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SUBROUTINE <a name="SSPEVX.1"></a><a href="sspevx.f.html#SSPEVX.1">SSPEVX</a>( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
$ ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL,
$ INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER JOBZ, RANGE, UPLO
INTEGER IL, INFO, IU, LDZ, M, N
REAL ABSTOL, VL, VU
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IFAIL( * ), IWORK( * )
REAL AP( * ), W( * ), WORK( * ), Z( LDZ, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="SSPEVX.22"></a><a href="sspevx.f.html#SSPEVX.1">SSPEVX</a> computes selected eigenvalues and, optionally, eigenvectors
</span><span class="comment">*</span><span class="comment"> of a real symmetric matrix A in packed storage. Eigenvalues/vectors
</span><span class="comment">*</span><span class="comment"> can be selected by specifying either a range of values or a range of
</span><span class="comment">*</span><span class="comment"> indices for the desired eigenvalues.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> JOBZ (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'N': Compute eigenvalues only;
</span><span class="comment">*</span><span class="comment"> = 'V': Compute eigenvalues and eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> RANGE (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'A': all eigenvalues will be found;
</span><span class="comment">*</span><span class="comment"> = 'V': all eigenvalues in the half-open interval (VL,VU]
</span><span class="comment">*</span><span class="comment"> will be found;
</span><span class="comment">*</span><span class="comment"> = 'I': the IL-th through IU-th eigenvalues will be found.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AP (input/output) REAL array, dimension (N*(N+1)/2)
</span><span class="comment">*</span><span class="comment"> On entry, the upper or lower triangle of the symmetric matrix
</span><span class="comment">*</span><span class="comment"> A, packed columnwise in a linear array. The j-th column of A
</span><span class="comment">*</span><span class="comment"> is stored in the array AP as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> On exit, AP is overwritten by values generated during the
</span><span class="comment">*</span><span class="comment"> reduction to tridiagonal form. If UPLO = 'U', the diagonal
</span><span class="comment">*</span><span class="comment"> and first superdiagonal of the tridiagonal matrix T overwrite
</span><span class="comment">*</span><span class="comment"> the corresponding elements of A, and if UPLO = 'L', the
</span><span class="comment">*</span><span class="comment"> diagonal and first subdiagonal of T overwrite the
</span><span class="comment">*</span><span class="comment"> corresponding elements of A.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> VL (input) REAL
</span><span class="comment">*</span><span class="comment"> VU (input) REAL
</span><span class="comment">*</span><span class="comment"> If RANGE='V', the lower and upper bounds of the interval to
</span><span class="comment">*</span><span class="comment"> be searched for eigenvalues. VL < VU.
</span><span class="comment">*</span><span class="comment"> Not referenced if RANGE = 'A' or 'I'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IL (input) INTEGER
</span><span class="comment">*</span><span class="comment"> IU (input) INTEGER
</span><span class="comment">*</span><span class="comment"> If RANGE='I', the indices (in ascending order) of the
</span><span class="comment">*</span><span class="comment"> smallest and largest eigenvalues to be returned.
</span><span class="comment">*</span><span class="comment"> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
</span><span class="comment">*</span><span class="comment"> Not referenced if RANGE = 'A' or 'V'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ABSTOL (input) REAL
</span><span class="comment">*</span><span class="comment"> The absolute error tolerance for the eigenvalues.
</span><span class="comment">*</span><span class="comment"> An approximate eigenvalue is accepted as converged
</span><span class="comment">*</span><span class="comment"> when it is determined to lie in an interval [a,b]
</span><span class="comment">*</span><span class="comment"> of width less than or equal to
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ABSTOL + EPS * max( |a|,|b| ) ,
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where EPS is the machine precision. If ABSTOL is less than
</span><span class="comment">*</span><span class="comment"> or equal to zero, then EPS*|T| will be used in its place,
</span><span class="comment">*</span><span class="comment"> where |T| is the 1-norm of the tridiagonal matrix obtained
</span><span class="comment">*</span><span class="comment"> by reducing AP to tridiagonal form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Eigenvalues will be computed most accurately when ABSTOL is
</span><span class="comment">*</span><span class="comment"> set to twice the underflow threshold 2*<a name="SLAMCH.88"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>('S'), not zero.
</span><span class="comment">*</span><span class="comment"> If this routine returns with INFO>0, indicating that some
</span><span class="comment">*</span><span class="comment"> eigenvectors did not converge, try setting ABSTOL to
</span><span class="comment">*</span><span class="comment"> 2*<a name="SLAMCH.91"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>('S').
