C C THIS DRIVER TESTS EISPACK FOR THE CLASS OF COMPLEX HERMITIAN C MATRICES SUMMARIZING THE FIGURES OF MERIT FOR ALL PATHS. C C THIS DRIVER IS CATALOGUED AS EISPDRV4(CHSUMARY). C C THE DIMENSION OF AR,AI,ZR, AND ZI SHOULD BE NM BY NM. C THE DIMENSION OF W,D,E,E2,IND,RV1,RV2,RV3,RV4,RV5,RV6, C W1, AND W2 SHOULD BE NM. C THE DIMENSION OF TAU SHOULD BE 2 BY NM. C THE DIMENSION OF ARHOLD AND AIHOLD SHOULD BE NM BY NM. C HERE NM = 20. C DOUBLE PRECISION AR( 20, 20),AI( 20, 20),ZR( 20, 20),ZI( 20, 20), X TAU( 2, 20),W( 20),D( 20),E( 20), X E2( 20),RV1( 20),RV2( 20),RV3( 20),RV4( 20),RV5( 20), X RV6( 20),W1( 20),W2( 20),TCRIT( 8),EPSLON,RESDUL, X MAXEIG,MAXDIF,U,LB,UB,EPS1,DFL DOUBLE PRECISION ARHOLD( 20, 20),AIHOLD( 20, 20) REAL XUB,XLB INTEGER IND( 20),IERR( 6),ERROR DATA IREAD1/1/,IREADC/5/,IWRITE/6/ C OPEN(UNIT=IREAD1,FILE='FILE43') OPEN(UNIT=IREADC,FILE='FILE44') REWIND IREAD1 REWIND IREADC C NM = 20 LCOUNT = 0 WRITE(IWRITE,1) 1 FORMAT(1H1,19X,57H EXPLANATION OF COLUMN ENTRIES FOR THE SUMMARY S XTATISTICS//1H ,95(1H-)/ 34H ORDER TQL2 TQLRAT IMTQL2 IMTQL1,4X, X56HLB UB M IMTQLV TSTURM BISECT M1 NO TRIDIB /1H , X95(1H-)//48H UNDER 'ORDER' IS THE ORDER OF EACH TEST MATRIX. // X95H UNDER 'TQL2 TQLRAT' ARE THREE NUMBERS. THE FIRST NUMBER, AN X INTEGER, IS THE ABSOLUTE SUM OF/ X61H THE ERROR FLAGS RETURNED SEPARATELY FROM TQL2 AND TQLRAT. , X34H THE SECOND NUMBER IS THE MEASURE/ X62H OF PERFORMANCE BASED UPON THE RESIDUAL COMPUTED FOR THE TQL2, X25H PATH. THE THIRD NUMBER / X62H MEASURES THE AGREEMENT OF THE EIGENVALUES FROM THE TQL2 AND, X16H TQLRAT PATHS. // X95H UNDER 'IMTQL2 IMTQL1' ARE THREE NUMBERS WITH MEANING LIKE THOS XE UNDER 'TQL2 TQLRAT'. // X95H UNDER 'LB' AND 'UB' ARE THE INPUT VARIABLES SPECIFYING THE INT XERVAL TO BISECT AND TSTURM. // X61H UNDER 'M' IS THE NUMBER OF EIGENVALUES DETERMINED BY BISECT , X30H AND TSTURM THAT LIE IN THE /18H INTERVAL (LB,UB).// X95H UNDER EACH OF 'IMTQLV', 'TSTURM', 'BISECT', AND 'TRIDIB' ARE T XWO NUMBERS. THE FIRST NUMBER, ) WRITE(IWRITE,2) 2 FORMAT( X95H AN INTEGER, IS THE ABSOLUTE SUM OF THE ERROR FLAGS RETURNED FR XOM THE RESPECTIVE PATH. / X95H THE SECOND NUMBER IS THE MEASURE OF PERFORMANCE BASED UPON THE X RESIDUAL COMPUTED FOR THE PATH.