Failed to Compute inverse

Hi,

Thank you for reporting. Can you post code here so we can take a a look?

Thanks.

Sure,

DenseMatrix Data; Data = new DenseMatrix(RawData); //RawData is a 2D double array (77 observations X 11 variables)

FactorAnalysis F = new FactorAnalysis(Data,5);

F.S(); // gives the same correlation matrix as in SAS, so it is totally fine. F.nFactors(); //=5, so again totally fine F.nVariables(); //Gives 11 variables, again totally fine. F.getEstimators(100); //crashes with the aforementioned error. `

Thanks in advance for your help and support.

Hi,

I’d need also the data to test. Could you post/attach a compile-able code? I suspect that it has something to do with the threshold/epsilon used (what is considered zero, rounding-error).

Thanks.

Thanks again for your support.

Below is a java compilable code, along with an attached CSV file for the data input.

looking forward for your reply. and really appreciate your help.

double[][] RawData = new double [78][11];
//data input through Scanner
Scanner dataIn =null;
String getDataIn;
getDataIn = “PATH\\rawData.csv”; //add your path to the rawData.csv file

/*just in case; path should be like, c:\\user\\documents\\rawData.csv*/

try{
dataIn = new Scanner (new BufferedReader (new FileReader (getDataIn)));
for(int i = 0; i< 78; i ++)
{
for (int j= 0; j < 11 ; j ++)
{
RawData[i][j] = dataIn.nextDouble();
}
}
}catch(Exception e)
{System.out.println(e);}

//FACTOR ANALYSIS
DenseMatrix Data;
Data = new DenseMatrix(RawData);

FactorAnalysis F = new FactorAnalysis(Data,5);

F.S();
F.nFactors();
F.nVariables();
F.getEstimators(100);

below is the raw data, just copy it in csv file, in one column.

