Annotation of rpl/lapack/lapack/dspgv.f, revision 1.10
1.9 bertrand 1: *> \brief \b DSPGST
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSPGV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgv.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSPGV( 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: * DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
30: * $ Z( LDZ, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> DSPGV 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
108: *> If INFO = 0, the eigenvalues in ascending order.
109: *> \endverbatim
110: *>
111: *> \param[out] Z
112: *> \verbatim
113: *> Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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: DPPTRF or DSPEV returned an error code:
139: *> <= N: if INFO = i, DSPEV 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 doubleOTHEReigen
159: *
160: * =====================================================================
1.1 bertrand 161: SUBROUTINE DSPGV( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
162: $ INFO )
163: *
1.9 bertrand 164: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 165: * -- LAPACK is a software package provided by Univ. of Tennessee, --
166: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 bertrand 167: * November 2011
1.1 bertrand 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;
1.8 bertrand 244: * backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
1.1 bertrand 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;
1.8 bertrand 260: * backtransform eigenvectors: x = L*y or U**T*y
1.1 bertrand 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: *
278: END
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