box_plot/box_plot.html

<html>

  <head>
    <title>
      BOX_PLOT - Integer Data Box Plots
    </title>
  </head>

  <body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">

    <h1 align = "center">
      BOX_PLOT <br> Integer Data Box Plots
    </h1>

    <hr>

    <p>
      <b>BOX_PLOT</b> 
      is a MATLAB program which 
      reads a file of integer
      coordinates and associated colors, and makes a plot, placing a unit
      box of the given color at each coordinate.
    </p>

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

    <p>
      <blockquote>
        <b>box_plot</b> ( <i>'input_filename'</i> )
      </blockquote>
      where
      <ul>
        <li>
          <i>'input_filename'</i> contains xy point coordinates and rgb colors.
        </li>
      </ul>
    </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">
      Languages:
    </h3>

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

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

    <p>
      <a href = "../../f_src/bar_plot/bar_plot.html">
      BAR_PLOT</a>,
      a FORTRAN90 program which 
      reads a set of data from
      a file and creates a bar plot.
    </p>
    <p>
      <a href = "../../m_src/box_display/box_display.html">
      BOX_DISPLAY</a>,
      a MATLAB program which
      displays a box plot, over integer pairs of data, of a function
      defined by two formulas.
    </p>

    <p>
      <a href = "../../m_src/cc_display/cc_display.html">
      CC_DISPLAY</a>,
      a MATLAB program which 
      displays the abscissas
      used in various kinds of Clenshaw Curtis quadrature rules.
    </p>

    <p>
      <a href = "../../m_src/circle_grid_display/circle_grid_display.html">
      CIRCLE_GRID_DISPLAY</a>,
      a MATLAB program which reads a matrix of integers, and draws a corresponding
      grid of circles filled with color.
    </p>

    <p>
      <a href = "../../m_src/gl_display/gl_display.html">
      GL_DISPLAY</a>,
      a MATLAB program which 
      displays the abscissas
      used in various kinds of Gauss Legendre quadrature rules.
    </p>

    <p>
      <a href = "../../m_src/gridlines/gridlines.html">
      GRIDLINES</a>,
      a MATLAB library which 
      gives the user more control over drawing gridlines on a graph
      than the builtin "grid on" command.
    </p>

    <p>
      <a href = "../../f_src/plot_points/plot_points.html">
      PLOT_POINTS</a>,
      a FORTRAN90 program which 
      reads a set of points from
      a file and plots them into an Encapsulated PostScript file.
    </p>

    <p>
      <a href = "../../m_src/prime_plot/prime_plot.html">
      PRIME_PLOT</a>
      a MATLAB program which 
      displays a box plot of the prime and composite numbers.
    </p>

    <p>
      <a href = "../../m_src/xy_display/xy_display.html">
      XY_DISPLAY</a>, 
      a MATLAB program which 
      reads a set of 2D points from
      a file and plots them in a the MATLAB graphics window.
    </p>

    <p> 
      <a href = "../../m_src/xyf_display/xyf_display.html">
      XYF_DISPLAY</a>, 
      a MATLAB program which
      reads XYF information defining points and faces in 2D, 
      and displays an image in a MATLAB graphics window.
    </p>

    <p> 
      <a href = "../../m_src/xyl_display/xyl_display.html">
      XYL_DISPLAY</a>, 
      a MATLAB program which
      reads XYL information defining points and lines in 2D, 
      and displays an image in a MATLAB graphics window.
    </p>

    <p>
      <a href = "../../m_src/xyz_display/xyz_display.html">
      XYZ_DISPLAY</a>,
      a MATLAB program which 
      reads a set of 3D points from
      a file and plots them in a the MATLAB graphics window.
    </p>

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

    <p>
      <ul>
        <li>
          <a href = "box_plot.m">box_plot.m</a> 
          the source code.
        </li>
      </ul>
    </p>

