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NewtonRaphson method with sql [message #444989] 
Thu, 25 February 2010 02:19 
steffeli
Messages: 112 Registered: July 2006

Senior Member 


Dear all,
Is it possible to solve an equation with the newtonraphson method with sql?
I have an equation f(x)=1a/x**2, f(x)'= 2a/x**3
and want to solve x for several a's
The newtonraphson methos uses the derivation as next approximation:
xn2 = xn1  f(x)/f(x)'
The result should be like this:
create table temp_res (a integer, res number);
insert into temp_res values(1, 1);
insert into temp_res values(2, 1.41421288939285);
insert into temp_res values(3, 1.73205078513617);
insert into temp_res values(4, 1.99999999999617);
insert into temp_res values(5, 2.23606797658102);
insert into temp_res values(6, 2.4494897130809);
insert into temp_res values(7, 2.64575095945042);
insert into temp_res values(8, 2.82842712474403);
Is there an efficient solution?
Thanks, Stefan





Re: NewtonRaphson method with sql [message #444993 is a reply to message #444989] 
Thu, 25 February 2010 02:34 
ayush_anand
Messages: 417 Registered: November 2008

Senior Member 


f(x)/f(x)'= (1  (1a)/(2a))
x(n+1)=x(n)  (1  (1a)/(2a))
you will require value for x(1) and a to get further answers.
Oracle provides a good function of achieving the same (with more accuracy than Newton Ralphson offcourse)
SQL> with data as (select rownum val from dual connect by level<=8)
2 select val,sqrt(val) from data
3 /
VAL SQRT(VAL)
 
1 1
2 1.41421356
3 1.73205081
4 2
5 2.23606798
6 2.44948974
7 2.64575131
8 2.82842712
8 rows selected.
[Updated on: Thu, 25 February 2010 02:40] Report message to a moderator






Re: NewtonRaphson method with sql [message #445001 is a reply to message #444996] 
Thu, 25 February 2010 03:27 
ayush_anand
Messages: 417 Registered: November 2008

Senior Member 


Quote:sqrt works for this equation, sure, but is there a general solution to solve non linear equations in oracle?
Quote:If you can express it in algorithm: yes.
Regards
Michel
To add to that I dont think in any language can solve equations unless you tell them what to do?
So you need to tell the language what to do with your data



Re: NewtonRaphson method with sql [message #445053 is a reply to message #444989] 
Thu, 25 February 2010 08:20 
_jum
Messages: 508 Registered: February 2008

Senior Member 


The model clause gives a possible solution (here a=8):
SELECT 'Stop bei i=' i' a=' a ' Delta='  d ' f(x)=' f erg FROM dual
MODEL
DIMENSION BY (1 as na)
MEASURES (0 as d, 1 as f, 0 as i, 8 as a)
RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1])  d[1]) <1E100
(
i[1] = ITERATION_NUMBER+1,
newtonraphson method: x(n+1)=x(n)(1a/x**2)/(2a/x**3)
d[1] = (1a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
f[1] = f[1]d[1]
);
ERG

Stop bei i=11 a=8 Delta=0 f(x)=2,82842712474619009760337744841939615714





Re: NewtonRaphson method with sql [message #445722 is a reply to message #445135] 
Wed, 03 March 2010 10:02 
steffeli
Messages: 112 Registered: July 2006

Senior Member 


Dear all, I have another question regarding iterations within the model clause. Is it possible to write a forloop in the iteration? I tried the code below, but the syntax seems to be wrong (don't mind the silly example in the forloop).
Thanks for your help.
SELECT 'Stop bei x=' x' i=' i' a=' a ' Delta='  d ' f(x)=' f erg FROM dual
MODEL
DIMENSION BY (1 as na)
MEASURES (0 as d, 1 as f, 0 as i, 8 as a, 2 as x)
RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1])  d[1]) <1E100
(
i[1] = ITERATION_NUMBER+1,
d[1] = (1a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
f[1] = f[1]d[1],
x[1] = for z in 2..9 loop
x[1]=f[i]+z
end loop
)




