 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dspev()

 subroutine dspev ( character JOBZ, character UPLO, integer N, double precision, dimension( * ) AP, double precision, dimension( * ) W, double precision, dimension( ldz, * ) Z, integer LDZ, double precision, dimension( * ) WORK, integer INFO )

DSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:
``` DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
real symmetric matrix A in packed storage.```
Parameters
 [in] JOBZ ``` JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] AP ``` AP is DOUBLE PRECISION 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.``` [out] W ``` W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order.``` [out] Z ``` Z is DOUBLE PRECISION 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.``` [in] LDZ ``` LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= max(1,N).``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (3*N)` [out] INFO ``` INFO is 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.```

Definition at line 129 of file dspev.f.

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 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dsteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
DSTEQR
Definition: dsteqr.f:131
subroutine dsterf(N, D, E, INFO)
DSTERF
Definition: dsterf.f:86
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
double precision function dlansp(NORM, UPLO, N, AP, WORK)
DLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlansp.f:114
subroutine dsptrd(UPLO, N, AP, D, E, TAU, INFO)
DSPTRD
Definition: dsptrd.f:150
subroutine dopgtr(UPLO, N, AP, TAU, Q, LDQ, WORK, INFO)
DOPGTR
Definition: dopgtr.f:114
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