1 EXPLANATION OF COLUMN ENTRIES FOR THE SUMMARY STATISTICS ----------------------------------------------------------------------------------------------- BALANCING NO BALANCING VECTORS SELECTED ------------------------ ------------------------ ------------------------ ORDER LOW UPP T COM-R2 COM-R CINVIT COM-R2 COM-R CINVIT ----------------------------------------------------------------------------------------------- 'BALANCING' IS THE OPTION THAT EMPLOYS SUBROUTINE CBAL TO BALANCE THE MATRIX BEFORE THE EIGENVALUES ARE COMPUTED AND CBABK2 TO BACK TRANSFORM THE EIGENVECTORS. 'VECTORS COMPUTED' IDENTIFIES BY POSITION, IN THE SET RETURNED BY COM-R, THOSE EIGENVALUES FOR WHICH CINVIT COMPUTED THE ASSOCIATED EIGENVECTORS. T INDEXES AN EIGENVALUE FOR WHICH THE EIGENVECTOR WAS COMPUTED AND F INDEXES A PASSED EIGENVALUE. UNDER 'ORDER' IS THE ORDER OF EACH TEST MATRIX. UNDER 'LOW' AND 'UPP' ARE INTEGERS INDICATING THE BOUNDARY INDICES FOR THE BALANCED MATRIX. UNDER 'T' IS THE LETTER L OR Q INDICATING THE USE OF ELEMENTARY OR UNITARY TRANSFORMATIONS. PERFORMANCE REPORTED UNDER 'COM-R2 COM-R' IS THAT OF COMLR2 AND COMLR ON LINE HEADED BY 'L' AND THAT OF COMQR2 AND COMQR ON LINE HEADED BY 'Q'. UNDER 'COM-R2 COM-R' ARE TWO NUMBERS AND A KEYWORD. THE FIRST NUMBER, AN INTEGER, IS THE ABSOLUTE SUM OF THE ERROR FLAGS RETURNED SEPARATELY FROM COM-R2 AND COM-R. THE SECOND NUMBER IS THE MEASURE OF PERFORMANCE BASED UPON THE RESIDUAL COMPUTED FOR THE COM-R2 PATH. THE KEYWORD REPORTS THE DUPLICATION OF THE COMPUTED EIGENVALUES FROM COM-R2 AND COM-R. 'SAME' MEANS THAT THE EIGENVALUES ARE EXACT DUPLICATES. 'DIFF' MEANS THAT FOR AT LEAST ONE PAIR OF CORRESPONDING EIGENVALUES, THE MEMBERS OF THE PAIR ARE NOT IDENTICAL. UNDER 'CINVIT' ARE TWO NUMBERS. THE FIRST NUMBER, AN INTEGER, IS THE ABSOLUTE SUM OF THE ERROR FLAGS RETURNED FROM THE PATH. THE SECOND NUMBER IS THE MEASURE OF PERFORMANCE BASED UPON THE RESIDUAL COMPUTED FOR THE PATH. -1.0 AS THE MEASURE OF PERFORMANCE IS PRINTED IF AN ERROR IN THE CORRESPONDING PATH HAS PREVENTED THE COMPUTATION OF THE EIGENVECTORS. 0FOR REDUCTIONS BY ELEMENTARY TRANSFORMATIONS THE COMLR2 PATH WITH BALANCING USES THE EISPACK CODES CBAL -COMHES-COMLR2-CBABK2. THE COMLR PATH WITH BALANCING USES THE EISPACK CODES CBAL -COMHES-COMLR . THE CINVIT PATH WITH BALANCING USES THE EISPACK CODES CBAL -COMHES-COMLR -CINVIT-COMBAK-CBABK2. THE COMLR2 PATH WITH NO BALANCING USES THE EISPACK CODES COMHES-COMLR2. THE COMLR PATH WITH NO BALANCING USES THE EISPACK CODES COMHES-COMLR . THE CINVIT PATH WITH NO BALANCING USES THE EISPACK CODES COMHES-COMLR -CINVIT-COMBAK. 0FOR REDUCTIONS BY UNITARY TRANSFORMATIONS THE COMQR2 PATH WITH BALANCING USES THE EISPACK CODES CBAL -CORTH -COMQR2-CBABK2, AS CALLED FROM DRIVER SUBROUTINE CG. THE COMQR PATH WITH BALANCING USES THE EISPACK CODES CBAL -CORTH -COMQR , AS CALLED FROM DRIVER SUBROUTINE CG. THE CINVIT PATH WITH BALANCING USES THE EISPACK CODES CBAL -CORTH -COMQR -CINVIT-CORTB -CBABK2. THE COMQR2 PATH WITH NO BALANCING USES THE EISPACK CODES CORTH -COMQR2. THE COMQR PATH WITH NO BALANCING USES THE EISPACK CODES CORTH -COMQR . THE CINVIT PATH WITH NO BALANCING USES THE EISPACK CODES CORTH -COMQR -CINVIT-CORTB . D.P. VERSION 04/15/83 1 TABULATION OF THE ERROR FLAG ERROR AND THE MEASURE OF PERFORMANCE Y FOR THE EISPACK CODES. THIS RUN DISPLAYS THESE STATISTICS FOR COMPLEX GENERAL MATRICES. BALANCING NO BALANCING VECTORS SELECTED ------------------------ ------------------------ ------------------------ ORDER LOW UPP T COM-R2 COM-R CINVIT COM-R2 COM-R CINVIT 4 1 4 L 0 .058 SAME 0 .145 0 .058 SAME 0 .145 tttt Q 0 .039 SAME 0 .128 0 .039 SAME 0 .128 10 1 10 L 0 .527 SAME 0 .457 0 .527 SAME 0 .457 tttttttttt Q 0 .082 SAME 0 .743 0 .082 SAME 0 .743 20 1 20 L 0 .631 SAME 0 .114 0 .631 SAME 0 .114 tttttttttttttttttttt Q 0 .023 SAME 0 .125 0 .023 SAME 0 .125 3 1 3 L 0 .012 SAME 0 .024 0 .012 SAME 0 .024 ttt Q 0 .034 SAME 0 .049 0 .034 SAME 0 .049 3 1 3 L 0 .025 SAME 0 .044 0 .025 SAME 0 .044 ttt Q 0 .107 SAME 0 .162 0 .107 SAME 0 .162 4 1 4 L 0 .028 SAME 0 .101 0 .028 SAME 0 .101 tttt Q 0 .069 SAME 0 .303 0 .069 SAME 0 .303 5 1 5 L 0 .086 SAME 0 .076 0 .086 SAME 0 .076 ttttt Q 0 .037 SAME 0 .115 0 .037 SAME 0 .115 7 2 5 L 0 .000 SAME 0 .000 0 .001 SAME 0 .000 ttttttt Q 0 .001 SAME 0 .000 0 .010 SAME 0 .013 0END OF DATA FOR SUBROUTINE CMATIN(CGREADI). 1