Re: NewtonRaphson method with sql [message #445777 is a reply to message #445727] 
Thu, 04 March 2010 01:52 
steffeli
Messages: 112 Registered: July 2006

Senior Member 


Hi Michel, thank you for your feedback, I wrote f[i] instead of f[1], sorry, but anyway I don't get it.
I want to loop several times (e.g. from z=2 to z=9) within an interation step.
Something like this:
x[1] = for z in 2..9 loop
x[1]= f[1]+z
end loop
or
x[1] = sum[ for z between 2..9, x[1]=f[1]+z ]
Could anyone help me with the correct syntax?
Thanks, Stefan



Re: NewtonRaphson method with sql [message #445779 is a reply to message #445777] 
Thu, 04 March 2010 02:00 
_jum
Messages: 508 Registered: February 2008

Senior Member 


Here the correct syntax for 'FOR' in MODEL computing your square root with babylon method
SELECT 'SQRT at inc='inc' x=' x' ' erg FROM dual
MODEL
DIMENSION BY (1 as inc)
MEASURES (8 as x)
RULES
(
x[FOR inc FROM 2 TO 10 INCREMENT 1] = 1/2*(x[1]/x[cv()1]+x[cv()1])
);
ERG

SQRT at inc=1 x=8
SQRT at inc=2 x=4,5
SQRT at inc=3 x=3,13888888888888888888888888888888888889
SQRT at inc=4 x=2,84378072763028515240904621435594886923
SQRT at inc=5 x=2,8284685718801466821819618416725070015
SQRT at inc=6 x=2,82842712504986412995671609183567406561
SQRT at inc=7 x=2,82842712474619009761967942719569409644
SQRT at inc=8 x=2,82842712474619009760337744841939615714
SQRT at inc=9 x=2,82842712474619009760337744841939615714
SQRT at inc=10 x=2,82842712474619009760337744841939615714
Please contact the fine manual at model clause
[Updated on: Thu, 04 March 2010 02:04] Report message to a moderator







Re: NewtonRaphson method with sql [message #445854 is a reply to message #445828] 
Thu, 04 March 2010 06:37 
steffeli
Messages: 112 Registered: July 2006

Senior Member 


thank you _jum, but I don't know how I can integrate a iteratecode (x[1]) into another iterate code. Does anyone know how to write this code?
SELECT 'Stop bei x=' x' i=' i' a=' a ' Delta='  d ' f(x)=' f erg FROM dual
MODEL
DIMENSION BY (1 as na)
MEASURES (0 as d, 1 as f, 0 as i, 8 as a, 2 as x)
RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1])  d[1]) <1E100
(
i[1] = ITERATION_NUMBER+1,
d[1] = (1a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
f[1] = f[1]d[1],
x[1] = for z in 2..9 loop 
x[1]=f[1]+z  how can I write this as an interation give that
this is within another iteration step?
end loop 
)
[Updated on: Thu, 04 March 2010 07:46] by Moderator Report message to a moderator





Re: NewtonRaphson method with sql [message #445873 is a reply to message #445854] 
Thu, 04 March 2010 08:14 
ayush_anand
Messages: 417 Registered: November 2008

Senior Member 


SQL> ed
Wrote file afiedt.buf
1 with at as (select rownum rn from dual connect by level <=10)
2 SELECT rn,' f(x)=' f erg
3 FROM at
4 MODEL
5 PARTITION BY (at.rn)
6 DIMENSION BY (1 as na)
7 MEASURES (0 as d, 1 as f, 0 as i, at.rn as a)
8 RULES ITERATE (9)
9 (
10 i[1] = ITERATION_NUMBER+1,
11 d[1] = (1a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
12 f[1] = f[1]d[1]
13 )
14* order by 1
SQL> /
RN ERG
 
1 f(x)=1
2 f(x)=1.41421356237309504880168872420969807857
3 f(x)=1.73205080756887729352744634150587236694
4 f(x)=2
5 f(x)=2.23606797749978969640917366873127623544
6 f(x)=2.44948974278317809819728407470589139196
7 f(x)=2.64575131106459059050161575363926042571
8 f(x)=2.82842712474619009760337744841939615714
9 f(x)=3
10 f(x)=3.16227766016837933199889354443271853371
10 rows selected.
SQL>
[Updated on: Thu, 04 March 2010 08:15] Report message to a moderator








