vpa/vpa.html

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      VPA - MATLAB's Variable Precision Arithmetic
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      VPA <br> MATLAB's Variable Precision Arithmetic
    </h1>

    <hr>

    <p>
      <b>VPA</b>
      contains MATLAB programs which
      demonstrate the use of variable precision arithmetic.
    </p>

    <p>
      MATLAB's variable precision arithmetic is only available through the
      Symbolic Math Toolbox.  To find out if you have this toolbox installed,
      you can type "ver" within your MATLAB session.
    </p>

    <p>
      In MATLAB, evaluating a symbolic variable means creating a representation of
      its value, to a given number of digits, as a floating point number.  The
      vpa() command is used to create the floating point representation.  
      Typical uses are:
      <pre>
        r = vpa ( s )
      </pre>
      which takes the symbolic object s and evaluates it as a symbolic real number
      to the current default number of digits or
      <pre>
        r = vpa ( s, d )
      </pre>
      which uses d digits in the real number representation.
    </p>

    <p>
      The current default number of digits can be found by using the digits() command:
      <pre>
        dignum = digits;
      </pre>
      or
      <pre>
        dignum = digits ( );
      </pre>
      The default number of digits can be changed by including an input argument
      to the digits() command:
      <pre>
        digits ( 50 );
      </pre>
    </p>

    <p>
      To my mind, a significant issue with the symbolic math toolbox is that it
      is not apparent how to control the printing of the value of a given variable.
      If I compute something to 80 digits, I can always display it by naming it.
      But what if I prefer a labeled printout?  Various alternatives involving
      "disp()" and "fprintf()" and string concatenation seem unsatisfactory.
    </p>

    <h3 align = "center">
      Licensing:
    </h3>

    <p>
      The computer code and data files made available on this web page
      are distributed under
      <a href = "mathworks_bsd_license.txt">the BSD license.</a>
    </p>

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      Languages:
    </h3>

    <p>
      <b>VPA</b> is available in
      <a href = "../../m_src/vpa/vpa.html">a MATLAB version</a>.
    </p>

    <h3 align = "center">
      Reference:
    </h3>

    <p>
      <ol>
        <li>
          David Bailey, Jonathan Borwein,<br>
          Experimental Mathematics: Examples, Methods and Implications,<br>
          Notices of the American Mathematical Society,<br>
          Volume 52, Number 5, pages 502-514.
        </li>
        <li>
          David Bailey, Karthik Jeyabalan, Xiaoye Li,<br>
          A Comparison of Three High-Precision Quadrature Schemes,<br>
          Experimental Mathematics,<br>
          Volume 14, Number 3, pages 317-329.
        </li>
        <li>
          Cleve Moler,<br>
          Cleve's Corner: Computing Pi,<br>
          MATLAB News and Notes,<br>
          February 2012.
        </li>
      </ol>
    </p>

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      Source Code:
    </h3>

    <p>
      <b>COMPUTING_PI</b> is a collection of three functions discussed by
      Cleve Moler for computing pi to many digits.
      <ul>
        <li>
          <a href = "agm_pi.m">agm_pi.m</a>,
          uses the arithmetic-geometric mean algorithm.
        </li>
        <li>
          <a href = "agm_pi_test.m">agm_pi_test.m</a>, 
          tests agm_pi.
        </li>
        <li>
          <a href = "bbp_pi.m">bbp_pi.m</a>,
          uses the Bailey-Borwein-Plouffe algorithm.
        </li>
        <li>
          <a href = "bbp_pi_test.m">bbp_pi_test.m</a>, 
          tests bbp_pi.
        </li>
        <li>
          <a href = "chud_pi.m">chud_pi.m</a>,
          uses the Chudnovsky algorithm.
        </li>
        <li>
          <a href = "chud_pi_test.m">chud_pi_test.m</a>, 
          tests chud_pi.
        </li>
        <li>
          <a href = "pi_test.m">pi_test.m</a>, calls all the tests;
        </li>
        <li>
          <a href = "pi_test_output.txt">pi_test_output.txt</a>,
          the output file.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../m_src.html">
      the MATLAB source codes</a>.
    </p>

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    <i>
      Last modified on 28 February 2012.
    </i>

    <!-- John Burkardt -->

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