From a773eae7d55ae96e15a3107c854c66a6477891d7 Mon Sep 17 00:00:00 2001
From: =?utf8?q?Bj=C3=B8rn=20Rustad?= <bjornrus@samfundet.no>
Date: Fri, 30 Sep 2011 21:45:15 +0200
Subject: [PATCH] More small fixes

---
 function.py |   1 +
 main.py     | 112 ++++++++++++++++++++++++++--------------------------
 newton.py   |   4 +-
 rapport.tex |  20 +++++-----
 steepest.py |   4 +-
 5 files changed, 72 insertions(+), 69 deletions(-)

diff --git a/function.py b/function.py
index a7a26a3..92cf714 100644
--- a/function.py
+++ b/function.py
@@ -13,6 +13,7 @@ def _C(x, c):
 
 # Calculate gradient of g in point x
 def gradient_g(x, H, b, c):
+    print _C(x,c)
     return -b + H.dot(x) + (1.0/3.0) * _C(x,c).dot(x)
 
 # Calculate hessian of g in point x
diff --git a/main.py b/main.py
index 8d2dd7a..bafd504 100644
--- a/main.py
+++ b/main.py
@@ -1,7 +1,7 @@
-from enthought.mayavi import mlab
+#from enthought.mayavi import mlab
 import time
 import numpy as np
-import matplotlib.pyplot as plt
+#import matplotlib.pyplot as plt
 import surf
 from steepest import steepest
 from function import function_g
@@ -44,60 +44,60 @@ def main():
     f_newton = []
     f_nwst = []
 
-    mlab.figure(figure="Surface", bgcolor=(1,1,1), fgcolor=(0,0,0))
-
-    plen = 15
-    for point in optimal_points[:plen]:
-        z = function_g(point, H, b, c)
-        f_optimal.append(z)
-        p = mlab.points3d([point[0]], [point[1]], [z], scale_factor=0.03, color=(0.7,0.2,0.2))
-
-    for point in constant_points[:plen]:
-        z = function_g(point, H, b, c)
-        f_constant.append(z)
-        p = mlab.points3d([point[0]], [point[1]], [z], scale_factor=0.02, color=(1,1,1))
-
-    for point in newton_points[:plen]:
-        z = function_g(point, H, b, c)
-        f_newton.append(z)
-
-    for point in nwst_points[:plen]:
-        z = function_g(point, H, b, c)
-        f_nwst.append(z)
-
-    last = optimal_points[len(optimal_points)-1]
-    X, Y, Z = surf.surf(H, b, c, last[0]-1, last[0]+1, last[1]-1, last[1]+1, -10, 3)
-
-    surface = mlab.mesh(X, Y, Z)
-    axes = mlab.axes(color=(0,0,0))
-    mlab.outline()
-    mlab.show()
-    
-    fig = plt.figure(1)
-    plt.rc('mathtext', default='regular')
-    fig.subplots_adjust(hspace=0.4)
-    ax = plt.subplot(211)
-    plt.title("Relative residual")
-    plt.xlabel("Iteration")
-    plt.ylabel("Relative residual")
-    plt.plot(optimal_residuals[:plen])
-    plt.plot(constant_residuals[:plen])
-    plt.plot(newton_residuals[:plen])
-    plt.plot(nwst_residuals[:plen])
-    plt.legend([r'Optimal $\alpha$', r'$\alpha$ = %.2f' % alpha, r'Newtons method', r'Steepest first, then Newton'])
-    ax.set_yscale('log')
-    
-    ax = plt.subplot(212)
-    plt.title("Function value")
-    plt.xlabel("Iteration")
-    plt.ylabel("g(x)")
-    plt.plot(f_optimal[:plen])
-    plt.plot(f_constant[:plen])
-    plt.plot(f_newton[:plen])
-    plt.plot(f_nwst[:plen])
-    
-    plt.show()
-    fig.savefig("steepest.eps", format="eps")
+#    mlab.figure(figure="Surface", bgcolor=(1,1,1), fgcolor=(0,0,0))
+#
+#    plen = 15
+#    for point in optimal_points[:plen]:
+#        z = function_g(point, H, b, c)
+#        f_optimal.append(z)
+#        p = mlab.points3d([point[0]], [point[1]], [z], scale_factor=0.03, color=(0.7,0.2,0.2))
+#
+#    for point in constant_points[:plen]:
+#        z = function_g(point, H, b, c)
+#        f_constant.append(z)
+#        p = mlab.points3d([point[0]], [point[1]], [z], scale_factor=0.02, color=(1,1,1))
+#
+#    for point in newton_points[:plen]:
+#        z = function_g(point, H, b, c)
+#        f_newton.append(z)
+#
+#    for point in nwst_points[:plen]:
+#        z = function_g(point, H, b, c)
+#        f_nwst.append(z)
+#
+#    last = optimal_points[len(optimal_points)-1]
+#    X, Y, Z = surf.surf(H, b, c, last[0]-1, last[0]+1, last[1]-1, last[1]+1, -10, 3)
+#
+#    surface = mlab.mesh(X, Y, Z)
+#    axes = mlab.axes(color=(0,0,0))
+#    mlab.outline()
+#    mlab.show()
+#    
+#    fig = plt.figure(1)
+#    plt.rc('mathtext', default='regular')
+#    fig.subplots_adjust(hspace=0.4)
+#    ax = plt.subplot(211)
+#    plt.title("Relative residual")
+#    plt.xlabel("Iteration")
+#    plt.ylabel("Relative residual")
+#    plt.plot(optimal_residuals[:plen])
+#    plt.plot(constant_residuals[:plen])
+#    plt.plot(newton_residuals[:plen])
+#    plt.plot(nwst_residuals[:plen])
+#    plt.legend([r'Optimal $\alpha$', r'$\alpha$ = %.2f' % alpha, r'Newtons method', r'Steepest first, then Newton'])
+#    ax.set_yscale('log')
+#    
+#    ax = plt.subplot(212)
+#    plt.title("Function value")
+#    plt.xlabel("Iteration")
+#    plt.ylabel("g(x)")
+#    plt.plot(f_optimal[:plen])
+#    plt.plot(f_constant[:plen])
+#    plt.plot(f_newton[:plen])
+#    plt.plot(f_nwst[:plen])
+#    
+#    plt.show()
+#    fig.savefig("steepest.eps", format="eps")
     