0.45093285 0.774907749 0.84057971 0.257559176 0 0 1 1 1 1 1 0.626531316 0.621771218 0.610766046 0.245458241 0.424345781 0 1 1 1 1 1 0.619625129 0.553505535 0.364389234 0.387167381 0.869364387 0 1 1 1 1 1 0.549145422 0.636531365 0.732919255 0.607204278 0.924726346 0 1 1 1 1 1 0.384004452 0.833948339 0.966873706 0.566523874 0.891621818 0 1 1 1 1 1 0.241693666 0.813653137 0.786749482 0.527281824 1 0 1 1 1 1 1 0.561613183 1 0.869565217 0.640755449 1 0 1 1 1 1 1 0.597707051 0.577490775 0.335403727 0.472217879 1 0 1 1 1 1 1 0.597707051 0.577490775 0.335403727 0.315640537 1 0 1 1 1 1 1 0.975715322 0.522140221 0.465838509 0.915043307 1 0 1 1 1 1 1 0.544035993 0.643911439 0.600414079 0.325443232 0.897900612 0 1 1 1 1 1 0.477930595 0.326568266 0.316770186 0.08326819 1 0 1 1 1 1 1 0.630518931 0.695571956 0.708074534 0.250023451 0.882048872 0 1 1 1 1 1 0.476065194 0.688191882 0.465838509 0.133610581 0.920471748 0 1 1 1 1 1 0.513690232 0.446494465 0.275362319 0.150558144 1 0 1 1 1 1 1 0.664625455 0.485239852 0.480331263 0.074638066 1 0 1 1 1 1 1 0 0 0 0.14824427 1 0 1 1 1 1 1 0.655185686 0.293357934 0.424430642 0.125386949 1 0 1 1 1 1 1 0.871893925 0.577490775 0.708074534 0.428285545 0.916300784 0 1 1 1 1 1 0.536569345 0.732472325 0.80952381 0.594571777 1 0 1 1 1 1 1 0.884839411 0.708487085 0.782608696 0.901160064 1 0 1 1 1 1 1 0.74839652 0.73800738 0.819875776 0.449360558 1 0 1 1 1 1 1 0.740239297 0.813653137 0.770186335 0.484944186 1 0 1 1 1 1 1 0.892628256 0.566420664 0.48447205 0.566492605 0.893944596 0 1 1 1 1 1 0.641782467 0.701107011 0.561076605 0.268878397 0.819217329 0 1 1 1 1 1 0.727327283 0.880073801 0.799171843 0.450767643 0.972246793 0 1 1 1 1 1 0.902106646 0.804428044 0.848861284 0.530283606 0.932805054 0 1 1 1 1 1 0.703258643 0.63099631 0.65010352 0 1 0 1 1 1 1 1 0.703258643 0.63099631 0.65010352 0 1 0 1 1 1 1 1 0.674344101 0.614391144 0.432712215 0.248710172 0.95322955 0 1 1 1 1 1 0.770054158 0.723247232 0.749482402 0.164222507 0.985764519 0 1 1 1 1 1 0.770054158 0.723247232 0.749482402 0.164222507 0.985764519 0 1 1 1 1 1 0.944049798 0.846863469 0.836438923 0.506800913 0.701970526 0 1 1 1 1 1 0.906254034 0.723247232 0.749482402 0.024389481 0.658539602 0 1 1 1 1 1 0.906254034 0.723247232 0.749482402 0.024389481 0.658539602 0 1 1 1 1 1 0.932987464 0.745387454 0.523809524 0.327100466 0.724177421 0 1 1 1 1 1 0.838641695 0.610701107 0.422360248 0.322722867 0.880022 0 1 1 1 1 1 0.909062229 0.730627306 0.66873706 0.526656452 0.960764737 0 1 1 1 1 1 0.909062229 0.730627306 0.66873706 0.121447109 0.960764737 0 1 1 1 1 1 0.906034849 0.32103321 0.453416149 0.460507802 1 0 1 1 1 1 1 0.682885597 0.666051661 0.633540373 0.622963635 0.826177285 0 1 1 1 1 1 0.721453267 0.568265683 0.6563147 0.64682155 1 0 1 1 1 1 1 0.602505014 0.7699877 0.816425121 0.307953681 0.853345019 0 1 1 1 1 1 0.733845545 0.686346863 0.82815735 0.488258654 1 1 0 0 0 0 0 0.629304206 0.671586716 0.670807453 0.348644508 0.865313241 1 0 0 0 0 0 0.630726452 0.701107011 0.296066253 0.370469967 0.893924125 1 0 0 0 0 0 0.785452447 0.535055351 0.275362319 0.248178606 1 1 0 0 0 0 0 0.985401189 0.531365314 0.50310559 0.678277727 0.945731406 1 0 0 0 0 0 0.917575558 0.557195572 0.308488613 0.266439448 0.48458827 1 0 0 0 0 0 0.917575558 0.557195572 0.308488613 0.266439448 0.48458827 1 0 0 0 0 0 0.928787902 0.798892989 0.604554865 0.404677777 0.898840383 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.958602018 0.636531365 0.409937888 0.372314812 0.331412703 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 1 0.749077491 0.625258799 0.36712423 0.976965081 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.903650297 0.756457565 0.677018634 0.315218411 0.928172432 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.903650297 0.756457565 0.677018634 0.315218411 0.928172432 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.846782669 0.638376384 0.755693582 0.295331603 0.727667269 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.724377256 0.712177122 0.85300207 0.583096213 0.927591512 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.695372133 0.682656827 1 0.686376286 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.817957979 0.71402214 0.65010352 0.541039992 0.769990836 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.844949271 0.767527675 0.869565217 0.740658516 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.610304168 0.588560886 0.409937888 0.421218849 0.907618697 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.938698051 0.741697417 0.677018634 0.556236515 0.840436522 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.735672079 0.647601476 0.583850932 0.384540821 0.749338731 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.754992802 0.629151292 0.577639752 0.273005847 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.864139037 0.658671587 0.540372671 0.31459304 0.904513724 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.971212643 0.619926199 0.855072464 0.479722335 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.689819104 0.413284133 0.672877847 0.197117038 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.677712365 0.466789668 0.333333333 0.264782214 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.733685421 0.374538745 0.103519669 0.086801538 0.748769706 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.728019531 0.728782288 0.832298137 0.199149495 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.494870017 0.726937269 0.722567288 0.395609893 0.918620988 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.467207547 0.8099631 0.552795031 0.286638942 0.32716574 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.503985229 0.693726937 0.679089027 0.272818236 0.84815487 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.674833805 0.354243542 0.314699793 0.219286451 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.72291715 0.601476015 0.689440994 0.395734968 0.280413263 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.885553306 0.867158672 0.931677019 1 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.766590782 0.518450185 0.265010352 0.190988399 1 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736 0.7129194 0.613468635 0.48447205 0.292079672 0.663824665 0.146597261 0.474820144 0.477292202 0.472868217 0.578947368 0.48944736

