cutaxes

Contents

• Arguments
• Description
  • Introduction
  • Titles, legends, datatips
• Examples
  • "ticksmode" and "widths" options. Addressing and customizing the curves
  • Replicated and inverted interval
  • Multi-scaled Y axis
  • Example with Matplot1()
• See also
• History

Arguments

x

vector or matrix of real abscissae of curves to plot.

• If x and y are vectors, we must have length(x)==length(y)
• If it is a vector and y is a matrix, the same abscissae are shared for all curves given as y columns, and we must have length(x)==size(y,1).
• If both x and y are matrices, they must have the same sizes, and x(:,i) are abscissae of y(:,i).

y

real numbers: ordinates of curves to plot. If y is a matrix, each of its columns represents a separate curve.

axes0

Input graphical axes to replot in a piecewise way. .isoview="off" is forced for all its piecewise replicates.

cutaxis

"x" or "y", specifying the discontinuous graphical axis.

intervals

(N x 2) matrix of real numbers: Each row provides both [start,end] bounds of an interval over which all given curves or the input axes0 must be plotted. According to the cutaxis value, given bounds are along the X axis or along the Y one. Any number of intervals may be specified as distinct intervals rows.

On the figure, intervals are plotted from left to right in the order they are specified in intervals. The user may organize and present them as wished.

When an interval is specified such that start > end, the axis is reversed on the interval.

"ticksmode"

By default, ticks and labels of the different parts of the discontinuous axis are drawn "aligned", without specific attribute to distinguish consecutive parts. "ticksmode" is an optional flag allowing to manage ticking and labelling of alternate pieces of the cut axis. It must be followed by one of the following values:

"alt"	Ticks and labels are drawn alternately on the bottom and top sides for the "x" discontinuous axis, or on the left and right sides for the "y" one.
"shift"	Ticks and labels are drawn with a small alternative shift for one interval over two of the discontinuous axis.

"widths"

By default, if N intervals are defined, the full plot width is split into N sections of equal widths, whatever are the |end - start| data ranges. This default plotting mode may be changed using the "widths" keyword, followed by one of the following specifications:

"-"	As the default mode, except that interspaces separating sections are removed.
"isoscaled"	This mode plots data with the same scale for all intervals along the discontinuous axis. The plotting width is proportional to the |end - start| range. "-isoscaled" will do the same, except that interspaces separating sections are removed.
widths	Vector of numbers giving the relative graphical widths of intervals along the discontinuous axis. The vector must have as many values as there are defined intervals. To remove the separating space before an interval, set its width as negative. Its absolute value will be used for the actual width. Only |widths| / sum(|widths|) is considered, in such a way that [1,2,2] and [0.5,1,1] or [0.2,0.4,0.4] are for instance equivalent.

Axes

vector of pointers on plotted sub-axes. The components allow to modify subaxes attributes, like the log mode of the piece of discontinuous axis, the grids, etc. See examples for illustrations.

Axes($) points to the common continuous axes. cutaxes() sets it as the current axes before returning.

curves

list of vectors of pointers on plotted curves (only when they are provided):

• curves(i) is a vector of graphic pointers on all sections drawn for the curve #i defined in y(:,i).
• curves(i)(j) points to the section #j drawn for the curve #i over intervals(j,:).

These identifiers allow to modify curves attributes after plotting. For instance, setting in red all pieces of the curve #2 will be done with curves(2).foreground = color("red"). Setting only its section #3 in dash style is done with curves(2)(3).line_style = 3. An example is given and illustrated below.

The vector of handles of curves #i1 to #i2 > #i1 of the same section #s may be retrieved with Axes(s).children($).children($-i1+1:-1:$-i2+1).

Description

cutaxes() allows to plot some curves along a non-regular axis, like having some hidden intervals. Consecutive visible intervals are drawn without loosing space in-between.

When an input axes axes0 is provided instead of curves, it is replicated as many times as there are intervals, each copy showing the axes contents over an interval. The X, Y, and Z labels as well as the title of axes0 are ignored.

In both cases, cutaxes() draws in the gca() plotting area. If axes0 is gca(), cutaxes() deletes it before returning. Otherwise, axes0 is kept in its own graphical area.

The intervals of the discontinous axis may have distinct scales, distinct linear or logarithmic modes, distinct direct or reversed modes.

