1 SUBROUTINE DSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
2 $ M, W, Z, LDZ, WORK, IWORK, IFAIL, 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, RANGE
11 INTEGER IL, INFO, IU, LDZ, M, N
12 DOUBLE PRECISION ABSTOL, VL, VU
13 * ..
14 * .. Array Arguments ..
15 INTEGER IFAIL( * ), IWORK( * )
16 DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * DSTEVX computes selected eigenvalues and, optionally, eigenvectors
23 * of a real symmetric tridiagonal matrix A. Eigenvalues and
24 * eigenvectors can be selected by specifying either a range of values
25 * or a range of indices for the desired eigenvalues.
26 *
27 * Arguments
28 * =========
29 *
30 * JOBZ (input) CHARACTER*1
31 * = 'N': Compute eigenvalues only;
32 * = 'V': Compute eigenvalues and eigenvectors.
33 *
34 * RANGE (input) CHARACTER*1
35 * = 'A': all eigenvalues will be found.
36 * = 'V': all eigenvalues in the half-open interval (VL,VU]
37 * will be found.
38 * = 'I': the IL-th through IU-th eigenvalues will be found.
39 *
40 * N (input) INTEGER
41 * The order of the matrix. N >= 0.
42 *
43 * D (input/output) DOUBLE PRECISION array, dimension (N)
44 * On entry, the n diagonal elements of the tridiagonal matrix
45 * A.
46 * On exit, D may be multiplied by a constant factor chosen
47 * to avoid over/underflow in computing the eigenvalues.
48 *
49 * E (input/output) DOUBLE PRECISION array, dimension (max(1,N-1))
50 * On entry, the (n-1) subdiagonal elements of the tridiagonal
51 * matrix A in elements 1 to N-1 of E.
52 * On exit, E may be multiplied by a constant factor chosen
53 * to avoid over/underflow in computing the eigenvalues.
54 *
55 * VL (input) DOUBLE PRECISION
56 * VU (input) DOUBLE PRECISION
57 * If RANGE='V', the lower and upper bounds of the interval to
58 * be searched for eigenvalues. VL < VU.
59 * Not referenced if RANGE = 'A' or 'I'.
60 *
61 * IL (input) INTEGER
62 * IU (input) INTEGER
63 * If RANGE='I', the indices (in ascending order) of the
64 * smallest and largest eigenvalues to be returned.
65 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
66 * Not referenced if RANGE = 'A' or 'V'.
67 *
68 * ABSTOL (input) DOUBLE PRECISION
69 * The absolute error tolerance for the eigenvalues.
70 * An approximate eigenvalue is accepted as converged
71 * when it is determined to lie in an interval [a,b]
72 * of width less than or equal to
73 *
74 * ABSTOL + EPS * max( |a|,|b| ) ,
75 *
76 * where EPS is the machine precision. If ABSTOL is less
77 * than or equal to zero, then EPS*|T| will be used in
78 * its place, where |T| is the 1-norm of the tridiagonal
79 * matrix.
80 *
81 * Eigenvalues will be computed most accurately when ABSTOL is
82 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
83 * If this routine returns with INFO>0, indicating that some
84 * eigenvectors did not converge, try setting ABSTOL to
85 * 2*DLAMCH('S').
86 *
87 * See "Computing Small Singular Values of Bidiagonal Matrices
88 * with Guaranteed High Relative Accuracy," by Demmel and
89 * Kahan, LAPACK Working Note #3.
90 *
91 * M (output) INTEGER
92 * The total number of eigenvalues found. 0 <= M <= N.
93 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
94 *
95 * W (output) DOUBLE PRECISION array, dimension (N)
96 * The first M elements contain the selected eigenvalues in
97 * ascending order.
98 *
99 * Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M) )
100 * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
101 * contain the orthonormal eigenvectors of the matrix A
102 * corresponding to the selected eigenvalues, with the i-th
103 * column of Z holding the eigenvector associated with W(i).
104 * If an eigenvector fails to converge (INFO > 0), then that
105 * column of Z contains the latest approximation to the
106 * eigenvector, and the index of the eigenvector is returned
107 * in IFAIL. If JOBZ = 'N', then Z is not referenced.
