134 |
134 |
135 \subsection{Initializing} |
135 \subsection{Initializing} |
136 \begin{frame}[fragile] |
136 \begin{frame}[fragile] |
137 \frametitle{Matrices: Initializing} |
137 \frametitle{Matrices: Initializing} |
138 \begin{lstlisting} |
138 \begin{lstlisting} |
139 In []: A = ([[5, 2, 4], |
139 In []: A = matrix([[ 1, 1, 2, -1], |
140 [-3, 6, 2], |
140 [ 2, 5, -1, -9], |
141 [3, -3, 1]]) |
141 [ 2, 1, -1, 3], |
142 |
142 [ 1, -3, 2, 7]]) |
143 In []: A |
143 In []: A |
144 Out[]: [[5, 2, 4], |
144 Out[]: |
145 [-3, 6, 2], |
145 matrix([[ 1, 1, 2, -1], |
146 [3, -3, 1]] |
146 [ 2, 5, -1, -9], |
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147 [ 2, 1, -1, 3], |
|
148 [ 1, -3, 2, 7]]) |
147 \end{lstlisting} |
149 \end{lstlisting} |
148 \end{frame} |
150 \end{frame} |
149 |
151 |
150 \subsection{Basic Operations} |
152 \subsection{Basic Operations} |
151 |
153 |
152 \begin{frame}[fragile] |
154 \begin{frame}[fragile] |
153 \frametitle{Transpose of a Matrix} |
155 \frametitle{Transpose of a Matrix} |
154 \begin{lstlisting} |
156 \begin{lstlisting} |
155 In []: linalg.transpose(A) |
157 In []: linalg.transpose(A) |
156 Out[]: |
158 Out[]: |
157 matrix([[ 5, -3, 3], |
159 matrix([[ 1, 2, 2, 1], |
158 [ 2, 6, -3], |
160 [ 1, 5, 1, -3], |
159 [ 4, 2, 1]]) |
161 [ 2, -1, -1, 2], |
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162 [-1, -9, 3, 7]]) |
160 \end{lstlisting} |
163 \end{lstlisting} |
161 \end{frame} |
164 \end{frame} |
162 |
165 |
163 \begin{frame}[fragile] |
166 \begin{frame}[fragile] |
164 \frametitle{Sum of all elements} |
167 \frametitle{Sum of all elements} |
165 \begin{lstlisting} |
168 \begin{lstlisting} |
166 In []: linalg.sum(A) |
169 In []: linalg.sum(A) |
167 Out[]: 17 |
170 Out[]: 12 |
168 \end{lstlisting} |
171 \end{lstlisting} |
169 \end{frame} |
172 \end{frame} |
170 |
173 |
171 \begin{frame}[fragile] |
174 \begin{frame}[fragile] |
172 \frametitle{Matrix Addition} |
175 \frametitle{Matrix Addition} |
173 \begin{lstlisting} |
176 \begin{lstlisting} |
174 In []: B = matrix([[3,2,-1], |
177 In []: B = matrix([[3,2,-1,5], |
175 [2,-2,4], |
178 [2,-2,4,9], |
176 [-1, 0.5, -1]]) |
179 [-1,0.5,-1,-7], |
177 |
180 [9,-5,7,3]]) |
178 In []: linalg.add(A, B) |
181 In []: linalg.add(A,B) |
179 Out[]: |
182 Out[]: |
180 matrix([[ 8. , 4. , 3. ], |
183 matrix([[ 4. , 3. , 1. , 4. ], |
181 [-1. , 4. , 6. ], |
184 [ 4. , 3. , 3. , 0. ], |
182 [ 2. , -2.5, 0. ]]) |
185 [ 1. , 1.5, -2. , -4. ], |
|
186 [ 10. , -8. , 9. , 10. ]]) |
183 \end{lstlisting} |
187 \end{lstlisting} |
184 \end{frame} |
188 \end{frame} |
185 |
189 |
186 \begin{frame}[fragile] |
190 \begin{frame}[fragile] |
187 \frametitle{Matrix Multiplication} |
191 \frametitle{Matrix Multiplication} |
188 \begin{lstlisting} |
192 \begin{lstlisting} |
189 In []: linalg.multiply(A, B) |
193 In []: linalg.multiply(A, B) |
190 Out[]: |
194 Out[]: |
191 matrix([[ 15. , 4. , -4. ], |
195 matrix([[ 3. , 2. , -2. , -5. ], |
192 [ -6. , -12. , 8. ], |
196 [ 4. , -10. , -4. , -81. ], |
193 [ -3. , -1.5, -1. ]]) |
197 [ -2. , 0.5, 1. , -21. ], |
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198 [ 9. , 15. , 14. , 21. ]]) |
194 \end{lstlisting} |
199 \end{lstlisting} |
195 \end{frame} |
200 \end{frame} |
196 |
201 |
197 \begin{frame}[fragile] |
202 \begin{frame}[fragile] |
198 \frametitle{Inverse of a Matrix} |
203 \frametitle{Inverse of a Matrix} |
199 \begin{small} |
204 \begin{small} |
200 \begin{lstlisting} |
205 \begin{lstlisting} |
201 In []: linalg.inv(A) |
206 In []: linalg.inv(A) |
202 Out[]: |
