Annotation of rpl/lapack/lapack/zhegv.f, revision 1.2
1.1 bertrand 1: SUBROUTINE ZHEGV( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
2: $ LWORK, RWORK, 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, LWORK, N
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION RWORK( * ), W( * )
15: COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZHEGV computes all the eigenvalues, and optionally, the eigenvectors
22: * of a complex generalized Hermitian-definite eigenproblem, of the form
23: * A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
24: * Here A and B are assumed to be Hermitian and B is also
25: * positive definite.
26: *
27: * Arguments
28: * =========
29: *
30: * ITYPE (input) INTEGER
31: * Specifies the problem type to be solved:
32: * = 1: A*x = (lambda)*B*x
33: * = 2: A*B*x = (lambda)*x
34: * = 3: B*A*x = (lambda)*x
35: *
36: * JOBZ (input) CHARACTER*1
37: * = 'N': Compute eigenvalues only;
38: * = 'V': Compute eigenvalues and eigenvectors.
39: *
40: * UPLO (input) CHARACTER*1
41: * = 'U': Upper triangles of A and B are stored;
42: * = 'L': Lower triangles of A and B are stored.
43: *
44: * N (input) INTEGER
45: * The order of the matrices A and B. N >= 0.
46: *
47: * A (input/output) COMPLEX*16 array, dimension (LDA, N)
48: * On entry, the Hermitian matrix A. If UPLO = 'U', the
49: * leading N-by-N upper triangular part of A contains the
50: * upper triangular part of the matrix A. If UPLO = 'L',
51: * the leading N-by-N lower triangular part of A contains
52: * the lower triangular part of the matrix A.
53: *
54: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
55: * matrix Z of eigenvectors. The eigenvectors are normalized
56: * as follows:
57: * if ITYPE = 1 or 2, Z**H*B*Z = I;
58: * if ITYPE = 3, Z**H*inv(B)*Z = I.
59: * If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
60: * or the lower triangle (if UPLO='L') of A, including the
61: * diagonal, is destroyed.
62: *
63: * LDA (input) INTEGER
64: * The leading dimension of the array A. LDA >= max(1,N).
65: *
66: * B (input/output) COMPLEX*16 array, dimension (LDB, N)
67: * On entry, the Hermitian positive definite matrix B.
68: * If UPLO = 'U', the leading N-by-N upper triangular part of B
69: * contains the upper triangular part of the matrix B.
70: * If UPLO = 'L', the leading N-by-N lower triangular part of B
71: * contains the lower triangular part of the matrix B.
72: *
73: * On exit, if INFO <= N, the part of B containing the matrix is
74: * overwritten by the triangular factor U or L from the Cholesky
75: * factorization B = U**H*U or B = L*L**H.
76: *
77: * LDB (input) INTEGER
78: * The leading dimension of the array B. LDB >= max(1,N).
79: *
80: * W (output) DOUBLE PRECISION array, dimension (N)
81: * If INFO = 0, the eigenvalues in ascending order.
82: *
83: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
84: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
85: *
86: * LWORK (input) INTEGER
87: * The length of the array WORK. LWORK >= max(1,2*N-1).
88: * For optimal efficiency, LWORK >= (NB+1)*N,
89: * where NB is the blocksize for ZHETRD returned by ILAENV.
90: *
91: * If LWORK = -1, then a workspace query is assumed; the routine
92: * only calculates the optimal size of the WORK array, returns
93: * this value as the first entry of the WORK array, and no error
94: * message related to LWORK is issued by XERBLA.
95: *
96: * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1, 3*N-2))
97: *
98: * INFO (output) INTEGER
99: * = 0: successful exit
100: * < 0: if INFO = -i, the i-th argument had an illegal value
101: * > 0: ZPOTRF or ZHEEV returned an error code:
102: * <= N: if INFO = i, ZHEEV failed to converge;
103: * i off-diagonal elements of an intermediate
104: * tridiagonal form did not converge to zero;
105: * > N: if INFO = N + i, for 1 <= i <= N, then the leading
106: * minor of order i of B is not positive definite.
