awk: Interpreting strings as mathematical expressions - shell

Question

Context: I have an input file that contains parameters with associated values followed by literal mathematical expressions such as:
PARAMETERS DEFINITION
A = 5; B = 2; C=1.5; D=7.5
MATHEMATICAL EXPRESSIONS
A*B
C/D
...
and I would like to get the strings of the second part to be interpreted as mathematical expressions so that I get the results of the expressions in my output file:
...
MATHEMATICAL EXPRESSIONS
10
0.2
...
What I did already: So far, using awk, I store all the parameters names and their corresponding values in two distinct arrays. I then replace each parameter with its value so that I am now in a similar situation as the author of this thread.
However, the answers s/he gets are not in awk except for the last one which is very specific to her/his situation, and hard to understand for me as a beginner with awk and shell scripting.
What I tried afterwards: As I have no clue how to do this in awk, the idea I had was to store the new field value in a variable, then use a shell command within the awk script like this:
#!bin/awk -f
BEGIN{}
{
myExpression=$1
system("echo $myExpression | bc")
}
END{}
This, unfortunately does not work as the variable is somehow not recognized by the echo command.
What I would like:
I would prefer a solution using awk alone with no call to external functions, however, I am not against one using a shell command if it is simpler.
EDIT Taking into account all the comments so far, I will be more precise, my input files look more like this:
PARAMETERS_DEFINITION
[param1] = 5
[param2] = 2
[param3] = 1.5
[param4] = 7.5
MATHEMATICAL_EXPRESSIONS
[param1]*[param2]
some text containing also numbers and formulas that I do not want to be affected.
e.g: 1.45*2.6 = x, de(x)/dx=e(x) ; blah,blah,blah
[param3]/[param4]
The names of the parameters are complex enough so that any match of the string: "[param#]" within the document corresponds to a parameter that I want changed for its value.
Below is the way I manage to store the parameters and their value in arrays is the following:
{
if (match($2,/PARAMETERS_DEFINITION/) != 0) {paramSwitch = 1}
if (match($2,/MATHEMATICAL_EXPRESSIONS/) != 0) {paramSwitch = 0}
if (paramSwitch == 1)
{
parameterName[numOfParam] = $1 ;
parameterVal[numOfParam] = $3 ;
numOfParam += 1
}
}

Answer 1

Instead of this:
{
myExpression=$1
system("echo $myExpression | bc")
}
I think you'd want this:
{
myExpression=$1
system("echo " myExpression " | bc")
}
That's because in awk, assignments do not end up as environment variables, and putting strings next to each other concatenates them.

Answer 2

You asking awk: Interpreting strings as mathematical expressions - this functionality usually called as eval, and no, (AFAIK) awk doesn't knows such function. Therefore your questions is an typical XY problem
The right tool for this is bc, where you (nearly) don't need modify anything, and simply feed the bc with your input, only ensure than the variables are are lowercase, such the following input (edited the your example)
#PARAMETERS DEFINITION
a=5; b=2; c=1.5; d=7.5
#MATHEMATICAL EXPRESSIONS
a*b
c/d
using like
bc -l < inputfile
produces
10
.20000000000000000000
EDIT
For your edit, for the new input data. The following
grep '\[' inputfile | sed 's/[][]//g' | bc -l
for the input
PARAMETERS_DEFINITION
[param1] = 5
[param2] = 2
[param3] = 1.5
[param4] = 7.5
MATHEMATICAL_EXPRESSIONS
[param1]*[param2]
some text containing also numbers and formulas that I do not want to be affected.
e.g: 1.45*2.6 = x, de(x)/dx=e(x) ; blah,blah,blah
[param3]/[param4]
produces the following output:
10
.20000000000000000000
e.g. grepping out only lines what contains [ - any param definition or expression, remove any [], e.g. creating the following bc program:
param1 = 5
param2 = 2
param3 = 1.5
param4 = 7.5
param1*param2
param3/param4
and send the whole "program" to bc...