A symetrical axis may be plotted by repeating an interval along the discontinuous axis and reverting the clone. See examples.

cutaxes() can be used in conjunction to the following features: subplot(..) or xsetech(..) can be used to define the plotting area before calling cutaxes(). A zoom box spanning over several pieces of the discontinuous axis may be selected interactively.

sca(axes(i));
legend(["Curve 1" "Curve 2"],"in_upper_left");

Examples

"ticksmode" and "widths" options. Addressing and customizing the curves

x = [-7.5:0.5:200]';
y =  exp(x/30).*(1+0.5*sin(x));

gcf().axes_size = [1000 300];
clf

intervals = [-4 6; 10 30 ; 40 100];
[a, c] = cutaxes(x, [y y/2], "x", intervals, "ticksmode", "alt", "widths", [1 1.5 3]);

// Special curves settings:
c(2).foreground = color("red");   // 2nd cuve in red
c1 = c(1);
c1(3).line_style = 8;             // 3rd section of 1st curve in small dashes
c1(3).thickness = 2;              //    .. and thicker

// Invert the common Y axis
//a.axes_reverse = ["off" "on"];

// Setting X-axis of the third section in log:
a(3).log_flags = "lnn";

Replicated and inverted interval

cutaxes() allows to specify overlaying intervals, or the same interval several times, or twice the same but in reverse order. This may be useful in various situations. For a positive radial coordinate, it is thus possible to tick a positive distance from the center on both sides. A side can be plotted in radial linear scale, and the other in radial logarithmic scale to show the asymptotical behavior:

x = logspace(-2,2,500)';
y = sin(10*log(x)).*(x.^0.3);

gcf().axes_size = [1000 370];
clf

intervals = [5 0 ; 0.01 11 ; 11 max(x)];
a = cutaxes(x, y, "x", intervals, "widths", -[2 3 2]);
a(2).log_flags = "lnn";
a(2).sub_ticks(1) = 8;
title "Radial singularity on 0"
ylabel Ordinates
xlabel(a(2), "Radius")

Multi-scaled Y axis:

Example #1, with curves legends:

x = [-8:0.2:100]';
y =  exp(x/14).*(1+0.5*sin(x));
intervals = [0.01 10 ; 10 max(y)];

gcf().axes_size = [1000 400];
clf
[a, c] = cutaxes(x, [y y/2], "y", intervals, "widths", -[1 2]);
c(2).foreground = color("red");
a(2).log_flags = "nln";
a(2).sub_ticks(2) = 8;
xlabel Abscissae
ylabel(a(2), "Ordinates") // a(2) is now the current axes
legend(["Curve 1" "Curve 2"], "in_upper_left");
// Grids
// a($).grid(1) = -1;       // removes the vertical shared grid
// a(1:$-1).grid(:,2)= -1;  // removes the horizontal grids

Example #2, from an axes: Low sinc²() bouncing wings

Here below we plot the curve to create its initial axes in subplot(1,2,1). Then we move gca() to subplot(1,2,2), and we call cutaxes(..) :

x = linspace(-15,15,400);
clf
subplot(1,2,1)
gcf().axes_size = [720 360];
h = plot2d(x, sinc(x).^2)
ax0 = gca();

d = datatipCreate(h, [7.7 0.02]);
xtitle("$\LARGE sinc^2$", "Abscissae [a.u.]", "Amplitude")
grey = color("grey60");
set(d, "mark_size",4, "foreground",grey, "font_foreground",grey, "orientation",8);

subplot(1,2,2)
Axes = cutaxes(ax0, "y",[0 0.1 ; 0.1 1], "widths","-");
is_handle_valid(ax0)  // %T: the initial axes still exists

Now, gca() is kept where we have initially plotted the curve, and we call cutaxes() to replicate it. As a consequence, cutaxes uses the same subplot area, and finally deletes the initial axes after its replication:

x = linspace(-15,15,400);
clf
subplot(1,2,1)
gcf().axes_size = [720 360];
plot2d(x, sinc(x).^2)
ax0 = gca();
Axes = cutaxes(ax0, "y",[0 0.1 ; 0.1 1], "widths","-");
is_handle_valid(ax0)  // %F: the initial axes has been deleted

Example with Matplot1():

clf
gcf().axes_size = [925 455];
subplot(1,2,1)
Matplot1();
xtitle("","","");
title "Matplot1() sample"
x0 = gca();

subplot(1,2,2)
intervals = [-0.03 -0.02; -0.013 -0.007 ; 0 0.01];
axes = cutaxes(x0, "y",intervals, "ticksmode","alt", "widths","isoscaled");

See Also

• plot — 2D plot
• plot2d — 2D plot
• subplot — grids the current figure or frame, and sets the current axes to a chosen cell
• xsetech — set the sub-window of a graphics window for plotting

History