PLOT - Version 1.72L February 26, 1993
====================
By:
John Cordes
Department of Physics
Dalhousie University
Halifax, N.S.
Canada B3H 3J5
Telephone: (902) 494-2313
email: cordes@ac.dal.ca
Copyright John Cordes 1990 - 93. PLOT is freely distributable
provided this document is distributed with the executable file
PLOT172L.PRG.
Bug reports, comments or suggestions are welcome.
**********************************************************************
Brief Description of PLOT:
---------------------------
PLOT is a two-dimensional plotting program for the Atari ST which runs
in high or medium (ST) resolution. Its main features are (1) that it
can plot a large variety of functions entered at the keyboard, (2) it
can plot data read from disk files or entered 'by hand' in a built-in
data editor, and (3) it can produce good quality hardcopy on a variety
of printers using GDOS printer drivers and fonts. PLOT was developed
in GFA Basic, Version 3; it is based on an earlier program I wrote in
True Basic. The present version (Plot 1.72L) is compiled in GFA
v3.5E.
'Any' number (i.e. no specific limit, just memory) of curves, in
various line and marker styles, may be overlaid on a single plot; any
combination of individual curves may be saved for printer output.
Brief, context sensitive, on-screen help is available at many stages of
the program at the touch of the <Help> key. Some, but not all, of the
information in the help screens will be repeated below; the user is
urged to read carefully the information in the help screens themselves.
**********************************************************************
============== A More Detailed Description of PLOT ==============
Please note: Additional information may be obtained by scanning the
Revision History notes at the end of this file.
When PLOT first starts up you are prompted to make a choice between
(k)eyboard or (a)rray input. This essentially means: do you want to plot
a function which you will type in at the keyboard ( keyboard input mode
option) or plot a set of data points (array input)? In the latter case
there will be a further prompt: should the data be read from a file, or
do you want to go directly to the data editor to enter some points?
Another possibility at startup is to hit the F1 function key, which
takes you to a GEM screen, with a number of drop down menus. There you
can do such things as run an external program, set some of PLOT's
options, check out which GDOS screen and printer fonts are available, or
call on a set of numerical utilities.
Returning to the command screen (Return to plots, UNDO or ^P from the
GEM screen), where all the real work in PLOT is done, let's suppose
you choose option (k), keyboard function entry.
1. Editing Keyboard Entry
When you are being prompted for entry of a function or a numeric
variable, the normal editing features are (usually) available: <Esc> to
clear the field, Delete, Backspace and Arrow keys all work; in addition
<Home> takes you to the beginning of the input string and <Control-Home>
takes you to the end. <Control-Left Arrow> and <Control-Right Arrow>
also move the cursor to the beginning and end, respectively, of the
input field.
When done entering a function (press the Help key at any time for
guidance on the available functions and other matters), just press
Return to get to the screen where the Plot Box parameters can be
entered/modified; you can simply accept Plot's defaults with a single
press of the Return key. See below (in Section 3: Function Plotting) for
some examples of possible functions for typing in at the keyboard.
2. The Plotting Box
This program doesn't go in for automatic scaling! The user is always
prompted at the beginning of plot construction for the range of the
plotting box (i.e. xlower, xupper, ylower, yupper) and tick/label
spacings, etc. The actual *size* and *location* on screen of the
plotting box can be set from the alternate (GEM) screen (the box
coordinates are described in the next paragraph); also the
presence/absence of the outer frame can be toggled from the menu bar.
If you wish to change the default settings of the size and location of
the plotting box on the screen, you should be aware that the coordinates
used are pixels, measured relative to the upper left hand corner of the
screen. For the high resolution screen the range is 0 to 639 pixels
horizontally and 0 to 399 pixels vertically. For the medium resolution
screen the range is 0 to 639 horizontally and 0 to 199 vertically.
A brief rundown on the variables you will be prompted for in setting up
the plotting box:
XLOWER: x-coordinate of left edge of plotting box
XUPPER: x-coordinate of right edge of plotting box
XTICK: spacing of the minor tick marks. If set to zero the x-axis will
be omitted entirely. If xtick < 0, there will be no major or minor
ticks on the x-axis but there will still be ticks on the surrounding
frame (which I refer to as the plotting box).
XLABEL: spacing of the major tick marks. The labels will be placed at
the major ticks if xlabel > 0. If xlabel = 0 there will be no major
ticks or labels anywhere. If xlabel < 0 there will be no labels but
major ticks will occur at spacing ABS(xlabel).
