LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sspgv()

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

SSPGV

Purpose:
``` SSPGV 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 REAL 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 REAL 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 REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.``` [out] Z ``` Z is REAL 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 REAL 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: SPPTRF or SSPEV returned an error code: <= N: if INFO = i, SSPEV 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 sspgv.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 REAL 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 spptrf, sspev, sspgst, stpmv, stpsv, 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( 'SSPGV ', -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 spptrf( 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 sspgst( itype, uplo, n, ap, bp, info )
228 CALL sspev( 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 stpsv( 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 stpmv( 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 SSPGV
273*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine sspgst(ITYPE, UPLO, N, AP, BP, INFO)
SSPGST
Definition: sspgst.f:113
subroutine spptrf(UPLO, N, AP, INFO)
SPPTRF
Definition: spptrf.f:119
subroutine sspev(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO)
SSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
Definition: sspev.f:130
subroutine stpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPMV
Definition: stpmv.f:142
subroutine stpsv(UPLO, TRANS, DIAG, N, AP, X, INCX)
STPSV
Definition: stpsv.f:144
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