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Posted to issues@commons.apache.org by "Tom Milac (JIRA)" <ji...@apache.org> on 2009/10/09 00:48:31 UTC
[jira] Created: (MATH-301) Erf(z) should return 1.0 for z 'large'
but fails with a MaxIterationsExceededException for z > 26.0.
Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
-----------------------------------------------------------------------------------------------------
Key: MATH-301
URL: https://issues.apache.org/jira/browse/MATH-301
Project: Commons Math
Issue Type: Bug
Affects Versions: 2.0
Environment: MacOS and Linux
Reporter: Tom Milac
Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
Sample code
-----------------
import org.apache.commons.math.MathException;
import org.apache.commons.math.special.Erf;
public class TestErf {
public TestErf() {
}
public static void main(String[] args) {
double z = Double.NEGATIVE_INFINITY;
try {
for(int i=0; i<100; i++) {
z = i;
System.out.println("z = " + z + " erf(z) = " + Erf.erf(z));
}
System.out.flush();
} catch (MathException mex) {
System.out.println("z failed = " + z);
mex.printStackTrace();
}
}
}
Output
---------
z = 0.0 erf(z) = 0.0
z = 1.0 erf(z) = 0.842700792949715
z = 2.0 erf(z) = 0.9953222650189528
z = 3.0 erf(z) = 0.9999779095030024
z = 4.0 erf(z) = 0.9999999845827416
z = 5.0 erf(z) = 0.9999999999984622
z = 6.0 erf(z) = 0.9999999999999997
z = 7.0 erf(z) = 1.000000000000001
z = 8.0 erf(z) = 0.9999999999999986
z = 9.0 erf(z) = 1.000000000000003
z = 10.0 erf(z) = 1.0000000000000115
z = 11.0 erf(z) = 1.0000000000000016
z = 12.0 erf(z) = 0.9999999999999941
z = 13.0 erf(z) = 0.9999999999999846
z = 14.0 erf(z) = 1.0000000000000024
z = 15.0 erf(z) = 0.9999999999999805
z = 16.0 erf(z) = 0.9999999999999988
z = 17.0 erf(z) = 0.9999999999999949
z = 18.0 erf(z) = 0.9999999999999907
z = 19.0 erf(z) = 0.9999999999999731
z = 20.0 erf(z) = 0.9999999999999862
z = 21.0 erf(z) = 0.9999999999999721
z = 22.0 erf(z) = 1.000000000000017
z = 23.0 erf(z) = 1.0000000000000577
z = 24.0 erf(z) = 1.000000000000054
z = 25.0 erf(z) = 1.0000000000000262
z = 26.0 erf(z) = 1.0000000000000735
z failed = 27.0
org.apache.commons.math.MaxIterationsExceededException: Maximal number of iterations (10,000) exceeded
at org.apache.commons.math.special.Gamma.regularizedGammaP(Gamma.java:181)
at org.apache.commons.math.special.Erf.erf(Erf.java:51)
at org.fhcrc.math.minimization.TestErf.main(TestErf.java:23)
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[jira] Commented: (MATH-301) Erf(z) should return 1.0 for z 'large'
but fails with a MaxIterationsExceededException for z > 26.0.
Posted by "Phil Steitz (JIRA)" <ji...@apache.org>.