*********** Summary of various tick/label settings ***********
1. xtick>0,xlabel>0: Standard case. Minor ticks at xtick; major
ticks and labels at xlabel.
2. xtick=0,xlabel>0: Omit x-axis. Major ticks and labels on box.
3. xtick<0,xlabel>0: Omits x-axis ticks. Major/minor ticks/labels
on box.
4. xtick>0,xlabel=0: No labels. Only (minor) ticks at xtick.
5. xtick=0,xlabel=0: No x-axis, no ticks, no labels.
6. xtick<0,xlabel=0: No x-axis ticks. Minor ticks on box; no
labels.
7. xtick>0,xlabel<0: Omits labels; still have x-axis
major/minor ticks.
8. xtick=0,xlabel<0: Omit x-axis. Major ticks on box, no labels.
9. xtick<0,xlabel<0: No x-axis ticks. Major/minor ticks on box; no
labels.
Of course, if the plot box (i.e. the outer frame) is not being drawn
(it can be toggled on/off in the alternate screen) some of the above
statements must be modified in a reasonably obvious way.
********************************************************************
YLOWER/YUPPER: Similar to xlower/xupper (see above).
YTICK/YLABEL: Similar to xtick/xlabel (see above).
GRAIN: This parameter determines the number of function evaluations,
i.e. the fineness of the 'mesh'. The recommended range is (4..2000),
but the actual lower limit is 1, while the upper limit is constrained
by the available memory in your machine, at least for screen plotting.
I have tried grain = 10,000 with no problem. However, saving a curve
for printer output is another matter. At the moment there is a hard
coded constraint of a little less than 10,000 for the total number of
function values which can be saved for later GDOS printing; if there
are arrays involved the x-coordinates need to be stored as well.
LINE STYLE/THICKNESS: The best way to find out about the line styles
available is to run the program and use the Help key to read help
screen number 3. The line thickness should be an odd number in the
range 1..35. No harm is done by entering an even number but you won't
get it! Also, if the line thickness chosen is anything greater than
one, the style reverts to the simple solid line (style 1). Therefore,
to get one of the styles 2..6 you must enter 1 for the line thickness.
The available line styles are:
1 = Solid
2 = Long dash
3 = Dot
4 = Dash,dot
5 = Dash
6 = Dash,dot,dot.
The negative line styles are used to access the individual point
plotting mode. E.g. entering line style -8 (negative 8) results in a
small solid box being plotted at each of the mesh points; no connecting
line is drawn in this case. See help screen 3 for descriptions of the
other 7 point styles.
Available marker (point) styles are:
-1 = Dot (.)
-2 = Plus (+)
-3 = Asterisk (*)
-4 = Square ([])
-5 = Diagonal Cross (X)
-6 = Diamond (<>)
-7 = Solid box
-8 = Small solid box
GRID: This parameter controls whether or not a pattern of grid lines
will appear on the plot. If set to 1, a mesh of horizontal and
vertical grid lines will appear at the major tick intervals; if grid
is set to 0 (the default) no grid lines appear. The line style for the
grid may also be chosen (styles 1-6).
3. Function Plotting
In addition to the standard arithmetic operators +, -, *, /, ^, the
following functions of the single variable x are supported: SIN, COS,
TAN, ASIN, ACOS, ATN, EXP, LOG, SQR, SINH, COSH, ABS, SGN, GAMMA, and
HVS (Heaviside step function: HVS(x) is defined to be equal to 1 for x
>= 0 and to be 0 for x < 0.). In addition, two kinds of Bessel
functions are supported at present: BSJ(a,x) - the Bessel function of
the first kind (usually called BesselJ(a,x), or J(a,x)) and BSI(a,x) -
the modified Bessel function I(a,x). The Bessel functions accept real
constants a (>=0) for the order; however, if the order entered is
non-integer, x will be restricted to values >=0. The Airy function,
AI(x) (x positive or negative), is also supported.
The function parser is not case sensitive - the function names are shown
in upper case in this document simply for easy visibility. [See also
below for the INTEGRATE command].
The maximum allowed length for a function is around 380 characters or
so. It's not the parser that's limited to any particular length, but
rather the limitation comes about from what is then done with the
function - e.g. plotting of a very long function is more likely to
cause a problem (such as error messages, followed by an exit from the
program, quite possibly) than using the expression evaluator. I have
successfully plotted functions with 387 characters, and have used longer
functions in the expression evaluator.
