Annotation of rpl/lapack/lapack/dsbgv.f, revision 1.4
1.1 bertrand 1: SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
2: $ LDZ, WORK, 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 AB( LDAB, * ), BB( LDBB, * ), W( * ),
15: $ WORK( * ), Z( LDZ, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * DSBGV computes all the eigenvalues, and optionally, the eigenvectors
22: * of a real generalized symmetric-definite banded eigenproblem, of
23: * the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
24: * and banded, and B is also positive definite.
25: *
26: * Arguments
27: * =========
28: *
29: * JOBZ (input) CHARACTER*1
30: * = 'N': Compute eigenvalues only;
31: * = 'V': Compute eigenvalues and eigenvectors.
32: *
33: * UPLO (input) CHARACTER*1
34: * = 'U': Upper triangles of A and B are stored;
35: * = 'L': Lower triangles of A and B are stored.
36: *
37: * N (input) INTEGER
38: * The order of the matrices A and B. N >= 0.
39: *
40: * KA (input) INTEGER
41: * The number of superdiagonals of the matrix A if UPLO = 'U',
42: * or the number of subdiagonals if UPLO = 'L'. KA >= 0.
43: *
44: * KB (input) INTEGER
45: * The number of superdiagonals of the matrix B if UPLO = 'U',
46: * or the number of subdiagonals if UPLO = 'L'. KB >= 0.
47: *
48: * AB (input/output) DOUBLE PRECISION array, dimension (LDAB, N)
49: * On entry, the upper or lower triangle of the symmetric band
50: * matrix A, stored in the first ka+1 rows of the array. The
51: * j-th column of A is stored in the j-th column of the array AB
52: * as follows:
53: * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
54: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
55: *
56: * On exit, the contents of AB are destroyed.
57: *
58: * LDAB (input) INTEGER
59: * The leading dimension of the array AB. LDAB >= KA+1.
60: *
61: * BB (input/output) DOUBLE PRECISION array, dimension (LDBB, N)
62: * On entry, the upper or lower triangle of the symmetric band
63: * matrix B, stored in the first kb+1 rows of the array. The
64: * j-th column of B is stored in the j-th column of the array BB
65: * as follows:
66: * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
67: * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
68: *
69: * On exit, the factor S from the split Cholesky factorization
70: * B = S**T*S, as returned by DPBSTF.
71: *
72: * LDBB (input) INTEGER
73: * The leading dimension of the array BB. LDBB >= KB+1.
74: *
75: * W (output) DOUBLE PRECISION array, dimension (N)
76: * If INFO = 0, the eigenvalues in ascending order.
77: *
78: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
79: * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
80: * eigenvectors, with the i-th column of Z holding the
81: * eigenvector associated with W(i). The eigenvectors are
82: * normalized so that Z**T*B*Z = I.
83: * If JOBZ = 'N', then Z is not referenced.
84: *
85: * LDZ (input) INTEGER
86: * The leading dimension of the array Z. LDZ >= 1, and if
87: * JOBZ = 'V', LDZ >= N.
88: *
89: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
90: *
91: * INFO (output) INTEGER
92: * = 0: successful exit
93: * < 0: if INFO = -i, the i-th argument had an illegal value
94: * > 0: if INFO = i, and i is:
95: * <= N: the algorithm failed to converge:
96: * i off-diagonal elements of an intermediate
97: * tridiagonal form did not converge to zero;
98: * > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
99: * returned INFO = i: B is not positive definite.
100: * The factorization of B could not be completed and
101: * no eigenvalues or eigenvectors were computed.
102: *
103: * =====================================================================
104: *
105: * .. Local Scalars ..
106: LOGICAL UPPER, WANTZ
107: CHARACTER VECT
108: INTEGER IINFO, INDE, INDWRK
109: * ..
110: * .. External Functions ..
111: LOGICAL LSAME
112: EXTERNAL LSAME
113: * ..
114: * .. External Subroutines ..
115: EXTERNAL DPBSTF, DSBGST, DSBTRD, DSTEQR, DSTERF, XERBLA
116: * ..
117: * .. Executable Statements ..
118: *
119: * Test the input parameters.
120: *
121: WANTZ = LSAME( JOBZ, 'V' )
122: UPPER = LSAME( UPLO, 'U' )
123: *
124: INFO = 0
125: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
126: INFO = -1
127: ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
128: INFO = -2
129: ELSE IF( N.LT.0 ) THEN
130: INFO = -3
131: ELSE IF( KA.LT.0 ) THEN
132: INFO = -4
133: ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
134: INFO = -5
135: ELSE IF( LDAB.LT.KA+1 ) THEN
136: INFO = -7
137: ELSE IF( LDBB.LT.KB+1 ) THEN
138: INFO = -9
139: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
140: INFO = -12
141: END IF
142: IF( INFO.NE.0 ) THEN
143: CALL XERBLA( 'DSBGV ', -INFO )
144: RETURN
145: END IF
146: *
147: * Quick return if possible
148: *
149: IF( N.EQ.0 )
150: $ RETURN
151: *
152: * Form a split Cholesky factorization of B.
153: *
154: CALL DPBSTF( UPLO, N, KB, BB, LDBB, INFO )
155: IF( INFO.NE.0 ) THEN
156: INFO = N + INFO
157: RETURN
158: END IF
159: *
160: * Transform problem to standard eigenvalue problem.
161: *
162: INDE = 1
163: INDWRK = INDE + N
164: CALL DSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ,
165: $ WORK( INDWRK ), IINFO )
166: *
167: * Reduce to tridiagonal form.
168: *
169: IF( WANTZ ) THEN
170: VECT = 'U'
171: ELSE
172: VECT = 'N'
173: END IF
174: CALL DSBTRD( VECT, UPLO, N, KA, AB, LDAB, W, WORK( INDE ), Z, LDZ,
175: $ WORK( INDWRK ), IINFO )
176: *
177: * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR.
178: *
179: IF( .NOT.WANTZ ) THEN
180: CALL DSTERF( N, W, WORK( INDE ), INFO )
181: ELSE
182: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
183: $ INFO )
184: END IF
185: RETURN
186: *
187: * End of DSBGV
188: *
189: END
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