Annotation of rpl/lapack/lapack/dsbgvd.f, revision 1.6
1.1 bertrand 1: SUBROUTINE DSBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
2: $ Z, LDZ, WORK, LWORK, 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, KA, KB, LDAB, LDBB, LDZ, LIWORK, LWORK, N
12: * ..
13: * .. Array Arguments ..
14: INTEGER IWORK( * )
15: DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
16: $ WORK( * ), Z( LDZ, * )
17: * ..
18: *
19: * Purpose
20: * =======
21: *
22: * DSBGVD computes all the eigenvalues, and optionally, the eigenvectors
23: * of a real generalized symmetric-definite banded eigenproblem, of the
24: * form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and
25: * banded, and B is also positive definite. If eigenvectors are
26: * 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: * JOBZ (input) CHARACTER*1
39: * = 'N': Compute eigenvalues only;
40: * = 'V': Compute eigenvalues and eigenvectors.
41: *
42: * UPLO (input) CHARACTER*1
43: * = 'U': Upper triangles of A and B are stored;
44: * = 'L': Lower triangles of A and B are stored.
45: *
46: * N (input) INTEGER
47: * The order of the matrices A and B. N >= 0.
48: *
49: * KA (input) INTEGER
50: * The number of superdiagonals of the matrix A if UPLO = 'U',
51: * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
52: *
53: * KB (input) INTEGER
54: * The number of superdiagonals of the matrix B if UPLO = 'U',
55: * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
56: *
57: * AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
58: * On entry, the upper or lower triangle of the symmetric band
59: * matrix A, stored in the first ka+1 rows of the array. The
60: * j-th column of A is stored in the j-th column of the array AB
61: * as follows:
62: * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
63: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
64: *
65: * On exit, the contents of AB are destroyed.
66: *
67: * LDAB (input) INTEGER
68: * The leading dimension of the array AB. LDAB >= KA+1.
69: *
70: * BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
71: * On entry, the upper or lower triangle of the symmetric band
72: * matrix B, stored in the first kb+1 rows of the array. The
73: * j-th column of B is stored in the j-th column of the array BB
74: * as follows:
75: * if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
76: * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
77: *
78: * On exit, the factor S from the split Cholesky factorization
79: * B = S**T*S, as returned by DPBSTF.
80: *
81: * LDBB (input) INTEGER
82: * The leading dimension of the array BB. LDBB >= KB+1.
83: *
84: * W (output) DOUBLE PRECISION array, dimension (N)
85: * If INFO = 0, the eigenvalues in ascending order.
86: *
87: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
88: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
89: * eigenvectors, with the i-th column of Z holding the
90: * eigenvector associated with W(i). The eigenvectors are
91: * normalized so Z**T*B*Z = I.
92: * If JOBZ = 'N', then Z is not referenced.
93: *
94: * LDZ (input) INTEGER
95: * The leading dimension of the array Z. LDZ >= 1, and if
96: * JOBZ = 'V', LDZ >= max(1,N).
97: *
98: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
99: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
100: *
101: * LWORK (input) INTEGER
102: * The dimension of the array WORK.
103: * If N <= 1, LWORK >= 1.
104: * If JOBZ = 'N' and N > 1, LWORK >= 3*N.
105: * If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.
106: *
107: * If LWORK = -1, then a workspace query is assumed; the routine
108: * only calculates the optimal sizes of the WORK and IWORK
109: * arrays, returns these values as the first entries of the WORK
110: * and IWORK arrays, and no error message related to LWORK or
111: * LIWORK is issued by XERBLA.
112: *
113: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
114: * On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
115: *
116: * LIWORK (input) INTEGER
117: * The dimension of the array IWORK.
118: * If JOBZ = 'N' or N <= 1, LIWORK >= 1.
119: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
120: *
121: * If LIWORK = -1, then a workspace query is assumed; the
122: * routine only calculates the optimal sizes of the WORK and
123: * IWORK arrays, returns these values as the first entries of
124: * the WORK and IWORK arrays, and no error message related to
125: * LWORK or LIWORK is issued by XERBLA.