[ https://issues.apache.org/jira/browse/MATH-301?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12836187#action_12836187 ]
Phil Steitz commented on MATH-301:
----------------------------------
>From commons-user, another example of inaccurate results for extreme erf values:
NormalDistribution normDist = new NormalDistributionImpl(40,1.5)
;
try{
System.out.println("cummulative probability::
"+normDist.cumulativeProbability(0.908789));
}
catch(MathException e){
e.printStackTrace();
}
*Result:*
cummulative probability:: *-8.104628079763643E-15*
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> -----------------------------------------------------------------------------------------------------
>
> Key: MATH-301
> URL: https://issues.apache.org/jira/browse/MATH-301
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.0
> Environment: MacOS and Linux
> Reporter: Tom Milac
> Fix For: 2.1
>
> Attachments: erf.txt
>
>
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> Sample code
> -----------------
> import org.apache.commons.math.MathException;
> import org.apache.commons.math.special.Erf;
> public class TestErf {
> public TestErf() {
> }
> public static void main(String[] args) {
> double z = Double.NEGATIVE_INFINITY;
> try {
> for(int i=0; i<100; i++) {
> z = i;
> System.out.println("z = " + z + " erf(z) = " + Erf.erf(z));
> }
> System.out.flush();
> } catch (MathException mex) {
> System.out.println("z failed = " + z);
> mex.printStackTrace();
> }
> }
> }
> Output
> ---------
> z = 0.0 erf(z) = 0.0
> z = 1.0 erf(z) = 0.842700792949715
> z = 2.0 erf(z) = 0.9953222650189528
> z = 3.0 erf(z) = 0.9999779095030024
> z = 4.0 erf(z) = 0.9999999845827416
> z = 5.0 erf(z) = 0.9999999999984622
> z = 6.0 erf(z) = 0.9999999999999997
> z = 7.0 erf(z) = 1.000000000000001
> z = 8.0 erf(z) = 0.9999999999999986
> z = 9.0 erf(z) = 1.000000000000003
> z = 10.0 erf(z) = 1.0000000000000115
> z = 11.0 erf(z) = 1.0000000000000016
> z = 12.0 erf(z) = 0.9999999999999941
> z = 13.0 erf(z) = 0.9999999999999846
> z = 14.0 erf(z) = 1.0000000000000024
> z = 15.0 erf(z) = 0.9999999999999805
> z = 16.0 erf(z) = 0.9999999999999988
> z = 17.0 erf(z) = 0.9999999999999949
> z = 18.0 erf(z) = 0.9999999999999907
> z = 19.0 erf(z) = 0.9999999999999731
> z = 20.0 erf(z) = 0.9999999999999862
> z = 21.0 erf(z) = 0.9999999999999721
> z = 22.0 erf(z) = 1.000000000000017
> z = 23.0 erf(z) = 1.0000000000000577
> z = 24.0 erf(z) = 1.000000000000054
> z = 25.0 erf(z) = 1.0000000000000262
> z = 26.0 erf(z) = 1.0000000000000735
> z failed = 27.0
> org.apache.commons.math.MaxIterationsExceededException: Maximal number of iterations (10,000) exceeded
> at org.apache.commons.math.special.Gamma.regularizedGammaP(Gamma.java:181)
> at org.apache.commons.math.special.Erf.erf(Erf.java:51)
> at org.fhcrc.math.minimization.TestErf.main(TestErf.java:23)
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[jira] Updated: (MATH-301) Erf(z) should return 1.0 for z 'large'
but fails with a MaxIterationsExceededException for z > 26.0.
Posted by "Phil Steitz (JIRA)" <ji...@apache.org>.
