Annotation of rpl/lapack/lapack/dsyev.f, revision 1.6
1.1 bertrand 1: SUBROUTINE DSYEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO )
2: *
3: * -- LAPACK driver routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER JOBZ, UPLO
10: INTEGER INFO, LDA, LWORK, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DSYEV computes all eigenvalues and, optionally, eigenvectors of a
20: * real symmetric matrix A.
21: *
22: * Arguments
23: * =========
24: *
25: * JOBZ (input) CHARACTER*1
26: * = 'N': Compute eigenvalues only;
27: * = 'V': Compute eigenvalues and eigenvectors.
28: *
29: * UPLO (input) CHARACTER*1
30: * = 'U': Upper triangle of A is stored;
31: * = 'L': Lower triangle of A is stored.
32: *
33: * N (input) INTEGER
34: * The order of the matrix A. N >= 0.
35: *
36: * A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
37: * On entry, the symmetric matrix A. If UPLO = 'U', the
38: * leading N-by-N upper triangular part of A contains the
39: * upper triangular part of the matrix A. If UPLO = 'L',
40: * the leading N-by-N lower triangular part of A contains
41: * the lower triangular part of the matrix A.
42: * On exit, if JOBZ = 'V', then if INFO = 0, A contains the
43: * orthonormal eigenvectors of the matrix A.
44: * If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
45: * or the upper triangle (if UPLO='U') of A, including the
46: * diagonal, is destroyed.
47: *
48: * LDA (input) INTEGER
49: * The leading dimension of the array A. LDA >= max(1,N).
50: *
51: * W (output) DOUBLE PRECISION array, dimension (N)
52: * If INFO = 0, the eigenvalues in ascending order.
53: *
54: * WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
55: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
56: *
57: * LWORK (input) INTEGER
58: * The length of the array WORK. LWORK >= max(1,3*N-1).
59: * For optimal efficiency, LWORK >= (NB+2)*N,
60: * where NB is the blocksize for DSYTRD returned by ILAENV.
61: *
62: * If LWORK = -1, then a workspace query is assumed; the routine
63: * only calculates the optimal size of the WORK array, returns
64: * this value as the first entry of the WORK array, and no error
65: * message related to LWORK is issued by XERBLA.
66: *
67: * INFO (output) INTEGER
68: * = 0: successful exit
69: * < 0: if INFO = -i, the i-th argument had an illegal value
70: * > 0: if INFO = i, the algorithm failed to converge; i
71: * off-diagonal elements of an intermediate tridiagonal
72: * form did not converge to zero.
73: *
74: * =====================================================================
75: *
76: * .. Parameters ..
77: DOUBLE PRECISION ZERO, ONE
78: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
79: * ..
80: * .. Local Scalars ..
81: LOGICAL LOWER, LQUERY, WANTZ
82: INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
83: $ LLWORK, LWKOPT, NB
84: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
85: $ SMLNUM
86: * ..
87: * .. External Functions ..
88: LOGICAL LSAME
89: INTEGER ILAENV
90: DOUBLE PRECISION DLAMCH, DLANSY
91: EXTERNAL LSAME, ILAENV, DLAMCH, DLANSY
92: * ..
93: * .. External Subroutines ..
94: EXTERNAL DLASCL, DORGTR, DSCAL, DSTEQR, DSTERF, DSYTRD,
95: $ XERBLA
96: * ..
97: * .. Intrinsic Functions ..
98: INTRINSIC MAX, SQRT
99: * ..
100: * .. Executable Statements ..
101: *
102: * Test the input parameters.
103: *
104: WANTZ = LSAME( JOBZ, 'V' )
105: LOWER = LSAME( UPLO, 'L' )
106: LQUERY = ( LWORK.EQ.-1 )
107: *
108: INFO = 0
109: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
110: INFO = -1
111: ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
112: INFO = -2
113: ELSE IF( N.LT.0 ) THEN
114: INFO = -3
115: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
116: INFO = -5
117: END IF
118: *
119: IF( INFO.EQ.0 ) THEN
120: NB = ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 )
121: LWKOPT = MAX( 1, ( NB+2 )*N )
122: WORK( 1 ) = LWKOPT
123: *
124: IF( LWORK.LT.MAX( 1, 3*N-1 ) .AND. .NOT.LQUERY )
125: $ INFO = -8
126: END IF
127: *
128: IF( INFO.NE.0 ) THEN
129: CALL XERBLA( 'DSYEV ', -INFO )
130: RETURN
131: ELSE IF( LQUERY ) THEN
132: RETURN
133: END IF
134: *
135: * Quick return if possible
136: *
137: IF( N.EQ.0 ) THEN
138: RETURN
139: END IF
140: *
141: IF( N.EQ.1 ) THEN
142: W( 1 ) = A( 1, 1 )
143: WORK( 1 ) = 2
144: IF( WANTZ )
145: $ A( 1, 1 ) = ONE
146: RETURN
147: END IF
148: *
149: * Get machine constants.
150: *
151: SAFMIN = DLAMCH( 'Safe minimum' )
152: EPS = DLAMCH( 'Precision' )
153: SMLNUM = SAFMIN / EPS
154: BIGNUM = ONE / SMLNUM
155: RMIN = SQRT( SMLNUM )
156: RMAX = SQRT( BIGNUM )
157: *
158: * Scale matrix to allowable range, if necessary.
159: *
160: ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK )
161: ISCALE = 0
162: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
163: ISCALE = 1
164: SIGMA = RMIN / ANRM
165: ELSE IF( ANRM.GT.RMAX ) THEN
166: ISCALE = 1
167: SIGMA = RMAX / ANRM
168: END IF
169: IF( ISCALE.EQ.1 )
170: $ CALL DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
171: *
172: * Call DSYTRD to reduce symmetric matrix to tridiagonal form.
173: *
174: INDE = 1
175: INDTAU = INDE + N
176: INDWRK = INDTAU + N
177: LLWORK = LWORK - INDWRK + 1
178: CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ),
179: $ WORK( INDWRK ), LLWORK, IINFO )
180: *
181: * For eigenvalues only, call DSTERF. For eigenvectors, first call
182: * DORGTR to generate the orthogonal matrix, then call DSTEQR.
183: *
184: IF( .NOT.WANTZ ) THEN
185: CALL DSTERF( N, W, WORK( INDE ), INFO )
186: ELSE
187: CALL DORGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
188: $ LLWORK, IINFO )
189: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), A, LDA, WORK( INDTAU ),
190: $ INFO )
191: END IF
192: *
193: * If matrix was scaled, then rescale eigenvalues appropriately.
194: *
195: IF( ISCALE.EQ.1 ) THEN
196: IF( INFO.EQ.0 ) THEN
197: IMAX = N
198: ELSE
199: IMAX = INFO - 1
200: END IF
201: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
202: END IF
203: *
204: * Set WORK(1) to optimal workspace size.
205: *
206: WORK( 1 ) = LWKOPT
207: *
208: RETURN
209: *
210: * End of DSYEV
211: *
212: END
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