    <h3 align = "center">
      Examples and Tests:
    </h3>

    <p>
      <b>ADAPTIVE</b> looks at the adaptive modification of a sparse grid 
      rule in 2D.
      <ul>
        <li>
          <a href = "adaptive_1.txt">adaptive_1.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "adaptive_1.png">adaptive_1.png</a>, 
        </li>
        <li>
          <a href = "adaptive_2.txt">adaptive_2.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "adaptive_2.png">adaptive_2.png</a>, 
        </li>
        <li>
          <a href = "adaptive_3.txt">adaptive_3.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "adaptive_3.png">adaptive_3.png</a>, 
        </li>
        <li>
          <a href = "adaptive_4.txt">adaptive_4.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "adaptive_4.png">adaptive_4.png</a>, 
        </li>
        <li>
          <a href = "adaptive_5.txt">adaptive_5.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "adaptive_5.png">adaptive_5.png</a>, 
        </li>
        <li>
          <a href = "abc.png">abc.png</a>, 
          steps 1 through 3 in one plot.
        </li>
        <li>
          <a href = "de.png">de.png</a>, 
          steps 4 through 5 in one plot.
        </li>
        <li>
          <a href = "abcde.png">abcde.png</a>, 
          steps 1 through 5 in one plot.
        </li>
      </ul>
    </p>

    <p>
      <b>ALPHA_1.0_1.0</b> prints some of the 64 pairs of values
      on an 8 by 8 grid.  Blue indicates "old" data, and red "new".
      <ul>
        <li>
          <a href = "alpha_1.0_1.0.txt">alpha_1.0_1.0.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "alpha_1.0_1.0.png">alpha_1.0_1.0.png</a>, 
          a PNG image of a plot of the points.
        </li>
      </ul>
    </p>

    <p>
      <b>ALPHA_1.0_1.5</b> prints some of the 64 pairs of values
      on an 8 by 8 grid.  Blue indicates "old" data, and red "new".
      <ul>
        <li>
          <a href = "alpha_1.0_1.5.txt">alpha_1.0_1.5.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "alpha_1.0_1.5.png">alpha_1.0_1.5.png</a>, 
          a PNG image of a plot of the points.
        </li>
      </ul>
    </p>

    <p>
      <b>ALPHA_1.0_2.0</b> prints some of the 64 pairs of values
      on an 8 by 8 grid.  Blue indicates "old" data, and red "new".
      <ul>
        <li>
          <a href = "alpha_1.0_2.0.txt">alpha_1.0_2.0.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "alpha_1.0_2.0.png">alpha_1.0_2.0.png</a>, 
          a PNG image of a plot of the points.
        </li>
      </ul>
    </p>

    <p>
      <b>BOXES</b> suggests the monomials that are exactly integrated
      by a 2D Clenshaw-Curtis sparse grid of levels 0 through 4.  Monomials 
      added on this level are red, old ones are blue.  A common 20x20 grid 
      is used for all the plots.
      <ul>
        <li>
          <a href = "boxes_level0.txt">boxes_level0.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "boxes_level0.png">boxes_level0.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "boxes_level1.txt">boxes_level1.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "boxes_level1.png">boxes_level1.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "boxes_level2.txt">boxes_level2.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "boxes_level2.png">boxes_level2.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "boxes_level3.txt">boxes_level3.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "boxes_level3.png">boxes_level3.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "boxes_level4.txt">boxes_level4.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "boxes_level4.png">boxes_level4.png</a>, 
          a PNG image of a plot of the points.
        </li>
      </ul>
    </p>

    <p>
      <b>CC</b> looks at the monomials that are exactly integrated by 
      2D Clenshaw-Curtis sparse grids of levels 0 through 6, using a common
      35x35 grid.
      <ul>
        <li>
          <a href = "cc_level0.txt">cc_level0.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cc_level0.png">cc_level0.png</a>, 
        </li>
        <li>
          <a href = "cc_level1.txt">cc_level1.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cc_level1.png">cc_level1.png</a>, 
        </li>
        <li>
          <a href = "cc_level2.txt">cc_level2.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cc_level2.png">cc_level2.png</a>, 
        </li>
        <li>
          <a href = "cc_level3.txt">cc_level3.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cc_level3.png">cc_level3.png</a>, 
        </li>
        <li>
          <a href = "cc_level4.txt">cc_level4.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cc_level4.png">cc_level4.png</a>, 
        </li>
        <li>
          <a href = "cc_level5.txt">cc_level5.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cc_level5.png">cc_level5.png</a>, 
        </li>
        <li>
          <a href = "cc_level6.txt">cc_level6.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cc_level6.png">cc_level6.png</a>, 
          (note that the data in columns 0 and 1, and rows 0 and 1,
          goes off the scale, to 65).
        </li>
      </ul>
    </p>

