Annotation of rpl/lapack/lapack/zhbev.f, revision 1.3
1.1 bertrand 1: SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
2: $ 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, KD, LDAB, LDZ, N
12: * ..
13: * .. Array Arguments ..
14: DOUBLE PRECISION RWORK( * ), W( * )
15: COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
22: * a complex Hermitian band matrix A.
23: *
24: * Arguments
25: * =========
26: *
27: * JOBZ (input) CHARACTER*1
28: * = 'N': Compute eigenvalues only;
29: * = 'V': Compute eigenvalues and eigenvectors.
30: *
31: * UPLO (input) CHARACTER*1
32: * = 'U': Upper triangle of A is stored;
33: * = 'L': Lower triangle of A is stored.
34: *
35: * N (input) INTEGER
36: * The order of the matrix A. N >= 0.
37: *
38: * KD (input) INTEGER
39: * The number of superdiagonals of the matrix A if UPLO = 'U',
40: * or the number of subdiagonals if UPLO = 'L'. KD >= 0.
41: *
42: * AB (input/output) COMPLEX*16 array, dimension (LDAB, N)
43: * On entry, the upper or lower triangle of the Hermitian band
44: * matrix A, stored in the first KD+1 rows of the array. The
45: * j-th column of A is stored in the j-th column of the array AB
46: * as follows:
47: * if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
48: * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
49: *
50: * On exit, AB is overwritten by values generated during the
51: * reduction to tridiagonal form. If UPLO = 'U', the first
52: * superdiagonal and the diagonal of the tridiagonal matrix T
53: * are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
54: * the diagonal and first subdiagonal of T are returned in the
55: * first two rows of AB.
56: *
57: * LDAB (input) INTEGER
58: * The leading dimension of the array AB. LDAB >= KD + 1.
59: *
60: * W (output) DOUBLE PRECISION array, dimension (N)
61: * If INFO = 0, the eigenvalues in ascending order.
62: *
63: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
64: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
65: * eigenvectors of the matrix A, with the i-th column of Z
66: * holding the eigenvector associated with W(i).
67: * If JOBZ = 'N', then Z is not referenced.
68: *
69: * LDZ (input) INTEGER
70: * The leading dimension of the array Z. LDZ >= 1, and if
71: * JOBZ = 'V', LDZ >= max(1,N).
72: *
73: * WORK (workspace) COMPLEX*16 array, dimension (N)
74: *
75: * RWORK (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2))
76: *
77: * INFO (output) INTEGER
78: * = 0: successful exit.
79: * < 0: if INFO = -i, the i-th argument had an illegal value.
80: * > 0: if INFO = i, the algorithm failed to converge; i
81: * off-diagonal elements of an intermediate tridiagonal
82: * form did not converge to zero.
83: *
84: * =====================================================================
85: *
86: * .. Parameters ..
87: DOUBLE PRECISION ZERO, ONE
88: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
89: * ..
90: * .. Local Scalars ..
91: LOGICAL LOWER, WANTZ
92: INTEGER IINFO, IMAX, INDE, INDRWK, ISCALE
93: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
94: $ SMLNUM
95: * ..
96: * .. External Functions ..
97: LOGICAL LSAME
98: DOUBLE PRECISION DLAMCH, ZLANHB
99: EXTERNAL LSAME, DLAMCH, ZLANHB
100: * ..
101: * .. External Subroutines ..
102: EXTERNAL DSCAL, DSTERF, XERBLA, ZHBTRD, ZLASCL, ZSTEQR
103: * ..
104: * .. Intrinsic Functions ..
105: INTRINSIC SQRT
106: * ..
107: * .. Executable Statements ..
108: *
109: * Test the input parameters.
110: *
111: WANTZ = LSAME( JOBZ, 'V' )
112: LOWER = LSAME( UPLO, 'L' )
113: *
114: INFO = 0
115: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
116: INFO = -1
117: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
118: INFO = -2
119: ELSE IF( N.LT.0 ) THEN
120: INFO = -3
121: ELSE IF( KD.LT.0 ) THEN
122: INFO = -4
123: ELSE IF( LDAB.LT.KD+1 ) THEN
124: INFO = -6
125: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
126: INFO = -9
127: END IF
128: *
129: IF( INFO.NE.0 ) THEN
130: CALL XERBLA( 'ZHBEV ', -INFO )
131: RETURN
132: END IF
133: *
134: * Quick return if possible
135: *
136: IF( N.EQ.0 )
137: $ RETURN
138: *
139: IF( N.EQ.1 ) THEN
140: IF( LOWER ) THEN
141: W( 1 ) = AB( 1, 1 )
142: ELSE
143: W( 1 ) = AB( KD+1, 1 )
144: END IF
145: IF( WANTZ )
146: $ Z( 1, 1 ) = ONE
147: RETURN
148: END IF
149: *
150: * Get machine constants.
151: *
152: SAFMIN = DLAMCH( 'Safe minimum' )
153: EPS = DLAMCH( 'Precision' )
154: SMLNUM = SAFMIN / EPS
155: BIGNUM = ONE / SMLNUM
156: RMIN = SQRT( SMLNUM )
157: RMAX = SQRT( BIGNUM )
158: *
159: * Scale matrix to allowable range, if necessary.
160: *
161: ANRM = ZLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
162: ISCALE = 0
163: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
164: ISCALE = 1
165: SIGMA = RMIN / ANRM
166: ELSE IF( ANRM.GT.RMAX ) THEN
167: ISCALE = 1
168: SIGMA = RMAX / ANRM
169: END IF
170: IF( ISCALE.EQ.1 ) THEN
171: IF( LOWER ) THEN
172: CALL ZLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
173: ELSE
174: CALL ZLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
175: END IF
176: END IF
177: *
178: * Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
179: *
180: INDE = 1
181: CALL ZHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, RWORK( INDE ), Z,
182: $ LDZ, WORK, IINFO )
183: *
184: * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
185: *
186: IF( .NOT.WANTZ ) THEN
187: CALL DSTERF( N, W, RWORK( INDE ), INFO )
188: ELSE
189: INDRWK = INDE + N
190: CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
191: $ RWORK( INDRWK ), INFO )
192: END IF
193: *
194: * If matrix was scaled, then rescale eigenvalues appropriately.
195: *
196: IF( ISCALE.EQ.1 ) THEN
197: IF( INFO.EQ.0 ) THEN
198: IMAX = N
199: ELSE
200: IMAX = INFO - 1
201: END IF
202: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
203: END IF
204: *
205: RETURN
206: *
207: * End of ZHBEV
208: *
209: END
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