ответвлено от main/it-labs
823 строки
17 KiB
Markdown
823 строки
17 KiB
Markdown
# Отчет по теме 2
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Пахомов Илья, А-03-24
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## 1 Установил в качестве текущей папки "ТЕМА2"
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## 2 Работа с данными из файла "dan_vuz.txt"
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Прочитал данные из файла командой
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```matlab
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>> XX=load('dan_vuz.txt')
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```
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На выходе получил матрицу из файла "dan_vuz.txt"
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Проверил размерность матрицы ХХ:
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```matlab
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>> size(XX)
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ans =
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290 15
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```
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В фале представленны данные о 290 вузвх
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Выделил в отдельную матрицу данные о показателях результативности:
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```matlab
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>> X=XX(:,3:13);
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```
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Рассчитал матрицу корреляций между показателями результативности:
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```matlab
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>> R=corr(X)
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R =
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1.0000e+00 4.4320e-01 4.5229e-01 4.4779e-01 3.8123e-01 4.6516e-01 3.1487e-01 6.5579e-02 2.9153e-01 4.8811e-01 3.9815e-01
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4.4320e-01 1.0000e+00 8.5319e-01 8.5331e-01 8.6240e-01 8.5436e-01 5.5145e-01 2.5082e-02 4.2348e-01 8.2170e-01 2.6183e-01
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4.5229e-01 8.5319e-01 1.0000e+00 8.4660e-01 8.8651e-01 9.0335e-01 5.5091e-01 3.8840e-03 4.4396e-01 7.8358e-01 2.6408e-01
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4.4779e-01 8.5331e-01 8.4660e-01 1.0000e+00 8.7038e-01 9.3849e-01 7.0924e-01 4.9500e-02 4.5873e-01 8.5183e-01 3.4420e-01
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3.8123e-01 8.6240e-01 8.8651e-01 8.7038e-01 1.0000e+00 9.3605e-01 5.7668e-01 3.7562e-02 3.8322e-01 7.7266e-01 1.8751e-01
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4.6516e-01 8.5436e-01 9.0335e-01 9.3849e-01 9.3605e-01 1.0000e+00 6.3033e-01 4.7121e-02 4.7592e-01 8.3810e-01 3.3118e-01
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3.1487e-01 5.5145e-01 5.5091e-01 7.0924e-01 5.7668e-01 6.3033e-01 1.0000e+00 7.9448e-02 4.1878e-01 6.2936e-01 2.8287e-01
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6.5579e-02 2.5082e-02 3.8840e-03 4.9500e-02 3.7562e-02 4.7121e-02 7.9448e-02 1.0000e+00 4.7985e-02 5.6462e-02 1.3662e-01
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2.9153e-01 4.2348e-01 4.4396e-01 4.5873e-01 3.8322e-01 4.7592e-01 4.1878e-01 4.7985e-02 1.0000e+00 6.2616e-01 4.5537e-01
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4.8811e-01 8.2170e-01 7.8358e-01 8.5183e-01 7.7266e-01 8.3810e-01 6.2936e-01 5.6462e-02 6.2616e-01 1.0000e+00 3.8799e-01
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3.9815e-01 2.6183e-01 2.6408e-01 3.4420e-01 1.8751e-01 3.3118e-01 2.8287e-01 1.3662e-01 4.5537e-01 3.8799e-01 1.0000e+00
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```
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Получение собственных значений и собственных векторов от квадратичной формы:
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```matlab
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>> [vect,lambda]=eig(X'*X)
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vect =
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1.3928e-03 3.7187e-02 -6.5276e-02 1.1402e-01 -5.7482e-02 -4.3369e-01 -8.6174e-01 1.8078e-02 -2.0942e-01 4.4068e-02 3.5306e-02
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-8.0998e-04 6.0909e-01 3.8181e-01 -5.6588e-01 -2.6231e-01 2.2396e-01 -1.8894e-01 -2.6535e-02 7.3599e-02 6.2111e-03 4.6772e-02
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-7.5396e-03 -4.5900e-01 -5.2153e-01 -6.7233e-01 -1.9752e-01 9.4377e-02 -1.1098e-01 -3.7697e-03 2.9602e-02 -4.1502e-02 4.8953e-02
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-1.5197e-04 -2.3868e-03 -3.9384e-02 2.0471e-02 2.9085e-02 -4.2879e-02 3.9810e-02 -2.5705e-01 1.7315e-01 7.2027e-01 6.1556e-01
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1.0985e-03 -2.1296e-02 -1.7772e-02 1.0189e-01 1.5147e-01 2.9246e-02 -2.2268e-01 9.3732e-02 8.4203e-01 -3.7246e-01 2.4277e-01