// X95H UNDER 'M1' AND 'NO' ARE THE VARIABLES SPECIFYING THE LOWER BOU XNDARY INDEX AND THE NUMBER / X27H OF EIGENVALUES TO TRIDIB. // X62H -1.0 AS THE MEASURE OF PERFORMANCE IS PRINTED IF AN ERROR IN, X27H THE CORRESPONDING PATH HAS / X47H PREVENTED THE COMPUTATION OF THE EIGENVECTORS. // X63H THE TQL2 PATH USES THE EISPACK CODES HTRIDI-TQL2 -HTRIBK X,1H, / X38H AS CALLED FROM DRIVER SUBROUTINE CH. / X62H THE TQLRAT PATH USES THE EISPACK CODES HTRIDI-TQLRAT, / X38H AS CALLED FROM DRIVER SUBROUTINE CH. / X63H THE IMTQL2 PATH USES THE EISPACK CODES HTRIDI-IMTQL2-HTRIBK X,1H. ) WRITE(IWRITE,3) 3 FORMAT( X62H THE IMTQL1 PATH USES THE EISPACK CODES HTRIDI-IMTQL1. / X63H THE IMTQLV PATH USES THE EISPACK CODES HTRID3-IMTQLV-TINVIT X ,8H-HTRIB3./ X64H THE TSTURM PATH USES THE EISPACK CODES HTRIDI-TSTURM-HTRIBK X. / X63H THE BISECT PATH USES THE EISPACK CODES HTRIDI-BISECT-TINVIT X ,8H-HTRIBK. / X63H THE TRIDIB PATH USES THE EISPACK CODES HTRIDI-TRIDIB-TINVIT X ,8H-HTRIBK. /) WRITE(IWRITE,15) 15 FORMAT(1X,21HD.P. VERSION 04/15/83 ) 5 FORMAT( 53H1 TABULATION OF THE ERROR FLAG ERROR AND THE , X 31HMEASURE OF PERFORMANCE Y FOR /5X, X 56HTHE EISPACK CODES. THIS RUN DISPLAYS THESE STATISTICS , X 33H FOR COMPLEX HERMITIAN MATRICES. / X 55H0ORDER TQL2 TQLRAT IMTQL2 IMTQL1 LB UB M , X 40HIMTQLV TSTURM BISECT M1 NO TRIDIB ) 10 CALL CMATIN(NM,N,AR,AI,ARHOLD,AIHOLD,0) READ(IREADC,50) MM,LB,UB,M11,NO 50 FORMAT(I4,2D24.16,2(4X,I4)) C C MM,LB,UB,M11, AND NO ARE READ FROM SYSIN AFTER THE MATRIX IS C GENERATED. MM,LB, AND UB SPECIFY TO BISECT THE MAXIMUM C NUMBER OF EIGENVALUES AND THE BOUNDS FOR THE INTERVAL WHICH IS C TO BE SEARCHED. M11 AND NO SPECIFY TO TRIDIB THE LOWER C BOUNDARY INDEX AND THE NUMBER OF DESIRED EIGENVALUES. C DO 230 ICALL = 1,10 IF( ICALL .NE. 1 ) CALL CMATIN(NM,N,AR,AI,ARHOLD,AIHOLD,1) C C IF TQLRAT PATH (LABEL 80) IS TAKEN THEN TQL2 PATH (LABEL 70) C MUST ALSO BE TAKEN IN ORDER THAT THE MEASURE OF PERFORMANCE BE C MEANINGFUL. C IF IMTQL1 PATH (LABEL 85) IS TAKEN THEN IMTQL2 PATH (LABEL 75) C MUST ALSO BE TAKEN IN ORDER THAT THE MEASURE OF PERFORMANCE BE C MEANINGFUL. C IF TQL2 (IMTQL2) PATH FAILS, THEN TQLRAT (IMTQL1) PATH IS C OMITTED AND PRINTOUT FLAGGED WITH -1.0. C GO TO (70,75,80,85,89,90,95,230,110,230), ICALL C C CHWZ USING TQL2 C INVOKED FROM DRIVER SUBROUTINE CH. C 70 ICT = 1 CALL CH(NM,N,AR,AI,W,1,ZR,ZI,E,E,TAU,ERROR) IERR(ICT) = ERROR M = ERROR - 1 IF( ERROR .NE. 0 ) GO TO 74 DO 71 I = 1,N W1(I) = W(I) 71 CONTINUE M = N 74 GO TO 190 C C CHWZ USING IMTQL2 C 75 ICT = 2 DO 77 I = 1,N DO 76 J = 1,N 76 ZR(I,J) = 0.0D0 77 ZR(I,I) = 1.0D0 CALL HTRIDI(NM,N,AR,AI,W,E,E,TAU) CALL IMTQL2(NM,N,W,E,ZR,ERROR) IERR(ICT) = ERROR M = ERROR - 1 IF( ERROR .NE. 0 ) GO TO 79 DO 78 I = 1,N 78 W2(I) = W(I) M = N 79 CALL HTRIBK(NM,N,AR,AI,TAU,M,ZR,ZI) GO TO 190 C C CHW USING TQLRAT C INVOKED FROM DRIVER SUBROUTINE CH. C 80 ICT = 7 IF( IERR(1) .NE. 0 ) GO TO 200 CALL CH(NM,N,AR,AI,W,0,AR,AI,E,E2,TAU,ERROR) IERR(1) = ERROR IF( ERROR .NE. 0 ) GO TO 200 MAXEIG = 0.0D0 MAXDIF = 0.0D0 DO 81 I = 1,N IF( DABS(W(I)) .GT. MAXEIG ) MAXEIG = DABS(W(I)) U = DABS(W1(I) - W(I)) IF( U .GT. MAXDIF ) MAXDIF = U 81 CONTINUE IF( MAXEIG .EQ. 0.0D0 ) MAXEIG = 1.0D0 DFL = 10*N TCRIT(7) = MAXDIF/EPSLON(MAXEIG*DFL) GO TO 230 C C CHW USING IMTQL1 C 85 ICT = 8 IF( IERR(2) .NE. 0 ) GO TO 200 CALL HTRIDI(NM,N,AR,AI,W,E,E,TAU) CALL IMTQL1(N,W,E,ERROR) IERR(2) = ERROR MAXEIG = 0.0D0 MAXDIF = 0.0D0 DO 86 I = 1,N IF( DABS(W(I)) .GT. MAXEIG ) MAXEIG = DABS(W(I)) U = DABS(W2(I) - W(I)) IF( U .GT. MAXDIF ) MAXDIF = U 86 CONTINUE IF( MAXEIG .EQ. 0.0D0 ) MAXEIG = 1.0D0 DFL = 10*N TCRIT(8) = MAXDIF/EPSLON(MAXEIG*DFL) GO TO 230 C C CHW1Z ( USAGE HERE COMPUTES ALL THE EIGENVECTORS ) C 89 ICT = 3 DO 892 I = 2,N IM1 = I - 1 DO 891 J = 1,IM1 AR(J,I) = AI(I,J) 891 CONTINUE 892 CONTINUE CALL HTRID3(NM,N,AR,D,E,E2,TAU) CALL IMTQLV(N,D,E,E2,W,IND,ERROR,RV1) IERR(ICT) = ERROR M = N IF( ERROR .NE. 0 ) M = ERROR - 1 CALL TINVIT(NM,N,D,E,E2,M,W,IND,ZR,ERROR,RV1,RV2,RV3,RV4,RV6) IERR(ICT) = IERR(ICT) + IABS(ERROR) CALL HTRIB3(NM,N,AR,TAU,M,ZR,ZI) CALL CMATIN(NM,N,AR,AI,ARHOLD,AIHOLD,1) GO TO 190 C C CH1W1Z USING TSTURM C 90 ICT = 4 EPS1 = 0.0D0 CALL HTRIDI(NM,N,AR,AI,D,E,E2,TAU) CALL TSTURM(NM,N,EPS1,D,E,E2,LB,UB,MM,M,W,ZR,ERROR, X RV1,RV2,RV3,RV4,RV5,RV6) IERR(ICT) = ERROR XLB = LB XUB = UB IF( ERROR .EQ. 3*N + 1 ) GO TO 200 IF( ERROR .GT. 4*N ) M = ERROR - 4*N - 1 CALL HTRIBK(NM,N,AR,AI,TAU,M,ZR,ZI) GO TO 190 C C CH1W1Z USING BISECT AND TINVIT C 95 ICT = 5 EPS1 = 0.0D0 CALL HTRIDI(NM,N,AR,AI,D,E,E2,TAU) CALL BISECT(N,EPS1,D,E,E2,LB,UB,MM,M,W,IND,ERROR,RV4,RV5) IERR(ICT) = ERROR MBISCT = M XLB = LB XUB = UB IF( ERROR .NE. 0 ) GO TO 200 CALL TINVIT(NM,N,D,E,E2,M,W,IND,ZR,ERROR,RV1,RV2,RV3,RV4,RV6) IERR(ICT) = IABS(ERROR) CALL