From 2a3d4887a0d0fc95c33f473cdafd587c3fdd9b25 Mon Sep 17 00:00:00 2001 From: AtsushiSakai Date: Sun, 30 Apr 2017 14:46:14 -0700 Subject: [PATCH] add code --- README.md | 5 +- .../figure/figure_1.png | Bin 0 -> 224450 bytes .../LagrangeMultiplierMethod.py | 60 ++++++++------- .../figure/figure_1.png | Bin 0 -> 253317 bytes .../NewtonMethod/figure/figure_1.png | Bin 0 -> 231740 bytes .../QuasiNewtonMethod/figure/figure_1.png | Bin 0 -> 231002 bytes .../SteepestDescentMethod.py | 70 +++++++++--------- .../SteepestDescentMethod/figure/figure_1.png | Bin 0 -> 231227 bytes 8 files changed, 73 insertions(+), 62 deletions(-) create mode 100644 scripts/optimization/ConjugateGradientMethod/figure/figure_1.png create mode 100644 scripts/optimization/LagrangeMultiplierMethod/figure/figure_1.png create mode 100644 scripts/optimization/NewtonMethod/figure/figure_1.png create mode 100644 scripts/optimization/QuasiNewtonMethod/figure/figure_1.png create mode 100644 scripts/optimization/SteepestDescentMethod/figure/figure_1.png diff --git a/README.md b/README.md index 66065a92..9d90c6a3 100644 --- a/README.md +++ b/README.md @@ -24,7 +24,10 @@ see (in Japanese) : A sample code for Dubins path planning. -![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/scripts/PathPlanning/DubinsPath/figures/figure_1.png) +[Dubins path - Wikipedia](https://en.wikipedia.org/wiki/Dubins_path) + +![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/scripts/PathPlanning/DubinsPath/figures/figure_15.png) +![PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/blob/master/scripts/PathPlanning/DubinsPath/figures/figure_13.png) # Optimization diff --git a/scripts/optimization/ConjugateGradientMethod/figure/figure_1.png 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b/scripts/optimization/LagrangeMultiplierMethod/LagrangeMultiplierMethod.py index 12a1fb8d..9b3c1280 100644 --- a/scripts/optimization/LagrangeMultiplierMethod/LagrangeMultiplierMethod.py +++ b/scripts/optimization/LagrangeMultiplierMethod/LagrangeMultiplierMethod.py @@ -4,60 +4,64 @@ import matplotlib.pyplot as plt import numpy as np import random from math import * -from scipy.optimize import fsolve delta = 0.1 -minXY=-5.0 -maxXY=5.0 -nContour=50 +minXY = -5.0 +maxXY = 5.0 +nContour = 50 + def dfunc(d): - x=d[0] - y=d[1] - l=d[2] - dx=-2*l+4*x*(x**2+y-11) - dy=l+2*x*x+2*y-22 - dl=-2*x+y-1 - return [dx,dy,dl] + x = d[0] + y = d[1] + l = d[2] + dx = -2 * l + 4 * x * (x ** 2 + y - 11) + dy = l + 2 * x * x + 2 * y - 22 + dl = -2 * x + y - 1 + return [dx, dy, dl] + + +def SampleFunc(x, y): + return (x ** 2 + y - 11) ** 2 -def SampleFunc(x,y): - return (x**2+y-11)**2 def ConstrainFunction(x): - return (2.0*x+1.0) + return (2.0 * x + 1.0) + def CreateMeshData(): x = np.arange(minXY, maxXY, delta) y = np.arange(minXY, maxXY, delta) X, Y = np.meshgrid(x, y) - Z=[SampleFunc(x,y) for (x,y) in zip(X,Y)] - return(X,Y,Z) + Z = [SampleFunc(ix, iy) for (ix, iy) in zip(X, Y)] + return(X, Y, Z) + # Main -start=np.matrix([random.uniform(minXY,maxXY),random.uniform(minXY,maxXY),0]) +start = np.matrix([random.uniform(minXY, maxXY), + random.uniform(minXY, maxXY), 0]) -(X,Y,Z)=CreateMeshData() -CS = plt.contour(X, Y, Z,nContour) +(X, Y, Z) = CreateMeshData() +CS = plt.contour(X, Y, Z, nContour) -Xc=np.arange(minXY,maxXY,delta) -Yc=[ConstrainFunction(x) for x in Xc] +Xc = np.arange(minXY, maxXY, delta) +Yc = [ConstrainFunction(x) for x