Exemple : Fonction Multidfit

Fonctions > Plan d'expériences > Analyse de régression > Exemple : Fonction Multidfit

Générez une matrice qui contient des exemples tirés des vecteurs X0, X1 et Y, pour les points N.

1. Définissez le nombre de points.

2. Générez les vecteurs X0 et X1.

3. Générez la perturbation pour le signal f(x).

4. Combinez les données d'argument.

5. Générez le vecteur de données Y en fonction des valeurs de la fonction f(x) et de la perturbation.

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  <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. Définissez la matrice Data.

7. Définissez la fonction d'ajustement F(x,u).

8. Trouvez les paramètres de la fonction d'ajustement à l'aide de l'ajustement général multivarié.

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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>

Vous avez obtenu une approximation des coefficients utilisés dans la fonction d'origine f(x).

9. Comparez la matrice Data et la surface approximée.

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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>

Rubriques associées

Ajustement multivarié général

A propos des fonctions d'analyse de régression

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