sspev()

subroutine sspev	(	character	jobz,
		character	uplo,
		integer	n,
		real, dimension( * )	ap,
		real, dimension( * )	w,
		real, dimension( ldz, * )	z,
		integer	ldz,
		real, dimension( * )	work,
		integer	info )

SSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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Purpose:

!>
!> SSPEV computes all the eigenvalues and, optionally, eigenvectors of a
!> real symmetric matrix A in packed storage.
!> 

Parameters

[in]	JOBZ	!> JOBZ is CHARACTER*1 !> = 'N': Compute eigenvalues only; !> = 'V': Compute eigenvalues and eigenvectors. !>
[in]	UPLO	!> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !>
[in]	N	!> N is INTEGER !> The order of the matrix A. N >= 0. !>
[in,out]	AP	!> AP is REAL array, dimension (N*(N+1)/2) !> On entry, the upper or lower triangle of the symmetric 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. !>
[out]	W	!> W is REAL array, dimension (N) !> If INFO = 0, the eigenvalues in ascending order. !>
[out]	Z	!> Z is REAL 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. !>
[in]	LDZ	!> LDZ is INTEGER !> The leading dimension of the array Z. LDZ >= 1, and if !> JOBZ = 'V', LDZ >= max(1,N). !>
[out]	WORK	!> WORK is REAL array, dimension (3*N) !>
[out]	INFO	!> INFO is 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. !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file sspev.f.

*
*  -- LAPACK driver routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, UPLO
      INTEGER            INFO, LDZ, N
*     ..
*     .. Array Arguments ..
      REAL               AP( * ), W( * ), WORK( * ), Z( LDZ, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e0, one = 1.0e0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            WANTZ
      INTEGER            IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE
      REAL               ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
     $                   SMLNUM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      REAL               SLAMCH, SLANSP
      EXTERNAL           lsame, slamch, slansp
*     ..
*     .. External Subroutines ..
      EXTERNAL           sopgtr, sscal, ssptrd, ssteqr, 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, 'U' ) .OR.
     $         lsame( uplo, 'L' ) ) )
     $          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( 'SSPEV ', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
      IF( n.EQ.1 ) THEN
         w( 1 ) = ap( 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 = slansp( 'M', uplo, n, ap, work )
      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 sscal( ( n*( n+1 ) ) / 2, sigma, ap, 1 )
      END IF
*
*     Call SSPTRD to reduce symmetric packed matrix to tridiagonal form.
*
      inde = 1
      indtau = inde + n
      CALL ssptrd( uplo, n, ap, w, work( inde ), work( indtau ),
     $             iinfo )
*
*     For eigenvalues only, call SSTERF.  For eigenvectors, first call
*     SOPGTR to generate the orthogonal matrix, then call SSTEQR.
*
      IF( .NOT.wantz ) THEN
         CALL ssterf( n, w, work( inde ), info )
      ELSE
         indwrk = indtau + n
         CALL sopgtr( uplo, n, ap, work( indtau ), z, ldz,
     $                work( indwrk ), iinfo )
         CALL ssteqr( jobz, n, w, work( inde ), z, ldz,
     $                work( indtau ),
     $                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 SSPEV
*

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