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Optional Arguments and FindRoot

• To: mathgroup at smc.vnet.net
• Subject: [mg13217] Optional Arguments and FindRoot
• From: sean_ross_at_pl-04m3 at smtpgw1.plk.af.mil
• Date: Mon, 13 Jul 1998 07:43:05 -0400
• Sender: owner-wri-mathgroup at wolfram.com

     I have a function which has an optional _Real argument with a
default 
     value of 0.0.  When I execute FindRoot on this function, it
executes 
     properly if I give a non-zero value for my optional parameter or
leave 
     it out.  If I specify a value of 0.0 for this parameter, then
FindRoot 
     substitutes an INTEGER zero.  Can anyone shed any light as to why
this 
     is occurring?  I fixed the problem with an extra function
definition 
     for Integer zero final arguments, so that is not an issue.  I am 
     interested in why FindRoot decided to put an Integer zero where I 
     specified a Real zero. 
     
      Thanks.  Sean
     
     
     Here is the definition of the function, with a final optional
argument 
     qsoi_Real:0.
     
     Dkopo[lp_Real:1.064, ls_Real, 
           Topo_Real /; Topo > 20. && Topo <= 200., qsoi_Real:0.] /; 
         ls > lp := 
       Module[{li, qioi}, 
         li = (1/lp - 1/ls)^(-1); 
         qioi = 
           ArcSin[li/
                 nextLiNbO3[li, Topo]*(
                   nextLiNbO3[ls, Topo]*Sin[qsoi])/ls]; 
         2*Pi*(nextLiNbO3[lp, Topo]/lp - 
               nextLiNbO3[ls, Topo]*Cos[qsoi]/ls - 
               nextLiNbO3[li, Topo]*Cos[qioi]/li - 
               1/Dopo[Topo])];
     
     Dopo[T_(*degrees C*)]:=
       Module[{a=1.54*^-5,  b=5.3*^-9},
         29.75 (1+a (T-25.)+ b (T-25.)^2)];
     
     Here is the FindRoot executing just fine if I leave the argument
out.
     
     FindRoot[Dkopo[1.064,x,45.],{x,1.54,1.55}]
     
     {x->1.52972}
     
     Here is the FindRoot executing just fine if I specify a non-zero 
     argument.
     
     FindRoot[Dkopo[1.064,x,45.,0.001],{x,1.54,1.55}]
     
     {x->1.52989}
     
     Here is the findroot function substituting an INTEGER zero into my 
     function rather than the REAL zero I specified.
     
     FindRoot[Dkopo[1.064,x,45.,0.000],{x,1.54,1.55}]
     
     FindRoot::"frnum": 
         "Function ({Dkopo[\(1.06400000000000005`, \
     1.54000000000000003`, 45.`, 0\)]}\) is not a length 1 list of
numbers 
     at x = 1.540"