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Re: conditional is giving wrong value

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73757] Re: conditional is giving wrong value
  • From: dh <dh at metrohm.ch>
  • Date: Tue, 27 Feb 2007 05:54:17 -0500 (EST)
  • References: <errljn$86m$1@smc.vnet.net>


Hi Peter,

the precision of your "x" variables decreases continually. Is your 

algorthm stable? Anyway, if the precision has reached 2 digits, another 

quirck of mathematica emerges, namly:

1`2 > 0 gives False

why this is so I can not tell, but I will post this to the group.

Daniel



Peter Jay Salzman wrote:

> I'm implementing the method of steepest descent to minimize a function in

> Mathematica and have a few nagging problems, the most serious being that a

> conditional is giving a wrong value.

> 

> Here's my code:

> 

> 

> (* Cell one ========================================================= *)

> 

> Clear[a, delf, delta, f, iteration, min, s, theA, tolerance, x, xNew ];

> << Calculus`VectorAnalysis`;

> 

> 

> (* Function to minimize *)

> f[x_,y_] := 1/2 * x^2  +  1/2 * y^2

> 

> (* Initial Guess. *)

> x  =  { {5.0`20, 1.0`20} }

> 

> (* Direction that points "downhill" from current location. *)

> s  =  {};

> 

> (* The gradient of the function to minimize *)

> (*

>    This doesn't work:

>    delf[x_,y_] := - Grad[f[x,y], Cartesian[x,y,z]];

>    delf[3,1]

> )*

> delf[x_,y_] := { x, 5*y };

> 

> 

> (* Cell two ========================================================= *)

> 

> 

> iteration = 0;

> tolerance = 10^(-30);

> delta = 10;

> 

> 

> While delta > tolerance,

> 

>    Print[{delta, N[tolerance], delta > tolerance}];

> 

>    (* Get direction to travel in (downhill) from grad f.  Ugly syntax! *)

>    s = Append[s, -delf[Last[x][[1]], Last[x][[2]]]];

>    Print["s: ", s];

> 

>    (* a tells us how far to travel.  Need to minimize f to find it. *)  

>    xNew = Last[x] + a*delf[Last[x][[1]], Last[x][[2]]];

> 

>    (* Minimize f wrt a.  Can I do this without using temp var theA? *)

>    {min, theA} = Minimize[f[xNew[[1]], xNew[[2]]], {a}];

>    Print["f at minimum of ", min, " when ", theA];

> 

>    (* Update x using the direction *)

>    xNew = xNew /. theA;

>    delta = Norm[Last[x] - xNew];

>    Print[delta];

>    x = Append[x, xNew /. theA];

> 

>    Print["The new x is ", N[xNew], 20];

>    iteration += 1;

> ]

> 

> Print["Convergence in ", iteration, " iterations."];

> Print["Minimum point at ", Last[x]];

> Print["Value of f at min point: ", f[Last[x][[1]], Last[x][[2]]] ];

> 

> (* ================================================================== *)

> 

> 

> 

> The most serious problem is that this program always terminates at the 23rd

> iteration.   At the last iteration, this line:

> 

>    Print[{delta, N[tolerance], delta > tolerance}];

> 

> prints:

> 

>    { 0.00046, 1.0x10^(-30), True }

> 

> which indicates that 4.6^-4 > 1.0^-30 is true.  What am I doing wrong??

> 

> 

> 

> Other less serious issues that I can live with:

> 

> 1. I'd like to define the gradient of the trial function without me

> explicitly finding the gradient.  For this f, it's nothing, but in

> principle, finding the gradient can be very tedious.  This doesn't work:

> 

>     delf[x_,y_] := - Grad[f[x,y], Cartesian[x,y,z]];

> 

> because when I type delf[3,2], the arguments get passed to Cartesian[] as

> {3,2,z}.  How can I get around this?

> 

> 

> 2. The first time I run this, Mathematica complains that "tolerance" is

> similar to "Tolerance" and "min" is similar to "Min.  How can I supress

> that?

> 

> 

> 3. When I run the first cell (the material above "new cell") Mathematica

>    prints out "Null^6".  What does this mean and why is it getting printed?

> 

> 

> 4. Any coding tips I should keep in mind to become a better Mathematica programmer?

> 

> Many thanks!

> Pete

> 




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