1 SUBROUTINE ZHPEVX( JOBZ, RANGE, UPLO, N, AP, VL, VU, IL, IU,
2 $ ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK,
3 $ IFAIL, INFO )
4 *
5 * -- LAPACK driver routine (version 3.2) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * November 2006
9 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBZ, RANGE, UPLO
12 INTEGER IL, INFO, IU, LDZ, M, N
13 DOUBLE PRECISION ABSTOL, VL, VU
14 * ..
15 * .. Array Arguments ..
16 INTEGER IFAIL( * ), IWORK( * )
17 DOUBLE PRECISION RWORK( * ), W( * )
18 COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * ZHPEVX computes selected eigenvalues and, optionally, eigenvectors
25 * of a complex Hermitian matrix A in packed storage.
26 * Eigenvalues/vectors can be selected by specifying either a range of
27 * values or a range of indices for the desired eigenvalues.
28 *
29 * Arguments
30 * =========
31 *
32 * JOBZ (input) CHARACTER*1
33 * = 'N': Compute eigenvalues only;
34 * = 'V': Compute eigenvalues and eigenvectors.
35 *
36 * RANGE (input) CHARACTER*1
37 * = 'A': all eigenvalues will be found;
38 * = 'V': all eigenvalues in the half-open interval (VL,VU]
39 * will be found;
40 * = 'I': the IL-th through IU-th eigenvalues will be found.
41 *
42 * UPLO (input) CHARACTER*1
43 * = 'U': Upper triangle of A is stored;
44 * = 'L': Lower triangle of A is stored.
45 *
46 * N (input) INTEGER
47 * The order of the matrix A. N >= 0.
48 *
49 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
50 * On entry, the upper or lower triangle of the Hermitian matrix
51 * A, packed columnwise in a linear array. The j-th column of A
52 * is stored in the array AP as follows:
53 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
54 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
55 *
56 * On exit, AP is overwritten by values generated during the
57 * reduction to tridiagonal form. If UPLO = 'U', the diagonal
58 * and first superdiagonal of the tridiagonal matrix T overwrite
59 * the corresponding elements of A, and if UPLO = 'L', the
60 * diagonal and first subdiagonal of T overwrite the
61 * corresponding elements of A.
62 *
63 * VL (input) DOUBLE PRECISION
64 * VU (input) DOUBLE PRECISION
65 * If RANGE='V', the lower and upper bounds of the interval to
66 * be searched for eigenvalues. VL < VU.
67 * Not referenced if RANGE = 'A' or 'I'.
68 *
69 * IL (input) INTEGER
70 * IU (input) INTEGER
71 * If RANGE='I', the indices (in ascending order) of the
72 * smallest and largest eigenvalues to be returned.
73 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
74 * Not referenced if RANGE = 'A' or 'V'.
75 *
76 * ABSTOL (input) DOUBLE PRECISION
77 * The absolute error tolerance for the eigenvalues.
78 * An approximate eigenvalue is accepted as converged
79 * when it is determined to lie in an interval [a,b]
80 * of width less than or equal to
81 *
82 * ABSTOL + EPS * max( |a|,|b| ) ,
83 *
84 * where EPS is the machine precision. If ABSTOL is less than
85 * or equal to zero, then EPS*|T| will be used in its place,
86 * where |T| is the 1-norm of the tridiagonal matrix obtained
87 * by reducing AP to tridiagonal form.
88 *
89 * Eigenvalues will be computed most accurately when ABSTOL is
90 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
91 * If this routine returns with INFO>0, indicating that some
92 * eigenvectors did not converge, try setting ABSTOL to
93 * 2*DLAMCH('S').
94 *
95 * See "Computing Small Singular Values of Bidiagonal Matrices
96 * with Guaranteed High Relative Accuracy," by Demmel and
97 * Kahan, LAPACK Working Note #3.
98 *
99 * M (output) INTEGER
100 * The total number of eigenvalues found. 0 <= M <= N.
101 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
102 *
103 * W (output) DOUBLE PRECISION array, dimension (N)
104 * If INFO = 0, the selected eigenvalues in ascending order.
