*DECK CHIEV SUBROUTINE CHIEV (A, LDA, N, E, V, LDV, WORK, JOB, INFO) C***BEGIN PROLOGUE CHIEV C***PURPOSE Compute the eigenvalues and, optionally, the eigenvectors C of a complex Hermitian matrix. C***LIBRARY SLATEC C***CATEGORY D4A3 C***TYPE COMPLEX (SSIEV-S, CHIEV-C) C***KEYWORDS COMPLEX HERMITIAN, EIGENVALUES, EIGENVECTORS, MATRIX, C SYMMETRIC C***AUTHOR Kahaner, D. K., (NBS) C Moler, C. B., (U. of New Mexico) C Stewart, G. W., (U. of Maryland) C***DESCRIPTION C C David Kahaner, Cleve Moler, G. W. Stewart, C N.B.S. U.N.M. N.B.S./U.MD. C C Abstract C CHIEV computes the eigenvalues and, optionally, C the eigenvectors of a complex Hermitian matrix. C C Call Sequence Parameters- C (the values of parameters marked with * (star) will be changed C by CHIEV.) C C A* COMPLEX(LDA,N) C complex Hermitian input matrix. C Only the upper triangle of A need be C filled in. Elements on diagonal must be real. C C LDA INTEGER C set by the user to C the leading dimension of the complex array A. C C N INTEGER C set by the user to C the order of the matrices A and V, and C the number of elements in E. C C E* REAL(N) C on return from CHIEV E contains the eigenvalues of A. C See also INFO below. C C V* COMPLEX(LDV,N) C on return from CHIEV if the user has set JOB C = 0 V is not referenced. C = nonzero the N eigenvectors of A are stored in the C first N columns of V. See also INFO below. C C LDV INTEGER C set by the user to C the leading dimension of the array V if JOB is also C set nonzero. In that case N must be .LE. LDV. C If JOB is set to zero LDV is not referenced. C C WORK* REAL(4N) C temporary storage vector. Contents changed by CHIEV. C C JOB INTEGER C set by the user to C = 0 eigenvalues only to be calculated by CHIEV. C Neither V nor LDV are referenced. C = nonzero eigenvalues and vectors to be calculated. C In this case A and V must be distinct arrays C also if LDA .GT. LDV CHIEV changes all the C elements of A thru column N. If LDA < LDV C CHIEV changes all the elements of V through C column N. If LDA = LDV only A(I,J) and V(I, C J) for I,J = 1,...,N are changed by CHIEV. C C INFO* INTEGER C on return from CHIEV the value of INFO is C = 0 normal return, calculation successful. C = K if the eigenvalue iteration fails to converge, C eigenvalues (and eigenvectors if requested) C 1 through K-1 are correct. C C Error Messages C No. 1 recoverable N is greater than LDA C No. 2 recoverable N is less than one. C No. 3 recoverable JOB is nonzero and N is greater than LDV C No. 4 warning LDA > LDV, elements of A other than the C N by N input elements have been changed C No. 5 warning LDA < LDV, elements of V other than the C N by N output elements have been changed C No. 6 recoverable nonreal element on diagonal of A. C C***REFERENCES (NONE) C***ROUTINES CALLED HTRIBK, HTRIDI, IMTQL2, SCOPY, SCOPYM, TQLRAT, C XERMSG C***REVISION HISTORY (YYMMDD) C 800808 DATE WRITTEN C 890531 Changed all specific intrinsics to generic. (WRB) C 890531 REVISION DATE from Version 3.2 C 891214 Prologue converted to Version 4.0 format. (BAB) C 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ) C***END PROLOGUE CHIEV INTEGER I,INFO,J,JOB,K,L,LDA,LDV,M,MDIM,N REAL A(*),E(*),WORK(*),V(*) C***FIRST EXECUTABLE STATEMENT CHIEV IF (N .GT. LDA) CALL XERMSG ('SLATEC', 'CHIEV', 'N .GT. LDA.', 1, + 1) IF(N .GT. LDA) RETURN IF (N .LT. 1) CALL XERMSG ('SLATEC', 'CHIEV', 'N .LT. 1', 2, 1) IF(N .LT. 1) RETURN IF(N .EQ. 1 .AND. JOB .EQ. 0) GO TO 35 MDIM = 2 * LDA IF(JOB .EQ. 0) GO TO 5 IF (N .GT. LDV) CALL XERMSG ('SLATEC', 'CHIEV', + 'JOB .NE. 0 AND N .GT. LDV.', 3, 1) IF(N .GT. LDV) RETURN IF(N .EQ. 1) GO TO 35 C C REARRANGE A IF NECESSARY WHEN LDA.GT.LDV AND JOB .NE.0 C MDIM = MIN(MDIM,2 * LDV) IF (LDA .LT. LDV) CALL XERMSG ('SLATEC', 'CHIEV', + 'LDA.LT.LDV, ELEMENTS OF V OTHER THAN THE N BY N OUTPUT ' // + 'ELEMENTS HAVE BEEN CHANGED.', 5, 0) IF(LDA.LE.LDV) GO TO 5 CALL XERMSG ('SLATEC', 'CHIEV', + 'LDA.GT.LDV, ELEMENTS OF A OTHER THAN THE N BY N INPUT ' // + 'ELEMENTS HAVE BEEN CHANGED.', 4, 0) L = N - 1 DO 4 J=1,L M = 1+J*2*LDV K = 1+J*2*LDA CALL SCOPY(2*N,A(K),1,A(M),1) 4 CONTINUE 5 CONTINUE C C FILL IN LOWER TRIANGLE OF A, COLUMN BY COLUMN. C DO 6 J = 1,N K = (J-1)*(MDIM+2)+1 IF (A(K+1) .NE. 0.0) CALL XERMSG ('SLATEC', 'CHIEV', + 'NONREAL ELEMENT ON DIAGONAL OF A', 6, 1) IF(A(K+1) .NE.0.0) RETURN CALL SCOPY(N-J+1,A(K),MDIM,A(K),2) CALL SCOPYM(N-J+1,A(K+1),MDIM,A(K+1),2) 6 CONTINUE C C SEPARATE REAL AND IMAGINARY PARTS C DO 10 J = 1, N K = (J-1) * MDIM +1 L = K + N CALL SCOPY(N,A(K+1),2,WORK(1),1) CALL SCOPY(N,A(K),2,A(K),1) CALL SCOPY(N,WORK(1),1,A(L),1) 10 CONTINUE C C REDUCE A TO TRIDIAGONAL MATRIX. C CALL HTRIDI(MDIM,N,A(1),A(N+1),E,WORK(1),WORK(N+1), 1 WORK(2*N+1)) IF(JOB .NE. 0) GOTO 15 C C EIGENVALUES ONLY. C CALL TQLRAT(N,E,WORK(N+1),INFO) RETURN C C EIGENVALUES AND EIGENVECTORS. C 15 DO 17 J = 1,N K = (J-1) * MDIM + 1 M = K + N - 1 DO 16 I = K,M 16 V(I) = 0. I = K + J - 1 V(I) = 1. 17 CONTINUE CALL IMTQL2(MDIM,N,E,WORK(1),V,INFO) IF(INFO .NE. 0) RETURN CALL HTRIBK(MDIM,N,A(1),A(N+1),WORK(2*N+1),N,V(1),V(N+1)) C C CONVERT EIGENVECTORS TO COMPLEX STORAGE. C DO 20 J = 1,N K = (J-1) * MDIM + 1 I = (J-1) * 2 * LDV + 1 L = K + N CALL SCOPY(N,V(K),1,WORK(1),1) CALL SCOPY(N,V(L),1,V(I+1),2) CALL SCOPY(N,WORK(1),1,V(I),2) 20 CONTINUE RETURN C C TAKE CARE OF N=1 CASE. C 35 IF (A(2) .NE. 0.) CALL XERMSG ('SLATEC', 'CHIEV', + 'NONREAL ELEMENT ON DIAGONAL OF A', 6, 1) IF(A(2) .NE. 0.) RETURN E(1) = A(1) INFO = 0 IF(JOB .EQ. 0) RETURN V(1) = A(1) V(2) = 0. RETURN END