[ https://issues.apache.org/jira/browse/MATH-301?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]
Phil Steitz updated MATH-301:
-----------------------------
Fix Version/s: 2.1
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> -----------------------------------------------------------------------------------------------------
>
> Key: MATH-301
> URL: https://issues.apache.org/jira/browse/MATH-301
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.0
> Environment: MacOS and Linux
> Reporter: Tom Milac
> Fix For: 2.1
>
> Attachments: erf.txt
>
>
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> Sample code
> -----------------
> import org.apache.commons.math.MathException;
> import org.apache.commons.math.special.Erf;
> public class TestErf {
> public TestErf() {
> }
> public static void main(String[] args) {
> double z = Double.NEGATIVE_INFINITY;
> try {
> for(int i=0; i<100; i++) {
> z = i;
> System.out.println("z = " + z + " erf(z) = " + Erf.erf(z));
> }
> System.out.flush();
> } catch (MathException mex) {
> System.out.println("z failed = " + z);
> mex.printStackTrace();
> }
> }
> }
> Output
> ---------
> z = 0.0 erf(z) = 0.0
> z = 1.0 erf(z) = 0.842700792949715
> z = 2.0 erf(z) = 0.9953222650189528
> z = 3.0 erf(z) = 0.9999779095030024
> z = 4.0 erf(z) = 0.9999999845827416
> z = 5.0 erf(z) = 0.9999999999984622
> z = 6.0 erf(z) = 0.9999999999999997
> z = 7.0 erf(z) = 1.000000000000001
> z = 8.0 erf(z) = 0.9999999999999986
> z = 9.0 erf(z) = 1.000000000000003
> z = 10.0 erf(z) = 1.0000000000000115
> z = 11.0 erf(z) = 1.0000000000000016
> z = 12.0 erf(z) = 0.9999999999999941
> z = 13.0 erf(z) = 0.9999999999999846
> z = 14.0 erf(z) = 1.0000000000000024
> z = 15.0 erf(z) = 0.9999999999999805
> z = 16.0 erf(z) = 0.9999999999999988
> z = 17.0 erf(z) = 0.9999999999999949
> z = 18.0 erf(z) = 0.9999999999999907
> z = 19.0 erf(z) = 0.9999999999999731
> z = 20.0 erf(z) = 0.9999999999999862
> z = 21.0 erf(z) = 0.9999999999999721
> z = 22.0 erf(z) = 1.000000000000017
> z = 23.0 erf(z) = 1.0000000000000577
> z = 24.0 erf(z) = 1.000000000000054
> z = 25.0 erf(z) = 1.0000000000000262
> z = 26.0 erf(z) = 1.0000000000000735
> z failed = 27.0
> org.apache.commons.math.MaxIterationsExceededException: Maximal number of iterations (10,000) exceeded
> at org.apache.commons.math.special.Gamma.regularizedGammaP(Gamma.java:181)
> at org.apache.commons.math.special.Erf.erf(Erf.java:51)
> at org.fhcrc.math.minimization.TestErf.main(TestErf.java:23)
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[jira] Updated: (MATH-301) Erf(z) should return 1.0 for z 'large'
but fails with a MaxIterationsExceededException for z > 26.0.
Posted by "Nipun Jawalkar (JIRA)" <ji...@apache.org>.
[ https://issues.apache.org/jira/browse/MATH-301?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]
Nipun Jawalkar updated MATH-301:
--------------------------------
Attachment: erf.txt
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> -----------------------------------------------------------------------------------------------------
>
> Key: MATH-301
> URL: https://issues.apache.org/jira/browse/MATH-301
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.0
> Environment: MacOS and Linux
> Reporter: Tom Milac
> Attachments: erf.txt
>
>
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> Sample code
> -----------------
> import org.apache.commons.math.MathException;
> import org.apache.commons.math.special.Erf;
> public class TestErf {
> public TestErf() {
> }
> public static void main(String[] args) {
> double z = Double.NEGATIVE_INFINITY;
> try {
> for(int i=0; i<100; i++) {
> z = i;
> System.out.println("z = " + z + " erf(z) = " + Erf.erf(z));
> }
> System.out.flush();
> } catch (MathException mex) {
> System.out.println("z failed = " + z);
> mex.printStackTrace();
> }
> }
> }
> Output
> ---------
> z = 0.0 erf(z) = 0.0
> z = 1.0 erf(z) = 0.842700792949715
> z = 2.0 erf(z) = 0.9953222650189528
> z = 3.0 erf(z) = 0.9999779095030024
> z = 4.0 erf(z) = 0.9999999845827416
