Gnuplot, GLPK

grammar and invocation | variables and expressions | arithmetic and logic | strings | dates and time | multidimensional arrays | sets | functions | execution control | file handles | directories | libraries and namespaces | processes and environment

optimization | linear regression

bar charts | scatter plots | line and surface charts | chart options

gnuplot glpk
version used
 		 5.0 4.52
show version
 		 $ gnuplot --version $ glpsol --version
grammar and invocation
gnuplot glpk
interpreter
 		 $ cat hello.gnuplot
print "Hello, World!"

$ gnuplot hello.gnuplot
Hello, World!		 $ cat hello.model
printf "Hello, World!\n";
end;

$ glpsol -m hello.model
Hello, World!
repl
 		 $ gnuplot none
compiler none none
command line program
 		 $ gnuplot -e 'print 1 + 1;' none
block delimiters
 		 { } { }

Curly braces are used to delimit the block of statements in the body of a for statement.

Curly braces are also used in indexing expressions and set literals.
statement separator newline or ;

A newline preceded by a backslash is ignored.		 ;
end-of-line comment
 		 # comment # comment
multiple line comment
 		 none /* comment line
another comment */
variables and expressions
gnuplot glpk
assignment x = 3.14 # parameters are write once:
param pi := 3.14;
null
 		 none none
null test
 		 none none
undefined variable access
 		 causes error causes error
undefined variable test exists("x") none
remove variable binding undefine x none
conditional expression
 		 x > 0 : x : -x if x > 0 then x else -x
arithmetic and logic
gnuplot glpk
true and false
 		 1 0 1 0

The boolean values are distinct from the integers 1 and 0. When displayed by printf '%s' they render as T and F. There are no boolean literals, however.
falsehoods
 		 0

0.0 is true		 0 0.0
logical operators && || ! and or not

&& || !
relational operators == != < > <= >=

# string comparision:
eq ne		 = <> < > <= >=

== and != are synonyms of = and <>
arithmetic operators

addition, subtraction, multiplication, division, modulus		 + - * / % + - * / mod
integer division
 		 int(x) / int(y) x div y
integer division by zero error error
float division (1.0 * x) / y 7 / 3
float division by zero error error
power 2 ** 32 2 ^ 32
2 ** 32
sqrt sqrt(2) sqrt(2)
sqrt -1
 		 # evaluates to {0.0, 1.0}:
sqrt(-1)		 # error:
sqrt(-1)
transcendental functions exp() log log10()
sin() cos() tan()
asin() acos() atan()
atan2()		 exp() log() log10()
sin() cos() none
none none atan()
atan(y, x)
transcendental constants
e and pi		 exp(1)
pi		 exp(1)
4 * atan(1)
float truncation
round towards zero, round to nearest integer, round down, round up		 int(x)
??
floor(x)
ceil(x)		 trunc(x)
round(x)
floor(x)
ceil(x)

# truncate/round to 2 decimal places:
trunc(x, 2)
round(x, 2)
absolute value
and signum		 abs(x)
sgn(x)		 abs(x)
none
integer overflow
 		 32 bit signed integers are used. Operations which overflow return a float. conversion to float
float overflow
 		 64 bit double precision floats are used. Operations which overflow raise an error. error
complex construction
 		 z = {1.0, 2.0} none
complex decomposition
real and imaginary part, argument and modulus, conjugate		 real(z)
imag(z)
arg(z)
abs(z)
??		 none
random number
uniform integer, uniform float, standard normal		 floor(rand(0) * 100)
rand(0)
none		 # Irand224() generates integer in [0, 2^24):
Irand224() mod 100
Uniform01()
Normal01()
random seed _ = rand(17) $ glpsol --seed 17 -m foo.model
bit operators
 		 << >> & | ^ ~ none
binary, octal, and hex literals none
052
0x2a		 none
strings
gnuplot glpk
string literals "don't say \"no\""
'don''t say "no"'		 "don't say ""no"""
'don''t say "no"'

Quotes can be omitted in the data section when the contents of the string are alphanumeric or match the character class [-+_.]
newline in literal no no
string literal escapes # in double quotes:
\n \r \t \o \oo \ooo		 # in printf format:
\n \t
length strlen("lorem ipsum") length("lorem ipsum")
concatenate "lorem " . "ipsum" "lorem " & "ipsum"
index of substring # indices start at 1;
# returns 0 if not found:
# strstrt("foo bar", "bar",		 none
extract substring substr("foo bar", 5, 8) substr("foo bar", 5, 3)
format string sprintf("%d %.2f %s", 7, 3.1415, "foo") none
number to string "foo" . 4 none
string to number "4" + 7

