       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"

```

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