From 538533c0df24fa8ebff019ab4a389f367a0132a2 Mon Sep 17 00:00:00 2001
From: Klaus <klaus.boehnlein@tu-dresden.de>
Date: Wed, 13 Oct 2021 20:42:59 +0200
Subject: [PATCH] recompute right value of a* and adjust dependencies
---
Matlab-Programs/symSolveSystem.m | 11 +++++++++--
src/ClassifyMin.py | 8 +++++---
src/Plot_CurvatureLemma1.4.py | 23 ++++++++++++++++-------
3 files changed, 30 insertions(+), 12 deletions(-)
diff --git a/Matlab-Programs/symSolveSystem.m b/Matlab-Programs/symSolveSystem.m
index 6424b5e7..5dde81e4 100644
--- a/Matlab-Programs/symSolveSystem.m
+++ b/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])
diff --git a/src/ClassifyMin.py b/src/ClassifyMin.py
index 02ce9e28..b4e83546 100644
--- a/src/ClassifyMin.py
+++ b/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
diff --git a/src/Plot_CurvatureLemma1.4.py b/src/Plot_CurvatureLemma1.4.py
index ea4f16b7..f2c9f2de 100644
--- a/src/Plot_CurvatureLemma1.4.py
+++ b/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)
--
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