108 * Note: the user must ensure that at least max(1,M) columns are
109 * supplied in the array Z; if RANGE = 'V', the exact value of M
110 * is not known in advance and an upper bound must be used.
111 *
112 * LDZ (input) INTEGER
113 * The leading dimension of the array Z. LDZ >= 1, and if
114 * JOBZ = 'V', LDZ >= max(1,N).
115 *
116 * WORK (workspace) DOUBLE PRECISION array, dimension (5*N)
117 *
118 * IWORK (workspace) INTEGER array, dimension (5*N)
119 *
120 * IFAIL (output) INTEGER array, dimension (N)
121 * If JOBZ = 'V', then if INFO = 0, the first M elements of
122 * IFAIL are zero. If INFO > 0, then IFAIL contains the
123 * indices of the eigenvectors that failed to converge.
124 * If JOBZ = 'N', then IFAIL is not referenced.
125 *
126 * INFO (output) INTEGER
127 * = 0: successful exit
128 * < 0: if INFO = -i, the i-th argument had an illegal value
129 * > 0: if INFO = i, then i eigenvectors failed to converge.
130 * Their indices are stored in array IFAIL.
131 *
132 * =====================================================================
133 *
134 * .. Parameters ..
135 DOUBLE PRECISION ZERO, ONE
136 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
137 * ..
138 * .. Local Scalars ..
139 LOGICAL ALLEIG, INDEIG, TEST, VALEIG, WANTZ
140 CHARACTER ORDER
141 INTEGER I, IMAX, INDIBL, INDISP, INDIWO, INDWRK,
142 $ ISCALE, ITMP1, J, JJ, NSPLIT
143 DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
144 $ TMP1, TNRM, VLL, VUU
145 * ..
146 * .. External Functions ..
147 LOGICAL LSAME
148 DOUBLE PRECISION DLAMCH, DLANST
149 EXTERNAL LSAME, DLAMCH, DLANST
150 * ..
151 * .. External Subroutines ..
152 EXTERNAL DCOPY, DSCAL, DSTEBZ, DSTEIN, DSTEQR, DSTERF,
153 $ DSWAP, XERBLA
154 * ..
155 * .. Intrinsic Functions ..
156 INTRINSIC MAX, MIN, SQRT
157 * ..
158 * .. Executable Statements ..
159 *
160 * Test the input parameters.
161 *
162 WANTZ = LSAME( JOBZ, 'V' )
163 ALLEIG = LSAME( RANGE, 'A' )
164 VALEIG = LSAME( RANGE, 'V' )
165 INDEIG = LSAME( RANGE, 'I' )
166 *
167 INFO = 0
168 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
169 INFO = -1
170 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
171 INFO = -2
172 ELSE IF( N.LT.0 ) THEN
173 INFO = -3
174 ELSE
175 IF( VALEIG ) THEN
176 IF( N.GT.0 .AND. VU.LE.VL )
177 $ INFO = -7
178 ELSE IF( INDEIG ) THEN
179 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
180 INFO = -8
181 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
182 INFO = -9
183 END IF
184 END IF
185 END IF
186 IF( INFO.EQ.0 ) THEN
187 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
188 $ INFO = -14
189 END IF
190 *
191 IF( INFO.NE.0 ) THEN
192 CALL XERBLA( 'DSTEVX', -INFO )
193 RETURN
194 END IF
195 *
196 * Quick return if possible
197 *
198 M = 0
199 IF( N.EQ.0 )
200 $ RETURN
201 *
202 IF( N.EQ.1 ) THEN
203 IF( ALLEIG .OR. INDEIG ) THEN
204 M = 1
205 W( 1 ) = D( 1 )
206 ELSE
207 IF( VL.LT.D( 1 ) .AND. VU.GE.D( 1 ) ) THEN
208 M = 1
209 W( 1 ) = D( 1 )
210 END IF
211 END IF
212 IF( WANTZ )
213 $ Z( 1, 1 ) = ONE
214 RETURN
215 END IF
216 *
217 * Get machine constants.
218 *
219 SAFMIN = DLAMCH( 'Safe minimum' )
220 EPS = DLAMCH( 'Precision' )
221 SMLNUM = SAFMIN / EPS
222 BIGNUM = ONE / SMLNUM
223 RMIN = SQRT( SMLNUM )
224 RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
225 *
226 * Scale matrix to allowable range, if necessary.
