Maxima Manual: Functions and Variables for statistical graphs

Previous: Functions and Variables for specific multivariate descriptive statistics, Nach oben: Package descriptive [Inhalt][Index]

### 39.5 Functions and Variables for statistical graphs

Function: barsplot (data1, data2, …, option_1, option_2, …)
Function: barsplot_description (…)

  Plots bars diagrams for discrete statistical variables, both for one or multiple samples.

  data can be a list of outcomes representing one sample, or a matrix of m rows and n columns, representing n samples of size m each.

  Available options are:

  - box_width (default, `3/4`): relative width of rectangles. This value must be in the range `[0,1]`.
  - grouping (default, `clustered`): indicates how multiple samples are shown. Valid values are: `clustered` and `stacked`.
  - groups_gap (default, `1`): a positive integer number representing the gap between two consecutive groups of bars.
  - bars_colors (default, `[]`): a list of colors for multiple samples. When there are more samples than specified colors, the extra necesary colors are chosen at random. See `color` to learn more about them.
  - frequency (default, `absolute`): indicates the scale of the ordinates. Possible values are: `absolute`, `relative`, and `percent`.
  - ordering (default, `orderlessp`): possible values are `orderlessp` or `ordergreatp`, indicating how statistical outcomes should be ordered on the `x`-axis.
  - sample_keys (default, `[]`): a list with the strings to be used in the legend. When the list length is other than `0` or the number of samples, an error message is returned.
  - start_at (default, `0`): indicates where the plot begins to be plotted on the `x`-axis.
  - All global `draw` options, except `xtics`, which is internally assigned by `barsplot`. If you want to set your own values for this option or want to build complex scenes, make use of `barsplot_description`. See example below.
  - The following local `draw` options: `key`, `color`, `fill_color`, `fill_density` and `line_width`. See also `bars`.

  Function `barsplot_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects. There is also a function `wxbarsplot` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Examples:

  Univariate sample in matrix form. Absolute frequencies.

      (%i1) load ("descriptive")$
      (%i2) m : read_matrix (file_search ("biomed.data"))$

      (%i3) barsplot(
              col(m,2),
              title        = "Ages",
              xlabel       = "years",
              box_width    = 1/2,
              fill_density = 3/4)$

  Two samples of different sizes, with relative frequencies and user declared colors.

      (%i1) load ("descriptive")$
      (%i2) l1:makelist(random(10),k,1,50)$
      (%i3) l2:makelist(random(10),k,1,100)$

      (%i4) barsplot(
              l1,l2,
              box_width    = 1,
              fill_density = 1,
              bars_colors  = [black, grey],
              frequency = relative,
              sample_keys = ["A", "B"])$

  Four non numeric samples of equal size.

      (%i1) load ("descriptive")$

      (%i2) barsplot(
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              title  = "Asking for something to four groups",
              ylabel = "# of individuals",
              groups_gap   = 3,
              fill_density = 0.5,
              ordering     = ordergreatp)$

  Stacked bars.

      (%i1) load ("descriptive")$

      (%i2) barsplot(
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              makelist([Yes, No, Maybe][random(3)+1],k,1,50),
              title  = "Asking for something to four groups",
              ylabel = "# of individuals",
              grouping     = stacked,
              fill_density = 0.5,
              ordering     = ordergreatp)$

  `barsplot` in a multiplot context.

      (%i1) load ("descriptive")$
      (%i2) l1:makelist(random(10),k,1,50)$
      (%i3) l2:makelist(random(10),k,1,100)$
      (%i4) bp1 :
              barsplot_description(
               l1,
               box_width = 1,
               fill_density = 0.5,
               bars_colors = [blue],
               frequency = relative)$

      (%i5) bp2 :
              barsplot_description(
               l2,
               box_width = 1,
               fill_density = 0.5,
               bars_colors = [red],
               frequency = relative)$

      (%i6) draw(gr2d(bp1), gr2d(bp2))$

  For bars diagrams related options, see `bars` of package `draw`. See also functions `histogram` and `piechart`.

Function: boxplot (data)
Function: boxplot (data, option_1, option_2, …)
Function: boxplot_description (…)

  This function plots box-and-whishker diagrams. Argument data can be a list, which is not of great interest, since these diagrams are mainly used for comparing different samples, or a matrix, so it is possible to compare two or more components of a multivariate statistical variable. But it is also allowed data to be a list of samples with possible different sample sizes, in fact this is the only function in package `descriptive` that admits this type of data structure.

  Available options are:

  - box_width (default, `3/4`): relative width of boxes. This value must be in the range `[0,1]`.
  - box_orientation (default, `vertical`): possible values: `vertical` and `horizontal`.
  - All `draw` options, except `points_joined`, `point_size`, `point_type`, `xtics`, `ytics`, `xrange`, and `yrange`, which are internally assigned by `boxplot`. If you want to set your own values for this options or want to build complex scenes, make use of `boxplot_description`.
  - The following local `draw` options: `key`, `color`, and `line_width`.

