1: *> \brief \b DSPGV
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 (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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
107: *> If INFO = 0, the eigenvalues in ascending order.
108: *> \endverbatim
109: *>
110: *> \param[out] Z
111: *> \verbatim
112: *> Z is DOUBLE PRECISION 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 DOUBLE PRECISION 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: DPPTRF or DSPEV returned an error code:
138: *> <= N: if INFO = i, DSPEV 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 doubleOTHEReigen
156: *
157: * =====================================================================
158: SUBROUTINE DSPGV( 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: 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: *
274: END
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