SUBROUTINE SSBGV_F95( A, B, W, UPLO, Z, 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 => SP USE LA_AUXMOD, ONLY: ERINFO, LSAME USE F77_LAPACK, ONLY: SBGV_F77 => LA_SBGV ! .. IMPLICIT STATEMENT .. IMPLICIT NONE ! .. SCALAR ARGUMENTS .. CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO INTEGER, INTENT(OUT), OPTIONAL :: INFO ! .. ARRAY ARGUMENTS .. REAL(WP), INTENT(INOUT) :: A(:,:), B(:,:) REAL(WP), INTENT(OUT) :: W(:) REAL(WP), INTENT(OUT), OPTIONAL, TARGET :: Z(:,:) !---------------------------------------------------------------------- ! ! Purpose ! ======= ! ! LA_SBGV, LA_SBGVD, LA_HBGV and LA_HBGVD compute all eigenvalues and, ! optionally, all eigenvectors of the generalized eigenvalue problem ! A*z = lambda*B*z, ! where A and B are real symmetric in the cases of LA_SBGV and LA_SBGVD ! and complex Hermitian in the cases of LA_HBGV and LA_HBGVD. Matrix B ! is positive definite. Matrices A and B are stored in a band format. ! LA_SBGVD and LA_HBGVD use a divide and conquer algorithm. If ! eigenvectors are desired, they can be much faster than LA_SBGV and ! LA_HBGV for large matrices but use more workspace. ! ! ========= ! ! SUBROUTINE LA_SBGV / LA_SBGVD / LA_HBGV / LA_HBGVD( AB, BB, & ! W, UPLO=uplo, Z=z, INFO=info ) ! (), INTENT(INOUT) :: AB(:,:), BB(:,:) ! REAL(), INTENT(OUT) :: W(:) ! CHARACTER(LEN=1), INTENT(IN), OPTIONAL :: UPLO ! (), INTENT(OUT), OPTIONAL :: Z(:,:) ! INTEGER, INTENT(OUT), OPTIONAL :: INFO ! where ! ::= REAL | COMPLEX ! ::= KIND(1.0) | KIND(1.0D0) ! ! Arguments ! ========= ! ! AB (input/output) REAL or COMPLEX array, shape (:,:) with ! size(AB,1) = ka + 1 and size(AB,2) = n, where ka is the number ! of subdiagonals or superdiagonals in the band and n is the ! order of A and B. ! On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') ! triangle of matrix A in band storage. The ka + 1 diagonals of ! A are stored in the rows of AB so that the j-th column of A ! is stored in the j-th column of AB as follows: ! if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j, ! 1<=j<=n ! if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka), ! 1<=j<=n. ! On exit, the contents of AB are destroyed. ! BB (input/output) REAL or COMPLEX array, shape (:,:) with ! size(BB,1) = kb + 1 and size(BB,2) = n, where kb is the number ! of subdiagonals or superdiagonals in the band of B. ! On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L') ! triangle of matrix B in band storage. The kb + 1 diagonals of ! B are stored in the rows of BB so that the j-th column of B ! is stored in the j-th column of BB as follows: ! if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j, ! 1<=j<=n ! if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb), ! 1<=j<=n. ! On exit, the factor S from the split Cholesky factorization ! B = S^H*S. ! W (output) REAL array, shape (:) with size(W) = n. ! The eigenvalues in ascending order. ! UPLO Optional (input) CHARACTER(LEN=1). ! = 'U': Upper triangles of A and B are stored; ! = 'L': Lower triangles of A and B are stored. ! Default value: 'U'. ! Z Optional (output) REAL or COMPLEX square array, shape (:,:) ! with size(Z,1) = n. ! The matrix Z of eigenvectors, normalized so that Z^H*B*Z = I. ! INFO Optional (output) INTEGER. ! = 0: successful exit. ! < 0: if INFO = -i, the i-th argument had an illegal value. ! > 0: the algorithm failed to converge or matrix B is not ! positive definite: ! <= n: if INFO = i, i off-diagonal elements of an ! intermediate tridiagonal form did not converge to ! zero. ! > n: if INFO = n+i, for 1<=i<=n, then the leading minor of ! order i of B is not positive definite. The factorization ! of B could not be completed and no eigenvalues or ! eigenvectors were computed. ! 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_SBGV' ! .. LOCAL SCALARS .. CHARACTER(LEN=1) :: LJOBZ, LUPLO INTEGER :: LINFO, N, ISTAT, ISTAT1, S1Z, S2Z, KA, KB, & LDA, LDB ! .. LOCAL ARRAYS .. REAL(WP), TARGET :: LLZ(1,1) REAL(WP), POINTER :: WORK(:) ! .. INTRINSIC FUNCTIONS .. INTRINSIC SIZE, MAX, PRESENT ! .. EXECUTABLE STATEMENTS .. LINFO = 0; KA = SIZE(A,1)-1; N = SIZE(A,2); LDA = MAX(SIZE(A,1),1) ISTAT = 0; KB = SIZE(B,1)-1; LDB = MAX(SIZE(B,1),1) IF( PRESENT(Z) )THEN; S1Z = SIZE(Z,1); S2Z = SIZE(Z,2); LJOBZ = 'V' ELSE; S1Z = 1; S2Z = 1; LJOBZ = 'N'; END IF IF( PRESENT(UPLO) ) THEN; LUPLO = UPLO; ELSE; LUPLO = 'U'; END IF ! .. TEST THE ARGUMENTS IF( KA < 0 .OR. N < 0 ) THEN; LINFO = -1 ELSE IF( KB < 0 .OR. SIZE(B,2) /= N ) THEN; LINFO = -2 ELSE IF( SIZE(W) /= N )THEN; LINFO = -3 ELSE IF( .NOT.LSAME(LUPLO,'U') .AND. .NOT.LSAME(LUPLO,'L') )THEN; LINFO = -4 ELSE IF( PRESENT(Z) .AND. ( S1Z /= N .OR. S2Z /= N ) )THEN; LINFO = -5 ELSE IF( N > 0 )THEN ALLOCATE(WORK(MAX(1,3*N)), STAT=ISTAT) IF( ISTAT == 0 )THEN IF( PRESENT(Z) )THEN CALL SBGV_F77( LJOBZ, LUPLO, N, KA, KB, A, LDA, B, LDB, W, Z, S1Z, & WORK, LINFO ) ELSE CALL SBGV_F77( LJOBZ, LUPLO, N, KA, KB, A, LDA, B, LDB, W, LLZ, S1Z, & WORK, LINFO ) ENDIF ELSE; LINFO = -100; ENDIF DEALLOCATE(WORK, STAT=ISTAT1) ENDIF CALL ERINFO(LINFO,SRNAME,INFO,ISTAT) END SUBROUTINE SSBGV_F95