SUBROUTINE DGEEV_F95( A, WR, WI, VL, VR, INFO ) ! ! -- LAPACK95 interface driver routine (version 3.0) -- ! UNI-C, Denmark; Univ. of Tennessee, USA; NAG Ltd., UK ! September, 2000 ! ! .. USE STATEMENTS .. USE LA_PRECISION, ONLY: WP => DP USE LA_AUXMOD, ONLY: ERINFO, LSAME USE F77_LAPACK, ONLY: GEEV_F77 => LA_GEEV ! .. IMPLICIT STATEMENT .. IMPLICIT NONE ! .. SCALAR ARGUMENTS .. INTEGER, INTENT(OUT), OPTIONAL :: INFO ! .. ARRAY ARGUMENTS .. REAL(WP), INTENT(INOUT) :: A(:,:) REAL(WP), INTENT(OUT) :: WR(:), WI(:) REAL(WP), INTENT(OUT), OPTIONAL, TARGET :: VL(:,:), VR(:,:) !---------------------------------------------------------------------- ! ! Purpose ! ======= ! ! LA_GEEV computes for a real or complex square matrix A, the ! eigenvalues and, optionally, the left and/or right eigenvectors. A ! right eigenvector v(j) of A satisfies ! A * v(j) = lambda(j) * v(j) ! where lambda(j) is its eigenvalue. A left eigenvector u(j) of A ! satisffies ! u(j)^H * A = lambda(j) * u(j)^H ! where u(j)^H denotes the conjugate-transpose of u(j). ! ! ========= ! ! SUBROUTINE LA_GEEV( A, , VL=vl, VR=vr, INFO=info ) ! (), INTENT(INOUT) :: A(:,:) ! (), INTENT(OUT) :: ! (), INTENT(OUT), OPTIONAL :: VL(:,:), VR(:,:) ! INTEGER, INTENT(OUT), OPTIONAL :: INFO ! where ! ::= REAL | COMPLEX ! ::= KIND(1.0) | KIND(1.0D0) ! ::= WR, WI | W ! ::= WR(:), WI(:) | W(:) ! ! Arguments ! ========= ! ! A (input/output) REAL or COMPLEX square array, shape (:,:). ! On entry, the matrix A. ! On exit, the contents of A are destroyed. ! (output) REAL or COMPLEX array, shape (:) with size(w) = ! size(A,1). ! The computed eigenvalues. ! ::= WR(:), WI(:) | W(:), ! where ! WR(:), WI(:) are of REAL type (for the real and imaginary ! parts) and W(:) is of COMPLEX type. ! Note: If A is real, then a complex-conjugate pair appear ! consecutively, with the eigenvalue having the positive ! imaginary part appearing first. ! VL Optional (output) REAL or COMPLEX square array, shape (:,:) ! with size(VL,1) = size(A,1). ! The left eigenvectors u(j) are stored in the columns of VL in ! the order of their eigenvalues. Each eigenvector is scaled so ! that the Euclidean norm is 1 and the largest component is real. ! Note: If A is real then complex eigenvectors, like their ! eigenvalues, occur in complex conjugate pairs. The real and ! imaginary parts of the first eigenvector of the pair are ! stored in VL(:,j) and VL(:,j+1). Thus a complex conjugate pair ! is given by ! u(j) = VL(:,j) + i*VL(:,j+1), u(j+1) = VL(:,j) - i*VL(:,j+1) ! VR Optional (output) REAL or COMPLEX square array, shape (:,:) ! with size(VR,1) = size(A,1). ! The right eigenvectors v(j) are stored in the columns of VR in ! the order of their eigenvalues. ! Each eigenvector is scaled so that the Euclidean norm is 1 and ! the largest component is