1: *> \brief \b ZHPGVD
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZHPGVD + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgvd.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhpgvd.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhpgvd.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
22: * LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IWORK( * )
30: * DOUBLE PRECISION RWORK( * ), W( * )
31: * COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZHPGVD computes all the eigenvalues and, optionally, the eigenvectors
41: *> of a complex generalized Hermitian-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 Hermitian, 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 COMPLEX*16 array, dimension (N*(N+1)/2)
90: *> On entry, the upper or lower triangle of the Hermitian 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 COMPLEX*16 array, dimension (N*(N+1)/2)
102: *> On entry, the upper or lower triangle of the Hermitian 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**H*U or B = L*L**H, 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 COMPLEX*16 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**H*B*Z = I;
125: *> if ITYPE = 3, Z**H*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 COMPLEX*16 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 >= N.
148: *> If JOBZ = 'V' and N > 1, LWORK >= 2*N.
149: *>
150: *> If LWORK = -1, then a workspace query is assumed; the routine
151: *> only calculates the required sizes of the WORK, RWORK and
152: *> IWORK arrays, returns these values as the first entries of
153: *> the WORK, RWORK and IWORK arrays, and no error message
154: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
155: *> \endverbatim
156: *>
157: *> \param[out] RWORK
158: *> \verbatim
159: *> RWORK is DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
160: *> On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
161: *> \endverbatim
162: *>
163: *> \param[in] LRWORK
164: *> \verbatim
165: *> LRWORK is INTEGER
166: *> The dimension of array RWORK.
167: *> If N <= 1, LRWORK >= 1.
168: *> If JOBZ = 'N' and N > 1, LRWORK >= N.
169: *> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
170: *>
171: *> If LRWORK = -1, then a workspace query is assumed; the
172: *> routine only calculates the required sizes of the WORK, RWORK
173: *> and IWORK arrays, returns these values as the first entries
174: *> of the WORK, RWORK and IWORK arrays, and no error message
175: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
176: *> \endverbatim
177: *>
178: *> \param[out] IWORK
179: *> \verbatim
180: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
181: *> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
182: *> \endverbatim
183: *>
184: *> \param[in] LIWORK
185: *> \verbatim
186: *> LIWORK is INTEGER
187: *> The dimension of array IWORK.
188: *> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
189: *> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
190: *>
191: *> If LIWORK = -1, then a workspace query is assumed; the
192: *> routine only calculates the required sizes of the WORK, RWORK
193: *> and IWORK arrays, returns these values as the first entries
194: *> of the WORK, RWORK and IWORK arrays, and no error message
195: *> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
196: *> \endverbatim
197: *>
198: *> \param[out] INFO
199: *> \verbatim
200: *> INFO is INTEGER
201: *> = 0: successful exit
202: *> < 0: if INFO = -i, the i-th argument had an illegal value
203: *> > 0: ZPPTRF or ZHPEVD returned an error code:
204: *> <= N: if INFO = i, ZHPEVD failed to converge;
205: *> i off-diagonal elements of an intermediate
206: *> tridiagonal form did not convergeto zero;
207: *> > N: if INFO = N + i, for 1 <= i <= n, then the leading
208: *> minor of order i of B is not positive definite.
209: *> The factorization of B could not be completed and
210: *> no eigenvalues or eigenvectors were computed.
211: *> \endverbatim
212: *
213: * Authors:
214: * ========
215: *
216: *> \author Univ. of Tennessee
217: *> \author Univ. of California Berkeley
218: *> \author Univ. of Colorado Denver
219: *> \author NAG Ltd.
220: *
221: *> \ingroup complex16OTHEReigen
222: *
223: *> \par Contributors:
224: * ==================
225: *>
226: *> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
227: *
228: * =====================================================================
229: SUBROUTINE ZHPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
230: $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
231: *
232: * -- LAPACK driver routine --
233: * -- LAPACK is a software package provided by Univ. of Tennessee, --
234: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
235: *
236: * .. Scalar Arguments ..
237: CHARACTER JOBZ, UPLO
238: INTEGER INFO, ITYPE, LDZ, LIWORK, LRWORK, LWORK, N
239: * ..
240: * .. Array Arguments ..
241: INTEGER IWORK( * )
242: DOUBLE PRECISION RWORK( * ), W( * )
243: COMPLEX*16 AP( * ), BP( * ), WORK( * ), Z( LDZ, * )
244: * ..
