NESTED_SEQUENCE_DISPLAY
Display a Nested Set of Sequences

NESTED_SEQUENCE_DISPLAY is a MATLAB program which displays a set of sequences, as lines of X values, "stacked up" in the Y direction. For cases where sequences share a value, a red vertical line is drawn to highlight this.

The purpose of the plot is to emphasize the structure of a nested sequence, although it is not actually necessary for the sequences to be related in any way.

The kind of plot we are thinking of though, might look something like this:

    Sequence 4: 1    3 4  5  6     8
                |    |    |        |
    Sequence 3: 1 2  |    5     7  |
                |    |          |  |
    Sequence 2: 1    3          7  |
                |               |  |
    Sequence 1: 1               7  8
      

For example, the program could be used to show the nesting of the family of Clenshaw Curtis points, when choosing orders 1, 3, 5, 9, 17, 33, 65, ...

Usage:

nested_sequence_display ()

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

GRIDLINES, a MATLAB library which gives the user more control over drawing gridlines on a graph than the builtin "grid on" command.

SEQUENCE_STREAK_DISPLAY, a MATLAB program which reads a file containing a sequence, and draws a "streak" plot in which, as each value joins the sequence, it starts a streak on the plot.

TABLE, a format which is used for the files containing the sequences.

TENSOR_GRID_DISPLAY, a MATLAB program which can display the grid points of a tensor product rule used for interpolation or quadrature, in 1D, 2D or 3D.

Source Code:

• nested_sequence_display.m, reads a list of files containing sequences and draws a plot that highlights any nesting between the sequences;

Examples and Tests:

CC is a set of files containing Clenshaw Curtis rules, with an "exponential" growth rule.

• cc_level0.txt, the abscissas for the rule of level 0.
• cc_level1.txt, the abscissas for the rule of level 1.
• cc_level2.txt, the abscissas for the rule of level 2.
• cc_level3.txt, the abscissas for the rule of level 3.
• cc_level4.txt, the abscissas for the rule of level 4.
• cc_level5.txt, the abscissas for the rule of level 5.
• cc_level6.txt, the abscissas for the rule of level 6.
• cc_sequence.png, a PNG image of the sequences.

GL is a set of files containing Gauss Legendre abscissas, with an "exponential" growth rule.

• gl_01.txt, the abscissas for the rule of order 1.
• gl_03.txt, the abscissas for the rule of order 3.
• gl_07.txt, the abscissas for the rule of order 7.
• gl_15.txt, the abscissas for the rule of order 15.
• gl_31.txt, the abscissas for the rule of order 31.
• gl_65.txt, the abscissas for the rule of order 65.
• gl_sequence.png, a PNG image of the sequences.

NCO is a set of files containing Newton Cotes Open abscissas, with a "linear" growth rule.

• nco_01.txt, the abscissas for the rule of order 1.
• nco_03.txt, the abscissas for the rule of order 3.
• nco_05.txt, the abscissas for the rule of order 5.
• nco_07.txt, the abscissas for the rule of order 7.
• nco_09.txt, the abscissas for the rule of order 9.
• nco_11.txt, the abscissas for the rule of order 11.
• nco_13.txt, the abscissas for the rule of order 13.
• nco_15.txt, the abscissas for the rule of order 15.
• nco_sequence.png, a PNG image of the sequences.

SCC is a set of files containing Clenshaw Curtis rules, with an "slow exponential" growth rule.

• scc_level0.txt, the abscissas for the rule of level 0.
• scc_level1.txt, the abscissas for the rule of level 1.
• scc_level2.txt, the abscissas for the rule of level 2.
• scc_level3.txt, the abscissas for the rule of level 3.
• scc_level4.txt, the abscissas for the rule of level 4.
• scc_level5.txt, the abscissas for the rule of level 5.
• scc_level6.txt, the abscissas for the rule of level 6.
• scc_sequence.png, a PNG image of the sequences.

You can go up one level to the MATLAB source codes.