Annotation of rpl/lapack/lapack/zhbgvd.f, revision 1.4
1.1 bertrand 1: SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
2: $ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK,
3: $ LIWORK, INFO )
4: *
5: * -- LAPACK driver routine (version 3.2) --
6: * -- LAPACK is a software package provided by Univ. of Tennessee, --
7: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8: * November 2006
9: *
10: * .. Scalar Arguments ..
11: CHARACTER JOBZ, UPLO
12: INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK,
13: $ LWORK, N
14: * ..
15: * .. Array Arguments ..
16: INTEGER IWORK( * )
17: DOUBLE PRECISION RWORK( * ), W( * )
18: COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
19: $ Z( LDZ, * )
20: * ..
21: *
22: * Purpose
23: * =======
24: *
25: * ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
26: * of a complex generalized Hermitian-definite banded eigenproblem, of
27: * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
28: * and banded, and B is also positive definite. If eigenvectors are
29: * desired, it uses a divide and conquer algorithm.
30: *
31: * The divide and conquer algorithm makes very mild assumptions about
32: * floating point arithmetic. It will work on machines with a guard
33: * digit in add/subtract, or on those binary machines without guard
34: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
35: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
36: * without guard digits, but we know of none.
37: *
38: * Arguments
39: * =========
40: *
41: * JOBZ (input) CHARACTER*1
42: * = 'N': Compute eigenvalues only;
43: * = 'V': Compute eigenvalues and eigenvectors.
44: *
45: * UPLO (input) CHARACTER*1
46: * = 'U': Upper triangles of A and B are stored;
47: * = 'L': Lower triangles of A and B are stored.
48: *
49: * N (input) INTEGER
50: * The order of the matrices A and B. N >= 0.
51: *
52: * KA (input) INTEGER
53: * The number of superdiagonals of the matrix A if UPLO = 'U',
54: * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
55: *
56: * KB (input) INTEGER
57: * The number of superdiagonals of the matrix B if UPLO = 'U',
58: * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
59: *
60: * AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
61: * On entry, the upper or lower triangle of the Hermitian band
62: * matrix A, stored in the first ka+1 rows of the array. The
63: * j-th column of A is stored in the j-th column of the array AB
64: * as follows:
65: * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
66: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
67: *
68: * On exit, the contents of AB are destroyed.
69: *
70: * LDAB (input) INTEGER
71: * The leading dimension of the array AB. LDAB >= KA+1.
72: *
73: * BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
74: * On entry, the upper or lower triangle of the Hermitian band
75: * matrix B, stored in the first kb+1 rows of the array. The
76: * j-th column of B is stored in the j-th column of the array BB
77: * as follows:
78: * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
79: * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
80: *
81: * On exit, the factor S from the split Cholesky factorization
82: * B = S**H*S, as returned by ZPBSTF.
83: *
84: * LDBB (input) INTEGER
85: * The leading dimension of the array BB. LDBB >= KB+1.
86: *
87: * W (output) DOUBLE PRECISION array, dimension (N)
88: * If INFO = 0, the eigenvalues in ascending order.
89: *
90: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
91: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
92: * eigenvectors, with the i-th column of Z holding the
93: * eigenvector associated with W(i). The eigenvectors are
94: * normalized so that Z**H*B*Z = I.
95: * If JOBZ = 'N', then Z is not referenced.
96: *
97: * LDZ (input) INTEGER
98: * The leading dimension of the array Z. LDZ >= 1, and if
99: * JOBZ = 'V', LDZ >= N.
100: *
101: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
102: * On exit, if INFO=0, WORK(1) returns the optimal LWORK.
103: *
104: * LWORK (input) INTEGER
105: * The dimension of the array WORK.
106: * If N <= 1, LWORK >= 1.
107: * If JOBZ = 'N' and N > 1, LWORK >= N.
108: * If JOBZ = 'V' and N > 1, LWORK >= 2*N**2.
109: *
110: * If LWORK = -1, then a workspace query is assumed; the routine
111: * only calculates the optimal sizes of the WORK, RWORK and
112: * IWORK arrays, returns these values as the first entries of
113: * the WORK, RWORK and IWORK arrays, and no error message
114: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
115: *
116: * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK))
117: * On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
118: *
119: * LRWORK (input) INTEGER
120: * The dimension of array RWORK.
121: * If N <= 1, LRWORK >= 1.
122: * If JOBZ = 'N' and N > 1, LRWORK >= N.
123: * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
124: *
125: * If LRWORK = -1, then a workspace query is assumed; the
126: * routine only calculates the optimal sizes of the WORK, RWORK
127: * and IWORK arrays, returns these values as the first entries
128: * of the WORK, RWORK and IWORK arrays, and no error message
129: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
130: *
131: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
132: * On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
133: *
134: * LIWORK (input) INTEGER
135: * The dimension of array IWORK.
