LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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
November 2015

Definition at line 163 of file dspgv.f.

163 *
164 * -- LAPACK driver routine (version 3.6.0) --
165 * -- LAPACK is a software package provided by Univ. of Tennessee, --
166 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
167 * November 2015
168 *
169 * .. Scalar Arguments ..
170  CHARACTER jobz, uplo
171  INTEGER info, itype, ldz, n
172 * ..
173 * .. Array Arguments ..
174  DOUBLE PRECISION ap( * ), bp( * ), w( * ), work( * ),
175  \$ z( ldz, * )
176 * ..
177 *
178 * =====================================================================
179 *
180 * .. Local Scalars ..
181  LOGICAL upper, wantz
182  CHARACTER trans
183  INTEGER j, neig
184 * ..
185 * .. External Functions ..
186  LOGICAL lsame
187  EXTERNAL lsame
188 * ..
189 * .. External Subroutines ..
190  EXTERNAL dpptrf, dspev, dspgst, dtpmv, dtpsv, xerbla
191 * ..
192 * .. Executable Statements ..
193 *
194 * Test the input parameters.
195 *
196  wantz = lsame( jobz, 'V' )
197  upper = lsame( uplo, 'U' )
198 *
199  info = 0
200  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
201  info = -1
202  ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
203  info = -2
204  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
205  info = -3
206  ELSE IF( n.LT.0 ) THEN
207  info = -4
208  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
209  info = -9
210  END IF
211  IF( info.NE.0 ) THEN
212  CALL xerbla( 'DSPGV ', -info )
213  RETURN
214  END IF
215 *
216 * Quick return if possible
217 *
218  IF( n.EQ.0 )
219  \$ RETURN
220 *
221 * Form a Cholesky factorization of B.
222 *
223  CALL dpptrf( uplo, n, bp, info )
224  IF( info.NE.0 ) THEN
225  info = n + info
226  RETURN
227  END IF
228 *
229 * Transform problem to standard eigenvalue problem and solve.
230 *
231  CALL dspgst( itype, uplo, n, ap, bp, info )
232  CALL dspev( jobz, uplo, n, ap, w, z, ldz, work, info )
233 *
234  IF( wantz ) THEN
235 *
236 * Backtransform eigenvectors to the original problem.
237 *
238  neig = n
239  IF( info.GT.0 )
240  \$ neig = info - 1
241  IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
242 *
243 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
244 * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
245 *
246  IF( upper ) THEN
247  trans = 'N'
248  ELSE
249  trans = 'T'
250  END IF
251 *
252  DO 10 j = 1, neig
253  CALL dtpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
254  \$ 1 )
255  10 CONTINUE
256 *
257  ELSE IF( itype.EQ.3 ) THEN
258 *
259 * For B*A*x=(lambda)*x;
260 * backtransform eigenvectors: x = L*y or U**T*y
261 *
262  IF( upper ) THEN
263  trans = 'T'
264  ELSE
265  trans = 'N'
266  END IF
267 *
268  DO 20 j = 1, neig
269  CALL dtpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
270  \$ 1 )
271  20 CONTINUE
272  END IF
273  END IF
274  RETURN
275 *
276 * End of DSPGV
277 *
subroutine dspgst(ITYPE, UPLO, N, AP, BP, INFO)
DSPGST
Definition: dspgst.f:115
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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dpptrf(UPLO, N, AP, INFO)
DPPTRF
Definition: dpptrf.f:121
subroutine dtpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPSV
Definition: dtpsv.f:146
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:144
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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