From e1a751442de8e4b5978335236d207ed130af4c12 Mon Sep 17 00:00:00 2001
From: =?utf8?q?Bj=C3=B8rn=20Rustad?= <rustadbjornen@gmail.com>
Date: Fri, 30 Sep 2011 15:17:58 +0200
Subject: [PATCH] Newtsteep

---
 backup.eps   | 2867 ++++++++++++++++++++++++++++++++++++++++++++++++++
 main.py      |    2 +-
 newtsteep.py |   25 +
 rapport.tex  |   11 +-
 steepest.eps |  274 +++--
 5 files changed, 3021 insertions(+), 158 deletions(-)
 create mode 100644 backup.eps
 create mode 100644 newtsteep.py

diff --git a/backup.eps b/backup.eps
new file mode 100644
index 0000000..bae093b
--- /dev/null
+++ b/backup.eps
@@ -0,0 +1,2867 @@
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diff --git a/main.py b/main.py
index 96e8a16..981ee9e 100644
--- a/main.py
+++ b/main.py
@@ -12,7 +12,7 @@ def main():
     b = np.array([-0.3119187,  0.14508516])
     c = np.array([ 0.47736331, 1.48834978])
 
-    x0 = np.array([ 3.1, 3.8])
+    x0 = np.array([-2.1, 3.2])
     
     function_values = []
     
diff --git a/newtsteep.py b/newtsteep.py
new file mode 100644
index 0000000..977a02f
--- /dev/null
+++ b/newtsteep.py
@@ -0,0 +1,25 @@
+import numpy as np
+import generate as g
+import steepest as sd
+import newton
+import surf 
+import matplotlib.pyplot as plt
+from function import gradient_g
+from numpy.linalg import norm
+
+def newtsteep(x0, H, b, c, steep_tol, newt_tol):
+    x = []
+    r = []
+
+    # Finne optimal alpha og kjore en iterasjon med steepest.
+    x0_norm = norm(gradient_g(x0, H, b, c))
+    points, residuals = sd.steepest(x0, H, b, c, steep_tol, 100, 0, x0_norm)
+    x.extend(points)
+    r.extend(residuals)
+
+    # Angir tolerance og kjorer Newtons til vi finner nullpunkt.
+    points, residuals = newton.newton(x[len(x)-1], H, b, c, newt_tol, 100, x0_norm)
+    x.extend(points[1:])
+    r.extend(residuals[1:])
+
+    return (x, r)
diff --git a/rapport.tex b/rapport.tex
index 29a90b1..b02424d 100644
--- a/rapport.tex
+++ b/rapport.tex
@@ -135,10 +135,17 @@ Hence $\mathbf{v}^{T}(H+C(\mathbf{x}))\mathbf{v} > 0$, and we see by definition
 
 To find the optimal step length, $\alpha^*$, we solve the equation
 \begin{eqnarray}
-\frac{\partial}{\partial \mathbf{\alpha}}g\left(\mathbf{x}^{(k)}+\alpha\mathbf{u}^{(k)}\right) &=& 0, \text{where  } \mathbf{u}^{(k)} = -\nabla g(\mathbf{x}^{(k)} )  \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\\
 %HER ER DET FEIL! 
-\frac{1}{3}(\mathbf{u}^{(k)})^TC(\mathbf{u}^{(k)})\mathbf{u}^{(k)}\alpha^3+ (\mathbf{x}^{(k)})^TC(\mathbf{u}^{(k)}) \mathbf{u}^{(k)}\alpha^2+(\mathbf{u}^{(k)})^TH\mathbf{u}^{(k)}+(\mathbf{u}^{(k)})^TC(\mathbf{x}^{(k)})\mathbf{u}^{(k)})\alpha + \frac{1}{3}(\mathbf{u}^{(k)})^TC(\mathbf{x}^{(k)})\mathbf{x}^{(k)}+(\mathbf{u}^{(k)})^TH\mathbf{x}^{(k)}-\mathbf{b}^T\mathbf{u}^{(k)} = 0
+A\alpha^3 + B\alpha^2 + C\alpha + D &=& 0,
+\end{eqnarray}
+der $A$, $B$, $C$ og $D$ er gitt ved
+\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 \\
+D &=& \frac{1}{3}(\mathbf{u})^TC(\mathbf{x})\mathbf{x}+(\mathbf{u})^TH\mathbf{x}-\mathbf{b}^T\mathbf{u}
 \end{eqnarray}
 
 % VI MÅ OGSÅ ha utledning av alt det andre, forklaring 
diff --git a/steepest.eps b/steepest.eps
index 7c543e6..bae093b 100644
--- a/steepest.eps
+++ b/steepest.eps
@@ -1,7 +1,7 @@
 %!PS-Adobe-3.0 EPSF-3.0
 %%Title: steepest.eps
 %%Creator: matplotlib version 0.99.3, http://matplotlib.sourceforge.net/
-%%CreationDate: Fri Sep 30 11:39:59 2011
+%%CreationDate: Fri Sep 30 11:50:53 2011
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2.47.3