1: SUBROUTINE ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
2: $ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
3: *
4: * -- LAPACK driver routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: CHARACTER JOBZ, UPLO
11: INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N
12: * ..
13: * .. Array Arguments ..
14: INTEGER IWORK( * )
15: DOUBLE PRECISION RWORK( * ), W( * )
16: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
17: * ..
18: *
19: * Purpose
20: * =======
21: *
22: * ZHEGVD computes all the eigenvalues, and optionally, the eigenvectors
23: * of a complex generalized Hermitian-definite eigenproblem, of the form
24: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
25: * B are assumed to be Hermitian and B is also positive definite.
26: * If eigenvectors are desired, it uses a divide and conquer algorithm.
27: *
28: * The divide and conquer algorithm makes very mild assumptions about
29: * floating point arithmetic. It will work on machines with a guard
30: * digit in add/subtract, or on those binary machines without guard
31: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
32: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
33: * without guard digits, but we know of none.
34: *
35: * Arguments
36: * =========
37: *
38: * ITYPE (input) INTEGER
39: * Specifies the problem type to be solved:
40: * = 1: A*x = (lambda)*B*x
41: * = 2: A*B*x = (lambda)*x
42: * = 3: B*A*x = (lambda)*x
43: *
44: * JOBZ (input) CHARACTER*1
45: * = 'N': Compute eigenvalues only;
46: * = 'V': Compute eigenvalues and eigenvectors.
47: *
48: * UPLO (input) CHARACTER*1
49: * = 'U': Upper triangles of A and B are stored;
50: * = 'L': Lower triangles of A and B are stored.
51: *
52: * N (input) INTEGER
53: * The order of the matrices A and B. N >= 0.
54: *
55: * A (input/output) COMPLEX*16 array, dimension (LDA, N)
56: * On entry, the Hermitian matrix A. If UPLO = 'U', the
57: * leading N-by-N upper triangular part of A contains the
58: * upper triangular part of the matrix A. If UPLO = 'L',
59: * the leading N-by-N lower triangular part of A contains
60: * the lower triangular part of the matrix A.
61: *
62: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
63: * matrix Z of eigenvectors. The eigenvectors are normalized
64: * as follows:
65: * if ITYPE = 1 or 2, Z**H*B*Z = I;
66: * if ITYPE = 3, Z**H*inv(B)*Z = I.
67: * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
68: * or the lower triangle (if UPLO='L') of A, including the
69: * diagonal, is destroyed.
70: *
71: * LDA (input) INTEGER
72: * The leading dimension of the array A. LDA >= max(1,N).
73: *
74: * B (input/output) COMPLEX*16 array, dimension (LDB, N)
75: * On entry, the Hermitian matrix B. If UPLO = 'U', the
76: * leading N-by-N upper triangular part of B contains the
77: * upper triangular part of the matrix B. If UPLO = 'L',
78: * the leading N-by-N lower triangular part of B contains
79: * the lower triangular part of the matrix B.
80: *
81: * On exit, if INFO <= N, the part of B containing the matrix is
82: * overwritten by the triangular factor U or L from the Cholesky
83: * factorization B = U**H*U or B = L*L**H.
84: *
85: * LDB (input) INTEGER
86: * The leading dimension of the array B. LDB >= max(1,N).
87: *
88: * W (output) DOUBLE PRECISION array, dimension (N)
89: * If INFO = 0, the eigenvalues in ascending order.
90: *
91: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
92: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
93: *
94: * LWORK (input) INTEGER
95: * The length of the array WORK.
96: * If N <= 1, LWORK >= 1.
97: * If JOBZ = 'N' and N > 1, LWORK >= N + 1.
98: * If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2.
99: *
100: * If LWORK = -1, then a workspace query is assumed; the routine
101: * only calculates the optimal sizes of the WORK, RWORK and
102: * IWORK arrays, returns these values as the first entries of
103: * the WORK, RWORK and IWORK arrays, and no error message
104: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
105: *
106: * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
107: * On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
108: *
109: * LRWORK (input) INTEGER
110: * The dimension of the array RWORK.
111: * If N <= 1, LRWORK >= 1.
112: * If JOBZ = 'N' and N > 1, LRWORK >= N.
113: * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
114: *
115: * If LRWORK = -1, then a workspace query is assumed; the
116: * routine only calculates the optimal sizes of the WORK, RWORK
117: * and IWORK arrays, returns these values as the first entries
118: * of the WORK, RWORK and IWORK arrays, and no error message
119: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
120: *
121: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
122: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
123: *
124: * LIWORK (input) INTEGER
125: * The dimension of the array IWORK.
126: * If N <= 1, LIWORK >= 1.
127: * If JOBZ = 'N' and N > 1, LIWORK >= 1.
