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SUBROUTINE SSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
*
* -- LAPACK driver routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER JOBZ
INTEGER INFO, LDZ, N
* ..
* .. Array Arguments ..
REAL D( * ), E( * ), WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* SSTEV computes all eigenvalues and, optionally, eigenvectors of a
* real symmetric tridiagonal matrix A.
*
* Arguments
* =========
*
* JOBZ (input) CHARACTER*1
* = 'N': Compute eigenvalues only;
* = 'V': Compute eigenvalues and eigenvectors.
*
* N (input) INTEGER
* The order of the matrix. N >= 0.
*
* D (input/output) REAL array, dimension (N)
* On entry, the n diagonal elements of the tridiagonal matrix
* A.
* On exit, if INFO = 0, the eigenvalues in ascending order.
*
* E (input/output) REAL array, dimension (N-1)
* On entry, the (n-1) subdiagonal elements of the tridiagonal
* matrix A, stored in elements 1 to N-1 of E.
* On exit, the contents of E are destroyed.
*
* 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 D(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 (max(1,2*N-2))
* If JOBZ = 'N', WORK is not referenced.
*
* 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 E did not converge to zero.
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
LOGICAL WANTZ
INTEGER IMAX, ISCALE
REAL BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
$ TNRM
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SLAMCH, SLANST
EXTERNAL LSAME, SLAMCH, SLANST
* ..
* .. External Subroutines ..
EXTERNAL SSCAL, 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( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -6
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SSTEV ', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( N.EQ.1 ) THEN
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.
*
ISCALE = 0
TNRM = SLANST( 'M', N, D, E )
IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
ISCALE = 1
SIGMA = RMIN / TNRM
ELSE IF( TNRM.GT.RMAX ) THEN
ISCALE = 1
SIGMA = RMAX / TNRM
END IF
IF( ISCALE.EQ.1 ) THEN
CALL SSCAL( N, SIGMA, D, 1 )
CALL SSCAL( N-1, SIGMA, E( 1 ), 1 )
END IF
*
* For eigenvalues only, call SSTERF. For eigenvalues and
* eigenvectors, call SSTEQR.
*
IF( .NOT.WANTZ ) THEN
CALL SSTERF( N, D, E, INFO )
ELSE
CALL SSTEQR( 'I', N, D, E, Z, LDZ, WORK, 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, D, 1 )
END IF
*
RETURN
*
* End of SSTEV
*
END
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