105 *
106 * Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
107 * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
108 * contain the orthonormal eigenvectors of the matrix A
109 * corresponding to the selected eigenvalues, with the i-th
110 * column of Z holding the eigenvector associated with W(i).
111 * If an eigenvector fails to converge, then that column of Z
112 * contains the latest approximation to the eigenvector, and
113 * the index of the eigenvector is returned in IFAIL.
114 * If JOBZ = 'N', then Z is not referenced.
115 * Note: the user must ensure that at least max(1,M) columns are
116 * supplied in the array Z; if RANGE = 'V', the exact value of M
117 * is not known in advance and an upper bound must be used.
118 *
119 * LDZ (input) INTEGER
120 * The leading dimension of the array Z. LDZ >= 1, and if
121 * JOBZ = 'V', LDZ >= max(1,N).
122 *
123 * WORK (workspace) COMPLEX*16 array, dimension (2*N)
124 *
125 * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
126 *
127 * IWORK (workspace) INTEGER array, dimension (5*N)
128 *
129 * IFAIL (output) INTEGER array, dimension (N)
130 * If JOBZ = 'V', then if INFO = 0, the first M elements of
131 * IFAIL are zero. If INFO > 0, then IFAIL contains the
132 * indices of the eigenvectors that failed to converge.
133 * If JOBZ = 'N', then IFAIL is not referenced.
134 *
135 * INFO (output) INTEGER
136 * = 0: successful exit
137 * < 0: if INFO = -i, the i-th argument had an illegal value
138 * > 0: if INFO = i, then i eigenvectors failed to converge.
139 * Their indices are stored in array IFAIL.
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144 DOUBLE PRECISION ZERO, ONE
145 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
146 COMPLEX*16 CONE
147 PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) )
148 * ..
149 * .. Local Scalars ..
150 LOGICAL ALLEIG, INDEIG, TEST, VALEIG, WANTZ
151 CHARACTER ORDER
152 INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
153 $ INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE,
154 $ ITMP1, J, JJ, NSPLIT
155 DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
156 $ SIGMA, SMLNUM, TMP1, VLL, VUU
157 * ..
158 * .. External Functions ..
159 LOGICAL LSAME
160 DOUBLE PRECISION DLAMCH, ZLANHP
161 EXTERNAL LSAME, DLAMCH, ZLANHP
162 * ..
163 * .. External Subroutines ..
164 EXTERNAL DCOPY, DSCAL, DSTEBZ, DSTERF, XERBLA, ZDSCAL,
165 $ ZHPTRD, ZSTEIN, ZSTEQR, ZSWAP, ZUPGTR, ZUPMTR
166 * ..
167 * .. Intrinsic Functions ..
168 INTRINSIC DBLE, MAX, MIN, SQRT
169 * ..
170 * .. Executable Statements ..
171 *
172 * Test the input parameters.
173 *
174 WANTZ = LSAME( JOBZ, 'V' )
175 ALLEIG = LSAME( RANGE, 'A' )
176 VALEIG = LSAME( RANGE, 'V' )
177 INDEIG = LSAME( RANGE, 'I' )
178 *
179 INFO = 0
180 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
181 INFO = -1
182 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
183 INFO = -2
184 ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) )
185 $ THEN
186 INFO = -3
187 ELSE IF( N.LT.0 ) THEN
188 INFO = -4
189 ELSE
190 IF( VALEIG ) THEN
191 IF( N.GT.0 .AND. VU.LE.VL )
192 $ INFO = -7
193 ELSE IF( INDEIG ) THEN
194 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
195 INFO = -8
196 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
197 INFO = -9
198 END IF
199 END IF
200 END IF
201 IF( INFO.EQ.0 ) THEN
202 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
203 $ INFO = -14
204 END IF
205 *
206 IF( INFO.NE.0 ) THEN
207 CALL XERBLA( 'ZHPEVX', -INFO )
208 RETURN
209 END IF
210 *
211 * Quick return if possible
212 *
213 M = 0
214 IF( N.EQ.0 )
215 $ RETURN
216 *
217 IF( N.EQ.1 ) THEN
218 IF( ALLEIG .OR. INDEIG ) THEN
219 M = 1
220 W( 1 ) = AP( 1 )
221 ELSE
222 IF( VL.LT.DBLE( AP( 1 ) ) .AND. VU.GE.DBLE( AP( 1 ) ) ) THEN
223 M = 1
224 W( 1 ) = AP( 1 )
225 END IF
226 END IF
227 IF( WANTZ )
228 $ Z( 1, 1 ) = CONE
229 RETURN
230 END IF
231 *
232 * Get machine constants.
