1 INPUT MATRIX SEE JOURNAL OF THE ACM - JANUARY, 1966, P. 141, EXAMPLE 3. ================================================================================ 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.200000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.200000000000000D+01, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 4 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.200000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 4 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.200000000000000D+01, 0.000000000000000D+00) 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 2222 0 EIGENVALUES _______________________________________________________ 1 ( 0.200000000000000D+01, 0.000000000000000D+00) 2 ( 0.200000000000000D+01, 0.000000000000000D+00) 3 ( 0.200000000000000D+01, 0.000000000000000D+00) 4 ( 0.200000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.800000000000000D+01, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.800000000000000D+01, 0.000000000000000D+00) 0EIGENVECTORS ARE... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( -0.826206522453754D-43, 0.000000000000000D+00) ( -0.244801932578890D-43, 0.000000000000000D+00) S 2 ( -0.189696395802365D-28, 0.000000000000000D+00) ( -0.843095092454957D-29, 0.000000000000000D+00) S 3 ( -0.435541497221981D-14, 0.000000000000000D+00) ( -0.290360998147988D-14, 0.000000000000000D+00) S 4 ( -0.100000000000000D+01, 0.000000000000000D+00) ( -0.100000000000000D+01, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( -0.306002415723613D-44, 0.000000000000000D+00) ( 0.483934996913313D-15, 0.000000000000000D+00) S 2 ( -0.210773773113739D-29, 0.000000000000000D+00) ( 0.483934996913313D-15, 0.000000000000000D+00) S 3 ( -0.145180499073994D-14, 0.000000000000000D+00) ( 0.483934996913313D-15, 0.000000000000000D+00) S 4 ( -0.100000000000000D+01, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.444089209850065D-14 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.133226762955019D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.257343585016949D-14 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.300096290986289D-59, 0.000000000000000D+00); ¦DET¦= 0.300096290986289D-59 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 1 0MATRIX OF RESIDUALS IN (A*X - LAMBDA*X) FOR ALL EIGENVALUES(LAMBDAS) TAKEN COLLECTIVELY... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( -0.840779078594890D-43, 0.000000000000000D+00) ( -0.252233723578467D-43, 0.000000000000000D+00) S 3 ( -0.189326617253043D-28, 0.000000000000000D+00) ( -0.867746995743113D-29, 0.000000000000000D+00) S 4 ( -0.444089209850063D-14, 0.000000000000000D+00) ( -0.310862446895044D-14, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( -0.280259692864963D-44, 0.000000000000000D+00) ( 0.483934996913313D-15, 0.000000000000000D+00) S 3 ( -0.197215226305253D-29, 0.000000000000000D+00) ( 0.483934996913313D-15, 0.000000000000000D+00) S 4 ( -0.133226762955019D-14, 0.000000000000000D+00) ( 0.444089209850063D-15, 0.000000000000000D+00) 1 INPUT MATRIX SEE JOURNAL OF THE ACM - JANUARY, 1966, P. 141, EXAMPLE 2. ================================================================================ 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( 0.100000000000000D-01, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+00, 0.000000000000000D+00) 0 ( , 3) 3 _______ ________ S 1 ( 0.100000000000000D-03, 0.000000000000000D+00) S 2 ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.100000000000000D+01, 0.000000000000000D+00) 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 222 0 EIGENVALUES _______________________________________________________ 1 ( 0.997679205583193D+00, 0.401973384383098D-02) 2 ( 0.997679205583193D+00, -0.401973384383098D-02) 3 ( 0.100464158883361D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.300000000000000D+01, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.300000000000000D+01, 0.000000000000000D+00) 0EIGENVECTORS ARE... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( -0.107721734501393D-01, -0.186579517236210D-01) ( -0.107721734501393D-01, 0.186579517236210D-01) S 2 ( -0.232079441681071D-01, 0.401973384383101D-01) ( -0.232079441681071D-01, -0.401973384383101D-01) S 3 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) 0 ( , 3) 3 _______ ________ S 1 ( 0.215161942343939D-01, 0.000000000000000D+00) S 2 ( 0.463552352560421D-01, 0.000000000000000D+00) S 3 ( 0.998693269002062D+00, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.345319228091073D-14 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.100675964418394D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.263771473533513D-14 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.125025982020590D-18, 0.518936244926601D-02); ¦DET¦= 0.518936244926601D-02 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 1 0MATRIX OF RESIDUALS IN (A*X - LAMBDA*X) FOR ALL EIGENVALUES(LAMBDAS) TAKEN COLLECTIVELY... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.298011601832481D-16, -0.102021730364991D-15) ( 0.298011601832481D-16, 0.102021730364991D-15) S 2 ( 0.868581465432450D-16, 0.221746449327598D-15) ( 0.868581465432450D-16, -0.221746449327598D-15) S 3 ( -0.310862446895044D-14, 0.286229373536173D-16) ( -0.310862446895044D-14, -0.286229373536173D-16) 0 ( , 3) 3 _______ ________ S 1 ( -0.201153384313951D-16, 0.000000000000000D+00) S 2 ( -0.467494424248593D-16, 0.000000000000000D+00) S 3 ( -0.939894863327684D-15, 0.000000000000000D+00) 1 INPUT MATRIX SEE COMM. ACM 11(12):820 CASE III. ================================================================================ 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( 0.100000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) 0 ( , 3) 3 _______ ________ S 1 ( 0.100000000000000D-01, 0.000000000000000D+00) S 2 ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.100000000000000D+01, 0.000000000000000D+00) 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 000 0 EIGENVALUES _______________________________________________________ 1 ( 0.173683729003825D+01, 0.699786424025278D-02) 2 ( 0.173683729003825D+01, -0.699786424025278D-02) 3 ( 0.174895794644684D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.300000000000000D+01, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.522263252652333D+01, 0.000000000000000D+00) 0EIGENVECTORS ARE... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( -0.932831789286712D-03, 0.000000000000000D+00) ( -0.932831789286712D-03, 0.000000000000000D+00) S 2 ( -0.215966639702979D-02, 0.000000000000000D+00) ( -0.215966639702979D-02, 0.000000000000000D+00) S 3 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) 0 ( , 3) 3 _______ ________ S 1 ( 0.186564292850866D-02, 0.000000000000000D+00) S 2 ( 0.431928498558382D-02, 0.000000000000000D+00) S 3 ( 0.999988931515583D+00, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.756281371370582D+00 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.751215551541170D+00 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.752904158150974D+00 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.279846439276125D-02, 0.000000000000000D+00); ¦DET¦= 0.279846439276125D-02 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 1 0MATRIX OF RESIDUALS IN (A*X - LAMBDA*X) FOR ALL EIGENVALUES(LAMBDAS) TAKEN COLLECTIVELY... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.106873452476796D-01, 0.652783022042050D-05) ( 0.106873452476796D-01, -0.652783022042050D-05) S 2 ( 0.149803955644542D-02, 0.151130522506503D-04) ( 0.149803955644542D-02, -0.151130522506503D-04) S 3 ( -0.738996956435277D+00, -0.699786424025278D-02) ( -0.738996956435277D+00, 0.699786424025278D-02) 0 ( , 3) 3 _______ ________ S 1 ( 0.860260121861691D-02, 0.000000000000000D+00) S 2 ( -0.304839852007065D-02, 0.000000000000000D+00) S 3 ( -0.744630371631895D+00, 0.000000000000000D+00) 1 INPUT MATRIX SYMMETRIC NON-DEGENERATE. ¦DET(ORTHONORMAL EIGENVECTOR MATRIX)¦=1. ================================================================================ 0EIGENVALUES SHOULD BE... 1 0.100000000000000D+01 2 0.200000000000000D+01 3 0.300000000000000D+01 4 0.400000000000000D+01 5 0.500000000000000D+01 6 0.600000000000000D+01 ************************************************************ 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.266666666666667D+01, 0.000000000000000D+00) ( 0.133333333333333D+01, 0.000000000000000D+00) S 2 ( 0.133333333333333D+01, 0.000000000000000D+00) ( 0.300000000000000D+01, 0.000000000000000D+00) S 3 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.666666666666667D+00, 0.000000000000000D+00) S 4 ( 0.666666666666667D+00, 0.000000000000000D+00) ( 0.333333333333333D+00, 0.000000000000000D+00) S 5 ( 0.333333333333333D+00, 0.000000000000000D+00) ( 0.111022302462516D-15, 0.000000000000000D+00) S 6 ( 0.000000000000000D+00, 0.000000000000000D+00) ( -0.333333333333333D+00, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.666666666666667D+00, 0.000000000000000D+00) S 2 ( 0.666666666666667D+00, 0.000000000000000D+00) ( 0.333333333333333D+00, 0.000000000000000D+00) S 3 ( 0.333333333333333D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 4 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.366666666666667D+01, 0.000000000000000D+00) S 5 ( -0.333333333333333D+00, 0.000000000000000D+00) ( -0.666666666666666D+00, 0.000000000000000D+00) S 6 ( -0.666666666666667D+00, 0.000000000000000D+00) ( -0.100000000000000D+01, 0.000000000000000D+00) 0 ( , 6) 5 6 _______ ________ ________ S 1 ( 0.333333333333333D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( 0.111022302462516D-15, 0.000000000000000D+00) ( -0.333333333333333D+00, 0.000000000000000D+00) S 3 ( -0.333333333333333D+00, 0.000000000000000D+00) ( -0.666666666666667D+00, 0.000000000000000D+00) S 4 ( -0.666666666666666D+00, 0.000000000000000D+00) ( -0.100000000000000D+01, 0.000000000000000D+00) S 5 ( 0.400000000000000D+01, 0.000000000000000D+00) ( -0.133333333333333D+01, 0.000000000000000D+00) S 6 ( -0.133333333333333D+01, 0.000000000000000D+00) ( 0.433333333333333D+01, 0.000000000000000D+00) 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.999999999999999D+00, 0.000000000000000D+00) 2 ( 0.600000000000000D+01, 0.000000000000000D+00) 3 ( 0.200000000000000D+01, 0.000000000000000D+00) 4 ( 0.500000000000000D+01, 0.000000000000000D+00) 5 ( 0.300000000000000D+01, 0.000000000000000D+00) 6 ( 0.400000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.210000000000000D+02, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.210000000000000D+02, 0.000000000000000D+00) 0EIGENVECTORS ARE... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.666666666666667D+00, 0.000000000000000D+00) ( -0.333333333333334D+00, 0.000000000000000D+00) S 2 ( -0.333333333333333D+00, 0.000000000000000D+00) ( -0.333333333333333D+00, 0.000000000000000D+00) S 3 ( -0.333333333333333D+00, 0.000000000000000D+00) ( -0.333333333333333D+00, 0.000000000000000D+00) S 4 ( -0.333333333333333D+00, 0.000000000000000D+00) ( -0.333333333333334D+00, 0.000000000000000D+00) S 5 ( -0.333333333333333D+00, 0.000000000000000D+00) ( -0.333333333333333D+00, 0.000000000000000D+00) S 6 ( -0.333333333333333D+00, 0.000000000000000D+00) ( 0.666666666666667D+00, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( -0.333333333333334D+00, 0.000000000000000D+00) ( 0.333333333333334D+00, 0.000000000000000D+00) S 2 ( 0.666666666666667D+00, 0.000000000000000D+00) ( 0.333333333333334D+00, 0.000000000000000D+00) S 3 ( -0.333333333333334D+00, 0.000000000000000D+00) ( 0.333333333333334D+00, 0.000000000000000D+00) S 4 ( -0.333333333333333D+00, 0.000000000000000D+00) ( 0.333333333333332D+00, 0.000000000000000D+00) S 5 ( -0.333333333333333D+00, 0.000000000000000D+00) ( -0.666666666666666D+00, 0.000000000000000D+00) S 6 ( -0.333333333333333D+00, 0.000000000000000D+00) ( 0.333333333333334D+00, 0.000000000000000D+00) 0 ( , 6) 5 6 _______ ________ ________ S 1 ( -0.333333333333334D+00, 0.000000000000000D+00) ( 0.333333333333333D+00, 0.000000000000000D+00) S 2 ( -0.333333333333333D+00, 0.000000000000000D+00) ( 0.333333333333332D+00, 0.000000000000000D+00) S 3 ( 0.666666666666667D+00, 0.000000000000000D+00) ( 0.333333333333333D+00, 0.000000000000000D+00) S 4 ( -0.333333333333334D+00, 0.000000000000000D+00) ( -0.666666666666667D+00, 0.000000000000000D+00) S 5 ( -0.333333333333334D+00, 0.000000000000000D+00) ( 0.333333333333335D+00, 0.000000000000000D+00) S 6 ( -0.333333333333334D+00, 0.000000000000000D+00) ( 0.333333333333333D+00, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.936262786049857D-14 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.943743781040007D-15 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.503917292731434D-14 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( -0.100000000000000D+01, 0.000000000000000D+00); ¦DET¦= 0.100000000000000D+01 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 6 0MATRIX OF RESIDUALS IN (A*X - LAMBDA*X) FOR ALL EIGENVALUES(LAMBDAS) TAKEN COLLECTIVELY... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.155431223447522D-14, 0.000000000000000D+00) ( -0.592082806394334D-15, 0.000000000000000D+00) S 2 ( 0.388578058618805D-15, 0.000000000000000D+00) ( -0.181332813348201D-14, 0.000000000000000D+00) S 3 ( -0.111022302462516D-15, 0.000000000000000D+00) ( -0.136923892363194D-14, 0.000000000000000D+00) S 4 ( 0.166533453693773D-15, 0.000000000000000D+00) ( -0.114719431870691D-14, 0.000000000000000D+00) S 5 ( -0.166533453693773D-15, 0.000000000000000D+00) ( -0.170230583101949D-14, 0.000000000000000D+00) S 6 ( -0.666133814775094D-15, 0.000000000000000D+00) ( 0.273847784726389D-14, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( -0.296041403197167D-15, 0.000000000000000D+00) ( 0.129562159612018D-15, 0.000000000000000D+00) S 2 ( -0.118427403300592D-14, 0.000000000000000D+00) ( -0.147993596544271D-15, 0.000000000000000D+00) S 3 ( -0.118421982289729D-14, 0.000000000000000D+00) ( 0.629162520693338D-15, 0.000000000000000D+00) S 4 ( 0.703159318965474D-15, 0.000000000000000D+00) ( 0.235000820886233D-14, 0.000000000000000D+00) S 5 ( 0.925203923890505D-15, 0.000000000000000D+00) ( -0.247957036847435D-14, 0.000000000000000D+00) S 6 ( -0.518086008122198D-15, 0.000000000000000D+00) ( 0.107325173054340D-14, 0.000000000000000D+00) 0 ( , 6) 5 6 _______ ________ ________ S 1 ( -0.369712940817557D-16, 0.000000000000000D+00) ( -0.518140218230823D-15, 0.000000000000000D+00) S 2 ( -0.536625865271700D-15, 0.000000000000000D+00) ( 0.370038201469303D-15, 0.000000000000000D+00) S 3 ( 0.740510083807600D-16, 0.000000000000000D+00) ( -0.140631863793095D-14, 0.000000000000000D+00) S 4 ( 0.185398571495021D-16, 0.000000000000000D+00) ( -0.118416561278867D-14, 0.000000000000000D+00) S 5 ( 0.240584462074533D-15, 0.000000000000000D+00) ( 0.814127411319365D-15, 0.000000000000000D+00) S 6 ( -0.369712940817557D-16, 0.000000000000000D+00) ( -0.962229428080885D-15, 0.000000000000000D+00) 1 INPUT MATRIX SYMMETRIC DEGENERATE. ¦DET(ORTHONORMAL EIGENVECTOR MATRIX)¦=1. ================================================================================ 0EIGENVALUES SHOULD BE... 1 0.100000000000000D+01 2 0.200000000000000D+01 3 0.300000000000000D+01 4 0.100000000000000D+01 5 0.200000000000000D+01 6 0.300000000000000D+01 ************************************************************ 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.166666666666667D+01, 0.000000000000000D+00) ( 0.333333333333333D+00, 0.000000000000000D+00) S 2 ( 0.333333333333333D+00, 0.000000000000000D+00) ( 0.200000000000000D+01, 0.000000000000000D+00) S 3 ( -0.555111512312578D-16, 0.000000000000000D+00) ( -0.333333333333333D+00, 0.000000000000000D+00) S 4 ( 0.666666666666667D+00, 0.000000000000000D+00) ( 0.333333333333333D+00, 0.000000000000000D+00) S 5 ( 0.333333333333333D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 6 ( 0.000000000000000D+00, 0.000000000000000D+00) ( -0.333333333333333D+00, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( -0.555111512312578D-16, 0.000000000000000D+00) ( 0.666666666666667D+00, 0.000000000000000D+00) S 2 ( -0.333333333333333D+00, 0.000000000000000D+00) ( 0.333333333333333D+00, 0.000000000000000D+00) S 3 ( 0.233333333333333D+01, 0.000000000000000D+00) ( 0.555111512312578D-16, 0.000000000000000D+00) S 4 ( 0.555111512312578D-16, 0.000000000000000D+00) ( 0.166666666666667D+01, 0.000000000000000D+00) S 5 ( -0.333333333333333D+00, 0.000000000000000D+00) ( 0.333333333333333D+00, 0.000000000000000D+00) S 6 ( -0.666666666666667D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) 0 ( , 6) 5 6 _______ ________ ________ S 1 ( 0.333333333333333D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( 0.000000000000000D+00, 0.000000000000000D+00) ( -0.333333333333333D+00, 0.000000000000000D+00) S 3 ( -0.333333333333333D+00, 0.000000000000000D+00) ( -0.666666666666667D+00, 0.000000000000000D+00) S 4 ( 0.333333333333333D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 5 ( 0.200000000000000D+01, 0.000000000000000D+00) ( -0.333333333333333D+00, 0.000000000000000D+00) S 6 ( -0.333333333333333D+00, 0.000000000000000D+00) ( 0.233333333333333D+01, 0.000000000000000D+00) 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.100000000000000D+01, 0.000000000000000D+00) 2 ( 0.200000000000000D+01, 0.000000000000000D+00) 3 ( 0.300000000000000D+01, 0.000000000000000D+00) 4 ( 0.100000000000000D+01, 0.000000000000000D+00) 5 ( 0.300000000000000D+01, 0.000000000000000D+00) 6 ( 0.200000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.120000000000000D+02, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.120000000000000D+02, 0.000000000000000D+00) 0EIGENVECTORS ARE... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.745355992499930D+00, 0.000000000000000D+00) ( -0.471404520791032D+00, 0.000000000000000D+00) S 2 ( -0.149071198499986D+00, 0.000000000000000D+00) ( 0.235702260395515D+00, 0.000000000000000D+00) S 3 ( -0.149071198499986D+00, 0.000000000000000D+00) ( -0.471404520791032D+00, 0.000000000000000D+00) S 4 ( -0.596284793999944D+00, 0.000000000000000D+00) ( -0.471404520791032D+00, 0.000000000000000D+00) S 5 ( -0.149071198499986D+00, 0.000000000000000D+00) ( 0.235702260395516D+00, 0.000000000000000D+00) S 6 ( -0.149071198499986D+00, 0.000000000000000D+00) ( -0.471404520791032D+00, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( -0.471404520791032D+00, 0.000000000000000D+00) ( 0.445308465129028D+00, 0.000000000000000D+00) S 2 ( -0.471404520791031D+00, 0.000000000000000D+00) ( -0.447687031671020D+00, 0.000000000000000D+00) S 3 ( 0.235702260395516D+00, 0.000000000000000D+00) ( -0.447687031671019D+00, 0.000000000000000D+00) S 4 ( -0.471404520791031D+00, 0.000000000000000D+00) ( 0.237856654199141D-02, 0.000000000000000D+00) S 5 ( -0.471404520791032D+00, 0.000000000000000D+00) ( -0.447687031671020D+00, 0.000000000000000D+00) S 6 ( 0.235702260395516D+00, 0.000000000000000D+00) ( -0.447687031671020D+00, 0.000000000000000D+00) 0 ( , 6) 5 6 _______ ________ ________ S 1 ( -0.106255917762273D-01, 0.000000000000000D+00) ( 0.130014058226637D-01, 0.000000000000000D+00) S 2 ( -0.106255917762272D-01, 0.000000000000000D+00) ( -0.713338497426402D+00, 0.000000000000000D+00) S 3 ( -0.701614334584796D+00, 0.000000000000000D+00) ( 0.130014058226643D-01, 0.000000000000000D+00) S 4 ( -0.106255917762275D-01, 0.000000000000000D+00) ( 0.130014058226642D-01, 0.000000000000000D+00) S 5 ( -0.106255917762269D-01, 0.000000000000000D+00) ( 0.700337091603737D+00, 0.000000000000000D+00) S 6 ( 0.712239926361022D+00, 0.000000000000000D+00) ( 0.130014058226641D-01, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.433388134407631D-14 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.116573417585641D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.229339824414025D-14 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.801401925668137D+00, 0.000000000000000D+00); ¦DET¦= 0.801401925668137D+00 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 6 0MATRIX OF RESIDUALS IN (A*X - LAMBDA*X) FOR ALL EIGENVALUES(LAMBDAS) TAKEN COLLECTIVELY... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( -0.553051528184856D-15, 0.000000000000000D+00) ( -0.111022302462516D-15, 0.000000000000000D+00) S 2 ( -0.377885114692667D-15, 0.000000000000000D+00) ( 0.555111512312578D-16, 0.000000000000000D+00) S 3 ( 0.149470822004283D-15, 0.000000000000000D+00) ( 0.222044604925031D-15, 0.000000000000000D+00) S 4 ( 0.264816380629584D-15, 0.000000000000000D+00) ( 0.111022302462516D-15, 0.000000000000000D+00) S 5 ( -0.170626316894906D-16, 0.000000000000000D+00) ( 0.111022302462516D-15, 0.000000000000000D+00) S 6 ( 0.399271002544943D-15, 0.000000000000000D+00) ( 0.555111512312578D-15, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( 0.112767867960217D-14, 0.000000000000000D+00) ( -0.123165366794353D-15, 0.000000000000000D+00) S 2 ( 0.350522562364564D-15, 0.000000000000000D+00) ( -0.710016897706445D-15, 0.000000000000000D+00) S 3 ( -0.702617217879231D-15, 0.000000000000000D+00) ( 0.733273034306259D-15, 0.000000000000000D+00) S 4 ( 0.572567167289595D-15, 0.000000000000000D+00) ( -0.285701248493560D-15, 0.000000000000000D+00) S 5 ( 0.739100620983368D-15, 0.000000000000000D+00) ( -0.210416536625124D-15, 0.000000000000000D+00) S 6 ( -0.841395095957376D-15, 0.000000000000000D+00) ( -0.993942341626086D-16, 0.000000000000000D+00) 0 ( , 6) 5 6 _______ ________ ________ S 1 ( 0.138293375232315D-15, 0.000000000000000D+00) ( -0.717199737099161D-16, 0.000000000000000D+00) S 2 ( 0.775780535731269D-16, 0.000000000000000D+00) ( -0.633607749600529D-15, 0.000000000000000D+00) S 3 ( 0.866711216684912D-15, 0.000000000000000D+00) ( 0.479922091650709D-15, 0.000000000000000D+00) S 4 ( 0.382889385345045D-15, 0.000000000000000D+00) ( -0.588667569551005D-15, 0.000000000000000D+00) S 5 ( -0.373450050180843D-15, 0.000000000000000D+00) ( 0.177917576504871D-15, 0.000000000000000D+00) S 6 ( -0.427392496393786D-15, 0.000000000000000D+00) ( 0.119099608647533D-15, 0.000000000000000D+00) 1 INPUT MATRIX SEE COMMUNICATIONS OF THE ACM - DECEMBER, 1968, P. 820. ================================================================================ 0 ( , 2) 1 2 _______ ________ ________ S 1 ( -0.500000000000000D+00, 0.000000000000000D+00) ( -0.100000000000000D+01, 0.000000000000000D+00) S 2 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 4 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 5 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( -0.100000000000000D+01, 0.000000000000000D+00) ( -0.500000000000000D+00, 0.000000000000000D+00) S 2 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 4 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 5 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) 0 ( , 5) 5 _______ ________ S 1 ( -0.100000000000000D+01, 0.000000000000000D+00) S 2 ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) S 4 ( 0.000000000000000D+00, 0.000000000000000D+00) S 5 ( 0.000000000000000D+00, 0.000000000000000D+00) 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222 0 EIGENVALUES _______________________________________________________ 1 ( -0.100000000000000D+01, 0.000000000000000D+00) 2 ( -0.250000000000000D+00, 0.968245836551854D+00) 3 ( -0.250000000000000D+00, -0.968245836551854D+00) 4 ( 0.500000000000000D+00, 0.866025403784439D+00) 5 ( 0.500000000000000D+00, -0.866025403784439D+00) _______________________________________________________ 0TRACE=( -0.500000000000000D+00, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( -0.500000000000001D+00, 0.000000000000000D+00) 0EIGENVECTORS ARE... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.447213595499958D+00, 0.000000000000000D+00) ( -0.250000000000000D+00, 0.968245836551854D+00) S 2 ( -0.447213595499958D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 3 ( 0.447213595499958D+00, 0.000000000000000D+00) ( -0.250000000000000D+00, -0.968245836551854D+00) S 4 ( -0.447213595499958D+00, 0.000000000000000D+00) ( -0.875000000000000D+00, 0.484122918275927D+00) S 5 ( 0.447213595499958D+00, 0.000000000000000D+00) ( 0.687500000000000D+00, 0.726184377413891D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( -0.250000000000000D+00, -0.968245836551854D+00) ( -0.500000000000000D+00, 0.866025403784439D+00) S 2 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.500000000000000D+00, 0.866025403784439D+00) S 3 ( -0.250000000000000D+00, 0.968245836551854D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 4 ( -0.875000000000000D+00, -0.484122918275927D+00) ( 0.500000000000000D+00, -0.866025403784439D+00) S 5 ( 0.687500000000000D+00, -0.726184377413891D+00) ( -0.500000000000000D+00, -0.866025403784438D+00) 0 ( , 5) 5 _______ ________ S 1 ( -0.500000000000000D+00, -0.866025403784439D+00) S 2 ( 0.500000000000000D+00, -0.866025403784439D+00) S 3 ( 0.100000000000000D+01, 0.000000000000000D+00) S 4 ( 0.500000000000000D+00, 0.866025403784439D+00) S 5 ( -0.500000000000000D+00, 0.866025403784438D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.242704077321743D-14 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.189692130333005D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.201143758237550D-14 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( -0.151875000000000D+02, -0.113767082337376D-14); ¦DET¦= 0.151875000000000D+02 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 5 0MATRIX OF RESIDUALS IN (A*X - LAMBDA*X) FOR ALL EIGENVALUES(LAMBDAS) TAKEN COLLECTIVELY... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.496510384889737D-15, 0.000000000000000D+00) ( -0.166316613259276D-15, -0.432650876930341D-15) S 2 ( -0.496510384889737D-15, 0.000000000000000D+00) ( 0.832667268468867D-16, 0.333066907387547D-15) S 3 ( 0.607532687352252D-15, 0.000000000000000D+00) ( 0.312033385241328D-15, -0.295174041459179D-16) S 4 ( -0.496510384889737D-15, 0.000000000000000D+00) ( -0.330681662608079D-17, -0.493854089567147D-15) S 5 ( 0.329976931195963D-15, 0.000000000000000D+00) ( -0.178568097808363D-15, 0.246059683045585D-15) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( -0.166316613259276D-15, 0.432650876930341D-15) ( 0.350197301712818D-16, 0.136772104059046D-15) S 2 ( 0.832667268468867D-16, -0.333066907387547D-15) ( 0.519712311380927D-15, -0.446149193977785D-16) S 3 ( 0.312033385241328D-15, 0.295174041459179D-16) ( 0.222044604925031D-15, -0.444089209850063D-15) S 4 ( -0.330681662608079D-17, 0.493854089567147D-15) ( 0.204914210599760D-16, -0.373697383801441D-15) S 5 ( -0.178568097808363D-15, -0.246059683045585D-15) ( -0.342282625853674D-15, -0.121918534295995D-15) 0 ( , 5) 5 _______ ________ S 1 ( 0.350197301712818D-16, -0.136772104059046D-15) S 2 ( 0.519712311380927D-15, 0.446149193977785D-16) S 3 ( 0.222044604925031D-15, 0.444089209850063D-15) S 4 ( 0.204914210599760D-16, 0.373697383801441D-15) S 5 ( -0.342282625853674D-15, 0.121918534295995D-15) 1 INPUT MATRIX SEE COMMUNICATIONS OF THE ACM - DECEMBER, 1968, P. 820. ================================================================================ 0 ( , 2) 1 2 _______ ________ ________ S 1 ( -0.200000000000000D+01, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 2 ( -0.700000000000000D+01, 0.000000000000000D+00) ( -0.500000000000000D+01, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( -0.100000000000000D+01, 0.000000000000000D+00) S 4 ( -0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 2 ( -0.200000000000000D+01, 0.000000000000000D+00) ( -0.200000000000000D+01, 0.000000000000000D+00) S 3 ( -0.300000000000000D+01, 0.000000000000000D+00) ( -0.200000000000000D+01, 0.000000000000000D+00) S 4 ( -0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 2222 0 EIGENVALUES _______________________________________________________ 1 ( -0.400000000000000D+01, 0.200000000000000D+01) 2 ( -0.400000000000000D+01, -0.200000000000000D+01) 3 ( -0.241421356237309D+01, 0.000000000000000D+00) 4 ( 0.414213562373095D+00, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( -0.100000000000000D+02, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( -0.100000000000000D+02, 0.000000000000000D+00) 0EIGENVECTORS ARE... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( -0.200000000000000D+00, -0.400000000000000D+00) ( -0.200000000000000D+00, 0.400000000000000D+00) S 2 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 3 ( 0.200000000000000D+00, 0.400000000000000D+00) ( 0.200000000000000D+00, -0.400000000000000D+00) S 4 ( -0.222763112028466D-16, 0.600353759602018D-16) ( -0.222763112028466D-16, -0.600353759602018D-16) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( 0.767593260503997D-01, 0.000000000000000D+00) ( 0.734662493242929D-01, 0.000000000000000D+00) S 2 ( -0.808700482200532D+00, 0.000000000000000D+00) ( -0.254521329842305D+00, 0.000000000000000D+00) S 3 ( 0.526873022751121D+00, 0.000000000000000D+00) ( -0.430803223107795D+00, 0.000000000000000D+00) S 4 ( 0.250032705560717D+00, 0.000000000000000D+00) ( 0.862687768445491D+00, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.825389730224788D-14 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.235107547037587D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.543924239674493D-14 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.199222149194211D-16, -0.488073739440850D+00); ¦DET¦= 0.488073739440850D+00 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 4 0MATRIX OF RESIDUALS IN (A*X - LAMBDA*X) FOR ALL EIGENVALUES(LAMBDAS) TAKEN COLLECTIVELY... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( -0.421863065314110D-15, -0.899237281859477D-15) ( -0.421863065314110D-15, 0.899237281859477D-15) S 2 ( 0.532907051820075D-14, 0.310862446895044D-14) ( 0.532907051820075D-14, -0.310862446895044D-14) S 3 ( -0.133248446998469D-15, 0.621681525703188D-15) ( -0.133248446998469D-15, -0.621681525703188D-15) S 4 ( 0.225254536418419D-15, 0.395716428709016D-15) ( 0.225254536418419D-15, -0.395716428709016D-15) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( 0.560396997903445D-15, 0.000000000000000D+00) ( -0.537933684142261D-16, 0.000000000000000D+00) S 2 ( -0.135883058277608D-14, 0.000000000000000D+00) ( 0.572750126406202D-15, 0.000000000000000D+00) S 3 ( -0.944014831583129D-15, 0.000000000000000D+00) ( -0.974209862086850D-15, 0.000000000000000D+00) S 4 ( 0.348570998454090D-16, 0.000000000000000D+00) ( -0.750322113468593D-15, 0.000000000000000D+00) 1 INPUT MATRIX EIGENVALUES: 1,1,1,-1,-1,-1,2,-2. SEE MATH. OF COMP. JAN. 1969, P.123. ================================================================================ 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 2 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 4 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 5 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 6 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 7 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 8 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 4 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 5 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 6 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 7 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 8 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) 0 ( , 6) 5 6 _______ ________ ________ S 1 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 2 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 4 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 5 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 6 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 7 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 8 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) 0 ( , 8) 7 8 _______ ________ ________ S 1 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 2 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 3 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 4 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 5 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 6 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) S 7 ( 0.000000000000000D+00, 0.000000000000000D+00) ( 0.100000000000000D+01, 0.000000000000000D+00) S 8 ( 0.100000000000000D+01, 0.000000000000000D+00) ( 0.000000000000000D+00, 0.000000000000000D+00) 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222222 0 EIGENVALUES _______________________________________________________ 1 ( -0.200000000000000D+01, 0.000000000000000D+00) 2 ( 0.200000000000000D+01, 0.000000000000000D+00) 3 ( -0.999999987996540D+00, 0.000000000000000D+00) 4 ( 0.999999987996540D+00, 0.000000000000000D+00) 5 ( -0.100000001200346D+01, 0.000000000000000D+00) 6 ( 0.100000001200346D+01, 0.000000000000000D+00) 7 ( -0.100000000000000D+01, 0.000000000000000D+00) 8 ( 0.100000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.000000000000000D+00, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.000000000000000D+00, 0.000000000000000D+00) 0EIGENVECTORS ARE... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( -0.353553390593274D+00, 0.000000000000000D+00) ( -0.353553390593274D+00, 0.000000000000000D+00) S 2 ( 0.353553390593274D+00, 0.000000000000000D+00) ( -0.353553390593274D+00, 0.000000000000000D+00) S 3 ( -0.353553390593274D+00, 0.000000000000000D+00) ( -0.353553390593274D+00, 0.000000000000000D+00) S 4 ( 0.353553390593274D+00, 0.000000000000000D+00) ( -0.353553390593274D+00, 0.000000000000000D+00) S 5 ( -0.353553390593274D+00, 0.000000000000000D+00) ( -0.353553390593274D+00, 0.000000000000000D+00) S 6 ( 0.353553390593273D+00, 0.000000000000000D+00) ( -0.353553390593273D+00, 0.000000000000000D+00) S 7 ( -0.353553390593274D+00, 0.000000000000000D+00) ( -0.353553390593274D+00, 0.000000000000000D+00) S 8 ( 0.353553390593274D+00, 0.000000000000000D+00) ( -0.353553390593274D+00, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( -0.267261257265281D+00, 0.000000000000000D+00) ( 0.267261257265282D+00, 0.000000000000000D+00) S 2 ( -0.267261228392744D+00, 0.000000000000000D+00) ( -0.267261228392744D+00, 0.000000000000000D+00) S 3 ( 0.534522482449966D+00, 0.000000000000000D+00) ( -0.534522482449966D+00, 0.000000000000000D+00) S 4 ( -0.267261247641102D+00, 0.000000000000000D+00) ( -0.267261247641102D+00, 0.000000000000000D+00) S 5 ( -0.267261238016924D+00, 0.000000000000000D+00) ( 0.267261238016923D+00, 0.000000000000000D+00) S 6 ( 0.534522482449966D+00, 0.000000000000000D+00) ( 0.534522482449966D+00, 0.000000000000000D+00) S 7 ( -0.267261238016924D+00, 0.000000000000000D+00) ( 0.267261238016923D+00, 0.000000000000000D+00) S 8 ( -0.267261247641102D+00, 0.000000000000000D+00) ( -0.267261247641102D+00, 0.000000000000000D+00) 0 ( , 6) 5 6 _______ ________ ________ S 1 ( -0.267261226559570D+00, 0.000000000000000D+00) ( 0.267261226559571D+00, 0.000000000000000D+00) S 2 ( -0.267261255432101D+00, 0.000000000000000D+00) ( -0.267261255432102D+00, 0.000000000000000D+00) S 3 ( 0.534522485199731D+00, 0.000000000000000D+00) ( -0.534522485199731D+00, 0.000000000000000D+00) S 4 ( -0.267261236183747D+00, 0.000000000000000D+00) ( -0.267261236183748D+00, 0.000000000000000D+00) S 5 ( -0.267261245807925D+00, 0.000000000000000D+00) ( 0.267261245807925D+00, 0.000000000000000D+00) S 6 ( 0.534522485199731D+00, 0.000000000000000D+00) ( 0.534522485199731D+00, 0.000000000000000D+00) S 7 ( -0.267261245807925D+00, 0.000000000000000D+00) ( 0.267261245807925D+00, 0.000000000000000D+00) S 8 ( -0.267261236183747D+00, 0.000000000000000D+00) ( -0.267261236183747D+00, 0.000000000000000D+00) 0 ( , 8) 7 8 _______ ________ ________ S 1 ( -0.464561030588397D+00, 0.000000000000000D+00) ( 0.463381444997419D+00, 0.000000000000000D+00) S 2 ( 0.322622661643980D+00, 0.000000000000000D+00) ( 0.325471151367979D+00, 0.000000000000000D+00) S 3 ( 0.141938368944417D+00, 0.000000000000000D+00) ( -0.137910293629440D+00, 0.000000000000000D+00) S 4 ( -0.464561030588397D+00, 0.000000000000000D+00) ( -0.463381444997419D+00, 0.000000000000000D+00) S 5 ( 0.322622661643980D+00, 0.000000000000000D+00) ( -0.325471151367979D+00, 0.000000000000000D+00) S 6 ( 0.141938368944417D+00, 0.000000000000000D+00) ( 0.137910293629440D+00, 0.000000000000000D+00) S 7 ( -0.464561030588397D+00, 0.000000000000000D+00) ( 0.463381444997419D+00, 0.000000000000000D+00) S 8 ( 0.322622661643979D+00, 0.000000000000000D+00) ( 0.325471151367979D+00, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.551658328393212D-14 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.777481377889355D-15 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.284393344919705D-14 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( -0.118321511493407D-14, 0.000000000000000D+00); ¦DET¦= 0.118321511493407D-14 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 6 0MATRIX OF RESIDUALS IN (A*X - LAMBDA*X) FOR ALL EIGENVALUES(LAMBDAS) TAKEN COLLECTIVELY... 0 ( , 2) 1 2 _______ ________ ________ S 1 ( 0.235488711863852D-15, 0.000000000000000D+00) ( -0.235488711863852D-15, 0.000000000000000D+00) S 2 ( -0.134441069388203D-16, 0.000000000000000D+00) ( -0.124466409401336D-15, 0.000000000000000D+00) S 3 ( 0.457533316788883D-15, 0.000000000000000D+00) ( -0.346511014326367D-15, 0.000000000000000D+00) S 4 ( -0.134441069388203D-16, 0.000000000000000D+00) ( 0.975781955236954D-16, 0.000000000000000D+00) S 5 ( -0.319622800448727D-15, 0.000000000000000D+00) ( 0.208600497986211D-15, 0.000000000000000D+00) S 6 ( -0.112366713156398D-14, 0.000000000000000D+00) ( -0.112366713156398D-14, 0.000000000000000D+00) S 7 ( 0.134441069388203D-16, 0.000000000000000D+00) ( -0.124466409401336D-15, 0.000000000000000D+00) S 8 ( -0.235488711863852D-15, 0.000000000000000D+00) ( -0.124466409401336D-15, 0.000000000000000D+00) 0 ( , 4) 3 4 _______ ________ ________ S 1 ( 0.141179385890200D-14, 0.000000000000000D+00) ( -0.420074131729509D-15, 0.000000000000000D+00) S 2 ( 0.510117122154430D-15, 0.000000000000000D+00) ( 0.544594751239469D-15, 0.000000000000000D+00) S 3 ( 0.226056152963228D-15, 0.000000000000000D+00) ( 0.337078455425743D-15, 0.000000000000000D+00) S 4 ( -0.103519623428916D-14, 0.000000000000000D+00) ( 0.258040117051550D-15, 0.000000000000000D+00) S 5 ( -0.595606463454912D-15, 0.000000000000000D+00) ( -0.595606463454912D-15, 0.000000000000000D+00) S 6 ( -0.995189174124445D-15, 0.000000000000000D+00) ( 0.329055359349351D-15, 0.000000000000000D+00) S 7 ( -0.151517253604849D-15, 0.000000000000000D+00) ( -0.960061023735914D-16, 0.000000000000000D+00) S 8 ( -0.591107024439097D-15, 0.000000000000000D+00) ( -0.241560244029770D-15, 0.000000000000000D+00) 0 ( , 6) 5 6 _______ ________ ________ S 1 ( 0.140794494118968D-14, 0.000000000000000D+00) ( -0.368411898210574D-15, 0.000000000000000D+00) S 2 ( 0.506241099387794D-15, 0.000000000000000D+00) ( 0.603981925237362D-15, 0.000000000000000D+00) S 3 ( 0.233753988387875D-15, 0.000000000000000D+00) ( 0.122731685925359D-15, 0.000000000000000D+00) S 4 ( -0.983561105824538D-15, 0.000000000000000D+00) ( 0.372938442280701D-15, 0.000000000000000D+00) S 5 ( -0.543971334990290D-15, 0.000000000000000D+00) ( -0.599482486221548D-15, 0.000000000000000D+00) S 6 ( -0.109851364116231D-14, 0.000000000000000D+00) ( 0.321357523924704D-15, 0.000000000000000D+00) S 7 ( -0.443709739089693D-16, 0.000000000000000D+00) ( -0.998821251402271D-16, 0.000000000000000D+00) S 8 ( -0.483960744743217D-15, 0.000000000000000D+00) ( -0.126661918800619D-15, 0.000000000000000D+00) 0 ( , 8) 7 8 _______ ________ ________ S 1 ( -0.594413841065178D-16, 0.000000000000000D+00) ( 0.106956544315695D-15, 0.000000000000000D+00) S 2 ( -0.202339230440107D-15, 0.000000000000000D+00) ( 0.147153339860595D-15, 0.000000000000000D+00) S 3 ( -0.435171646981369D-16, 0.000000000000000D+00) ( -0.209603384995760D-15, 0.000000000000000D+00) S 4 ( -0.594413841065178D-16, 0.000000000000000D+00) ( 0.115088060609336D-15, 0.000000000000000D+00) S 5 ( -0.913169279775916D-16, 0.000000000000000D+00) ( -0.916421886293373D-16, 0.000000000000000D+00) S 6 ( 0.123016288995637D-15, 0.000000000000000D+00) ( 0.430699313019867D-16, 0.000000000000000D+00) S 7 ( 0.515809183559979D-16, 0.000000000000000D+00) ( -0.406575814682064D-17, 0.000000000000000D+00) S 8 ( -0.146828079208849D-15, 0.000000000000000D+00) ( 0.202664491091853D-15, 0.000000000000000D+00) 1 INPUT MATRIX NON-SYM. MATRIX WITH 11 ZERO ROOTS. SEE MATH. OF COMP., JAN. 1969 P. 124. ================================================================================ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 2222222222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( -0.400000000000000D+01, 0.000000000000000D+00) 2 ( 0.400000000000000D+01, 0.000000000000000D+00) 3 ( -0.200000001535400D+01, 0.000000000000000D+00) 4 ( 0.200000001535400D+01, 0.000000000000000D+00) 5 ( -0.200000000300954D+01, 0.000000000000000D+00) 6 ( 0.200000000300954D+01, 0.000000000000000D+00) 7 ( -0.199999999699046D+01, 0.000000000000000D+00) 8 ( 0.199999999699046D+01, 0.000000000000000D+00) 9 ( -0.199999998464601D+01, 0.000000000000000D+00) 10 ( 0.199999998464601D+01, 0.000000000000000D+00) 11 ( -0.200000000000000D+01, 0.000000000000000D+00) 12 ( 0.200000000000000D+01, 0.000000000000000D+00) 13 ( -0.200000000000000D+01, 0.000000000000000D+00) 14 ( 0.200000000000000D+01, 0.000000000000000D+00) 15 ( 0.000000000000000D+00, 0.000000000000000D+00) 16 ( 0.000000000000000D+00, 0.000000000000000D+00) 17 ( -0.659950340971885D-08, 0.000000000000000D+00) 18 ( 0.659950340971885D-08, 0.000000000000000D+00) 19 ( 0.000000000000000D+00, 0.970885952395236D-08) 20 ( 0.000000000000000D+00, -0.970885952395236D-08) 21 ( -0.348621489707452D-08, 0.000000000000000D+00) 22 ( 0.348621489707452D-08, 0.000000000000000D+00) 23 ( 0.000000000000000D+00, 0.000000000000000D+00) 24 ( 0.000000000000000D+00, 0.000000000000000D+00) 25 ( 0.000000000000000D+00, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.000000000000000D+00, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.000000000000000D+00, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.100533024919340D-13 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.330513299993556D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.550690563177685D-14 