Answer 3

Using BIDMAS as a basis i have created this mathematical function in awk
I have not included brackets(or indices) yet as they will require some extra effort but i may add them later
This awk script effectively works as bc does.
No system call required, all in awk.
Generic version for all applications
awk '{split($0,a,"+")
for(i in a){
split(a[i],s,"-")
for(j in s){
split(s[j],m,"*")
for(k in m){
split(m[k],d,"/")
for(l in d){
if(l>1)d[1]=d[1]/d[l]
}
m[k]=d[1]
delete d
if(k>1)m[1]=m[1]*m[k]
}
s[j]=m[1]
delete m
if(j>1)s[1]=s[1]-s[j]
}
a[i]=s[1]
delete s
}
for(i in a)b=b+a[i];print b}{b=0}' file
For your specific example
awk '
/MATHEMATICAL_EXPRESSIONS/{z=1}
NR>1&&!z{split($0,y," = ");x[y[1]]=y[2]}
z&&/[\+\-\/\*]/{
for (n in x)gsub(n,x[n])
split($0,a,"+")
for(i in a){
split(a[i],s,"-")
for(j in s){
split(s[j],m,"*")
for(k in m){
split(m[k],d,"/")
for(l in d){
if(l>1)d[1]=d[1]/d[l]
}
m[k]=d[1]
delete d
if(k>1)m[1]=m[1]*m[k]
}
s[j]=m[1]
delete m
if(j>1)s[1]=s[1]-s[j]
}
a[i]=s[1]
delete s
}
for(i in a)b=b+a[i];print b}{b=0}' file

Answer 4

There's something like an eval for awk, its a magical conversion when needed in the context, here adding +0 would do the convertion.
What I got for you (detailled version below) with a file named awkinput with your exemple input
awk '/[A-Z]=[0-9.]+;/ { for (i=1;i<=NF ;i++) { print "working on "$i; split($i,fields,"="); sub(/;/,"",fields[2]); params[fields[1]]=strtonum(fields[2]) } }; /[A-Z](*|\/|+|-)[A-Z]/ { for (p in params) { sub(p, params[p],$0); }; system("echo " $0 " | bc -ql") }' awkinput
Detailled:
/[A-Z]=[0-9.]+;?/ { # if we match something like A=4.2 with or wothout a ; at end
for (i=1;i<=NF ;i++) { # loop through the fields (separated by space, the default Field Separator of awk)
print "working on "$i; # inform on what we do
split($i,fields,"="); # split in an array to get param and value
sub(/;/,"",fields[2]); # Eventually remove the ; at end
params[fields[1]]=strtonum(fields[2]) # new array of parameters where the values are numeric
}
}
/[A-Z](*|\/|+|-)[A-Z]/ { #when the line match a math operation with one param on each side (at least)
for (p in params) { # loop over know params
sub(p, params[p],$0); # replace each param with its value
};
system("echo " $0 " | bc -ql") # print the result (no way to get of system call here)
}
Drawback:
A math of the form AB*C would be resolved to 52*1.5

Answer 5

$ cat test
PARAMETERS DEFINITION
A=5; B=2; C=1.5; D=7.5
MATHEMATICAL EXPRESSIONS
A*B
C/D
$ awk -vRS='[= ;\n]' '{if ($0 ~ /[0-9]/){a[x] = $0; print x"="a[x]}else{x=$0}}/MATHEMATICAL/{print "MATHEMATICAL EXPRESSIONS"}{if ($0~"*") print a[substr($0,1,1)] * a[substr($0,3,1)]}{if ($0~"/") print a[substr($0,1,1)] / a[substr($0,3,1)]}' test
A=5
B=2
C=1.5
D=7.5
MATHEMATICAL EXPRESSIONS
10
0.2
Formatted nicely:
$ cat test.awk
# Store all variables in an array
{
if ($0 ~ /[0-9]/){
a[x] = $0;
print x " = " a[x] # Print the keys & values
}
else{
x = $0
}
}
# Print header
/MATHEMATICAL/ {print "MATHEMATICAL EXPRESSIONS"}
# Do the maths (case can work too, but it's not as widely available)
{
if ($0~"*")
print a[substr($0,1,1)] * a[substr($0,3,1)]
}
{
if ($0~"/")
print a[substr($0,1,1)] / a[substr($0,3,1)]
}
{
if ($0~"+")
print a[substr($0,1,1)] + a[substr($0,3,1)]
}
{
if ($0~"-")
print a[substr($0,1,1)] - a[substr($0,3,1)]
}
$ cat test
PARAMETERS DEFINITION
A=5; B=2; C=1.5; D=7.5
MATHEMATICAL EXPRESSIONS
A*B
C/D
D+C
C-A
$ awk -f test.awk -vRS='[= ;\n]' test
A = 5
B = 2
C = 1.5
D = 7.5
MATHEMATICAL EXPRESSIONS
10
0.2
9
-3.5