233 *
234 SAFMIN = DLAMCH( 'Safe minimum' )
235 EPS = DLAMCH( 'Precision' )
236 SMLNUM = SAFMIN / EPS
237 BIGNUM = ONE / SMLNUM
238 RMIN = SQRT( SMLNUM )
239 RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
240 *
241 * Scale matrix to allowable range, if necessary.
242 *
243 ISCALE = 0
244 ABSTLL = ABSTOL
245 IF( VALEIG ) THEN
246 VLL = VL
247 VUU = VU
248 ELSE
249 VLL = ZERO
250 VUU = ZERO
251 END IF
252 ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK )
253 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
254 ISCALE = 1
255 SIGMA = RMIN / ANRM
256 ELSE IF( ANRM.GT.RMAX ) THEN
257 ISCALE = 1
258 SIGMA = RMAX / ANRM
259 END IF
260 IF( ISCALE.EQ.1 ) THEN
261 CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
262 IF( ABSTOL.GT.0 )
263 $ ABSTLL = ABSTOL*SIGMA
264 IF( VALEIG ) THEN
265 VLL = VL*SIGMA
266 VUU = VU*SIGMA
267 END IF
268 END IF
269 *
270 * Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form.
271 *
272 INDD = 1
273 INDE = INDD + N
274 INDRWK = INDE + N
275 INDTAU = 1
276 INDWRK = INDTAU + N
277 CALL ZHPTRD( UPLO, N, AP, RWORK( INDD ), RWORK( INDE ),
278 $ WORK( INDTAU ), IINFO )
279 *
280 * If all eigenvalues are desired and ABSTOL is less than or equal
281 * to zero, then call DSTERF or ZUPGTR and ZSTEQR. If this fails
282 * for some eigenvalue, then try DSTEBZ.
283 *
284 TEST = .FALSE.
285 IF (INDEIG) THEN
286 IF (IL.EQ.1 .AND. IU.EQ.N) THEN
287 TEST = .TRUE.
288 END IF
289 END IF
290 IF ((ALLEIG .OR. TEST) .AND. (ABSTOL.LE.ZERO)) THEN
291 CALL DCOPY( N, RWORK( INDD ), 1, W, 1 )
292 INDEE = INDRWK + 2*N
293 IF( .NOT.WANTZ ) THEN
294 CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
295 CALL DSTERF( N, W, RWORK( INDEE ), INFO )
296 ELSE
297 CALL ZUPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
298 $ WORK( INDWRK ), IINFO )
299 CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
300 CALL ZSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ,
301 $ RWORK( INDRWK ), INFO )
302 IF( INFO.EQ.0 ) THEN
303 DO 10 I = 1, N
304 IFAIL( I ) = 0
305 10 CONTINUE
306 END IF
307 END IF
308 IF( INFO.EQ.0 ) THEN
309 M = N
310 GO TO 20
311 END IF
312 INFO = 0
313 END IF
314 *
315 * Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN.
316 *
317 IF( WANTZ ) THEN
318 ORDER = 'B'
319 ELSE
320 ORDER = 'E'
321 END IF
322 INDIBL = 1
323 INDISP = INDIBL + N
324 INDIWK = INDISP + N
325 CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
326 $ RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W,
327 $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
328 $ IWORK( INDIWK ), INFO )
329 *
330 IF( WANTZ ) THEN
331 CALL ZSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W,
332 $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
333 $ RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO )
334 *
335 * Apply unitary matrix used in reduction to tridiagonal
336 * form to eigenvectors returned by ZSTEIN.