in Xc] # plt.plot(start[0,0],start[0,1],"xr"); -plt.plot(Xc,Yc,"-r"); +plt.plot(Xc, Yc, "-r") # X1 = fsolve(dfunc, [-3, -3, 10]) # print(X1) # print(dfunc(X1)) # the answer from sympy -result=np.matrix([ -[-1,-1], -# [-1+sqrt(11),-1+2*sqrt(11)], -# [-sqrt(11)-1,-2*sqrt(11)-1]]) +result = np.matrix([ + [-1, -1], + [-1 + sqrt(11), -1 + 2 * sqrt(11)], + [-sqrt(11) - 1, -2 * sqrt(11) - 1]]) print(result) -plt.plot(result[:,0],result[:,1],"or"); +plt.plot(result[:, 0], result[:, 1], "or") plt.axis([minXY, maxXY, minXY, maxXY]) plt.show() - diff --git a/scripts/optimization/LagrangeMultiplierMethod/figure/figure_1.png b/scripts/optimization/LagrangeMultiplierMethod/figure/figure_1.png new file mode 100644 index 0000000000000000000000000000000000000000..1adcd226623b104db510499af07d0df4eda76ce8 GIT binary patch literal 253317 zcmeEt^Lu1nuyx1w#I|iGGqG*kwkOWSHYT=h8xz}^*ml02_dfR@_Xj% z*|n=`ty()mK~5Y276%pp03b+8h$sO7paB2?$PP3l@E!KqjRW8dxbt^O6=>kY2ihbY zIEHbM&~yd>kPQDFAf%X_9cKG=+it&Buf zSV%!cM9A{CK(jZHN?+(#z^kZN>MeSBfD82R;Edqlg{jAki!Rx&9>HmD)`m=70}e%r z$4>nkUsE@;%c=9rt|QNBWr0{j&6E(af>{eToM^LQ1HV;5q5m0(-EE8V2H-^h_dizn z3xE~S0yvmtY6L6&&s>ak;16Qn|C~Do|KtCR|L<=6fBQzQ|0m4GxM3=?FyZ_S6mQuKG<}^V1~cvT)uEs6blP0ueO%S zX2hIi4P*mRWsQ@XT9P*);|u4vf<;&%osXWNT&i)$H1i5)6eTlartL_PLSP?q6K+PC zhDzhWbQ`PkgC(hH2m1N-_RZ)HRRs0Tx@!);BSPP|WfyTM9mf!l_cQ&0J}CRAuYy?_ 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dx=4*x**3+4*x*y-44*x+2*x+2*y**2-14 - dy=2*x**2+4*x*y+4*y**3-26*y-22 - J=np.matrix([dx,dy]) + x = state[0, 0] + y = state[0, 1] + dx = 4 * x ** 3 + 4 * x * y - 44 * x + 2 * x + 2 * y ** 2 - 14 + dy = 2 * x ** 2 + 4 * x * y + 4 * y ** 3 - 26 * y - 22 + J = np.matrix([dx, dy]) return J -def HimmelblauFunction(x,y): + +def HimmelblauFunction(x, y): u""" Himmelblau's function - see Himmelblau's function - Wikipedia, the free encyclopedia + see Himmelblau's function - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Himmelblau%27s_function """ - return (x**2+y-11)**2+(x+y**2-7)**2 + return (x ** 2 + y - 11) ** 2 + (x + y ** 2 - 7) ** 2 + def ConstrainFunction(x): - return (2.0*x+1.0) + return (2.0 * x + 1.0) + def CreateMeshData(): x = np.arange(minXY, maxXY, delta) y = np.arange(minXY, maxXY, delta) X, Y = np.meshgrid(x, y) - Z=[HimmelblauFunction(x,y) for (x,y) in zip(X,Y)] - return(X,Y,Z) + Z = [HimmelblauFunction(ix, iy) for (ix, iy) in zip(X, Y)] + return(X, Y, Z) -def SteepestDescentMethod(start,Jacob): + +def SteepestDescentMethod(start, Jacob): u""" Steepest Descent Method Optimization """ - result=start - x=start + result = start + x = start while 1: - J=Jacob(x) - sumJ=np.sum(abs(alpha*J)) - if sumJ<=0.01: + J = Jacob(x) + sumJ = np.sum(abs(alpha * J)) + if sumJ <= 0.01: print("OK") break - x=x-alpha*J - result=np.vstack((result,x)) + x = x - alpha * J + result = np.vstack((result, x)) return result + # Main -start=np.matrix([random.uniform(minXY,maxXY),random.uniform(minXY,maxXY)]) +start = np.matrix([random.uniform(minXY, maxXY), random.uniform(minXY, maxXY)]) -result=SteepestDescentMethod(start,Jacob) -(X,Y,Z)=CreateMeshData() -CS = plt.contour(X, Y, Z,nContour) +result = SteepestDescentMethod(start, Jacob) +(X, Y, Z) = CreateMeshData() +CS = plt.contour(X, Y, Z, nContour) -Xc=np.arange(minXY,maxXY,delta) -Yc=[ConstrainFunction(x) for x in Xc] +Xc = np.arange(minXY, maxXY, delta) +Yc = [ConstrainFunction(x) for x in Xc] 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