範例：線性內插

函數 > 數據分析 > 內插與預測 > 範例：線性內插

範例：線性內插

使用 linterp 函數執行線性內插。

1. 定義 y 值集合。

按一下以複製此運算式

<region id="ID0ET4DV" top="168" left="24" xml:lang="zh_TW" height="154.883" width="57.5533333333333" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <id xml:lang="zh_TW" label="None">Y</id>
      <matrix rows="10" cols="1" xml:lang="zh_TW">
        <real xml:lang="zh_TW">2.7</real>
        <real xml:lang="zh_TW">7.6</real>
        <real xml:lang="zh_TW">3.6</real>
        <real xml:lang="zh_TW">4.7</real>
        <real xml:lang="zh_TW">8.4</real>
        <real xml:lang="zh_TW">1.8</real>
        <real xml:lang="zh_TW">6.9</real>
        <real xml:lang="zh_TW">6</real>
        <real xml:lang="zh_TW">2.2</real>
        <real xml:lang="zh_TW">8.6</real>
      </matrix>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

2. 定義相符的 x 值集合。這些值必須依遞增排序。

按一下以複製此運算式

按一下以複製此運算式

3. 定義要內插曲線的 x 值向量。

按一下以複製此運算式

按一下以複製此運算式

4. 呼叫 linterp 函數執行數據點之間的線性內插。

按一下以複製此運算式

<region id="ID0EFEEV" top="432" left="48" xml:lang="zh_TW" height="29.835" width="164.566666666667" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math xml:lang="zh_TW">
    <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">
      <apply xml:lang="zh_TW">
        <indexer xml:lang="zh_TW" />
        <id xml:lang="zh_TW" label="None">Y_int</id>
        <id xml:lang="zh_TW" label="None">j</id>
      </apply>
      <apply xml:lang="zh_TW">
        <id xml:lang="zh_TW">linterp</id>
        <sequence xml:lang="zh_TW">
          <id xml:lang="zh_TW">X</id>
          <id xml:lang="zh_TW">Y</id>
          <apply xml:lang="zh_TW">
            <indexer xml:lang="zh_TW" />
            <id xml:lang="zh_TW">X_int</id>
            <id xml:lang="zh_TW">j</id>
          </apply>
        </sequence>
      </apply>
    </define>
    <resultFormat xml:lang="zh_TW">
      <decimal precision="round-trip-decimal-places" show-trailing-zeros="false" radix="dec" imaginary-value="i" xml:lang="zh_TW" />
      <matrix size="12,12" offset="0,0" xml:lang="zh_TW" />
    </resultFormat>
  </math>
</region>

5. 繪製數據點與內插曲線。

按一下以複製此運算式

<region id="ID0E1FEV" top="456" left="24" xml:lang="zh_TW" height="312" width="493" xmlns="http://schemas.mathsoft.com/worksheet50">
  <plot origin-positioning="false" xml:lang="zh_TW">
    <xyPlot xml:lang="zh_TW">
      <title class="- topic/title " xml:lang="zh_TW" toc="yes" wwtype:type="Paragraph" xmlns:wwtype="urn:WebWorks-Type-Schema" />
      <legend xml:lang="zh_TW" />
      <traces xml:lang="zh_TW">
        <trace xml:lang="zh_TW">
          <traceStyle color="#FF00008B" symbol="x" line-weight="1" line-style="None" xml:lang="zh_TW">線條</traceStyle>
        </trace>
        <trace xml:lang="zh_TW">
          <traceStyle color="#FF000000" symbol="none" line-weight="1" line-style="Solid" xml:lang="zh_TW">線條</traceStyle>
        </trace>
      </traces>
      <axes xml:lang="zh_TW">
        <xAxis rank="1" legend-position="PlotBoundaryBottom" xml:lang="zh_TW">
          <axisLine position="bottom" positionticmark="-1" xml:lang="zh_TW" />
          <axisGrid xml:lang="zh_TW">
            <gridFrequency xml:lang="zh_TW">11</gridFrequency>
            <gridLabels display="true" xml:lang="zh_TW" />
            <gridLines xml:lang="zh_TW" />
            <tickMarks display="true" xml:lang="zh_TW" />
          </axisGrid>
          <axisLabel xml:lang="zh_TW" />
          <markers xml:lang="zh_TW" />
          <numberFormat xml:lang="zh_TW" />
          <plotEquations xml:lang="zh_TW">
            <plotEquation xml:lang="zh_TW">
              <math xml:lang="zh_TW">
                <id xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">X</id>
              </math>
              <math xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math xml:lang="zh_TW">
                <id xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">X_int</id>
              </math>
              <math xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW">
            <startValue xml:lang="zh_TW">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">0</real>
            </startValue>
            <endValue xml:lang="zh_TW">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">9</real>
            </endValue>
          </xyDomain>
        </xAxis>
        <yAxis rank="1" legend-position="PlotBoundaryLeft" xml:lang="zh_TW">
          <axisLine position="ticknumberlock" positionticmark="5" xml:lang="zh_TW" />
          <axisGrid xml:lang="zh_TW">
            <gridFrequency xml:lang="zh_TW">11</gridFrequency>
            <gridLabels display="true" xml:lang="zh_TW" />
            <gridLines xml:lang="zh_TW" />
            <tickMarks display="true" xml:lang="zh_TW" />
          </axisGrid>
          <axisLabel xml:lang="zh_TW" />
          <markers xml:lang="zh_TW" />
          <numberFormat xml:lang="zh_TW" />
          <plotEquations xml:lang="zh_TW">
            <plotEquation xml:lang="zh_TW">
              <math xml:lang="zh_TW">
                <id xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">Y</id>
              </math>
              <math xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
            <plotEquation xml:lang="zh_TW">
              <math xml:lang="zh_TW">
                <id xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">Y_int</id>
              </math>
              <math xml:lang="zh_TW">
                <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
              </math>
            </plotEquation>
          </plotEquations>
          <xyDomain scale-type="linear" auto-scale="true" xml:lang="zh_TW">
            <startValue xml:lang="zh_TW">
              <real xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50">1</real>
            </startValue>
            <endValue xml:lang="zh_TW">
              <placeholder xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50" />
            </endValue>
          </xyDomain>
        </yAxis>
      </axes>
    </xyPlot>
  </plot>
</region>

一如預期，linterp 函數會繪出各數據點集合之間的直線。

內插假設最後的近似函數 (在最後兩點之間計算者)，對值域結尾處所有其他點而言持續為真。此假設極不恰當。存在不同的方法可預測數據值圍外的值。

使用線性內插建立的曲線，在每個連接數據點上都不平滑，所以內插曲線沒有已定義的導數。因此，您可能希望使用立方雲規線或 B 雲規線擬合數據。