126: *
127: * INFO (output) INTEGER
128: * = 0: successful exit
129: * < 0: if INFO = -i, the i-th argument had an illegal value
130: * > 0: if INFO = i, and i is:
131: * <= N: the algorithm failed to converge:
132: * i off-diagonal elements of an intermediate
133: * tridiagonal form did not converge to zero;
134: * > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
135: * returned INFO = i: B is not positive definite.
136: * The factorization of B could not be completed and
137: * no eigenvalues or eigenvectors were computed.
138: *
139: * Further Details
140: * ===============
141: *
142: * Based on contributions by
143: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
144: *
145: * =====================================================================
146: *
147: * .. Parameters ..
148: DOUBLE PRECISION ONE, ZERO
149: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
150: * ..
151: * .. Local Scalars ..
152: LOGICAL LQUERY, UPPER, WANTZ
153: CHARACTER VECT
154: INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLWRK2,
155: $ LWMIN
156: * ..
157: * .. External Functions ..
158: LOGICAL LSAME
159: EXTERNAL LSAME
160: * ..
161: * .. External Subroutines ..
162: EXTERNAL DGEMM, DLACPY, DPBSTF, DSBGST, DSBTRD, DSTEDC,
163: $ DSTERF, XERBLA
164: * ..
165: * .. Executable Statements ..
166: *
167: * Test the input parameters.
168: *
169: WANTZ = LSAME( JOBZ, 'V' )
170: UPPER = LSAME( UPLO, 'U' )
171: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
172: *
173: INFO = 0
174: IF( N.LE.1 ) THEN
175: LIWMIN = 1
176: LWMIN = 1
177: ELSE IF( WANTZ ) THEN
178: LIWMIN = 3 + 5*N
179: LWMIN = 1 + 5*N + 2*N**2
180: ELSE
181: LIWMIN = 1
182: LWMIN = 2*N
183: END IF
184: *
185: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
186: INFO = -1
187: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
188: INFO = -2
189: ELSE IF( N.LT.0 ) THEN
190: INFO = -3
191: ELSE IF( KA.LT.0 ) THEN
192: INFO = -4
193: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
194: INFO = -5
195: ELSE IF( LDAB.LT.KA+1 ) THEN
196: INFO = -7
197: ELSE IF( LDBB.LT.KB+1 ) THEN
198: INFO = -9
199: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
200: INFO = -12
201: END IF
202: *
203: IF( INFO.EQ.0 ) THEN
204: WORK( 1 ) = LWMIN
205: IWORK( 1 ) = LIWMIN
206: *
207: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
208: INFO = -14
209: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
210: INFO = -16
211: END IF
212: END IF
213: *
214: IF( INFO.NE.0 ) THEN
215: CALL XERBLA( 'DSBGVD', -INFO )
216: RETURN
217: ELSE IF( LQUERY ) THEN
218: RETURN
219: END IF
220: *
221: * Quick return if possible
222: *
223: IF( N.EQ.0 )
224: $ RETURN
225: *
226: * Form a split Cholesky factorization of B.
227: *
228: CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO )
229: IF( INFO.NE.0 ) THEN
230: INFO = N + INFO
231: RETURN
232: END IF
233: *
234: * Transform problem to standard eigenvalue problem.
235: *
236: INDE = 1
237: INDWRK = INDE + N
238: INDWK2 = INDWRK + N*N
239: LLWRK2 = LWORK - INDWK2 + 1
240: CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
241: $ WORK( INDWRK ), IINFO )
242: *
243: * Reduce to tridiagonal form.
244: *
245: IF( WANTZ ) THEN
246: VECT = 'U'
247: ELSE
248: VECT = 'N'
249: END IF
250: CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
251: $ WORK( INDWRK ), IINFO )
252: *
253: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEDC.
254: *
255: IF( .NOT.WANTZ ) THEN
256: CALL DSTERF( N, W, WORK( INDE ), INFO )
257: ELSE
258: CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N,
259: $ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO )
260: CALL DGEMM( 'N', 'N', N, N, N, ONE, Z, LDZ, WORK( INDWRK ), N,
261: $ ZERO, WORK( INDWK2 ), N )
262: CALL DLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ )
263: END IF
264: *
265: WORK( 1 ) = LWMIN
266: IWORK( 1 ) = LIWMIN
267: *
268: RETURN
269: *
270: * End of DSBGVD
271: *
272: END
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