1: SUBROUTINE DSTEVD( JOBZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
2: $ LIWORK, 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
11: INTEGER INFO, LDZ, LIWORK, LWORK, N
12: * ..
13: * .. Array Arguments ..
14: INTEGER IWORK( * )
15: DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * DSTEVD computes all eigenvalues and, optionally, eigenvectors of a
22: * real symmetric tridiagonal matrix. If eigenvectors are desired, it
23: * uses a divide and conquer algorithm.
24: *
25: * The divide and conquer algorithm makes very mild assumptions about
26: * floating point arithmetic. It will work on machines with a guard
27: * digit in add/subtract, or on those binary machines without guard
28: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
29: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
30: * without guard digits, but we know of none.
31: *
32: * Arguments
33: * =========
34: *
35: * JOBZ (input) CHARACTER*1
36: * = 'N': Compute eigenvalues only;
37: * = 'V': Compute eigenvalues and eigenvectors.
38: *
39: * N (input) INTEGER
40: * The order of the matrix. N >= 0.
41: *
42: * D (input/output) DOUBLE PRECISION array, dimension (N)
43: * On entry, the n diagonal elements of the tridiagonal matrix
44: * A.
45: * On exit, if INFO = 0, the eigenvalues in ascending order.
46: *
47: * E (input/output) DOUBLE PRECISION array, dimension (N-1)
48: * On entry, the (n-1) subdiagonal elements of the tridiagonal
49: * matrix A, stored in elements 1 to N-1 of E.
50: * On exit, the contents of E are destroyed.
51: *
52: * Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
53: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
54: * eigenvectors of the matrix A, with the i-th column of Z
55: * holding the eigenvector associated with D(i).
56: * If JOBZ = 'N', then Z is not referenced.
57: *
58: * LDZ (input) INTEGER
59: * The leading dimension of the array Z. LDZ >= 1, and if
60: * JOBZ = 'V', LDZ >= max(1,N).
61: *
62: * WORK (workspace/output) DOUBLE PRECISION array,
63: * dimension (LWORK)
64: * On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
65: *
66: * LWORK (input) INTEGER
67: * The dimension of the array WORK.
68: * If JOBZ = 'N' or N <= 1 then LWORK must be at least 1.
69: * If JOBZ = 'V' and N > 1 then LWORK must be at least
70: * ( 1 + 4*N + N**2 ).
71: *
72: * If LWORK = -1, then a workspace query is assumed; the routine
73: * only calculates the optimal sizes of the WORK and IWORK
74: * arrays, returns these values as the first entries of the WORK
75: * and IWORK arrays, and no error message related to LWORK or
76: * LIWORK is issued by XERBLA.
77: *
78: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
79: * On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
80: *
81: * LIWORK (input) INTEGER
82: * The dimension of the array IWORK.
83: * If JOBZ = 'N' or N <= 1 then LIWORK must be at least 1.
84: * If JOBZ = 'V' and N > 1 then LIWORK must be at least 3+5*N.
85: *
86: * If LIWORK = -1, then a workspace query is assumed; the
87: * routine only calculates the optimal sizes of the WORK and
88: * IWORK arrays, returns these values as the first entries of
89: * the WORK and IWORK arrays, and no error message related to
90: * LWORK or LIWORK is issued by XERBLA.
91: *
92: * INFO (output) INTEGER
93: * = 0: successful exit
94: * < 0: if INFO = -i, the i-th argument had an illegal value
95: * > 0: if INFO = i, the algorithm failed to converge; i
96: * off-diagonal elements of E did not converge to zero.
97: *
98: * =====================================================================
99: *
100: * .. Parameters ..
101: DOUBLE PRECISION ZERO, ONE
102: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
103: * ..
104: * .. Local Scalars ..
105: LOGICAL LQUERY, WANTZ
106: INTEGER ISCALE, LIWMIN, LWMIN
107: DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
108: $ TNRM
109: * ..
110: * .. External Functions ..
111: LOGICAL LSAME
112: DOUBLE PRECISION DLAMCH, DLANST
113: EXTERNAL LSAME, DLAMCH, DLANST
114: * ..
115: * .. External Subroutines ..
116: EXTERNAL DSCAL, DSTEDC, DSTERF, XERBLA
117: * ..
118: * .. Intrinsic Functions ..
119: INTRINSIC SQRT
120: * ..
121: * .. Executable Statements ..
122: *
123: * Test the input parameters.
124: *
125: WANTZ = LSAME( JOBZ, 'V' )
126: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
127: *
128: INFO = 0
129: LIWMIN = 1
130: LWMIN = 1
131: IF( N.GT.1 .AND. WANTZ ) THEN
132: LWMIN = 1 + 4*N + N**2
133: LIWMIN = 3 + 5*N
134: END IF
135: *
136: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
137: INFO = -1
138: ELSE IF( N.LT.0 ) THEN
139: INFO = -2
140: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
141: INFO = -6
142: END IF
143: *
144: IF( INFO.EQ.0 ) THEN
145: WORK( 1 ) = LWMIN
146: IWORK( 1 ) = LIWMIN
147: *
148: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
149: INFO = -8
150: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
151: INFO = -10
152: END IF
153: END IF
154: *
155: IF( INFO.NE.0 ) THEN
156: CALL XERBLA( 'DSTEVD', -INFO )
157: RETURN
158: ELSE IF( LQUERY ) THEN
159: RETURN
160: END IF
161: *
162: * Quick return if possible
163: *
164: IF( N.EQ.0 )
165: $ RETURN
166: *
167: IF( N.EQ.1 ) THEN
168: IF( WANTZ )
169: $ Z( 1, 1 ) = ONE
170: RETURN
171: END IF
172: *
173: * Get machine constants.
174: *
175: SAFMIN = DLAMCH( 'Safe minimum' )
176: EPS = DLAMCH( 'Precision' )
177: SMLNUM = SAFMIN / EPS
178: BIGNUM = ONE / SMLNUM
179: RMIN = SQRT( SMLNUM )
180: RMAX = SQRT( BIGNUM )
181: *
182: * Scale matrix to allowable range, if necessary.
183: *
184: ISCALE = 0
185: TNRM = DLANST( 'M', N, D, E )
186: IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
187: ISCALE = 1
188: SIGMA = RMIN / TNRM
189: ELSE IF( TNRM.GT.RMAX ) THEN
190: ISCALE = 1
191: SIGMA = RMAX / TNRM
192: END IF
193: IF( ISCALE.EQ.1 ) THEN
194: CALL DSCAL( N, SIGMA, D, 1 )
195: CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
196: END IF
197: *
198: * For eigenvalues only, call DSTERF. For eigenvalues and
199: * eigenvectors, call DSTEDC.
200: *
201: IF( .NOT.WANTZ ) THEN
202: CALL DSTERF( N, D, E, INFO )
203: ELSE
204: CALL DSTEDC( 'I', N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK,
205: $ INFO )
206: END IF
207: *
208: * If matrix was scaled, then rescale eigenvalues appropriately.
209: *
210: IF( ISCALE.EQ.1 )
211: $ CALL DSCAL( N, ONE / SIGMA, D, 1 )
212: *
213: WORK( 1 ) = LWMIN
214: IWORK( 1 ) = LIWMIN
215: *
216: RETURN
217: *
218: * End of DSTEVD
219: *
220: END
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