LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dspgv()

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

DSPGV

Purpose:
``` DSPGV computes all the eigenvalues and, optionally, the eigenvectors
of a real generalized symmetric-definite eigenproblem, of the form
A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
Here A and B are assumed to be symmetric, stored in packed format,
and B is also positive definite.```
Parameters
 [in] ITYPE ``` ITYPE is INTEGER Specifies the problem type to be solved: = 1: A*x = (lambda)*B*x = 2: A*B*x = (lambda)*x = 3: B*A*x = (lambda)*x``` [in] JOBZ ``` JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.``` [in] N ``` N is INTEGER The order of the matrices A and B. 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, the contents of AP are destroyed.``` [in,out] BP ``` BP is DOUBLE PRECISION array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix B, packed columnwise in a linear array. The j-th column of B is stored in the array BP as follows: if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j; if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n. On exit, the triangular factor U or L from the Cholesky factorization B = U**T*U or B = L*L**T, in the same storage format as B.``` [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 matrix Z of eigenvectors. The eigenvectors are normalized as follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3, Z**T*inv(B)*Z = 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: DPPTRF or DSPEV returned an error code: <= N: if INFO = i, DSPEV failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. > N: if INFO = n + i, for 1 <= i <= n, then the leading minor of order i of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.```
Date
June 2017

Definition at line 162 of file dspgv.f.

162 *
163 * -- LAPACK driver routine (version 3.7.1) --
164 * -- LAPACK is a software package provided by Univ. of Tennessee, --
165 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166 * June 2017
167 *
168 * .. Scalar Arguments ..
169  CHARACTER jobz, uplo
170  INTEGER info, itype, ldz, n
171 * ..
172 * .. Array Arguments ..
173  DOUBLE PRECISION ap( * ), bp( * ), w( * ), work( * ),
174  \$ z( ldz, * )
175 * ..
176 *
177 * =====================================================================
178 *
179 * .. Local Scalars ..
180  LOGICAL upper, wantz
181  CHARACTER trans
182  INTEGER j, neig
183 * ..
184 * .. External Functions ..
185  LOGICAL lsame
186  EXTERNAL lsame
187 * ..
188 * .. External Subroutines ..
189  EXTERNAL dpptrf, dspev, dspgst, dtpmv, dtpsv, xerbla
190 * ..
191 * .. Executable Statements ..
192 *
193 * Test the input parameters.
194 *
195  wantz = lsame( jobz, 'V' )
196  upper = lsame( uplo, 'U' )
197 *
198  info = 0
199  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
200  info = -1
201  ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
202  info = -2
203  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
204  info = -3
205  ELSE IF( n.LT.0 ) THEN
206  info = -4
207  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
208  info = -9
209  END IF
210  IF( info.NE.0 ) THEN
211  CALL xerbla( 'DSPGV ', -info )
212  RETURN
213  END IF
214 *
215 * Quick return if possible
216 *
217  IF( n.EQ.0 )
218  \$ RETURN
219 *
220 * Form a Cholesky factorization of B.
221 *
222  CALL dpptrf( uplo, n, bp, info )
223  IF( info.NE.0 ) THEN
224  info = n + info
225  RETURN
226  END IF
227 *
228 * Transform problem to standard eigenvalue problem and solve.
229 *
230  CALL dspgst( itype, uplo, n, ap, bp, info )
231  CALL dspev( jobz, uplo, n, ap, w, z, ldz, work, info )
232 *
233  IF( wantz ) THEN
234 *
235 * Backtransform eigenvectors to the original problem.
236 *
237  neig = n
238  IF( info.GT.0 )
239  \$ neig = info - 1
240  IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
241 *
242 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
243 * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
244 *
245  IF( upper ) THEN
246  trans = 'N'
247  ELSE
248  trans = 'T'
249  END IF
250 *
251  DO 10 j = 1, neig
252  CALL dtpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
253  \$ 1 )
254  10 CONTINUE
255 *
256  ELSE IF( itype.EQ.3 ) THEN
257 *
258 * For B*A*x=(lambda)*x;
259 * backtransform eigenvectors: x = L*y or U**T*y
260 *
261  IF( upper ) THEN
262  trans = 'T'
263  ELSE
264  trans = 'N'
265  END IF
266 *
267  DO 20 j = 1, neig
268  CALL dtpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
269  \$ 1 )
270  20 CONTINUE
271  END IF
272  END IF
273  RETURN
274 *
275 * End of DSPGV
276 *
subroutine dspgst(ITYPE, UPLO, N, AP, BP, INFO)
DSPGST
Definition: dspgst.f:115
subroutine dtpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPSV
Definition: dtpsv.f:146
subroutine dpptrf(UPLO, N, AP, INFO)
DPPTRF
Definition: dpptrf.f:121
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:144
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dspev(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO)
DSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition: dspev.f:132
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