  Function `boxplot_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects. There is also a function `wxboxplot` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Examples:

  Box-and-whishker diagram from a multivariate sample.

      (%i1) load ("descriptive")$
      (%i2) s2 : read_matrix(file_search("wind.data"))$

      (%i3) boxplot(s2,
              box_width  = 0.2,
              title      = "Windspeed in knots",
              xlabel     = "Stations",
              color      = red,
              line_width = 2)$

  Box-and-whishker diagram from three samples of different sizes.

      (%i1) load ("descriptive")$

      (%i2) A :
             [[6, 4, 6, 2, 4, 8, 6, 4, 6, 4, 3, 2],
              [8, 10, 7, 9, 12, 8, 10],
              [16, 13, 17, 12, 11, 18, 13, 18, 14, 12]]$

      (%i3) boxplot (A, box_orientation = horizontal)$

Function: histogram (list)
Function: histogram (list, option_1, option_2, …)
Function: histogram (one_column_matrix)
Function: histogram (one_column_matrix, option_1, option_2, …)
Function: histogram (one_row_matrix)
Function: histogram (one_row_matrix, option_1, option_2, …)
Function: histogram_description (…)

  This function plots an histogram from a continuous sample. Sample data must be stored in a list of numbers or an one dimensional matrix.

  Available options are:

  - nclasses (default, `10`): number of classes of the histogram, or a list indicating the limits of the classes and the number of them, or only the limits.
  - frequency (default, `absolute`): indicates the scale of the ordinates. Possible values are: `absolute`, `relative`, and `percent`.
  - htics (default, `auto`): format of the histogram tics. Possible values are: `auto`, `endpoints`, `intervals`, or a list of labels.
  - All global `draw` options, except `xrange`, `yrange`, and `xtics`, which are internally assigned by `histogram`. If you want to set your own values for these options, make use of `histogram_description`. See examples bellow.
  - The following local `draw` options: `key`, `color`, `fill_color`, `fill_density` and `line_width`. See also `bars`.

  Function `histogram_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects. There is also a function `wxhistogram` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Examples:

  A simple with eight classes:

      (%i1) load ("descriptive")$
      (%i2) s1 : read_list (file_search ("pidigits.data"))$
      (%i3) histogram (
                 s1,
                 nclasses     = 8,
                 title        = "pi digits",
                 xlabel       = "digits",
                 ylabel       = "Absolute frequency",
                 fill_color   = grey,
                 fill_density = 0.6)$

  Setting the limits of the histogram to -2 and 12, with 3 classes. Also, we introduce predefined tics:

      (%i1) load ("descriptive")$
      (%i2) s1 : read_list (file_search ("pidigits.data"))$
      (%i3) histogram (
                 s1,
                 nclasses     = [-2,12,3],
                 htics        = ["A", "B", "C"],
                 terminal     = png,
                 fill_color   = "#23afa0",
                 fill_density = 0.6)$

  We make use of `histogram_description` for setting the `xrange` and adding an explicit curve into the scene:

      (%i1) load ("descriptive")$
      (%i2) ( load("distrib"),
              m: 14, s: 2,
              s2: random_normal(m, s, 1000) ) $
      (%i3) draw2d(
              grid   = true,
              xrange = [5, 25],
              histogram_description(
                s2,
                nclasses     = 9,
                frequency    = relative,
                fill_density = 0.5),
              explicit(pdf_normal(x,m,s), x, m - 3*s, m + 3* s))$

Function: piechart (list)
Function: piechart (list, option_1, option_2, …)
Function: piechart (one_column_matrix)
Function: piechart (one_column_matrix, option_1, option_2, …)
Function: piechart (one_row_matrix)
Function: piechart (one_row_matrix, option_1, option_2, …)
Function: piechart_description (…)

  Similar to `barsplot`, but plots sectors instead of rectangles.

  Available options are:

  - sector_colors (default, `[]`): a list of colors for sectors. When there are more sectors than specified colors, the extra necesary colors are chosen at random. See `color` to learn more about them.
  - pie_center (default, `[0,0]`): diagram’s center.
  - pie_radius (default, `1`): diagram’s radius.
  - All global `draw` options, except `key`, which is internally assigned by `piechart`. If you want to set your own values for this option or want to build complex scenes, make use of `piechart_description`.
  - The following local `draw` options: `key`, `color`, `fill_density` and `line_width`. See also `ellipse`.

