I need to write a SELECT query for some users that will return a ratio. The math involved would just be the simple division of two numbers. However, they would like to have the ratio presented as a fraction rather than as a decimal. What is the best way to do that in SQL using Oracle 10g?
You can define a function in Oracle to calculate greatest common divisor (taken from here):
CREATE FUNCTION gcd (x INTEGER, y INTEGER) RETURN INTEGER AS
ans INTEGER;
BEGIN
IF (y <= x) AND (x MOD y = 0) THEN
ans := y;
ELSIF x < y THEN
ans := gcd(y, x); -- Recursive call
ELSE
ans := gcd(y, x MOD y); -- Recursive call
END IF;
RETURN ans;
END;
And then use that function in your SQL to concatenate a fraction string:
SELECT CAST(TRUNC(A / GCD(A, B)) AS VARCHAR2(10))
|| ' / ' ||
CAST(TRUNC(B / GCD(A, B)) AS VARCHAR2(10)) AS FRACTION FROM TABLE
Related
If f(u,v) = vsinu+v^2, u(x,y)=tan^−1(y/x), v=sqrt(x^2 + y^2)
Calculate using chain rule and directly substituting for u(x,y), v(x,y).
Your syntax is not altogether clear to me, but I am guessing you are trying to achieve something like this:
uveqs := [u(x,y)=arctan(y/x), v(x,y)=sqrt(x^2+y^2)]:
f := v(x,y)*sin(u(x,y))+v(x,y)^2:
Differentiate f with respect to x (noticing the effect of the chain-rule),
K := diff(f,x):
diff(v(x,y),x) * sin(u(x,y))
+ v(x,y) * diff(u(x,y),x) * cos(u(x,y))
+ 2*v(x,y) * diff(v(x,y),x)
Now substitute for u(x,y) and v(x,u), and simplify,
S1 := eval(K,uveqs):
simplify(S1);
2 x
Alternatively, first substitute for u(x,y) and v(x,y) into f itself,
fxy := eval(f,uveqs):
(x^2+y^2)^(1/2)*y/x/(1+y^2/x^2)^(1/2)+x^2+y^2
And then differentiate with respect to x, and simplify,
S2 := diff(fxy,x):
simplify(S2);
2 x
If you have trouble understanding the mechanisms, you might also compare these two pairs of operations,
diff( v(x,y), x );
eval( %, uveqs );
and,
eval( v(x,y), uveqs );
diff( %, x );
Today I tried to write a UDF in standard SQL language in the Web Editor UI, and I have already unchecked the option 'Use Legacy SQL', but it returned to me the following error message:
Not Implemented: You cannot use legacy SQL UDFs with standard SQL queries. See https://cloud.google.com/bigquery/docs/reference/standard-sql/migrating-from-legacy-sql#differences_in_user-defined_javascript_functions
Therefore I tried an example of external UDF provided on the Google Cloud Platform: https://cloud.google.com/bigquery/docs/reference/standard-sql/user-defined-functions. But it still returns to me the same error message. In the following the example:
CREATE TEMPORARY FUNCTION multiplyInputs(x FLOAT64, y FLOAT64)
RETURNS FLOAT64
LANGUAGE js AS """
return x*y;
""";
WITH numbers AS
(SELECT 1 AS x, 5 as y
UNION ALL
SELECT 2 AS x, 10 as y
UNION ALL
SELECT 3 as x, 15 as y)
SELECT x, y, multiplyInputs(x, y) as product
FROM numbers;
Question: How to use external UDF with standard SQL in Web UI?
Make sure not to enter the input in the "UDF Editor" panel. It should go with the rest of your query. See the topic in the migration guide for an example:
#standardSQL
-- Computes the harmonic mean of the elements in 'arr'.
-- The harmonic mean of x_1, x_2, ..., x_n can be expressed as:
-- n / ((1 / x_1) + (1 / x_2) + ... + (1 / x_n))
CREATE TEMPORARY FUNCTION HarmonicMean(arr ARRAY<FLOAT64>)
RETURNS FLOAT64 LANGUAGE js AS """
var sum_of_reciprocals = 0;
for (var i = 0; i < arr.length; ++i) {
sum_of_reciprocals += 1 / arr[i];
}
return arr.length / sum_of_reciprocals;
""";
WITH T AS (
SELECT GENERATE_ARRAY(1.0, x * 4, x) AS arr
FROM UNNEST([1, 2, 3, 4, 5]) AS x
)
SELECT arr, HarmonicMean(arr) AS h_mean
FROM T;
ORA-06550: line 20, column 4:
PLS-00103: Encountered the symbol ";" when expecting one of the following:
if
1. declare
2. a number;
3. b number;
4. c number;
declare
a number;
b number;
c number;
d number;
function findMaxOfAll(x in number, y in number, z in number)
return number
is
m number;
begin
if x > y and x > z then
m:=x;
else if y > x and y > z then
m:=y;
else
m:=z;
end if;
return m;
end;
begin
a:=34;
b:=76;
c:=56;
d:=findMaxOfAll(a, b, c);
dbms_output.put_line('Max of all is: ' || d);
end;
The trouble is with the ELSE IF.
