1*> \brief <b> DSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspev.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          JOBZ, UPLO
25*       INTEGER            INFO, LDZ, N
26*       ..
27*       .. Array Arguments ..
28*       DOUBLE PRECISION   AP( * ), W( * ), WORK( * ), Z( LDZ, * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
38*> real symmetric matrix A in packed storage.
39*> \endverbatim
40*
41*  Arguments:
42*  ==========
43*
44*> \param[in] JOBZ
45*> \verbatim
46*>          JOBZ is CHARACTER*1
47*>          = 'N':  Compute eigenvalues only;
48*>          = 'V':  Compute eigenvalues and eigenvectors.
49*> \endverbatim
50*>
51*> \param[in] UPLO
52*> \verbatim
53*>          UPLO is CHARACTER*1
54*>          = 'U':  Upper triangle of A is stored;
55*>          = 'L':  Lower triangle of A is stored.
56*> \endverbatim
57*>
58*> \param[in] N
59*> \verbatim
60*>          N is INTEGER
61*>          The order of the matrix A.  N >= 0.
62*> \endverbatim
63*>
64*> \param[in,out] AP
65*> \verbatim
66*>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
67*>          On entry, the upper or lower triangle of the symmetric matrix
68*>          A, packed columnwise in a linear array.  The j-th column of A
69*>          is stored in the array AP as follows:
70*>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
71*>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
72*>
73*>          On exit, AP is overwritten by values generated during the
74*>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
75*>          and first superdiagonal of the tridiagonal matrix T overwrite
76*>          the corresponding elements of A, and if UPLO = 'L', the
77*>          diagonal and first subdiagonal of T overwrite the
78*>          corresponding elements of A.
79*> \endverbatim
80*>
81*> \param[out] W
82*> \verbatim
83*>          W is DOUBLE PRECISION array, dimension (N)
84*>          If INFO = 0, the eigenvalues in ascending order.
85*> \endverbatim
86*>
87*> \param[out] Z
88*> \verbatim
89*>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
90*>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
91*>          eigenvectors of the matrix A, with the i-th column of Z
92*>          holding the eigenvector associated with W(i).
93*>          If JOBZ = 'N', then Z is not referenced.
94*> \endverbatim
95*>
96*> \param[in] LDZ
97*> \verbatim
98*>          LDZ is INTEGER
99*>          The leading dimension of the array Z.  LDZ >= 1, and if
100*>          JOBZ = 'V', LDZ >= max(1,N).
101*> \endverbatim
102*>
103*> \param[out] WORK
104*> \verbatim
105*>          WORK is DOUBLE PRECISION array, dimension (3*N)
106*> \endverbatim
107*>
108*> \param[out] INFO
109*> \verbatim
110*>          INFO is INTEGER
111*>          = 0:  successful exit.
112*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
113*>          > 0:  if INFO = i, the algorithm failed to converge; i
114*>                off-diagonal elements of an intermediate tridiagonal
115*>                form did not converge to zero.
116*> \endverbatim
117*
118*  Authors:
119*  ========
120*
121*> \author Univ. of Tennessee
122*> \author Univ. of California Berkeley
123*> \author Univ. of Colorado Denver
124*> \author NAG Ltd.
125*
126*> \ingroup doubleOTHEReigen
127*
128*  =====================================================================
129      SUBROUTINE DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
130*
131*  -- LAPACK driver routine --
132*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
133*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134*
135*     .. Scalar Arguments ..
136      CHARACTER          JOBZ, UPLO
137      INTEGER            INFO, LDZ, N
138*     ..
139*     .. Array Arguments ..
140      DOUBLE PRECISION   AP( * ), W( * ), WORK( * ), Z( LDZ, * )
141*     ..
142*
143*  =====================================================================
144*
145*     .. Parameters ..
146      DOUBLE PRECISION   ZERO, ONE
147      PARAMETER          ( ZERO = 0.0D0, ONE = 1.0D0 )
148*     ..
149*     .. Local Scalars ..
150      LOGICAL            WANTZ
151      INTEGER            IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE
152      DOUBLE PRECISION   ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
153     $                   SMLNUM
154*     ..
155*     .. External Functions ..
156      LOGICAL            LSAME
157      DOUBLE PRECISION   DLAMCH, DLANSP
158      EXTERNAL           LSAME, DLAMCH, DLANSP
159*     ..
160*     .. External Subroutines ..
161      EXTERNAL           DOPGTR, DSCAL, DSPTRD, DSTEQR, DSTERF, XERBLA
162*     ..
163*     .. Intrinsic Functions ..
164      INTRINSIC          SQRT
165*     ..
166*     .. Executable Statements ..
167*
168*     Test the input parameters.
169*
170      WANTZ = LSAME( JOBZ, 'V' )
171*
172      INFO = 0
173      IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
174         INFO = -1
175      ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
176     $          THEN
177         INFO = -2
178      ELSE IF( N.LT.0 ) THEN
179         INFO = -3
180      ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
181         INFO = -7
182      END IF
183*
184      IF( INFO.NE.0 ) THEN
185         CALL XERBLA( 'DSPEV ', -INFO )
186         RETURN
187      END IF
188*
189*     Quick return if possible
190*
191      IF( N.EQ.0 )
192     $   RETURN
193*
194      IF( N.EQ.1 ) THEN
195         W( 1 ) = AP( 1 )
196         IF( WANTZ )
197     $      Z( 1, 1 ) = ONE
198         RETURN
199      END IF
200*
201*     Get machine constants.
202*
203      SAFMIN = DLAMCH( 'Safe minimum' )
204      EPS = DLAMCH( 'Precision' )
205      SMLNUM = SAFMIN / EPS
206      BIGNUM = ONE / SMLNUM
207      RMIN = SQRT( SMLNUM )
208      RMAX = SQRT( BIGNUM )
209*
210*     Scale matrix to allowable range, if necessary.
211*
212      ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
213      ISCALE = 0
214      IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
215         ISCALE = 1
216         SIGMA = RMIN / ANRM
217      ELSE IF( ANRM.GT.RMAX ) THEN
218         ISCALE = 1
219         SIGMA = RMAX / ANRM
220      END IF
221      IF( ISCALE.EQ.1 ) THEN
222         CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
223      END IF
224*
225*     Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
226*
227      INDE = 1
228      INDTAU = INDE + N
229      CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
230*
231*     For eigenvalues only, call DSTERF.  For eigenvectors, first call
232*     DOPGTR to generate the orthogonal matrix, then call DSTEQR.
233*
234      IF( .NOT.WANTZ ) THEN
235         CALL DSTERF( N, W, WORK( INDE ), INFO )
236      ELSE
237         INDWRK = INDTAU + N
238         CALL DOPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
239     $                WORK( INDWRK ), IINFO )
240         CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDTAU ),
241     $                INFO )
242      END IF
243*
244*     If matrix was scaled, then rescale eigenvalues appropriately.
245*
246      IF( ISCALE.EQ.1 ) THEN
247         IF( INFO.EQ.0 ) THEN
248            IMAX = N
249         ELSE
250            IMAX = INFO - 1
251         END IF
252         CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
253      END IF
254*
255      RETURN
256*
257*     End of DSPEV
258*
259      END
260