Ticket #3813: trac_3813-review.patch

a/sage/plot/plot.py

@@ -3414 +3414 @@
-
-    PLOT OPTIONS:
-    The plot options are
-the number of points to initially plot before
-doing adaptive refinement
-how many levels of recursion to go before
-giving up when doing adaptive refinement
-
+(default: 200) the number of points to initially plot
+before the adaptive refinement.
+(default: 10) how many levels of recursion to go 
+before giving up when doing adaptive refinement.
+.
-        adaptive_tolerance -- how large a difference should be before the
-                              adaptive refinement code considers it significant.
-                              This depends on the interval you use by default.
@@ -3511 +3511 @@
-        sage: p += text('D', (0.53, 0.18), rgbcolor='red')
-        sage: p
-    
-
-
-
-
-
-
-
-
+
+
+
+
+
+
-
-    The actual sample points are slightly randomized, so the above
-    plots may look slightly different each time you draw them.
@@ -3562 +3560 @@
-    def _reset(self):
-        o = self.options
-        o['plot_points'] = 200
-      
+
-        o['rgbcolor'] = (0,0,1)   
-
-    def __repr__(self):
@@ -3630 +3628 @@
-        plot_points = int(options['plot_points'])
-        del options['plot_points']
-        x, data = var_and_list_of_values(xrange, plot_points)
-        data = list(data)
-        xmin = data[0]
-        xmax = data[-1]
-
@@ -3680 +3677 @@
-        adaptive_recursion = int(options['adaptive_recursion'])
-        del options['adaptive_recursion']
-        
-        def refine(f, p1, p2, level=0):
-            if level >= adaptive_recursion:
-                return []
-            x = float((p1[0] + p2[0])/2)
-            try:
-                y = float(f(x))
-            except (ZeroDivisionError, TypeError, ValueError), msg:
-                sage.misc.misc.verbose("%s\nUnable to compute f(%s)"%(msg, x), 1)
-                # give up for this branch
-                return []
-            # this distance calculation is not perfect.
-            if abs((p1[1] + p2[1])/2 - y) > adaptive_tolerance:
-                return refine(f, p1, (x, y), level+1) + [(x, y)] +\
-                        refine(f, (x, y), p2, level+1)
-            else:
-                return []
-        
-        while i < len(data) - 1:
-
+
+
-                data.insert(i+1, p)
-                i += 1
-            i += 1
@@ -4479 +4460 @@
-                g.append(fast_float(f, str(xvar), str(yvar)))
-            
-    return g, xstep, ystep, xrange, yrange
+
+def adaptive_refinement(f, p1, p2, adaptive_tolerance=0.01, adaptive_recursion=10, level=0):
+    r"""
+    The adaptive refinement algorithm for plotting a function f. See the
+    docstring for plot or PlotFactory for a description of the algorithm.
+
+    INPUT:
+        f -- a function of one variable
+        p1, p2 -- two points to compare
+        adaptive_recursion -- (default: 10) how many levels of recursion to go 
+                              before giving up when doing adaptive refinement.
+                              Setting this to 0 disables adaptive refinement.
+        adaptive_tolerance -- how large a difference should be before the
+                              adaptive refinement code considers it significant.
+                              This depends on the interval you use by default.
+
+    TESTS:
+        sage: from sage.plot.plot import adaptive_refinement
+        sage: adaptive_refinement(sin, (0,0), (pi,0), 0.01, level=10)
+        []
+        sage: adaptive_refinement(sin, (0,0), (pi,0), 0.01)
+        [(pi/8, 0.38268343236508978), (3*pi/16, 0.55557023301960218), (pi/4, 0.70710678118654746), (5*pi/16, 0.83146961230254524), (3*pi/8, 0.92387953251128674), (7*pi/16, 0.98078528040323043), (pi/2, 1.0), (9*pi/16, 0.98078528040323043), (5*pi/8, 0.92387953251128674), (11*pi/16, 0.83146961230254546), (3*pi/4, 0.70710678118654757), (13*pi/16, 0.55557023301960218), (7*pi/8, 0.38268343236508989)]
+    """
+    if level >= adaptive_recursion:
+        return []
+    x = (p1[0] + p2[0])/2
+    try:
+        y = float(f(x))
+    except (ZeroDivisionError, TypeError, ValueError), msg:
+        sage.misc.misc.verbose("%s\nUnable to compute f(%s)"%(msg, x), 1)
+        # give up for this branch
+        return []
+    # this distance calculation is not perfect.
+    if abs((p1[1] + p2[1])/2 - y) > adaptive_tolerance:
+        return adaptive_refinement(f, p1, (x, y), 
+                        adaptive_tolerance=adaptive_tolerance,
+                        adaptive_recursion=adaptive_recursion,
+                        level=level+1) \
+               + [(x, y)] + \
+               adaptive_refinement(f, (x, y), p2,
+                        adaptive_tolerance=adaptive_tolerance,
+                        adaptive_recursion=adaptive_recursion,
+                        level=level+1)
+    else:
+        return []