Some effort is made to trap singular behaviour so that, for example, the
function 1/x can be plotted in a solid line style over a region spanning
the origin. Some mathematical liberties are taken in the process, so
that, for example, if a plot of SQR(x) is requested in the range -5 < x
< 5, the plot is given properly for positive x but nothing is shown in
the region where x is negative and the square root doesn't exist (in the
domain of real numbers). The lesson here is that in certain cases the
apparent plotting of a zero value should not necessarily be taken to
mean that the function is actually zero there! In addition you should
be warned that if you try taking a *function* of SQR(x) (such as
SIN(SQR(x)) or BSJ(1,SQR(x)), say ), with negative values of x being
required in the plotting range, a fatal error may well occur; the
program will quite likely quit abruptly and ungracefully exit back to
the desktop (or shell or whatever). Sorry about that.
Some examples of functions which could be entered at the (k)eyboard
prompt are:
SIN(pi*x/4) - Ordinary trigonometric function
BSJ(1,x^2) - Bessel function J(1,x^2)
BSJ(.5,x) - Bessel function of order 1/2
.5*HVS(3+x)*HVS(3-x) - Draws a sort of 'top hat' function in range (-3,3)
4. Integration
An additional possibility in function plotting mode is to plot the
integral of a function, from a specified lower limit to the variable
upper limit x. The syntax for this is to enter INTEG(f(x),a) where f(x)
can be composed of the functions listed above and 'a' is the lower limit
of the integral. So for example
INTEG(.5*BSJ(1,x),0) - Integrates (1/2) times the Bessel function
J(1,x), with lower limit of integration 0.
x
/
i.e. | dx [0.5*J(1,x)] will be plotted as a function of x.
/
0
SIN(pi*x)*INTEG(BSJ(1,x),0)/COS(x) is also allowed. (Try to avoid
dividing by a zero value though, since an error will likely occur.)
However, the integration cannot occur as the argument of some other
function, so:
SIN(INTEG(x,0)) is ILLEGAL.
The rule is simply that there must not be parentheses around the INTEG.
HINT: If a syntax error is reported (e.g. missing parenthesis or Bessel
function index not a constant) when entering a function, and you have
trouble getting rid of the error message no matter how you edit your
function, try exiting function entry mode (use ESC to clear the edit
line and enter a backslash '\'), then go into (k)eyboard mode and try
again.
5. Coordinate Mode
When the function has been plotted the console bell will sound and you
will see a notice on the screen to the effect that pressing <Esc> will
take you into coordinate mode. If you accept this invitation the mouse
cursor will become a crosshair with which you can read off the (x,y)
coordinates of any point on the screen. This feature is especially
handy for finding zeros of functions, or the x-value at which two curves
cross.
Saving the Coordinates:
After clicking the mouse at a point on the plot, if you press the <s>
key, a little message will flash on the screen saying 'saved'. This
means that the coordinates of that point have been recorded for possible
later saving in a disk file. When you exit coordinate mode with another
<Esc>, if any 'saves' have been made you will be asked if you really
want to save a file and then be prompted for a disk file name (in an
item selector box - the default extension .COO doesn't have to be used);
the file is a simple ascii file with a list of the coordinate pairs
selected.
If you do not want to enter coordinate mode, just touch another key,
such as the space bar. If you exit (or bypass) coordinate mode without
meaning to you can still press <Esc> later to re-enter coordinate mode.
6. After Coordinate Mode
(a). Pressing <Help> gives access to the 9 built-in help screens, as
usual.
(b). Pressing <F1> takes you directly to the 'alternate screen'. This
is a screen with a standard drop-down menu bar, from which various
parameters may be set or utilities accessed. Access to desk accessories
is also available here. Under File there are options to save a plot as
an uncompressed Degas file (.PI3 or .PI2, depending on the resolution),
or to run an external program. The printer device number can also be
altered from the default value (21) in this screen.
(c). Pressing <L> enters legend mode. Assuming you are running with GDOS
active, you will be prompted first for the Font ID number to be used.
This will be, for example, 2 for a Swiss font, 14 for a Dutch font, etc.
If you don't know the ID numbers for the fonts you have available, don't
despair! By going to the GEM screen (with the F1 key) and selecting
Fonts... under the Printer menu heading, PLOT will load the disk-based
screen and printer fonts available and present a table of those found.
The screen fonts will have the appropriate Font ID's listed for each
face; make a note of the ID numbers for future reference. The tables
will show the point sizes available for each typeface. After specifying
the typeface to be used by entering a Font ID, next enter the point
size. For comparison, the axis labels in PLOT are in Swiss 18 point.
For best results, try to use a point size for which you have both screen
and printer fonts available.
