|
36 | 36 | }, |
37 | 37 | { |
38 | 38 | "cell_type": "code", |
39 | | - "execution_count": 4, |
| 39 | + "execution_count": null, |
40 | 40 | "metadata": {}, |
41 | | - "outputs": [ |
42 | | - { |
43 | | - "data": {}, |
44 | | - "metadata": {}, |
45 | | - "output_type": "display_data" |
46 | | - }, |
47 | | - { |
48 | | - "data": { |
49 | | - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaQAAAFoCAMAAAAvuH/IAAAANlBMVEUAAAAzMzNNTU1oaGh8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", |
50 | | - "text/plain": [ |
51 | | - "plot without title" |
52 | | - ] |
53 | | - }, |
54 | | - "metadata": {}, |
55 | | - "output_type": "display_data" |
56 | | - } |
57 | | - ], |
| 41 | + "outputs": [], |
58 | 42 | "source": [ |
59 | 43 | "library(ggplot2)\n", |
60 | 44 | "library(NISTunits) # Libary to work netween degrees and radians\n", |
|
87 | 71 | }, |
88 | 72 | { |
89 | 73 | "cell_type": "code", |
90 | | - "execution_count": 6, |
| 74 | + "execution_count": null, |
91 | 75 | "metadata": {}, |
92 | | - "outputs": [ |
93 | | - { |
94 | | - "name": "stdout", |
95 | | - "output_type": "stream", |
96 | | - "text": [ |
97 | | - " x y\n", |
98 | | - "2 1 0.5\n" |
99 | | - ] |
100 | | - }, |
101 | | - { |
102 | | - "data": {}, |
103 | | - "metadata": {}, |
104 | | - "output_type": "display_data" |
105 | | - }, |
106 | | - { |
107 | | - "data": { |
108 | | - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaQAAAFoCAMAAAAvuH/IAAAANlBMVEUAAAAzMzNNTU1oaGh8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", |
109 | | - "text/plain": [ |
110 | | - "plot without title" |
111 | | - ] |
112 | | - }, |
113 | | - "metadata": {}, |
114 | | - "output_type": "display_data" |
115 | | - } |
116 | | - ], |
| 76 | + "outputs": [], |
117 | 77 | "source": [ |
118 | 78 | "b = v / 2\n", |
119 | 79 | "print(b[2,])\n", |
|
152 | 112 | }, |
153 | 113 | { |
154 | 114 | "cell_type": "code", |
155 | | - "execution_count": 19, |
| 115 | + "execution_count": null, |
156 | 116 | "metadata": {}, |
157 | | - "outputs": [ |
158 | | - { |
159 | | - "data": { |
160 | | - "text/html": [ |
161 | | - "-4" |
162 | | - ], |
163 | | - "text/latex": [ |
164 | | - "-4" |
165 | | - ], |
166 | | - "text/markdown": [ |
167 | | - "-4" |
168 | | - ], |
169 | | - "text/plain": [ |
170 | | - "[1] -4" |
171 | | - ] |
172 | | - }, |
173 | | - "metadata": {}, |
174 | | - "output_type": "display_data" |
175 | | - } |
176 | | - ], |
| 117 | + "outputs": [], |
177 | 118 | "source": [ |
178 | 119 | "## Another data frame s\n", |
179 | 120 | "s = data.frame(x = c(0,-3), y = c(0,2))\n", |
|
216 | 157 | }, |
217 | 158 | { |
218 | 159 | "cell_type": "code", |
219 | | - "execution_count": 26, |
| 160 | + "execution_count": null, |
220 | 161 | "metadata": {}, |
221 | | - "outputs": [ |
222 | | - { |
223 | | - "data": { |
224 | | - "text/html": [ |
225 | | - "119.744898585964" |
226 | | - ], |
227 | | - "text/latex": [ |
228 | | - "119.744898585964" |
