Group Abstract

Message Boards

WOLFRAM COMMUNITY

5K Views

4 Replies

3 Total Likes

View groups...

Follow this post

Share this post:

GROUPS:

Mathematica Algebra Wolfram Language Numerical Computation

Limiting the output from an NSolve problem to Reals

Doug Stoll

Doug Stoll, Home user

Posted 12 years ago

I am trying to solve a set of 6 equations in 6 unknowns using NSolve and I am only interested in solutions with real values not complex values. As I investigate this area of interest with a sequence of increasing complexity of equations, I find there was only a few solutions with 3 equations/3 unks then many more with 4 eqns/4 unks (with many complex solutions) and at 5 eqns/5 unks 2 separate real solutions (only the 1st one was appropriate to my interest and to many complex solutions to list. But I could get a response. The first real "answer" was the one I was looking for. When I go to 6 eqns/6unks I can't seem to get any response even after over 24 hours of "running time". How do I instruct NSolve to ignore complex solutions so I can examine the real ones -- and get an answer is short time. Here is the NSolve problem I am working. NSolve[{a + a b + a^2 c + a^3 d + a^4 f + a^5 h == 1, b^2 + 2 a b c + 3 a^2 b d + 4 a^3 b f + 5 a^4 b h == 1, b c + b^2 c + 2 a c^2 + 3 a b^2 d + 3 a^2 c d + 6 a^2 b^2 f + 4 a^3 c f + 10 a^3 b^2 h + 5 a^4 c h == 1/2, 2 b c^2 + b d + b^3 d + 2 a c d + 6 a b c d + 3 a^2 d^2 + 4 a b^3 f + 12 a^2 b c f + 4 a^3 d f + 10 a^2 b^3 h + 20 a^3 b c h + 5 a^4 d h == 1/6, c^3 + 2 b c d + 3 b^2 c d + 3 a c^2 d + 6 a b d^2 + b f + b^4 f + 2 a c f + 12 a b^2 c f + 6 a^2 c^2 f + 3 a^2 d f + 12 a^2 b d f + 4 a^3 f^2 + 5 a b^4 h + 30 a^2 b^2 c h + 10 a^3 c^2 h + 20 a^3 b d h + 5 a^4 f h == 1/24, 2 c^2 d + 3 b c^2 d + 3 b^2 d^2 + 6 a c d^2 + 2 b c f + 4 b^3 c f + 12 a b c^2 f + 6 a b d f + 12 a b^2 d f + 12 a^2 c d f + 12 a^2 b f^2 + b h + b^5 h + 2 a c h + 20 a b^3 c h + 30 a^2 b c^2 h + 3 a^2 d h + 30 a^2 b^2 d h + 20 a^3 c d h + 4 a^3 f h + 20 a^3 b f h + 5 a^4 h^2 == 1/120}, {a, b, c, d, f, h}] Thank you.

I am trying to solve a set of 6 equations in 6 unknowns using NSolve and I am only interested in solutions with real values not complex values. As I investigate this area of interest with a sequence of increasing complexity of equations, I find there was only a few solutions with 3 equations/3 unks then many more with 4 eqns/4 unks (with many complex solutions) and at 5 eqns/5 unks 2 separate real solutions (only the 1st one was appropriate to my interest and to many complex solutions to list. But I could get a response. The first real "answer" was the one I was looking for.

When I go to 6 eqns/6unks I can't seem to get any response even after over 24 hours of "running time". How do I instruct NSolve to ignore complex solutions so I can examine the real ones -- and get an answer is short time.

Here is the NSolve problem I am working.

NSolve[{a + a b + a^2 c + a^3 d + a^4 f + a^5 h == 1,   b^2 + 2 a b c + 3 a^2 b d + 4 a^3 b f + 5 a^4 b h  == 1, 
  b c + b^2 c + 2 a c^2 + 3 a b^2 d + 3 a^2 c d + 6 a^2 b^2 f +     4 a^3 c f + 10 a^3 b^2 h + 5 a^4 c h == 1/2, 
  2 b c^2 + b d + b^3 d + 2 a c d + 6 a b c d + 3 a^2 d^2 + 4 a b^3 f + 12 a^2 b c f + 4 a^3 d f + 10 a^2 b^3 h + 20 a^3 b c h + 5 a^4 d h == 1/6, 
  c^3 + 2 b c d + 3 b^2 c d + 3 a c^2 d + 6 a b d^2 + b f + b^4 f + 2 a c f + 12 a b^2 c f + 6 a^2 c^2 f + 3 a^2 d f + 12 a^2 b d f + 
    4 a^3 f^2 + 5 a b^4 h + 30 a^2 b^2 c h + 10 a^3 c^2 h + 20 a^3 b d h + 5 a^4 f h == 1/24,  2 c^2 d + 3 b c^2 d + 3 b^2 d^2 + 6 a c d^2 + 2 b c f + 4 b^3 c f + 12 a b c^2 f + 6 a b d f + 12 a b^2 d f + 12 a^2 c d f + 12 a^2 b f^2 + b h + b^5 h + 2 a c h + 20 a b^3 c h + 30 a^2 b c^2 h + 3 a^2 d h + 30 a^2 b^2 d h + 20 a^3 c d h + 4 a^3 f h + 20 a^3 b f h + 5 a^4 h^2 == 1/120}, {a, b, c, d, f,  h}]

Thank you.