337 *
338 INDWRK = INDTAU + N
339 CALL ZUPMTR( 'L', UPLO, 'N', N, M, AP, WORK( INDTAU ), Z, LDZ,
340 $ WORK( INDWRK ), IINFO )
341 END IF
342 *
343 * If matrix was scaled, then rescale eigenvalues appropriately.
344 *
345 20 CONTINUE
346 IF( ISCALE.EQ.1 ) THEN
347 IF( INFO.EQ.0 ) THEN
348 IMAX = M
349 ELSE
350 IMAX = INFO - 1
351 END IF
352 CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
353 END IF
354 *
355 * If eigenvalues are not in order, then sort them, along with
356 * eigenvectors.
357 *
358 IF( WANTZ ) THEN
359 DO 40 J = 1, M - 1
360 I = 0
361 TMP1 = W( J )
362 DO 30 JJ = J + 1, M
363 IF( W( JJ ).LT.TMP1 ) THEN
364 I = JJ
365 TMP1 = W( JJ )
366 END IF
367 30 CONTINUE
368 *
369 IF( I.NE.0 ) THEN
370 ITMP1 = IWORK( INDIBL+I-1 )
371 W( I ) = W( J )
372 IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
373 W( J ) = TMP1
374 IWORK( INDIBL+J-1 ) = ITMP1
375 CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
376 IF( INFO.NE.0 ) THEN
377 ITMP1 = IFAIL( I )
378 IFAIL( I ) = IFAIL( J )
379 IFAIL( J ) = ITMP1
380 END IF
381 END IF
382 40 CONTINUE
383 END IF
384 *
385 RETURN
386 *
387 * End of ZHPEVX
388 *
389 END
2 $ ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK,
3 $ IFAIL, INFO )
4 *
5 * -- LAPACK driver routine (version 3.2) --
6 * -- LAPACK is a software package provided by Univ. of Tennessee, --
7 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
8 * November 2006
9 *
10 * .. Scalar Arguments ..
11 CHARACTER JOBZ, RANGE, UPLO
12 INTEGER IL, INFO, IU, LDZ, M, N
13 DOUBLE PRECISION ABSTOL, VL, VU
14 * ..
15 * .. Array Arguments ..
16 INTEGER IFAIL( * ), IWORK( * )
17 DOUBLE PRECISION RWORK( * ), W( * )
18 COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
19 * ..
20 *
21 * Purpose
22 * =======
23 *
24 * ZHPEVX computes selected eigenvalues and, optionally, eigenvectors
25 * of a complex Hermitian matrix A in packed storage.
26 * Eigenvalues/vectors can be selected by specifying either a range of
27 * values or a range of indices for the desired eigenvalues.
28 *
29 * Arguments
30 * =========
31 *
32 * JOBZ (input) CHARACTER*1
33 * = 'N': Compute eigenvalues only;
34 * = 'V': Compute eigenvalues and eigenvectors.
35 *
36 * RANGE (input) CHARACTER*1
37 * = 'A': all eigenvalues will be found;
38 * = 'V': all eigenvalues in the half-open interval (VL,VU]
39 * will be found;
40 * = 'I': the IL-th through IU-th eigenvalues will be found.
41 *
42 * UPLO (input) CHARACTER*1
43 * = 'U': Upper triangle of A is stored;
44 * = 'L': Lower triangle of A is stored.
45 *
46 * N (input) INTEGER
47 * The order of the matrix A. N >= 0.
48 *
49 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
50 * On entry, the upper or lower triangle of the Hermitian matrix
51 * A, packed columnwise in a linear array. The j-th column of A
52 * is stored in the array AP as follows:
53 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
54 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
55 *
56 * On exit, AP is overwritten by values generated during the
57 * reduction to tridiagonal form. If UPLO = 'U', the diagonal
58 * and first superdiagonal of the tridiagonal matrix T overwrite
59 * the corresponding elements of A, and if UPLO = 'L', the
60 * diagonal and first subdiagonal of T overwrite the
61 * corresponding elements of A.