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4.6341e-05 2.4446e-02 3.4514e-02 6.8266e-03 -2.8773e-02 -3.6347e-02 1.2360e-01 5.5571e-02 -4.0806e-01 -5.1787e-01 7.3685e-01
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1.1860e-03 4.2558e-03 2.3496e-02 -4.8185e-02 -1.5673e-02 -5.8142e-02 5.8108e-02 9.5701e-01 5.2365e-03 2.5496e-01 9.5893e-02
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-9.9994e-01 5.6340e-04 6.5198e-03 4.0470e-03 7.5475e-03 1.2608e-03 -2.3724e-03 1.4645e-03 -1.0271e-03 5.5851e-04 1.6945e-04
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-1.6282e-03 4.6826e-01 -6.5978e-01 2.6872e-01 2.8869e-02 4.9535e-01 -1.2025e-01 5.8771e-02 -9.1452e-02 2.0459e-02 1.7911e-02
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1.7002e-03 -4.2581e-01 3.3001e-01 2.8074e-01 -3.9004e-01 6.2610e-01 -2.7487e-01 3.6416e-02 -5.9676e-02 5.3342e-02 5.9523e-02
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7.7010e-03 -1.2368e-01 1.7350e-01 -2.2481e-01 8.4320e-01 3.2876e-01 -2.2260e-01 1.8627e-02 -1.7997e-01 4.8313e-02 1.7425e-02
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lambda =
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Diagonal Matrix
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2.2947e+01 0 0 0 0 0 0 0 0 0 0
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0 1.9317e+03 0 0 0 0 0 0 0 0 0
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0 0 2.5940e+03 0 0 0 0 0 0 0 0
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0 0 0 3.4573e+03 0 0 0 0 0 0 0
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0 0 0 0 5.6252e+03 0 0 0 0 0 0
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0 0 0 0 0 8.6721e+03 0 0 0 0 0
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0 0 0 0 0 0 1.8915e+04 0 0 0 0
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0 0 0 0 0 0 0 4.7523e+04 0 0 0
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0 0 0 0 0 0 0 0 5.7484e+04 0 0
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0 0 0 0 0 0 0 0 0 2.2565e+05 0
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0 0 0 0 0 0 0 0 0 0 7.4946e+06
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```
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В матрице lambda собственные значения расположены в возрастающем порядке на диагонали. Выделим их в отдельный вектор:
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```matlab
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>> Sobst=diag(lambda);
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```
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Представим их на экране с заголовком:
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```matlab
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>> fprintf('Eigenvalues:\n %f \n',Sobst)
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Eigenvalues:
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22.946585
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Eigenvalues:
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1931.665464
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Eigenvalues:
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2593.979592
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Eigenvalues:
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3457.339562
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Eigenvalues:
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5625.151474
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Eigenvalues:
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8672.065947
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Eigenvalues:
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18914.627989
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Eigenvalues:
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47522.678185
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Eigenvalues:
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57483.681267
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Eigenvalues:
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225653.068540
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Eigenvalues:
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7494628.795394
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>> fprintf('\n')
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```
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Выделим наибольшее собственное значение и соответствующий ему собственный вектор:
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```matlab
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>> SobMax=Sobst(end)
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SobMax = 7.4946e+06
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```
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```matlab
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>> GlComp=vect(:,end)
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GlComp =
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3.5306e-02
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4.6772e-02
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4.8953e-02