  Function `piechart_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects. There is also a function `wxpiechart` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Example:

      (%i1) load ("descriptive")$
      (%i2) s1 : read_list (file_search ("pidigits.data"))$
      (%i3) piechart(
              s1,
              xrange  = [-1.1, 1.3],
              yrange  = [-1.1, 1.1],
              title   = "Digit frequencies in pi")$

  See also function `barsplot`.

Function: scatterplot (list)
Function: scatterplot (list, option_1, option_2, …)
Function: scatterplot (matrix)
Function: scatterplot (matrix, option_1, option_2, …)
Function: scatterplot_description (…)

  Plots scatter diagrams both for univariate (list) and multivariate (matrix) samples.

  Available options are the same admitted by `histogram`.

  Function `scatterplot_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects. There is also a function `wxscatterplot` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Examples:

  Univariate scatter diagram from a simulated Gaussian sample.

      (%i1) load ("descriptive")$
      (%i2) load ("distrib")$

      (%i3) scatterplot(
              random_normal(0,1,200),
              xaxis      = true,
              point_size = 2,
              dimensions = [600,150])$

  Two dimensional scatter plot.

      (%i1) load ("descriptive")$
      (%i2) s2 : read_matrix (file_search ("wind.data"))$

      (%i3) scatterplot(
             submatrix(s2, 1,2,3),
             title      = "Data from stations #4 and #5",
             point_type = diamant,
             point_size = 2,
             color      = blue)$

  Three dimensional scatter plot.

      (%i1) load ("descriptive")$
      (%i2) s2 : read_matrix (file_search ("wind.data"))$
      (%i3) scatterplot(submatrix (s2, 1,2), nclasses=4)$

  Five dimensional scatter plot, with five classes histograms.

      (%i1) load ("descriptive")$
      (%i2) s2 : read_matrix (file_search ("wind.data"))$

      (%i3) scatterplot(
              s2,
              nclasses     = 5,
              frequency    = relative,
              fill_color   = blue,
              fill_density = 0.3,
              xtics        = 5)$

  For plotting isolated or line-joined points in two and three dimensions, see `points`. See also `histogram`.

Function: starplot (data1, data2, …, option_1, option_2, …)
Function: starplot_description (…)

  Plots star diagrams for discrete statistical variables, both for one or multiple samples.

  data can be a list of outcomes representing one sample, or a matrix of m rows and n columns, representing n samples of size m each.

  Available options are:

  - stars_colors (default, `[]`): a list of colors for multiple samples. When there are more samples than specified colors, the extra necesary colors are chosen at random. See `color` to learn more about them.
  - frequency (default, `absolute`): indicates the scale of the radii. Possible values are: `absolute` and `relative`.
  - ordering (default, `orderlessp`): possible values are `orderlessp` or `ordergreatp`, indicating how statistical outcomes should be ordered.
  - sample_keys (default, `[]`): a list with the strings to be used in the legend. When the list length is other than 0 or the number of samples, an error message is returned.
  - star_center (default, `[0,0]`): diagram’s center.
  - star_radius (default, `1`): diagram’s radius.
  - All global `draw` options, except `points_joined`, `point_type`, and `key`, which are internally assigned by `starplot`. If you want to set your own values for this options or want to build complex scenes, make use of `starplot_description`.
  - The following local `draw` option: `line_width`.

  Function `starplot_description` creates a graphic object suitable for creating complex scenes, together with other graphic objects. There is also a function `wxstarplot` for creating embedded histograms in interfaces wxMaxima and iMaxima.

  Example:

  Plot based on absolute frequencies. Location and radius defined by the user.

      (%i1) load ("descriptive")$
      (%i2) l1: makelist(random(10),k,1,50)$
      (%i3) l2: makelist(random(10),k,1,200)$

      (%i4) starplot(
              l1, l2,
              stars_colors = [blue,red],
              sample_keys = ["1st sample", "2nd sample"],
              star_center = [1,2],
              star_radius = 4,
              proportional_axes = xy,
              line_width = 2 ) $

Function: stemplot (data)
Function: stemplot (data, option)

  Plots stem and leaf diagrams. Unique available option is:

  - leaf_unit (default, `1`): indicates the unit of the leaves; must be a power of `10`.

  Example:

      (%i1) load ("descriptive")$
      (%i2) load("distrib")$
      (%i3) stemplot(
              random_normal(15, 6, 100),
              leaf_unit = 0.1);
      -5|4
       0|37
       1|7
       3|6
       4|4
       5|4
       6|57
       7|0149
       8|3
       9|1334588
      10|07888
      11|01144467789
      12|12566889
      13|24778
      14|047
      15|223458
      16|4
      17|11557
      18|000247
      19|4467799
      20|00
      21|1
      22|2335
      23|01457
      24|12356
      25|455
      27|79
      key: 6|3 =  6.3
      (%o3)                  done

Previous: Functions and Variables for specific multivariate descriptive statistics, Nach oben: Package descriptive [Inhalt][Index]