FPL Statistics Group

MINPACK Problems

In the course of running the MINPACK test problems (here are the materials needed to run the FORTRAN test routines), I noticed some discrepancies among various sets of results:

The results from the FORTRAN run of lmder.
The lmder results from JDK 1.1.6 (September 1998 version?) when Math.pow(x,2) has not been replaced by x*x for the Powell problem. Here.
The lmder results from JDK 1.1.6 (September 1998 version?) when Math.pow(x,2) has been replaced by x*x for the Powell problem. Here.
The lmder results from Java 2 SDK, version 1.3.0 (June 2000 version?) when Math.pow(x,2) has not been replaced by x*x for the Powell problem. Here.
The results from the FORTRAN run of lmdif.
The lmdif results from Java 2 SDK, version 1.3.0 (June 2000 version?) when Math.pow(x,2) has not been replaced by x*x. Here.

Under the older version of Java, replacing x**2 in the FORTRAN lmder code for the Powell function with x*x in the Java lmder code led to distinguishable results. On the other hand, replacing x**2 in the FORTRAN code for the Powell function with Math.pow(x,2) in the Java code led to indistinguishable results.

The newer version of Java yields lmder results that differ slightly (5th or 6th digit) from the FORTRAN results for the Meyer problem.

The newer version of Java yields lmdif results that differ from the FORTRAN results for the Brown and Dennis problem. These results can differ in the 4th digit. Presumably (???) this is due to differences in the FORTRAN and Java implementations of the sine and cosine functions.

I am not a numerical analyst and have made no effort to analyze these differences further. I did hand recheck the code and I did run debugging sessions to follow the development of differences. I assume that the differences are due to problems associated with semi-pathological functions and machine precision. However, it is of course possible that there are errors in the Java translation. If you detect an error, PLEASE contact me (Steve Verrill) at sverrill@fs.fed.us.

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Last modified on 2/6/02.