136: * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
137: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
138: *
139: * If LIWORK = -1, then a workspace query is assumed; the
140: * routine only calculates the optimal sizes of the WORK, RWORK
141: * and IWORK arrays, returns these values as the first entries
142: * of the WORK, RWORK and IWORK arrays, and no error message
143: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
144: *
145: * INFO (output) INTEGER
146: * = 0: successful exit
147: * < 0: if INFO = -i, the i-th argument had an illegal value
148: * > 0: if INFO = i, and i is:
149: * <= N: the algorithm failed to converge:
150: * i off-diagonal elements of an intermediate
151: * tridiagonal form did not converge to zero;
152: * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
153: * returned INFO = i: B is not positive definite.
154: * The factorization of B could not be completed and
155: * no eigenvalues or eigenvectors were computed.
156: *
157: * Further Details
158: * ===============
159: *
160: * Based on contributions by
161: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
162: *
163: * =====================================================================
164: *
165: * .. Parameters ..
166: COMPLEX*16 CONE, CZERO
167: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
168: $ CZERO = ( 0.0D+0, 0.0D+0 ) )
169: * ..
170: * .. Local Scalars ..
171: LOGICAL LQUERY, UPPER, WANTZ
172: CHARACTER VECT
173: INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK,
174: $ LLWK2, LRWMIN, LWMIN
175: * ..
176: * .. External Functions ..
177: LOGICAL LSAME
178: EXTERNAL LSAME
179: * ..
180: * .. External Subroutines ..
181: EXTERNAL DSTERF, XERBLA, ZGEMM, ZHBGST, ZHBTRD, ZLACPY,
182: $ ZPBSTF, ZSTEDC
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**2
199: LRWMIN = 1 + 5*N + 2*N**2
200: LIWMIN = 3 + 5*N
201: ELSE
202: LWMIN = N
203: LRWMIN = N
204: LIWMIN = 1
205: END IF
206: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
207: INFO = -1
208: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
209: INFO = -2
210: ELSE IF( N.LT.0 ) THEN
211: INFO = -3
212: ELSE IF( KA.LT.0 ) THEN
213: INFO = -4
214: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
215: INFO = -5
216: ELSE IF( LDAB.LT.KA+1 ) THEN
217: INFO = -7
218: ELSE IF( LDBB.LT.KB+1 ) THEN
219: INFO = -9
220: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
221: INFO = -12
222: END IF
223: *
224: IF( INFO.EQ.0 ) THEN
225: WORK( 1 ) = LWMIN
226: RWORK( 1 ) = LRWMIN
227: IWORK( 1 ) = LIWMIN
228: *
229: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
230: INFO = -14
231: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
232: INFO = -16
233: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
234: INFO = -18
235: END IF
236: END IF
237: *
238: IF( INFO.NE.0 ) THEN
239: CALL XERBLA( 'ZHBGVD', -INFO )
240: RETURN
241: ELSE IF( LQUERY ) THEN
242: RETURN
243: END IF
244: *
245: * Quick return if possible
246: *
247: IF( N.EQ.0 )
248: $ RETURN
249: *
250: * Form a split Cholesky factorization of B.
251: *
252: CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
253: IF( INFO.NE.0 ) THEN
254: INFO = N + INFO
255: RETURN
256: END IF
257: *
258: * Transform problem to standard eigenvalue problem.
259: *
260: INDE = 1
261: INDWRK = INDE + N
262: INDWK2 = 1 + N*N
263: LLWK2 = LWORK - INDWK2 + 2
264: LLRWK = LRWORK - INDWRK + 2
265: CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
266: $ WORK, RWORK( INDWRK ), IINFO )
267: *
268: * Reduce Hermitian band matrix to tridiagonal form.
269: *
270: IF( WANTZ ) THEN
271: VECT = 'U'
272: ELSE
273: VECT = 'N'
274: END IF
275: CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
276: $ LDZ, WORK, IINFO )
277: *
278: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC.
279: *
280: IF( .NOT.WANTZ ) THEN
281: CALL DSTERF( N, W, RWORK( INDE ), INFO )
282: ELSE
283: CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ),
284: $ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK,
285: $ INFO )
286: CALL ZGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO,
287: $ WORK( INDWK2 ), N )
288: CALL ZLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
289: END IF
290: *
291: WORK( 1 ) = LWMIN
292: RWORK( 1 ) = LRWMIN
293: IWORK( 1 ) = LIWMIN
294: RETURN
295: *
296: * End of ZHBGVD
297: *
298: END
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