Can you let me know if this is the result that you are expecting?

[0.671284, 0.310371, 0.293983, 0.592302, 0.688795, -0.000000, -0.000000, 0.000000, 0.000000, -0.000000, -0.000000]

If so, it has something to do with rounding error, the way SS automatically compute an epsilon for taking inverse.

I believe it is not. (unless we are talking on a different output). Below are the results obtained from SAS9.4 in regard to the same data set.

The Final Communality Estimates: 0.99925838 0.88832449 0.88605910 0.99928299 0.99697740 0.80521685 0.98770304 0.98833947 0.98719052 0.99946914 0.99125603

and the Five factors loadings:

-0.28043 0.42526 0.05983 0.85611 0.05725 0.06484 0.86355 -0.26673 -0.14103 0.21763 0.19418 0.86708 -0.08375 -0.20553 0.21742 -0.05097 0.66501 0.42314 -0.09374 -0.60549 0.17313 -0.00400 0.91313 -0.06730 0.35868 -0.89287 -0.04851 0.03081 -0.06856 -0.00182 0.99195 -0.02698 -0.01059 0.04564 -0.02866 0.99227 -0.02660 -0.01071 0.04580 -0.02852 0.99168 -0.02729 -0.01050 0.04551 -0.02877 0.99793 -0.00913 -0.01592 0.05272 -0.02200 0.99377 -0.02466 -0.01131 0.04662 -0.02782

Hi,

Does your matrix look like what is in the picture?

If so, it should give an error instead of giving any estimators. You are expected to get the errors you reported.

We verified this in R, and see the same computational error.

