoystickButton']
@@ -41,7 +42,7 @@ class JoystickButton(QtGui.QPushButton):
         
     def setState(self, *xy):
         xy = list(xy)
-        d = (xy[0]**2 + xy[1]**2)**0.5
+        d = hypot(xy[0], xy[1])  # length
         nxy = [0, 0]
         for i in [0,1]:
             if xy[i] == 0:
@@ -84,7 +85,7 @@ class JoystickButton(QtGui.QPushButton):
         
         
 if __name__ == '__main__':
-    app = pg.mkQApp()
+    app = mkQApp()
     w = QtGui.QMainWindow()
     b = JoystickButton()
     w.setCentralWidget(b)