POSTED BY: Doug Stoll

4 Replies

Sort By:

Doug Stoll

Doug Stoll, Home user

Posted 12 years ago

YES!!! This is precisely what I was expecting. I see rather than NSolve, NMinimize finds it "good enough" . This confirms my direction and I can continue -- thank you very much. Doug

POSTED BY: Doug Stoll

Bill Simpson

Posted 12 years ago

Is there any chance that this solution, which took three seconds to find, might provide what you need? In[1]:= NMinimize[(a + a b + a^2 c + a^3 d + a^4 f + a^5 h - 1)^2 + (b^2 + 2 a b c + 3 a^2 b d + 4 a^3 b f + 5 a^4 b h - 1)^2 + (b c + b^2 c + 2 a c^2 + 3 a b^2 d + 3 a^2 c d + 6 a^2 b^2 f + 4 a^3 c f + 10 a^3 b^2 h + 5 a^4 c h - 1/2)^2 + (2 b c^2 + b d + b^3 d + 2 a c d + 6 a b c d + 3 a^2 d^2 + 4 a b^3 f + 12 a^2 b c f + 4 a^3 d f + 10 a^2 b^3 h + 20 a^3 b c h + 5 a^4 d h - 1/6)^2 + (c^3 + 2 b c d + 3 b^2 c d + 3 a c^2 d + 6 a b d^2 + b f + b^4 f + 2 a c f + 12 a b^2 c f + 6 a^2 c^2 f + 3 a^2 d f + 12 a^2 b d f + 4 a^3 f^2 + 5 a b^4 h + 30 a^2 b^2 c h + 10 a^3 c^2 h + 20 a^3 b d h + 5 a^4 f h - 1/24)^2 + (2 c^2 d + 3 b c^2 d + 3 b^2 d^2 + 6 a c d^2 + 2 b c f + 4 b^3 c f + 12 a b c^2 f + 6 a b d f + 12 a b^2 d f + 12 a^2 c d f + 12 a^2 b f^2 + b h + b^5 h + 2 a c h + 20 a b^3 c h + 30 a^2 b c^2 h + 3 a^2 d h + 30 a^2 b^2 d h + 20 a^3 c d h + 4 a^3 f h + 20 a^3 b f h + 5 a^4 h^2 - 1/120)^2, {a, b, c, d, f, h}, WorkingPrecision -> 32] Out[1a -> 0.49856360414273480029211060957388, b -> 0.87633476418476006219360546358197, c -> 0.24754664962461521368380404047430, d -> 0.024575890793505412193353159356018, f -> -0.00093201041042137425003951844268342, h -> 0.00026544139408412758868359779800026}} If that isn't the solution you need then perhaps there is another minimization method which might accept a starting position, find a "nearby" solution and you try random starting positions until you get what you need. Or you might use a minimization method which allows you to specify constraints on the variables to help find the solution that you need.

Is there any chance that this solution, which took three seconds to find, might provide what you need?

In[1]:= NMinimize[(a + a b + a^2 c + a^3 d + a^4 f + a^5 h - 1)^2 +
 (b^2 + 2 a b c + 3 a^2 b d + 4 a^3 b f + 5 a^4 b h - 1)^2 +
 (b c + b^2 c + 2 a c^2 + 3 a b^2 d + 3 a^2 c d + 6 a^2 b^2 f + 4 a^3 c f + 10 a^3 b^2 h + 5 a^4 c h - 1/2)^2 +
 (2 b c^2 + b d + b^3 d + 2 a c d + 6 a b c d + 3 a^2 d^2 + 4 a b^3 f + 12 a^2 b c f + 4 a^3 d f + 10 a^2 b^3 h + 20 a^3 b c h + 5 a^4 d h - 1/6)^2 +
 (c^3 + 2 b c d + 3 b^2 c d + 3 a c^2 d + 6 a b d^2 + b f + b^4 f + 2 a c f + 12 a b^2 c f + 6 a^2 c^2 f + 3 a^2 d f + 12 a^2 b d f + 4 a^3 f^2 + 5 a b^4 h + 30 a^2 b^2 c h + 10 a^3 c^2 h + 20 a^3 b d h + 5 a^4 f h - 1/24)^2 +
 (2 c^2 d + 3 b c^2 d + 3 b^2 d^2 + 6 a c d^2 + 2 b c f + 4 b^3 c f + 12 a b c^2 f + 6 a b d f + 12 a b^2 d f + 12 a^2 c d f + 12 a^2 b f^2 + b h + b^5 h + 2 a c h + 20 a b^3 c h + 30 a^2 b c^2 h + 3 a^2 d h + 30 a^2 b^2 d h + 20 a^3 c d h + 4 a^3 f h + 20 a^3 b f h + 5 a^4 h^2 - 1/120)^2,
 {a, b, c, d, f, h}, WorkingPrecision -> 32]

Out[1a -> 0.49856360414273480029211060957388, 
  b -> 0.87633476418476006219360546358197, 
  c -> 0.24754664962461521368380404047430, 
  d -> 0.024575890793505412193353159356018, 
  f -> -0.00093201041042137425003951844268342, 
  h -> 0.00026544139408412758868359779800026}}

If that isn't the solution you need then perhaps there is another minimization method which might accept a starting position, find a "nearby" solution and you try random starting positions until you get what you need. Or you might use a minimization method which allows you to specify constraints on the variables to help find the solution that you need.

POSTED BY: Bill Simpson

Doug Stoll

Doug Stoll, Home user

Posted 12 years ago

POSTED BY: Doug Stoll

Frank Kampas

Frank Kampas, Physicist at Large Consulting

Posted 12 years ago

In[2]:= NSolve[x^4 - 1 == 0, {x}] Out[2]= {{x -> -1.}, {x -> 0. - 1. I}, {x -> 0. + 1. I}, {x -> 1.}} In[1]:= NSolve[x^4 - 1 == 0, {x}, Reals] Out[1]= {{x -> -1.}, {x -> 1.}}

POSTED BY: Frank Kampas

Reply to this discussion

Reply Preview

Attachments

Remove Add a file to this post

Follow this discussion

or Discard

Feedback