Annotation of rpl/lapack/lapack/zhbgv.f, revision 1.6
1.1 bertrand 1: SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
2: $ LDZ, WORK, 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, KA, KB, LDAB, LDBB, LDZ, N
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION RWORK( * ), W( * )
15: COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
16: $ Z( LDZ, * )
17: * ..
18: *
19: * Purpose
20: * =======
21: *
22: * ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
23: * of a complex generalized Hermitian-definite banded eigenproblem, of
24: * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
25: * and banded, and B is also positive definite.
26: *
27: * Arguments
28: * =========
29: *
30: * JOBZ (input) CHARACTER*1
31: * = 'N': Compute eigenvalues only;
32: * = 'V': Compute eigenvalues and eigenvectors.
33: *
34: * UPLO (input) CHARACTER*1
35: * = 'U': Upper triangles of A and B are stored;
36: * = 'L': Lower triangles of A and B are stored.
37: *
38: * N (input) INTEGER
39: * The order of the matrices A and B. N >= 0.
40: *
41: * KA (input) INTEGER
42: * The number of superdiagonals of the matrix A if UPLO = 'U',
43: * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
44: *
45: * KB (input) INTEGER
46: * The number of superdiagonals of the matrix B if UPLO = 'U',
47: * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
48: *
49: * AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
50: * On entry, the upper or lower triangle of the Hermitian band
51: * matrix A, stored in the first ka+1 rows of the array. The
52: * j-th column of A is stored in the j-th column of the array AB
53: * as follows:
54: * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
55: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
56: *
57: * On exit, the contents of AB are destroyed.
58: *
59: * LDAB (input) INTEGER
60: * The leading dimension of the array AB. LDAB >= KA+1.
61: *
62: * BB (input/output) COMPLEX*16 array, dimension (LDBB, N)
63: * On entry, the upper or lower triangle of the Hermitian band
64: * matrix B, stored in the first kb+1 rows of the array. The
65: * j-th column of B is stored in the j-th column of the array BB
66: * as follows:
67: * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
68: * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
69: *
70: * On exit, the factor S from the split Cholesky factorization
71: * B = S**H*S, as returned by ZPBSTF.
72: *
73: * LDBB (input) INTEGER
74: * The leading dimension of the array BB. LDBB >= KB+1.
75: *
76: * W (output) DOUBLE PRECISION array, dimension (N)
77: * If INFO = 0, the eigenvalues in ascending order.
78: *
79: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
80: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
81: * eigenvectors, with the i-th column of Z holding the
82: * eigenvector associated with W(i). The eigenvectors are
83: * normalized so that Z**H*B*Z = I.
84: * If JOBZ = 'N', then Z is not referenced.
85: *
86: * LDZ (input) INTEGER
87: * The leading dimension of the array Z. LDZ >= 1, and if
88: * JOBZ = 'V', LDZ >= N.
89: *
90: * WORK (workspace) COMPLEX*16 array, dimension (N)
91: *
92: * RWORK (workspace) DOUBLE PRECISION array, dimension (3*N)
93: *
94: * INFO (output) INTEGER
95: * = 0: successful exit
96: * < 0: if INFO = -i, the i-th argument had an illegal value
97: * > 0: if INFO = i, and i is:
98: * <= N: the algorithm failed to converge:
99: * i off-diagonal elements of an intermediate
100: * tridiagonal form did not converge to zero;
101: * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
102: * returned INFO = i: B is not positive definite.
103: * The factorization of B could not be completed and
104: * no eigenvalues or eigenvectors were computed.
105: *
106: * =====================================================================
107: *
108: * .. Local Scalars ..
109: LOGICAL UPPER, WANTZ
110: CHARACTER VECT
111: INTEGER IINFO, INDE, INDWRK
112: * ..
113: * .. External Functions ..
114: LOGICAL LSAME
115: EXTERNAL LSAME
116: * ..
117: * .. External Subroutines ..
118: EXTERNAL DSTERF, XERBLA, ZHBGST, ZHBTRD, ZPBSTF, ZSTEQR
119: * ..
120: * .. Executable Statements ..
121: *
122: * Test the input parameters.
123: *
124: WANTZ = LSAME( JOBZ, 'V' )
125: UPPER = LSAME( UPLO, 'U' )
126: *
127: INFO = 0
128: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
129: INFO = -1
130: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
131: INFO = -2
132: ELSE IF( N.LT.0 ) THEN
133: INFO = -3
134: ELSE IF( KA.LT.0 ) THEN
135: INFO = -4
136: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
137: INFO = -5
138: ELSE IF( LDAB.LT.KA+1 ) THEN
139: INFO = -7
140: ELSE IF( LDBB.LT.KB+1 ) THEN
141: INFO = -9
142: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
143: INFO = -12
144: END IF
145: IF( INFO.NE.0 ) THEN
146: CALL XERBLA( 'ZHBGV ', -INFO )
147: RETURN
148: END IF
149: *
150: * Quick return if possible
151: *
152: IF( N.EQ.0 )
153: $ RETURN
154: *
155: * Form a split Cholesky factorization of B.
156: *
157: CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO )
158: IF( INFO.NE.0 ) THEN
159: INFO = N + INFO
160: RETURN
161: END IF
162: *
163: * Transform problem to standard eigenvalue problem.
164: *
165: INDE = 1
166: INDWRK = INDE + N
167: CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
168: $ WORK, RWORK( INDWRK ), IINFO )
169: *
170: * Reduce to tridiagonal form.
171: *
172: IF( WANTZ ) THEN
173: VECT = 'U'
174: ELSE
175: VECT = 'N'
176: END IF
177: CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z,
178: $ LDZ, WORK, IINFO )
179: *
180: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
181: *
182: IF( .NOT.WANTZ ) THEN
183: CALL DSTERF( N, W, RWORK( INDE ), INFO )
184: ELSE
185: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
186: $ RWORK( INDWRK ), INFO )
187: END IF
188: RETURN
189: *
190: * End of ZHBGV
191: *
192: END
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