128: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
129: *
130: * If LIWORK = -1, then a workspace query is assumed; the
131: * routine only calculates the optimal sizes of the WORK, RWORK
132: * and IWORK arrays, returns these values as the first entries
133: * of the WORK, RWORK and IWORK arrays, and no error message
134: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
135: *
136: * INFO (output) INTEGER
137: * = 0: successful exit
138: * < 0: if INFO = -i, the i-th argument had an illegal value
139: * > 0: ZPOTRF or ZHEEVD returned an error code:
140: * <= N: if INFO = i and JOBZ = 'N', then the algorithm
141: * failed to converge; i off-diagonal elements of an
142: * intermediate tridiagonal form did not converge to
143: * zero;
144: * if INFO = i and JOBZ = 'V', then the algorithm
145: * failed to compute an eigenvalue while working on
146: * the submatrix lying in rows and columns INFO/(N+1)
147: * through mod(INFO,N+1);
148: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
149: * minor of order i of B is not positive definite.
150: * The factorization of B could not be completed and
151: * no eigenvalues or eigenvectors were computed.
152: *
153: * Further Details
154: * ===============
155: *
156: * Based on contributions by
157: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
158: *
159: * Modified so that no backsubstitution is performed if ZHEEVD fails to
160: * converge (NEIG in old code could be greater than N causing out of
161: * bounds reference to A - reported by Ralf Meyer). Also corrected the
162: * description of INFO and the test on ITYPE. Sven, 16 Feb 05.
163: * =====================================================================
164: *
165: * .. Parameters ..
166: COMPLEX*16 CONE
167: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
168: * ..
169: * .. Local Scalars ..
170: LOGICAL LQUERY, UPPER, WANTZ
171: CHARACTER TRANS
172: INTEGER LIOPT, LIWMIN, LOPT, LROPT, LRWMIN, LWMIN
173: * ..
174: * .. External Functions ..
175: LOGICAL LSAME
176: EXTERNAL LSAME
177: * ..
178: * .. External Subroutines ..
179: EXTERNAL XERBLA, ZHEEVD, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
180: * ..
181: * .. Intrinsic Functions ..
182: INTRINSIC DBLE, MAX
183: * ..
184: * .. Executable Statements ..
185: *
186: * Test the input parameters.
187: *
188: WANTZ = LSAME( JOBZ, 'V' )
189: UPPER = LSAME( UPLO, 'U' )
190: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
191: *
192: INFO = 0
193: IF( N.LE.1 ) THEN
194: LWMIN = 1
195: LRWMIN = 1
196: LIWMIN = 1
197: ELSE IF( WANTZ ) THEN
198: LWMIN = 2*N + N*N
199: LRWMIN = 1 + 5*N + 2*N*N
200: LIWMIN = 3 + 5*N
201: ELSE
202: LWMIN = N + 1
203: LRWMIN = N
204: LIWMIN = 1
205: END IF
206: LOPT = LWMIN
207: LROPT = LRWMIN
208: LIOPT = LIWMIN
209: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
210: INFO = -1
211: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
212: INFO = -2
213: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
214: INFO = -3
215: ELSE IF( N.LT.0 ) THEN
216: INFO = -4
217: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
218: INFO = -6
219: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
220: INFO = -8
221: END IF
222: *
223: IF( INFO.EQ.0 ) THEN
224: WORK( 1 ) = LOPT
225: RWORK( 1 ) = LROPT
226: IWORK( 1 ) = LIOPT
227: *
228: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
229: INFO = -11
230: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
231: INFO = -13
232: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
233: INFO = -15
234: END IF
235: END IF
236: *
237: IF( INFO.NE.0 ) THEN
238: CALL XERBLA( 'ZHEGVD', -INFO )
239: RETURN
240: ELSE IF( LQUERY ) THEN
241: RETURN
242: END IF
243: *
244: * Quick return if possible
245: *
246: IF( N.EQ.0 )
247: $ RETURN
248: *
249: * Form a Cholesky factorization of B.
250: *
251: CALL ZPOTRF( UPLO, N, B, LDB, INFO )
252: IF( INFO.NE.0 ) THEN
253: INFO = N + INFO
254: RETURN
255: END IF
256: *
257: * Transform problem to standard eigenvalue problem and solve.
258: *
259: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
260: CALL ZHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK,
261: $ IWORK, LIWORK, INFO )
262: LOPT = MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) )
263: LROPT = MAX( DBLE( LROPT ), DBLE( RWORK( 1 ) ) )
264: LIOPT = MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) )
265: *
266: IF( WANTZ .AND. INFO.EQ.0 ) THEN
267: *
268: * Backtransform eigenvectors to the original problem.
269: *
270: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
271: *
272: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
273: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
274: *
275: IF( UPPER ) THEN
276: TRANS = 'N'
277: ELSE
278: TRANS = 'C'
279: END IF
280: *
281: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
282: $ B, LDB, A, LDA )
283: *
284: ELSE IF( ITYPE.EQ.3 ) THEN
285: *
286: * For B*A*x=(lambda)*x;
287: * backtransform eigenvectors: x = L*y or U'*y
288: *
289: IF( UPPER ) THEN
290: TRANS = 'C'
291: ELSE
292: TRANS = 'N'
293: END IF
294: *
295: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, CONE,
296: $ B, LDB, A, LDA )
297: END IF
298: END IF
299: *
300: WORK( 1 ) = LOPT
301: RWORK( 1 ) = LROPT
302: IWORK( 1 ) = LIOPT
303: *
304: RETURN
305: *
306: * End of ZHEGVD
307: *
308: END
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