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> See "Computing Small Singular Values of Bidiagonal Matrices
</span><span class="comment">*</span><span class="comment"> with Guaranteed High Relative Accuracy," by Demmel and
</span><span class="comment">*</span><span class="comment"> Kahan, LAPACK Working Note #3.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (output) INTEGER
</span><span class="comment">*</span><span class="comment"> The total number of eigenvalues found. 0 <= M <= N.
</span><span class="comment">*</span><span class="comment"> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W (output) REAL array, dimension (N)
</span><span class="comment">*</span><span class="comment"> If INFO = 0, the selected eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (output) REAL array, dimension (LDZ, max(1,M))
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
</span><span class="comment">*</span><span class="comment"> contain the orthonormal eigenvectors of the matrix A
</span><span class="comment">*</span><span class="comment"> corresponding to the selected eigenvalues, with the i-th
</span><span class="comment">*</span><span class="comment"> column of Z holding the eigenvector associated with W(i).
</span><span class="comment">*</span><span class="comment"> If an eigenvector fails to converge, then that column of Z
</span><span class="comment">*</span><span class="comment"> contains the latest approximation to the eigenvector, and the
</span><span class="comment">*</span><span class="comment"> index of the eigenvector is returned in IFAIL.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N', then Z is not referenced.
</span><span class="comment">*</span><span class="comment"> Note: the user must ensure that at least max(1,M) columns are
</span><span class="comment">*</span><span class="comment"> supplied in the array Z; if RANGE = 'V', the exact value of M
</span><span class="comment">*</span><span class="comment"> is not known in advance and an upper bound must be used.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Z. LDZ >= 1, and if
</span><span class="comment">*</span><span class="comment"> JOBZ = 'V', LDZ >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) REAL array, dimension (8*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IWORK (workspace) INTEGER array, dimension (5*N)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IFAIL (output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V', then if INFO = 0, the first M elements of
</span><span class="comment">*</span><span class="comment"> IFAIL are zero. If INFO > 0, then IFAIL contains the
</span><span class="comment">*</span><span class="comment"> indices of the eigenvectors that failed to converge.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N', then IFAIL is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = i, then i eigenvectors failed to converge.
</span><span class="comment">*</span><span class="comment"> Their indices are stored in array IFAIL.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL ALLEIG, INDEIG, TEST, VALEIG, WANTZ
CHARACTER ORDER
INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
$ INDISP, INDIWO, INDTAU, INDWRK, ISCALE, ITMP1,
$ J, JJ, NSPLIT
REAL ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
$ SIGMA, SMLNUM, TMP1, VLL, VUU
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.153"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
REAL <a name="SLAMCH.154"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANSP.154"></a><a href="slansp.f.html#SLANSP.1">SLANSP</a>
EXTERNAL <a name="LSAME.155"></a><a href="lsame.f.html#LSAME.1">LSAME</a>, <a name="SLAMCH.155"></a><a href="slamch.f.html#SLAMCH.1">SLAMCH</a>, <a name="SLANSP.155"></a><a href="slansp.f.html#SLANSP.1">SLANSP</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL SCOPY, <a name="SOPGTR.158"></a><a href="sopgtr.f.html#SOPGTR.1">SOPGTR</a>, <a name="SOPMTR.158"></a><a href="sopmtr.f.html#SOPMTR.1">SOPMTR</a>, SSCAL, <a name="SSPTRD.158"></a><a href="ssptrd.f.html#SSPTRD.1">SSPTRD</a>, <a name="SSTEBZ.158"></a><a href="sstebz.f.html#SSTEBZ.1">SSTEBZ</a>,
$ <a name="SSTEIN.159"></a><a href="sstein.f.html#SSTEIN.1">SSTEIN</a>, <a name="SSTEQR.159"></a><a href="ssteqr.f.html#SSTEQR.1">SSTEQR</a>, <a name="SSTERF.159"></a><a href="ssterf.f.html#SSTERF.1">SSTERF</a>, SSWAP, <a name="XERBLA.159"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX, MIN, SQRT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Test the input parameters.
</span><span class="comment">*</span><span class="comment">
</span> WANTZ = <a name="LSAME.168"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'V'</span> )
ALLEIG = <a name="LSAME.169"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'A'</span> )
VALEIG = <a name="LSAME.170"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'V'</span> )
INDEIG = <a name="LSAME.171"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( RANGE, <span class="string">'I'</span> )
<span class="comment">*</span><span class="comment">
</span> INFO = 0
IF( .NOT.( WANTZ .OR. <a name="LSAME.174"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( JOBZ, <span class="string">'N'</span> ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
INFO = -2
ELSE IF( .NOT.( <a name="LSAME.178"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'L'</span> ) .OR. <a name="LSAME.178"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) )
$ THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE
IF( VALEIG ) THEN
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