 LAPACK  3.10.1 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.```

Definition at line 158 of file dspgv.f.

160 *
161 * -- LAPACK driver routine --
162 * -- LAPACK is a software package provided by Univ. of Tennessee, --
163 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
164 *
165 * .. Scalar Arguments ..
166  CHARACTER JOBZ, UPLO
167  INTEGER INFO, ITYPE, LDZ, N
168 * ..
169 * .. Array Arguments ..
170  DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
171  \$ Z( LDZ, * )
172 * ..
173 *
174 * =====================================================================
175 *
176 * .. Local Scalars ..
177  LOGICAL UPPER, WANTZ
178  CHARACTER TRANS
179  INTEGER J, NEIG
180 * ..
181 * .. External Functions ..
182  LOGICAL LSAME
183  EXTERNAL lsame
184 * ..
185 * .. External Subroutines ..
186  EXTERNAL dpptrf, dspev, dspgst, dtpmv, dtpsv, xerbla
187 * ..
188 * .. Executable Statements ..
189 *
190 * Test the input parameters.
191 *
192  wantz = lsame( jobz, 'V' )
193  upper = lsame( uplo, 'U' )
194 *
195  info = 0
196  IF( itype.LT.1 .OR. itype.GT.3 ) THEN
197  info = -1
198  ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
199  info = -2
200  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
201  info = -3
202  ELSE IF( n.LT.0 ) THEN
203  info = -4
204  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
205  info = -9
206  END IF
207  IF( info.NE.0 ) THEN
208  CALL xerbla( 'DSPGV ', -info )
209  RETURN
210  END IF
211 *
212 * Quick return if possible
213 *
214  IF( n.EQ.0 )
215  \$ RETURN
216 *
217 * Form a Cholesky factorization of B.
218 *
219  CALL dpptrf( uplo, n, bp, info )
220  IF( info.NE.0 ) THEN
221  info = n + info
222  RETURN
223  END IF
224 *
225 * Transform problem to standard eigenvalue problem and solve.
226 *
227  CALL dspgst( itype, uplo, n, ap, bp, info )
228  CALL dspev( jobz, uplo, n, ap, w, z, ldz, work, info )
229 *
230  IF( wantz ) THEN
231 *
232 * Backtransform eigenvectors to the original problem.
233 *
234  neig = n
235  IF( info.GT.0 )
236  \$ neig = info - 1
237  IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
238 *
239 * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
240 * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
241 *
242  IF( upper ) THEN
243  trans = 'N'
244  ELSE
245  trans = 'T'
246  END IF
247 *
248  DO 10 j = 1, neig
249  CALL dtpsv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
250  \$ 1 )
251  10 CONTINUE
252 *
253  ELSE IF( itype.EQ.3 ) THEN
254 *
255 * For B*A*x=(lambda)*x;
256 * backtransform eigenvectors: x = L*y or U**T*y
257 *
258  IF( upper ) THEN
259  trans = 'T'
260  ELSE
261  trans = 'N'
262  END IF
263 *
264  DO 20 j = 1, neig
265  CALL dtpmv( uplo, trans, 'Non-unit', n, bp, z( 1, j ),
266  \$ 1 )
267  20 CONTINUE
268  END IF
269  END IF
270  RETURN
271 *
272 * End of DSPGV
273 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dtpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPSV
Definition: dtpsv.f:144
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:142
subroutine dpptrf(UPLO, N, AP, INFO)
DPPTRF
Definition: dpptrf.f:119
subroutine dspgst(ITYPE, UPLO, N, AP, BP, INFO)
DSPGST
Definition: dspgst.f:113
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 matrices
Definition: dspev.f:130
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