> z = 5.0 erf(z) = 0.9999999999984622
> z = 6.0 erf(z) = 0.9999999999999997
> z = 7.0 erf(z) = 1.000000000000001
> z = 8.0 erf(z) = 0.9999999999999986
> z = 9.0 erf(z) = 1.000000000000003
> z = 10.0 erf(z) = 1.0000000000000115
> z = 11.0 erf(z) = 1.0000000000000016
> z = 12.0 erf(z) = 0.9999999999999941
> z = 13.0 erf(z) = 0.9999999999999846
> z = 14.0 erf(z) = 1.0000000000000024
> z = 15.0 erf(z) = 0.9999999999999805
> z = 16.0 erf(z) = 0.9999999999999988
> z = 17.0 erf(z) = 0.9999999999999949
> z = 18.0 erf(z) = 0.9999999999999907
> z = 19.0 erf(z) = 0.9999999999999731
> z = 20.0 erf(z) = 0.9999999999999862
> z = 21.0 erf(z) = 0.9999999999999721
> z = 22.0 erf(z) = 1.000000000000017
> z = 23.0 erf(z) = 1.0000000000000577
> z = 24.0 erf(z) = 1.000000000000054
> z = 25.0 erf(z) = 1.0000000000000262
> z = 26.0 erf(z) = 1.0000000000000735
> z failed = 27.0
> org.apache.commons.math.MaxIterationsExceededException: Maximal number of iterations (10,000) exceeded
> at org.apache.commons.math.special.Gamma.regularizedGammaP(Gamma.java:181)
> at org.apache.commons.math.special.Erf.erf(Erf.java:51)
> at org.fhcrc.math.minimization.TestErf.main(TestErf.java:23)
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[jira] Closed: (MATH-301) Erf(z) should return 1.0 for z 'large'
but fails with a MaxIterationsExceededException for z > 26.0.
Posted by "Phil Steitz (JIRA)" <ji...@apache.org>.
[ https://issues.apache.org/jira/browse/MATH-301?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]
Phil Steitz closed MATH-301.
----------------------------
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> -----------------------------------------------------------------------------------------------------
>
> Key: MATH-301
> URL: https://issues.apache.org/jira/browse/MATH-301
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.0
> Environment: MacOS and Linux
> Reporter: Tom Milac
> Fix For: 2.1
>
> Attachments: erf.txt
>
>
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> Sample code
> -----------------
> import org.apache.commons.math.MathException;
> import org.apache.commons.math.special.Erf;
> public class TestErf {
> public TestErf() {
> }
> public static void main(String[] args) {
> double z = Double.NEGATIVE_INFINITY;
> try {
> for(int i=0; i<100; i++) {
> z = i;
> System.out.println("z = " + z + " erf(z) = " + Erf.erf(z));
> }
> System.out.flush();
> } catch (MathException mex) {
> System.out.println("z failed = " + z);
> mex.printStackTrace();
> }
> }
> }
> Output
> ---------
> z = 0.0 erf(z) = 0.0
> z = 1.0 erf(z) = 0.842700792949715
> z = 2.0 erf(z) = 0.9953222650189528
> z = 3.0 erf(z) = 0.9999779095030024
> z = 4.0 erf(z) = 0.9999999845827416
> z = 5.0 erf(z) = 0.9999999999984622
> z = 6.0 erf(z) = 0.9999999999999997
> z = 7.0 erf(z) = 1.000000000000001
> z = 8.0 erf(z) = 0.9999999999999986
> z = 9.0 erf(z) = 1.000000000000003
> z = 10.0 erf(z) = 1.0000000000000115
> z = 11.0 erf(z) = 1.0000000000000016
> z = 12.0 erf(z) = 0.9999999999999941
> z = 13.0 erf(z) = 0.9999999999999846
> z = 14.0 erf(z) = 1.0000000000000024
> z = 15.0 erf(z) = 0.9999999999999805
> z = 16.0 erf(z) = 0.9999999999999988
> z = 17.0 erf(z) = 0.9999999999999949
> z = 18.0 erf(z) = 0.9999999999999907
> z = 19.0 erf(z) = 0.9999999999999731
> z = 20.0 erf(z) = 0.9999999999999862
> z = 21.0 erf(z) = 0.9999999999999721
> z = 22.0 erf(z) = 1.000000000000017
> z = 23.0 erf(z) = 1.0000000000000577
> z = 24.0 erf(z) = 1.000000000000054
> z = 25.0 erf(z) = 1.0000000000000262
> z = 26.0 erf(z) = 1.0000000000000735
> z failed = 27.0
> org.apache.commons.math.MaxIterationsExceededException: Maximal number of iterations (10,000) exceeded
> at org.apache.commons.math.special.Gamma.regularizedGammaP(Gamma.java:181)
> at org.apache.commons.math.special.Erf.erf(Erf.java:51)
> at org.fhcrc.math.minimization.TestErf.main(TestErf.java:23)
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[jira] Resolved: (MATH-301) Erf(z) should return 1.0 for z 'large'
but fails with a MaxIterationsExceededException for z > 26.0.
