SUBROUTINE ZHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK, \$ INFO ) * * -- LAPACK driver routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, LDZ, N * .. * .. Array Arguments .. DOUBLE PRECISION RWORK( * ), W( * ) COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * ) * .. * * Purpose * ======= * * ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a * complex Hermitian matrix in packed storage. * * Arguments * ========= * * JOBZ (input) CHARACTER*1 * = 'N': Compute eigenvalues only; * = 'V': Compute eigenvalues and eigenvectors. * * UPLO (input) CHARACTER*1 * = 'U': Upper triangle of A is stored; * = 'L': Lower triangle of A is stored. * * N (input) INTEGER * The order of the matrix A. N >= 0. * * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) * On entry, the upper or lower triangle of the Hermitian matrix * A, packed columnwise in a linear array. The j-th column of A * is stored in the array AP as follows: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. * * On exit, AP is overwritten by values generated during the * reduction to tridiagonal form. If UPLO = 'U', the diagonal * and first superdiagonal of the tridiagonal matrix T overwrite * the corresponding elements of A, and if UPLO = 'L', the * diagonal and first subdiagonal of T overwrite the * corresponding elements of A. * * W (output) DOUBLE PRECISION array, dimension (N) * If INFO = 0, the eigenvalues in ascending order. * * Z (output) COMPLEX*16 array, dimension (LDZ, N) * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal * eigenvectors of the matrix A, with the i-th column of Z * holding the eigenvector associated with W(i). * If JOBZ = 'N', then Z is not referenced. * * LDZ (input) INTEGER * The leading dimension of the array Z. LDZ >= 1, and if * JOBZ = 'V', LDZ >= max(1,N). * * WORK (workspace) COMPLEX*16 array, dimension (max(1, 2*N-1)) * * 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: if INFO = i, the algorithm failed to converge; i * off-diagonal elements of an intermediate tridiagonal * form did not converge to zero. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. LOGICAL WANTZ INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK, \$ ISCALE DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, \$ SMLNUM * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANHP EXTERNAL LSAME, DLAMCH, ZLANHP * .. * .. External Subroutines .. EXTERNAL DSCAL, DSTERF, XERBLA, ZDSCAL, ZHPTRD, ZSTEQR, \$ ZUPGTR * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) * INFO = 0 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN INFO = -1 ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) ) \$ THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN INFO = -7 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZHPEV ', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * IF( N.EQ.1 ) THEN W( 1 ) = AP( 1 ) RWORK( 1 ) = 1 IF( WANTZ ) \$ Z( 1, 1 ) = ONE RETURN END IF * * Get machine constants. * SAFMIN = DLAMCH( 'Safe minimum' ) EPS = DLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = SQRT( BIGNUM ) * * Scale matrix to allowable range, if necessary. * ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK ) ISCALE = 0 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN ISCALE = 1 SIGMA = RMIN / ANRM ELSE IF( ANRM.GT.RMAX ) THEN ISCALE = 1 SIGMA = RMAX / ANRM END IF IF( ISCALE.EQ.1 ) THEN CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 ) END IF * * Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form. * INDE = 1 INDTAU = 1 CALL ZHPTRD( UPLO, N, AP, W, RWORK( INDE ), WORK( INDTAU ), \$ IINFO ) * * For eigenvalues only, call DSTERF. For eigenvectors, first call * ZUPGTR to generate the orthogonal matrix, then call ZSTEQR. * IF( .NOT.WANTZ ) THEN CALL DSTERF( N, W, RWORK( INDE ), INFO ) ELSE INDWRK = INDTAU + N CALL ZUPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ, \$ WORK( INDWRK ), IINFO ) INDRWK = INDE + N CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ, \$ RWORK( INDRWK ), INFO ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) THEN IF( INFO.EQ.0 ) THEN IMAX = N ELSE IMAX = INFO - 1 END IF CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * RETURN * * End of ZHPEV * END