You will be prompted to enter some text. When done press <Return> and
you will be asked whether the legend, or floating label, should be
horizontal or vertical. After answering that query, you can move the
legend around the screen with the mouse - click with the left button to
'deposit' the text on the screen at the desired places. When you have
finished clicking press <Esc> to 'paste' down your choices, or <Undo> to
remove all the legends just deposited. Sorry, but there is at the
present no way to move (or remove) floating labels once they have been
pasted in place. You may notice that the labels are not always
immediately re-drawn on the screen after some activity; they will
(usually!) appear 'soon' and in any case will almost certainly be
printed. You can press <L> again to add further legends or proceed to
step (d).
(d). Pressing <S> is essentially a 'continue' command: you will be
asked whether you want to save this curve for printing (this assumes
GDOS is present in the system; if it isn't this prompt will be
bypassed); assume for now that you answer no. You will then be asked if
you want to change the plot parameters (if this is the first curve in
the plot) or if you want to plot any more curves (if this is not the
first curve or if you have finished trying new settings for the plot
parameters (such things as xlower, grain, style, etc.).
7. Array Plotting
Choosing, at startup, option (a) for array plotting presents the user
with a further choice: reading a data file off disk (f) or using the
simple built-in data editor (e). Then, either (option (f)) a file
selector box will appear (default extender ".ASC") for choosing a data
file, or option (e) lands you in the data editor.
If a data file is read in you will be told the number of points read
(the maximum number allowed is 2048) and then given the option of
looking at or modifying the data in the editor, transforming the data in
various ways, or plotting the data either 'as is' or with fitted curves
(a linear fit, a polynomial fit (more about this later), a fast cubic
spline which passes through all the data points, or a smoother (but MUCH
slower) spline fit which doesn't necessarily pass through the data
points. For this latter option (ArrayOp 4) the spline order may be
input - the allowed values are 1, 2, or 3 (e.g. this last would mean
the spline is with cubic curves). More details on these options may be
found below.
============= Data Files ====================
The format of the data files is illustrated in the following examples
(see also the file SAMPLE1.ASC, which should be included in this
distribution):
; comment1: this data file might be output from a Fortran program, say.
; comment2
.
.
.
; commentN
.27 3.4
1e-11 4e12
0 0
11 -.1
Any number of comment lines may occur at the BEGINNING of the file. The
*first* character on a comment line must be a semi-colon <;> . After
this come the x-y coordinate pairs. The separators may be spaces (any
number) or a comma; the separator type should not be mixed in a single
file, however; i.e. don't use commas for some coordinate pairs and
spaces only for other pairs. The following is ok, though:
.27, 3.4
1,2
-2.5, 7
i.e. when a comma is (consistently) used as the separator there may
also be leading/trailing spaces on the x and y values.
Summary of Array Options:
=========================
ArrayOp 0: Just pressing <Return> at the Array Ops menu gives this by
default. Plots the data points 'as is'. This allows for using
individual markers for the data points (use a negative line style) or
drawing a continuous curve through the points (as in function plotting).
ArrayOp 1: Linear fit - a simple least squares straight line fit. The
slope(m) and intercept(b) are shown on the screen with the fitted line.
There is no way to recover these values once this screen has been left.
At the moment this option is somewhat superfluous since option 2 (see
below) can be used with degree set to 1.
ArrayOp 2: Polynomial fit - the user is prompted for the degree of the
polynomial to be used (this is the exponent of the highest power of x in
the polynomial). E.g. a(1)+a(2)*x+a(3)*x^2 has degree 2, and 3
coefficients to be determined, so at least 3 data points are required.
If you enter a degree which is greater than one less than the number of
data points the program sets degree=Ndatapoints -1. The fitting is done
by a singular value decomposition of the 'design' matrix, rather than
directly solving the so-called normal equations. This SVD technique is
slower (and takes a lot more code) than using the normal equations but
is much more informative and reliable (see, e.g. Numerical Recipes, by
Press, Flannery, Teukolsky and Vetterling, p.518 in the Fortran volume).
After entering the desired degree for the fitting polynomial you will be
asked for the range of x - values over which the polynomial should be
drawn (you may only want the fitted curve to be shown in the
neighbourhood of the data points rather than over the whole range of the
plotting box). Then the curve will be plotted.