Posted by "Phil Steitz (JIRA)" <ji...@apache.org>.
[ https://issues.apache.org/jira/browse/MATH-301?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]
Phil Steitz resolved MATH-301.
------------------------------
Resolution: Fixed
Fixed in r920558.
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> -----------------------------------------------------------------------------------------------------
>
> Key: MATH-301
> URL: https://issues.apache.org/jira/browse/MATH-301
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.0
> Environment: MacOS and Linux
> Reporter: Tom Milac
> Fix For: 2.1
>
> Attachments: erf.txt
>
>
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> Sample code
> -----------------
> import org.apache.commons.math.MathException;
> import org.apache.commons.math.special.Erf;
> public class TestErf {
> public TestErf() {
> }
> public static void main(String[] args) {
> double z = Double.NEGATIVE_INFINITY;
> try {
> for(int i=0; i<100; i++) {
> z = i;
> System.out.println("z = " + z + " erf(z) = " + Erf.erf(z));
> }
> System.out.flush();
> } catch (MathException mex) {
> System.out.println("z failed = " + z);
> mex.printStackTrace();
> }
> }
> }
> Output
> ---------
> z = 0.0 erf(z) = 0.0
> z = 1.0 erf(z) = 0.842700792949715
> z = 2.0 erf(z) = 0.9953222650189528
> z = 3.0 erf(z) = 0.9999779095030024
> z = 4.0 erf(z) = 0.9999999845827416
> z = 5.0 erf(z) = 0.9999999999984622
> z = 6.0 erf(z) = 0.9999999999999997
> z = 7.0 erf(z) = 1.000000000000001
> z = 8.0 erf(z) = 0.9999999999999986
> z = 9.0 erf(z) = 1.000000000000003
> z = 10.0 erf(z) = 1.0000000000000115
> z = 11.0 erf(z) = 1.0000000000000016
> z = 12.0 erf(z) = 0.9999999999999941
> z = 13.0 erf(z) = 0.9999999999999846
> z = 14.0 erf(z) = 1.0000000000000024
> z = 15.0 erf(z) = 0.9999999999999805
> z = 16.0 erf(z) = 0.9999999999999988
> z = 17.0 erf(z) = 0.9999999999999949
> z = 18.0 erf(z) = 0.9999999999999907
> z = 19.0 erf(z) = 0.9999999999999731
> z = 20.0 erf(z) = 0.9999999999999862
> z = 21.0 erf(z) = 0.9999999999999721
> z = 22.0 erf(z) = 1.000000000000017
> z = 23.0 erf(z) = 1.0000000000000577
> z = 24.0 erf(z) = 1.000000000000054
> z = 25.0 erf(z) = 1.0000000000000262
> z = 26.0 erf(z) = 1.0000000000000735
> z failed = 27.0
> org.apache.commons.math.MaxIterationsExceededException: Maximal number of iterations (10,000) exceeded
> at org.apache.commons.math.special.Gamma.regularizedGammaP(Gamma.java:181)
> at org.apache.commons.math.special.Erf.erf(Erf.java:51)
> at org.fhcrc.math.minimization.TestErf.main(TestErf.java:23)
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[jira] Commented: (MATH-301) Erf(z) should return 1.0 for z 'large'
but fails with a MaxIterationsExceededException for z > 26.0.