# causes error:
"foo" + 7		 none
dates and time
gnuplot glpk
current time as unix epoch # seconds since Jan 1, 2000
# add 946684800.0 to get unix epoch:
now = time(0)

# as float:
real_now = time(0.0)		 gmtime()
format time strftime('%Y-%m-%d %H:%M:%S', now) time2str(gmtime(), '%Y-%m-%d %H:%M:%S')
parse time s = "2014-11-30 03:53:59"
t = strptime('%Y-%m-%d %H:%M:%S', s)		 str2time("2014-12-01 19:38:09", "%Y-%m-%d %H:%M:%S")
sleep pause 10

# with message:
pause 10 'sleeping 10s...'		 none
multidimensional arrays
gnuplot glpk
2d literal in separate file; one line for each data point; whitespace delimited:

$ cat data.txt
7 8
9 10
11 12		 # declare in model section:
param a {1..2, 1..2};

# define in data section:
param a: 1  2 :=
      1  7  8
      2  9 10;
3d literal in separate file; one line for each data point:

$ cat data.txt
# city data:
"Los Angeles" 3 7
"New York" 8 4
"San Francisco" 12 1

comment lines are ignored; data which contains whitespace must be quoted
sets
gnuplot glpk
literal set digits := {1, 2, 3, 4, 5};
set from arithmetic sequence

unit difference, non-unit difference		 set digits := {1 .. 5};

set leap_years := {2000 .. 2096 by 4};
membership set s := {1, 2, 3};
set str := if 4 in s then 'yes' else 'no';
intersection set s1 := {1, 2, 3};
set s2 := {2, 3, 4, 5};

set s3 := s1 inter s2;
union set s3 := s1 union s2;
relative complement, symmetric difference set s3 := s1 diff s2;
set s4 := s1 symdiff s2;
cartesian product # 12 pairs:
set s3 := s1 cross s2;
map set s := 1 .. 10;
set squares := setof {i in s} i * i;
reduce set s := 1 .. 10;

param n1 := min {i in s} i;  # 1
param n2 := max {i in s} i;  # 10
param n3 := sum {i in s} i;  # 55
param n4 := prod {i in s} i;  # 10!

# sum of squares:
param n5 := sum {i in s} i * i;
universal test set str1 := if (forall {i in s} i > 5) then 'yes' else 'no';
existential test set str2 = if (exists {i in s} i > 5) then 'yes' else 'no';
functions
gnuplot glpk
define function # body of function must be an expression:
add(x, y) = x + y		 none
invoke function add(3, 7) none
list functions show functions none
missing argument behavior error none
extra argument behavior error none
return value value of the expression which is the function body none
execution control
gnuplot glpk
if if (x > 0) {
  print "positive"
}
else {
  if (x < 0) {
    print "negative"
  }
  else {
    print "zero"
  }
}		 none
while i = 0

while (i < 10) {
  print i
  i = i + 1
}		 none
for do for [i = 1:10] {
  print i
}		 for {i in {1..10}}
{
  printf "%d\n", i;
}
break continue
raise exception
file handles
gnuplot glpk
write line to stdout print "Hello, World!" printf "Hello, World!\n";
write formatted string to stdout printf "%d %.2f %s", 7, 3.1415, 'foo';
write to file # overwrites contents of /tmp/foo.txt:
printf "lorem ispum" > "/tmp/foo.txt";
append to file printf "dolor sit amet" >> "/tmp/foo.txt";
pretty print set s := {1, 2, 3, 4, 5};
param x := 3;
param str symbolic := 'lorem ispum';

display "set: ", s,
  "param: ", x,
  "string: ", str;
directories
gnuplot glpk
working directory # writes working dir to stdout:
pwd

cd "/tmp"		 none
libraries and namespaces
gnuplot glpk
load $ cat foo.gnuplot
print "loaded!"