Viewing the Fitting Parameters and Singular Values
--------------------------------------------------
After finishing with the coordinate display mode and pressing <S> to
move on, you will be asked if you want to see the results of the fitting
routine. Here you see not only the polynomial coefficients but also the
singular values of the design matrix. Some of these may have been set
to zero by the program because they fall below the limit set by the
relative error tolerance. PLOT uses a default tolerance of 1.0E-06;
this may be modified while you are on the fitting parameters screen by
pressing <Control-T>. (The new value will stay in effect until the
present series of plots is completed unless of course the value is
edited again.) When you leave the parameters screen the fitting
parameters and the coefficients are lost, so write them down if you need
them! However, the polynomial coefficients can optionally be saved into
a file before leaving this screen.
The next query is whether anything more is to be done with the data?
Answer yes if you want to plot the individual points (Option 0), try a
different fitting routine, use the data editor, etc.
ArrayOp 3: This is a fast cubic spline interpolation through all the
data points. PLOT will prompt for xmin and xmax values for drawing the
resulting curve.
ArrayOp 4: This is a slow spline fit (not just interpolation) to the
data. It is so slow that it is probably impractical for data sets with
more than about 15 - 20 points, say (unless you are very patient!). The
order of the spline is input by the user; 3 is a cubic spline (but *not*
the same as option 3 - try it out and see).
*********************************************************
8. Printing
Good quality hard copy is possible if GDOS is present in the machine and
a suitable printer driver plus font files are available on disk. The
default device number for the printer driver (the number used in your
ASSIGN.SYS file) is 21 - this can be altered with a drop down menu
selection in the alternate screen; if you *are* going to alter the
device number I strongly recommend that you do it when starting up PLOT,
before you forget (the voice of experience speaking...). The program has
been tested with the 9-pin driver FX80.SYS (on a Citizen 120D), the
24-pin driver LQ800.SYS (on a Star NX-2400 and an Epson LQ500) and the
Atari laser printer driver SLM804.SYS (on an SLM804; I haven't tried it
on an SLM605 but assume it will work).
If GDOS is present, (it, or a replacement, such as G+Plus must have been
loaded at boot time by being in the AUTO folder), you will be prompted
at a suitable stage to see if a given curve should be saved for
printing. I will elaborate a little on this: You can overlay as many
curves as you please in a single plot, and any or all curves can be
tagged for plotting. This means that the selected curves, together with
any floating labels/legends which you may have added to the plot via the
<L> key, will be printed on a single plot, after you have declared that
no more curves are to be added to the plot.
Warning: saving array plots can be deceptive. The way things are set
up at the moment, only one curve is saved (the most recent) for each
data array that is read in. This means that if you want to plot both
the 'raw' data points and a cubic spline fit, and have both curves
printed, you must load the data file twice: the first time plot the
points only (ArrayOp 0) and save the curve for printing, the second
time plot the cubic spline (ArrayOp 3) and save that curve for
printing.
You can also save the plot to a file GEMFILE.GEM by 'printing' with
device number set to 31 (metafile) - the ASSIGN.SYS file must contain
the metafile driver META.SYS for this to work. This file can then be
printed with Migraph's OUTPRINT.PRG; I don't particularly recommend
trying to do much with the file in EASYDRAW itself, you'll find it's
pretty 'messy'.
[If GDOS is NOT present the only reasonable prospects for hardcopy are
either saving as a Degas picture or doing a screendump with Alt-Help;
SNAPSHOT.ACC doesn't get along well with PLOT at all.]
At the time when a curve is first selected for printing, PLOT will go to
disk and look for the printer driver according to the device number
chosen (default: 21). This number should match the number given to the
printer driver in the ASSIGN.SYS file. If the driver is found PLOT will
offer some default scaling factors for both the horizontal and vertical
directions, appropriate to the resolution of the device to which you are
planning to send the output. These typically result in a printed plot
of about 5.5" (horizontal) by 4.5" (vertical) on a 24-pin printer and
about 4.25" by 3.25" on a 9-pin printer; this assumes that you have not
altered the default plotting box size for the on-screen display. Your
results may vary, however; do some experimenting with the scale factors!
The printouts look much better on the 24-pin printers (using Migraph's
printer drivers) than on the 9-pin -- at least, that's been my
experience.
============= ASSIGN.SYS files ================
I usually use the same ASSIGN.SYS file used by EASYDRAW. The actual
printer driver and font files must be available on disk in the location
shown in the PATH variable (in the ASSIGN.SYS example file below the
fonts and driver would be in folder GEMSYS on drive A:).
PATH = A:\GEMSYS\
; Change A: to drive with \GEMSYS\ folder
00p screen.sys
; --START OF SCREEN FONTS--
01p screen.sys
02p screen.sys
03p screen.sys
; list your medium res screen fonts here.
04p screen.sys
; list your screen fonts for the ST mono screen here.
