Just one addition to this. I noticed that its not really true that the output can be used in R verbatim since the C output uses pow instead of ^; however, if one replaces the "code c" statement with the statement "list export" then it is valid R. That is the input to mathomatic should be:
mean = a/(a+b) variance = (a*b)/(((a+b)^2) * (a+b+1)) eliminate b a simplify list export eliminate a b simplify list export On 11/30/05, Gabor Grothendieck <[EMAIL PROTECTED]> wrote: > Sorry I seemed to have messed up the copying and pasting. > Here it is again. > > --- > > Go to http://mathomatic.orgserve.de/math/ and install mathomatic > (its free) or just connect to the online server and do this. > > The C output, i.e the result of the two code c commands, > can be used verbatim in R. > > Note that mathomatic does not support logs but for simple > problems like this its very useful. > > Note that 1-> and 2-> are the mathomatic prompts and what > comes after them are what I typed in. The entry goes into > the corresponding equation space, i.e. equation 1 or equation 2. > > This is what you enter: > > mean = a/(a+b) > variance = (a*b)/(((a+b)^2) * (a+b+1)) > > eliminate b > a > simplify > code c > > eliminate a > b > simplify > code c > > and this is the entire session: > > > 1-> mean = a/(a+b) > > a > #1: mean = ------- > (a + b) > > 1-> variance = (a*b)/(((a+b)^2) * (a+b+1)) > > a*b > #2: variance = ------------------------- > (((a + b)^2)*(a + b + 1)) > > 2-> eliminate b > Solving equation #1 for (b)... > > 1 > (a^2)*(---- - 1) > mean > #2: variance = --------------------------------------------------- > 1 1 > (((a + (a*(---- - 1)))^2)*(a + (a*(---- - 1)) + 1)) > mean mean > > 2-> a > > mean*(1 - mean) > #2: a = mean*(--------------- - 1) > variance > > 2-> simplify > > ((mean^2) - (mean^3)) > #2: a = --------------------- - mean > variance > > 2-> code c > a = ((((mean * mean) - pow(mean, 3.0)) / variance) - mean); > > 2-> eliminate a > Solving equation #1 for (a)... > > b*mean ((mean^2) - (mean^3)) > #2: ---------- = --------------------- - mean > (1 - mean) variance > > 2-> b > > mean*(1 - mean) > #2: b = (--------------- - 1)*(1 - mean) > variance > > 2-> simplify > > ((mean^2) - mean) > #2: b = (1 + -----------------)*(mean - 1) > variance > > 2-> code c > b = ((1.0 + (((mean * mean) - mean) / variance)) * (mean - 1.0)); > > > > > On 11/30/05, Gabor Grothendieck <[EMAIL PROTECTED]> wrote: > > Go to http://mathomatic.orgserve.de/math/ and install mathomatic > > (its free) or just connect to the online server and do this. > > > > The C output, i.e the result of the two code c commands, > > can be used verbatim in R. > > > > Note that mathomatic does not support logs but for simply > > problems like this its very useful. > > > > Note that 1-> and 2-> are the mathomatic prompts and what > > comes after them are what I typed in. The entry goes into > > the corresponding equation space, i.e. equation 1 or equation 2. > > > > 1-> mean = a/(a+b) > > > > a > > #1: mean = ------- > > (a + b) > > > > 1-> variance = (a*b)/(((a+b)^2) * (a+b+1)) > > > > a*b > > #2: variance = ------------------------- > > (((a + b)^2)*(a + b + 1)) > > > > 2-> eliminate b > > Solving equation #1 for (b)... > > > > 1 > > (a^2)*(---- - 1) > > mean > > #2: variance = --------------------------------------------------- > > 1 1 > > (((a + (a*(---- - 1)))^2)*(a + (a*(---- - 1)) + 1)) > > mean mean > > > > 2-> a > > > > mean*(1 - mean) > > #2: a = mean*(--------------- - 1) > > variance > > > > 2-> simplify > > > > ((mean^2) - (mean^3)) > > #2: a = --------------------- - mean > > variance > > > > 2-> eliminate a > > Solving equation #1 for (a)... > > > > b*mean ((mean^2) - (mean^3)) > > #2: ---------- = --------------------- - mean > > (1 - mean) variance > > > > 2-> b > > > > mean*(1 - mean) > > #2: b = (--------------- - 1)*(1 - mean) > > variance > > 2-> simplify > > > > ((mean^2) - mean) > > #2: b = (1 + -----------------)*(mean - 1) > > variance > > > > > > 2-> code c > > b = ((1.0 + (((mean * mean) - mean) / variance)) * (mean - 1.0)); > > > > 2-> #1 > > > > b*mean > > #1: a = ---------- > > (1 - mean) > > > > 1-> code c > > a = (b * mean / (1.0 - mean)); > > > > > > > > On 11/30/05, Scott Story <[EMAIL PROTECTED]> wrote: > > > I am trying to write a function that will solve a simple system of > > > nonlinear equations for the parameters that describe the beta > > > distribution (a,b) given the mean and variance. > > > > > > > > > mean = a/(a+b) > > > variance = (a*b)/(((a+b)^2) * (a+b+1)) > > > > > > Any help as to where to start would be welcome. > > > > > > > > > > > > -- > > > Scott Story > > > Graduate Student > > > MSU Ecology Department > > > 319 Lewis Hall > > > Bozeman, Mt 59717 > > > 406.994.2670 > > > [EMAIL PROTECTED] > > > > > > ______________________________________________ > > > [email protected] mailing list > > > https://stat.ethz.ch/mailman/listinfo/r-help > > > PLEASE do read the posting guide! > > > http://www.R-project.org/posting-guide.html > > > > > > ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