    <p>
      <b>CCS</b> looks at the monomials that are exactly integrated by 
      2D Clenshaw-Curtis "Slow exponential" sparse grids of levels 0 through 
      6, using a common 35x35 grid.  This is a variant of the Clenshaw Curtis
      rule that tries to delay the exponential growth of the orders.  Differences
      only appear once level 4 has been reached.
      <ul>
        <li>
          <a href = "ccs_level0.txt">ccs_level0.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "ccs_level0.png">ccs_level0.png</a>, 
        </li>
        <li>
          <a href = "ccs_level1.txt">ccs_level1.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "ccs_level1.png">ccs_level1.png</a>, 
        </li>
        <li>
          <a href = "ccs_level2.txt">ccs_level2.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "ccs_level2.png">ccs_level2.png</a>, 
        </li>
        <li>
          <a href = "ccs_level3.txt">ccs_level3.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "ccs_level3.png">ccs_level3.png</a>, 
        </li>
        <li>
          <a href = "ccs_level4.txt">ccs_level4.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "ccs_level4.png">ccs_level4.png</a>, 
        </li>
        <li>
          <a href = "ccs_level5.txt">ccs_level5.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "ccs_level5.png">ccs_level5.png</a>, 
        </li>
        <li>
          <a href = "ccs_level6.txt">ccs_level6.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "ccs_level6.png">ccs_level6.png</a>, 
        </li>
      </ul>
    </p>

    <p>
      <b>CGW</b> looks at the first eight rules in an anisotropic
      sparse grid that has double the growth in X as in Y:
      <ul>
        <li>
          <a href = "cgw_boxes_level0.txt">cgw_boxes_level0.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cgw_boxes_level0.png">cgw_boxes_level0.png</a>, 
        </li>
        <li>
          <a href = "cgw_boxes_level1.txt">cgw_boxes_level1.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cgw_boxes_level1.png">cgw_boxes_level1.png</a>, 
        </li>
        <li>
          <a href = "cgw_boxes_level2.txt">cgw_boxes_level2.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cgw_boxes_level2.png">cgw_boxes_level2.png</a>, 
        </li>
        <li>
          <a href = "cgw_boxes_level3.txt">cgw_boxes_level3.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cgw_boxes_level3.png">cgw_boxes_level3.png</a>, 
        </li>
        <li>
          <a href = "cgw_boxes_level4.txt">cgw_boxes_level4.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cgw_boxes_level4.png">cgw_boxes_level4.png</a>, 
        </li>
        <li>
          <a href = "cgw_boxes_level5.txt">cgw_boxes_level5.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cgw_boxes_level5.png">cgw_boxes_level5.png</a>, 
        </li>
        <li>
          <a href = "cgw_boxes_level6.txt">cgw_boxes_level6.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cgw_boxes_level6.png">cgw_boxes_level6.png</a>, 
        </li>
        <li>
          <a href = "cgw_boxes_level7.txt">cgw_boxes_level7.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cgw_boxes_level7.png">cgw_boxes_level7.png</a>, 
        </li>
        <li>
          <a href = "cgw_boxes_level8.txt">cgw_boxes_level8.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "cgw_boxes_level8.png">cgw_boxes_level8.png</a>, 
        </li>
      </ul>
    </p>

    <p>
      <b>CHECKERBOARD</b> is a set of 64 pairs of integers and colors
      that correspond to a checkerboard.
      <ul>
        <li>
          <a href = "checkerboard.txt">checkerboard.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "checkerboard.png">checkerboard.png</a>, 
          a PNG image of a plot of the points.
        </li>
      </ul>
    </p>

    <p>
      <b>CLAY</b> is a set of pairs of integers that record the
      basic method (1,1) in blue, some low order methods in green,
      and secondary refinements in red.
      <ul>
        <li>
          <a href = "clay.txt">clay.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "clay.png">clay.png</a>, 
          a PNG image of a plot of the points.
        </li>
      </ul>
    </p>

    <p>
      <b>F</b> is a set of points that can make the letter F:
      <ul>
        <li>
          <a href = "f.txt">f.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "f.png">f.png</a>, 
          a PNG image of a plot of the points.
        </li>
      </ul>
    </p>

    <p>
      <b>GP</b> looks at the monomials that are exactly integrated by 
      2D Gauss-Patterson sparse grids of levels 0 through 
      5, using a common 35x35 grid. 
      <ul>
        <li>
          <a href = "gp_level0.txt">gp_level0.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gp_level0.png">gp_level0.png</a>, 
        </li>
        <li>
          <a href = "gp_level1.txt">gp_level1.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gp_level1.png">gp_level1.png</a>, 
        </li>
        <li>
          <a href = "gp_level2.txt">gp_level2.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gp_level2.png">gp_level2.png</a>, 
        </li>
        <li>
          <a href = "gp_level3.txt">gp_level3.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gp_level3.png">gp_level3.png</a>, 
        </li>
        <li>
          <a href = "gp_level4.txt">gp_level4.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gp_level4.png">gp_level4.png</a>, 
        </li>
        <li>
          <a href = "gp_level5.txt">gp_level5.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gp_level5.png">gp_level5.png</a>, 
        </li>
      </ul>
    </p>