227 *
228 ISCALE = 0
229 IF( VALEIG ) THEN
230 VLL = VL
231 VUU = VU
232 ELSE
233 VLL = ZERO
234 VUU = ZERO
235 END IF
236 TNRM = DLANST( 'M', N, D, E )
237 IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
238 ISCALE = 1
239 SIGMA = RMIN / TNRM
240 ELSE IF( TNRM.GT.RMAX ) THEN
241 ISCALE = 1
242 SIGMA = RMAX / TNRM
243 END IF
244 IF( ISCALE.EQ.1 ) THEN
245 CALL DSCAL( N, SIGMA, D, 1 )
246 CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
247 IF( VALEIG ) THEN
248 VLL = VL*SIGMA
249 VUU = VU*SIGMA
250 END IF
251 END IF
252 *
253 * If all eigenvalues are desired and ABSTOL is less than zero, then
254 * call DSTERF or SSTEQR. If this fails for some eigenvalue, then
255 * try DSTEBZ.
256 *
257 TEST = .FALSE.
258 IF( INDEIG ) THEN
259 IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
260 TEST = .TRUE.
261 END IF
262 END IF
263 IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
264 CALL DCOPY( N, D, 1, W, 1 )
265 CALL DCOPY( N-1, E( 1 ), 1, WORK( 1 ), 1 )
266 INDWRK = N + 1
267 IF( .NOT.WANTZ ) THEN
268 CALL DSTERF( N, W, WORK, INFO )
269 ELSE
270 CALL DSTEQR( 'I', N, W, WORK, Z, LDZ, WORK( INDWRK ), INFO )
271 IF( INFO.EQ.0 ) THEN
272 DO 10 I = 1, N
273 IFAIL( I ) = 0
274 10 CONTINUE
275 END IF
276 END IF
277 IF( INFO.EQ.0 ) THEN
278 M = N
279 GO TO 20
280 END IF
281 INFO = 0
282 END IF
283 *
284 * Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN.
285 *
286 IF( WANTZ ) THEN
287 ORDER = 'B'
288 ELSE
289 ORDER = 'E'
290 END IF
291 INDWRK = 1
292 INDIBL = 1
293 INDISP = INDIBL + N
294 INDIWO = INDISP + N
295 CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTOL, D, E, M,
296 $ NSPLIT, W, IWORK( INDIBL ), IWORK( INDISP ),
297 $ WORK( INDWRK ), IWORK( INDIWO ), INFO )
298 *
299 IF( WANTZ ) THEN
300 CALL DSTEIN( N, D, E, M, W, IWORK( INDIBL ), IWORK( INDISP ),
301 $ Z, LDZ, WORK( INDWRK ), IWORK( INDIWO ), IFAIL,
302 $ INFO )
303 END IF
304 *
305 * If matrix was scaled, then rescale eigenvalues appropriately.
306 *
307 20 CONTINUE
308 IF( ISCALE.EQ.1 ) THEN
309 IF( INFO.EQ.0 ) THEN
310 IMAX = M
311 ELSE
312 IMAX = INFO - 1
313 END IF
314 CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
315 END IF
316 *
317 * If eigenvalues are not in order, then sort them, along with
318 * eigenvectors.
319 *
320 IF( WANTZ ) THEN
321 DO 40 J = 1, M - 1
322 I = 0
323 TMP1 = W( J )
324 DO 30 JJ = J + 1, M
325 IF( W( JJ ).LT.TMP1 ) THEN
326 I = JJ
327 TMP1 = W( JJ )
328 END IF
329 30 CONTINUE
330 *
331 IF( I.NE.0 ) THEN
332 ITMP1 = IWORK( INDIBL+I-1 )
333 W( I ) = W( J )
334 IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
335 W( J ) = TMP1
336 IWORK( INDIBL+J-1 ) = ITMP1
337 CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
338 IF( INFO.NE.0 ) THEN
339 ITMP1 = IFAIL( I )
340 IFAIL( I ) = IFAIL( J )
341 IFAIL( J ) = ITMP1
342 END IF
343 END IF
344 40 CONTINUE
345 END IF
346 *
347 RETURN
348 *
349 * End of DSTEVX
350 *
351 END
2 $ M, W, Z, LDZ, WORK, IWORK, IFAIL, 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, RANGE
11 INTEGER IL, INFO, IU, LDZ, M, N
12 DOUBLE PRECISION ABSTOL, VL, VU
13 * ..