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.543928026837235D-75, -0.122323897654561D-59); ¦DET¦= 0.122323897654561D-59 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 12 1 INPUT MATRIX DEGENERATE POSITIVE NON-SYMMETRIC MATRIX WITH KNOWN EIGENVALUES. ================================================================================ 0EIGENVALUES SHOULD BE... 1 0.300000000000000D+02 2 0.250000000000000D+02 3 0.250000000000000D+02 4 0.250000000000000D+02 5 0.250000000000000D+02 6 0.250000000000000D+02 7 0.250000000000000D+02 8 0.250000000000000D+02 9 0.250000000000000D+02 10 0.250000000000000D+02 11 0.200000000000000D+02 12 0.190000000000000D+02 13 0.180000000000000D+02 14 0.170000000000000D+02 15 0.160000000000000D+02 16 0.150000000000000D+02 17 0.140000000000000D+02 18 0.130000000000000D+02 19 0.120000000000000D+02 20 0.110000000000000D+02 21 0.100000000000000D+01 22 0.100000000000000D+01 23 0.100000000000000D+01 24 0.100000000000000D+01 25 0.100000000000000D+01 26 0.100000000000000D+01 27 0.100000000000000D+01 28 0.100000000000000D+01 29 0.100000000000000D+01 30 0.100000000000000D+01 ************************************************************ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 222222222222222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.300000000000000D+02, 0.000000000000000D+00) 2 ( 0.110000000000000D+02, 0.000000000000000D+00) 3 ( 0.200000000000000D+02, 0.000000000000000D+00) 4 ( 0.120000000000000D+02, 0.000000000000000D+00) 5 ( 0.190000000000000D+02, 0.000000000000000D+00) 6 ( 0.130000000000000D+02, 0.000000000000000D+00) 7 ( 0.180000000000000D+02, 0.000000000000000D+00) 8 ( 0.140000000000000D+02, 0.000000000000000D+00) 9 ( 0.160000000000000D+02, 0.000000000000000D+00) 10 ( 0.150000000000000D+02, 0.000000000000000D+00) 11 ( 0.170000000000000D+02, 0.000000000000000D+00) 12 ( 0.100000000000000D+01, 0.000000000000000D+00) 13 ( 0.250000000000000D+02, 0.000000000000000D+00) 14 ( 0.999999999999999D+00, 0.000000000000000D+00) 15 ( 0.250000000000000D+02, 0.000000000000000D+00) 16 ( 0.999999999999999D+00, 0.000000000000000D+00) 17 ( 0.250000000000000D+02, 0.000000000000000D+00) 18 ( 0.999999999999999D+00, 0.000000000000000D+00) 19 ( 0.250000000000000D+02, 0.000000000000000D+00) 20 ( 0.100000000000000D+01, 0.000000000000000D+00) 21 ( 0.250000000000000D+02, 0.000000000000000D+00) 22 ( 0.999999999999999D+00, 0.000000000000000D+00) 23 ( 0.250000000000000D+02, 0.000000000000000D+00) 24 ( 0.100000000000000D+01, 0.000000000000000D+00) 25 ( 0.250000000000000D+02, 0.000000000000000D+00) 26 ( 0.999999999999999D+00, 0.000000000000000D+00) 27 ( 0.250000000000000D+02, 0.000000000000000D+00) 28 ( 0.999999999999999D+00, 0.000000000000000D+00) 29 ( 0.250000000000000D+02, 0.000000000000000D+00) 30 ( 0.100000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.420000000000000D+03, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.420000000000000D+03, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.123996661567692D-11 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.132869619983138D-13 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.167802384425869D-12 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.129177285360129D-11, 0.000000000000000D+00); ¦DET¦= 0.129177285360129D-11 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 24 1 INPUT MATRIX SYMMETRIC, DEGENERATE, POSITIVE-DEFINITE MATRIX. DET(EIGENVECTOR MATRIX)=1 ================================================================================ 0EIGENVALUES SHOULD BE... 1 0.300000000000000D+02 2 0.250000000000000D+02 3 0.250000000000000D+02 4 0.250000000000000D+02 5 0.250000000000000D+02 6 0.250000000000000D+02 7 0.250000000000000D+02 8 0.250000000000000D+02 9 0.250000000000000D+02 10 0.250000000000000D+02 11 0.200000000000000D+02 12 0.190000000000000D+02 13 0.180000000000000D+02 14 0.170000000000000D+02 15 0.160000000000000D+02 16 0.150000000000000D+02 17 0.140000000000000D+02 18 0.130000000000000D+02 19 0.120000000000000D+02 20 0.110000000000000D+02 21 0.100000000000000D+01 22 0.100000000000000D+01 23 0.100000000000000D+01 24 0.100000000000000D+01 25 0.100000000000000D+01 26 0.100000000000000D+01 27 0.100000000000000D+01 28 0.100000000000000D+01 29 0.100000000000000D+01 30 0.100000000000000D+01 ************************************************************ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 222222222222222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.300000000000000D+02, 0.000000000000000D+00) 2 ( 0.110000000000000D+02, 0.000000000000000D+00) 3 ( 0.200000000000000D+02, 0.000000000000000D+00) 4 ( 0.120000000000000D+02, 0.000000000000000D+00) 5 ( 0.190000000000000D+02, 0.000000000000000D+00) 6 ( 0.130000000000000D+02, 0.000000000000000D+00) 7 ( 0.180000000000000D+02, 0.000000000000000D+00) 8 ( 0.140000000000000D+02, 0.000000000000000D+00) 9 ( 0.160000000000000D+02, 0.000000000000000D+00) 10 ( 0.150000000000000D+02, 0.000000000000000D+00) 11 ( 0.170000000000000D+02, 0.000000000000000D+00) 12 ( 0.100000000000000D+01, 0.000000000000000D+00) 13 ( 0.250000000000000D+02, 0.000000000000000D+00) 14 ( 0.250000000000000D+02, 0.000000000000000D+00) 15 ( 0.100000000000000D+01, 0.000000000000000D+00) 16 ( 0.250000000000000D+02, 0.000000000000000D+00) 17 ( 0.100000000000000D+01, 0.000000000000000D+00) 18 ( 0.250000000000000D+02, 0.000000000000000D+00) 19 ( 0.100000000000000D+01, 0.000000000000000D+00) 20 ( 0.250000000000000D+02, 0.000000000000000D+00) 21 ( 0.100000000000000D+01, 0.000000000000000D+00) 22 ( 0.250000000000001D+02, 0.000000000000000D+00) 23 ( 0.999999999999992D+00, 0.000000000000000D+00) 24 ( 0.250000000000000D+02, 0.000000000000000D+00) 25 ( 0.999999999999995D+00, 0.000000000000000D+00) 26 ( 0.250000000000000D+02, 0.000000000000000D+00) 27 ( 0.999999999999995D+00, 0.000000000000000D+00) 28 ( 0.250000000000000D+02, 0.000000000000000D+00) 29 ( 0.999999999999998D+00, 0.000000000000000D+00) 30 ( 0.100000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.420000000000000D+03, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.420000000000000D+03, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.621309371613417D-12 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.205921131603721D-13 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.125495454782574D-12 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( -0.211227206290704D-08, 0.000000000000000D+00); ¦DET¦= 0.211227206290704D-08 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 27 1 INPUT MATRIX ILL-CONDITIONING TEST. ¦MAX(VALUE)¦=10**J * ¦MIN(VALUE)¦ J= 2 ================================================================================ 0EIGENVALUES SHOULD BE... 1 0.100000000000000D+03 2 0.900000000000000D+01 3 0.900000000000000D+01 4 0.800000000000000D+01 5 0.800000000000000D+01 6 0.700000000000000D+01 7 0.700000000000000D+01 8 0.600000000000000D+01 9 0.600000000000000D+01 10 0.500000000000000D+01 11 0.500000000000000D+01 12 0.400000000000000D+01 13 0.400000000000000D+01 14 0.300000000000000D+01 15 0.300000000000000D+01 16 0.200000000000000D+01 17 0.200000000000000D+01 18 0.100000000000000D+01 19 0.100000000000000D+01 20 0.100000000000000D+01 ************************************************************ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.100000000000000D+03, 0.000000000000000D+00) 2 ( 0.900000000000001D+01, 0.000000000000000D+00) 3 ( 0.799999999999999D+01, 0.000000000000000D+00) 4 ( 0.900000000000002D+01, 0.000000000000000D+00) 5 ( 0.200000000000000D+01, 0.000000000000000D+00) 6 ( 0.800000000000001D+01, 0.000000000000000D+00) 7 ( 0.200000000000000D+01, 0.000000000000000D+00) 8 ( 0.700000000000000D+01, 0.000000000000000D+00) 9 ( 0.300000000000000D+01, 0.000000000000000D+00) 10 ( 0.700000000000000D+01, 0.000000000000000D+00) 11 ( 0.300000000000000D+01, 0.000000000000000D+00) 12 ( 0.400000000000000D+01, 0.000000000000000D+00) 13 ( 0.599999999999999D+01, 0.000000000000000D+00) 14 ( 0.400000000000001D+01, 0.000000000000000D+00) 15 ( 0.600000000000000D+01, 0.000000000000000D+00) 16 ( 0.500000000000000D+01, 0.000000000000000D+00) 17 ( 0.100000000000000D+01, 0.000000000000000D+00) 18 ( 0.499999999999999D+01, 0.000000000000000D+00) 19 ( 0.100000000000000D+01, 0.000000000000000D+00) 20 ( 0.100000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.191000000000000D+03, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.191000000000000D+03, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.286349069456016D-12 