Higher-Level Routines


This chapter describes a number of ``high level'' routines that simplify the composition of complicated graphical images. They include routines for drawing graphs of one variable or function against another (``xy-plots''), histograms, and display of two-dimensional data (functions of two variables). Rather than giving complete details of all the available routines, this chapter just points out some of the ways that they can be used. See Appendix A for details of the calling sequences.


The basic technique for drawing xy-plots is described in Chapter 2, which showed how to make scatter plots using graph markers produced by PGPT and line plots produced by PGLINE. Considerable variation in the appearance of the graph can be achieved using the following techniques.


Use different attributes to distinguish different datasets. Graph markers can be distinguished by choosing different markers, different colors, or different sizes (character height attribute). Lines and curves can be distinguished by line-style, color, or line-width.

Box parameters

If routine PGENV is replaced by calls to the more basic routines (see Section 3.6), including PGBOX, considerable variety in the appearance of the graph can be achieved. For example, one can suppress the tick marks, draw the tick marks projecting out of the box instead of into it, or draw a grid over the whole viewport. Note that PGBOX may be called many times: one might call it once to draw a grid using thin dotted lines, and again to draw the frame and tick marks using thick lines:
      CALL PGSLW(1)
      CALL PGSLS(4)
      CALL PGBOX('G',30.0,0,'G',0.2,0)
      CALL PGSLW(3)
      CALL PGSLS(1)
      CALL PGBOX('ABCTSN',90.0,3,'ABCTSNV',0.0,0)
Note that in this example we have also specified tick intervals explicitly. If the horizontal axis is to represent an angle in degrees, it is convenient to choose a tick interval that is a simple fraction of 360; here we have a major tick interval of 90 degrees and a minor tick interval of 30 degrees.

Stepped-line plots

As an alternative to PGLINE, which ``joins up the dots'' using straight line segments, it is sometimes appropriate to use PGBIN which produces a ``stepped line plot'' (sometimes misleadingly called a histogram) with horizontal line segments at each data point and vertical line segments joining them. This is often used, for example, in displaying digitized spectra.

Error bars

Graphs of real data often require the inclusion of error bars. The two routines PGERRX and PGERRY draw horizontal and vertical error bars, respectively. These routines are usually used in combination with PGPT, e.g., to draw a set of points with 2-sigma error-bars:
      DO 10 I=1,15
          YHI = YPTS(I) + 2.0*ERR(I)
          YLO = YPTS(I) - 2.0*ERR(I)
          CALL PGPT(1, XPTS(I), YPTS(I), 17)
          CALL PGERRY(1, XPTS(I), YLO, YHI, 1.0)

Logarithmic axes

It is commonly required that the x-axis, the y-axis, or both, be logarithmic instead of linear; that is, one wishes to plot the logarithm of the quantity instead of its actual value. PGPLOT doesn't provide any automatic mechanism to do this: one has to adopt log10 x and/or log10 y instead of x and y as world-coordinates; i.e., if the range of x is to be 1 to 1000, choose as world-coordinate limits for the window log 1 = 0.0 and log 1000 = 3.0, and supply the logarithms of x to PGPT and PGLINE. However, PGENV and PGBOX have options for labeling the axis logarithmically; if this option is used in our example, the axis will have labeled major tick marks at 1, 10, 100, and 1000, with logarithmically-spaced minor tick marks at 2, 3, 4, ..., 20, 30, 40, etc. An example may make this clearer:
      CALL PGENV(-2.0,2.0,-0.5,2.5,1,30)
      CALL PGLAB('Frequency, \gn (GHz)',
     1           'Flux Density, S\d\gn\u (Jy)', ' ')
      DO 10 I=1,15
          XPTS(I) = ALOG10(FREQ(I))
          YPTS(I) = ALOG10(FLUX(I))
      CALL PGPT(15, XPTS, YPTS, 17)
This is a fragment of a program to draw the spectrum of a radio source, which is usually plotted as a log--log plot of flux density v. frequency. It first calls PGENV to initialize the viewport and window; the AXIS argument is 30 so both axes will be logarithmic. The x-axis (frequency) runs from 0.01 to 100 GHz, the y-axis (flux density) runs from 0.3 to 300 Jy. Note that it is necessary to specify the logarithms of these limits in the call to PGENV. The penultimate argument requests equal scales in x and y so that slopes will be correct. The program then marks 15 data points, supplying the logarithms of frequency and flux density to PGPT.