Posted by "Nipun Jawalkar (JIRA)" <ji...@apache.org>.
[ https://issues.apache.org/jira/browse/MATH-301?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12771637#action_12771637 ]
Nipun Jawalkar commented on MATH-301:
-------------------------------------
Hi,
Here's a patch that uses a different algorithm to calculate erf(x). It's adapted from "Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, by Milton Abramowitz and Irene A. Stegun".
It no longer throws a MathException if x is too large or small. I've added one test to check erf(x) for 20<=x<40, and all previous tests pass also.
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> -----------------------------------------------------------------------------------------------------
>
> Key: MATH-301
> URL: https://issues.apache.org/jira/browse/MATH-301
> Project: Commons Math
> Issue Type: Bug
> Affects Versions: 2.0
> Environment: MacOS and Linux
> Reporter: Tom Milac
>
> Erf(z) should return 1.0 for z 'large' but fails with a MaxIterationsExceededException for z > 26.0.
> Sample code
> -----------------
> import org.apache.commons.math.MathException;
> import org.apache.commons.math.special.Erf;
> public class TestErf {
> public TestErf() {
> }
> public static void main(String[] args) {
> double z = Double.NEGATIVE_INFINITY;
> try {
> for(int i=0; i<100; i++) {
> z = i;
> System.out.println("z = " + z + " erf(z) = " + Erf.erf(z));
> }
> System.out.flush();
> } catch (MathException mex) {
> System.out.println("z failed = " + z);
> mex.printStackTrace();
> }
> }
> }
> Output
> ---------
> z = 0.0 erf(z) = 0.0
> z = 1.0 erf(z) = 0.842700792949715
> z = 2.0 erf(z) = 0.9953222650189528
> z = 3.0 erf(z) = 0.9999779095030024
> z = 4.0 erf(z) = 0.9999999845827416
> z = 5.0 erf(z) = 0.9999999999984622
> z = 6.0 erf(z) = 0.9999999999999997
> z = 7.0 erf(z) = 1.000000000000001
> z = 8.0 erf(z) = 0.9999999999999986
> z = 9.0 erf(z) = 1.000000000000003
> z = 10.0 erf(z) = 1.0000000000000115
> z = 11.0 erf(z) = 1.0000000000000016
> z = 12.0 erf(z) = 0.9999999999999941
> z = 13.0 erf(z) = 0.9999999999999846
> z = 14.0 erf(z) = 1.0000000000000024
> z = 15.0 erf(z) = 0.9999999999999805
> z = 16.0 erf(z) = 0.9999999999999988
> z = 17.0 erf(z) = 0.9999999999999949
> z = 18.0 erf(z) = 0.9999999999999907
> z = 19.0 erf(z) = 0.9999999999999731
> z = 20.0 erf(z) = 0.9999999999999862
> z = 21.0 erf(z) = 0.9999999999999721
> z = 22.0 erf(z) = 1.000000000000017
> z = 23.0 erf(z) = 1.0000000000000577
> z = 24.0 erf(z) = 1.000000000000054
> z = 25.0 erf(z) = 1.0000000000000262
> z = 26.0 erf(z) = 1.0000000000000735
> z failed = 27.0
> org.apache.commons.math.MaxIterationsExceededException: Maximal number of iterations (10,000) exceeded
> at org.apache.commons.math.special.Gamma.regularizedGammaP(Gamma.java:181)
> at org.apache.commons.math.special.Erf.erf(Erf.java:51)
> at org.fhcrc.math.minimization.TestErf.main(TestErf.java:23)
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