107: * The factorization of B could not be completed and
108: * no eigenvalues or eigenvectors were computed.
109: *
110: * =====================================================================
111: *
112: * .. Parameters ..
113: COMPLEX*16 ONE
114: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
115: * ..
116: * .. Local Scalars ..
117: LOGICAL LQUERY, UPPER, WANTZ
118: CHARACTER TRANS
119: INTEGER LWKOPT, NB, NEIG
120: * ..
121: * .. External Functions ..
122: LOGICAL LSAME
123: INTEGER ILAENV
124: EXTERNAL LSAME, ILAENV
125: * ..
126: * .. External Subroutines ..
127: EXTERNAL XERBLA, ZHEEV, ZHEGST, ZPOTRF, ZTRMM, ZTRSM
128: * ..
129: * .. Intrinsic Functions ..
130: INTRINSIC MAX
131: * ..
132: * .. Executable Statements ..
133: *
134: * Test the input parameters.
135: *
136: WANTZ = LSAME( JOBZ, 'V' )
137: UPPER = LSAME( UPLO, 'U' )
138: LQUERY = ( LWORK.EQ.-1 )
139: *
140: INFO = 0
141: IF( ITYPE.LT.1 .OR. ITYPE.GT.3 ) THEN
142: INFO = -1
143: ELSE IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
144: INFO = -2
145: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
146: INFO = -3
147: ELSE IF( N.LT.0 ) THEN
148: INFO = -4
149: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
150: INFO = -6
151: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
152: INFO = -8
153: END IF
154: *
155: IF( INFO.EQ.0 ) THEN
156: NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 )
157: LWKOPT = MAX( 1, ( NB + 1 )*N )
158: WORK( 1 ) = LWKOPT
159: *
160: IF( LWORK.LT.MAX( 1, 2*N - 1 ) .AND. .NOT.LQUERY ) THEN
161: INFO = -11
162: END IF
163: END IF
164: *
165: IF( INFO.NE.0 ) THEN
166: CALL XERBLA( 'ZHEGV ', -INFO )
167: RETURN
168: ELSE IF( LQUERY ) THEN
169: RETURN
170: END IF
171: *
172: * Quick return if possible
173: *
174: IF( N.EQ.0 )
175: $ RETURN
176: *
177: * Form a Cholesky factorization of B.
178: *
179: CALL ZPOTRF( UPLO, N, B, LDB, INFO )
180: IF( INFO.NE.0 ) THEN
181: INFO = N + INFO
182: RETURN
183: END IF
184: *
185: * Transform problem to standard eigenvalue problem and solve.
186: *
187: CALL ZHEGST( ITYPE, UPLO, N, A, LDA, B, LDB, INFO )
188: CALL ZHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO )
189: *
190: IF( WANTZ ) THEN
191: *
192: * Backtransform eigenvectors to the original problem.
193: *
194: NEIG = N
195: IF( INFO.GT.0 )
196: $ NEIG = INFO - 1
197: IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
198: *
199: * For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
200: * backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
201: *
202: IF( UPPER ) THEN
203: TRANS = 'N'
204: ELSE
205: TRANS = 'C'
206: END IF
207: *
208: CALL ZTRSM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
209: $ B, LDB, A, LDA )
210: *
211: ELSE IF( ITYPE.EQ.3 ) THEN
212: *
213: * For B*A*x=(lambda)*x;
214: * backtransform eigenvectors: x = L*y or U'*y
215: *
216: IF( UPPER ) THEN
217: TRANS = 'C'
218: ELSE
219: TRANS = 'N'
220: END IF
221: *
222: CALL ZTRMM( 'Left', UPLO, TRANS, 'Non-unit', N, NEIG, ONE,
223: $ B, LDB, A, LDA )
224: END IF
225: END IF
226: *
227: WORK( 1 ) = LWKOPT
228: *
229: RETURN
230: *
231: * End of ZHEGV
232: *
233: END
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