207 Out[]: |
203 array([[ 0.28571429, -0.33333333, -0.47619048], |
208 matrix([[-0.5 , 0.55, -0.15, 0.7 ], |
204 [ 0.21428571, -0.16666667, -0.52380952], |
209 [ 0.75, -0.5 , 0.5 , -0.75], |
205 [-0.21428571, 0.5 , 0.85714286]]) |
210 [ 0.5 , -0.15, -0.05, -0.1 ], |
|
211 [ 0.25, -0.25, 0.25, -0.25]]) |
206 \end{lstlisting} |
212 \end{lstlisting} |
207 \end{small} |
213 \end{small} |
208 \end{frame} |
214 \end{frame} |
209 |
215 |
210 \begin{frame}[fragile] |
216 \begin{frame}[fragile] |
211 \frametitle{Determinant} |
217 \frametitle{Determinant} |
212 \begin{lstlisting} |
218 \begin{lstlisting} |
213 In []: det(A) |
219 In []: det(A) |
214 Out[]: 42.0 |
220 Out[66]: 80.0 |
215 \end{lstlisting} |
221 \end{lstlisting} |
216 \end{frame} |
222 \end{frame} |
217 |
223 |
218 \begin{frame}[fragile] |
224 \begin{frame}[fragile] |
219 \frametitle{Eigen Values and Eigen Matrix} |
225 \frametitle{Eigen Values and Eigen Matrix} |
220 \begin{small} |
226 \begin{small} |
221 \begin{lstlisting} |
227 \begin{lstlisting} |
222 In []: linalg.eig(A) |
228 In []: linalg.eig(A) |
223 Out[]: |
229 Out[]: |
224 (array([ 7., 2., 3.]), |
230 (array([ 11.41026155, 3.71581643, -0.81723144, -2.30884654]), |
225 matrix([[-0.57735027, 0.42640143, 0.37139068], |
231 matrix([[ 0.12300187, -0.53899627, 0.63269982, 0.56024583], |
226 [ 0.57735027, 0.63960215, 0.74278135], |
232 [ 0.8225266 , -0.67562403, -0.63919634, -0.20747251], |
227 [-0.57735027, -0.63960215, -0.55708601]])) |
233 [-0.04763219, -0.47575453, -0.3709497 , -0.80066041], |
|
234 [-0.55321941, -0.16331814, -0.23133374, 0.04497415]])) |
228 \end{lstlisting} |
235 \end{lstlisting} |
229 \end{small} |
236 \end{small} |
230 \end{frame} |
237 \end{frame} |
231 |
238 |
232 \begin{frame}[fragile] |
239 \begin{frame}[fragile] |
233 \frametitle{Computing Norms} |
240 \frametitle{Computing Norms} |
234 \begin{lstlisting} |
241 \begin{lstlisting} |
235 In []: linalg.norm(A) |
242 In []: linalg.norm(A) |
236 Out[]: 10.63014581273465 |
243 Out[]: 14.0 |
237 \end{lstlisting} |
244 \end{lstlisting} |
238 \end{frame} |
245 \end{frame} |
239 |
246 |
240 \begin{frame}[fragile] |
247 \begin{frame}[fragile] |
241 \frametitle{Single Value Decomposition} |
248 \frametitle{Single Value Decomposition} |
242 \begin{small} |
249 \begin{small} |
243 \begin{lstlisting} |
250 \begin{lstlisting} |
244 In []: linalg.svd(A) |
251 In []: linalg.svd(A) |
245 Out[]: |
252 Out[]: |
246 (matrix([[-0.13391246, -0.94558684, -0.29653495], |
253 (matrix([[-0.08588113, 0.29164297, -0.74892678, 0.58879325], |
247 [ 0.84641267, -0.26476432, 0.46204486], |
254 [-0.79093255, 0.39530483, -0.11188116, -0.45347812], |
248 [-0.51541542, -0.18911737, 0.83581192]]), |
255 [ 0.1523891 , 0.78799358, 0.51966138, 0.29290907], |
249 array([ 7.96445022, 7. , 0.75334767]), |
256 [ 0.58636823, 0.37113957, -0.39565558, -0.60156827]]), |
250 matrix([[-0.59703387, 0.79815896, 0.08057807], |
257 array([ 13.17656506, 3.76954116, 2.79959047, 0.57531379]), |
251 [-0.64299905, -0.41605821, -0.64299905], |
258 matrix([[-0.05893795, -0.42858358, 0.12442679, 0.89295039], |
252 [-0.47969029, -0.43570384, 0.7616163 ]])) |
259 [ 0.80364672, 0.51537891, 0.03774111, 0.29514767], |
253 \end{lstlisting} |
260 [-0.11752501, 0.14226922, -0.96333552, 0.19476145], |
|
261 [-0.58040171, 0.72832696, 0.23468759, 0.27855956]])) |
|
262 \end{lstlisting} |
254 \end{small} |
263 \end{small} |
255 \end{frame} |
264 \end{frame} |
256 |
265 |
257 \section{Solving linear equations} |
266 \section{Solving linear equations} |
258 |
267 |