14 * .. Array Arguments ..
15 INTEGER IFAIL( * ), IWORK( * )
16 DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * DSTEVX computes selected eigenvalues and, optionally, eigenvectors
23 * of a real symmetric tridiagonal matrix A. Eigenvalues and
24 * eigenvectors can be selected by specifying either a range of values
25 * or a range of indices for the desired eigenvalues.
26 *
27 * Arguments
28 * =========
29 *
30 * JOBZ (input) CHARACTER*1
31 * = 'N': Compute eigenvalues only;
32 * = 'V': Compute eigenvalues and eigenvectors.
33 *
34 * RANGE (input) CHARACTER*1
35 * = 'A': all eigenvalues will be found.
36 * = 'V': all eigenvalues in the half-open interval (VL,VU]
37 * will be found.
38 * = 'I': the IL-th through IU-th eigenvalues will be found.
39 *
40 * N (input) INTEGER
41 * The order of the matrix. N >= 0.
42 *
43 * D (input/output) DOUBLE PRECISION array, dimension (N)
44 * On entry, the n diagonal elements of the tridiagonal matrix
45 * A.
46 * On exit, D may be multiplied by a constant factor chosen
47 * to avoid over/underflow in computing the eigenvalues.
48 *
49 * E (input/output) DOUBLE PRECISION array, dimension (max(1,N-1))
50 * On entry, the (n-1) subdiagonal elements of the tridiagonal
51 * matrix A in elements 1 to N-1 of E.
52 * On exit, E may be multiplied by a constant factor chosen
53 * to avoid over/underflow in computing the eigenvalues.
54 *
55 * VL (input) DOUBLE PRECISION
56 * VU (input) DOUBLE PRECISION
57 * If RANGE='V', the lower and upper bounds of the interval to
58 * be searched for eigenvalues. VL < VU.
59 * Not referenced if RANGE = 'A' or 'I'.
60 *
61 * IL (input) INTEGER
62 * IU (input) INTEGER
63 * If RANGE='I', the indices (in ascending order) of the
64 * smallest and largest eigenvalues to be returned.
65 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
66 * Not referenced if RANGE = 'A' or 'V'.
67 *
68 * ABSTOL (input) DOUBLE PRECISION
69 * The absolute error tolerance for the eigenvalues.
70 * An approximate eigenvalue is accepted as converged
71 * when it is determined to lie in an interval [a,b]
72 * of width less than or equal to
73 *
74 * ABSTOL + EPS * max( |a|,|b| ) ,
75 *
76 * where EPS is the machine precision. If ABSTOL is less
77 * than or equal to zero, then EPS*|T| will be used in
78 * its place, where |T| is the 1-norm of the tridiagonal
79 * matrix.
80 *
81 * Eigenvalues will be computed most accurately when ABSTOL is
82 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
83 * If this routine returns with INFO>0, indicating that some
84 * eigenvectors did not converge, try setting ABSTOL to
85 * 2*DLAMCH('S').
86 *
87 * See "Computing Small Singular Values of Bidiagonal Matrices
88 * with Guaranteed High Relative Accuracy," by Demmel and
89 * Kahan, LAPACK Working Note #3.
90 *
91 * M (output) INTEGER
92 * The total number of eigenvalues found. 0 <= M <= N.
93 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
94 *
95 * W (output) DOUBLE PRECISION array, dimension (N)
96 * The first M elements contain the selected eigenvalues in
97 * ascending order.
98 *
99 * Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M) )
100 * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
101 * contain the orthonormal eigenvectors of the matrix A
102 * corresponding to the selected eigenvalues, with the i-th
103 * column of Z holding the eigenvector associated with W(i).
104 * If an eigenvector fails to converge (INFO > 0), then that
105 * column of Z contains the latest approximation to the
106 * eigenvector, and the index of the eigenvector is returned
107 * in IFAIL. If JOBZ = 'N', then Z is not referenced.