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6.1556e-01
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2.4277e-01
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7.3685e-01
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9.5893e-02
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1.6945e-04
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1.7911e-02
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5.9523e-02
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1.7425e-02
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```
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Рассчитал долю информации о результативности НИР, содержащуюся в главной компоненте и отобразил ее на экране:
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```matlab
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>> Delt=100*SobMax/sum(Sobst)
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Delt = 95.273
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```
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```matlab
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>> fprintf('Delta= %d \n ',round(Delt))
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Delta= 95
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```
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С использованием главной компоненты рассчитал оценки обобщенной результативности в каждом из представленных в матрице вузов и отобразил ее с указанием кода вуза:
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```matlab
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>> Res=X*GlComp
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Res =
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9.2542e+01
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7.3433e+01
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5.8855e+00
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3.5300e+01
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7.0208e+01
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2.8096e+01
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8.7136e+01
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7.9776e+01
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3.6243e+01
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1.8250e+01
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4.9667e+01
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4.5067e+01
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8.1785e+01
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5.5559e+00
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1.0536e+02
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4.5755e+00
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3.8120e+02
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2.6713e+01
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8.0376e+00
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1.1963e+02
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1.0061e+01
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6.3763e+01
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9.0877e+00
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4.1684e+01
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3.5907e+01
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7.6140e+01
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2.3753e+01
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1.4222e+02
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6.7756e+01
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2.0598e+01
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7.6819e+01
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1.0428e+02
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1.8542e+01
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4.4740e+00
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3.5809e+00
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2.2476e+02
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2.6864e+01
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2.1291e+02
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5.0922e+01
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3.3628e+01
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4.2168e+01
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1.0370e+02
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1.3606e+02
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7.1371e+02
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3.4027e+01
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4.1023e+00
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2.7087e+01
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2.6675e+00
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2.4976e+00
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1.0383e+02
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7.4607e+00
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3.4755e+01
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4.3597e+00
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5.7412e+00
