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February 13, 2017 17:07
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PHY 512 Assignment 3 Bonus Question
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{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Assignment 3 Bonus Quesion (Problem 3.3.4)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"** Sam Weiss <br />\n", | |
"PHY 512 <br />\n", | |
"2/9/17**" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Activate a matlab-like interactive interface." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 141, | |
"metadata": { | |
"collapsed": false, | |
"deletable": true, | |
"editable": true | |
}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
"Populating the interactive namespace from numpy and matplotlib\n" | |
] | |
} | |
], | |
"source": [ | |
"%pylab inline" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 142, | |
"metadata": { | |
"collapsed": true, | |
"deletable": true, | |
"editable": true | |
}, | |
"outputs": [], | |
"source": [ | |
"from mpl_toolkits.mplot3d import Axes3D" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Define the matrix and vectors needed for the problem." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 143, | |
"metadata": { | |
"collapsed": false, | |
"deletable": true, | |
"editable": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"matrix([[ 0.8 , 0.6 , 0. ],\n", | |
" [-0.48, 0.64, 0.6 ],\n", | |
" [ 0.36, -0.48, 0.8 ]])" | |
] | |
}, | |
"execution_count": 143, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"s = mat('0.8 0.6 0; -0.48 0.64 0.6; 0.36 -0.48 0.8')\n", | |
"s" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 144, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"matrix([[1],\n", | |
" [0],\n", | |
" [1]])" | |
] | |
}, | |
"execution_count": 144, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"a = mat('1; 0; 1')\n", | |
"a" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 145, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"matrix([[ 0],\n", | |
" [ 2],\n", | |
" [-1]])" | |
] | |
}, | |
"execution_count": 145, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"b = mat('0; 2; -1')\n", | |
"b" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Part (a): Calculate det(s)." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 146, | |
"metadata": { | |
"collapsed": false, | |
"deletable": true, | |
"editable": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"1.0" | |
] | |
}, | |
"execution_count": 146, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"linalg.det(s)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Part (b): Verify that a.T * b is invariant under application of s to a and b. \n", | |
"\n", | |
"As shown below, the answers are invariant when computer rounding error is taken into account." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 147, | |
"metadata": { | |
"collapsed": false, | |
"deletable": true, | |
"editable": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"-1" | |
] | |
}, | |
"execution_count": 147, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"(a.T * b).item(0)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 148, | |
"metadata": { | |
"collapsed": false, | |
"deletable": true, | |
"editable": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"-1.0000000000000004" | |
] | |
}, | |
"execution_count": 148, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"((s * a).T * (s * b)).item(0)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Calculate the lengths of a and b and their rotated versions. Then, calculate their angles (in degrees).\n", | |
"\n", | |
"As shown, the vectors are only rotated when transformed. Their lengths stay constant." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 149, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"1.4142135623730951" | |
] | |
}, | |
"execution_count": 149, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"len_a = norm(a)\n", | |
"len_a" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 150, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"1.4142135623730951" | |
] | |
}, | |
"execution_count": 150, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"len_sa = norm(s * a)\n", | |
"len_sa" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 151, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"2.2360679774997898" | |
] | |
}, | |
"execution_count": 151, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"len_b = norm(b)\n", | |
"len_b" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 152, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"2.2360679774997898" | |
] | |
}, | |
"execution_count": 152, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"len_sb = norm(s * b)\n", | |
"len_sb" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 153, | |
"metadata": { | |
"collapsed": false, | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"11.47834095453361" | |
] | |
}, | |