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.448686227061401D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.640652190207079D-13 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( -0.767310218968531D-05, 0.000000000000000D+00); ¦DET¦= 0.767310218968531D-05 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 19 1 INPUT MATRIX ILL-CONDITIONING TEST. ¦MAX(VALUE)¦=10**J * ¦MIN(VALUE)¦ J= 6 ================================================================================ 0EIGENVALUES SHOULD BE... 1 0.100000000000000D+07 2 0.900000000000000D+01 3 0.900000000000000D+01 4 0.800000000000000D+01 5 0.800000000000000D+01 6 0.700000000000000D+01 7 0.700000000000000D+01 8 0.600000000000000D+01 9 0.600000000000000D+01 10 0.500000000000000D+01 11 0.500000000000000D+01 12 0.400000000000000D+01 13 0.400000000000000D+01 14 0.300000000000000D+01 15 0.300000000000000D+01 16 0.200000000000000D+01 17 0.200000000000000D+01 18 0.100000000000000D+01 19 0.100000000000000D+01 20 0.100000000000000D+01 ************************************************************ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.100000000003772D+01, 0.000000000000000D+00) 2 ( 0.100000000000000D+07, 0.000000000000000D+00) 3 ( 0.800000000000000D+01, 0.000000000000000D+00) 4 ( 0.900000000000000D+01, 0.000000000000000D+00) 5 ( 0.999999999999996D+00, 0.000000000000000D+00) 6 ( 0.700000000000000D+01, 0.000000000000000D+00) 7 ( 0.599999999999999D+01, 0.000000000000000D+00) 8 ( 0.300000000000000D+01, 0.000000000000000D+00) 9 ( 0.400000000000000D+01, 0.000000000000000D+00) 10 ( 0.500000000000000D+01, 0.000000000000000D+00) 11 ( 0.200000000000000D+01, 0.000000000000000D+00) 12 ( 0.799999999999999D+01, 0.000000000000000D+00) 13 ( 0.899999999999999D+01, 0.000000000000000D+00) 14 ( 0.100000000000000D+01, 0.000000000000000D+00) 15 ( 0.700000000000001D+01, 0.000000000000000D+00) 16 ( 0.200000000000000D+01, 0.000000000000000D+00) 17 ( 0.600000000000000D+01, 0.000000000000000D+00) 18 ( 0.400000000000000D+01, 0.000000000000000D+00) 19 ( 0.500000000000000D+01, 0.000000000000000D+00) 20 ( 0.300000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.100009100000000D+07, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.100009100000000D+07, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.299452594276772D-06 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.575528433490272D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.149752831371053D-07 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( -0.326880236269364D-03, 0.000000000000000D+00); ¦DET¦= 0.326880236269364D-03 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 19 1 INPUT MATRIX ILL-CONDITIONING TEST. ¦MAX(VALUE)¦=10**J * ¦MIN(VALUE)¦ J=10 ================================================================================ 0EIGENVALUES SHOULD BE... 1 0.100000000000000D+11 2 0.900000000000000D+01 3 0.900000000000000D+01 4 0.800000000000000D+01 5 0.800000000000000D+01 6 0.700000000000000D+01 7 0.700000000000000D+01 8 0.600000000000000D+01 9 0.600000000000000D+01 10 0.500000000000000D+01 11 0.500000000000000D+01 12 0.400000000000000D+01 13 0.400000000000000D+01 14 0.300000000000000D+01 15 0.300000000000000D+01 16 0.200000000000000D+01 17 0.200000000000000D+01 18 0.100000000000000D+01 19 0.100000000000000D+01 20 0.100000000000000D+01 ************************************************************ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.100000008274058D+01, 0.000000000000000D+00) 2 ( 0.100000000000000D+11, 0.000000000000000D+00) 3 ( 0.100000000000154D+01, 0.000000000000000D+00) 4 ( 0.899999999999999D+01, 0.000000000000000D+00) 5 ( 0.800000000000000D+01, 0.000000000000000D+00) 6 ( 0.200000000000000D+01, 0.000000000000000D+00) 7 ( 0.700000000000000D+01, 0.000000000000000D+00) 8 ( 0.300000000000000D+01, 0.000000000000000D+00) 9 ( 0.499999999999999D+01, 0.000000000000000D+00) 10 ( 0.400000000000000D+01, 0.000000000000000D+00) 11 ( 0.600000000000000D+01, 0.000000000000000D+00) 12 ( 0.100000000000000D+01, 0.000000000000000D+00) 13 ( 0.900000000000001D+01, 0.000000000000000D+00) 14 ( 0.800000000000000D+01, 0.000000000000000D+00) 15 ( 0.200000000000000D+01, 0.000000000000000D+00) 16 ( 0.700000000000001D+01, 0.000000000000000D+00) 17 ( 0.500000000000000D+01, 0.000000000000000D+00) 18 ( 0.400000000000000D+01, 0.000000000000000D+00) 19 ( 0.300000000000000D+01, 0.000000000000000D+00) 20 ( 0.600000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.100000000910000D+11, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.100000000910000D+11, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.180833661230281D+00 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.248473615756514D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.904168741310549D-02 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( -0.102653345542834D-01, 0.000000000000000D+00); ¦DET¦= 0.102653345542834D-01 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 20 1 INPUT MATRIX ILL-CONDITIONING TEST. ¦MAX(VALUE)¦=10**J * ¦MIN(VALUE)¦ J=14 ================================================================================ 0EIGENVALUES SHOULD BE... 1 0.100000000000000D+15 2 0.900000000000000D+01 3 0.900000000000000D+01 4 0.800000000000000D+01 5 0.800000000000000D+01 6 0.700000000000000D+01 7 0.700000000000000D+01 8 0.600000000000000D+01 9 0.600000000000000D+01 10 0.500000000000000D+01 11 0.500000000000000D+01 12 0.400000000000000D+01 13 0.400000000000000D+01 14 0.300000000000000D+01 15 0.300000000000000D+01 16 0.200000000000000D+01 17 0.200000000000000D+01 18 0.100000000000000D+01 19 0.100000000000000D+01 20 0.100000000000000D+01 ************************************************************ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.999200722162641D+00, 0.000000000000000D+00) 2 ( 0.100000000000000D+15, 0.000000000000000D+00) 3 ( 0.100000000006731D+01, 0.000000000000000D+00) 4 ( 0.200000015580628D+01, 0.000000000000000D+00) 5 ( 0.899999999944019D+01, 0.000000000000000D+00) 6 ( 0.299999988779717D+01, 0.000000000000000D+00) 7 ( 0.799999924847277D+01, 0.000000000000000D+00) 8 ( 0.400000001889596D+01, 0.000000000000000D+00) 9 ( 0.700000060311763D+01, 0.000000000000000D+00) 10 ( 0.599999825785972D+01, 0.000000000000000D+00) 11 ( 0.500000182860930D+01, 0.000000000000000D+00) 12 ( 0.100000000000057D+01, 0.000000000000000D+00) 13 ( 0.899998007473269D+01, 0.000000000000000D+00) 14 ( 0.200000757947996D+01, 0.000000000000000D+00) 15 ( 0.800001624605386D+01, 0.000000000000000D+00) 16 ( 0.699999604190245D+01, 0.000000000000000D+00) 17 ( 0.300000063792223D+01, 0.000000000000000D+00) 18 ( 0.499997819695070D+01, 0.000000000000000D+00) 19 ( 0.400002129752643D+01, 0.000000000000000D+00) 20 ( 0.599999992543113D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.100000000000091D+15, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.100000000000091D+15, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.260777732471466D+06 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.234310621710982D-08 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.130388867359593D+05 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.102110938508610D-02, 0.000000000000000D+00); ¦DET¦= 0.102110938508610D-02 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 20 1 INPUT MATRIX ILL-CONDITIONING TEST. ¦MAX(VALUE)¦=10**J * ¦MIN(VALUE)¦ J=18 ================================================================================ 0EIGENVALUES SHOULD BE... 1 0.100000000000000D+19 2 0.900000000000000D+01 3 0.900000000000000D+01 4 0.800000000000000D+01 5 0.800000000000000D+01 6 0.700000000000000D+01 7 0.700000000000000D+01 8 0.600000000000000D+01 9 0.600000000000000D+01 10 0.500000000000000D+01 11 0.500000000000000D+01 12 0.400000000000000D+01 13 0.400000000000000D+01 14 0.300000000000000D+01 15 0.300000000000000D+01 16 0.200000000000000D+01 17 0.200000000000000D+01 18 0.100000000000000D+01 19 0.100000000000000D+01 20 0.100000000000000D+01 ************************************************************ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.000000000000000D+00, 0.000000000000000D+00) 2 ( 0.100000000000000D+19, 0.000000000000000D+00) 3 ( 0.100000001301243D+01, 0.000000000000000D+00) 4 ( 0.714140253150026D+01, 0.000000000000000D+00) 5 ( 0.599280251629118D+01, 