LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ dstev()

 subroutine dstev ( character jobz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info )

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

Purpose:
``` DSTEV computes all eigenvalues and, optionally, eigenvectors of a
real symmetric tridiagonal matrix A.```
Parameters
 [in] JOBZ ``` JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.``` [in] N ``` N is INTEGER The order of the matrix. N >= 0.``` [in,out] D ``` D is DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the tridiagonal matrix A. On exit, if INFO = 0, the eigenvalues in ascending order.``` [in,out] E ``` E is DOUBLE PRECISION 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.``` [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 D(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 (max(1,2*N-2)) If JOBZ = 'N', WORK is not referenced.``` [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 E did not converge to zero.```

Definition at line 115 of file dstev.f.

116*
117* -- LAPACK driver routine --
118* -- LAPACK is a software package provided by Univ. of Tennessee, --
119* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120*
121* .. Scalar Arguments ..
122 CHARACTER JOBZ
123 INTEGER INFO, LDZ, N
124* ..
125* .. Array Arguments ..
126 DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
127* ..
128*
129* =====================================================================
130*
131* .. Parameters ..
132 DOUBLE PRECISION ZERO, ONE
133 parameter( zero = 0.0d0, one = 1.0d0 )
134* ..
135* .. Local Scalars ..
136 LOGICAL WANTZ
137 INTEGER IMAX, ISCALE
138 DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
139 \$ TNRM
140* ..
141* .. External Functions ..
142 LOGICAL LSAME
143 DOUBLE PRECISION DLAMCH, DLANST
144 EXTERNAL lsame, dlamch, dlanst
145* ..
146* .. External Subroutines ..
147 EXTERNAL dscal, dsteqr, dsterf, xerbla
148* ..
149* .. Intrinsic Functions ..
150 INTRINSIC sqrt
151* ..
152* .. Executable Statements ..
153*
154* Test the input parameters.
155*
156 wantz = lsame( jobz, 'V' )
157*
158 info = 0
159 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
160 info = -1
161 ELSE IF( n.LT.0 ) THEN
162 info = -2
163 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
164 info = -6
165 END IF
166*
167 IF( info.NE.0 ) THEN
168 CALL xerbla( 'DSTEV ', -info )
169 RETURN
170 END IF
171*
172* Quick return if possible
173*
174 IF( n.EQ.0 )
175 \$ RETURN
176*
177 IF( n.EQ.1 ) THEN
178 IF( wantz )
179 \$ z( 1, 1 ) = one
180 RETURN
181 END IF
182*
183* Get machine constants.
184*
185 safmin = dlamch( 'Safe minimum' )
186 eps = dlamch( 'Precision' )
187 smlnum = safmin / eps
188 bignum = one / smlnum
189 rmin = sqrt( smlnum )
190 rmax = sqrt( bignum )
191*
192* Scale matrix to allowable range, if necessary.
193*
194 iscale = 0
195 tnrm = dlanst( 'M', n, d, e )
196 IF( tnrm.GT.zero .AND. tnrm.LT.rmin ) THEN
197 iscale = 1
198 sigma = rmin / tnrm
199 ELSE IF( tnrm.GT.rmax ) THEN
200 iscale = 1
201 sigma = rmax / tnrm
202 END IF
203 IF( iscale.EQ.1 ) THEN
204 CALL dscal( n, sigma, d, 1 )
205 CALL dscal( n-1, sigma, e( 1 ), 1 )
206 END IF
207*
208* For eigenvalues only, call DSTERF. For eigenvalues and
209* eigenvectors, call DSTEQR.
210*
211 IF( .NOT.wantz ) THEN
212 CALL dsterf( n, d, e, info )
213 ELSE
214 CALL dsteqr( 'I', n, d, e, z, ldz, work, info )
215 END IF
216*
217* If matrix was scaled, then rescale eigenvalues appropriately.
218*
219 IF( iscale.EQ.1 ) THEN
220 IF( info.EQ.0 ) THEN
221 imax = n
222 ELSE
223 imax = info - 1
224 END IF
225 CALL dscal( imax, one / sigma, d, 1 )
226 END IF
227*
228 RETURN
229*
230* End of DSTEV
231*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function dlanst(norm, n, d, e)
DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition dlanst.f:100
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
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
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