108 * Note: the user must ensure that at least max(1,M) columns are
109 * supplied in the array Z; if RANGE = 'V', the exact value of M
110 * is not known in advance and an upper bound must be used.
111 *
112 * LDZ (input) INTEGER
113 * The leading dimension of the array Z. LDZ >= 1, and if
114 * JOBZ = 'V', LDZ >= max(1,N).
115 *
116 * WORK (workspace) DOUBLE PRECISION array, dimension (5*N)
117 *
118 * IWORK (workspace) INTEGER array, dimension (5*N)
119 *
120 * IFAIL (output) INTEGER array, dimension (N)
121 * If JOBZ = 'V', then if INFO = 0, the first M elements of
122 * IFAIL are zero. If INFO > 0, then IFAIL contains the
123 * indices of the eigenvectors that failed to converge.
124 * If JOBZ = 'N', then IFAIL is not referenced.
125 *
126 * INFO (output) INTEGER
127 * = 0: successful exit
128 * < 0: if INFO = -i, the i-th argument had an illegal value
129 * > 0: if INFO = i, then i eigenvectors failed to converge.
130 * Their indices are stored in array IFAIL.
131 *
132 * =====================================================================
133 *
134 * .. Parameters ..
135 DOUBLE PRECISION ZERO, ONE
136 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
137 * ..
138 * .. Local Scalars ..
139 LOGICAL ALLEIG, INDEIG, TEST, VALEIG, WANTZ
140 CHARACTER ORDER
141 INTEGER I, IMAX, INDIBL, INDISP, INDIWO, INDWRK,
142 $ ISCALE, ITMP1, J, JJ, NSPLIT
143 DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
144 $ TMP1, TNRM, VLL, VUU
145 * ..
146 * .. External Functions ..
147 LOGICAL LSAME
148 DOUBLE PRECISION DLAMCH, DLANST
149 EXTERNAL LSAME, DLAMCH, DLANST
150 * ..
151 * .. External Subroutines ..
152 EXTERNAL DCOPY, DSCAL, DSTEBZ, DSTEIN, DSTEQR, DSTERF,
153 $ DSWAP, XERBLA
154 * ..
155 * .. Intrinsic Functions ..
156 INTRINSIC MAX, MIN, SQRT
157 * ..
158 * .. Executable Statements ..
159 *
160 * Test the input parameters.
161 *
162 WANTZ = LSAME( JOBZ, 'V' )
163 ALLEIG = LSAME( RANGE, 'A' )
164 VALEIG = LSAME( RANGE, 'V' )
165 INDEIG = LSAME( RANGE, 'I' )
166 *
167 INFO = 0
168 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
169 INFO = -1
170 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
171 INFO = -2
172 ELSE IF( N.LT.0 ) THEN
173 INFO = -3
174 ELSE
175 IF( VALEIG ) THEN
176 IF( N.GT.0 .AND. VU.LE.VL )
177 $ INFO = -7
178 ELSE IF( INDEIG ) THEN
179 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
180 INFO = -8
181 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
182 INFO = -9
183 END IF
184 END IF
185 END IF
186 IF( INFO.EQ.0 ) THEN
187 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
188 $ INFO = -14
189 END IF
190 *
191 IF( INFO.NE.0 ) THEN
192 CALL XERBLA( 'DSTEVX', -INFO )
193 RETURN
194 END IF
195 *
196 * Quick return if possible
197 *
198 M = 0
199 IF( N.EQ.0 )
200 $ RETURN
201 *
202 IF( N.EQ.1 ) THEN
203 IF( ALLEIG .OR. INDEIG ) THEN
204 M = 1
205 W( 1 ) = D( 1 )
206 ELSE
207 IF( VL.LT.D( 1 ) .AND. VU.GE.D( 1 ) ) THEN
208 M = 1
209 W( 1 ) = D( 1 )
210 END IF
211 END IF
212 IF( WANTZ )
213 $ Z( 1, 1 ) = ONE
214 RETURN
215 END IF
216 *
217 * Get machine constants.
218 *
219 SAFMIN = DLAMCH( 'Safe minimum' )
220 EPS = DLAMCH( 'Precision' )
221 SMLNUM = SAFMIN / EPS
222 BIGNUM = ONE / SMLNUM
223 RMIN = SQRT( SMLNUM )
224 RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
225 *
226 * Scale matrix to allowable range, if necessary.
