 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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 *
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
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
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