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SUBROUTINE CHPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, RWORK,
$ INFO )
*
* -- LAPACK driver routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
INTEGER INFO, LDZ, N
* ..
* .. Array Arguments ..
REAL RWORK( * ), W( * )
COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* CHPEV 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 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) REAL array, dimension (N)
* If INFO = 0, the eigenvalues in ascending order.
*
* Z (output) COMPLEX 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 array, dimension (max(1, 2*N-1))
*
* RWORK (workspace) REAL 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 ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
LOGICAL WANTZ
INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
$ ISCALE
REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANHP, SLAMCH
EXTERNAL LSAME, CLANHP, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CHPTRD, CSSCAL, CSTEQR, CUPGTR, SSCAL, SSTERF,
$ XERBLA
* ..
* .. 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( 'CHPEV ', -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 = SLAMCH( 'Safe minimum' )
EPS = SLAMCH( 'Precision' )
SMLNUM = SAFMIN / EPS
BIGNUM = ONE / SMLNUM
RMIN = SQRT( SMLNUM )
RMAX = SQRT( BIGNUM )
*
* Scale matrix to allowable range, if necessary.
*
ANRM = CLANHP( '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 CSSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
END IF
*
* Call CHPTRD to reduce Hermitian packed matrix to tridiagonal form.
*
INDE = 1
INDTAU = 1
CALL CHPTRD( UPLO, N, AP, W, RWORK( INDE ), WORK( INDTAU ),
$ IINFO )
*
* For eigenvalues only, call SSTERF. For eigenvectors, first call
* CUPGTR to generate the orthogonal matrix, then call CSTEQR.
*
IF( .NOT.WANTZ ) THEN
CALL SSTERF( N, W, RWORK( INDE ), INFO )
ELSE
INDWRK = INDTAU + N
CALL CUPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
$ WORK( INDWRK ), IINFO )
INDRWK = INDE + N
CALL CSTEQR( 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 SSCAL( IMAX, ONE / SIGMA, W, 1 )
END IF
*
RETURN
*
* End of CHPEV
*
END
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