Annotation of rpl/lapack/lapack/dspev.f, revision 1.14
1.8 bertrand 1: *> \brief <b> DSPEV 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 DSPEV + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspev.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dspev.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dspev.f">
1.8 bertrand 15: *> [TXT]</a>
1.14 ! bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
1.14 ! bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * CHARACTER JOBZ, UPLO
25: * INTEGER INFO, LDZ, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
29: * ..
1.14 ! bertrand 30: *
1.8 bertrand 31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
38: *> real symmetric matrix A in packed storage.
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] UPLO
52: *> \verbatim
53: *> UPLO is CHARACTER*1
54: *> = 'U': Upper triangle of A is stored;
55: *> = 'L': Lower triangle of A is stored.
56: *> \endverbatim
57: *>
58: *> \param[in] N
59: *> \verbatim
60: *> N is INTEGER
61: *> The order of the matrix A. N >= 0.
62: *> \endverbatim
63: *>
64: *> \param[in,out] AP
65: *> \verbatim
66: *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
67: *> On entry, the upper or lower triangle of the symmetric matrix
68: *> A, packed columnwise in a linear array. The j-th column of A
69: *> is stored in the array AP as follows:
70: *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
71: *> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
72: *>
73: *> On exit, AP is overwritten by values generated during the
74: *> reduction to tridiagonal form. If UPLO = 'U', the diagonal
75: *> and first superdiagonal of the tridiagonal matrix T overwrite
76: *> the corresponding elements of A, and if UPLO = 'L', the
77: *> diagonal and first subdiagonal of T overwrite the
78: *> corresponding elements of A.
79: *> \endverbatim
80: *>
81: *> \param[out] W
82: *> \verbatim
83: *> W is DOUBLE PRECISION array, dimension (N)
84: *> If INFO = 0, the eigenvalues in ascending order.
85: *> \endverbatim
86: *>
87: *> \param[out] Z
88: *> \verbatim
89: *> Z is DOUBLE PRECISION array, dimension (LDZ, N)
90: *> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
91: *> eigenvectors of the matrix A, with the i-th column of Z
92: *> holding the eigenvector associated with W(i).
93: *> If JOBZ = 'N', then Z is not referenced.
94: *> \endverbatim
95: *>
96: *> \param[in] LDZ
97: *> \verbatim
98: *> LDZ is INTEGER
99: *> The leading dimension of the array Z. LDZ >= 1, and if
100: *> JOBZ = 'V', LDZ >= max(1,N).
101: *> \endverbatim
102: *>
103: *> \param[out] WORK
104: *> \verbatim
105: *> WORK is DOUBLE PRECISION array, dimension (3*N)
106: *> \endverbatim
107: *>
108: *> \param[out] INFO
109: *> \verbatim
110: *> INFO is INTEGER
111: *> = 0: successful exit.
112: *> < 0: if INFO = -i, the i-th argument had an illegal value.
113: *> > 0: if INFO = i, the algorithm failed to converge; i
114: *> off-diagonal elements of an intermediate tridiagonal
115: *> form did not converge to zero.
116: *> \endverbatim
117: *
118: * Authors:
119: * ========
120: *
1.14 ! bertrand 121: *> \author Univ. of Tennessee
! 122: *> \author Univ. of California Berkeley
! 123: *> \author Univ. of Colorado Denver
! 124: *> \author NAG Ltd.
1.8 bertrand 125: *
1.14 ! bertrand 126: *> \date December 2016
1.8 bertrand 127: *
128: *> \ingroup doubleOTHEReigen
129: *
130: * =====================================================================
1.1 bertrand 131: SUBROUTINE DSPEV( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, INFO )
132: *
1.14 ! bertrand 133: * -- LAPACK driver routine (version 3.7.0) --
1.1 bertrand 134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 ! bertrand 136: * December 2016
1.1 bertrand 137: *
138: * .. Scalar Arguments ..
