Annotation of rpl/lapack/lapack/dsygvx.f, revision 1.4
1.1 bertrand 1: SUBROUTINE DSYGVX( ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
2: $ VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
3: $ LWORK, IWORK, IFAIL, 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, RANGE, UPLO
12: INTEGER IL, INFO, ITYPE, IU, LDA, LDB, LDZ, LWORK, M, N
13: DOUBLE PRECISION ABSTOL, VL, VU
14: * ..
15: * .. Array Arguments ..
16: INTEGER IFAIL( * ), IWORK( * )
17: DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * ),
18: $ Z( LDZ, * )
19: * ..
20: *
21: * Purpose
22: * =======
23: *
24: * DSYGVX computes selected eigenvalues, and optionally, eigenvectors
25: * of a real generalized symmetric-definite eigenproblem, of the form
26: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A
27: * and B are assumed to be symmetric and B is also positive definite.
28: * Eigenvalues and eigenvectors can be selected by specifying either a
29: * range of values or a range of indices for the desired eigenvalues.
30: *
31: * Arguments
32: * =========
33: *
34: * ITYPE (input) INTEGER
35: * Specifies the problem type to be solved:
36: * = 1: A*x = (lambda)*B*x
37: * = 2: A*B*x = (lambda)*x
38: * = 3: B*A*x = (lambda)*x
39: *
40: * JOBZ (input) CHARACTER*1
41: * = 'N': Compute eigenvalues only;
42: * = 'V': Compute eigenvalues and eigenvectors.
43: *
44: * RANGE (input) CHARACTER*1
45: * = 'A': all eigenvalues will be found.
46: * = 'V': all eigenvalues in the half-open interval (VL,VU]
47: * will be found.
48: * = 'I': the IL-th through IU-th eigenvalues will be found.
49: *
50: * UPLO (input) CHARACTER*1
51: * = 'U': Upper triangle of A and B are stored;
52: * = 'L': Lower triangle of A and B are stored.
53: *
54: * N (input) INTEGER
55: * The order of the matrix pencil (A,B). N >= 0.
56: *
57: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
58: * On entry, the symmetric matrix A. If UPLO = 'U', the
59: * leading N-by-N upper triangular part of A contains the
60: * upper triangular part of the matrix A. If UPLO = 'L',
61: * the leading N-by-N lower triangular part of A contains
62: * the lower triangular part of the matrix A.
63: *
64: * On exit, the lower triangle (if UPLO='L') or the upper
65: * triangle (if UPLO='U') of A, including the diagonal, is
66: * destroyed.
67: *
68: * LDA (input) INTEGER
69: * The leading dimension of the array A. LDA >= max(1,N).
70: *
71: * B (input/output) DOUBLE PRECISION array, dimension (LDA, N)
72: * On entry, the symmetric matrix B. If UPLO = 'U', the
73: * leading N-by-N upper triangular part of B contains the
74: * upper triangular part of the matrix B. If UPLO = 'L',
75: * the leading N-by-N lower triangular part of B contains
76: * the lower triangular part of the matrix B.
77: *
78: * On exit, if INFO <= N, the part of B containing the matrix is
79: * overwritten by the triangular factor U or L from the Cholesky
80: * factorization B = U**T*U or B = L*L**T.
81: *
82: * LDB (input) INTEGER
83: * The leading dimension of the array B. LDB >= max(1,N).
84: *
85: * VL (input) DOUBLE PRECISION
86: * VU (input) DOUBLE PRECISION
87: * If RANGE='V', the lower and upper bounds of the interval to
88: * be searched for eigenvalues. VL < VU.
89: * Not referenced if RANGE = 'A' or 'I'.
90: *
91: * IL (input) INTEGER
92: * IU (input) INTEGER
93: * If RANGE='I', the indices (in ascending order) of the
94: * smallest and largest eigenvalues to be returned.
95: * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
96: * Not referenced if RANGE = 'A' or 'V'.
97: *
98: * ABSTOL (input) DOUBLE PRECISION
99: * The absolute error tolerance for the eigenvalues.