245: *
246: * =====================================================================
247: *
248: * .. Local Scalars ..
249: LOGICAL LQUERY, UPPER, WANTZ
250: CHARACTER TRANS
251: INTEGER J, LIWMIN, LRWMIN, LWMIN, NEIG
252: * ..
253: * .. External Functions ..
254: LOGICAL LSAME
255: EXTERNAL LSAME
256: * ..
257: * .. External Subroutines ..
258: EXTERNAL XERBLA, ZHPEVD, ZHPGST, ZPPTRF, ZTPMV, ZTPSV
259: * ..
260: * .. Intrinsic Functions ..
261: INTRINSIC DBLE, MAX
262: * ..
263: * .. Executable Statements ..
264: *
265: * Test the input parameters.
266: *
267: WANTZ = LSAME( JOBZ, 'V' )
268: UPPER = LSAME( UPLO, 'U' )
269: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
270: *
271: INFO = 0
272: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
273: INFO = -1
274: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
275: INFO = -2
276: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
277: INFO = -3
278: ELSE IF( N.LT.0 ) THEN
279: INFO = -4
280: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
281: INFO = -9
282: END IF
283: *
284: IF( INFO.EQ.0 ) THEN
285: IF( N.LE.1 ) THEN
286: LWMIN = 1
287: LIWMIN = 1
288: LRWMIN = 1
289: ELSE
290: IF( WANTZ ) THEN
291: LWMIN = 2*N
292: LRWMIN = 1 + 5*N + 2*N**2
293: LIWMIN = 3 + 5*N
294: ELSE
295: LWMIN = N
296: LRWMIN = N
297: LIWMIN = 1
298: END IF
299: END IF
300: *
301: WORK( 1 ) = LWMIN
302: RWORK( 1 ) = LRWMIN
303: IWORK( 1 ) = LIWMIN
304: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
305: INFO = -11
306: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
307: INFO = -13
308: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
309: INFO = -15
310: END IF
311: END IF
312: *
313: IF( INFO.NE.0 ) THEN
314: CALL XERBLA( 'ZHPGVD', -INFO )
315: RETURN
316: ELSE IF( LQUERY ) THEN
317: RETURN
318: END IF
319: *
320: * Quick return if possible
321: *
322: IF( N.EQ.0 )
323: $ RETURN
324: *
325: * Form a Cholesky factorization of B.
326: *
327: CALL ZPPTRF( UPLO, N, BP, INFO )
328: IF( INFO.NE.0 ) THEN
329: INFO = N + INFO
330: RETURN
331: END IF
332: *
333: * Transform problem to standard eigenvalue problem and solve.
334: *
335: CALL ZHPGST( ITYPE, UPLO, N, AP, BP, INFO )
336: CALL ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK,
337: $ LRWORK, IWORK, LIWORK, INFO )
338: LWMIN = INT( MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) ) )
339: LRWMIN = INT( MAX( DBLE( LRWMIN ), DBLE( RWORK( 1 ) ) ) )
340: LIWMIN = INT( MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) ) )
341: *
342: IF( WANTZ ) THEN
343: *
344: * Backtransform eigenvectors to the original problem.
345: *
346: NEIG = N
347: IF( INFO.GT.0 )
348: $ NEIG = INFO - 1
349: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
350: *
351: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
352: * backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
353: *
354: IF( UPPER ) THEN
355: TRANS = 'N'
356: ELSE
357: TRANS = 'C'
358: END IF
359: *
360: DO 10 J = 1, NEIG
361: CALL ZTPSV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
362: $ 1 )
363: 10 CONTINUE
364: *
365: ELSE IF( ITYPE.EQ.3 ) THEN
366: *
367: * For B*A*x=(lambda)*x;
368: * backtransform eigenvectors: x = L*y or U**H *y
369: *
370: IF( UPPER ) THEN
371: TRANS = 'C'
372: ELSE
373: TRANS = 'N'
374: END IF
375: *
376: DO 20 J = 1, NEIG
377: CALL ZTPMV( UPLO, TRANS, 'Non-unit', N, BP, Z( 1, J ),
378: $ 1 )
379: 20 CONTINUE
380: END IF
381: END IF
382: *
383: WORK( 1 ) = LWMIN
384: RWORK( 1 ) = LRWMIN
385: IWORK( 1 ) = LIWMIN
386: RETURN
387: *
388: * End of ZHPGVD
389: *
390: END
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