LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
sspgv.f
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1 *> \brief \b SSPGST
2 *
3 * =========== DOCUMENTATION ===========
4 *
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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
81 *> (N*(N+1)/2)
82 *> On entry, the upper or lower triangle of the symmetric matrix
83 *> A, packed columnwise in a linear array. The j-th column of A
84 *> is stored in the array AP as follows:
85 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
86 *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
87 *>
88 *> On exit, the contents of AP are destroyed.
89 *> \endverbatim
90 *>
91 *> \param[in,out] BP
92 *> \verbatim
93 *> BP is REAL array, dimension (N*(N+1)/2)
94 *> On entry, the upper or lower triangle of the symmetric matrix
95 *> B, packed columnwise in a linear array. The j-th column of B
96 *> is stored in the array BP as follows:
97 *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
98 *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
99 *>
100 *> On exit, the triangular factor U or L from the Cholesky
101 *> factorization B = U**T*U or B = L*L**T, in the same storage
102 *> format as B.
103 *> \endverbatim
104 *>
105 *> \param[out] W
106 *> \verbatim
107 *> W is REAL array, dimension (N)
108 *> If INFO = 0, the eigenvalues in ascending order.
109 *> \endverbatim
110 *>
111 *> \param[out] Z
112 *> \verbatim
113 *> Z is REAL array, dimension (LDZ, N)
114 *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
115 *> eigenvectors. The eigenvectors are normalized as follows:
116 *> if ITYPE = 1 or 2, Z**T*B*Z = I;
117 *> if ITYPE = 3, Z**T*inv(B)*Z = I.
118 *> If JOBZ = 'N', then Z is not referenced.
119 *> \endverbatim
120 *>
121 *> \param[in] LDZ
122 *> \verbatim
123 *> LDZ is INTEGER
124 *> The leading dimension of the array Z. LDZ >= 1, and if
125 *> JOBZ = 'V', LDZ >= max(1,N).
126 *> \endverbatim
127 *>
128 *> \param[out] WORK
129 *> \verbatim
130 *> WORK is REAL array, dimension (3*N)
131 *> \endverbatim
132 *>
133 *> \param[out] INFO
134 *> \verbatim
135 *> INFO is INTEGER
136 *> = 0: successful exit
137 *> < 0: if INFO = -i, the i-th argument had an illegal value
138 *> > 0: SPPTRF or SSPEV returned an error code:
139 *> <= N: if INFO = i, SSPEV failed to converge;
140 *> i off-diagonal elements of an intermediate
141 *> tridiagonal form did not converge to zero.
142 *> > N: if INFO = n + i, for 1 <= i <= n, then the leading
143 *> minor of order i of B is not positive definite.
144 *> The factorization of B could not be completed and
145 *> no eigenvalues or eigenvectors were computed.
146 *> \endverbatim
147 *
148 * Authors:
149 * ========
150 *
151 *> \author Univ. of Tennessee
152 *> \author Univ. of California Berkeley
153 *> \author Univ. of Colorado Denver
154 *> \author NAG Ltd.
155 *
156 *> \date November 2011
157 *
158 *> \ingroup realOTHEReigen
159 *
160 * =====================================================================
161  SUBROUTINE sspgv( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
162  \$ info )
163 *
164 * -- LAPACK driver routine (version 3.4.0) --
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 2011
168 *
169 * .. Scalar Arguments ..
170  CHARACTER jobz, uplo
171  INTEGER info, itype, ldz, n
172 * ..
173 * .. Array Arguments ..
174  REAL 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 spptrf, sspev, sspgst, stpmv, stpsv, 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( 'SSPGV ', -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 spptrf( 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 sspgst( itype, uplo, n, ap, bp, info )
232  CALL sspev( 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 stpsv( 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 stpmv( 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 SSPGV
277 *
278  END