[examples] added examples from pyIbex

examples/examples_from_pyibex/ex_ctcRaster.py

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+from codac import *
+from codac.unsupported import *
+
+import os
+import scipy.misc
+import scipy.ndimage as ndimage
+import numpy as np
+
+ain = np.zeros((200, 200), dtype=np.int64)
+ain[75:125, 50:125] = 1
+ain[25:100, 25:50] = 1
+
+# over approximation of the set X
+aout = np.zeros((200, 200), dtype=np.int64)
+aout[74:126, 49:126] = 1
+aout[24:101, 24:51] = 1
+
+img_out = aout.cumsum(0).cumsum(1)
+img_in = (1 - ain).cumsum(0).cumsum(1)
+
+
+img = 127*(aout+ain).T
+scipy.misc.imsave('test.png', img.astype(np.uint8))
+
+
+
+ctcOut = CtcRaster(img_out, -5, 5, 0.1, -0.1)
+ctcIn = CtcRaster(img_in, -5, 5, 0.1, -0.1)
+sep = SepCtcPair(ctcIn, ctcOut)
+
+
+
+X0 = IntervalVector(2, [-15,15])
+
+beginDrawing()
+fig = VIBesFig('CtcImage')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(X0)
+# X0 = IntervalVector([[4, 10], [-6, -4]])
+# X0 = IntervalVector([[-2.47, -2.17], [-0.5, 0.17]])
+# X0 = IntervalVector([[-2.47, -2.17], [-0.1, 0.17]])
+# X0_res = IntervalVector([[-2.47, -2.17], [-0.1, 0])
+# X0 = IntervalVector([ [2.05, 2.15],  [-0.08, -0.02] ])
+# X0 = IntervalVector([ [2.05, 2.15],  [-0.08, -0.0] ])
+#
+#vibes.drawRaster(os.path.abspath('test.png'), -5,5, 0.1, -0.1)
+# vibes.drawBox(X0[0][0], X0[0][1], X0[1][0], X0[1][1], '[#FF000055]')
+# self.ctcOut.contract(X0)
+# vibes.drawBox(X0[0][0], X0[0][1], X0[1][0], X0[1][1], '[#0000FF55]')
+
+SIVIA(X0, sep, 0.2)
+# pySIVIA(X0, sep, 0.05, use_patch=True)

examples/examples_from_pyibex/example1.py

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+# Codac - Examples
+# Originated from the former pyIbex library (Benoît Desrochers)
+# Author: Benoît Desrochers
+# ----------------------------------------------------------------------------
+# Simple example of a separator
+
+from codac import *
+
+f = Function('x', 'y', 'x*cos(x-y)+y')
+sep = SepFwdBwd(f, CmpOp.LEQ)
+x = IntervalVector(2, [-10, 10])
+
+beginDrawing()
+fig = VIBesFig('Example')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(x)
+SIVIA(x, sep, 0.2)
+endDrawing()

examples/examples_from_pyibex/example2.py

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+# Codac - Examples
+# Originated from the former pyIbex library (Benoît Desrochers)
+# Author: Benoît Desrochers
+# ----------------------------------------------------------------------------
+# Custom contractor
+# Writes a custom contractor for the equation
+# (x-a)^2 + (y-b)^2 \in r^2
+
+from codac import *
+
+class MyCtc(Ctc):
+
+  def __init__(self, a, b, r):
+    Ctc.__init__(self, 2)
+    self.a = Interval(a)
+    self.b = Interval(b)
+    self.r = r
+
+  def contract(self, x):
+    i1 = x[0] - Interval(self.a)
+    i2 = x[1] - Interval(self.b)
+
+    i3 = sqr(i1)
+    i4 = sqr(i2)
+
+    i5 = i3 + i4
+    i5 &= sqr(self.r)
+
+    bwd_add(i5, i3, i4)
+    bwd_sqr(i4, i2)
+    bwd_sqr(i3, i1)
+
+    bwd_sub(i1, x[0], Interval(self.a))
+    bwd_sub(i2, x[1], Interval(self.b))
+
+    return x
+
+
+ctc = MyCtc(1, 2, Interval(1, 2))
+x = IntervalVector(2, [-8, 8])
+
+beginDrawing()
+fig = VIBesFig('Result')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(x)
+SIVIA(x, ctc, 0.3)
+endDrawing()