0.000000000000000D+00) 6 ( 0.604866675057479D+01, 0.000000000000000D+00) 7 ( 0.577395829610142D+01, 0.000000000000000D+00) 8 ( 0.485629017668916D+01, 0.000000000000000D+00) 9 ( 0.518696752258720D+01, 0.000000000000000D+00) 10 ( 0.420351050581692D+01, 0.000000000000000D+00) 11 ( 0.479640170037216D+01, 0.000000000000000D+00) 12 ( 0.100000000006691D+01, 0.000000000000000D+00) 13 ( 0.891215567017601D+01, 0.000000000000000D+00) 14 ( 0.645855212200637D+01, 0.000000000000000D+00) 15 ( 0.335678523369121D+01, 0.000000000000000D+00) 16 ( 0.677940056019882D+01, 0.000000000000000D+00) 17 ( 0.422758042272684D+01, 0.000000000000000D+00) 18 ( 0.358112088571210D+01, 0.000000000000000D+00) 19 ( 0.567340089376644D+01, 0.000000000000000D+00) 20 ( 0.501100421172223D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.100000000000000D+19, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.100000000000000D+19, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.117914597320469D+12 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.160163772748113D-07 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.589572986858562D+10 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( -0.154471195056810D-04, 0.000000000000000D+00); ¦DET¦= 0.154471195056810D-04 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 19 1 INPUT MATRIX ILL-CONDITIONING TEST. SEPARATED VALUES. EPSILON=0. WILKINSON P 90-92. ================================================================================ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.200000000000000D+02, 0.000000000000000D+00) 2 ( 0.190000000000000D+02, 0.000000000000000D+00) 3 ( 0.180000000000000D+02, 0.000000000000000D+00) 4 ( 0.170000000000000D+02, 0.000000000000000D+00) 5 ( 0.160000000000000D+02, 0.000000000000000D+00) 6 ( 0.150000000000000D+02, 0.000000000000000D+00) 7 ( 0.140000000000000D+02, 0.000000000000000D+00) 8 ( 0.130000000000000D+02, 0.000000000000000D+00) 9 ( 0.120000000000000D+02, 0.000000000000000D+00) 10 ( 0.110000000000000D+02, 0.000000000000000D+00) 11 ( 0.100000000000000D+02, 0.000000000000000D+00) 12 ( 0.900000000000000D+01, 0.000000000000000D+00) 13 ( 0.800000000000000D+01, 0.000000000000000D+00) 14 ( 0.700000000000000D+01, 0.000000000000000D+00) 15 ( 0.600000000000000D+01, 0.000000000000000D+00) 16 ( 0.500000000000000D+01, 0.000000000000000D+00) 17 ( 0.400000000000000D+01, 0.000000000000000D+00) 18 ( 0.300000000000000D+01, 0.000000000000000D+00) 19 ( 0.200000000000000D+01, 0.000000000000000D+00) 20 ( 0.100000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.210000000000000D+03, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.210000000000000D+03, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.670949027673645D-14 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.000000000000000D+00 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.259652399714701D-14 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.446402594115325D-66, 0.000000000000000D+00); ¦DET¦= 0.446402594115325D-66 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 3 1 INPUT MATRIX ILL-CONDITIONING TEST. SEPARATED VALUES. EPSILON=1.E-10. WILKINSON P 90-92 ================================================================================ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.995754390564611D+00, 0.000000000000000D+00) 2 ( 0.210924183511600D+01, 0.000000000000000D+00) 3 ( 0.257488140356256D+01, 0.000000000000000D+00) 4 ( 0.396533070241893D+01, 0.108773569790651D+01) 5 ( 0.396533070241893D+01, -0.108773569790651D+01) 6 ( 0.589397754868594D+01, 0.194852926724564D+01) 7 ( 0.589397754868594D+01, -0.194852926724564D+01) 8 ( 0.811807337524286D+01, 0.252918173481928D+01) 9 ( 0.811807337524286D+01, -0.252918173481928D+01) 10 ( 0.105000000000014D+02, 0.273339736289719D+01) 11 ( 0.105000000000014D+02, -0.273339736289719D+01) 12 ( 0.128819266247548D+02, 0.252918173481746D+01) 13 ( 0.128819266247548D+02, -0.252918173481746D+01) 14 ( 0.151060224513119D+02, 0.194852926724894D+01) 15 ( 0.151060224513119D+02, -0.194852926724894D+01) 16 ( 0.200042456094353D+02, 0.000000000000000D+00) 17 ( 0.170346692975829D+02, 0.108773569791149D+01) 18 ( 0.170346692975829D+02, -0.108773569791149D+01) 19 ( 0.184251185964413D+02, 0.000000000000000D+00) 20 ( 0.188907581648829D+02, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.210000000000000D+03, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.210000000000000D+03, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.867815443202566D-10 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.181557308928290D-14 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.275276001258092D-10 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( -0.119951707964613D-65, 0.908975845776717D-76); ¦DET¦= 0.119951707964613D-65 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 3 1 INPUT MATRIX 50X50 DIAG(A(I,I)=1.0 FOR I=1,10,20,30,40,50). ================================================================================ 0*** DMXDQV/EIGENP TEST *** 0INDICATORS SHOULD ALL BE 2 22222222222222222222222222222222222222222222222222 0 EIGENVALUES _______________________________________________________ 1 ( 0.100000000000000D+01, 0.000000000000000D+00) 2 ( 0.000000000000000D+00, 0.000000000000000D+00) 3 ( 0.000000000000000D+00, 0.000000000000000D+00) 4 ( 0.000000000000000D+00, 0.000000000000000D+00) 5 ( 0.000000000000000D+00, 0.000000000000000D+00) 6 ( 0.000000000000000D+00, 0.000000000000000D+00) 7 ( 0.000000000000000D+00, 0.000000000000000D+00) 8 ( 0.000000000000000D+00, 0.000000000000000D+00) 9 ( 0.000000000000000D+00, 0.000000000000000D+00) 10 ( 0.100000000000000D+01, 0.000000000000000D+00) 11 ( 0.000000000000000D+00, 0.000000000000000D+00) 12 ( 0.000000000000000D+00, 0.000000000000000D+00) 13 ( 0.000000000000000D+00, 0.000000000000000D+00) 14 ( 0.000000000000000D+00, 0.000000000000000D+00) 15 ( 0.000000000000000D+00, 0.000000000000000D+00) 16 ( 0.000000000000000D+00, 0.000000000000000D+00) 17 ( 0.000000000000000D+00, 0.000000000000000D+00) 18 ( 0.000000000000000D+00, 0.000000000000000D+00) 19 ( 0.000000000000000D+00, 0.000000000000000D+00) 20 ( 0.100000000000000D+01, 0.000000000000000D+00) 21 ( 0.000000000000000D+00, 0.000000000000000D+00) 22 ( 0.000000000000000D+00, 0.000000000000000D+00) 23 ( 0.000000000000000D+00, 0.000000000000000D+00) 24 ( 0.000000000000000D+00, 0.000000000000000D+00) 25 ( 0.000000000000000D+00, 0.000000000000000D+00) 26 ( 0.000000000000000D+00, 0.000000000000000D+00) 27 ( 0.000000000000000D+00, 0.000000000000000D+00) 28 ( 0.000000000000000D+00, 0.000000000000000D+00) 29 ( 0.000000000000000D+00, 0.000000000000000D+00) 30 ( 0.100000000000000D+01, 0.000000000000000D+00) 31 ( 0.000000000000000D+00, 0.000000000000000D+00) 32 ( 0.000000000000000D+00, 0.000000000000000D+00) 33 ( 0.000000000000000D+00, 0.000000000000000D+00) 34 ( 0.000000000000000D+00, 0.000000000000000D+00) 35 ( 0.000000000000000D+00, 0.000000000000000D+00) 36 ( 0.000000000000000D+00, 0.000000000000000D+00) 37 ( 0.000000000000000D+00, 0.000000000000000D+00) 38 ( 0.000000000000000D+00, 0.000000000000000D+00) 39 ( 0.000000000000000D+00, 0.000000000000000D+00) 40 ( 0.100000000000000D+01, 0.000000000000000D+00) 41 ( 0.000000000000000D+00, 0.000000000000000D+00) 42 ( 0.000000000000000D+00, 0.000000000000000D+00) 43 ( 0.000000000000000D+00, 0.000000000000000D+00) 44 ( 0.000000000000000D+00, 0.000000000000000D+00) 45 ( 0.000000000000000D+00, 0.000000000000000D+00) 46 ( 0.000000000000000D+00, 0.000000000000000D+00) 47 ( 0.000000000000000D+00, 0.000000000000000D+00) 48 ( 0.000000000000000D+00, 0.000000000000000D+00) 49 ( 0.000000000000000D+00, 0.000000000000000D+00) 50 ( 0.100000000000000D+01, 0.000000000000000D+00) _______________________________________________________ 0TRACE=( 0.600000000000000D+01, 0.000000000000000D+00) SUM OF THE EIGENVALUES = ( 0.600000000000000D+01, 0.000000000000000D+00) 01-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.488498130835069D-14 MINIMUM ABS. RESIDUAL OF ¦¦A*X - LAMBDA*X¦¦ IS 0.000000000000000D+00 AVERAGE-NORM OF ¦¦A*X - LAMBDA*X¦¦ IS 0.494535210798967D-15 0DETERMINANT OF THE EIGENVECTOR MATRIX = ( 0.228577815622804D-28, 0.000000000000000D+00); ¦DET¦= 0.228577815622804D-28 0HEURISTIC RANK OF THE EIGENVECTOR MATRIX IS 50 1 INPUT MATRIX TEST ERROR OPTION( &SN). THIS ERROR IS MATRIX ORDER=0. ================================================================================