added Gauss and LU

ayr13001 · Oct 6, 2017 · e7abd64 · e7abd64
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commit e7abd64
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diff --git a/09_Linear-Algebra/.ipynb_checkpoints/09_Linear-Algebra-checkpoint.ipynb b/09_Linear-Algebra/.ipynb_checkpoints/09_Linear-Algebra-checkpoint.ipynb
@@ -205,7 +205,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 7,
    "metadata": {
     "collapsed": false,
     "slideshow": {
@@ -227,18 +227,25 @@
       "    1    2    3    4\n",
       "    5    6    7    8\n",
       "    9   10   11   12\n",
+      "\n",
+      "C =\n",
+      "\n",
+      "   20   28   36   44\n",
+      "   38   44   50   56\n",
       "\n"
      ]
     }
    ],
    "source": [
     "A=[5,3,0;1,2,3] \n",
-    "B=[1,2,3,4;5,6,7,8;9,10,11,12]"
+    "B=[1,2,3,4;5,6,7,8;9,10,11,12]\n",
+    "C=A*B;\n",
+    "C"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 6,
    "metadata": {
     "collapsed": false,
     "slideshow": {
@@ -372,10 +379,19 @@
     "\n",
     "Consider 4 masses connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? \n",
     "\n",
-    "![Springs-masses](mass_springs.svg)\n",
-    "\n",
-    "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:\n",
+    "![Springs-masses](mass_springs.png)\n",
     "\n",
+    "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "subslide"
+    }
+   },
+   "source": [
     "$m_{1}g+k(x_{2}-x_{1})-kx_{1}=0$\n",
     "\n",
     "$m_{2}g+k(x_{3}-x_{2})-k(x_{2}-x_{1})=0$\n",
@@ -414,7 +430,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
    "metadata": {
     "collapsed": false,
     "slideshow": {
@@ -426,20 +442,6 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "K =\n",
-      "\n",
-      "   20  -10    0    0\n",
-      "  -10   20  -10    0\n",
-      "    0  -10   20  -10\n",
-      "    0    0  -10   10\n",
-      "\n",
-      "y =\n",
-      "\n",
-      "    9.8100\n",
-      "   19.6200\n",
-      "   29.4300\n",
-      "   39.2400\n",
-      "\n",
       "x =\n",
       "\n",
       "    9.8100\n",
@@ -457,17 +459,21 @@
     "m3=3;\n",
     "m4=4;\n",
     "g=9.81; % m/s^2\n",
-    "K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k]\n",
-    "y=[m1*g;m2*g;m3*g;m4*g]\n",
+    "K=[2*k -k 0 0; -k 2*k -k 0; 0 -k 2*k -k; 0 0 -k k];\n",
+    "y=[m1*g;m2*g;m3*g;m4*g];\n",
     "\n",
     "x=K\\y"
    ]
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
    "source": [
-    "## Matrix Operations\n",
+    "## Special Matrices\n",
     "\n",
     "Identity matrix `eye(M,N)` **Assume M=N unless specfied**\n",
     "\n",
@@ -487,8 +493,13 @@
   },
   {
    "cell_type": "markdown",
-   "metadata": {},
+   "metadata": {
+    "slideshow": {
+     "slide_type": "subslide"
+    }
+   },
    "source": [
+    "## Matrix operations\n",
     "### Transpose\n",
     "\n",
     "The transpose of a matrix changes the rows -> columns and columns-> rows\n",
@@ -514,9 +525,12 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 13,
    "metadata": {
-    "collapsed": false
+    "collapsed": false,
+    "slideshow": {
+     "slide_type": "subslide"
+    }
    },
    "outputs": [
     {
@@ -602,7 +616,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 15,
    "metadata": {
     "collapsed": false,
     "slideshow": {
@@ -619,15 +633,16 @@
       "Diagonal Matrix\n",
       "\n",
       "   1   0   0\n",
-      "   0   1   0\n",
+      "   0   4   0\n",
       "   0   0   1\n",
       "\n",
-      "ans =  3\n"
+      "ans =  6\n"