; -- START OF PRINTER FONTS --
;21 FX80.SYS ; Epson 9-pin and compatibles printer driver
; SWISS (Sans Serif) 9-pin printer fonts
;EPSHSS07.FNT
;ATSS10EP.FNT
;ATSS12EP.FNT
;EPSHSS14.FNT
;ATSS18EP.FNT
;ATSS24EP.FNT
;EPSHSS28.FNT
;EPSHSS36.FNT
21 LQ800.SYS ; Epson 24-pin and compatibles printer driver
; SWISS 24-pin printer fonts
P24MSS07.FNT
ATSS10SP.FNT
ATSS12SP.FNT
ATSS18SP.FNT
ATSS24SP.FNT
P24MSS36.FNT
; METAFILE
31r META.SYS
Memory
------
Memory can be a problem in using GDOS and its associated drivers and
fonts. When PLOT is first run it displays the free memory remaining -
this figure must be at least around 330K for the 9-pin or 24-pin drivers
to work. If you're close to the limit you may only get a few fonts
loaded; also I'm not sure what happens if the memory is very tight and
you try to save several curves for printing on the same plot - one or
two curves should be alright. I have tried to put in a fair amount of
intelligent error trapping in case insufficient memory is found, but
it's always possible you could have a crash.
In some tests with the SLM804 I used a Mega-4 and allocated over 3
Megabytes for the GDOS stuff (combination of the large printer
resolution and many fonts in the ASSIGN.SYS file). 1.4 Megabytes or so
will allow several SLM804 printer fonts (and the SLM driver). The
minimum memory required to allocate to the laser printer driver itself
(no fonts) seems to be about 980,000 bytes, though in some tests I've
seen this go as low as 940,000 bytes. The additional memory required by
each font to be loaded corresponds quite well to the size of the font
file itself. The order of fonts in your ASSIGN.SYS file is the order in
which fonts will be loaded (this is true on my system anyway, using
G+Plus; I don't know if it's universally true), so if there are 2 or 3
printer fonts you want to be available, list them first. You can use the
Font display feature of PLOT (function key F8 in the GEM screen) to
experiment a little with some of this; the information may also be
useful for operating other GDOS based programs. Be warned that if you
set the memory to be reserved for the program too low a crash will
result, requiring a re-set.
**********************************************************************
Revision History
================
1.72L:
1. Fixed a couple of places where the path information introduced in
v1.72H was getting lost.
1.72J:
1. Speeded up data window scrolling with the arrow keys.
1.72I:
1. Changed screen input routine for the range limits in cubic spline
fit plotting, to allow for arrays which might have x-coords such as
2E13; previously such a large number would not have been displayed
correctly.
1.72H:
1. In array plotting mode, it's now allowed to go in and out of
cross-hair mode (with the ESC key) repeatedly.
2. Introduced new path saving features for data files and running
external programs. The program is now much more convenient to use
when several data files are to be read from some folder.
1.72E:
1. Changed the GDOS printer device detection routine to recognize more
printers, including the DeskJet 500.
2. Minor improvements to the data editor window handling, especially
for cases where the number of data points is 17 (the maximum which
can be displayed in the window at a time) or a little over.
3. Fixed a recently appearing bug which messed up the invocation of the
data editor without a data file having being read in.
1.72A:
1. Corrected a bug in the data file reading routine whereby the last
line of data was missed if there was no blank line at the end of
the file.
1.72:
1. Grid lines may now be put on the plot.
2. Automatic sorting of data arrays is no longer done. Sorting was added
in v1.52, but was concealed from the user. As of version 1.72,
sorting is an option available in the data editor screen by pressing
the <s> key. This should speed up operations on large arrays which
don't need sorting. Note that if you insert points (in the data
editor) out of order, it will be advisable to do a sort before
leaving the editor if you plan to plot in a continuous line style; if
you're just going to plot individual points then there's no need to
do a sort.
3. Keyboard controls have been introduced for scrolling the data editor
window, to complement the usual mouse operated scroll bar. Up/down
arrows scroll one line at a time, shift up/down scroll by a
screenful, and Home/Shift-Home move to the beginning/end of the
array.
1.71:
1. Many of the information boxes resulting from menu selections in the
GEM screen have been re-written as conventional GEM dialog boxes
(with embedded code, so there's still no .RSC file with PLOT).
2. Legends, or floating labels as they are sometimes called, now make
use of GDOS screen fonts, if GDOS is active. Any of the typefaces
and point sizes available may be used. Lists of the (GDOS) screen
and printer fonts and point sizes available may be viewed under the
Printer menu heading in the GEM screen (or function key F8).