Re: NewtonRaphson method with sql [message #445892 is a reply to message #445883] 
Thu, 04 March 2010 09:23 
steffeli
Messages: 112 Registered: July 2006

Senior Member 


@ayush_anand: you are totally right, it is a silly example (as I already wrote), but I need an iteration within another iteration step. Let't make a more realistic case. I can calculate x[1] as below, but this is obviously not a very smooth solution, I want to iterate or loop from 2 to 9 (since my real x[1] is a much more complicate formula and otherwise I'd have to write a lot of code).
SELECT 'Stop bei x=' x' i=' i' a=' a ' Delta='  d ' f(x)=' f erg FROM dual
MODEL
DIMENSION BY (1 as na)
MEASURES (0 as d, 1 as f, 0 as i, 8 as a, 2 as x)
RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1])  d[1]) <1E100
(
i[1] = ITERATION_NUMBER+1,
d[1] = (1a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
f[1] = f[1]d[1],
 x = z*x + power(2,z) for z in 2..9
x[1] = ( 2*x[1] + power(2,2) )
+( 3*x[1] + power(2,3) )
+( 4*x[1] + power(2,4) )
+( 5*x[1] + power(2,5) )
+( 6*x[1] + power(2,6) )
+( 7*x[1] + power(2,7) )
+( 8*x[1] + power(2,8) )
+( 9*x[1] + power(2,9) )
)
[Updated on: Thu, 04 March 2010 09:28] Report message to a moderator



Re: NewtonRaphson method with sql [message #445927 is a reply to message #445892] 
Thu, 04 March 2010 12:55 
ayush_anand
Messages: 417 Registered: November 2008

Senior Member 


same as this
SQL> SELECT 'Stop bei x=' x' i=' i' a=' a ' Delta='  d ' f(x)=' f erg FROM dual
2 MODEL
3 DIMENSION BY (1 as na)
4 MEASURES (0 as d, 1 as f, 0 as i, 8 as a, 2 as x)
5 RULES ITERATE (3000) UNTIL ABS(PREVIOUS(d[1])  d[1]) <1E100
6 (
7 i[1] = ITERATION_NUMBER+1,
8 d[1] = (1a[1]/POWER(f[1],2))/(2*a[1]/POWER(f[1],3)),
9 f[1] = f[1]d[1],
10  x = z*x + power(2,z) for z in 2..9
11 x[1] = ( 2+3+4+5+6+7+8+9)*x[1] + power(2, ( 2+3+4+5+6+7+8+9))
12 )
13 /
ERG

Stop bei x=489588034328312985544036450304 i=11 a=8 Delta=0 f(x)=2.82842712474619
009760337744841939615714
[Updated on: Thu, 04 March 2010 12:56] Report message to a moderator





Re: NewtonRaphson method with sql [message #445994 is a reply to message #445927] 
Fri, 05 March 2010 01:29 
steffeli
Messages: 112 Registered: July 2006

Senior Member 


@ayush_anand: I know that it is possible to simplify this code
x[1] = ( 2*x[1] + power(2,2) )
+( 3*x[1] + power(2,3) )
+( 4*x[1] + power(2,4) )
+( 5*x[1] + power(2,5) )
+( 6*x[1] + power(2,6) )
+( 7*x[1] + power(2,7) )
+( 8*x[1] + power(2,8) )
+( 9*x[1] + power(2,9) )
but as I already wrote, the real formula for x is much more complicate and I need a LOOP OR ITERATION WITHIN ANOTHER ITERATION step.
Thank you for the this
measure_column [ { { condition
 expr
 single_column_for_loop
}
[, { condition
 expr
 single_column_for_loop
}
]...
 multi_column_for_loop
}
]
Note: The outer square brackets are part of the syntax.
In this case, they do not indicate optionality.
but I still don't know how I can write the correct syntax for my problem above. I'd really appreciate your help!
[Updated on: Fri, 05 March 2010 01:30] Report message to a moderator




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