Annotation of rpl/lapack/lapack/dsygvd.f, revision 1.2
1.1 bertrand 1: SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
2: $ 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, ITYPE, LDA, LDB, LIWORK, LWORK, N
12: * ..
13: * .. Array Arguments ..
14: INTEGER IWORK( * )
15: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * DSYGVD computes all the eigenvalues, and optionally, the eigenvectors
22: * of a real generalized symmetric-definite eigenproblem, of the form
23: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
24: * B are assumed to be symmetric and B is also positive definite.
25: * If eigenvectors are desired, it uses a divide and conquer algorithm.
26: *
27: * The divide and conquer algorithm makes very mild assumptions about
28: * floating point arithmetic. It will work on machines with a guard
29: * digit in add/subtract, or on those binary machines without guard
30: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
31: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
32: * without guard digits, but we know of none.
33: *
34: * Arguments
35: * =========
36: *
37: * ITYPE (input) INTEGER
38: * Specifies the problem type to be solved:
39: * = 1: A*x = (lambda)*B*x
40: * = 2: A*B*x = (lambda)*x
41: * = 3: B*A*x = (lambda)*x
42: *
43: * JOBZ (input) CHARACTER*1
44: * = 'N': Compute eigenvalues only;
45: * = 'V': Compute eigenvalues and eigenvectors.
46: *
47: * UPLO (input) CHARACTER*1
48: * = 'U': Upper triangles of A and B are stored;
49: * = 'L': Lower triangles of A and B are stored.
50: *
51: * N (input) INTEGER
52: * The order of the matrices A and B. N >= 0.
53: *
54: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
55: * On entry, the symmetric matrix A. If UPLO = 'U', the
56: * leading N-by-N upper triangular part of A contains the
57: * upper triangular part of the matrix A. If UPLO = 'L',
58: * the leading N-by-N lower triangular part of A contains
59: * the lower triangular part of the matrix A.
60: *
61: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
62: * matrix Z of eigenvectors. The eigenvectors are normalized
63: * as follows:
64: * if ITYPE = 1 or 2, Z**T*B*Z = I;
65: * if ITYPE = 3, Z**T*inv(B)*Z = I.
66: * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
67: * or the lower triangle (if UPLO='L') of A, including the
68: * diagonal, is destroyed.
69: *
70: * LDA (input) INTEGER
71: * The leading dimension of the array A. LDA >= max(1,N).
72: *
73: * B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
74: * On entry, the symmetric matrix B. If UPLO = 'U', the
75: * leading N-by-N upper triangular part of B contains the
76: * upper triangular part of the matrix B. If UPLO = 'L',
77: * the leading N-by-N lower triangular part of B contains
78: * the lower triangular part of the matrix B.
79: *
80: * On exit, if INFO <= N, the part of B containing the matrix is
81: * overwritten by the triangular factor U or L from the Cholesky
82: * factorization B = U**T*U or B = L*L**T.
83: *
84: * LDB (input) INTEGER
85: * The leading dimension of the array B. LDB >= max(1,N).
86: *
87: * W (output) DOUBLE PRECISION array, dimension (N)
88: * If INFO = 0, the eigenvalues in ascending order.
89: *
90: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
91: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
92: *
93: * LWORK (input) INTEGER
94: * The dimension of the array WORK.
95: * If N <= 1, LWORK >= 1.
96: * If JOBZ = 'N' and N > 1, LWORK >= 2*N+1.
97: * If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
98: *
99: * If LWORK = -1, then a workspace query is assumed; the routine
100: * only calculates the optimal sizes of the WORK and IWORK
101: * arrays, returns these values as the first entries of the WORK
102: * and IWORK arrays, and no error message related to LWORK or
103: * LIWORK is issued by XERBLA.
104: *
105: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
106: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
107: *
108: * LIWORK (input) INTEGER
109: * The dimension of the array IWORK.
110: * If N <= 1, LIWORK >= 1.
111: * If JOBZ = 'N' and N > 1, LIWORK >= 1.
112: * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
113: *
114: * If LIWORK = -1, then a workspace query is assumed; the
115: * routine only calculates the optimal sizes of the WORK and
116: * IWORK arrays, returns these values as the first entries of
117: * the WORK and IWORK arrays, and no error message related to
118: * LWORK or LIWORK is issued by XERBLA.