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1.5989e+01
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4.5400e+01
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2.4622e+00
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6.4244e+00
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6.6503e+01
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7.3936e+01
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1.1131e+01
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3.6843e+00
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9.9705e+00
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2.8031e+01
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1.3524e+00
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4.0905e+01
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1.1723e+01
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3.0793e+01
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4.2716e+01
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1.0023e+01
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3.2260e+01
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2.5495e+01
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3.6870e+01
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4.2948e+01
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8.7963e+01
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2.2867e+02
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9.9146e+01
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2.8750e+01
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9.6222e+00
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1.3600e+00
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5.4214e+01
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1.0755e+02
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1.1611e+02
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2.9910e+02
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1.4333e+01
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2.0479e+01
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1.4491e+02
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1.4953e+01
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2.5976e+01
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2.6815e+02
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1.2354e+01
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4.5261e+00
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1.0466e+02
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9.1265e+01
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2.0933e+02
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1.9645e+02
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4.8121e+00
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1.3877e+00
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5.0733e+01
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1.1863e+02
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2.1253e+02
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3.7745e+01
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3.0102e+01
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3.2067e+02
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0
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4.1450e+01
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1.4112e+02
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4.0535e+02
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1.2875e+01
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1.1761e+02
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8.9899e+00
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7.4655e+01
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8.9566e+01
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3.7993e+01
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4.0600e+01
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3.7339e+01
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1.4293e+02
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9.1226e+00
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5.3464e+01
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9.3290e+01
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5.7155e+01
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1.9139e+01
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5.4915e+00
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8.5213e+01
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1.7064e+02
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9.0454e+01
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5.7811e+01
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7.3730e+00
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9.6149e+00
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1.8467e+00
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1.7647e+01
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1.5391e+02
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1.1984e+02
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5.0102e+00