      ]
     }
    ],
    "source": [
-    "id_m=eye(3)\n",
+    "id_m=eye(3);\n",
+    "id_m(2,2)=4\n",
     "trace(id_m)"
    ]
   },
@@ -658,7 +673,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 16,
    "metadata": {
     "collapsed": false,
     "slideshow": {
@@ -672,9 +687,9 @@
      "text": [
       "A =\n",
       "\n",
-      "   0.5762106   0.3533174   0.7172134\n",
-      "   0.7061664   0.4863733   0.9423436\n",
-      "   0.4255961   0.0016613   0.3561407\n",
+      "   0.71624   0.28713   0.91248\n",
+      "   0.43423   0.50924   0.89731\n",
+      "   0.81776   0.15682   0.48825\n",
       "\n"
      ]
     }
@@ -685,7 +700,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 17,
    "metadata": {
     "collapsed": false,
     "slideshow": {
@@ -699,9 +714,9 @@
      "text": [
       "Ainv =\n",
       "\n",
-      "   41.5613  -30.1783   -3.8467\n",
-      "   36.2130  -24.2201   -8.8415\n",
-      "  -49.8356   36.1767    7.4460\n",
+      "  -1.189272  -0.032028   2.281478\n",
+      "  -5.750167   4.369462   2.716129\n",
+      "   3.838847  -1.349811  -2.645516\n",
       "\n"
      ]
     }
@@ -712,7 +727,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 18,
    "metadata": {
     "collapsed": false,
     "slideshow": {
@@ -726,9 +741,9 @@
      "text": [
       "B =\n",
       "\n",
-      "   0.524529   0.470856   0.708116\n",
-      "   0.084491   0.730986   0.528292\n",
-      "   0.303545   0.782522   0.389282\n",
+      "   0.88372   0.43914   0.13476\n",
+      "   0.43439   0.34519   0.30337\n",
+      "   0.84604   0.86479   0.21558\n",
       "\n"
      ]
     }
@@ -739,7 +754,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 20,
    "metadata": {
     "collapsed": false,
     "slideshow": {
@@ -753,34 +768,22 @@
      "text": [
       "ans =\n",
       "\n",
-      "  -182.185   125.738    40.598\n",
-      "  -133.512    97.116    17.079\n",
-      "   282.422  -200.333   -46.861\n",
-      "\n",
-      "ans =\n",
-      "\n",
-      "  -182.185   125.738    40.598\n",
-      "  -133.512    97.116    17.079\n",
-      "   282.422  -200.333   -46.861\n",
-      "\n",
-      "ans =\n",
-      "\n",
-      "   41.5613   36.2130  -49.8356\n",
-      "  -30.1783  -24.2201   36.1767\n",
-      "   -3.8467   -8.8415    7.4460\n",
+      "  -1.189272  -5.750167   3.838847\n",
+      "  -0.032028   4.369462  -1.349811\n",
+      "   2.281478   2.716129  -2.645516\n",
       "\n",
       "ans =\n",
       "\n",
-      "   41.5613   36.2130  -49.8356\n",
-      "  -30.1783  -24.2201   36.1767\n",
-      "   -3.8467   -8.8415    7.4460\n",
+      "  -1.189272  -5.750167   3.838847\n",
+      "  -0.032028   4.369462  -1.349811\n",
+      "   2.281478   2.716129  -2.645516\n",
       "\n"
      ]
     }
    ],
    "source": [
-    "inv(A*B)\n",
-    "inv(B)*inv(A)\n",
+    "%inv(A*B)\n",
+    "%inv(B)*inv(A)\n",
     "\n",
     "inv(A')\n",
     "\n",

diff --git a/09_Linear-Algebra/09_Linear-Algebra.ipynb b/09_Linear-Algebra/09_Linear-Algebra.ipynb
@@ -379,7 +379,7 @@
     "\n",
     "Consider 4 masses connected in series to 4 springs with K=10 N/m. What are the final positions of the masses? \n",
     "\n",
-    "![Springs-masses](mass_springs.svg)\n",
+    "![Springs-masses](mass_springs.png)\n",
     "\n",
     "The masses haves the following amounts, 1, 2, 3, and 4 kg for masses 1-4. Using a FBD for each mass:"
    ]

diff --git a/09_Linear-Algebra/octave-workspace b/09_Linear-Algebra/octave-workspace