Convert equation from string in postgresql - regex

Question

I am trying to write a query that takes in a string, where an equation in the form
x^3 + 0.0046x^2 - 0.159x +1.713
is expected. The equation is used to calculate new values in the output table from a list of existing values. Hence I will need to convert whatever the input equation string is into an equation that postgresql can process, e.g.
power(data.value,3) + 0.0046 * power(data.value,2) - 0.159 * data.value + 1.713
A few comforting constraints in this task are
The equation will always be in the form of a polynomial, e.g. sum(A_n * x^n)
The user will always use 'x' to represent the variable in the input equation
I have been pushing my queries into a string and executing it at the end, e.g.
_query TEXT;
SELECT 'select * from ' INTO _query;
SELECT _query || 'product.getlength( ' || min || ',' || max || ')' INTO _query;
RETURN QUERY EXECUTE _query;
Hence I know I only need to somehow
Replace the 'x''s to 'data.values'
Find all the places in the equation string where a number
immediately precede a 'x', and add a '*'
Find all exponential operations (x^n) in the equation string and
convert them to power(x,n)
This may very well be something very trivial for a lot of people, unfortunately postgresql is not my best skill and I have already spent way more time than I can afford to get this working. Any type of help is highly appreciated, cheers.

Answer 1

Your 9am-noon time frame is over, but here goes.
Every term of the polynomial has 4 elements:
Addition/subtraction modifier
Multiplier
Parameter, always x in your case
Power
The problem is that these elements are not always present. The first term has no addition element, although it could have a subtraction sign - which is then typically connected to the multiplier. Multipliers are only given when not equal to 1. The parameter is not present in the last term and neither is a power in the last two terms.
With optional capture groups in regular expression parsing you can sort out this mess and PostgreSQL has the handy regexp_matches() function for this:
SELECT * FROM
regexp_matches('x^3 + 0.0046x^2 - 0.159x +1.713',
'\s*([+-]?)\s*([0-9.]*)(x?)\^?([0-9]*)', 'g') AS r (terms);
The regular expression says this:
\s* Read 0 or more spaces.
([+-]?) Capture 0 or 1 plus or minus sign.
\s* Read 0 or more spaces.
([0-9.]*) Capture a number consisting of digit and a decimal dot, if present.
(x?) Capture the parameter x. This is necessary to differentiate between the last two terms, see query below.
\^? Read the power symbol, if present. Must be escaped because ^ is the constraint character.
([0-9]*) Capture an integer number, if present.
The g modifier repeats this process for every matching pattern in the string.
On your string this yields, in the form of string arrays:
| terms |
|-----------------|
| {'','',x,3} |
| {+,0.0046,x,2} |
| {-,0.159,x,''} |
| {+,1.713,'',''} |
| {'','','',''} |
(I have no idea why the last line with all empty strings comes out. Maybe a real expert can explain that.)
With this result, you can piece your query together:
SELECT id, sum(term)
FROM (
SELECT id,
CASE WHEN terms[1] = '-' THEN -1
WHEN terms[1] = '+' THEN 1
WHEN terms[3] = 'x' THEN 1 -- If no x then NULL
END *
CASE terms[2] WHEN '' THEN 1. ELSE terms[2]::float
END *
value ^ CASE WHEN terms[3] = '' THEN 0 -- If no x then 0 (x^0)
WHEN terms[4] = '' THEN 1 -- If no power then 1 (x^1)
ELSE terms[4]::int
END AS term
FROM data
JOIN regexp_matches('x^3 + 0.0046x^2 - 0.159x +1.713',
'\s*([+-]?)\s*([0-9.]*)(x?)\^?([0-9]*)', 'g') AS r (terms) ON true
) sub
GROUP BY id
ORDER BY id;
SQLFiddle
This assumes you have an id column to join on. If all you have is a value then you can still do it but you should then wrap the above query in a function that you feed the polynomial and the value. The power is assumed to be integral but you can easily turn that into a real number by adding a dot . to the regular expression and a ::float cast instead of ::int in the CASE statement. You can also support negative powers by adding another capture group to the regular expression and a case statement in the query, same as for the multiplier term; I leave this for your next weekend hackfest.
This query will also handle "odd" polynomials such as -4.3x^3+ 101.2 + 0.0046x^6 - 0.952x^7 +4x just so long as the pattern described above is maintained.