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SUBROUTINE SSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
$ LIWORK, INFO )
*
* -- LAPACK driver routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
INTEGER INFO, LDA, LIWORK, LWORK, N
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
REAL A( LDA, * ), W( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* SSYEVD computes all eigenvalues and, optionally, eigenvectors of a
* real symmetric matrix A. If eigenvectors are desired, it uses a
* divide and conquer algorithm.
*
* The divide and conquer algorithm makes very mild assumptions about
* floating point arithmetic. It will work on machines with a guard
* digit in add/subtract, or on those binary machines without guard
* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
* Cray-2. It could conceivably fail on hexadecimal or decimal machines
* without guard digits, but we know of none.
*
* 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.
*
* A (input/output) REAL array, dimension (LDA, N)
* On entry, the symmetric matrix A. If UPLO = 'U', the
* leading N-by-N upper triangular part of A contains the
* upper triangular part of the matrix A. If UPLO = 'L',
* the leading N-by-N lower triangular part of A contains
* the lower triangular part of the matrix A.
* On exit, if JOBZ = 'V', then if INFO = 0, A contains the
* orthonormal eigenvectors of the matrix A.
* If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
* or the upper triangle (if UPLO='U') of A, including the
* diagonal, is destroyed.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* W (output) REAL array, dimension (N)
* If INFO = 0, the eigenvalues in ascending order.
*
* WORK (workspace/output) REAL array,
* dimension (LWORK)
* On exit, if LWORK > 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
* If N <= 1, LWORK must be at least 1.
* If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1.
* If JOBZ = 'V' and N > 1, LWORK must be at least
* 1 + 5*N + 2*N*lg N + 3*N**2,
* where lg( N ) = smallest integer k such
* that 2**k >= N.
*
* IWORK (workspace/output) INTEGER array, dimension (LIWORK)
* On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
*
* LIWORK (input) INTEGER
* The dimension of the array IWORK.
* If N <= 1, LIWORK must be at least 1.
* If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
* If JOBZ = 'V' and N > 1, LIWORK must be at least 2 + 5*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, TWO
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 )
* ..
* .. Local Scalars ..
*
LOGICAL LOWER, WANTZ
INTEGER IINFO, INDE, INDTAU, INDWK2, INDWRK, ISCALE,
$ LGN, LIOPT, LIWMIN, LLWORK, LLWRK2, LOPT, LWMIN
REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SLAMCH, SLANSY
EXTERNAL LSAME, SLAMCH, SLANSY
* ..
* .. External Subroutines ..
EXTERNAL SLACPY, SLASCL, SORMTR, SSCAL, SSTEDC, SSTERF,
$ SSYTRD, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC INT, LOG, MAX, REAL, SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
LOWER = LSAME( UPLO, 'L' )
*
INFO = 0
IF( N.LE.1 ) THEN
LGN = 0
LIWMIN = 1
LWMIN = 1
LOPT = LWMIN
LIOPT = LIWMIN
ELSE
LGN = INT( LOG( REAL( N ) ) / LOG( TWO ) )
IF( 2**LGN.LT.N )
$ LGN = LGN + 1
IF( 2**LGN.LT.N )
$ LGN = LGN + 1
IF( WANTZ ) THEN
LIWMIN = 2 + 5*N
LWMIN = 1 + 5*N + 2*N*LGN + 3*N**2
ELSE
LIWMIN = 1
LWMIN = 2*N + 1
END IF
LOPT = LWMIN
LIOPT = LIWMIN
END IF
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
ELSE IF( LWORK.LT.LWMIN ) THEN
INFO = -8
ELSE IF( LIWORK.LT.LIWMIN ) THEN
INFO = -10
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SSYEVD ', -INFO )
GO TO 10
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ GO TO 10
*
IF( N.EQ.1 ) THEN
W( 1 ) = A( 1, 1 )
IF( WANTZ )
$ A( 1, 1 ) = ONE
GO TO 10
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 = SLANSY( 'M', UPLO, N, A, LDA, 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 )
$ CALL SLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
*
* Call SSYTRD to reduce symmetric matrix to tridiagonal form.
*
INDE = 1
INDTAU = INDE + N
INDWRK = INDTAU + N
LLWORK = LWORK - INDWRK + 1
INDWK2 = INDWRK + N*N
LLWRK2 = LWORK - INDWK2 + 1
*
CALL SSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ),
$ WORK( INDWRK ), LLWORK, IINFO )
LOPT = 2*N + WORK( INDWRK )
*
* For eigenvalues only, call SSTERF. For eigenvectors, first call
* SSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
* tridiagonal matrix, then call SORMTR to multiply it by the
* Householder transformations stored in A.
*
IF( .NOT.WANTZ ) THEN
CALL SSTERF( N, W, WORK( INDE ), INFO )
ELSE
CALL SSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
$ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
CALL SORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ),
$ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO )
CALL SLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA )
LOPT = MAX( LOPT, 1+5*N+2*N*LGN+3*N**2 )
END IF
*
* If matrix was scaled, then rescale eigenvalues appropriately.
*
IF( ISCALE.EQ.1 )
$ CALL SSCAL( N, ONE / SIGMA, W, 1 )
10 CONTINUE
IF( LWORK.GT.0 )
$ WORK( 1 ) = LOPT
IF( LIWORK.GT.0 )
$ IWORK( 1 ) = LIOPT
RETURN
*
* End of SSYEVD
*
END
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