a1 = c(0.45093285, 0.774907749, 0.84057971, 0.257559176, 0, 0, 1, 1, 1, 1, 1, 0.626531316, 0.621771218, 0.610766046, 0.245458241, 0.424345781, 0, 1, 1, 1, 1, 1, 0.619625129, 0.553505535, 0.364389234, 0.387167381, 0.869364387, 0, 1, 1, 1, 1, 1, 0.549145422, 0.636531365, 0.732919255, 0.607204278, 0.924726346, 0, 1, 1, 1, 1, 1, 0.384004452, 0.833948339, 0.966873706, 0.566523874, 0.891621818, 0, 1, 1, 1, 1, 1, 0.241693666, 0.813653137, 0.786749482, 0.527281824, 1, 0, 1, 1, 1, 1, 1, 0.561613183, 1, 0.869565217, 0.640755449, 1, 0, 1, 1, 1, 1, 1, 0.597707051, 0.577490775, 0.335403727, 0.472217879, 1, 0, 1, 1, 1, 1, 1, 0.597707051, 0.577490775, 0.335403727, 0.315640537, 1, 0, 1, 1, 1, 1, 1, 0.975715322, 0.522140221, 0.465838509, 0.915043307, 1, 0, 1, 1, 1, 1, 1, 0.544035993, 0.643911439, 0.600414079, 0.325443232, 0.897900612, 0, 1, 1, 1, 1, 1, 0.477930595, 0.326568266, 0.316770186, 0.08326819, 1, 0, 1, 1, 1, 1, 1, 0.630518931, 0.695571956, 0.708074534, 0.250023451, 0.882048872, 0, 1, 1, 1, 1, 1, 0.476065194, 0.688191882, 0.465838509, 0.133610581, 0.920471748, 0, 1, 1, 1, 1, 1, 0.513690232, 0.446494465, 0.275362319, 0.150558144, 1, 0, 1, 1, 1, 1, 1, 0.664625455, 0.485239852, 0.480331263, 0.074638066, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0.14824427, 1, 0, 1, 1, 1, 1, 1, 0.655185686, 0.293357934, 0.424430642, 0.125386949, 1, 0, 1, 1, 1, 1, 1, 0.871893925, 0.577490775, 0.708074534, 0.428285545, 0.916300784, 0, 1, 1, 1, 1, 1, 0.536569345, 0.732472325, 0.80952381, 0.594571777, 1, 0, 1, 1, 1, 1, 1, 0.884839411, 0.708487085, 0.782608696, 0.901160064, 1, 0, 1, 1, 1, 1, 1, 0.74839652, 0.73800738, 0.819875776, 0.449360558, 1, 0, 1, 1, 1, 1, 1, 0.740239297, 0.813653137, 0.770186335, 0.484944186, 1, 0, 1, 1, 1, 1, 1, 0.892628256, 0.566420664, 0.48447205, 0.566492605, 0.893944596, 0, 1, 1, 1, 1, 1, 0.641782467, 0.701107011, 0.561076605, 0.268878397, 0.819217329, 0, 1, 1, 1, 1, 1, 0.727327283, 0.880073801, 0.799171843, 0.450767643, 0.972246793, 0, 1, 1, 1, 1, 1, 0.902106646, 0.804428044, 0.848861284, 0.530283606, 0.932805054, 0, 1, 1, 1, 1, 1, 0.703258643, 0.63099631, 0.65010352, 0, 1, 0, 1, 1, 1, 1, 1, 0.703258643, 0.63099631, 0.65010352, 0, 1, 0, 1, 1, 1, 1, 1, 0.674344101, 0.614391144, 0.432712215, 0.248710172, 0.95322955, 0, 1, 1, 1, 1, 1, 0.770054158, 0.723247232, 0.749482402, 0.164222507, 0.985764519, 0, 1, 1, 1, 1, 1, 0.770054158, 0.723247232, 0.749482402, 0.164222507, 0.985764519, 0, 1, 1, 1, 1, 1, 0.944049798, 0.846863469, 0.836438923, 0.506800913, 0.701970526, 0, 1, 1, 1, 1, 1, 0.906254034, 0.723247232, 0.749482402, 0.024389481, 0.658539602, 0, 1, 1, 1, 1, 1, 0.906254034, 0.723247232, 0.749482402, 0.024389481, 0.658539602, 0, 1, 1, 1, 1, 1, 0.932987464, 0.745387454, 0.523809524, 0.327100466, 0.724177421, 0, 1, 1, 1, 1, 1, 0.838641695, 0.610701107, 0.422360248, 0.322722867, 0.880022, 0, 1, 1, 1, 1, 1, 0.909062229, 0.730627306, 0.66873706, 0.526656452, 0.960764737, 0, 1, 1, 1, 1, 1, 0.909062229, 0.730627306, 0.66873706, 0.121447109, 0.960764737, 0, 1, 1, 1, 1, 1, 0.906034849, 0.32103321, 0.453416149, 0.460507802, 1, 0, 1, 1, 1, 1, 1, 0.682885597, 0.666051661, 0.633540373, 0.622963635, 0.826177285, 0, 1, 1, 1, 1, 1, 0.721453267, 0.568265683, 0.6563147, 0.64682155, 1, 0, 1, 1, 1, 1, 1, 0.602505014, 0.7699877, 0.816425121, 0.307953681, 0.853345019, 0, 1, 1, 1, 1, 1, 0.733845545, 0.686346863, 0.82815735, 0.488258654, 1, 1, 0, 0, 0, 0, 0, 0.629304206, 0.671586716, 0.670807453, 0.348644508, 0.865313241, 1, 0, 0, 0, 0, 0, 0.630726452, 0.701107011, 0.296066253, 0.370469967, 0.893924125, 1, 0, 0, 0, 0, 0, 0.785452447, 0.535055351, 0.275362319, 0.248178606, 1, 1, 0, 0, 0, 0, 0, 0.985401189, 0.531365314, 