$ cat main.gnuplot
load 'foo.gnuplot'

$ gnuplot main.gnuplot
loaded!		 none
processes and environment
gnuplot glpk
command line arguments $ cat test.gnuplot
print foo
print bar

$ gnuplot -e 'foo=3; bar=4' test.gnuplot		 none
exit # no way to set exit status:
exit

# or:
quit		 none
command substitution ls_output = system("ls") none
optimization
gnuplot glpk
linear minimization var x1;
var x2;
var x3;

minimize obj: x1 + x2 + x3;

c1: x1 + x2 >= 1;
c2: x2 + x3 >= 1;
c3: x1 + x3 >= 1;

solve;
display obj, x1, x2, x3;
end;
decision variable array set I := {1 .. 3};
var x{I};

minimize obj: sum{i in I} x[i];

c1: x[1] + x[2] >= 1;
c2: x[2] + x[3] >= 1;
c3: x[1] + x[3] >= 1;

solve;
display obj, x;
end;
linear maximization set I := {1 .. 3};
var x{I};

maximize obj: sum{i in I} x[i];

c1: x[1] + x[2] <= 1;
c2: x[2] + x[3] <= 1;
c3: x[1] + x[3] <= 1;

solve;
display obj, x;
end;
constraint in variable declaration set I := {1 .. 3};
var x{I} >= 0;

minimize obj: sum{i in I} x[i];

c1: -x[1] + x[2] >= 1;
c2: x[2] + x[3] >= 1;
c3: -x[1] + x[3] >= 1;

solve;
display obj, x;
end;
unbounded behavior
 		 # Stops execution after solve statement with "LP HAS UNBOUNDED PRIMAL SOLUTION" message.
infeasible behavior # Stops execution after solve statement with "LP HAS NO PRIMAL FEASIBLE SOLUTION" message.
integer decision variable set I := {1 .. 3};
var x{I} integer;

minimize obj: sum{i in I} x[i];

c1: x[1] + x[2] >= 1;
c2: x[2] + x[3] >= 1;
c3: x[1] + x[3] >= 1;

solve;
display obj, x;
end;
binary decision variable set I := {1 .. 3};
var x{I} binary;

minimize obj: sum{i in I} x[i];

c1: x[1] + x[2] >= 1;
c2: x[2] + x[3] >= 1;
c3: x[1] + x[3] >= 1;

solve;
display obj, x;
end;
linear regression
gnuplot glpk
bar charts
gnuplot glpk
vertical-bar-chart.jpg
vertical bar chart		 # echo $'7\n3\n8\n5\n5' > data.txt

set terminal png size 400,300
set output "barchart.png"
set boxwidth 0.9
set style fill solid 1.0
plot [0:6] [0:9] "data.txt" \
  using 0:1 notitle with boxes
horizontal-bar-chart.jpg
horizontal bar chart
stacked-bar-chart.jpg
stacked bar chart
grouped-bar-chart.jpg
grouped bar chart
pie-chart.jpg
pie chart		 see note
histogram.jpg
histogram		 # awk '{ print length($0)}' /usr/share/dict/words > hist.txt

set terminal png size 400,300
set output "histogram.png"
binwidth=1
bin(x,width)=width*floor(x/width)
unset key
plot "hist.txt" \
  using (bin($1,binwidth)):(1.0) \
  smooth freq with boxes
box-plot.jpg
box plot		 # seq 100 | awk '{print rand() ** 3}' > data.txt

set terminal png size 400,300
set output "boxplot.png"
set style boxplot outliers pointtype 7
set style data boxplot
set boxwidth 0.2
plot [0.5:1.5] [0.0:1.1] "data.txt" \
  using (1.0):1:(0.3) notitle
scatter plots
gnuplot glpk
scatter-plot.jpg
scatter plot		 # seq 50 | awk '{x=rand(); print x,x+rand()}' > data.txt

set terminal png size 400,300
set output "scatter.png"
unset key
plot "data.txt"
bubble chart
3d scatter plot
linear-regression-line.jpg
linear regression line
q-q-plot.jpg
quantile-quantile plot
line and surface charts
gnuplot glpk
polygonal-line-plot.jpg
polygonal line plot		 # seq 1 20 | awk '{print rand() + rand() + rand()}' > data.txt

set terminal png size 400,300
set output "polygonal.png"
unset key
plot "data.txt" using 0:1 with lines
additional-line.jpg
additional line		 # seq 1 20 | awk '{print rand() + rand(), rand() + rand()}' \
#   > data.txt