examples/examples_from_pyibex/example3.py

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+# Codac - Examples
+# Originated from the former pyIbex library (Benoît Desrochers)
+# Author: Benoît Desrochers
+# ----------------------------------------------------------------------------
+# Simple range-only localization using separators
+# We consider the localisation of a robot measuring distances w.r.t three landmaks.
+
+from codac import *
+import numpy as np
+
+# Theorical (unknown) position of the robot
+robot = [-2,4]
+
+# Position of the landmarks
+landmarks = [[6,12], [-2,-5], [-3,10]]
+
+# Distances measured w.r.t to landmaks
+dist = [Interval(11,12), Interval(8,10), Interval(5,7)]
+
+# Creation of a separator
+seps = [] # empty list of separators
+# Iterate over landmarks and distances
+for (m_x, m_y), d in zip(landmarks, dist):
+  # Create the constraint function
+  f = Function("x[2]", "(x[0]-%f)^2+(x[1]-%f)^2"%(m_x, m_y))
+  # Create the fwdbwd separator for: f(x) \in d
+  sep = SepFwdBwd(f, sqr(d))
+  seps.append(sep)
+
+# Create the separator as intersection of the previous separators
+sep = SepInter(seps)
+
+# Create the initial box
+x0 = IntervalVector([[-12,11], [-6,17]])
+
+# Init graphics
+beginDrawing()
+fig = VIBesFig('Localization')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(x0)
+
+# Running the paver
+SIVIA(x0, sep, 0.1)
+
+# Displaying ranges of measurements
+for (x, y), d in zip(landmarks, dist):
+  fig.draw_circle(x, y, 0.1, "[k]")
+  fig.draw_circle(x, y, d.lb(), "k")
+  fig.draw_circle(x, y, d.ub(), "k")
+fig.draw_vehicle(robot[0], robot[1], np.rad2deg(0.3), 1, 'k[y]')
+
+endDrawing()

examples/examples_from_pyibex/example_paving_transform.py

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+# Codac - Examples
+# Originated from the former pyIbex library (Benoît Desrochers)
+# Author: Benoît Desrochers
+# ----------------------------------------------------------------------------
+
+from codac import *
+from codac.unsupported import *
+
+x0 = IntervalVector(2, [-5, 5])
+sep = SepFwdBwd(Function("x[2]", "x[0]^2 + x[1]^2"), Interval(-oo, 4))
+#P = SepPaving(x0, sep, 0.1)
+
+f = Function("x", 'y', '(0.5*x, 2*y)')
+sep2 = SepInverse(sep, f)
+
+beginDrawing()
+
+fig = VIBesFig('test 1')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(x0)
+SIVIA(x0,sep,0.1)
+
+fig = VIBesFig('test 2')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(x0)
+SIVIA(x0,sep2,0.1)
+
+endDrawing()

examples/examples_from_pyibex/example_polar.py

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+# Codac - Examples
+# Originated from the former pyIbex library (Benoît Desrochers)
+# Author: Benoît Desrochers
+# ----------------------------------------------------------------------------
+
+from codac import *
+from codac.unsupported import *
+import numpy as np
+
+sep1 = SepPolarXY(Interval(4,5), Interval(np.deg2rad(-570), np.deg2rad(-450)))
+
+f1 = Function("x", 'y', '(x + 2; y - 2)')
+f2 = Function("x", 'y', '(x - 2; y + 2)')
+sep = SepTransform(sep1, f1, f2)
+
+x = IntervalVector([[-10,10],[-10,10]])
+
+
+beginDrawing()
+fig = VIBesFig('SIVIA')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(x)
+SIVIA(x, sep1, 0.1)