HTRIBK(NM,N,AR,AI,TAU,M,ZR,ZI) GO TO 190 C C CH1W1Z USING TRIDIB AND TINVIT C 110 ICT = 6 EPS1 = 0.0D0 CALL HTRIDI(NM,N,AR,AI,D,E,E2,TAU) CALL TRIDIB(N,EPS1,D,E,E2,LB,UB,M11,NO,W,IND,ERROR,RV4,RV5) IERR(ICT) = ERROR IF( ERROR .NE. 0 ) GO TO 200 M = NO CALL TINVIT(NM,N,D,E,E2,M,W,IND,ZR,ERROR,RV1,RV2,RV3,RV4,RV6) IERR(ICT) = IABS(ERROR) CALL HTRIBK(NM,N,AR,AI,TAU,M,ZR,ZI) C 190 IF( M .EQ. 0 .AND. ERROR .NE. 0 ) GO TO 200 DO 195 I = 1,N AI(I,I) = 0.0D0 195 CONTINUE CALL CHWZR(NM,N,M,AR,AI,W,ZR,ZI,RV1,RESDUL) DFL = 10 * N TCRIT(ICT) = RESDUL/EPSLON(DFL) GO TO 230 200 TCRIT(ICT) = -1.0D0 230 CONTINUE C IF( MOD(LCOUNT,35) .EQ. 0 ) WRITE(IWRITE,5) LCOUNT = LCOUNT + 1 WRITE(IWRITE,240) N,IERR(1),TCRIT(1),TCRIT(7),IERR(2),TCRIT(2), X TCRIT(8),XLB,XUB,MBISCT,(IERR(I),TCRIT(I),I=3,5), X M11,NO,IERR(6),TCRIT(6) 240 FORMAT(I4,2(I3,2F6.3),2(1PE8.0),I3,3(I3,0PF6.3),3I3,F6.3) GO TO 10 END SUBROUTINE CMATIN(NM,N,AR,AI,ARHOLD,AIHOLD,INITIL) C C THIS INPUT SUBROUTINE READS A COMPLEX MATRIX A = (AR,AI) C FROM SYSIN OF ORDER N. C TO GENERATE THE MATRIX A INITIALLY, INITIL IS TO BE 0. C TO REGENERATE THE MATRIX A FOR THE PURPOSE OF THE RESIDUAL C CALCULATION, INITIL IS TO BE 1. C C THIS ROUTINE IS CATALOGUED AS EISPDRV4(CGREADI). C DOUBLE PRECISION AR(NM,NM),AI(NM,NM),ARHOLD(NM,NM),AIHOLD(NM,NM) INTEGER IAR( 20), IAI( 20) DATA IREADA/1/,IWRITE/6/ C IF( INITIL .EQ. 1 ) GO TO 30 READ(IREADA,5) N 5 FORMAT(I6) IF( N .EQ. 0 ) GO TO 70 DO 15 I = 1,N READ(IREADA,10) (IAR(J),IAI(J),J=1,N) 10 FORMAT(2I18) DO 15 J = 1,N AR(I,J) = IAR(J) 15 AI(I,J) = IAI(J) DO 20 I = 1,N DO 20 J = 1,N ARHOLD(I,J) = AR(I,J) 20 AIHOLD(I,J) = AI(I,J) RETURN 30 DO 40 I = 1,N DO 40 J = 1,N AR(I,J) = ARHOLD(I,J) 40 AI(I,J) = AIHOLD(I,J) RETURN 70 WRITE(IWRITE,80) 80 FORMAT(44H0END OF DATA FOR SUBROUTINE CMATIN(CGREADI). /1H1) STOP END SUBROUTINE CHWZR(NM,N,M,AR,AI,W,ZR,ZI,NORM,RESDUL) C DOUBLE PRECISION NORM(M),W(M),AR(NM,N),AI(NM,N), X ZR(NM,M),ZI(NM,M),NORMA,XR,XI,S,SUMA,SUMZ,SUMR,SUMI,RESDUL DOUBLE PRECISION PYTHAG C C THIS SUBROUTINE FORMS THE 1-NORM OF THE RESIDUAL MATRIX C A*Z-Z*DIAG(W) WHERE A IS A HERMITIAN MATRIX, W IS C A VECTOR WHICH CONTAINS M EIGENVALUES OF A, AND Z C IS AN ARRAY WHICH CONTAINS THE M CORRESPONDING EIGENVECTORS OF C A. ALL NORMS APPEARING IN THE COMMENTS BELOW ARE 1-NORMS. C