The routine PGHIST draws a histogram, that is, the frequency distribution of measured values in a dataset. Suppose we have 500 measurements of a quantity (the sky brightness temperature at 20 GHz, say, in mK) stored in Fortran array VALUES. The following program-fragment draws a histogram of the distribution of these values in the range 0.0 to 5.0, using 25 bins (so that each bin is 0.2 K wide, the first running from 0.0 to 0.2, the second from 0.2 to 0.4, etc.):
      DO 10 I=1,500
          VALUES(I) = ....
      CALL PGHIST(500, VALUES, 0.00, 5.00, 25, 0)
      CALL PGLAB('Temperature (K)',
     1           'Number of measurements',
     2           'Sky Brightness at 20 GHz' )
The histogram does not depend on the order of the values within the array.

Functions of two variables

A function of two variables, f(x,y), really needs a three-dimensional display. PGPLOT does not have any three-dimensional display capability, but it provides three methods for two-dimensional display of three-dimensional data.

Contour maps

In a contour map of f(x,y), the world-coordinates are x and y and the contours are lines of constant f. The PGPLOT contouring routines (PGCONT and PGCONS) require the input data to be stored in a two-dimensional Fortran array F, with element F(I,J) containing the value of the function f(x,y) for a point (xi, yj). Furthermore, the function must be sampled on a regular grid: the (x,y) coordinates corresponding to (I,J) must be related to I and J by:
x = a + bI + cJ,
y = d + eI + fJ.
The constants a, b, c, d, e, f are supplied to PGCONT in a six-element Fortran array. The other input required is an array containing the contour values, i.e., the constant values of f corresponding to each contour to be drawn. In the following example, we assume that values have been assigned to the elements of array F. We first find the maximum and minimum values of F, and choose 10 contour levels evenly spaced between the maximum and minimum:
      REAL F(50,50), ALEV(10), TR(6)
      FMIN = F(1,1)
      FMAX = F(1,1)
      DO 300 I=1,50
        DO 200 J=1,50
          FMIN = MIN(F(I,J),FMIN)
          FMAX = MAX(F(I,J),FMAX)
  200   CONTINUE
      DO 400 I=1,10
        ALEV(I) = FMIN + (I-1)*(FMAX-FMIN)/9.0
Next, we choose a window and viewport, and set up an array TR containing the 6 constants in the transformation between array indices and world coordinates. In this case, the transformation is simple, as we want x = I, y = J:
      CALL PGENV(0.,50.,5.,45.,0,2)
      TR(1) = 0.0
      TR(2) = 1.0
      TR(3) = 0.0
      TR(4) = 0.0
      TR(5) = 0.0
      TR(6) = 1.0
Finally, we call PGCONT; actually, we call it twice, to draw the first five contours in color index 2 (red) and the remaining 5 in color index 3 (green):
      CALL PGSCI(2)
      CALL PGCONT(F,50,50,1,50,1,50,ALEV,5,TR)
      CALL PGSCI(3)
      CALL PGCONT(F,50,50,1,50,1,50,ALEV(6),5,TR)
Normally PGCONT is preferable to PGCONS. See the description in Appendix A for suggestions as to when PGCONS should be used.

Gray-scale plots

The routine PGGRAY is used in a similar way to PGCONT. Instead of drawing contours, it shades the interior of the viewport, the intensity of shading representing the value of the function at each point. The exact appearance of the resulting ``image'' is device-dependent. On some devices, PGGRAY does the shading by drawing many dots, so it can be very slow.

Cross sections

Routine PGHI2D draws a series of cross-sections through a two-dimensional data array. Each cross-section ``hides'' those that appear behind it, giving a three-dimensional effect. See Appendix A for details.