100: * An approximate eigenvalue is accepted as converged
101: * when it is determined to lie in an interval [a,b]
102: * of width less than or equal to
103: *
104: * ABSTOL + EPS * max( |a|,|b| ) ,
105: *
106: * where EPS is the machine precision. If ABSTOL is less than
107: * or equal to zero, then EPS*|T| will be used in its place,
108: * where |T| is the 1-norm of the tridiagonal matrix obtained
109: * by reducing A to tridiagonal form.
110: *
111: * Eigenvalues will be computed most accurately when ABSTOL is
112: * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
113: * If this routine returns with INFO>0, indicating that some
114: * eigenvectors did not converge, try setting ABSTOL to
115: * 2*DLAMCH('S').
116: *
117: * M (output) INTEGER
118: * The total number of eigenvalues found. 0 <= M <= N.
119: * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
120: *
121: * W (output) DOUBLE PRECISION array, dimension (N)
122: * On normal exit, the first M elements contain the selected
123: * eigenvalues in ascending order.
124: *
125: * Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M))
126: * If JOBZ = 'N', then Z is not referenced.
127: * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
128: * contain the orthonormal eigenvectors of the matrix A
129: * corresponding to the selected eigenvalues, with the i-th
130: * column of Z holding the eigenvector associated with W(i).
131: * The eigenvectors are normalized as follows:
132: * if ITYPE = 1 or 2, Z**T*B*Z = I;
133: * if ITYPE = 3, Z**T*inv(B)*Z = I.
134: *
135: * If an eigenvector fails to converge, then that column of Z
136: * contains the latest approximation to the eigenvector, and the
137: * index of the eigenvector is returned in IFAIL.
138: * Note: the user must ensure that at least max(1,M) columns are
139: * supplied in the array Z; if RANGE = 'V', the exact value of M
140: * is not known in advance and an upper bound must be used.
141: *
142: * LDZ (input) INTEGER
143: * The leading dimension of the array Z. LDZ >= 1, and if
144: * JOBZ = 'V', LDZ >= max(1,N).
145: *
146: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
147: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
148: *
149: * LWORK (input) INTEGER
150: * The length of the array WORK. LWORK >= max(1,8*N).
151: * For optimal efficiency, LWORK >= (NB+3)*N,
152: * where NB is the blocksize for DSYTRD returned by ILAENV.
153: *
154: * If LWORK = -1, then a workspace query is assumed; the routine
155: * only calculates the optimal size of the WORK array, returns
156: * this value as the first entry of the WORK array, and no error
157: * message related to LWORK is issued by XERBLA.
158: *
159: * IWORK (workspace) INTEGER array, dimension (5*N)
160: *
161: * IFAIL (output) INTEGER array, dimension (N)
162: * If JOBZ = 'V', then if INFO = 0, the first M elements of
163: * IFAIL are zero. If INFO > 0, then IFAIL contains the
164: * indices of the eigenvectors that failed to converge.
165: * If JOBZ = 'N', then IFAIL is not referenced.
166: *
167: * INFO (output) INTEGER
168: * = 0: successful exit
169: * < 0: if INFO = -i, the i-th argument had an illegal value
170: * > 0: DPOTRF or DSYEVX returned an error code:
171: * <= N: if INFO = i, DSYEVX failed to converge;
172: * i eigenvectors failed to converge. Their indices
173: * are stored in array IFAIL.
174: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
175: * minor of order i of B is not positive definite.
176: * The factorization of B could not be completed and
177: * no eigenvalues or eigenvectors were computed.
178: *
179: * Further Details
180: * ===============
181: *
182: * Based on contributions by
183: * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
184: *
185: * =====================================================================
186: *
187: * .. Parameters ..
188: DOUBLE PRECISION ONE
189: PARAMETER ( ONE = 1.0D+0 )
190: * ..
191: * .. Local Scalars ..
192: LOGICAL ALLEIG, INDEIG, LQUERY, UPPER, VALEIG, WANTZ
193: CHARACTER TRANS
194: INTEGER LWKMIN, LWKOPT, NB
195: * ..
