Annotation of rpl/lapack/lapack/dstev.f, revision 1.8
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: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 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">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER JOBZ
! 25: * INTEGER INFO, LDZ, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
! 29: * ..
! 30: *
! 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: *
! 107: *> \author Univ. of Tennessee
! 108: *> \author Univ. of California Berkeley
! 109: *> \author Univ. of Colorado Denver
! 110: *> \author NAG Ltd.
! 111: *
! 112: *> \date November 2011
! 113: *
! 114: *> \ingroup doubleOTHEReigen
! 115: *
! 116: * =====================================================================
1.1 bertrand 117: SUBROUTINE DSTEV( JOBZ, N, D, E, Z, LDZ, WORK, INFO )
118: *
1.8 ! bertrand 119: * -- LAPACK driver routine (version 3.4.0) --
1.1 bertrand 120: * -- LAPACK is a software package provided by Univ. of Tennessee, --
121: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 122: * November 2011
1.1 bertrand 123: *
124: * .. Scalar Arguments ..
125: CHARACTER JOBZ
126: INTEGER INFO, LDZ, N
127: * ..
128: * .. Array Arguments ..
129: DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * )
130: * ..
131: *
132: * =====================================================================
133: *
134: * .. Parameters ..
135: DOUBLE PRECISION ZERO, ONE
136: PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
137: * ..
138: * .. Local Scalars ..
139: LOGICAL WANTZ
140: INTEGER IMAX, ISCALE
141: DOUBLE PRECISION BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
142: $ TNRM
143: * ..
144: * .. External Functions ..
145: LOGICAL LSAME
146: DOUBLE PRECISION DLAMCH, DLANST
147: EXTERNAL LSAME, DLAMCH, DLANST
148: * ..
149: * .. External Subroutines ..
150: EXTERNAL DSCAL, DSTEQR, DSTERF, XERBLA
151: * ..
152: * .. Intrinsic Functions ..
153: INTRINSIC SQRT
154: * ..
155: * .. Executable Statements ..
156: *
157: * Test the input parameters.
158: *
159: WANTZ = LSAME( JOBZ, 'V' )
160: *
161: INFO = 0
162: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
163: INFO = -1
164: ELSE IF( N.LT.0 ) THEN
165: INFO = -2
166: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
167: INFO = -6
168: END IF
169: *
170: IF( INFO.NE.0 ) THEN
171: CALL XERBLA( 'DSTEV ', -INFO )
172: RETURN
173: END IF
174: *
175: * Quick return if possible
176: *
177: IF( N.EQ.0 )
178: $ RETURN
179: *
180: IF( N.EQ.1 ) THEN
181: IF( WANTZ )
182: $ Z( 1, 1 ) = ONE
183: RETURN
184: END IF
185: *
186: * Get machine constants.
187: *
188: SAFMIN = DLAMCH( 'Safe minimum' )
189: EPS = DLAMCH( 'Precision' )
190: SMLNUM = SAFMIN / EPS
191: BIGNUM = ONE / SMLNUM
192: RMIN = SQRT( SMLNUM )
193: RMAX = SQRT( BIGNUM )
194: *
195: * Scale matrix to allowable range, if necessary.
196: *
197: ISCALE = 0
198: TNRM = DLANST( 'M', N, D, E )
199: IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
200: ISCALE = 1
201: SIGMA = RMIN / TNRM
202: ELSE IF( TNRM.GT.RMAX ) THEN
203: ISCALE = 1
204: SIGMA = RMAX / TNRM
205: END IF
206: IF( ISCALE.EQ.1 ) THEN
207: CALL DSCAL( N, SIGMA, D, 1 )
208: CALL DSCAL( N-1, SIGMA, E( 1 ), 1 )
209: END IF
210: *
211: * For eigenvalues only, call DSTERF. For eigenvalues and
212: * eigenvectors, call DSTEQR.
213: *
214: IF( .NOT.WANTZ ) THEN
215: CALL DSTERF( N, D, E, INFO )
216: ELSE
217: CALL DSTEQR( 'I', N, D, E, Z, LDZ, WORK, INFO )
218: END IF
219: *
220: * If matrix was scaled, then rescale eigenvalues appropriately.
221: *
222: IF( ISCALE.EQ.1 ) THEN
223: IF( INFO.EQ.0 ) THEN
224: IMAX = N
225: ELSE
226: IMAX = INFO - 1
227: END IF
228: CALL DSCAL( IMAX, ONE / SIGMA, D, 1 )
229: END IF
230: *
231: RETURN
232: *
233: * End of DSTEV
234: *
235: END
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