C C THIS DRIVER TESTS EISPACK FOR THE CLASS OF REAL SYMMETRIC C PACKED MATRICES SUMMARIZING THE FIGURES OF MERIT FOR ALL PATHS. C C THIS DRIVER IS CATALOGUED AS EISPDRV4(RSPSUMAR). C C THE DIMENSION OF A SHOULD BE NNN AND THE DIMENSION C OF 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 NNN. C HERE NM = 20, AND NNN = NM*(NM+1)/2. C REAL A(210),Z(20,20),AHOLD(210),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,DFL REAL XUB,XLB INTEGER IND( 20),IERR( 6),ERROR DATA IREAD1/1/,IREADC/5/,IWRITE/6/ C OPEN(IREAD1,FILE='FILE35') OPEN(IREADC,FILE='FILE36') REWIND IREAD1 REWIND IREADC C NM = 20 NNN = (NM*(NM+1))/2 LCOUNT = 0 WRITE(*,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., 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(*,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. // X64H THE TQL2 PATH USES THE EISPACK CODES TRED3-TQL2 -TRBAK3 X, / X39H AS CALLED FROM DRIVER SUBROUTINE RSP. / X62H THE TQLRAT PATH USES THE EISPACK CODES TRED3-TQLRAT, / X39H AS CALLED FROM DRIVER SUBROUTINE RSP. / X64H THE IMTQL2 PATH USES THE EISPACK CODES TRED3-IMTQL2-TRBAK3 X. ) WRITE(*,3) 3 FORMAT( X62H THE IMTQL1 PATH USES THE EISPACK CODES TRED3-IMTQL1. / X63H THE IMTQLV PATH USES THE EISPACK CODES TRED3-IMTQLV-TINVIT X ,8H-TRBAK3./ X64H THE TSTURM PATH USES THE EISPACK CODES TRED3-TSTURM-TRBAK3 X. / X63H THE BISECT PATH USES THE EISPACK CODES TRED3-BISECT-TINVIT X ,8H-TRBAK3. / X63H THE TRIDIB PATH USES THE EISPACK CODES TRED3-TRIDIB-TINVIT X ,8H-TRBAK3. /) WRITE(*,15) 15 FORMAT(1X,21HS.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 40H FOR REAL SYMMETRIC PACKED MATRICES. / X 55H0ORDER TQL2 TQLRAT IMTQL2 IMTQL1 LB UB M , X 40HIMTQLV TSTURM BISECT M1 NO TRIDIB ) 10 CALL RMATIN(NNN,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(NNN,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 RSPWZ USING TQL2 C INVOKED FROM DRIVER SUBROUTINE RSP. C 70 ICT = 1 CALL RSP(NM,N,NNN,A,W,1,Z,E,E,ERROR) IERR(ICT) = ERROR M = ERROR - 1 IF( ERROR .NE. 0 ) GO TO 74 M = N DO 71 I = 1,N W1(I) = W(I) 71 CONTINUE 74 GO TO 190 C C RSPWZ USING IMTQL2 C 75 ICT = 2 DO 77 I=1,N DO 76 J=1,N 76 Z(I,J)=0.0E0 77 Z(I,I)=1.0E0 CALL TRED3(N,NNN,A,W,E,E) CALL IMTQL2(NM,N,W,E,Z,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 TRBAK3(NM,N,NNN,A,M,Z) GO TO 190 C C RSPW USING TQLRAT C INVOKED FROM DRIVER SUBROUTINE RSP. C 80 ICT = 7 IF( IERR(1) .NE. 0 ) GO TO 200 CALL RSP(NM,N,NNN,A,W,0,Z,E,E2,ERROR) IERR(1) = ERROR IF( ERROR .NE. 0 ) GO TO 200 MAXEIG = 0.0E0 MAXDIF = 0.0E0 DO 81 I = 1,N IF( ABS(W(I)) .GT. MAXEIG ) MAXEIG = ABS(W(I)) U = ABS(W1(I) - W(I)) IF( U .GT. MAXDIF ) MAXDIF = U 81 CONTINUE IF( MAXEIG .EQ. 0.0E0 ) MAXEIG = 1.0E0 DFL = 10 * N TCRIT(7) = MAXDIF/EPSLON(MAXEIG*DFL) GO TO 230 C C RSPW USING IMTQL1 C 85 ICT = 8 IF( IERR(2) .NE. 0 ) GO TO 200 CALL TRED3(N,NNN,A,W,E,E) CALL IMTQL1(N,W,E,ERROR) IERR(2) = ERROR MAXEIG = 0.0E0 MAXDIF = 0.0E0 DO 86 I = 1,N IF( ABS(W(I)) .GT. MAXEIG ) MAXEIG = ABS(W(I)) U = ABS(W2(I) - W(I)) IF( U .GT. MAXDIF ) MAXDIF = U 86 CONTINUE IF( MAXEIG .EQ. 0.0E0 ) MAXEIG = 1.0E0 DFL = 10 * N TCRIT(8) = MAXDIF/EPSLON(MAXEIG*DFL) GO TO 230 C C RSPW1Z ( USAGE HERE COMPUTES ALL THE EIGENVECTORS ) C 89 ICT = 3 CALL TRED3(N,NNN,A,D,E,E2) 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,Z,ERROR,RV1,RV2,RV3,RV4,RV6) IERR(ICT) = IERR(ICT) + IABS(ERROR) CALL TRBAK3(NM,N,NNN,A,M,Z) GO TO 190 C C RSP1W1Z USING TSTURM C 90 ICT = 4 EPS1 = 0.0E0 CALL TRED3(N,NNN,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 TRBAK3(NM,N,NNN,A,M,Z) GO TO 190 C C RSP1W1Z USING BISECT AND TINVIT C 95 ICT = 5 EPS1 = 0.0E0 CALL TRED3(N,NNN,A,D,E,E2) CALL BISECT(N,EPS1,D,E,E2,LB,UB,MM,M,W,IND,ERROR,RV1,RV2) 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 TRBAK3(NM,N,NNN,A,M,Z) GO TO 190 C C RSP1W1Z USING TRIDIB AND TINVIT C 110 ICT = 6 EPS1 = 0.0E0 CALL TRED3(N,NNN,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 TRBAK3(NM,N,NNN,A,M,Z) C 190 IF( M .EQ. 0 .AND. ERROR .NE. 0 ) GO TO 200 CALL RMATIN(NNN,N,A,AHOLD,1) CALL RSPWZR(NM,N,NNN,M,A,W,Z,RV1,RESDUL) DFL = 10 * N TCRIT(ICT) = RESDUL/EPSLON(DFL) GO TO 230 200 TCRIT(ICT) = -1.0E0 230 CONTINUE C IF( MOD(LCOUNT,35) .EQ. 0 ) WRITE(*,5) LCOUNT = LCOUNT + 1 WRITE(*,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 RSPWZR(NM,N,NNN,M,A,W,Z,NORM,RESDUL) C REAL NORM(M), W(M), A(NNN), Z(NM,M), NORMA, S, SUM, X SUMA, SUMZ, RESDUL, TNORM 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 STORED IN C PACKED FORM, W IS A VECTOR WHICH CONTAINS M EIGENVALUES OF C A , AND Z IS AN ARRAY WHICH CONTAINS THE CORRESPONDING EIGEN- C VECTORS OF A . ALL NORMS APPEARING IN THE COMMENTS BELOW ARE C 1-NORMS. C C THIS SUBROUTINE IS CATALOGUED AS EISPDRV4(RSPWZR). 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 NNN IS THE DIMENSION OF THE ARRAY PARAMETER A; C C M IS THE NUMBER OF EIGENVECTORS FOR WHICH RESIDUALS ARE C DESIRED; C C A(N*(N+1)/2) IS A VECTOR WHICH CONTAINS THE ELEMENTS OF THE C LOWER TRIANGULAR PART OF THE MATRIX A (AS MENTIONED ABOVE) C IN PACKED FORM. BY PACKED FORM, WE MEAN THAT THE FIRST ROW C OF THE TRIANGLE IS STORED