示例：Multidfit 函数

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示例：Multidfit 函数

生成一个矩阵，其中包含从 N 点获取的矢量 X0、X1 和 Y 的样本。

1. 定义点数。

2. 生成矢量 X0 和 X1。

3. 生成信号 f(x) 的扰动。

4. 合并自变量数据。

5. 根据 f(x) 函数值和扰动生成 Y 数据矢量。

<region id="ID0EKF4W" actualWidth="261.26333333333332" actualHeight="129.4" top="940.80000000000018" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="25">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <indexer />
        <id labels="VARIABLE" xml:space="preserve">Y</id>
        <id labels="*" xml:space="preserve">i</id>
      </apply>
      <eval>
        <apply>
          <plus />
          <apply>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">f</id>
            <apply>
              <transpose />
              <parens>
                <apply>
                  <matrow />
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">X</id>
                  <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">i</id>
                </apply>
              </parens>
            </apply>
          </apply>
          <apply>
            <indexer />
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">disturb</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">i</id>
          </apply>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
    <resultFormat>
      <matrix size="5,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

6. 定义矩阵 Data。

7. 定义拟合函数 F(x,u)。

8. 使用常规多变量拟合查找拟合函数的参数。

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  <math resultRef="28">
    <define xmlns="http://schemas.mathsoft.com/math50">
      <id labels="VARIABLE" xml:space="preserve">U</id>
      <eval>
        <apply>
          <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">multidfit</id>
          <sequence>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">X</id>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">Y</id>
            <matrix rows="3" cols="1">
              <real>0</real>
              <real>0</real>
              <real>0</real>
            </matrix>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">F</id>
          </sequence>
        </apply>
        <unitOverride>
          <placeholder />
        </unitOverride>
      </eval>
    </define>
  </math>
</region>

已获得原始函数 f(x) 中使用的系数的近似值。

9. 比较 Data 矩阵和近似曲面。

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  <plot background-type="transparent">
    <plot3D>
      <traces>
        <trace3D num-of-points="41" resultRef="34">
          <traceStyle color="#FFED1D2F" symbol="point" line-style="None" line-weight="6" automaticStyle="true">curve</traceStyle>
        </trace3D>
        <trace3D num-of-points="41" resultRef="35">
          <traceStyle color="#FF2E3192" automaticStyle="true">surface</traceStyle>
        </trace3D>
      </traces>
      <graph-size width="230.39999999999998" height="230.39999999999998" />
      <axes>
        <xAxis start="0" end="1" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue resultRef="29">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue resultRef="30">
              <real xmlns="http://schemas.mathsoft.com/math50">1</real>
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis start="0" end="1" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>5</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <xyDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue resultRef="31">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue resultRef="32">
              <real xmlns="http://schemas.mathsoft.com/math50">1</real>
            </endValue>
          </xyDomain>
        </yAxis>
        <zAxis start="0" end="3.0000000000000004" rank="1">
          <axisLine />
          <axisGrid>
            <gridFrequency>6</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
          </axisGrid>
          <axisLabel />
          <zDomain scale-type="linear" allow-negative-values="true" auto-scale="true">
            <startValue resultRef="33">
              <real xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue />
          </zDomain>
        </zAxis>
      </axes>
      <plotEquations>
        <plotEquation>
          <math>
            <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true" xmlns="http://schemas.mathsoft.com/math50">Data</id>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
        <plotEquation>
          <math>
            <apply xmlns="http://schemas.mathsoft.com/math50">
              <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">F</id>
              <sequence>
                <matrix rows="2" cols="1">
                  <id xml:space="preserve">x</id>
                  <id xml:space="preserve">y</id>
                </matrix>
                <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">U</id>
              </sequence>
            </apply>
          </math>
          <math>
            <placeholder xmlns="http://schemas.mathsoft.com/math50" />
          </math>
        </plotEquation>
      </plotEquations>
      <CameraTransformMatrix Rows="4" Columns="4">
        <Cells>
          <Cell>0.97823637763401561</Cell>
          <Cell>-0.048952317111439492</Cell>
          <Cell>-0.20163645534203492</Cell>
          <Cell>0</Cell>
          <Cell>0.030218490424354278</Cell>
          <Cell>0.995022135742543</Cell>
          <Cell>-0.094962056732260353</Cell>
          <Cell>0</Cell>
          <Cell>0.20528134915269952</Cell>
          <Cell>0.086802189095488161</Cell>
          <Cell>0.97484611486032935</Cell>
          <Cell>0</Cell>
          <Cell>-0.046477228889917177</Cell>
          <Cell>0.0051324295900421132</Cell>
          <Cell>0.03898830210146071</Cell>
          <Cell>1</Cell>
        </Cells>
      </CameraTransformMatrix>
    </plot3D>
  </plot>
</region>