C C THIS DRIVER TESTS EISPACK FOR THE CLASS OF REAL SYMMETRIC C MATRICES SUMMARIZING THE FIGURES OF MERIT FOR ALL PATHS. C C THIS DRIVER IS CATALOGUED AS EISPDRV4(RSSUMARY). C C THE DIMENSION OF A AND Z 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 AHOLD SHOULD BE NM BY NM. C HERE NM = 20. C DOUBLE PRECISION A(20,20),Z(20,20),AHOLD(20,20),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,MAXEIG, X MAXDIF,U,LB,UB,EPS1,FWORK(1600),DFL REAL XUB,XLB INTEGER IND( 20),IERR( 6),ERROR DATA IREAD1/1/,IREADC/5/,IWRITE/6/ C OPEN(UNIT=IREAD1,FILE='FILE35') OPEN(UNIT=IREADC,FILE='FILE36') 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-)/96H ORDER TQL2 TQLRAT IMTQL2 IMTQL1 LB X 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., X33H 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, X29H 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 / X28H 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. // X62H THE TQL2 PATH USES THE EISPACK CODES TRED2-TQL2 , / X38H AS CALLED FROM DRIVER SUBROUTINE RS. / X62H THE TQLRAT PATH USES THE EISPACK CODES TRED1-TQLRAT, / X38H AS CALLED FROM DRIVER SUBROUTINE RS. / X62H THE IMTQL2 PATH USES THE EISPACK CODES TRED2-IMTQL2. / X62H THE IMTQL1 PATH USES THE EISPACK CODES TRED1-IMTQL1. / X63H THE IMTQLV PATH USES THE EISPACK CODES TRED1-IMTQLV-TINVIT X ,8H-TRBAK , / X38H AS CALLED FROM DRIVER SUBROUTINE RSM. ) WRITE(IWRITE,3) 3 FORMAT( X64H THE TSTURM PATH USES THE EISPACK CODES TRED1-TSTURM-TRBAK1 X. / X63H THE BISECT PATH USES THE EISPACK CODES TRED1-BISECT-TINVIT X ,8H-TRBAK1. / X63H THE TRIDIB PATH USES THE EISPACK CODES TRED1-TRIDIB-TINVIT X ,8H-TRBAK1. /) 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 REAL SYMMETRIC MATRICES. / X 55H0ORDER TQL2 TQLRAT IMTQL2 IMTQL1 LB UB M , X 40HIMTQLV TSTURM BISECT M1 NO TRIDIB ) 10 CALL RMATIN(NM,N,A,AHOLD,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 RMATIN(NM,N,A,AHOLD,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 RSWZ USING TQL2 C INVOKED FROM DRIVER SUBROUTINE RS. C 70 ICT = 1 CALL RS(NM,N,A,W,1,Z,E,E,ERROR) IERR(ICT) = ERROR M = ERROR - 1 IF( ERROR .NE. 0 ) GO TO 190 DO 73 I=1,N 73 W1(I) = W(I) M = N GO TO 190 C C RSWZ USING IMTQL2 C 75 ICT = 2 CALL TRED2(NM,N,A,W,E,Z) CALL IMTQL2(NM,N,W,E,Z,ERROR) IERR(ICT) = ERROR M = ERROR - 1 IF( ERROR .NE. 0 ) GO TO 190 DO 76 I = 1,N W2(I) = W(I) 76 CONTINUE M = N GO TO 190 C C RSW USING TQLRAT C INVOKED FROM DRIVER SUBROUTINE RS. C 80 ICT = 7 IF( IERR(1) .NE. 0 ) GO TO 200 CALL RS(NM,N,A,W,0,A,E,E2,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 RSW USING IMTQL1 C 85 ICT = 8 IF( IERR(2) .NE. 0 ) GO TO 200 CALL TRED1(NM,N,A,W,E,E) 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 RSW1Z ( USAGE HERE COMPUTES ALL THE EIGENVECTORS ) C INVOKED FROM DRIVER SUBROUTINE RSM. C 89 ICT = 3 M = N CALL RSM(NM,N,A,W,M,Z,FWORK,IND,ERROR) IERR(ICT) = IABS(ERROR) GO TO 190 C C RS1W1Z USING TSTURM C 90 ICT = 4 EPS1 = 0.0D0 CALL TRED1(NM,N,A,D,E,E2) CALL TSTURM(NM,N,EPS1,D,E,E2,LB,UB,MM,M,W,Z,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 TRBAK1(NM,N,A,E,M,Z) GO TO 190 C C RS1W1Z USING BISECT AND TINVIT C 95 ICT = 5 EPS1 = 0.0D0 CALL TRED1(NM,N,A,D,E,E2) 