[BioC] "leading minor...is not positive definite" in flowStats warpSet() function

[Moshe Olshansky]

Hi Andrew,

I am not familiar with the flowStat package, but Cholesky factorization is
used to solve system(s) of linear equations where the matrix is symmetric 
and POSITIVE DEFINITE. All leading minors of positive definite matrix are
positive. So your error message means that your matrix is not positive
definite. It may be either indefinite (i.e. have both positive and
negative eigenvalues) or your matrix may be near singular, i.e. it's
smallest eigenvalue is very close to 0 (and so computationally it is 0).

Regards,
Moshe.

> Folks,
>
> Could anyone provide any advice to resolve the error "the leading minor
> of order 6 is not positive definite" in the flowStats warpSet()
> function?  Are negative SSC values problematic?  Error transcript,
> traceback and sessionInfo() are below.
>
> Any pointers much appreciated,
>
> Andrew Hill.
>
>
>> ret.f1.aligned <- warpSet(ret.f1[2:4], c("SSC","CD45"))
> Estimating landmarks for channel CD45 ...
> Registering curves for parameter SSC ...
> Error in chol.default(Asym) :
>   the leading minor of order 6 is not positive definite
>> traceback()
> 13: .Call("La_chol", as.matrix(x), PACKAGE = "base")
> 12: chol.default(Asym)
> 11: chol(Asym)
> 10: symsolve(hessmat, Flist$grad)
> 9: linesearch.smooth.morph(Flist, hessmat, dbglev)
> 8: smooth.morph(xval, yval, WfdPar)
> 7: landmarkreg(fdobj, landmarks, WfdPar = WfdPar, monwrd = monwrd,
>        ...)
> 6: eval(expr, envir, enclos)
> 5: eval(expr, pf)
> 4: withVisible(eval(expr, pf))
> 3: evalVis(expr)
> 2: capture.output(regDens <- landmarkreg(fdobj, landmarks, WfdPar =
> WfdPar,
>        monwrd = monwrd, ...))
> 1: warpSet(ret.f1[2:4], c("SSC", "CD45"))
>
>> ret.f1
> A flowSet with 20 experiments.
>
> An object of class "AnnotatedDataFrame"
>   rowNames: <..snip..> (20 total)
>   varLabels: <...snip..>... Total.Damage.Score (115 total)
>   varMetadata: labelDescription
>
>   column names:
>   SSC CD45
>
>> do.call("cbind",summary(ret.f1[,"SSC"]))
>            SSC    SSC      SSC      SSC    SSC    SSC      SSC    SSC
> SSC
> Min.      2261   1934    268.8 -8791000   4763   4204 -8683000   2048
> 1992
> 1st Qu.  57360  27130  14930.0    13260  51160  14530    22090  65940
> 94290
> Median   97900  91620  27190.0    26260 131700  34020   117000 112400
> 124000
> Mean     89660  82570  60440.0   -10950 113800  63580    86300 103000
> 116800
> 3rd Qu. 120700 121600 107900.0   132800 160900 114300   151000 136700
> 149600
> Max.    262100 262100 262100.0   262100 262100 262100   262100 262100
> 262100
>            SSC    SSC      SSC    SSC    SSC    SSC    SSC    SSC
> SSC
> Min.    -60080   5147   -450.5   3594 -55360   1834   3173   3043
> -8493000
> 1st Qu.  52640  32330  20260.0  18420  19210  43810  15090  19980
> 15820
> Median   96830 110100  76910.0 109400  88820  80520  35470  39070
> 55720
> Mean     93650  96740  68640.0  90390  77760  79980  62560  65690
> 39280
> 3rd Qu. 118800 135300  98780.0 142700 111900 107500 110800 107100
> 136400
> Max.    262100 262100 262100.0 262100 262100 262100 262100 262100
> 262100
>            SSC      SSC
> Min.      4443    716.9
> 1st Qu.  21060  17850.0
> Median   47510  67560.0
> Mean     77130  84110.0
> 3rd Qu. 131400 143300.0
> Max.    262100 262100.0
>
>> sessionInfo()
> R version 2.13.0 (2011-04-13)
> Platform: x86_64-unknown-linux-gnu (64-bit)
>
> locale:
> [1] C
>
> attached base packages:
> [1] splines   stats     graphics  grDevices utils     datasets  methods
>
> [8] base
>
> other attached packages:
>  [1] bsub_1.0.0            flowStats_1.10.0      cluster_1.13.3
>  [4] mvoutlier_1.8         robCompositions_1.5.0 car_2.0-10
>  [7] survival_2.36-5       nnet_7.3-1            compositions_1.10-1
> [10] energy_1.3-0          MASS_7.3-12           boot_1.2-43
> [13] tensorA_0.36          rgl_0.92.798          fda_2.2.6
> [16] zoo_1.6-5             flowViz_1.16.0        lattice_0.19-26
> [19] flowCore_1.18.0       rrcov_1.3-00          pcaPP_1.8-3
> [22] mvtnorm_0.9-999       robustbase_0.7-3      Biobase_2.12.1
>
> loaded via a namespace (and not attached):
>  [1] KernSmooth_2.23-4   RColorBrewer_1.0-2  feature_1.2.7
>  [4] graph_1.30.0        grid_2.13.0         ks_1.8.1
>  [7] latticeExtra_0.6-16 stats4_2.13.0       tcltk_2.13.0
> [10] tools_2.13.0
>
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>


-- 
Moshe Olshansky
Division of Bioinformatics
The Walter & Eliza Hall Institute of Medical Research
1G Royal Parade, Parkville, Vic 3052
e-mail: olshansky at wehi.edu.au
tel: (03) 9345 2697


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