1.68:
1. The modified Bessel functions BSI(order,x) now allow a real, not
just integer, constant for the order.
2. The Airy function, Ai(x), is now built in. It's evaluation is
expensive, since it is calculated in terms of fractional order
Bessel functions, which are themselves much more time consuming
than integer order Bessel functions.
1.66:
1. Changed GDOS printer driver detection routine to allow a range of
resolutions for each class of printer; these had previously been
hardcoded to specific values (e.g. INTOUT(0) = 2399 for the
SLM804).
1.65:
1. Fixed bug which caused program to quit if the (d)efault option
was used at the plot parameters screen.
2. A few changes were made concerning the entry of very long
functions in keyboard mode. There should now be less chance
of overflow onto a second line.
3. A problem which sometimes arose in calculating Bessel functions
of order 2.5 and greater, for x > 25, has been fixed.
1.64a:
1. The configuration file has been extended to include the functions
in the history buffer, as well as the GDOS device number. Config
files can be saved (^G) and loaded (Alt-G) at the alternate GEM
screen. As before, if a config file is called PLOT.CFG and is
located in the directory from which PLOT is run, it will be
automatically read in at startup.
1.60:
1. The INTEGration feature has been enhanced by allowing for
additional functions to appear before and after the integral,
e.g. it is now permissible to do
sin(x)*integ(x,0)/pi
The integral cannot, however, appear as the argument of a
function, so there should never be parentheses around
integ(x,a).
2. The Bessel functions BSJ (Bessel functions of the first kind)
now accept real constants (not just integer) for their order.
This enables one to use the root-finding capability in PLOT
(Alt-Z at the GEM menu bar screen) to find the zeros of
spherical Bessel functions, since they are the same as the
zeros of half-integer order J's. The real constant for the
order must be non-negative, and if the order is indeed
non-integer, the function BSJ will only return sensible values
for non-negative x. It should be noted that the Bessel function
calculation with fractional order is much slower than in the
case of integer order; I will be attempting to optimize this
somewhat but am not expecting very significant improvements.
Technical note: the integer order Bessel function calculations
are done using polynomial approximations, but for fractional
order a backwards recursion calculation is carried out.
3. The saving of functions into the function history buffer can be
toggled with Alt-F. If one of the previously saved functions is
called up, using the up- and/or down-arrow keys, any edits to
that function are automatically saved. This means that even
when function saving is OFF, the previously saved functions
always contain the most recently used set of parameters.
4. In the Calculator, or expression evaluating, mode (Alt-C in
the alternate screen), a feature has been added to make it
simpler to repeatedly evaluate a function at different values
of x. Just type a vertical bar (Shift-backslash) right after
the function and then type the numerical value of x at which
you want the function evaluated. For example
sin(x)|22
will return the value of sin(22), and the cursor will
automatically be positioned after the bar, ready for input of
another value.
5. The small solid box style (style number = -8) has been made
twice as big, so that printouts on a laser printer would turn
out better. The problem is that on the SLM804 the default line
thickness for curves is one, but that is too fine (in most
cases) on the laser, so I find it better to go to line
thickness 3. But then the small solid box didn't show up very
well over the thicker solid line, consequently I've rather
arbitrarily doubled the size of the small box. The effects of
this have not been tested on a dot-matrix printer; hope it
doesn't cause anybody a problem.
6. It was sometimes a nuisance not being able to get back into
coordinate reading mode, once it had been exited or by-passed.
It is now possible to just hit <Esc> anytime after coordinate
mode has been left, or by-passed, until the <S> key has been
pressed. It's in fact easy now to go repeatedly into and out of
coordinate mode, whenever you're at the 'bare' plot, i.e. no
other prompt is requesting input at the time.
7. The GAMMA function (syntax: gamma(x)) has been added. This
enables the factorials to be accessed, through the relation
Gamma(n+1)=n!
8. I have begun to explore the possibilities of a config file, to
at least partially customize the setup of PLOT for a
particular user. So far all that is possible is to have a one
line ascii file, PLOT.CFG, containing a single number which is
the printer device number, for GDOS printing. Since PLOT comes
with a default device number of 21, some users might wish to
create a file containing the number 23, for instance, if their
ASSIGN.SYS file assigns 23 to their printer driver (otherwise
you have to remember to change the device number in the
drop-down menu screen). The presence of the file PLOT.CFG will
be checked for when PLOT is first run (in the directory from
which PLOT is run) and, if present, will be read.