C THIS SUBROUTINE IS CATALOGUED AS EISPDRV4(CHWZR). C C INPUT. C C NM IS THE ROW DIMENSION OF TWO-DIMENSIONAL ARRAY PARAMETERS C AS DECLARED IN THE CALLING PROGRAM DIMENSION STATEMENT; C C N IS THE ORDER OF THE MATRIX A; C C M IS THE NUMBER OF EIGENVECTORS FOR WHICH RESIDUALS ARE C DESIRED; C C AI(NM,N), AR(NM,N) ARE ARRAYS CONTAINING THE REAL AND C IMAGINARY PARTS OF A. ONLY THE FULL UPPER TRIANGLE C NEED BE SUPPLIED; C C W(M) IS A VECTOR WHOSE FIRST M COMPONENTS CONTAIN M C EIGENVALUES OF A; C C ZR(NM,M), ZI(NM,M) ARE ARRAYS WHOSE FIRST M COLUMNS CONTAIN C THE REAL AND IMAGINARY PARTS OF THE ELEMENTS OF Z. C C OUTPUT. C C ZR(NM,M), ZI(NM,M) ARE ARRAYS WHOSE COLUMNS CONTAIN THE C REAL AND IMAGINARY PARTS OF THE NORMALIZED APPROXIMATE C EIGENVECTORS OF A. THE EIGENVECTORS ARE NORMALIZED BY C THE 1-NORM IN SUCH A WAY THAT THE FIRST ELEMENT WHOSE C MAGNITUDE IS LARGER THAN THE NORM OF THE EIGENVECTOR C DIVIDED BY N IS REAL AND POSITIVE; C C NORM(N) IS AN ARRAY SUCH THAT FOR EACH K, C NORM(K) = !!A*Z(K)-Z(K)*(W(K))!!/(!!A!!*!!Z(K)!!) C WHERE Z(K) IS THE K-TH EIGENVECTOR; C C RESDUL IS THE REAL NUMBER C !!A*Z-Z*DIAG(W)!!/(!!A!!*!!Z!!). C C ---------------------------------------------------------------- C NORMA = 0.0D0 RESDUL = 0.0D0 IF( M .EQ. 0 ) RETURN C DO 40 I=1,N SUMA = 0.0D0 IF(I .EQ. 1) GO TO 20 C DO 10 L=2,I AR(I,L-1) = AR(L-1,I) AI(I,L-1) = -AI(L-1,I) 10 CONTINUE C 20 DO 30 L=1,N 30 SUMA = SUMA + PYTHAG(AR(I,L),AI(I,L)) C 40 NORMA = DMAX1(NORMA,SUMA) C IF(NORMA .EQ. 0.0D0) NORMA = 1.0D0 C DO 100 I=1,M S = 0.0D0 SUMZ = 0.0D0 C DO 60 L=1,N SUMZ = SUMZ + PYTHAG(ZR(L,I),ZI(L,I)) SUMR = -W(I)*ZR(L,I) SUMI = -W(I)*ZI(L,I) C DO 50 K=1,N SUMR = SUMR + AR(L,K)*ZR(K,I) - AI(L,K)*ZI(K,I) 50 SUMI = SUMI + AR(L,K)*ZI(K,I) + AI(L,K)*ZR(K,I) C 60 S = S + PYTHAG(SUMR,SUMI) C NORM(I) = SUMZ IF( SUMZ .EQ. 0.0D0 ) GO TO 100 C ..........THIS LOOP WILL NEVER BE COMPLETED SINCE THERE C WILL ALWAYS EXIST AN ELEMENT IN THE VECTOR Z(I) C LARGER THAN !!Z(I)!!/N.......... DO 70 L=1,N IF(PYTHAG(ZR(L,I),ZI(L,I)) .GE. NORM(I)/N) 1 GO TO 80 70 CONTINUE C 80 XR = NORM(I)*ZR(L,I)/PYTHAG(ZR(L,I),ZI(L,I)) XI = NORM(I)*ZI(L,I)/PYTHAG(ZR(L,I),ZI(L,I)) C DO 90 L=1,N CALL CDIV(ZR(L,I),ZI(L,I),XR,XI,ZR(L,I),ZI(L,I)) 90 CONTINUE C NORM(I) = S/(NORM(I)*NORMA) 100 RESDUL = DMAX1(NORM(I),RESDUL) C RETURN END