set terminal png size 400,300
set output "two-lines.png"
unset key
plot "data.txt" using 0:1 with lines, \
  "data.txt" using 0:2 with lines
line types
cubic-spline.jpg
cubic spline
function-plot.jpg
function plot		 set terminal png size 400,300
set output 'sin.png'
unset key
plot [-4:4] sin(x)
area-chart.jpg
area chart
surface plot
contour plot
chart-options
gnuplot glpk
set chart title set title "a plot"
plot "data.txt"
axis label
axis limits
logarithmic y-axis
legend # seq 1 20 | awk '{print rand() + rand(), rand() + rand()}' \
#   > data.txt

set terminal png size 400,300
set output "legend.png"
plot "data.txt" using 0:1 with lines title "first", \
  "data.txt" using 0:2 with lines title "second"
legend options
colors # use a string to specify a color:
set terminal png background "black"
set terminal png background "#000000"

# list recognized color names:
show colors
___________________________________________________________________ ___________________________________________________________________

General

version used

The version used to test examples in this sheet.

show version

How to determine the version.

Grammar and Invocation

interpreter

How to execute a script.

pari/gp

The shebang style notation doesn't work because GP doesn't recognize the hash tag # as the start of a comment.

The -q option suppresses the GP startup message.

After the script finishes it will drop the user into the REPL unless there is a quit statement in the script:

print("Hello, World!")

quit

Variables and Expressions

Arithmetic and Logic

Strings

Dates and Time

Multidimensional Arrays

Sets

Functions

Execution Control

File Handles

Directories

Libraries and Namespaces

Processes and Environment

Optimization

Linear Regression

Bar Charts

pie chart

gnuplot:

set terminal png size 400,400
set output "piechart.png"
set style fill solid 1.0 border -1

tot = 7 + 3 + 8 + 5 + 5
angle1 = 7.0 / tot * 360
angle2 = (7.0 + 3) / tot * 360
angle3 = (7.0 + 3 + 8) / tot * 360
angle4 = (7.0 + 3 + 8 + 5) / tot * 360

set object 1 circle at screen 0.5,0.5 size \
  screen 0.45 arc [0:angle1] fillcolor rgb "#FF0000" front
set object 2 circle at screen 0.5,0.5 size \
  screen 0.45 arc [angle1:angle2] fillcolor rgb "yellow" front
set object 3 circle at screen 0.5,0.5 size \
  screen 0.45 arc [angle2:angle3] fillcolor rgb "orange" front
set object 4 circle at screen 0.5,0.5 size \
  screen 0.45 arc [angle3:angle4] fillcolor rgb "green" front
set object 5 circle at screen 0.5,0.5 size \
  screen 0.45 arc [angle4:360] fillcolor rgb "blue" front

unset border
unset tics
unset key
plot x with lines lc rgb "#ffffff"

Scatter Plots

Line and Surface Charts

Chart Options

Gnuplot

gnuplot 5.0 (pdf)

Gnuplot provides two plotting commands, plot for 2-dimensional plots and splot for 3-dimensional plots.

plot and splot can be used to plot data (1) generated by a function, (2) in a file, or (3) defined in the program using a named data block. The syntax for a named data block is similar to a shell script here document.

When the data to be plotted is in a file, plot or splot read the file directly. There is no way to read the data into a variable which can be manipulated by the program.

Data in a file must be in a tabular format. By default, whitespace is the column separator, but it can be changed to tabs, commas, or a set of characters specified with a string.

set datafile separator "\t"

Headers and comments are permitted in the data file. By default, comments begin with a number sign #.

The type of plot created by plot or splot can be selected using the set style command. It can also be selected using a with clause in the plot or splot command. The default style is points. Here are some of the available styles:

dots scatterplot with single pixel points
lines
points

set and options

GLPK

Modeling Language GNU MathProg (pdf)

GLPK is a C library for solving linear programming problems, including mixed integer linear programming problems A command line interface called glpsol is also provided.

GLPK allows the problems to be specified in several formats, but we describe the MathProg or GMPL format, which is a subset of AMPL implemented by GLPK.

Input data is declared with the param statement, and values to be found by the solver are declared with the var statmement. Both parameters and variables can be scalars or multi-dimensional arrays. The types can be float, integer, binary, or string.

sets

constraints and objective functions

data section; can everything be defined in model? data section or -d flag; what happens when data section misses parameters; data section limitations: parameters and sets, with just literals for values

page revision: 359, last edited: 10 Aug 2016 22:26
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