recompute right value of a* and adjust dependencies

Matlab-Programs/symSolveSystem.m

@@ -2,9 +2,16 @@
 
 syms q1 q2 q3 q12 b1 b2  a1 a2 
 
-eqn1 = q1 * a1 + (q3 + (q12/2)) *a2 == -2*q1*b1 - q12*b2
+% eqn1 = q1 * a1 + (q3 + (q12/2)) *a2 == -2*q1*b1 - q12*b2
+% 
+% eqn2 = (q3 + (q12/2)) * a1 + q2 *a2 == -2*q2*b2 - q12*b1
+
+
+eqn1 = q1 * a1 + (q3 + (q12/2)) *a2 == q1*b1 + (q12*b2/2)
+
+eqn2 = (q3 + (q12/2)) * a1 + q2 *a2 == q2*b2 + (q12*b1/2)
+
 
-eqn2 = (q3 + (q12/2)) * a1 + q2 *a2 == -2*q2*b2 - q12*b1
 
 [A,B] = equationsToMatrix([eqn1, eqn2], [a1,a2])
 

src/ClassifyMin.py

@@ -177,7 +177,9 @@ def classifyMin(q1, q2, q3, q12, b1, b2,  print_Cases=False, print_Output=False)
                 # is the “exact” solution of the equation. Else, x minimizes the
                 # Euclidean 2-norm || b-Ax ||. If there are multiple minimizing solutions,
                 # the one with the smallest 2-norm  is returned. ""
-                a = np.linalg.lstsq(A, B)[0]                            # TODO check is this Ok ?
+
+                # a = np.linalg.lstsq(A, B)[0]                            # TODO check is this Ok ?
+                a = np.linalg.lstsq(A, -B/2)[0]                            # TODO check is this Ok ? (UPDATE 13-10-21)
                 print("Solution LGS: a =", a)
                 a1 = a[0]
                 a2 = a[1]
@@ -211,9 +213,9 @@ def classifyMin(q1, q2, q3, q12, b1, b2,  print_Cases=False, print_Output=False)
     # ------------------------------------ Elliptic Case -----------------------------------
     if determinant >= epsilon:
         if print_Cases: print('E : elliptic case (determinant greater zero)')
-        a1_star = -(2*(b1*(q12**2) + 2*b1*q3*q12 - 4*b1*q1*q2 + 4*b2*q2*q3)) / \
+        a1_star = (b1*(q12**2) + 2*b1*q3*q12 - 4*b1*q1*q2 + 4*b2*q2*q3) / \
             (4*(q3**2) + 4*q3*q12 + (q12**2) - 4*q1*q2)
-        a2_star = -(2*(b2*(q12**2) + 2*b2*q3*q12 + 4*b1*q1*q3 - 4*b2*q1*q2)) / \
+        a2_star = (b2*(q12**2) + 2*b2*q3*q12 + 4*b1*q1*q3 - 4*b2*q1*q2) / \
             (4*(q3**2) + 4*q3*q12 + (q12**2) - 4*q1*q2)
         prod = a1_star*a2_star
 

src/Plot_CurvatureLemma1.4.py

@@ -118,13 +118,14 @@ print('gamma:', gamma)
 print('----------------------------')
 
 
-# TODO? : Ask User for Input ...
+# Optional - TODO? :
+# -Ask User for Input ...
 # function = input("Enter value you want to plot (y-value):\n")
 # print(f'You entered {function}')
 # parameter = input("Enter Parameter this value depends on (x-value) :\n")
 # print(f'You entered {parameter}')
 
-# Add Option to change NumberOfElements used for computation of Cell-Problem
+# -Add Option to change NumberOfElements used for computation of Cell-Problem
 
 
 # --- Define Quantity of interest:
@@ -222,7 +223,7 @@ for theta in X_Values:
             print('angle used')
             Y_Values.append(type)
         if yName =='curvature':
-            print('angle used')
+            print('curvature used')
             Y_Values.append(curvature)
 
 
@@ -230,9 +231,12 @@ print("(Output) Values of " + yName + ": ", Y_Values)
 
 
 idx = find_nearestIdx(Y_Values, 0)
-print(' Idx of value  closest to 0', idx)
+print(' Idx of value  closest to 0:', idx)
 ValueClose = Y_Values[idx]
-print('GammaValue(Idx) with mu_gamma closest to q_3^*', ValueClose)
+print('GammaValue(Idx) with mu_gamma closest to q_3^*:', ValueClose)
+print('Theta(Idx) with curvature closest to 0:', ValueClose)
+
+
 
 
 
@@ -312,14 +316,19 @@ f,ax=plt.subplots(1)
 
 
 # ax.plot(X_Values, Y_Values)
-ax.scatter(X_Values, Y_Values)
+# ax.scatter(X_Values, Y_Values)
 # plt.plot(x_plotValues, y_plotValues,'.')
 # plt.scatter(X_Values, Y_Values, alpha=0.3)
 # plt.scatter(X_Values, Y_Values)
 # plt.plot(X_Values, Y_Values,'.')
-plt.plot([X_Values[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
+
+
+# plt.plot([X_Values[0],X_Values[-1]], [Y_Values[0],Y_Values[-1]])
 # plt.axis([0, 6, 0, 20])
 
+ax.plot(X_Values[X_Values>jump_xValues[0]], Y_Values[X_Values>jump_xValues[0]] ,'b')
+ax.plot(X_Values[X_Values<jump_xValues[0]], Y_Values[X_Values<jump_xValues[0]], 'b')
+
 plt.xlabel(xName)
 # plt.ylabel(yName)