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,Z,ERROR,RV1,RV2,RV3,RV4,RV6) IERR(ICT) = IABS(ERROR) CALL TRBAK1(NM,N,A,E,M,Z) GO TO 190 C C RS1W1Z USING TRIDIB AND TINVIT C 110 ICT = 6 EPS1 = 0.0D0 CALL TRED1(NM,N,A,D,E,E2) 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,Z,ERROR,RV1,RV2,RV3,RV4,RV6) IERR(ICT) = IABS(ERROR) CALL TRBAK1(NM,N,A,E,M,Z) C 190 IF( M .EQ. 0 .AND. ERROR .NE. 0 ) GO TO 200 CALL RSWZR(NM,N,M,AHOLD,W,Z,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 RSWZR(NM,N,M,A,W,Z,NORM,RESDUL) C DOUBLE PRECISION NORM(M),W(M),A(NM,N),Z(NM,M),NORMA,TNORM,S,SUM, X SUMZ, SUMA, RESDUL C C THIS SUBROUTINE FORMS THE 1-NORM OF THE RESIDUAL MATRIX C A*Z-Z*DIAG(W) WHERE A IS A REAL SYMMETRIC 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 OF A. ALL NORMS APPEARING IN THE COMMENTS BELOW ARE 1-NORMS. C C THIS SUBROUTINE IS CATALOGUED AS EISPDRV4(RSWZR). 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 M IS THE NUMBER OF EIGENVECTORS FOR WHICH RESIDUALS ARE C DESIRED; C C N IS THE ORDER OF THE MATRIX A; C C A(NM,N) IS A REAL SYMMETRIC MATRIX. ONLY THE FULL UPPER C TRIANGLE NEED BE SUPPLIED; C C Z(NM,M) IS A REAL MATRIX WHOSE FIRST M COLUMNS CONTAIN THE C APPROXIMATE EIGENVECTORS OF A; C C W(M) IS A VECTOR WHOSE FIRST M COMPONENTS CONTAIN THE C APPROXIMATE EIGENVALUES OF A. W(I) IS ASSOCIATED WITH THE C I-TH COLUMN OF Z. C C OUTPUT. C C Z(NM,M) IS AN ARRAY WHICH CONTAINS M NORMALIZED C APPROXIMATE EIGENVECTORS OF A. THE EIGENVECTORS ARE C NORMALIZED USING THE 1-NORM IN SUCH A WAY THAT THE FIRST C ELEMENT WHOSE MAGNITUDE IS LARGER THAN THE NORM OF THE C EIGENVECTOR DIVIDED BY N IS POSITIVE; C C A(NM,N) IS ALTERED BY MAKING THE LOWER TRIANGLE OF A C SYMMETRIC WITH THE UPPER TRIANGLE OF A; C C NORM(M) 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 RESDUL = 0.0D0 IF( M .EQ. 0 ) RETURN NORMA = 0.0D0 C DO 40 I=1,N SUMA = 0.0D0 IF(I .EQ. 1) GO TO 20 C DO 10 L=2,I A(I,L-1) = A(L-1,I) 10 CONTINUE C 20 DO 30 L=1,N 30 SUMA = SUMA + DABS(A(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 + DABS(Z(L,I)) SUM = -W(I)*Z(L,I) C DO 50 K=1,N 50 SUM = SUM + A(L,K)*Z(K,I) C 60 S = S + DABS(SUM) 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(DABS(Z(L,I)) .GE. NORM(I)/N) GO TO 80 70 CONTINUE C 80 TNORM = DSIGN(NORM(I),Z(L,I)) C DO 90 L=1,N 90 Z(L,I) = Z(L,I)/TNORM C NORM(I) = S/(NORM(I)*NORMA) 100 RESDUL = DMAX1(NORM(I), RESDUL) C RETURN END SUBROUTINE RMATIN(NM,N,A,AHOLD,INITIL) C C THIS INPUT SUBROUTINE READS A REAL MATRIX FROM SYSIN OF C 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(RGREADI). C DOUBLE PRECISION A(NM,NM),AHOLD(NM,NM) INTEGER IA( 20) DATA IREADA/1/,IWRITE/6/ C IF( INITIL .EQ. 1 ) GO TO 30 READ(IREADA,5)N, M 5 FORMAT(I6,6X,I6) IF( N .EQ. 0 ) GO TO 70 IF (M .NE. 1) GO TO 14 DO 13 I = 1,N READ(IREADA,16) (IA(J), J=I,N) DO 12 J = I,N A(I,J) = IA(J) 12 A(J,I) = A(I,J) 13 CONTINUE GO TO 19 14 DO 17 I = 1,N READ(IREADA,16) (IA(J), J=1,N) 16 FORMAT(6I12) DO 17 J = 1,N 17 A(I,J) = IA(J) 19 DO 20 I = 1,N DO 20 J = 1,N 20 AHOLD(I,J) = A(I,J) RETURN 30 DO 40 I = 1,N DO 40 J = 1,N 40 A(I,J) = AHOLD(I,J) RETURN 70 WRITE(IWRITE,80) 80 FORMAT(46H0END OF DATA FOR SUBROUTINE RMATIN(RGREADI). /1H1) STOP END