SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, \$ LWORK, RWORK, INFO ) * * -- LAPACK driver routine (version 3.3.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * -- April 2011 -- * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, ITYPE, LDA, LDB, LWORK, N * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) * .. * * Purpose * ======= * * ZHEGV computes all the eigenvalues, and optionally, the eigenvectors * of a complex generalized Hermitian-definite eigenproblem, of the form * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. * Here A and B are assumed to be Hermitian and B is also * positive definite. * * Arguments * ========= * * ITYPE (input) INTEGER * Specifies the problem type to be solved: * = 1: A*x = (lambda)*B*x * = 2: A*B*x = (lambda)*x * = 3: B*A*x = (lambda)*x * * JOBZ (input) CHARACTER*1 * = 'N': Compute eigenvalues only; * = 'V': Compute eigenvalues and eigenvectors. * * UPLO (input) CHARACTER*1 * = 'U': Upper triangles of A and B are stored; * = 'L': Lower triangles of A and B are stored. * * N (input) INTEGER * The order of the matrices A and B. N >= 0. * * A (input/output) COMPLEX*16 array, dimension (LDA, N) * On entry, the Hermitian matrix A. If UPLO = 'U', the * leading N-by-N upper triangular part of A contains the * upper triangular part of the matrix A. If UPLO = 'L', * the leading N-by-N lower triangular part of A contains * the lower triangular part of the matrix A. * * On exit, if JOBZ = 'V', then if INFO = 0, A contains the * matrix Z of eigenvectors. The eigenvectors are normalized * as follows: * if ITYPE = 1 or 2, Z**H*B*Z = I; * if ITYPE = 3, Z**H*inv(B)*Z = I. * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U') * or the lower triangle (if UPLO='L') of A, including the * diagonal, is destroyed. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * B (input/output) COMPLEX*16 array, dimension (LDB, N) * On entry, the Hermitian positive definite matrix B. * If UPLO = 'U', the leading N-by-N upper triangular part of B * contains the upper triangular part of the matrix B. * If UPLO = 'L', the leading N-by-N lower triangular part of B * contains the lower triangular part of the matrix B. * * On exit, if INFO <= N, the part of B containing the matrix is * overwritten by the triangular factor U or L from the Cholesky * factorization B = U**H*U or B = L*L**H. * * LDB (input) INTEGER * The leading dimension of the array B. LDB >= max(1,N). * * W (output) DOUBLE PRECISION array, dimension (N) * If INFO = 0, the eigenvalues in ascending order. * * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. * * LWORK (input) INTEGER * The length of the array WORK. LWORK >= max(1,2*N-1). * For optimal efficiency, LWORK >= (NB+1)*N, * where NB is the blocksize for ZHETRD returned by ILAENV. * * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the optimal size of the WORK array, returns * this value as the first entry of the WORK array, and no error * message related to LWORK is issued by XERBLA. * * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2)) * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * > 0: ZPOTRF or ZHEEV returned an error code: * <= N: if INFO = i, ZHEEV failed to converge; * 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. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL LQUERY, UPPER, WANTZ CHARACTER TRANS INTEGER LWKOPT, NB, NEIG * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL XERBLA, ZHEEV, ZHEGST, ZPOTRF, ZTRMM, ZTRSM * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) UPPER = LSAME( UPLO, 'U' ) LQUERY = ( LWORK.EQ.-1 ) * INFO = 0 IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN INFO = -1 ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -2 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN INFO = -3 ELSE IF( N.LT.0 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -6 ELSE IF( LDB.LT.MAX( 1, N ) ) THEN INFO = -8 END IF * IF( INFO.EQ.0 ) THEN NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) LWKOPT = MAX( 1, ( NB + 1 )*N ) WORK( 1 ) = LWKOPT * IF( LWORK.LT.MAX( 1, 2*N - 1 ) .AND. .NOT.LQUERY ) THEN INFO = -11 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHEGV ', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * * Form a Cholesky factorization of B. * CALL ZPOTRF( UPLO, N, B, LDB, INFO ) IF( INFO.NE.0 ) THEN INFO = N + INFO RETURN END IF * * Transform problem to standard eigenvalue problem and solve. * CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) CALL ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO ) * IF( WANTZ ) THEN * * Backtransform eigenvectors to the original problem. * NEIG = N IF( INFO.GT.0 ) \$ NEIG = INFO - 1 IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN * * For A*x=(lambda)*B*x and A*B*x=(lambda)*x; * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y * IF( UPPER ) THEN TRANS = 'N' ELSE TRANS = 'C' END IF * CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, \$ B, LDB, A, LDA ) * ELSE IF( ITYPE.EQ.3 ) THEN * * For B*A*x=(lambda)*x; * backtransform eigenvectors: x = L*y or U**H *y * IF( UPPER ) THEN TRANS = 'C' ELSE TRANS = 'N' END IF * CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE, \$ B, LDB, A, LDA ) END IF END IF * WORK( 1 ) = LWKOPT * RETURN * * End of ZHEGV * END