1.50:
1. pi (=3.14159...) can be used in function entry,
though not when you're being prompted for a *constant*.
Thus, for example, pi/2*cos(pi*x/2) is a legal function
entry, but xupper=pi/2 is not allowed.
2. A function history buffer is now built in, so that
(up to 20) previously entered functions can be scrolled
through with the up/down arrow keys when you're being
prompted for function entry. (Function saving can be
toggled in v1.60).
3. A new menu item, Numeric, appears on the alternate
(GEM) screen. Here you'll find several useful utilities:
Calculator: An expression evaluator. Just type in any
(numerical) expression, such as sin(22), 2.5*bsj(0,pi/2),
etc. and the result will be displayed. If an 'x' appears
anywhere it will be taken to be 0. (See new stuff for
v1.60 for an improvement).
Zeros: Computes zeros for functions entered at the
keyboard. e.g. you could enter the function (at the y:
prompt) 'x^2-9', or something much more complicated. You
will also have to enter the beginning and end of the
x-interval (x1 and x2) which will be searched, and specify
if one (option 0) or 'all' (option 1) roots are wanted.
What does this mean? Well, if all roots are requested
(the default case), the grain setting (defaults to 100) is
used to divide the interval (x1,x2) into sub-intervals and
any sub-intervals for which the function has opposite sign
at the two ends will result in a zero being found. If
only one zero is requested, the first zero will be located
(assuming f(x1)*f(x2) < 0).
Integration: A numerical integration routine, using 20
point Gaussian quadrature in each panel. The number of
panels into which the interval is divided has a default
value of 1, but can be altered easily. If more than 10
panels are set, intermediate (cumulative) results are
shown after each 10 panel set is completed. In most
cases, you'll soon find that accuracy is rarely increased
by setting more than 1 or at most a few panels.
Polynomial Roots: Here a polynomial (of degree up to
size 20) can be entered. Only univariate (single variable)
polynomials are allowed, but the coefficients may be
complex. The (possibly complex) roots are then computed
and displayed.
While in any of these numerical utilities, screen output
may be paused (usually) by pressing any key (other than
Escape - see next sentence) (any key resumes). Pressing
<Esc> aborts the current operation. For example, if you
want to cut short the computation of zeros of some function,
pressing <Esc> aborts and returns you to the function entry
line.
Also: Fixed a bug whereby a (c)ontinue after printing
hardcopy (with GDOS) messed up screen output (some plot size
parameters needed resetting after the workstation output).
1.42:
Fixed a small problem where sometimes the user would be
prompted for curve printing even when no curves had been
saved for printing. This only happened after a (c)ontinue
sequence.
1.41:
The Help screens (accessible by pressing the <Help> key)
are now available at the ArrayOps screen.
Changed the default printer device number (for GDOS) to
21 for the high resolution screen (it used to be set to 23).
Now 21 is used for both cases: monochrome and colour
monitors.
1.34:
Corrected a problem where there was some confusion as to
whether the data editor should show the transformed or
untransformed data. Found that the GFA Interpreter has a
bug to do with arrays, but things are OK in the compiled
version. Same problem occurs with the 3.5E interpreter.
1.33: Fixed some problems with line thicknesses for the curves
occasionally interfering with box frame thickness.
1.30: Changed method of inputting plotting box parameters
(xlower..yupper, line style, etc.) from the 'line at a time'
approach to a full screen editing approach. Now a single
<Return> accepts all the defaults and gets on with the job.
1.26: Added save to disk feature for coordinate pairs read off
the plot.
1.25: Added save to disk feature for the polynomial fit
parameters.
1.23: <t>rim feature added to editor. This enables a data array
to be reduced (trimmed) in size. In the data editor,
pressing the <t> key puts up a small box in which four
parameters are set. These are:
(1) nstart - the number of the first data point to be retained.
(2) nstop - the number of the last data point to be retained (with a
possible exception if lastpoint is set).
(3) ntrim - the trim spacing. E.g. if nstart=2 and ntrim=3, then
every third point will be retained, starting with the second.
Thus the points retained in this example are 2,5,8,... .
(4) lastpoint - Setting this to 1 forces the last (of the original
data set) point to be retained; leaving it at the default of 0
means that the trimmed array will terminate at whatever data pair
occurs at a value of nstart+(integer)*ntrim which is less than or
equal to nstop.
Note that this trimming procedure can be used to delete any
contiguous blocks of data, by using ntrim=1 and suitable values for
nstart and nstop. The deletions occur only in memory, not on disk.
They cannot be undone, except by reading in the disk file again.