196: * .. External Functions ..
197: LOGICAL LSAME
198: INTEGER ILAENV
199: EXTERNAL LSAME, ILAENV
200: * ..
201: * .. External Subroutines ..
202: EXTERNAL DPOTRF, DSYEVX, DSYGST, DTRMM, DTRSM, XERBLA
203: * ..
204: * .. Intrinsic Functions ..
205: INTRINSIC MAX, MIN
206: * ..
207: * .. Executable Statements ..
208: *
209: * Test the input parameters.
210: *
211: UPPER = LSAME( UPLO, 'U' )
212: WANTZ = LSAME( JOBZ, 'V' )
213: ALLEIG = LSAME( RANGE, 'A' )
214: VALEIG = LSAME( RANGE, 'V' )
215: INDEIG = LSAME( RANGE, 'I' )
216: LQUERY = ( LWORK.EQ.-1 )
217: *
218: INFO = 0
219: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
220: INFO = -1
221: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
222: INFO = -2
223: ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
224: INFO = -3
225: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
226: INFO = -4
227: ELSE IF( N.LT.0 ) THEN
228: INFO = -5
229: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
230: INFO = -7
231: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
232: INFO = -9
233: ELSE
234: IF( VALEIG ) THEN
235: IF( N.GT.0 .AND. VU.LE.VL )
236: $ INFO = -11
237: ELSE IF( INDEIG ) THEN
238: IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
239: INFO = -12
240: ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
241: INFO = -13
242: END IF
243: END IF
244: END IF
245: IF (INFO.EQ.0) THEN
246: IF (LDZ.LT.1 .OR. (WANTZ .AND. LDZ.LT.N)) THEN
247: INFO = -18
248: END IF
249: END IF
250: *
251: IF( INFO.EQ.0 ) THEN
252: LWKMIN = MAX( 1, 8*N )
253: NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
254: LWKOPT = MAX( LWKMIN, ( NB + 3 )*N )
255: WORK( 1 ) = LWKOPT
256: *
257: IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
258: INFO = -20
259: END IF
260: END IF
261: *
262: IF( INFO.NE.0 ) THEN
263: CALL XERBLA( 'DSYGVX', -INFO )
264: RETURN
265: ELSE IF( LQUERY ) THEN
266: RETURN
267: END IF
268: *
269: * Quick return if possible
270: *
271: M = 0
272: IF( N.EQ.0 ) THEN
273: RETURN
274: END IF
275: *
276: * Form a Cholesky factorization of B.
277: *
278: CALL DPOTRF( UPLO, N, B, LDB, INFO )
279: IF( INFO.NE.0 ) THEN
280: INFO = N + INFO
281: RETURN
282: END IF
283: *
284: * Transform problem to standard eigenvalue problem and solve.
285: *
286: CALL DSYGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
287: CALL DSYEVX( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL,
288: $ M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO )
289: *
290: IF( WANTZ ) THEN
291: *
292: * Backtransform eigenvectors to the original problem.
293: *
294: IF( INFO.GT.0 )
295: $ M = INFO - 1
296: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
297: *
298: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
299: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
300: *
301: IF( UPPER ) THEN
302: TRANS = 'N'
303: ELSE
304: TRANS = 'T'
305: END IF
306: *
307: CALL DTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, M, ONE, B,
308: $ LDB, Z, LDZ )
309: *
310: ELSE IF( ITYPE.EQ.3 ) THEN
311: *
312: * For B*A*x=(lambda)*x;
313: * backtransform eigenvectors: x = L*y or U'*y
314: *
315: IF( UPPER ) THEN
316: TRANS = 'T'
317: ELSE
318: TRANS = 'N'
319: END IF
320: *
321: CALL DTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, M, ONE, B,
322: $ LDB, Z, LDZ )
323: END IF
324: END IF
325: *
326: * Set WORK(1) to optimal workspace size.
327: *
328: WORK( 1 ) = LWKOPT
329: *
330: RETURN
331: *
332: * End of DSYGVX
333: *
334: END
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