Annotation of rpl/lapack/lapack/dstev.f, revision 1.17
1.8 bertrand 1: *> \brief <b> DSTEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.14 bertrand 9: *> Download DSTEV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstev.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstev.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstev.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
1.14 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER JOBZ
25: * INTEGER INFO, LDZ, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
29: * ..
1.14 bertrand 30: *
1.8 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DSTEV computes all eigenvalues and, optionally, eigenvectors of a
38: *> real symmetric tridiagonal matrix A.
39: *> \endverbatim
40: *
41: * Arguments:
42: * ==========
43: *
44: *> \param[in] JOBZ
45: *> \verbatim
46: *> JOBZ is CHARACTER*1
47: *> = 'N': Compute eigenvalues only;
48: *> = 'V': Compute eigenvalues and eigenvectors.
49: *> \endverbatim
50: *>
51: *> \param[in] N
52: *> \verbatim
53: *> N is INTEGER
54: *> The order of the matrix. N >= 0.
55: *> \endverbatim
56: *>
57: *> \param[in,out] D
58: *> \verbatim
59: *> D is DOUBLE PRECISION array, dimension (N)
60: *> On entry, the n diagonal elements of the tridiagonal matrix
61: *> A.
62: *> On exit, if INFO = 0, the eigenvalues in ascending order.
63: *> \endverbatim
64: *>
65: *> \param[in,out] E
66: *> \verbatim
67: *> E is DOUBLE PRECISION array, dimension (N-1)
68: *> On entry, the (n-1) subdiagonal elements of the tridiagonal
69: *> matrix A, stored in elements 1 to N-1 of E.
70: *> On exit, the contents of E are destroyed.
71: *> \endverbatim
72: *>
73: *> \param[out] Z
74: *> \verbatim
75: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
76: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
77: *> eigenvectors of the matrix A, with the i-th column of Z
78: *> holding the eigenvector associated with D(i).
79: *> If JOBZ = 'N', then Z is not referenced.
80: *> \endverbatim
81: *>
82: *> \param[in] LDZ
83: *> \verbatim
84: *> LDZ is INTEGER
85: *> The leading dimension of the array Z. LDZ >= 1, and if
86: *> JOBZ = 'V', LDZ >= max(1,N).
87: *> \endverbatim
88: *>
89: *> \param[out] WORK
90: *> \verbatim
91: *> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2))
92: *> If JOBZ = 'N', WORK is not referenced.
93: *> \endverbatim
94: *>
95: *> \param[out] INFO
96: *> \verbatim
97: *> INFO is INTEGER
98: *> = 0: successful exit
99: *> < 0: if INFO = -i, the i-th argument had an illegal value
100: *> > 0: if INFO = i, the algorithm failed to converge; i
101: *> off-diagonal elements of E did not converge to zero.
102: *> \endverbatim
103: *
104: * Authors:
105: * ========
106: *
1.14 bertrand 107: *> \author Univ. of Tennessee
108: *> \author Univ. of California Berkeley
109: *> \author Univ. of Colorado Denver
110: *> \author NAG Ltd.
1.8 bertrand 111: *
112: *> \ingroup doubleOTHEReigen
113: *
114: * =====================================================================
1.1 bertrand 115: SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
116: *
1.17 ! bertrand 117: * -- LAPACK driver routine --
1.1 bertrand 118: * -- LAPACK is a software package provided by Univ. of Tennessee, --
119: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120: *
121: * .. Scalar Arguments ..
122: CHARACTER JOBZ
123: INTEGER INFO, LDZ, N
124: * ..
125: * .. Array Arguments ..
126: DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
127: * ..
128: *
129: * =====================================================================
130: *
131: * .. Parameters ..
132: DOUBLE PRECISION ZERO, ONE
133: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
134: * ..
135: * .. Local Scalars ..
136: LOGICAL WANTZ
137: INTEGER IMAX, ISCALE
138: DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
139: $ TNRM
140: * ..
141: * .. External Functions ..
142: LOGICAL LSAME
143: DOUBLE PRECISION DLAMCH, DLANST
144: EXTERNAL LSAME, DLAMCH, DLANST
145: * ..
146: * .. External Subroutines ..
147: EXTERNAL DSCAL, DSTEQR, DSTERF, XERBLA
148: * ..
149: * .. Intrinsic Functions ..
150: INTRINSIC SQRT
151: * ..
152: * .. Executable Statements ..
153: *
154: * Test the input parameters.
155: *
156: WANTZ = LSAME( JOBZ, 'V' )
157: *
158: INFO = 0
159: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
160: INFO = -1
161: ELSE IF( N.LT.0 ) THEN
162: INFO = -2
163: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
164: INFO = -6
165: END IF
166: *
167: IF( INFO.NE.0 ) THEN
168: CALL XERBLA( 'DSTEV ', -INFO )
169: RETURN
170: END IF
171: *
172: * Quick return if possible
173: *
174: IF( N.EQ.0 )
175: $ RETURN
176: *
177: IF( N.EQ.1 ) THEN
178: IF( WANTZ )
179: $ Z( 1, 1 ) = ONE
180: RETURN
181: END IF
182: *
183: * Get machine constants.
184: *
185: SAFMIN = DLAMCH( 'Safe minimum' )
186: EPS = DLAMCH( 'Precision' )
187: SMLNUM = SAFMIN / EPS
188: BIGNUM = ONE / SMLNUM
189: RMIN = SQRT( SMLNUM )
190: RMAX = SQRT( BIGNUM )
191: *
192: * Scale matrix to allowable range, if necessary.
193: *
194: ISCALE = 0
195: TNRM = DLANST( 'M', N, D, E )
196: IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
197: ISCALE = 1
198: SIGMA = RMIN / TNRM
199: ELSE IF( TNRM.GT.RMAX ) THEN
200: ISCALE = 1
201: SIGMA = RMAX / TNRM
202: END IF
203: IF( ISCALE.EQ.1 ) THEN
204: CALL DSCAL( N, SIGMA, D, 1 )
205: CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
206: END IF
207: *
208: * For eigenvalues only, call DSTERF. For eigenvalues and
209: * eigenvectors, call DSTEQR.
210: *
211: IF( .NOT.WANTZ ) THEN
212: CALL DSTERF( N, D, E, INFO )
213: ELSE
214: CALL DSTEQR( 'I', N, D, E, Z, LDZ, WORK, INFO )
215: END IF
216: *
217: * If matrix was scaled, then rescale eigenvalues appropriately.
218: *
219: IF( ISCALE.EQ.1 ) THEN
220: IF( INFO.EQ.0 ) THEN
221: IMAX = N
222: ELSE
223: IMAX = INFO - 1
224: END IF
225: CALL DSCAL( IMAX, ONE / SIGMA, D, 1 )
226: END IF
227: *
228: RETURN
229: *
230: * End of DSTEV
231: *
232: END
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