227 *
228 ISCALE = 0
229 IF( VALEIG ) THEN
230 VLL = VL
231 VUU = VU
232 ELSE
233 VLL = ZERO
234 VUU = ZERO
235 END IF
236 TNRM = DLANST( 'M', N, D, E )
237 IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
238 ISCALE = 1
239 SIGMA = RMIN / TNRM
240 ELSE IF( TNRM.GT.RMAX ) THEN
241 ISCALE = 1
242 SIGMA = RMAX / TNRM
243 END IF
244 IF( ISCALE.EQ.1 ) THEN
245 CALL DSCAL( N, SIGMA, D, 1 )
246 CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
247 IF( VALEIG ) THEN
248 VLL = VL*SIGMA
249 VUU = VU*SIGMA
250 END IF
251 END IF
252 *
253 * If all eigenvalues are desired and ABSTOL is less than zero, then
254 * call DSTERF or SSTEQR. If this fails for some eigenvalue, then
255 * try DSTEBZ.
256 *
257 TEST = .FALSE.
258 IF( INDEIG ) THEN
259 IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
260 TEST = .TRUE.
261 END IF
262 END IF
263 IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
264 CALL DCOPY( N, D, 1, W, 1 )
265 CALL DCOPY( N-1, E( 1 ), 1, WORK( 1 ), 1 )
266 INDWRK = N + 1
267 IF( .NOT.WANTZ ) THEN
268 CALL DSTERF( N, W, WORK, INFO )
269 ELSE
270 CALL DSTEQR( 'I', N, W, WORK, Z, LDZ, WORK( INDWRK ), INFO )
271 IF( INFO.EQ.0 ) THEN
272 DO 10 I = 1, N
273 IFAIL( I ) = 0
274 10 CONTINUE
275 END IF
276 END IF
277 IF( INFO.EQ.0 ) THEN
278 M = N
279 GO TO 20
280 END IF
281 INFO = 0
282 END IF
283 *
284 * Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN.
285 *
286 IF( WANTZ ) THEN
287 ORDER = 'B'
288 ELSE
289 ORDER = 'E'
290 END IF
291 INDWRK = 1
292 INDIBL = 1
293 INDISP = INDIBL + N
294 INDIWO = INDISP + N
295 CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTOL, D, E, M,
296 $ NSPLIT, W, IWORK( INDIBL ), IWORK( INDISP ),
297 $ WORK( INDWRK ), IWORK( INDIWO ), INFO )
298 *
299 IF( WANTZ ) THEN
300 CALL DSTEIN( N, D, E, M, W, IWORK( INDIBL ), IWORK( INDISP ),
301 $ Z, LDZ, WORK( INDWRK ), IWORK( INDIWO ), IFAIL,
302 $ INFO )
303 END IF
304 *
305 * If matrix was scaled, then rescale eigenvalues appropriately.
306 *
307 20 CONTINUE
308 IF( ISCALE.EQ.1 ) THEN
309 IF( INFO.EQ.0 ) THEN
310 IMAX = M
311 ELSE
312 IMAX = INFO - 1
313 END IF
314 CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
315 END IF
316 *
317 * If eigenvalues are not in order, then sort them, along with
318 * eigenvectors.
319 *
320 IF( WANTZ ) THEN
321 DO 40 J = 1, M - 1
322 I = 0
323 TMP1 = W( J )
324 DO 30 JJ = J + 1, M
325 IF( W( JJ ).LT.TMP1 ) THEN
326 I = JJ
327 TMP1 = W( JJ )
328 END IF
329 30 CONTINUE
330 *
331 IF( I.NE.0 ) THEN
332 ITMP1 = IWORK( INDIBL+I-1 )
333 W( I ) = W( J )
334 IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
335 W( J ) = TMP1
336 IWORK( INDIBL+J-1 ) = ITMP1
337 CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
338 IF( INFO.NE.0 ) THEN
339 ITMP1 = IFAIL( I )
340 IFAIL( I ) = IFAIL( J )
341 IFAIL( J ) = ITMP1
342 END IF
343 END IF
344 40 CONTINUE
345 END IF
346 *
347 RETURN
348 *
349 * End of DSTEVX
350 *
351 END