Example: The impact of CTOL on Solve Blocks

Solve Blocks > Example: The impact of CTOL on Solve Blocks

Example: The impact of CTOL on Solve Blocks

You can use CTOL to set the accuracy of the results os a solve block.

1. Set the value of CTOL.

2. Define the solve block.

Click to copy this expression

<region id="ID0EDEDLB" actualWidth="194.98333333333335" actualHeight="191.70000000000002" top="57.600000000000009" left="38.400000000000006" height="191.70000000000002" width="194.98333333333335" xmlns="http://schemas.mathsoft.com/worksheet50">
  <solveblock>
    <regions>
      <region id="" actualWidth="41.346666666666664" actualHeight="25.6" top="38.400000000000006" left="38.400000000000006" solve-block-category="guess-value">
        <math resultRef="14">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id labels="VARIABLE" xml:space="preserve">x</id>
            <real>2</real>
          </define>
        </math>
      </region>
      <region id="" actualWidth="78.173333333333346" actualHeight="25.6" top="76.800000000000011" left="38.400000000000006" solve-block-category="constraint">
        <math resultRef="15">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <id xml:space="preserve">exp</id>
              <id xml:space="preserve">x</id>
            </apply>
            <real>2</real>
          </apply>
        </math>
      </region>
      <region id="" actualWidth="67.516666666666666" actualHeight="25.6" top="115.20000000000002" left="38.400000000000006" solve-block-category="constraint">
        <math resultRef="16">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <lessThan />
            <id xml:space="preserve">x</id>
            <real>0.693</real>
          </apply>
        </math>
      </region>
      <region id="" actualWidth="156.58333333333334" actualHeight="25.6" top="172.8" left="38.400000000000006" solve-block-category="solver">
        <math resultRef="17">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id labels="VARIABLE" xml:space="preserve">res</id>
            <eval>
              <apply>
                <id labels="KEYWORD" xml:space="preserve" algorithm="autoSelect-nonlinearLevenbergMarquardt">find</id>
                <id labels="SYSTEM" xml:space="preserve" label-is-contextual="true">x</id>
              </apply>
              <unitOverride>
                <placeholder />
              </unitOverride>
            </eval>
          </define>
        </math>
      </region>
    </regions>
  </solveblock>
</region>

3. Compare with the exact answer.

Comparing the difference between the result and the constraint to CTOL, we see that the result is in the range that was set.

4. You can reduce the value of CTOL.

5. The constraint is verified with the new CTOL value.

Click to copy this expression

<region id="ID0ETJDLB" actualWidth="191.666666666667" actualHeight="191.7" top="460.80000000000007" left="38.400000000000006" height="191.7" width="191.666666666667" xmlns="http://schemas.mathsoft.com/worksheet50">
  <solveblock>
    <regions>
      <region id="" actualWidth="41.346666666666664" actualHeight="25.6" top="38.4" left="38.4" solve-block-category="guess-value">
        <math resultRef="21">
          <define xmlns="http://schemas.mathsoft.com/math50">
            <id labels="VARIABLE" xml:space="preserve">x</id>
            <real>2</real>
          </define>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
      <region id="" actualWidth="78.173333333333346" actualHeight="25.6" top="76.8" left="38.4" solve-block-category="constraint">
        <math resultRef="22">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <equal />
            <apply>
              <id xml:space="preserve">exp</id>
              <id xml:space="preserve">x</id>
            </apply>
            <real>2</real>
          </apply>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
      <region id="" actualWidth="67.516666666666666" actualHeight="25.6" top="115.2" left="38.4" solve-block-category="constraint">
        <math resultRef="23">
          <apply xmlns="http://schemas.mathsoft.com/math50">
            <lessThan />
            <id xml:space="preserve">x</id>
            <real>0.693</real>
          </apply>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
      <region id="" actualWidth="90.186666666666667" actualHeight="25.6" top="172.8" left="38.4" solve-block-category="solver">
        <math resultRef="24">
          <eval xmlns="http://schemas.mathsoft.com/math50">
            <apply>
              <id labels="KEYWORD" xml:space="preserve" algorithm="">find</id>
              <id xml:space="preserve">x</id>
            </apply>
            <unitOverride>
              <placeholder />
            </unitOverride>
          </eval>
          <resultFormat>
            <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
          </resultFormat>
        </math>
      </region>
    </regions>
  </solveblock>
</region>

The result is not in the range.

Related Topics

About Solve Blocks

TOL and CTOL

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