範例：函數的線性組合

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範例：函數的線性組合

使用 linfit 函數以項數的線性總和，設定數據集模型。每個項數都是由要擬合之函數與 linfit 計算所得的係數所構成。

1. 定義以下矩陣。

按一下以複製此運算式

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        <real xml:lang="zh_TW">5</real>
        <real xml:lang="zh_TW">6</real>
        <real xml:lang="zh_TW">7</real>
        <real xml:lang="zh_TW">8</real>
        <real xml:lang="zh_TW">9</real>
        <real xml:lang="zh_TW">10</real>
        <real xml:lang="zh_TW">11</real>
        <real xml:lang="zh_TW">12</real>
        <real xml:lang="zh_TW">13</real>
        <real xml:lang="zh_TW">14</real>
        <real xml:lang="zh_TW">15</real>
        <real xml:lang="zh_TW">16</real>
        <real xml:lang="zh_TW">17</real>
        <real xml:lang="zh_TW">18</real>
        <real xml:lang="zh_TW">19</real>
        <real xml:lang="zh_TW">20</real>
        <real xml:lang="zh_TW">21</real>
        <real xml:lang="zh_TW">22</real>
        <real xml:lang="zh_TW">23</real>
        <real xml:lang="zh_TW">24</real>
        <real xml:lang="zh_TW">25</real>
        <real xml:lang="zh_TW">26</real>
        <real xml:lang="zh_TW">27</real>
        <real xml:lang="zh_TW">28</real>
        <real xml:lang="zh_TW">29</real>
        <real xml:lang="zh_TW">30</real>
        <real xml:lang="zh_TW">31</real>
        <real xml:lang="zh_TW">4.181</real>
        <real xml:lang="zh_TW">4.665</real>
        <real xml:lang="zh_TW">5.296</real>
        <real xml:lang="zh_TW">5.365</real>
        <real xml:lang="zh_TW">5.448</real>
        <real xml:lang="zh_TW">5.744</real>
        <real xml:lang="zh_TW">5.653</real>
        <real xml:lang="zh_TW">5.844</real>
        <real xml:lang="zh_TW">6.362</real>
        <real xml:lang="zh_TW">6.38</real>
        <real xml:lang="zh_TW">6.311</real>
        <real xml:lang="zh_TW">6.457</real>
        <real xml:lang="zh_TW">6.479</real>
        <real xml:lang="zh_TW">6.59</real>
        <real xml:lang="zh_TW">6.74</real>
        <real xml:lang="zh_TW">6.58</real>
        <real xml:lang="zh_TW">6.852</real>
        <real xml:lang="zh_TW">6.531</real>
        <real xml:lang="zh_TW">6.682</real>
        <real xml:lang="zh_TW">7.013</real>
        <real xml:lang="zh_TW">6.82</real>
        <real xml:lang="zh_TW">6.647</real>
        <real xml:lang="zh_TW">6.951</real>
        <real xml:lang="zh_TW">7.121</real>
        <real xml:lang="zh_TW">7.143</real>
        <real xml:lang="zh_TW">6.914</real>
        <real xml:lang="zh_TW">6.941</real>
        <real xml:lang="zh_TW">7.226</real>
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2. 定義要擬合的函數向量。

按一下以複製此運算式

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模型函數是 y(x) = c0 * ln(x) + c1 * sqrt x +c3。

3. 呼叫 linfit 函數計算每個函數的係數。以向量 c 記錄係數。

按一下以複製此運算式

按一下以複製此運算式

按一下以複製此運算式

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4. 定義擬合函數 f 使其成為 vf 中函數線性組合乘以 c 中的係數。

按一下以複製此運算式

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5. 繪製數據點與擬合函數。

按一下以複製此運算式

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函數的線性組合對數據而言是良好的擬合。經由相關係數值近似於 1 即可證實：

按一下以複製此運算式

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