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2.6920e+00
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3.7930e+02
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1.3497e+01
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2.4622e+00
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1.9718e+01
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2.0067e+02
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9.3618e+01
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2.5651e+01
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2.6345e+01
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6.5286e+01
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2.1515e+01
|
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1.7651e+02
|
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1.8989e+03
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9.1241e+01
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3.0455e+02
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6.3560e+00
|
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3.4394e+00
|
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1.5886e+02
|
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1.8780e+02
|
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2.6561e+01
|
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8.6579e+00
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1.1032e+02
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2.1287e+01
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8.0285e+00
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7.6977e+01
|
|
1.4832e+02
|
|
9.7178e+01
|
|
6.7131e+00
|
|
8.8631e+01
|
|
3.3340e+02
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|
2.7838e+01
|
|
1.1663e+01
|
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0
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7.1250e+01
|
|
3.6976e-01
|
|
1.0361e+01
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|
3.8551e+00
|
|
8.1569e+01
|
|
5.4637e+01
|
|
2.3502e+01
|
|
9.0447e+01
|
|
5.7162e+01
|
|
1.6285e+02
|
|
3.0587e+02
|
|
6.3233e+00
|
|
5.9416e+01
|
|
4.6966e+01
|
|
5.6661e+01
|
|
8.1568e+02
|
|
4.7723e+01
|
|
2.7702e+02
|
|
3.2809e+02
|
|
1.1359e+02
|
|
1.1709e+01
|
|
3.3970e+01
|
|
9.1338e-01
|
|
1.2267e+02
|
|
5.9979e+01
|
|
7.4911e+00
|
|
1.2504e+01
|
|
2.4209e+01
|
|
4.0011e+02
|
|
2.6358e+02
|
|
2.5931e+01
|
|
3.6895e+01
|
|
2.5478e+02
|
|
6.8701e+00
|
|
1.2626e+01
|
|
2.3784e+01
|
|
3.1599e+00
|
|
5.1518e+00
|
|
0
|
|
1.0677e+02
|
|
1.5783e+01
|
|
3.0701e+01
|
|
6.4990e+01
|
|
4.3088e+01
|
|
3.1124e+01
|
|
5.1718e+00
|
|
4.8085e+01
|
|
5.3479e+00
|
|
2.1246e+00
|
|
8.2078e-02
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|
2.1636e+01
|
|
5.2057e+01
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|
2.5625e+01
|
|
9.7502e+00
|
|
3.6203e+01
|
|
4.6267e+00
|
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3.1906e+00
|
|
9.5783e+00
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6.3749e+00
|
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3.6845e+00
|
|
5.7848e+00
|
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8.2368e+00
|
|
6.8726e+00
|
|
4.1305e+01
|
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1.9885e+00
|
|
7.5713e+00
|
|
1.2311e+00
|
|
5.0811e+00
|
|
2.1547e+01
|
|
3.0300e+01
|
|
4.5504e+01
|
|
9.0939e+00
|
|
1.0370e+01
|
|
7.1259e+00
|
|
1.4133e+01
|
|
2.6102e+01
|
|
5.0720e+00
|
|
1.2085e+01
|
|
7.1347e-01
|
|
6.7509e-01
|
|
4.0925e+00
|
|
7.4541e+00
|
|
1.8466e+02
|
|
1.0455e+01
|
|
7.4481e+00
|
|
6.2425e+00
|
|
8.8602e+00
|
|
3.9992e+01
|
|
6.8910e+00
|
|
5.1607e+00
|
|
1.5490e+01
|
|
5.5905e+00
|
|
2.7378e+01
|
|
1.0801e+01
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|
2.3751e+01
|
|
1.1426e+01
|
|
8.4732e+00
|
|
6.8984e+00
|
|
3.4163e+00
|
|
2.0875e+02
|
|
1.2158e+01
|
|
3.5632e+00
|
|
4.1589e+00
|
|
0
|
|
1.8479e+00
|
|
8.4788e+00
|
|
1.2779e+00
|
|
3.5306e-02
|
|
7.0611e-02
|
|
3.5306e-02
|
|
3.0393e+00
|
|
0
|
|
4.2057e+00
|
|
3.0095e+01
|
|
2.0128e+01
|
|
5.7737e+00
|
|
3.1540e+01
|
|
1.4739e+02
|
|
1.8314e+01
|
|
3.2846e+01
|
|
1.4511e+01
|
|
1.9235e+01
|
|
0
|
|
|
|
```
|
|
|
|
```matlab
|
|
|
|
>> fprintf(' Results \n ')
|
|
Results
|
|
>> fprintf('%d %f \n ',[XX(:,1),Res] ')
|
|
197 92.541636
|
|
198 73.432513
|
|
199 5.885468
|
|
200 35.300393
|
|
201 70.208100
|
|
202 28.096191
|
|
203 87.136298
|
|
204 79.776499
|
|
205 36.243011
|
|
206 18.249808
|
|
207 49.666520
|
|
208 45.067095
|
|
209 81.785392
|
|
210 5.555862
|
|
211 105.361366
|
|
212 4.575460
|
|
213 381.204021
|
|
214 26.712747
|
|
216 8.037618
|
|
217 119.627795
|
|
218 10.061485
|
|
219 63.762947
|
|
220 9.087658
|
|
221 41.684105
|
|
222 35.907417
|
|
223 76.139589
|
|
224 23.752550
|
|
225 142.216169
|
|
226 67.755801
|
|
227 20.597788
|
|
228 76.818771
|
|
229 104.284923
|
|
230 18.541601
|
|
231 4.473983
|
|
232 3.580878
|
|
233 224.758597
|
|
234 26.863645
|
|
235 212.911324
|
|
236 50.921549
|
|
237 33.628254
|
|
238 42.168327
|
|
239 103.701129
|
|
240 136.060809
|
|
241 713.711764
|
|
242 34.027235
|
|
245 4.102289
|
|
246 27.086730
|
|
247 2.667541
|
|
248 2.497556
|