62 *
63 * VL (input) DOUBLE PRECISION
64 * VU (input) DOUBLE PRECISION
65 * If RANGE='V', the lower and upper bounds of the interval to
66 * be searched for eigenvalues. VL < VU.
67 * Not referenced if RANGE = 'A' or 'I'.
68 *
69 * IL (input) INTEGER
70 * IU (input) INTEGER
71 * If RANGE='I', the indices (in ascending order) of the
72 * smallest and largest eigenvalues to be returned.
73 * 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
74 * Not referenced if RANGE = 'A' or 'V'.
75 *
76 * ABSTOL (input) DOUBLE PRECISION
77 * The absolute error tolerance for the eigenvalues.
78 * An approximate eigenvalue is accepted as converged
79 * when it is determined to lie in an interval [a,b]
80 * of width less than or equal to
81 *
82 * ABSTOL + EPS * max( |a|,|b| ) ,
83 *
84 * where EPS is the machine precision. If ABSTOL is less than
85 * or equal to zero, then EPS*|T| will be used in its place,
86 * where |T| is the 1-norm of the tridiagonal matrix obtained
87 * by reducing AP to tridiagonal form.
88 *
89 * Eigenvalues will be computed most accurately when ABSTOL is
90 * set to twice the underflow threshold 2*DLAMCH('S'), not zero.
91 * If this routine returns with INFO>0, indicating that some
92 * eigenvectors did not converge, try setting ABSTOL to
93 * 2*DLAMCH('S').
94 *
95 * See "Computing Small Singular Values of Bidiagonal Matrices
96 * with Guaranteed High Relative Accuracy," by Demmel and
97 * Kahan, LAPACK Working Note #3.
98 *
99 * M (output) INTEGER
100 * The total number of eigenvalues found. 0 <= M <= N.
101 * If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
102 *
103 * W (output) DOUBLE PRECISION array, dimension (N)
104 * If INFO = 0, the selected eigenvalues in ascending order.
105 *
106 * Z (output) COMPLEX*16 array, dimension (LDZ, max(1,M))
107 * If JOBZ = 'V', then if INFO = 0, the first M columns of Z
108 * contain the orthonormal eigenvectors of the matrix A
109 * corresponding to the selected eigenvalues, with the i-th
110 * column of Z holding the eigenvector associated with W(i).
111 * If an eigenvector fails to converge, then that column of Z
112 * contains the latest approximation to the eigenvector, and
113 * the index of the eigenvector is returned in IFAIL.
114 * If JOBZ = 'N', then Z is not referenced.
115 * Note: the user must ensure that at least max(1,M) columns are
116 * supplied in the array Z; if RANGE = 'V', the exact value of M
117 * is not known in advance and an upper bound must be used.
118 *
119 * LDZ (input) INTEGER
120 * The leading dimension of the array Z. LDZ >= 1, and if
121 * JOBZ = 'V', LDZ >= max(1,N).
122 *
123 * WORK (workspace) COMPLEX*16 array, dimension (2*N)
124 *
125 * RWORK (workspace) DOUBLE PRECISION array, dimension (7*N)
126 *
127 * IWORK (workspace) INTEGER array, dimension (5*N)
128 *
129 * IFAIL (output) INTEGER array, dimension (N)
130 * If JOBZ = 'V', then if INFO = 0, the first M elements of
131 * IFAIL are zero. If INFO > 0, then IFAIL contains the
132 * indices of the eigenvectors that failed to converge.
133 * If JOBZ = 'N', then IFAIL is not referenced.
134 *
135 * INFO (output) INTEGER
136 * = 0: successful exit
137 * < 0: if INFO = -i, the i-th argument had an illegal value
138 * > 0: if INFO = i, then i eigenvectors failed to converge.
139 * Their indices are stored in array IFAIL.
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144 DOUBLE PRECISION ZERO, ONE
145 PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
146 COMPLEX*16 CONE
147 PARAMETER ( CONE = ( 1.0D0, 0.0D0 ) )
148 * ..
149 * .. Local Scalars ..