"execution_count": 153, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"(arccos(((s * a).T * a) / (len_sa * len_a)) * (180 / pi)).item(0)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 154, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"51.391172304587116" | |
] | |
}, | |
"execution_count": 154, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"(arccos(((s * b).T * b) / (len_sb * len_b)) * (180 / pi)).item(0)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Part (c): Determine what happens to a X b under application of s to a and b. Is this what is expected?\n", | |
"\n", | |
"The length of the cross product does not change, but it is rotated. Given the rotations computed above, the cross product's rotation after transformation seems reasonable. Plotted below is the cross product before and after transformation." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 155, | |
"metadata": { | |
"collapsed": false, | |
"deletable": true, | |
"editable": true, | |
"scrolled": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([-2, 1, 2])" | |
] | |
}, | |
"execution_count": 155, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"a_x_b = cross(a.T, b.T)[0]\n", | |
"a_x_b" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 156, | |
"metadata": { | |
"collapsed": false, | |
"deletable": true, | |
"editable": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"array([-1. , 2.8, 0.4])" | |
] | |
}, | |
"execution_count": 156, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"sa_x_sb = cross((s * a).T, (s * b).T)[0]\n", | |
"sa_x_sb" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 157, | |
"metadata": { | |
"collapsed": false, | |
"deletable": true, | |
"editable": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"3.0" | |
] | |
}, | |
"execution_count": 157, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"len_axb = norm(a_x_b)\n", | |
"len_axb" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 158, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"3.0000000000000004" | |
] | |
}, | |
"execution_count": 158, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"len_saxsb = norm(sa_x_sb)\n", | |
"len_saxsb" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 159, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"51.521404866702071" | |
] | |
}, | |
"execution_count": 159, | |
"metadata": {}, | |
"output_type": "execute_result" | |
} | |
], | |
"source": [ | |
"arccos(dot(a_x_b, sa_x_sb) / (len_axb * len_saxsb)) * (180 / pi)" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Cross product before transformation:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 160, | |
"metadata": { | |
"collapsed": false, | |
"deletable": true, | |
"editable": true | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(-1, 3)" | |
] | |
}, | |
"execution_count": 160, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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WMiGLgaIolJeX5xw0KuSrLMUFbr5SFn6/v2AN8p///Gc888wzWLt2Lasf//a3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\nAVwi+P8/4JbZybAExAAAAABJRU5ErkJggg==\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x1135b2550>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig = plt.figure()\n", | |
"ax = fig.add_subplot(111, projection='3d')\n", | |
"ax.quiver([0, 0, 0] , [0, 0, 0], [0, 0, 0], [a[0], b[0], a_x_b[0]], [a[1], b[1], a_x_b[1]], [a[2], b[2], a_x_b[2]])\n", | |
"ax.set_xlim([-2.5, 1])\n", | |
"ax.set_ylim([-3, 1])\n", | |
"ax.set_zlim([-1, 3])" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"Cross product after transformation:" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 161, | |
"metadata": { | |
"collapsed": false | |
}, | |
"outputs": [ | |
{ | |
"data": { | |
"text/plain": [ | |
"(-1, 3)" | |
] | |
}, | |
"execution_count": 161, | |
"metadata": {}, | |
"output_type": "execute_result" | |
}, | |
{ | |
"data": { | |
"image/png": 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yiMfjNWuQ/+u//gvf+973cPz4cUE//od/+IdYWloCAHz2s5/FCy+8gG9+85sw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\nrkJggg==\n", | |
"text/plain": [ | |
"<matplotlib.figure.Figure at 0x112ea22b0>" | |
] | |
}, | |
"metadata": {}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"fig = plt.figure()\n", | |
"ax = fig.add_subplot(111, projection='3d')\n", | |
"ax.quiver([0, 0, 0] , [0, 0, 0], [0, 0, 0], [(s * a)[0], (s * b)[0], sa_x_sb[0]], \n", | |
" [(s * a)[1], (s * b)[1], sa_x_sb[1]], \n", | |
" [(s * a)[1], (s * b)[1], sa_x_sb[1]])\n", | |
"ax.set_xlim([-2.5, 1])\n", | |
"ax.set_ylim([-3, 1])\n", | |
"ax.set_zlim([-1, 3])" | |
] | |
} | |
], | |
"metadata": { | |
"kernelspec": { | |
"display_name": "Python 3", | |
"language": "python", | |
"name": "python3" | |
}, | |
"language_info": { | |
"codemirror_mode": { | |
"name": "ipython", | |
"version": 3 | |
}, | |
"file_extension": ".py", | |
"mimetype": "text/x-python", | |
"name": "python", | |
"nbconvert_exporter": "python", | |
"pygments_lexer": "ipython3", | |
"version": "3.5.3" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
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