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Failed to Compute inverse

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  • #5415
    saeid
    Member

    I am using the Factor Analysis module.

    I already used the same model before on different data and worked fine. However, with the current data, when using “getEstimators” function, it gives me the following error:
    Exception in thread “AWT-EventQueue-0” java.lang.RuntimeException: failed to compute inverse
    at com.numericalmethod.suanshu.algebra.linear.matrix.doubles.operation.Inverse.for(rqb:250)
    at com.numericalmethod.suanshu.algebra.linear.matrix.doubles.operation.Inverse.for(rqb:300)
    at com.numericalmethod.suanshu.algebra.linear.matrix.doubles.operation.Inverse.for(rqb:193)
    at com.numericalmethod.suanshu.algebra.linear.matrix.doubles.operation.Inverse.void(rqb:157)
    at com.numericalmethod.suanshu.algebra.linear.matrix.doubles.operation.Inverse.this(rqb:88)
    at com.numericalmethod.suanshu.algebra.linear.matrix.doubles.operation.Inverse.(rqb:72)
    at com.numericalmethod.suanshu.algebra.linear.matrix.doubles.operation.Inverse.(rqb:166)
    at com.numericalmethod.suanshu.stats.factoranalysis.FactorAnalysis.getEstimators(zz:104)

    I already calculated the factors and all for these data using SAS9.4 (to verify everything is in order).

    #5417
    Ryu
    Member

    Hi,

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

    Thanks.

    #5449
    saeid
    Member

    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.

    #5450
    Ryu
    Member

    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.

    #5451
    saeid
    Member

    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);

    #5452
    saeid
    Member

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

    0.45093285
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    0.84057971
    0.257559176
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    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
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    1
    1
    1
    1
    0.384004452
    0.833948339
    0.966873706
    0.566523874
    0.891621818
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    1
    1
    1
    1
    1
    0.241693666
    0.813653137
    0.786749482
    0.527281824
    1
    0
    1
    1
    1
    1
    1
    0.561613183
    1
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    0.640755449
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    0
    1
    1
    1
    1
    1
    0.597707051
    0.577490775
    0.335403727
    0.472217879
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    1
    1
    1
    1
    1
    0.597707051
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    0.335403727
    0.315640537
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    1
    1
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    1
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    1
    1
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    1
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    0.63099631
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    0.703258643
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    1
    0.146597261
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    1
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    0.8099631
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    0.146597261
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    0.503985229
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    0.679089027
    0.272818236
    0.84815487
    0.146597261
    0.474820144
    0.477292202
    0.472868217
    0.578947368
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    0.674833805
    0.354243542
    0.314699793
    0.219286451
    1
    0.146597261
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    0.72291715
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    0.578947368
    0.48944736
    0.885553306
    0.867158672
    0.931677019
    1
    1
    0.146597261
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    1
    0.146597261
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    0.477292202
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    0.48944736

    #5453
    Ryu
    Member

    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.

    #5455
    saeid
    Member

    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

    #5456
    Ryu
    Member

    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

    #5458
    Ryu
    Member

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

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