real. ! Note: If A is real then complex eigenvectors, like their ! eigenvalues, occur in complex conjugate pairs. The real and ! imaginary parts of the first eigenvector of the pair are stored ! in VR(:,j) and VR(:,j+1). Thus a complex conjugate pair is ! given by ! v(j) = VR(:,j) + i*VR(:,j+1), v(j+1) = VR(:,j) - i*VR(:,j+1) ! INFO Optional (output) INTEGER. ! = 0: successful exit. ! < 0: if INFO = -i, the i-th argument had an illegal value. ! > 0: if INFO = i, the QR algorithm failed to compute all the ! eigenvalues and no eigenvectors were computed. Elements ! i+1 : n of contain eigenvalues which have converged. ! n is the order of A ! If INFO is not present and an error occurs, then the program ! is terminated with an error message. !---------------------------------------------------------------------- ! .. LOCAL PARAMETERS .. CHARACTER(LEN=7), PARAMETER :: SRNAME = 'LA_GEEV' ! .. LOCAL SCALARS .. CHARACTER(LEN=1) :: LJOBVL, LJOBVR INTEGER, SAVE :: LWORK = 0 INTEGER :: N, NN, LINFO, LD, ISTAT, ISTAT1, S1VL, S2VL, S1VR, S2VR ! .. LOCAL ARRAYS .. REAL(WP), TARGET :: LLVL(1,1), LLVR(1,1) REAL(WP), POINTER :: WORK(:) ! .. INTRINSIC FUNCTIONS .. INTRINSIC MAX, PRESENT, SIZE ! .. EXECUTABLE STATEMENTS .. LINFO = 0; ISTAT = 0; N = SIZE(A,1); LD = MAX(1,N) IF( PRESENT(VL) )THEN; S1VL = SIZE(VL,1); S2VL = SIZE(VL,2); LJOBVL = 'V' ELSE; S1VL = 1; S2VL = 1; LJOBVL = 'N'; END IF IF( PRESENT(VR) )THEN; S1VR = SIZE(VR,1); S2VR = SIZE(VR,2); LJOBVR = 'V' ELSE; S1VR = 1; S2VR = 1; LJOBVR = 'N'; END IF ! .. TEST THE ARGUMENTS IF( N < 0 .OR. SIZE(A,2) /= N )THEN; LINFO = -1 ELSE IF( SIZE( WR ) /= N )THEN; LINFO = -2 ELSE IF( SIZE( WI ) /= N )THEN; LINFO = -3 ELSE IF( PRESENT(VL) .AND. ( S1VL /= N .OR. S2VL /= N ) )THEN; LINFO = -4 ELSE IF( PRESENT(VR) .AND. ( S1VR /= N .OR. S2VR /= N ) )THEN; LINFO = -5 ELSE IF( N > 0 )THEN NN = 3; IF( LSAME(LJOBVL,'V').OR.LSAME(LJOBVR,'V') ) NN = NN + 1 LWORK = MAX( 1, NN*N, LWORK); ALLOCATE(WORK(LWORK), STAT=ISTAT) IF( ISTAT /= 0 )THEN; DEALLOCATE(WORK,STAT=ISTAT1) LWORK = MAX( 1, NN*N ); ALLOCATE(WORK(LWORK), STAT=ISTAT) IF( ISTAT == 0) CALL ERINFO( -200, SRNAME, LINFO ) END IF IF( ISTAT == 0 ) THEN IF( PRESENT(VL) )THEN IF( PRESENT(VR) )THEN CALL GEEV_F77( LJOBVL, LJOBVR, N, A, LD, WR, WI, & VL, S1VL, VR, S1VR, WORK, LWORK, LINFO ) ELSE CALL GEEV_F77( LJOBVL, LJOBVR, N, A, LD, WR, WI, & VL, S1VL, LLVR, S1VR, WORK, LWORK, LINFO ) ENDIF ELSE IF( PRESENT(VR) )THEN CALL GEEV_F77( LJOBVL, LJOBVR, N, A, LD, WR, WI, & LLVL, S1VL, VR, S1VR, WORK, LWORK, LINFO ) ELSE CALL GEEV_F77( LJOBVL, LJOBVR, N, A, LD, WR, WI, & LLVL, S1VL, LLVR, S1VR, WORK, LWORK, LINFO ) ENDIF ENDIF IF( LINFO == 0 ) LWORK = INT(WORK(1)+1) ELSE; LINFO = -100; ENDIF DEALLOCATE(WORK, STAT=ISTAT1) ENDIF CALL ERINFO(LINFO,SRNAME,INFO,ISTAT) END SUBROUTINE DGEEV_F95