LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
sspgv.f
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1 *> \brief \b SSPGV
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
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13 *> [ZIP]</a>
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
22 * INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER JOBZ, UPLO
26 * INTEGER INFO, ITYPE, LDZ, N
27 * ..
28 * .. Array Arguments ..
29 * REAL AP( * ), BP( * ), W( * ), WORK( * ),
30 * $ Z( LDZ, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> SSPGV computes all the eigenvalues and, optionally, the eigenvectors
40 *> of a real generalized symmetric-definite eigenproblem, of the form
41 *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
42 *> Here A and B are assumed to be symmetric, stored in packed format,
43 *> and B is also positive definite.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] ITYPE
50 *> \verbatim
51 *> ITYPE is INTEGER
52 *> Specifies the problem type to be solved:
53 *> = 1: A*x = (lambda)*B*x
54 *> = 2: A*B*x = (lambda)*x
55 *> = 3: B*A*x = (lambda)*x
56 *> \endverbatim
57 *>
58 *> \param[in] JOBZ
59 *> \verbatim
60 *> JOBZ is CHARACTER*1
61 *> = 'N': Compute eigenvalues only;
62 *> = 'V': Compute eigenvalues and eigenvectors.
63 *> \endverbatim
64 *>
65 *> \param[in] UPLO
66 *> \verbatim
67 *> UPLO is CHARACTER*1
68 *> = 'U': Upper triangles of A and B are stored;
69 *> = 'L': Lower triangles of A and B are stored.
70 *> \endverbatim
71 *>
72 *> \param[in] N
73 *> \verbatim
74 *> N is INTEGER
75 *> The order of the matrices A and B. N >= 0.
76 *> \endverbatim
77 *>
78 *> \param[in,out] AP
79 *> \verbatim
80 *> AP is REAL array, dimension (N*(N+1)/2)
81 *> On entry, the upper or lower triangle of the symmetric matrix
82 *> A, packed columnwise in a linear array. The j-th column of A
83 *> is stored in the array AP as follows:
84 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
85 *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
86 *>
87 *> On exit, the contents of AP are destroyed.
88 *> \endverbatim
89 *>
90 *> \param[in,out] BP
91 *> \verbatim
92 *> BP is REAL array, dimension (N*(N+1)/2)
93 *> On entry, the upper or lower triangle of the symmetric matrix
94 *> B, packed columnwise in a linear array. The j-th column of B
95 *> is stored in the array BP as follows:
96 *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
97 *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
98 *>
99 *> On exit, the triangular factor U or L from the Cholesky
100 *> factorization B = U**T*U or B = L*L**T, in the same storage
101 *> format as B.
102 *> \endverbatim
103 *>
104 *> \param[out] W
105 *> \verbatim
106 *> W is REAL array, dimension (N)
107 *> If INFO = 0, the eigenvalues in ascending order.
108 *> \endverbatim
109 *>
110 *> \param[out] Z
111 *> \verbatim
112 *> Z is REAL array, dimension (LDZ, N)
113 *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
114 *> eigenvectors. The eigenvectors are normalized as follows:
115 *> if ITYPE = 1 or 2, Z**T*B*Z = I;
116 *> if ITYPE = 3, Z**T*inv(B)*Z = I.
117 *> If JOBZ = 'N', then Z is not referenced.
118 *> \endverbatim
119 *>
120 *> \param[in] LDZ
121 *> \verbatim
122 *> LDZ is INTEGER
123 *> The leading dimension of the array Z. LDZ >= 1, and if
124 *> JOBZ = 'V', LDZ >= max(1,N).
125 *> \endverbatim
126 *>
127 *> \param[out] WORK
128 *> \verbatim
129 *> WORK is REAL array, dimension (3*N)
130 *> \endverbatim
131 *>
132 *> \param[out] INFO
133 *> \verbatim
134 *> INFO is INTEGER
135 *> = 0: successful exit
136 *> < 0: if INFO = -i, the i-th argument had an illegal value
137 *> > 0: SPPTRF or SSPEV returned an error code:
138 *> <= N: if INFO = i, SSPEV failed to converge;
139 *> i off-diagonal elements of an intermediate
140 *> tridiagonal form did not converge to zero.
141 *> > N: if INFO = n + i, for 1 <= i <= n, then the leading
142 *> minor of order i of B is not positive definite.
143 *> The factorization of B could not be completed and
144 *> no eigenvalues or eigenvectors were computed.
145 *> \endverbatim
146 *
147 * Authors:
148 * ========
149 *
150 *> \author Univ. of Tennessee
151 *> \author Univ. of California Berkeley
152 *> \author Univ. of Colorado Denver
153 *> \author NAG Ltd.
154 *
155 *> \ingroup realOTHEReigen
156 *
157 * =====================================================================
158  SUBROUTINE sspgv( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
159  $ INFO )
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 *
274  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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 sspgv(ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK, INFO)
SSPGV
Definition: sspgv.f:160
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