229 | | - ], |
230 | | - "text/markdown": [ |
231 | | - "119.744898585964" |
232 | | - ], |
233 | | - "text/plain": [ |
234 | | - "[1] 119.7449" |
235 | | - ] |
236 | | - }, |
237 | | - "metadata": {}, |
238 | | - "output_type": "display_data" |
239 | | - } |
240 | | - ], |
| 162 | + "outputs": [], |
241 | 163 | "source": [ |
242 | 164 | "norm_v = norm(v, '2')\n", |
243 | 165 | "norm_s = norm(s, '2')\n", |
|
274 | 196 | }, |
275 | 197 | { |
276 | 198 | "cell_type": "code", |
277 | | - "execution_count": 32, |
| 199 | + "execution_count": null, |
278 | 200 | "metadata": {}, |
279 | | - "outputs": [ |
280 | | - { |
281 | | - "data": { |
282 | | - "text/html": [ |
283 | | - "<table>\n", |
284 | | - "<tbody>\n", |
285 | | - "\t<tr><td>6</td></tr>\n", |
286 | | - "</tbody>\n", |
287 | | - "</table>\n" |
288 | | - ], |
289 | | - "text/latex": [ |
290 | | - "\\begin{tabular}{l}\n", |
291 | | - "\t 6\\\\\n", |
292 | | - "\\end{tabular}\n" |
293 | | - ], |
294 | | - "text/markdown": [ |
295 | | - "\n", |
296 | | - "| 6 | \n", |
297 | | - "\n", |
298 | | - "\n" |
299 | | - ], |
300 | | - "text/plain": [ |
301 | | - " [,1]\n", |
302 | | - "[1,] 6 " |
303 | | - ] |
304 | | - }, |
305 | | - "metadata": {}, |
306 | | - "output_type": "display_data" |
307 | | - }, |
308 | | - { |
309 | | - "data": { |
310 | | - "text/html": [ |
311 | | - "<table>\n", |
312 | | - "<tbody>\n", |
313 | | - "\t<tr><td>2 </td><td>4 </td><td>-4</td></tr>\n", |
314 | | - "\t<tr><td>3 </td><td>6 </td><td>-6</td></tr>\n", |
315 | | - "\t<tr><td>1 </td><td>2 </td><td>-2</td></tr>\n", |
316 | | - "</tbody>\n", |
317 | | - "</table>\n" |
318 | | - ], |
319 | | - "text/latex": [ |
320 | | - "\\begin{tabular}{lll}\n", |
321 | | - "\t 2 & 4 & -4\\\\\n", |
322 | | - "\t 3 & 6 & -6\\\\\n", |
323 | | - "\t 1 & 2 & -2\\\\\n", |
324 | | - "\\end{tabular}\n" |
325 | | - ], |
326 | | - "text/markdown": [ |
327 | | - "\n", |
328 | | - "| 2 | 4 | -4 | \n", |
329 | | - "| 3 | 6 | -6 | \n", |
330 | | - "| 1 | 2 | -2 | \n", |
331 | | - "\n", |
332 | | - "\n" |
333 | | - ], |
334 | | - "text/plain": [ |
335 | | - " [,1] [,2] [,3]\n", |
336 | | - "[1,] 2 4 -4 \n", |
337 | | - "[2,] 3 6 -6 \n", |
338 | | - "[3,] 1 2 -2 " |
339 | | - ] |
340 | | - }, |
341 | | - "metadata": {}, |
342 | | - "output_type": "display_data" |
343 | | - } |
344 | | - ], |
| 201 | + "outputs": [], |
345 | 202 | "source": [ |
| 203 | + "## Need the cross function from the pracma package\n", |
| 204 | + "install.packages('pracma')\n", |
| 205 | + "library(pracma)\n", |
| 206 | + "\n", |
346 | 207 | "## Define the two vectors\n", |
347 | 208 | "p = c(2,3,1)\n", |
348 | 209 | "q = c(1,2,-2)\n", |
349 | 210 | "\n", |
350 | 211 | "## Outer cross product of two vectors\n", |
351 | | - "tcrossprod(p,q)" |
| 212 | + "cat('\\nCross product of vectors')\n", |
| 213 | + "cross(p,q)" |
352 | 214 | ] |
353 | 215 | } |
354 | 216 | ], |
|
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