sspev.f

          SUBROUTINE SSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
    *
    *  -- LAPACK driver routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          JOBZ, UPLO
          INTEGER            INFO, LDZ, N
    *     ..
    *     .. Array Arguments ..
          REAL               AP( * ), W( * ), WORK( * ), Z( LDZ, * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SSPEV computes all the eigenvalues and, optionally, eigenvectors of a
    *  real symmetric matrix A 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) 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.
    *
    *  W       (output) REAL array, dimension (N)
    *          If INFO = 0, the eigenvalues in ascending order.
    *
    *  Z       (output) 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.
    *
    *  LDZ     (input) INTEGER
    *          The leading dimension of the array Z.  LDZ >= 1, and if
    *          JOBZ = 'V', LDZ >= max(1,N).
    *
    *  WORK    (workspace) REAL array, dimension (3*N)
    *
    *  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, 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
    *
          END