sequence/sequence.html

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      SEQUENCE - Fill in a Sequence
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    <h1 align = "center">
      SEQUENCE <br> Fill in a Sequence
    </h1>

    <hr>

    <p>
      <b>SEQUENCE</b>
      is a FORTRAN90 program which
      reads a numeric sequence with missing values,
      and fills in the missing values.
    </p>

    <p>
      The input to the program is a string representing a sequence,
      with missing values denoted by question marks.  For instance,
      we might enter the following sequence:
      <pre>
        ? 3 6 ? 15
      </pre>
      The program will try to determine the simplest rule of a certain
      kind that can be used to fill in the question marks.
    </p>

    <p>
      The rule deduced for the sequence is found by constructing the
      polynomial that interpolates the known data.  Abscissas for the
      data are assigned by position in the sequence.  Thus for the
      above sequence, the three known values have abscissas of 2, 3
      and 5, which means we might think of the sequence as a table:
      <table "border" = 1>
        <tr>
          <td>1</td><td>2</td><td>3</td><td>4</td><td>5</td>
        </tr>
        <tr>
          <td>?</td><td>3</td><td>6</td><td>?</td><td>15</td>
        </tr>
      </table>
    </p>

    <p>
      Once the interpolating polynomial is found, it is evaluated at
      the points where data was not given, and the results are reported
      back to the user.  In the example case, we would get the
      filled in sequence:
      <pre>
        1 3 6 10 15
      </pre>
    </p>

    <p>
      Note that this procedure will always be able to produce a result,
      but it may not be the expected result.  This is particularly so
      when the sequence is most easily represented in terms of a geometric
      calculation, as in
      <pre>
        1 2 4 8 16 32
      </pre>
      or as in the Fibonacci sequence:
      <pre>
        1 1 2 3 5 8 13 21 34 55
      </pre>
      both of which this program will be unable to recognize.
    </p>

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

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

    <h3 align = "center">
      Related Data and Programs:
    </h3>

    <p>
      <a href = "../../f_src/puzzles/puzzles.html">
      PUZZLES</a>,
      FORTRAN90 programs which
      were used to solve various puzzles.
    </p>

    <h3 align = "center">
      Source code:
    </h3>

    <p>
      <ul>
        <li>
          <a href = "sequence.f90">sequence.f90</a>, the source code;
        </li>
        <li>
          <a href = "sequence.sh">sequence.sh</a>,
          commands to compile, link and load the source code;
        </li>
        <li>
          <a href = "sequence_input.txt">sequence_input.txt</a>, sample input;
        </li>
        <li>
          <a href = "sequence_output.txt">sequence_output.txt</a>, the output file;
        </li>
      </ul>
    </p>

    <h3 align = "center">
      List of Routines:
    </h3>

    <p>
      <ul>
        <li>
          <b>SEQUENCE</b> reads in a sequence and calls SEQUENCE_FILLER to fill it in.
        </li>
        <li>
          <b>CH_CAP</b> capitalizes a single character.
        </li>
        <li>
          <b>CH_EQI</b> is a case insensitive comparison of two characters for equality.
        </li>
        <li>
          <b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
        </li>
        <li>
          <b>DATA_TO_DIF</b> sets up a divided difference table from raw data.
        </li>
        <li>
          <b>DIF_TO_POLY</b> converts a divided difference polynomial to standard form.
        </li>
        <li>
          <b>DIF_VAL</b> evaluates a divided difference polynomial at a point.
        </li>
        <li>
          <b>POLY_PRINT</b> prints out a polynomial.
        </li>
        <li>
          <b>R4VEC_DISTINCT</b> is true if the entries in an R4VEC are distinct.
        </li>
        <li>
          <b>S_EQI</b> is a case insensitive comparison of two strings for equality.
        </li>
        <li>
          <b>S_IS_R</b> is TRUE if a string represents a real number.
        </li>
        <li>
          <b>S_TO_R</b> reads a real number from a string.
        </li>
        <li>
          <b>SEQUENCE_FILLER</b> "fills in" a sequence with missing values.
        </li>
        <li>
          <b>WORD_NEXT_READ</b> "reads" words from a string, one at a time.
        </li>
      </ul>
    </p>

    <p>
      You can go up one level to <a href = "../f_src.html">
      the FORTRAN90 source codes</a>.
    </p>

    <hr>

    <i>
      Last revised on 23 April 2008.
    </i>

    <!-- John Burkardt -->

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