119: *
120: * INFO (output) INTEGER
121: * = 0: successful exit
122: * < 0: if INFO = -i, the i-th argument had an illegal value
123: * > 0: DPOTRF or DSYEVD returned an error code:
124: * <= N: if INFO = i and JOBZ = 'N', then the algorithm
125: * failed to converge; i off-diagonal elements of an
126: * intermediate tridiagonal form did not converge to
127: * zero;
128: * if INFO = i and JOBZ = 'V', then the algorithm
129: * failed to compute an eigenvalue while working on
130: * the submatrix lying in rows and columns INFO/(N+1)
131: * through mod(INFO,N+1);
132: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
133: * minor of order i of B is not positive definite.
134: * The factorization of B could not be completed and
135: * no eigenvalues or eigenvectors were computed.
136: *
137: * Further Details
138: * ===============
139: *
140: * Based on contributions by
141: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
142: *
143: * Modified so that no backsubstitution is performed if DSYEVD fails to
144: * converge (NEIG in old code could be greater than N causing out of
145: * bounds reference to A - reported by Ralf Meyer). Also corrected the
146: * description of INFO and the test on ITYPE. Sven, 16 Feb 05.
147: * =====================================================================
148: *
149: * .. Parameters ..
150: DOUBLE PRECISION ONE
151: PARAMETER ( ONE = 1.0D+0 )
152: * ..
153: * .. Local Scalars ..
154: LOGICAL LQUERY, UPPER, WANTZ
155: CHARACTER TRANS
156: INTEGER LIOPT, LIWMIN, LOPT, LWMIN
157: * ..
158: * .. External Functions ..
159: LOGICAL LSAME
160: EXTERNAL LSAME
161: * ..
162: * .. External Subroutines ..
163: EXTERNAL DPOTRF, DSYEVD, DSYGST, DTRMM, DTRSM, XERBLA
164: * ..
165: * .. Intrinsic Functions ..
166: INTRINSIC DBLE, MAX
167: * ..
168: * .. Executable Statements ..
169: *
170: * Test the input parameters.
171: *
172: WANTZ = LSAME( JOBZ, 'V' )
173: UPPER = LSAME( UPLO, 'U' )
174: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
175: *
176: INFO = 0
177: IF( N.LE.1 ) THEN
178: LIWMIN = 1
179: LWMIN = 1
180: ELSE IF( WANTZ ) THEN
181: LIWMIN = 3 + 5*N
182: LWMIN = 1 + 6*N + 2*N**2
183: ELSE
184: LIWMIN = 1
185: LWMIN = 2*N + 1
186: END IF
187: LOPT = LWMIN
188: LIOPT = LIWMIN
189: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
190: INFO = -1
191: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
192: INFO = -2
193: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
194: INFO = -3
195: ELSE IF( N.LT.0 ) THEN
196: INFO = -4
197: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
198: INFO = -6
199: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
200: INFO = -8
201: END IF
202: *
203: IF( INFO.EQ.0 ) THEN
204: WORK( 1 ) = LOPT
205: IWORK( 1 ) = LIOPT
206: *
207: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
208: INFO = -11
209: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
210: INFO = -13
211: END IF
212: END IF
213: *
214: IF( INFO.NE.0 ) THEN
215: CALL XERBLA( 'DSYGVD', -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 Cholesky factorization of B.
227: *
228: CALL DPOTRF( UPLO, N, B, LDB, INFO )
229: IF( INFO.NE.0 ) THEN
230: INFO = N + INFO
231: RETURN
232: END IF
233: *
234: * Transform problem to standard eigenvalue problem and solve.
235: *
236: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
237: CALL DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, LIWORK,
238: $ INFO )
239: LOPT = MAX( DBLE( LOPT ), DBLE( WORK( 1 ) ) )
240: LIOPT = MAX( DBLE( LIOPT ), DBLE( IWORK( 1 ) ) )
241: *
242: IF( WANTZ .AND. INFO.EQ.0 ) THEN
243: *
244: * Backtransform eigenvectors to the original problem.
245: *
246: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
247: *
248: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
249: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
250: *
251: IF( UPPER ) THEN
252: TRANS = 'N'
253: ELSE
254: TRANS = 'T'
255: END IF
256: *
257: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE,
258: $ B, LDB, A, LDA )
259: *
260: ELSE IF( ITYPE.EQ.3 ) THEN
261: *
262: * For B*A*x=(lambda)*x;
263: * backtransform eigenvectors: x = L*y or U'*y
264: *
265: IF( UPPER ) THEN
266: TRANS = 'T'
267: ELSE
268: TRANS = 'N'
269: END IF
270: *
271: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, N, ONE,
272: $ B, LDB, A, LDA )
273: END IF
274: END IF
275: *
276: WORK( 1 ) = LOPT
277: IWORK( 1 ) = LIOPT
278: *
279: RETURN
280: *
281: * End of DSYGVD
282: *
283: END
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