150 LOGICAL ALLEIG, INDEIG, TEST, VALEIG, WANTZ
151 CHARACTER ORDER
152 INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
153 $ INDISP, INDIWK, INDRWK, INDTAU, INDWRK, ISCALE,
154 $ ITMP1, J, JJ, NSPLIT
155 DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
156 $ SIGMA, SMLNUM, TMP1, VLL, VUU
157 * ..
158 * .. External Functions ..
159 LOGICAL LSAME
160 DOUBLE PRECISION DLAMCH, ZLANHP
161 EXTERNAL LSAME, DLAMCH, ZLANHP
162 * ..
163 * .. External Subroutines ..
164 EXTERNAL DCOPY, DSCAL, DSTEBZ, DSTERF, XERBLA, ZDSCAL,
165 $ ZHPTRD, ZSTEIN, ZSTEQR, ZSWAP, ZUPGTR, ZUPMTR
166 * ..
167 * .. Intrinsic Functions ..
168 INTRINSIC DBLE, MAX, MIN, SQRT
169 * ..
170 * .. Executable Statements ..
171 *
172 * Test the input parameters.
173 *
174 WANTZ = LSAME( JOBZ, 'V' )
175 ALLEIG = LSAME( RANGE, 'A' )
176 VALEIG = LSAME( RANGE, 'V' )
177 INDEIG = LSAME( RANGE, 'I' )
178 *
179 INFO = 0
180 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
181 INFO = -1
182 ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
183 INFO = -2
184 ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) )
185 $ THEN
186 INFO = -3
187 ELSE IF( N.LT.0 ) THEN
188 INFO = -4
189 ELSE
190 IF( VALEIG ) THEN
191 IF( N.GT.0 .AND. VU.LE.VL )
192 $ INFO = -7
193 ELSE IF( INDEIG ) THEN
194 IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
195 INFO = -8
196 ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
197 INFO = -9
198 END IF
199 END IF
200 END IF
201 IF( INFO.EQ.0 ) THEN
202 IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
203 $ INFO = -14
204 END IF
205 *
206 IF( INFO.NE.0 ) THEN
207 CALL XERBLA( 'ZHPEVX', -INFO )
208 RETURN
209 END IF
210 *
211 * Quick return if possible
212 *
213 M = 0
214 IF( N.EQ.0 )
215 $ RETURN
216 *
217 IF( N.EQ.1 ) THEN
218 IF( ALLEIG .OR. INDEIG ) THEN
219 M = 1
220 W( 1 ) = AP( 1 )
221 ELSE
222 IF( VL.LT.DBLE( AP( 1 ) ) .AND. VU.GE.DBLE( AP( 1 ) ) ) THEN
223 M = 1
224 W( 1 ) = AP( 1 )
225 END IF
226 END IF
227 IF( WANTZ )
228 $ Z( 1, 1 ) = CONE
229 RETURN
230 END IF
231 *
232 * Get machine constants.
233 *
234 SAFMIN = DLAMCH( 'Safe minimum' )
235 EPS = DLAMCH( 'Precision' )
236 SMLNUM = SAFMIN / EPS
237 BIGNUM = ONE / SMLNUM
238 RMIN = SQRT( SMLNUM )
239 RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
240 *
241 * Scale matrix to allowable range, if necessary.
242 *
243 ISCALE = 0
244 ABSTLL = ABSTOL
245 IF( VALEIG ) THEN
246 VLL = VL
247 VUU = VU
248 ELSE
249 VLL = ZERO
250 VUU = ZERO
251 END IF
252 ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK )
253 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
254 ISCALE = 1
255 SIGMA = RMIN / ANRM
256 ELSE IF( ANRM.GT.RMAX ) THEN
257 ISCALE = 1
258 SIGMA = RMAX / ANRM
259 END IF
260 IF( ISCALE.EQ.1 ) THEN
261 CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
262 IF( ABSTOL.GT.0 )
263 $ ABSTLL = ABSTOL*SIGMA
264 IF( VALEIG ) THEN
265 VLL = VL*SIGMA
266 VUU = VU*SIGMA
267 END IF
268 END IF
269 *
270 * Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form.