 if __name__ == "__main__":
     main()
diff --git a/newton.py b/newton.py
index c639229..9eb559a 100644
--- a/newton.py
+++ b/newton.py
@@ -1,9 +1,9 @@
-from enthought.mayavi import mlab
+#from enthought.mayavi import mlab
 from function import function_g, gradient_g, hessian_g
 import generate
 import surf
 import numpy as np
-import matplotlib.pyplot as plt
+#import matplotlib.pyplot as plt
 from numpy.linalg import norm, inv
 
 # Calculate the next iteration of the Newton method
diff --git a/rapport.tex b/rapport.tex
index f7816dd..015b481 100644
--- a/rapport.tex
+++ b/rapport.tex
@@ -34,7 +34,7 @@
 
 \begin{document}
 
-\title{Semester Project 1 TMA4215}
+\title{Semester Project 1 in TMA4215}
 \author{
 	KANDIDATNUMMER! \footnote{Skriv noe her.} \\
 	Hva med noe her også?
@@ -123,15 +123,15 @@ that the Hessian, $\nabla^{2}g(\mathbf{x})$, is positive definite.
 \begin{figure}[htb]
   \centering
   \includegraphics[width=0.9\textwidth]{steepest}
-  \caption{Plot of relative residual and function values for iterations of the steepest descent method with optimal $\alpha$}
-  \label{fig:fn_resid}
+  \caption{Plot of relative residual and function values for iterations of the
+  steepest descent method with optimal $\alpha$} \label{fig:fn_resid}
 \end{figure}
 
 \begin{figure}[htb]
   \centering
   \includegraphics[width=0.9\textwidth]{surface}
-  \caption{Surface plot of function with points showing iteration of steepest descent method, both with optimal and constant $\alpha$}
-  \label{fig:surface}
+  \caption{Surface plot of function with points showing iteration of steepest
+  descent method, both with optimal and constant $\alpha$} \label{fig:surface}
 \end{figure}
 
 Consider the equation
@@ -151,12 +151,14 @@ where $t_{n+1} = t_n + \alpha$. Looking at this result, we see that it is equiva
 
 To find the optimal step length, $\alpha^*$, we solve the equation
 \begin{eqnarray}
-  \frac{\partial}{\partial \mathbf{\alpha}}g\left(\mathbf{x}+\alpha\mathbf{u}\right) &=& 0, \text{where  } \mathbf{u} = -\nabla g(\mathbf{x} )  \nonumber \\
-  &\Updownarrow& \nonumber\\
+  \frac{\partial}{\partial
+    \mathbf{\alpha}}g\left(\mathbf{x}+\alpha\mathbf{u}\right) &=& 0, \text{where  }
+    \mathbf{u} = -\nabla g(\mathbf{x} )  \nonumber \\
+  &\Updownarrow& \nonumber \\
   A\alpha^3 + B\alpha^2 + C\alpha + D &=& 0,
-  \end{eqnarray}
+\end{eqnarray}
 where $A$, $B$, $C$, and $D$ is given by
-  \begin{eqnarray}
+\begin{eqnarray}
   A &=& \frac{1}{3}\mathbf{u}^TC(\mathbf{u})\mathbf{u} \nonumber \\
   B &=& \mathbf{x}^TC(\mathbf{u}) \mathbf{u} \nonumber \\
   C &=& \mathbf{u}^TH\mathbf{u}+\mathbf{u}^TC(\mathbf{x})\mathbf{u} \nonumber \\
diff --git a/steepest.py b/steepest.py
index 976388c..2d5d401 100644
--- a/steepest.py
+++ b/steepest.py
@@ -1,9 +1,9 @@
-from enthought.mayavi import mlab
+#from enthought.mayavi import mlab
 from function import function_g, gradient_g, _C
 import generate
 import surf
 import numpy as np
-import matplotlib.pyplot as plt
+#import matplotlib.pyplot as plt
 import time
 from numpy.linalg import norm
 
-- 
2.47.3