IN THE FIRST POSITION OF A , THE C SECOND ROW OF THE TRIANGLE IS STORED IN THE NEXT TWO C POSITIONS, AND SO FORTH UNTIL WE HAVE THE N-TH ROW STORED C IN THE LAST N POSITIONS OF A; C C W(M) IS AN ARRAY CONTAINING THE EIGENVALUES OF A; C C Z(NM,M) IS AN ARRAY WHICH CONTAINS THE EIGENVECTORS OF A. C C C OUTPUT. C C Z(NM,M) IS AN ARRAY WHICH CONTAINS THE NORMALIZED C APPROXIMATE EIGENVECTORS OF A. THE EIGENVECTORS C ARE NORMALIZED USING THE 1-NORM IN SUCH A WAY C THAT THE FIRST ELEMENT WHOSE MAGNITUDE IS LARGER C THAN THE NORM OF THE EIGENVECTOR DIVIDED BY N IS C POSITIVE; 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 = 0.0E0 IF( M .EQ. 0 ) RETURN NORMA = 0.0E0 INCMT = 0 C DO 40 I=1,N J=I-1 SUMA = 0.0E0 ISP = INCMT INCMT = INCMT + I LSTOP = N+1-I C IF(I .EQ. 1) GO TO 25 C DO 20 L=1,J L1 = ISP + L 20 SUMA = SUMA + ABS(A(L1)) 25 ISP = ISP + 1 DO 30 L=1,LSTOP ISP = ISP + J SUMA = SUMA + ABS(A(ISP)) 30 J = J+1 C 40 NORMA = AMAX1(NORMA,SUMA) C IF(NORMA .EQ. 0.0E0) NORMA = 1.0E0 C DO 100 I=1,M S = 0.0E0 SUMZ = 0.0E0 INCMT = 0 C DO 65 L=1,N SUMZ = SUMZ + ABS(Z(L,I)) SUM = -W(I)*Z(L,I) J = L-1 ISP = INCMT INCMT = INCMT + L KSTOP = N+1-L C IF(L .EQ. 1) GO TO 55 C DO 50 K=1,J K1 = ISP + K 50 SUM = SUM + A(K1)*Z(K,I) 55 ISP = ISP + 1 DO 60 K=1,KSTOP ISP =ISP + J K2 = K - 1 + L SUM =SUM + A(ISP)*Z(K2,I) 60 J = J + 1 65 S = S + ABS(SUM) C NORM(I) = SUMZ C IF(SUMZ .EQ. 0.0E0) 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(ABS(Z(L,I)) .GE. NORM(I)/N) GO TO 80 70 CONTINUE C 80 TNORM = SIGN(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 = AMAX1(NORM(I),RESDUL) C RETURN END SUBROUTINE RMATIN(NNM,N,A,AHOLD,INITIL) C C THIS INPUT SUBROUTINE READS A REAL SYMMETRIC MATRIX FROM SYSIN OF C ORDER N AND STORES IT IN PACKED FORM. THE INPUT MATRIX IS READ C AS A FULL MATRIX (MM IS EQUAL TO ZERO) OR AS ROWS OF AN UPPER C TRIANGULAR MATRIX (MM IS NOT EQUAL TO ZERO) . 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(RSPREADI). C REAL A(NNM),AHOLD(NNM) INTEGER IA( 20) DATA IREADA/1/,IWRITE/6/ C IF( INITIL .EQ. 1 ) GO TO 30 READ(IREADA,5) N,MM 5 FORMAT(I6,6X,I6) IF( N .EQ. 0 ) GO TO 70 INCMT=1 DO 15 L=1,N JST = L IF( MM .EQ. 0 ) JST = 1 READ(IREADA,10) (IA(J),J=JST,N) 10 FORMAT(6I12) J = L - 1 ISP = INCMT INCMT =INCMT + L DO 12 K = L,N ISP = ISP + J A(ISP) = IA(J + 1) 12 J = J + 1 15 CONTINUE NNN = (N*(N+1))/2 DO 20 I = 1,NNN 20 AHOLD(I) = A(I) RETURN 30 NNN = (N*(N+1))/2 DO 40 I = 1,NNN 40 A(I) = AHOLD(I) RETURN 70 WRITE(*,80) 80 FORMAT(47H0END OF DATA FOR SUBROUTINE RMATIN(RSPREADI). /1H1) STOP END 