examples/examples_from_pyibex/example_projection1.py

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+# Codac - Examples
+# Originated from the former pyIbex library (Benoît Desrochers)
+# Author: Benoît Desrochers
+# ----------------------------------------------------------------------------
+# Example from Applied Interval Analysis (L. Jaulin et.al. ) §6.3.4
+
+from codac import *
+from codac.unsupported import *
+import math
+
+def export_data(Y, T):
+  vibes.newFigure('Data')
+  vibes.setFigureProperties({'x': 0, 'y': 0, 'width': 1000, 'height': 1000})
+  print("#"*50)
+  print("Data to use")
+  for i,(y,t) in enumerate(zip(Y[::-1], T[::-1])):
+    # print(" %d & %s & %s \\\\ \\hline"%(i+1,t,y))
+    print("\\draw[boxColor] (%f, %f) rectangle (%f, %f);"%(t[0], y[0], t[1], y[1]))
+    # vibes.drawBox(t[0], t[1], y[0], y[1], 'k[lightGray]')
+  print("#"*50)
+
+
+def test_paramEstim( useSepProj=False):
+
+  f = Function("p1", "p2", "t", "20*exp(-p1*t)-8*exp(-p2*t)");
+
+  Y = [
+    Interval(2.7,12.1),
+    Interval(1.04,7.14),
+    Interval(-0.13,3.61),
+    Interval(-0.95,1.15),
+    Interval(-4.85,-0.29),
+    Interval(-5.06,-0.36),
+    Interval(-4.1,-0.04),
+    Interval(-3.16,0.3),
+    Interval(-2.5,0.51),
+    Interval(-2,0.67)
+  ]
+
+  T = [
+    Interval(-0.25,1.75),
+    Interval(0.5,2.5),
+    Interval(1.25,3.25),
+    Interval(2,4),
+    Interval(5,7),
+    Interval(8,10),
+    Interval(12,14),
+    Interval(16,18),
+    Interval(20,22),
+    Interval(24,26)
+  ]
+
+  seps = []
+
+  for y_i,t_i in zip(Y, T):
+    if useSepProj == False:
+      seps.append( SepCtcPairProj( SepFwdBwd(f, y_i ), t_i, 1e-3) )
+    else:
+      seps.append( SepProj( SepFwdBwd(f, y_i ), t_i, 1e-3) )
+
+  sep = SepInter(seps)
+
+  X0 = IntervalVector(2,Interval(0,1.2));
+  X0[1] = Interval(0,0.5);
+
+
+  return sep, X0, 0.01
+
+
+
+
+sep, X0, eps = test_paramEstim(True)
+
+
+
+beginDrawing()
+fig = VIBesFig('Result')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(X0)
+
+# run SIVIA
+SIVIA(X0, sep, eps)
+
+endDrawing()

examples/examples_from_pyibex/sphereProj.py

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+# Codac - Examples
+# Originated from the former pyIbex library (Benoît Desrochers)
+# Author: Benoît Desrochers
+# ----------------------------------------------------------------------------
+# Simple example of the projection of a sphere
+
+from codac import *
+from codac.unsupported import *
+
+f = Function("x[2]","y","x[0]^2+x[1]^2+y^2")
+S1=SepFwdBwd(f,Interval(4,9))
+Y=IntervalVector([[-1,1]])
+#S2=SepCtcPairProj(S1,Y,0.01) 
+S2=SepProj(S1,Y,0.01)
+X0 =IntervalVector([[-10,10],[-10,10]]);
+
+beginDrawing()
+fig = VIBesFig('Proj')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(X0)
+SIVIA(X0,S2,0.1)
+endDrawing()

examples/examples_from_pyibex/test_Img.py

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+# Codac - Examples
+# Originated from the former pyIbex library (Benoît Desrochers)
+# Author: Benoît Desrochers
+# ----------------------------------------------------------------------------
+
+import numpy as np
+import scipy.ndimage as ndi
+
+from codac import *
+from codac.unsupported import *
+
+import os
+
+import matplotlib.pyplot as plt
+# load image data
+img_gray = ndi.imread('./test.png', 'L').T
+img_out = np.zeros(img_gray.shape, dtype=np.uint64)
+img_in = np.zeros(img_gray.shape, dtype=np.uint64)
+
+img_out[img_gray >= 127 ] = 1
+img_in[img_gray != 255] = 1
+
+# compute summed tables
+img_out = img_out.cumsum(0).cumsum(1)
+img_in = img_in.cumsum(0).cumsum(1)
+
+# create contractors with CtcRaster
+# top left corner is at position (-5, 5)
+# pixel size is 0.1 by -0.1
+ctcOut = CtcRaster(img_out, -5, 5, 0.1, -0.1)
+ctcIn = CtcRaster(img_in, -5, 5, 0.1, -0.1)
+sep = SepCtcPair(ctcIn, ctcOut)
+
+
+X0 = IntervalVector(2, [-15,15])
+
+beginDrawing()
+fig = VIBesFig('CtcImage')
+fig.set_properties(x=100, y=100, width=600, height=600)
+fig.axis_limits(X0)
+
+#vibes.drawRaster(os.path.abspath('test.png'), -5,5, 0.1, -0.1)
+SIVIA(X0, sep, 0.2)
+
+endDrawing()