    <p>
      <b>GPS</b> looks at the monomials that are exactly integrated by 
      2D slow-growth Gauss-Patterson sparse grids of levels 0 through 
      5, using a common 35x35 grid. 
      <ul>
        <li>
          <a href = "gps_level0.txt">gps_level0.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gps_level0.png">gps_level0.png</a>, 
        </li>
        <li>
          <a href = "gps_level1.txt">gps_level1.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gps_level1.png">gps_level1.png</a>, 
        </li>
        <li>
          <a href = "gps_level2.txt">gps_level2.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gps_level2.png">gps_level2.png</a>, 
        </li>
        <li>
          <a href = "gps_level3.txt">gps_level3.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gps_level3.png">gps_level3.png</a>, 
        </li>
        <li>
          <a href = "gps_level4.txt">gps_level4.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gps_level4.png">gps_level4.png</a>, 
        </li>
        <li>
          <a href = "gps_level5.txt">gps_level5.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "gps_level5.png">gps_level5.png</a>, 
        </li>
      </ul>
    </p>

    <p>
      <b>SM</b> symbolically displays the monomials that will be integrated
      precisely by a Smolyak sparse grid rule of given level if the 1D factor 
      rules form a family of precisions at least 1, 3, 5, 7, 9, ...
      <ul>
        <li>
          <a href = "sm_level0.txt">boxes_level0.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "sm_level0.png">sm_level0.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sm_level1.txt">sm_level1.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "sm_level1.png">sm_level1.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sm_level2.txt">sm_level2.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "sm_level2.png">sm_level2.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sm_level3.txt">sm_level3.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "sm_level3.png">sm_level3.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sm_level4.txt">sm_level4.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "sm_level4.png">sm_level4.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sm_level5.txt">sm_level5.txt</a>, 
          the coordinates and colors.
        </li>
        <li>
          <a href = "sm_level5.png">sm_level5.png</a>, 
          a PNG image of a plot of the points.
        </li>
      </ul>
    </p>

    <p>
      <b>SPARSE</b> is a sequence of plots that suggest how a sparse grid
      is put together in such a way as to capture all monomials up to a
      specific total degree.
      <ul>
        <li>
          <a href = "sparse1.txt">sparse1.txt</a>, 
          indicates the monomials to be captured.
        </li>
        <li>
          <a href = "sparse1.png">sparse1.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sparse2.txt">sparse2.txt</a>, 
          shows how a product rule would capture the monomials (and more).
        </li>
        <li>
          <a href = "sparse2.png">sparse2.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sparse3.txt">sparse3.txt</a>, 
          begins a sparse grid by adding Q(0x3).
        </li>
        <li>
          <a href = "sparse3.png">sparse3.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sparse4.txt">sparse4.txt</a>, 
          continues a sparse grid by adding Q(2x2).
        </li>
        <li>
          <a href = "sparse4.png">sparse4.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sparse5.txt">sparse5.txt</a>, 
          continues a sparse grid by subtracting Q(0x2).
        </li>
        <li>
          <a href = "sparse5.png">sparse5.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sparse6.txt">sparse6.txt</a>, 
          continues a sparse grid by adding Q(2x1).
        </li>
        <li>
          <a href = "sparse6.png">sparse6.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sparse7.txt">sparse7.txt</a>, 
          continues a sparse grid by subtracting Q(1x1).
        </li>
        <li>
          <a href = "sparse7.png">sparse7.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sparse8.txt">sparse8.txt</a>, 
          continues a sparse grid by adding Q(3,0).
        </li>
        <li>
          <a href = "sparse8.png">sparse8.png</a>, 
          a PNG image of a plot of the points.
        </li>
        <li>
          <a href = "sparse9.txt">sparse9.txt</a>, 
          completes the sparse grid by subtracting Q(2x0).
        </li>
        <li>
          <a href = "sparse9.png">sparse9.png</a>, 
          a PNG image of a plot of the points.
        </li>
      </ul>
    </p>

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

    <hr>

    <i>
      Last revised on 09 January 2014.
    </i>

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