Change it to ELSIF.
if x > y and x > z then
m:=x;
elsif y > x and y > z then
m:=y;
else
m:=z;
end if;
I donot understand the use of this snippet as oracle already provides GREATEST Function to execute this type of operations.
These are easier to use and optimized.
Hope this helps.
SELECT greatest('&x','&y','&z') FROM dual;
how do you do it?
I am very new to this and I am sure this is easy enough but i can't seem to figure out how
here is some pseudo code
port(x,y: in std_logic_vector (2 downto 0) -- 3 bit input that is basically counted eg ("000", "001", "010"... "111", "000" ...)
q_out : out integer); -- this is just an example
signal temp_q_out: integer;
when x (or y) increments -- THIS IS THE PART I CAN'T GET
temp_q_out <= temp_ q_out + 1;
case temp_q_out is
when 0 q_out <= 7
when 1 q_out <= 12
when 2 q_out <= 4
when others q_out <= 100
How do I make my temp_q_out count only when x or y increments and at no other time? I want my output q_out to be constantly 7 until x or y changes then be 12 till x or y changes again then be 2. What usually happens is that the output becomes 100 straight away.
Any help at all will be appreciated
Cheers Guys :-)
I don't think there is a safe way to do what you want with asynchronous logic. Assuming you want to synthesize this, you need a clock input. Then, you can add a process that stores the previous values of x and y, and checks whether the new value is equal to the old value or not. Here's an example:
process(clk)
variable prev_x, prev_y : std_logic_vector(2 downto 0) := (others => '0');
begin
if rising_edge(clk) then
if (x /= prev_x) or (y /= prev_y) then
temp_q_out <= temp_q_out + 1;
end if;
prev_x := x;
prev_y := y;
end if;
end process;
Use processes. Processes are executed like atomic statements. You can use variables inside them. The following process listens on the x and y signals. When one of them changes, the process is executed sequentially.
process(x, y)
variable tmpX: integer := -1;
variable tmpY: integer := -1;
begin
if (x = tmpX + 1) or (y = tmpY + 1) then
temp_q_out <= temp_ q_out + 1;
tmpX := x;
tmpY := y;
end process;
The first execution of the process depends on your specific case, so modify the "-1" value as you please.
We have a relatively small table that we would like to sort based on rating, using the Wilson interval or a reasonable equivalent. I'm a reasonably smart guy, but my math fu is nowhere near strong enough to understand this:
The above formula, I am told, calculates a score for a positive/negative (thumbs up/thumbs down) voting system. I've never taken a statistics course, and it's been 15 years since I've done any sort of advanced mathematics. I don't have a clue what the little hat that the p is wearing means, or what the backwards Jesus fish beneath z indicates.
I would like to know two things:
Can this formula be altered to accommodate a 5-star rating system? I found this, but the author expresses his doubts as to the accuracy of his formula.
How can this formula be expressed in a SQL function? Note that I do not need to calculate and sort in real-time. The score can be calculated and cached daily.
Am I overlooking something built-in to Microsoft SQL Server?
Instead of trying to manipulate the Wilson's algorithm to do a 5 star rating system. Why don't you look into a different algorithm? This is what imdb uses for their top 250: Bayesian Estimate
As for explaining the math in the Wilson's algorithm, below was posted on the link in your first post. It is written in Ruby.
require 'statistics2'
def ci_lower_bound(pos, n, power)
if n == 0
return 0
end
z = Statistics2.pnormaldist(1-power/2)
phat = 1.0*pos/n
(phat + z*z/(2*n) - z * Math.sqrt((phat*(1-phat)+z*z/(4*n))/n))/(1+z*z/n)
end
If you'd like another example, here is one in PHP:
http://www.derivante.com/2009/09/01/php-content-rating-confidence/
Edit: It seems that derivante.com is no longer around. You can see the original article on archive.org - https://web.archive.org/web/20121018032822/http://derivante.com/2009/09/01/php-content-rating-confidence/ and I've added the code from the article below.
class Rating
{
public static function ratingAverage($positive, $total, $power = '0.05')
{
if ($total == 0)
return 0;
$z = Rating::pnormaldist(1-$power/2,0,1);
$p = 1.0 * $positive / $total;
$s = ($p + $z*$z/(2*$total) - $z * sqrt(($p*(1-$p)+$z*$z/(4*$total))/$total))/(1+$z*$z/$total);
return $s;
}
public static function pnormaldist($qn)
{
$b = array(
1.570796288, 0.03706987906, -0.8364353589e-3,
-0.2250947176e-3, 0.6841218299e-5, 0.5824238515e-5,
-0.104527497e-5, 0.8360937017e-7, -0.3231081277e-8,
0.3657763036e-10, 0.6936233982e-12);
if ($qn < 0.0 || 1.0 < $qn)
return 0.0;
if ($qn == 0.5)
return 0.0;
$w1 = $qn;
if ($qn > 0.5)
$w1 = 1.0 - $w1;
$w3 = - log(4.0 * $w1 * (1.0 - $w1));
$w1 = $b[0];
for ($i = 1;$i <= 10; $i++)
$w1 += $b[$i] * pow($w3,$i);
if ($qn > 0.5)
return sqrt($w1 * $w3);
return - sqrt($w1 * $w3);
}
}
As for doing this in SQL, SQL has all these Math functions already in it's library. If I were you I'd do this in your application though. Make your application update your database every so often (hours? days?) instead of doing this on the fly or your application will become very slow.
