Implemented eliptical regression test. It's very close to machine pre…

…cision

ias15PDE.py

@@ -87,16 +87,16 @@ def calculateNodePositions(Bx, By, xi, yi, func: callable, gunc: callable, dt, h
                                 By[6])))))))
     return xh, yh
 
-def calculateNewPosition(B, xi, ti, func: callable, gunc: callable, dt):
-    newPosition = calculateNodePositions(B, xi, ti, func, gunc, dt, hp = np.array([1]))
+def calculateNewPosition(Bx, By, xi, yi, func: callable, gunc: callable, dt):
+    newPosition = calculateNodePositions(Bx, By, xi, yi, func, gunc, dt, hp = np.array([1]))
     return newPosition
 
-def calculateDerivatives(func: callable, gunc: callable, x, t):
+def calculateDerivatives(x, y, func: callable, gunc: callable):
     Fx = np.zeros(len(x))
     Fy = np.zeros(len(x))
     for i in range(len(x)):
-        Fy[i] = func(x[i], t[i])
-        Fx[i] = gunc(x[i], t[i])
+        Fy[i] = func(x[i], y[i])
+        Fx[i] = gunc(x[i], y[i])
     return Fx, Fy
 
 def calculateB_xy(Gx, Gy):

regression_elipse.py

@@ -8,12 +8,41 @@
 x0 = 1
 y0 = 0
 
-dt = 1
-Bx = np.zeros(7)
-By = np.zeros(7)
-for i in range(12):
-    xh, yh = ias15.calculateNodePositions(Bx, By, x0, y0, dxds, dyds, dt)
-    Fx, Fy = ias15.calculateDerivatives(dxds, dyds, xh, yh)
-    Gx, Gy = ias15.calculateGFromF_xy(Fx, Fy)
-    Bx, By = ias15.calculateB_xy(Gx, Gy)
-
+ds = .001
+s_final = np.pi*2
+nSteps = int(s_final/ds)
+s = np.linspace(0,s_final,nSteps+1, endpoint=True)
+x = np.zeros(nSteps+1)
+y = np.zeros(nSteps+1)
+x[0] = x0
+y[0] = y0
+Bxi = np.zeros(7)
+Byi = np.zeros(7)
+for i in range(1,nSteps+1):
+    x[i], y[i], Bxf, Byf = ias15.push(dyds, dxds, x[i-1], y[i-1], ds, Bxi, Byi)
+    Bxi = Bxf
+    Byi = Byf
+
+radius  = np.sqrt(x**2 + y**2)
+
+fig = plt.figure()
+ax1 = fig.add_subplot(121)
+ax2 = fig.add_subplot(122)
+
+ax1.plot(x,y,'r.')
+ax1.set_xlim(-1.5,1.5)
+ax1.set_ylim(-1.5,1.5)
+ax1.set_title("Elliptical Orbit")
+ax1.set_xlabel("x")
+ax1.set_ylabel("y")
+#Set aspect ratio to be square
+ax1.set_aspect('equal')
+ax1.grid()
+
+ax2.plot(s,radius-1,'r.')
+ax2.set_title("Radius - 1")
+ax2.set_xlabel("s")
+ax2.set_ylabel("radius - 1")
+ax2.grid()
+plt.savefig("figures/elliptical_orbit.png")
+plt.show()