1: *> \brief <b> DSPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSPEVD + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspevd.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspevd.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspevd.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
22: * IWORK, LIWORK, INFO )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER JOBZ, UPLO
26: * INTEGER INFO, LDZ, LIWORK, LWORK, N
27: * ..
28: * .. Array Arguments ..
29: * INTEGER IWORK( * )
30: * DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> DSPEVD computes all the eigenvalues and, optionally, eigenvectors
40: *> of a real symmetric matrix A in packed storage. If eigenvectors are
41: *> desired, it uses a divide and conquer algorithm.
42: *>
43: *> The divide and conquer algorithm makes very mild assumptions about
44: *> floating point arithmetic. It will work on machines with a guard
45: *> digit in add/subtract, or on those binary machines without guard
46: *> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
47: *> Cray-2. It could conceivably fail on hexadecimal or decimal machines
48: *> without guard digits, but we know of none.
49: *> \endverbatim
50: *
51: * Arguments:
52: * ==========
53: *
54: *> \param[in] JOBZ
55: *> \verbatim
56: *> JOBZ is CHARACTER*1
57: *> = 'N': Compute eigenvalues only;
58: *> = 'V': Compute eigenvalues and eigenvectors.
59: *> \endverbatim
60: *>
61: *> \param[in] UPLO
62: *> \verbatim
63: *> UPLO is CHARACTER*1
64: *> = 'U': Upper triangle of A is stored;
65: *> = 'L': Lower triangle of A is stored.
66: *> \endverbatim
67: *>
68: *> \param[in] N
69: *> \verbatim
70: *> N is INTEGER
71: *> The order of the matrix A. N >= 0.
72: *> \endverbatim
73: *>
74: *> \param[in,out] AP
75: *> \verbatim
76: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
77: *> On entry, the upper or lower triangle of the symmetric matrix
78: *> A, packed columnwise in a linear array. The j-th column of A
79: *> is stored in the array AP as follows:
80: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
81: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
82: *>
83: *> On exit, AP is overwritten by values generated during the
84: *> reduction to tridiagonal form. If UPLO = 'U', the diagonal
85: *> and first superdiagonal of the tridiagonal matrix T overwrite
86: *> the corresponding elements of A, and if UPLO = 'L', the
87: *> diagonal and first subdiagonal of T overwrite the
88: *> corresponding elements of A.
89: *> \endverbatim
90: *>
91: *> \param[out] W
92: *> \verbatim
93: *> W is DOUBLE PRECISION array, dimension (N)
94: *> If INFO = 0, the eigenvalues in ascending order.
95: *> \endverbatim
96: *>
97: *> \param[out] Z
98: *> \verbatim
99: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
100: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
101: *> eigenvectors of the matrix A, with the i-th column of Z
102: *> holding the eigenvector associated with W(i).
103: *> If JOBZ = 'N', then Z is not referenced.
104: *> \endverbatim
105: *>
106: *> \param[in] LDZ
107: *> \verbatim
108: *> LDZ is INTEGER
109: *> The leading dimension of the array Z. LDZ >= 1, and if
110: *> JOBZ = 'V', LDZ >= max(1,N).
111: *> \endverbatim
112: *>
113: *> \param[out] WORK
114: *> \verbatim
115: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
116: *> On exit, if INFO = 0, WORK(1) returns the required LWORK.
117: *> \endverbatim
118: *>
119: *> \param[in] LWORK
120: *> \verbatim
121: *> LWORK is INTEGER
122: *> The dimension of the array WORK.
123: *> If N <= 1, LWORK must be at least 1.
124: *> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N.
125: *> If JOBZ = 'V' and N > 1, LWORK must be at least
126: *> 1 + 6*N + N**2.
127: *>
128: *> If LWORK = -1, then a workspace query is assumed; the routine
129: *> only calculates the required sizes of the WORK and IWORK
130: *> arrays, returns these values as the first entries of the WORK
131: *> and IWORK arrays, and no error message related to LWORK or
132: *> LIWORK is issued by XERBLA.
133: *> \endverbatim
134: *>
135: *> \param[out] IWORK
136: *> \verbatim
137: *> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
138: *> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
139: *> \endverbatim
140: *>
141: *> \param[in] LIWORK
142: *> \verbatim
143: *> LIWORK is INTEGER
144: *> The dimension of the array IWORK.
145: *> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
146: *> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
147: *>
148: *> If LIWORK = -1, then a workspace query is assumed; the
149: *> routine only calculates the required sizes of the WORK and
150: *> IWORK arrays, returns these values as the first entries of
151: *> the WORK and IWORK arrays, and no error message related to
152: *> LWORK or LIWORK is issued by XERBLA.
153: *> \endverbatim
154: *>
155: *> \param[out] INFO
156: *> \verbatim
157: *> INFO is INTEGER
158: *> = 0: successful exit
159: *> < 0: if INFO = -i, the i-th argument had an illegal value.
160: *> > 0: if INFO = i, the algorithm failed to converge; i
161: *> off-diagonal elements of an intermediate tridiagonal
162: *> form did not converge to zero.
