1: *> \brief \b DSPGVD
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSPGVD + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspgvd.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspgvd.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspgvd.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
22: * LWORK, IWORK, LIWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IWORK( * )
30: * DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
31: * $ Z( LDZ, * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
41: *> of a real generalized symmetric-definite eigenproblem, of the form
42: *> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
43: *> B are assumed to be symmetric, stored in packed format, and B is also
44: *> positive definite.
45: *> If eigenvectors are desired, it uses a divide and conquer algorithm.
46: *>
47: *> The divide and conquer algorithm makes very mild assumptions about
48: *> floating point arithmetic. It will work on machines with a guard
49: *> digit in add/subtract, or on those binary machines without guard
50: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
51: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
52: *> without guard digits, but we know of none.
53: *> \endverbatim
54: *
55: * Arguments:
56: * ==========
57: *
58: *> \param[in] ITYPE
59: *> \verbatim
60: *> ITYPE is INTEGER
61: *> Specifies the problem type to be solved:
62: *> = 1: A*x = (lambda)*B*x
63: *> = 2: A*B*x = (lambda)*x
64: *> = 3: B*A*x = (lambda)*x
65: *> \endverbatim
66: *>
67: *> \param[in] JOBZ
68: *> \verbatim
69: *> JOBZ is CHARACTER*1
70: *> = 'N': Compute eigenvalues only;
71: *> = 'V': Compute eigenvalues and eigenvectors.
72: *> \endverbatim
73: *>
74: *> \param[in] UPLO
75: *> \verbatim
76: *> UPLO is CHARACTER*1
77: *> = 'U': Upper triangles of A and B are stored;
78: *> = 'L': Lower triangles of A and B are stored.
79: *> \endverbatim
80: *>
81: *> \param[in] N
82: *> \verbatim
83: *> N is INTEGER
84: *> The order of the matrices A and B. N >= 0.
85: *> \endverbatim
86: *>
87: *> \param[in,out] AP
88: *> \verbatim
89: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
90: *> On entry, the upper or lower triangle of the symmetric matrix
91: *> A, packed columnwise in a linear array. The j-th column of A
92: *> is stored in the array AP as follows:
93: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
94: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
95: *>
96: *> On exit, the contents of AP are destroyed.
97: *> \endverbatim
98: *>
99: *> \param[in,out] BP
100: *> \verbatim
101: *> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
102: *> On entry, the upper or lower triangle of the symmetric matrix
103: *> B, packed columnwise in a linear array. The j-th column of B
104: *> is stored in the array BP as follows:
105: *> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
106: *> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
107: *>
108: *> On exit, the triangular factor U or L from the Cholesky
109: *> factorization B = U**T*U or B = L*L**T, in the same storage
110: *> format as B.
111: *> \endverbatim
112: *>
113: *> \param[out] W
114: *> \verbatim
115: *> W is DOUBLE PRECISION array, dimension (N)
116: *> If INFO = 0, the eigenvalues in ascending order.
117: *> \endverbatim
118: *>
119: *> \param[out] Z
120: *> \verbatim
121: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
122: *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
123: *> eigenvectors. The eigenvectors are normalized as follows:
124: *> if ITYPE = 1 or 2, Z**T*B*Z = I;
125: *> if ITYPE = 3, Z**T*inv(B)*Z = I.
126: *> If JOBZ = 'N', then Z is not referenced.
127: *> \endverbatim
128: *>
129: *> \param[in] LDZ
130: *> \verbatim
131: *> LDZ is INTEGER
132: *> The leading dimension of the array Z. LDZ >= 1, and if
133: *> JOBZ = 'V', LDZ >= max(1,N).
134: *> \endverbatim
135: *>
136: *> \param[out] WORK
137: *> \verbatim
138: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
139: *> On exit, if INFO = 0, WORK(1) returns the required LWORK.
140: *> \endverbatim
141: *>
142: *> \param[in] LWORK
143: *> \verbatim
144: *> LWORK is INTEGER
145: *> The dimension of the array WORK.
146: *> If N <= 1, LWORK >= 1.
147: *> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
148: *> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
149: *>
150: *> If LWORK = -1, then a workspace query is assumed; the routine
151: *> only calculates the required sizes of the WORK and IWORK
152: *> arrays, returns these values as the first entries of the WORK
153: *> and IWORK arrays, and no error message related to LWORK or
154: *> LIWORK is issued by XERBLA.
155: *> \endverbatim
156: *>
157: *> \param[out] IWORK
158: *> \verbatim
159: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
160: *> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
161: *> \endverbatim
162: *>
163: *> \param[in] LIWORK
164: *> \verbatim
165: *> LIWORK is INTEGER
166: *> The dimension of the array IWORK.
167: *> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
168: *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
169: *>
170: *> If LIWORK = -1, then a workspace query is assumed; the
171: *> routine only calculates the required sizes of the WORK and
172: *> IWORK arrays, returns these values as the first entries of
173: *> the WORK and IWORK arrays, and no error message related to
174: *> LWORK or LIWORK is issued by XERBLA.
