[Rd] "Unable to optimize" error returned in factanal using R-3.0.1, Windows 64 bit, and OpenBLAS

[Adler, Avraham]

Hello,

I have been trying for weeks to compile a 64-bit Rblas. I started with ATLAS where I have had success in the past, but 64 bit was not behaving, and as each compilation takes between 9 and 12 hours, "test, check, and revise" was not going to be really viable. I therefore switched to OpenBLas (OPBL). I was successful in compiling R-3.0.1 and an OPBL-based BLAS for Windows 64bit SANDYBRIDGE (Corei7-avx) which passes all of OPBL's internal checks, and all but *one* of R's checks (it passes the spline one failed by the 32-bit version which I asked about yesterday). Well, it fails the same procedure twice, but not all the time.

The error is found in a call to the `factanal` procedure, specifically the call to `optim` therein, and it returns an error code "NEW_X", which I have never seen before. It fails this call in the checks for both stats.R and datasets.R, but does not fail them all, and for those it works, it returns the proper answers.

The first call that fails is in statsEx.Rout

		fa <- factanal( ~., 2, data = swiss)
		Error in factanal(~., 2, data = swiss) :
		  unable to optimize from this starting value 

Interestingly, using 1 or 3 as the value for factor works fine, it is 2 which fails.

The other failed call is in datasetsEx, and it is...

		(Harman23.FA <- factanal(factors = 1, covmat = Harman23.cor)) 

		...other code...

		for(factors in 2:4) print(update(Harman23.FA, factors = factors)) 

...when the value for factors is 4 (1, 2, and 3 work fine).

I understand that "unable to optimize" can only come from no convergent "best fit" being found in the `factanal.fit.mle` procedure. Some detective work shows that the failure is in the call to `optim`. Specifically, when the  call __passes__, it returns:

		> nfit

		Call:
		NULL

		Uniquenesses:
			   Fertility      Agriculture      Examination        Education
				   0.420            0.492            0.270            0.005
				Catholic Infant.Mortality
				   0.061            0.960

		Loadings:
						 Factor1 Factor2
		Fertility        -0.674   0.356
		Agriculture      -0.648   0.297
		Examination       0.713  -0.471
		Education         0.997
		Catholic         -0.178   0.953
		Infant.Mortality -0.104   0.169

					   Factor1 Factor2
		SS loadings      2.419   1.373
		Proportion Var   0.403   0.229
		Cumulative Var   0.403   0.632

		The degrees of freedom for the model is 4 and the fit was 0.5017
		> nfit$converged
		[1] TRUE

But when it __fails__ it returns:

		> nfit

		Call:
		NULL

		Uniquenesses:
			   Fertility      Agriculture      Examination        Education
				   0.417            0.487            0.258            0.012
				Catholic Infant.Mortality
				   0.097            0.951

		Loadings:
						 Factor1 Factor2
		Fertility        -0.683   0.340
		Agriculture      -0.658   0.282
		Examination       0.728  -0.461
		Education         0.993
		Catholic         -0.203   0.929
		Infant.Mortality -0.110   0.171

					   Factor1 Factor2
		SS loadings      2.469   1.302
		Proportion Var   0.411   0.217
		Cumulative Var   0.411   0.628

		The degrees of freedom for the model is 4 and the fit was 0.5042
		> nfit$converged
		[1] FALSE

This results in a different set of starting values being passed to `optim`, namely:

__FAIL__:

		$par
							  [,1]
		Fertility        0.4180782
		Agriculture      0.4898004
		Examination      0.2608759
		Education        0.0005000
		Catholic         0.1028010
		Infant.Mortality 0.9454609

		$value
		[1] 0.5015197

		$counts
		function gradient
			 302      302

		$convergence
		[1] 1

		$message
		[1] "NEW_X"

_____________________________________________

__PASS__:

		$par
							   [,1]
		Fertility        0.41936338
		Agriculture      0.49205978
		Examination      0.26976286
		Education        0.00050000
		Catholic         0.06973751
		Infant.Mortality 0.96007318

		$value
		[1] 0.5008949

		$counts
		function gradient
			  22       22

		$convergence
		[1] 0

		$message
		[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"

I have never seen that particular failure message from `optim` before, "NEW_X", and I cannot locate what it means. It is possible, if not probably, that it has to do with one of the functions internal to `factanal.fit.mle`, possibly the call to `eigen` as I presume that calls Rblas, but without knowing what the error means, I'm not sure what else to do. I know the errors are significant, as the SurviveGoto2 Blas's compiled by Dr. Nakama do not exhibit these errors, but I have no idea as to what is causing it.

What I am hoping is that one of the experts on this list (perhaps one of the members of the core team who helped write `factanal`) can recognize what may be causing the call to `optim` to fails sometimes, and could suggest some possible investigatory paths or explain why it may not be possible to be solved. I'd also be happy to e-mail or post the compiled dll's if anyone wants to look at them directly, although that would require access to a SandyBridge running Windows 64 bit.

Thank you very much,

Avraham Adler