0.50310559, 0.678277727, 0.945731406, 1, 0, 0, 0, 0, 0, 0.917575558, 0.557195572, 0.308488613, 0.266439448, 0.48458827, 1, 0, 0, 0, 0, 0, 0.917575558, 0.557195572, 0.308488613, 0.266439448, 0.48458827, 1, 0, 0, 0, 0, 0, 0.928787902) a2= c(0.798892989, 0.604554865, 0.404677777, 0.898840383, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.958602018, 0.636531365, 0.409937888, 0.372314812, 0.331412703, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 1, 0.749077491, 0.625258799, 0.36712423, 0.976965081, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.903650297, 0.756457565, 0.677018634, 0.315218411, 0.928172432, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.903650297, 0.756457565, 0.677018634, 0.315218411, 0.928172432, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.846782669, 0.638376384, 0.755693582, 0.295331603, 0.727667269, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.724377256, 0.712177122, 0.85300207, 0.583096213, 0.927591512, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.695372133, 0.682656827, 1, 0.686376286, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.817957979, 0.71402214, 0.65010352, 0.541039992, 0.769990836, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.844949271, 0.767527675, 0.869565217, 0.740658516, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.610304168, 0.588560886, 0.409937888, 0.421218849, 0.907618697, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.938698051, 0.741697417, 0.677018634, 0.556236515, 0.840436522, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.735672079, 0.647601476, 0.583850932, 0.384540821, 0.749338731, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.754992802, 0.629151292, 0.577639752, 0.273005847, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.864139037, 0.658671587, 0.540372671, 0.31459304, 0.904513724, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.971212643, 0.619926199, 0.855072464, 0.479722335, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.689819104, 0.413284133, 0.672877847, 0.197117038, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.677712365, 0.466789668, 0.333333333, 0.264782214, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.733685421, 0.374538745, 0.103519669, 0.086801538, 0.748769706, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.728019531, 0.728782288, 0.832298137, 0.199149495, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.494870017, 0.726937269, 0.722567288, 0.395609893, 0.918620988, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.467207547, 0.8099631, 0.552795031, 0.286638942, 0.32716574, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.503985229, 0.693726937, 0.679089027, 0.272818236, 0.84815487, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.674833805, 0.354243542, 0.314699793, 0.219286451, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.72291715, 0.601476015, 0.689440994, 0.395734968, 0.280413263, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.885553306, 0.867158672, 0.931677019, 1, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.766590782, 0.518450185, 0.265010352, 0.190988399, 1, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736, 0.7129194, 0.613468635, 0.48447205, 0.292079672, 0.663824665, 0.146597261, 0.474820144, 0.477292202, 0.472868217, 0.578947368, 0.48944736) a = c(a1, a2)

m1 = matrix(a, 11, 78) m2 = t(m1) > factanal(m2, factors = 5) **Error in solve.default(cv): system is computationally singular: reciprocal condition number = 1.71141e-16 **

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You can also tell from all the 1’s in the last few columns. The input matrix is a bad input.