|
252 103.829221
|
|
253 7.460715
|
|
256 34.755449
|
|
257 4.359736
|
|
258 5.741187
|
|
259 15.989432
|
|
261 45.399798
|
|
264 2.462250
|
|
267 6.424390
|
|
268 66.503024
|
|
273 73.935542
|
|
275 11.130530
|
|
296 3.684256
|
|
304 9.970486
|
|
305 28.031419
|
|
311 1.352414
|
|
318 40.905330
|
|
322 11.722703
|
|
325 30.793455
|
|
326 42.716264
|
|
329 10.023429
|
|
330 32.260491
|
|
334 25.495269
|
|
335 36.870098
|
|
336 42.948416
|
|
339 87.963238
|
|
340 228.668981
|
|
341 99.146097
|
|
342 28.749899
|
|
343 9.622160
|
|
346 1.359974
|
|
347 54.213640
|
|
348 107.547742
|
|
349 116.106427
|
|
352 299.102890
|
|
356 14.333164
|
|
357 20.479493
|
|
362 144.908794
|
|
365 14.952535
|
|
366 25.976099
|
|
371 268.149429
|
|
372 12.353605
|
|
373 4.526119
|
|
376 104.664655
|
|
377 91.264814
|
|
379 209.329940
|
|
381 196.452926
|
|
383 4.812125
|
|
387 1.387719
|
|
388 50.732954
|
|
389 118.633179
|
|
391 212.528679
|
|
392 37.744725
|
|
393 30.102473
|
|
394 320.669960
|
|
395 0.000000
|
|
399 41.450044
|
|
410 141.123026
|
|
412 405.347359
|
|
413 12.875247
|
|
414 117.612150
|
|
441 8.989886
|
|
446 74.655250
|
|
448 89.566395
|
|
451 37.992598
|
|
456 40.599701
|
|
465 37.339465
|
|
466 142.928780
|
|
467 9.122607
|
|
472 53.463843
|
|
476 93.289532
|
|
477 57.155319
|
|
484 19.139209
|
|
1001 5.491474
|
|
1002 85.213352
|
|
1004 170.642969
|
|
1017 90.453986
|
|
1030 57.810669
|
|
1034 7.372961
|
|
1035 9.614944
|
|
1037 1.846687
|
|
1038 17.646937
|
|
1039 153.910670
|
|
1041 119.835954
|
|
1044 5.010210
|
|
1 2.691959
|
|
2 379.300890
|
|
3 13.497203
|
|
4 2.462250
|
|
6 19.718182
|
|
7 200.667783
|
|
8 93.618235
|
|
9 25.650544
|
|
10 26.344823
|
|
11 65.285854
|
|
12 21.514761
|
|
13 176.510003
|
|
14 1898.884523
|
|
15 91.241365
|
|
16 304.552394
|
|
17 6.355976
|
|
18 3.439437
|
|
19 158.859588
|
|
20 187.802059
|
|
21 26.561371
|
|
22 8.657907
|
|
23 110.316703
|
|
26 21.286647
|
|
28 8.028500
|
|
29 76.976887
|
|
33 148.320170
|
|
34 97.178361
|
|
35 6.713123
|
|
36 88.631285
|
|
37 333.404629
|
|
38 27.838269
|
|
40 11.662869
|
|
41 0.000000
|
|
42 71.250154
|
|
43 0.369757
|
|
44 10.360736
|
|
45 3.855089
|
|
51 81.568715
|
|
52 54.636552
|
|
53 23.501931
|
|
54 90.446620
|
|
55 57.162095
|
|
56 162.850196
|
|
57 305.874565
|
|
58 6.323299
|
|
59 59.415851
|
|
60 46.966205
|
|
62 56.660855
|
|
63 815.675312
|
|
64 47.723188
|
|
65 277.021471
|
|
66 328.086215
|
|
67 113.590454
|
|
68 11.709047
|
|
69 33.969900
|
|
71 0.913379
|
|
72 122.671912
|
|
73 59.978744
|
|
74 7.491057
|
|
75 12.504248
|
|
76 24.208529
|
|
77 400.110964
|
|
78 263.576362
|
|
79 25.930889
|
|
80 36.895259
|
|
81 254.783774
|
|
82 6.870138
|
|
84 12.625935
|
|
85 23.783568
|
|
86 3.159890
|
|
87 5.151827
|
|
88 0.000000
|
|
89 106.765711
|
|
90 15.783445
|
|
91 30.701284
|
|
92 64.989933
|
|
93 43.087958
|
|
94 31.124285
|
|
95 5.171761
|
|
96 48.085148
|
|
97 5.347890
|
|
99 2.124571
|
|
100 0.082078
|
|
101 21.635603
|
|
102 52.057076
|
|
103 25.625192
|
|
104 9.750228
|
|
105 36.202865
|
|
107 4.626653
|
|
108 3.190574
|
|
109 9.578291
|
|
110 6.374896
|
|
111 3.684453
|
|
112 5.784829
|
|
113 8.236760
|
|
114 6.872598
|
|
115 41.304826
|
|
116 1.988474
|
|
118 7.571316
|
|
119 1.231125
|
|
120 5.081094
|
|
121 21.547440
|
|
122 30.299927
|
|
123 45.503740
|
|
124 9.093912
|
|
132 10.369658
|
|
133 7.125935
|
|
134 14.133228
|
|
135 26.102416
|
|
136 5.071976
|
|
137 12.085286
|
|
138 0.713469
|
|
139 0.675086
|
|
140 4.092547
|
|
141 7.454102
|
|
142 184.663991
|
|
143 10.455368
|
|
144 7.448129
|
|
146 6.242521
|
|
147 8.860180
|
|
148 39.991951
|
|
149 6.891026
|
|
150 5.160709
|
|
151 15.489599
|
|
152 5.590467
|
|
153 27.378151
|
|
154 10.801195
|
|
162 23.750968
|
|
166 11.426264
|
|
167 8.473236
|
|
168 6.898371
|
|
170 3.416283
|
|
171 208.746883
|
|
172 12.158394
|
|
173 3.563165
|
|
174 4.158866
|
|
175 0.000000
|
|
176 1.847873
|
|
177 8.478820
|
|
178 1.277897
|
|
179 0.035306
|
|
180 0.070611
|
|
181 0.035306
|
|
182 3.039279
|
|
183 0.000000
|
|
184 4.205715
|
|
185 30.094936
|
|
186 20.128055
|
|
187 5.773718
|
|
188 31.539990
|
|
189 147.387148
|
|
190 18.314164
|
|
191 32.846011
|
|
192 14.511067
|
|
193 19.235467
|
|
194 0.000000
|
|
|
|
```
|
|
|
|
Сохранил вектор оценок результативности в отдельном бинарном (mat) файле:
|
|
|
|
```matlab
|
|
|
|
>> save res.mat Res -mat
|
|
|
|
```
|
|
|
|
Представил распределение оценок результативности в виде гистограммы с 20 интервалами и с обозначением осей:
|
|
|
|
```matlab
|
|
|
|
>> hist(Res,20)
|
|
>> xlabel('Results ')
|
|
>> ylabel('Number of Unis ')
|
|
|
|
```
|
|
|
|
|
|
|
|
Сохранил изображение гистограммы в файле формата jpg
|
|
|
|
```matlab
|
|
|
|
>> saveas(gcf, 'Hist.jpg ', 'jpg ')
|
|
DEBUG: FC_WEIGHT didn't match
|
|
|
|
```
|
|
|
|
|
|
Рассчитал и отобразил оценку корреляции обобщенной результативности с финансированием, выделенным на проведение НИР:
|
|
|
|
```matlab
|
|
|
|
>> CorFin=corr(Res,XX(:,2))
|
|
CorFin = 0.8437
|
|
>> fprintf('Correlation of Results and Money = %f \n',CorFin)
|
|
Correlation of Results and Money = 0.843710
|
|
|
|
```
|
|
|
|
## 3 |