271 *
272 INDD = 1
273 INDE = INDD + N
274 INDRWK = INDE + N
275 INDTAU = 1
276 INDWRK = INDTAU + N
277 CALL ZHPTRD( UPLO, N, AP, RWORK( INDD ), RWORK( INDE ),
278 $ WORK( INDTAU ), IINFO )
279 *
280 * If all eigenvalues are desired and ABSTOL is less than or equal
281 * to zero, then call DSTERF or ZUPGTR and ZSTEQR. If this fails
282 * for some eigenvalue, then try DSTEBZ.
283 *
284 TEST = .FALSE.
285 IF (INDEIG) THEN
286 IF (IL.EQ.1 .AND. IU.EQ.N) THEN
287 TEST = .TRUE.
288 END IF
289 END IF
290 IF ((ALLEIG .OR. TEST) .AND. (ABSTOL.LE.ZERO)) THEN
291 CALL DCOPY( N, RWORK( INDD ), 1, W, 1 )
292 INDEE = INDRWK + 2*N
293 IF( .NOT.WANTZ ) THEN
294 CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
295 CALL DSTERF( N, W, RWORK( INDEE ), INFO )
296 ELSE
297 CALL ZUPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
298 $ WORK( INDWRK ), IINFO )
299 CALL DCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
300 CALL ZSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ,
301 $ RWORK( INDRWK ), INFO )
302 IF( INFO.EQ.0 ) THEN
303 DO 10 I = 1, N
304 IFAIL( I ) = 0
305 10 CONTINUE
306 END IF
307 END IF
308 IF( INFO.EQ.0 ) THEN
309 M = N
310 GO TO 20
311 END IF
312 INFO = 0
313 END IF
314 *
315 * Otherwise, call DSTEBZ and, if eigenvectors are desired, ZSTEIN.
316 *
317 IF( WANTZ ) THEN
318 ORDER = 'B'
319 ELSE
320 ORDER = 'E'
321 END IF
322 INDIBL = 1
323 INDISP = INDIBL + N
324 INDIWK = INDISP + N
325 CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
326 $ RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W,
327 $ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
328 $ IWORK( INDIWK ), INFO )
329 *
330 IF( WANTZ ) THEN
331 CALL ZSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W,
332 $ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
333 $ RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO )
334 *
335 * Apply unitary matrix used in reduction to tridiagonal
336 * form to eigenvectors returned by ZSTEIN.
337 *
338 INDWRK = INDTAU + N
339 CALL ZUPMTR( 'L', UPLO, 'N', N, M, AP, WORK( INDTAU ), Z, LDZ,
340 $ WORK( INDWRK ), IINFO )
341 END IF
342 *
343 * If matrix was scaled, then rescale eigenvalues appropriately.
344 *
345 20 CONTINUE
346 IF( ISCALE.EQ.1 ) THEN
347 IF( INFO.EQ.0 ) THEN
348 IMAX = M
349 ELSE
350 IMAX = INFO - 1
351 END IF
352 CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
353 END IF
354 *
355 * If eigenvalues are not in order, then sort them, along with
356 * eigenvectors.
357 *
358 IF( WANTZ ) THEN
359 DO 40 J = 1, M - 1
360 I = 0
361 TMP1 = W( J )
362 DO 30 JJ = J + 1, M
363 IF( W( JJ ).LT.TMP1 ) THEN
364 I = JJ
365 TMP1 = W( JJ )
366 END IF
367 30 CONTINUE
368 *
369 IF( I.NE.0 ) THEN
370 ITMP1 = IWORK( INDIBL+I-1 )
371 W( I ) = W( J )
372 IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
373 W( J ) = TMP1
374 IWORK( INDIBL+J-1 ) = ITMP1
375 CALL ZSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
376 IF( INFO.NE.0 ) THEN
377 ITMP1 = IFAIL( I )
378 IFAIL( I ) = IFAIL( J )
379 IFAIL( J ) = ITMP1
380 END IF
381 END IF
382 40 CONTINUE
383 END IF
384 *
385 RETURN
386 *
387 * End of ZHPEVX
388 *
389 END