Regarding your first question (adjusting the formula to the 5-stars system) I would agree with Paul Creasey.
conversion formula: [3 +/- i stars -> i up/down-votes] (3 stars -> 0)
example: 4 stars -> +1 up-vote, 5 stars -> +2, 1 -> -2 and so on.
I would note though that instead of the lower bound of the interval that both ruby and php functions compute, I would just compute the much more simple wilson midpoint:
(x + (z^2)/2) / (n + z^2)
where:
n = Sum(up_votes) + Sum(|down_votes|)
x = (positive votes)/n = Sum(up_votes) / n
z = 1.96 (fixed value)
Taking Williams link to the php solution http://www.derivante.com/2009/09/01/php-content-rating-confidence/ and making your system such that it just postive and negative (5 stars could be 2 pos, 1 start could be 2 neg perhaps) then it would be fairly easy to convert it to T-SQL, but you'd be much better off doing it in the server side logic.
The author of the first link recently added an SQL implementation to his post.
Here it is:
SELECT widget_id, ((positive + 1.9208) / (positive + negative) -
1.96 * SQRT((positive * negative) / (positive + negative) + 0.9604) /
(positive + negative)) / (1 + 3.8416 / (positive + negative))
AS ci_lower_bound FROM widgets WHERE positive + negative > 0
ORDER BY ci_lower_bound DESC;
Whether this can be accommodated to a 5-star rating system is beyond me too.
I have uploaded an Oracle PL/SQL implementation to https://github.com/mattgrogan/stats_wilson_score
create or replace function stats_wilson_score(
/*****************************************************************************************************************
Author : Matthew Grogan
Website : https://github.com/mattgrogan
Name : stats_wilson_score.sql
Description : Oracle PL/SQL function to return the Wilson Score Interval for the given proportion.
Citation : Wilson E.B. J Am Stat Assoc 1927, 22, 209-212
Example:
select
round(29 / 250, 4) point_estimate,
stats_wilson_score(29, 250, 0.10, 'LCL') lcl,
stats_wilson_score(29, 250, 0.10, 'UCL') ucl
from dual;
******************************************************************************************************************/
x integer, -- Number of successes
m integer, -- Number of trials
alpha number default 0.95, -- Probability of a Type I error
return_value varchar2 default 'LCL' -- LCL = Lower control limit, UCL = upper control limit
)
return number is
z float(10);
phat float(10) := 0.0;
lcl float(10) := 0.0;
ucl float(10) := 0.0;
begin
if m = 0 then
return(0);
end if;
case alpha
when 0.10 then z := 1.644854;
when 0.05 then z := 1.959964;
when 0.01 then z := 2.575829;
else return(null); -- No Z value for this alpha
end case;
phat := x/m;
lcl := (phat + z*z/(2*m) - z * sqrt( (phat * (1-phat) ) / m + z * z / (4 * (m * m)) ) ) / (1 + z * z / m);
ucl := (phat + z*z/(2*m) + z * sqrt((phat*(1-phat)+z*z/(4*m))/m))/(1+z*z/m);
case return_value
when 'LCL' then return(lcl);
when 'UCL' then return(ucl);
else return(null);
end case;
end;
/
grant execute on stats_wilson_score to public;
The Wilson score is actually not a very good of a way of sorting items by rating. It's certainly better than just sorting by mean review score, but it still has a lot of problems. For example, an item with 1 negative review (whose quality is still very uncertain) will be sorted below an item with 10 negative reviews and 1 positive review (which we can be fairly certain is bad quality).
I would recommend using an adaptation of the SteamDB rating formula instead (by Reddit user /u/tornmandate). In addition to being better suited to this sort of thing than the Wilson score (for reasons that are explained in the linked article), it can also be adapted to a 5-star rating system much more easily than Wilson.
Original SteamDB formula:
( Total Reviews = Positive Reviews + Negative Reviews )
( Review Score = frac{Positive Reviews}{Total Reviews} )
( Rating = Review Score - (Review Score - 0.5)*2^{-log_{10}(Total Reviews + 1)} )
5-star version (note the change from 0.5 (a 50% score with up/down votes) to 2.5 (a 50% score with 5-star ratings)):
( Total Reviews = total count of all reviews )
( Review Score = mean star rating of all reviews )
( Rating = Review Score - (Review Score - 2.5)*2^{-log_{10}(Total Reviews + 1)} )
The formula is also much more understandable by non-mathematicians and easy to translate into code.