163: *> \endverbatim
164: *
165: * Authors:
166: * ========
167: *
168: *> \author Univ. of Tennessee
169: *> \author Univ. of California Berkeley
170: *> \author Univ. of Colorado Denver
171: *> \author NAG Ltd.
172: *
173: *> \ingroup doubleOTHEReigen
174: *
175: * =====================================================================
176: SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
177: $ IWORK, LIWORK, INFO )
178: *
179: * -- LAPACK driver routine --
180: * -- LAPACK is a software package provided by Univ. of Tennessee, --
181: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
182: *
183: * .. Scalar Arguments ..
184: CHARACTER JOBZ, UPLO
185: INTEGER INFO, LDZ, LIWORK, LWORK, N
186: * ..
187: * .. Array Arguments ..
188: INTEGER IWORK( * )
189: DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
190: * ..
191: *
192: * =====================================================================
193: *
194: * .. Parameters ..
195: DOUBLE PRECISION ZERO, ONE
196: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
197: * ..
198: * .. Local Scalars ..
199: LOGICAL LQUERY, WANTZ
200: INTEGER IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN,
201: $ LLWORK, LWMIN
202: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
203: $ SMLNUM
204: * ..
205: * .. External Functions ..
206: LOGICAL LSAME
207: DOUBLE PRECISION DLAMCH, DLANSP
208: EXTERNAL LSAME, DLAMCH, DLANSP
209: * ..
210: * .. External Subroutines ..
211: EXTERNAL DOPMTR, DSCAL, DSPTRD, DSTEDC, DSTERF, XERBLA
212: * ..
213: * .. Intrinsic Functions ..
214: INTRINSIC SQRT
215: * ..
216: * .. Executable Statements ..
217: *
218: * Test the input parameters.
219: *
220: WANTZ = LSAME( JOBZ, 'V' )
221: LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
222: *
223: INFO = 0
224: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
225: INFO = -1
226: ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
227: $ THEN
228: INFO = -2
229: ELSE IF( N.LT.0 ) THEN
230: INFO = -3
231: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
232: INFO = -7
233: END IF
234: *
235: IF( INFO.EQ.0 ) THEN
236: IF( N.LE.1 ) THEN
237: LIWMIN = 1
238: LWMIN = 1
239: ELSE
240: IF( WANTZ ) THEN
241: LIWMIN = 3 + 5*N
242: LWMIN = 1 + 6*N + N**2
243: ELSE
244: LIWMIN = 1
245: LWMIN = 2*N
246: END IF
247: END IF
248: IWORK( 1 ) = LIWMIN
249: WORK( 1 ) = LWMIN
250: *
251: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
252: INFO = -9
253: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
254: INFO = -11
255: END IF
256: END IF
257: *
258: IF( INFO.NE.0 ) THEN
259: CALL XERBLA( 'DSPEVD', -INFO )
260: RETURN
261: ELSE IF( LQUERY ) THEN
262: RETURN
263: END IF
264: *
265: * Quick return if possible
266: *
267: IF( N.EQ.0 )
268: $ RETURN
269: *
270: IF( N.EQ.1 ) THEN
271: W( 1 ) = AP( 1 )
272: IF( WANTZ )
273: $ Z( 1, 1 ) = ONE
274: RETURN
275: END IF
276: *
277: * Get machine constants.
278: *
279: SAFMIN = DLAMCH( 'Safe minimum' )
280: EPS = DLAMCH( 'Precision' )
281: SMLNUM = SAFMIN / EPS
282: BIGNUM = ONE / SMLNUM
283: RMIN = SQRT( SMLNUM )
284: RMAX = SQRT( BIGNUM )
285: *
286: * Scale matrix to allowable range, if necessary.
287: *
288: ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
289: ISCALE = 0
290: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
291: ISCALE = 1
292: SIGMA = RMIN / ANRM
293: ELSE IF( ANRM.GT.RMAX ) THEN
294: ISCALE = 1
295: SIGMA = RMAX / ANRM
296: END IF
297: IF( ISCALE.EQ.1 ) THEN
298: CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
299: END IF
300: *
301: * Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
302: *
303: INDE = 1
304: INDTAU = INDE + N
305: CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
306: *
307: * For eigenvalues only, call DSTERF. For eigenvectors, first call
308: * DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
309: * tridiagonal matrix, then call DOPMTR to multiply it by the
310: * Householder transformations represented in AP.
311: *
312: IF( .NOT.WANTZ ) THEN
313: CALL DSTERF( N, W, WORK( INDE ), INFO )
314: ELSE
315: INDWRK = INDTAU + N
316: LLWORK = LWORK - INDWRK + 1
317: CALL DSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
318: $ LLWORK, IWORK, LIWORK, INFO )
319: CALL DOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
320: $ WORK( INDWRK ), IINFO )
321: END IF
322: *
323: * If matrix was scaled, then rescale eigenvalues appropriately.
324: *
325: IF( ISCALE.EQ.1 )
326: $ CALL DSCAL( N, ONE / SIGMA, W, 1 )
327: *
328: WORK( 1 ) = LWMIN
329: IWORK( 1 ) = LIWMIN
330: RETURN
331: *
332: * End of DSPEVD
333: *
334: END
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