139: CHARACTER JOBZ, UPLO
140: INTEGER INFO, LDZ, N
141: * ..
142: * .. Array Arguments ..
143: DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
144: * ..
145: *
146: * =====================================================================
147: *
148: * .. Parameters ..
149: DOUBLE PRECISION ZERO, ONE
150: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
151: * ..
152: * .. Local Scalars ..
153: LOGICAL WANTZ
154: INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE
155: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
156: $ SMLNUM
157: * ..
158: * .. External Functions ..
159: LOGICAL LSAME
160: DOUBLE PRECISION DLAMCH, DLANSP
161: EXTERNAL LSAME, DLAMCH, DLANSP
162: * ..
163: * .. External Subroutines ..
164: EXTERNAL DOPGTR, DSCAL, DSPTRD, DSTEQR, DSTERF, XERBLA
165: * ..
166: * .. Intrinsic Functions ..
167: INTRINSIC SQRT
168: * ..
169: * .. Executable Statements ..
170: *
171: * Test the input parameters.
172: *
173: WANTZ = LSAME( JOBZ, 'V' )
174: *
175: INFO = 0
176: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
177: INFO = -1
178: ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
179: $ THEN
180: INFO = -2
181: ELSE IF( N.LT.0 ) THEN
182: INFO = -3
183: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
184: INFO = -7
185: END IF
186: *
187: IF( INFO.NE.0 ) THEN
188: CALL XERBLA( 'DSPEV ', -INFO )
189: RETURN
190: END IF
191: *
192: * Quick return if possible
193: *
194: IF( N.EQ.0 )
195: $ RETURN
196: *
197: IF( N.EQ.1 ) THEN
198: W( 1 ) = AP( 1 )
199: IF( WANTZ )
200: $ Z( 1, 1 ) = ONE
201: RETURN
202: END IF
203: *
204: * Get machine constants.
205: *
206: SAFMIN = DLAMCH( 'Safe minimum' )
207: EPS = DLAMCH( 'Precision' )
208: SMLNUM = SAFMIN / EPS
209: BIGNUM = ONE / SMLNUM
210: RMIN = SQRT( SMLNUM )
211: RMAX = SQRT( BIGNUM )
212: *
213: * Scale matrix to allowable range, if necessary.
214: *
215: ANRM = DLANSP( 'M', UPLO, N, AP, WORK )
216: ISCALE = 0
217: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
218: ISCALE = 1
219: SIGMA = RMIN / ANRM
220: ELSE IF( ANRM.GT.RMAX ) THEN
221: ISCALE = 1
222: SIGMA = RMAX / ANRM
223: END IF
224: IF( ISCALE.EQ.1 ) THEN
225: CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
226: END IF
227: *
228: * Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
229: *
230: INDE = 1
231: INDTAU = INDE + N
232: CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
233: *
234: * For eigenvalues only, call DSTERF. For eigenvectors, first call
235: * DOPGTR to generate the orthogonal matrix, then call DSTEQR.
236: *
237: IF( .NOT.WANTZ ) THEN
238: CALL DSTERF( N, W, WORK( INDE ), INFO )
239: ELSE
240: INDWRK = INDTAU + N
241: CALL DOPGTR( UPLO, N, AP, WORK( INDTAU ), Z, LDZ,
242: $ WORK( INDWRK ), IINFO )
243: CALL DSTEQR( JOBZ, N, W, WORK( INDE ), Z, LDZ, WORK( INDTAU ),
244: $ INFO )
245: END IF
246: *
247: * If matrix was scaled, then rescale eigenvalues appropriately.
248: *
249: IF( ISCALE.EQ.1 ) THEN
250: IF( INFO.EQ.0 ) THEN
251: IMAX = N
252: ELSE
253: IMAX = INFO - 1
254: END IF
255: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
256: END IF
257: *
258: RETURN
259: *
260: * End of DSPEV
261: *
262: END
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