Newtsteep

diff --git a/backup.eps b/backup.eps
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+%%CreationDate: Fri Sep 30 11:50:53 2011
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diff --git a/main.py b/main.py
index 96e8a16d5edde1610210b051c77027d2e479b281..981ee9e8dc9f26b314aeccc08723740a368fab79 100644 (file)
--- 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 (file)
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 29a90b1b21a28db486890ad544c9154f52cb2284..b02424d073492a614a953c9f2e06a78df7cefe23 100644 (file)
--- 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
 \r
 To find the optimal step length, $\alpha^*$, we solve the equation\r
 \begin{eqnarray}\r
-\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 \\\r
+\frac{\partial}{\partial \mathbf{\alpha}}g\left(\mathbf{x}+\alpha\mathbf{u}\right) &=& 0, \text{where  } \mathbf{u} = -\nabla g(\mathbf{x} )  \nonumber \\\r
 &\Updownarrow& \nonumber\\\r
 %HER ER DET FEIL! \r
-\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\r
+A\alpha^3 + B\alpha^2 + C\alpha + D &=& 0,\r
+\end{eqnarray}\r
+der $A$, $B$, $C$ og $D$ er gitt ved\r
+\begin{eqnarray}\r
+A &=& \frac{1}{3}\mathbf{u}^TC(\mathbf{u}\mathbf{u} \nonumber \\\r
+B &=& (\mathbf{x})^TC(\mathbf{u}) \mathbf{u} \nonumber \\\r
+C &=& (\mathbf{u})^TH\mathbf{u}+(\mathbf{u})^TC(\mathbf{x})\mathbf{u}) \nonumber \\\r
+D &=& \frac{1}{3}(\mathbf{u})^TC(\mathbf{x})\mathbf{x}+(\mathbf{u})^TH\mathbf{x}-\mathbf{b}^T\mathbf{u}\r
 \end{eqnarray}\r
 \r
 % VI MÅ OGSÅ ha utledning av alt det andre, forklaring \r

diff --git a/steepest.eps b/steepest.eps
index 7c543e697a367cae3f46e090cdf3840f4a64644d..bae093b7eaff525fca132649fabda0dc6e3eaa43 100644 (file)
--- a/steepest.eps
+++ b/steepest.eps
@@ -1,7 +1,7 @@
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 %%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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