diff --git a/Week 4/8 Eigenvalues and Eigenvectors.ipynb b/Week 4/8 Eigenvalues and Eigenvectors.ipynb index c3a2616..05c2149 100644 --- a/Week 4/8 Eigenvalues and Eigenvectors.ipynb +++ b/Week 4/8 Eigenvalues and Eigenvectors.ipynb @@ -66,7 +66,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "deletable": false, "nbgrader": { @@ -137,7 +137,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "deletable": false, "nbgrader": { @@ -201,7 +201,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "deletable": false, "nbgrader": { @@ -216,7 +216,30 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "For sigma = 0.03\n", + "b = [ 0.45440139 -0.76618454 0.45440139]\n", + "lam = [0.62771919 0.62771831 0.62771919]\n", + "\n", + "\n", + "For sigma = 6.0\n", + "b = [0.54177432 0.64262054 0.54177432]\n", + "lam = [6.37228128 6.37228139 6.37228128]\n", + "\n", + "\n", + "For sigma = 1.99999989999999\n", + "b = [-7.07106781e-01 -4.21799612e-14 7.07106781e-01]\n", + "lam = [ 2. -0. 2.]\n", + "\n", + "\n", + "[6.37228132 2. 0.62771868]\n" + ] + } + ], "source": [ "# Use this cell for your own testing ...\n", "\n", @@ -239,7 +262,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "deletable": false, "nbgrader": { @@ -305,7 +328,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": { "deletable": false, "nbgrader": { @@ -347,7 +370,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "deletable": false, "nbgrader": { @@ -362,7 +385,28 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(3,) (3, 3) () (1, 3)\n", + "(3,) (3, 3) () (0, 3)\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[ 3. , -2.23606798, 0. ],\n", + " [-2.23606798, 4.6 , 1.2 ],\n", + " [ 0. , 1.2 , 1.4 ]])" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "B = np.array([[3,2,1],[2,3,2],[1,2,3]])\n", "\n", @@ -405,7 +449,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "deletable": false, "nbgrader": { @@ -443,7 +487,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": { "deletable": false, "nbgrader": { @@ -458,7 +502,19 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(3,) (3, 3) () (1, 3)\n", + "(3,) (3, 3) () (0, 3)\n", + "[[ 3. -2.23606798 0. ]\n", + " [-2.23606798 4.6 1.2 ]\n", + " [ 0. 1.2 1.4 ]]\n" + ] + } + ], "source": [ "A_tridiag = tridiagonalize(A)\n", "print(A_tridiag)" @@ -466,7 +522,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": { "deletable": false, "nbgrader": { @@ -481,7 +537,15 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[6.37228126 2.00000006 0.62771869]\n" + ] + } + ], "source": [ "def test_QREig():\n", " \"\"\"\n", @@ -520,7 +584,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": { "deletable": false, "nbgrader": { @@ -535,7 +599,17 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(array([ 0.54177424, -0.81706617, -0.1971891 ]), 3)\n", + "(array([0.70710833, 0.31623112, 0.63245212]), 2)\n", + "(array([ 0.45440144, 0.48208191, -0.749077 ]), 3)\n" + ] + } + ], "source": [ "\"\"\"\n", "Eigenvalues and -vectors calculated numerically for matrix A using functions from previous tasks.\n", @@ -587,7 +661,18 @@ "task": false } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(5,) (5, 5) () (3, 5)\n", + "(5,) (5, 5) () (2, 5)\n", + "(5,) (5, 5) () (1, 5)\n", + "(5,) (5, 5) () (0, 5)\n" + ] + } + ], "source": [ "\"\"\"\n", "Completely 'random' and totally not self-made matrices C and D are being tridiagonalized and its eigenvalues and -vectors are\n", @@ -623,7 +708,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" },