175: *> \endverbatim
176: *>
177: *> \param[out] INFO
178: *> \verbatim
179: *> INFO is INTEGER
180: *> = 0: successful exit
181: *> < 0: if INFO = -i, the i-th argument had an illegal value
182: *> > 0: DPPTRF or DSPEVD returned an error code:
183: *> <= N: if INFO = i, DSPEVD failed to converge;
184: *> i off-diagonal elements of an intermediate
185: *> tridiagonal form did not converge to zero;
186: *> > N: if INFO = N + i, for 1 <= i <= N, then the leading
187: *> minor of order i of B is not positive definite.
188: *> The factorization of B could not be completed and
189: *> no eigenvalues or eigenvectors were computed.
190: *> \endverbatim
191: *
192: * Authors:
193: * ========
194: *
195: *> \author Univ. of Tennessee
196: *> \author Univ. of California Berkeley
197: *> \author Univ. of Colorado Denver
198: *> \author NAG Ltd.
199: *
200: *> \ingroup doubleOTHEReigen
201: *
202: *> \par Contributors:
203: * ==================
204: *>
205: *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
206: *
207: * =====================================================================
208: SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
209: $ LWORK, IWORK, LIWORK, INFO )
210: *
211: * -- LAPACK driver routine --
212: * -- LAPACK is a software package provided by Univ. of Tennessee, --
213: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
214: *
215: * .. Scalar Arguments ..
216: CHARACTER JOBZ, UPLO
217: INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
218: * ..
219: * .. Array Arguments ..
220: INTEGER IWORK( * )
221: DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
222: $ Z( LDZ, * )
223: * ..
224: *
225: * =====================================================================
226: *
227: * .. Local Scalars ..
228: LOGICAL LQUERY, UPPER, WANTZ
229: CHARACTER TRANS
230: INTEGER J, LIWMIN, LWMIN, NEIG
231: * ..
232: * .. External Functions ..
233: LOGICAL LSAME
234: EXTERNAL LSAME
235: * ..
236: * .. External Subroutines ..
237: EXTERNAL DPPTRF, DSPEVD, DSPGST, DTPMV, DTPSV, XERBLA
238: * ..
239: * .. Intrinsic Functions ..
240: INTRINSIC DBLE, MAX
241: * ..
242: * .. Executable Statements ..
243: *
244: * Test the input parameters.
245: *
246: WANTZ = LSAME( JOBZ, 'V' )
247: UPPER = LSAME( UPLO, 'U' )
248: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
249: *
250: INFO = 0
251: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
252: INFO = -1
253: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
254: INFO = -2
255: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
256: INFO = -3
257: ELSE IF( N.LT.0 ) THEN
258: INFO = -4
259: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
260: INFO = -9
261: END IF
262: *
263: IF( INFO.EQ.0 ) THEN
264: IF( N.LE.1 ) THEN
265: LIWMIN = 1
266: LWMIN = 1
267: ELSE
268: IF( WANTZ ) THEN
269: LIWMIN = 3 + 5*N
270: LWMIN = 1 + 6*N + 2*N**2
271: ELSE
272: LIWMIN = 1
273: LWMIN = 2*N
274: END IF
275: END IF
276: WORK( 1 ) = LWMIN
277: IWORK( 1 ) = LIWMIN
278: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
279: INFO = -11
280: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
281: INFO = -13
282: END IF
283: END IF
284: *
285: IF( INFO.NE.0 ) THEN
286: CALL XERBLA( 'DSPGVD', -INFO )
287: RETURN
288: ELSE IF( LQUERY ) THEN
289: RETURN
290: END IF
291: *
292: * Quick return if possible
293: *
294: IF( N.EQ.0 )
295: $ RETURN
296: *
297: * Form a Cholesky factorization of BP.
298: *
299: CALL DPPTRF( UPLO, N, BP, INFO )
300: IF( INFO.NE.0 ) THEN
301: INFO = N + INFO
302: RETURN
303: END IF
304: *
305: * Transform problem to standard eigenvalue problem and solve.
306: *
307: CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
308: CALL DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
309: $ LIWORK, INFO )
310: LWMIN = INT( MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) ) )
311: LIWMIN = INT( MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) ) )
312: *
313: IF( WANTZ ) THEN
314: *
315: * Backtransform eigenvectors to the original problem.
316: *
317: NEIG = N
318: IF( INFO.GT.0 )
319: $ NEIG = INFO - 1
320: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
321: *
322: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
323: * backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
324: *
325: IF( UPPER ) THEN
326: TRANS = 'N'
327: ELSE
328: TRANS = 'T'
329: END IF
330: *
331: DO 10 J = 1, NEIG
332: CALL DTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
333: $ 1 )
334: 10 CONTINUE
335: *
336: ELSE IF( ITYPE.EQ.3 ) THEN
337: *
338: * For B*A*x=(lambda)*x;
339: * backtransform eigenvectors: x = L*y or U**T *y
340: *
341: IF( UPPER ) THEN
342: TRANS = 'T'
343: ELSE
344: TRANS = 'N'
345: END IF
346: *
347: DO 20 J = 1, NEIG
348: CALL DTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
349: $ 1 )
350: 20 CONTINUE
351: END IF
352: END IF
353: *
354: WORK( 1 ) = LWMIN
355: IWORK( 1 ) = LIWMIN
356: *
357: RETURN
358: *
359: * End of DSPGVD
360: *
361: END
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