Annotation of rpl/lapack/lapack/dlaed1.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b DLAED1
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DLAED1 + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed1.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed1.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed1.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
! 22: * INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * INTEGER CUTPNT, INFO, LDQ, N
! 26: * DOUBLE PRECISION RHO
! 27: * ..
! 28: * .. Array Arguments ..
! 29: * INTEGER INDXQ( * ), IWORK( * )
! 30: * DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * )
! 31: * ..
! 32: *
! 33: *
! 34: *> \par Purpose:
! 35: * =============
! 36: *>
! 37: *> \verbatim
! 38: *>
! 39: *> DLAED1 computes the updated eigensystem of a diagonal
! 40: *> matrix after modification by a rank-one symmetric matrix. This
! 41: *> routine is used only for the eigenproblem which requires all
! 42: *> eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles
! 43: *> the case in which eigenvalues only or eigenvalues and eigenvectors
! 44: *> of a full symmetric matrix (which was reduced to tridiagonal form)
! 45: *> are desired.
! 46: *>
! 47: *> T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
! 48: *>
! 49: *> where Z = Q**T*u, u is a vector of length N with ones in the
! 50: *> CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
! 51: *>
! 52: *> The eigenvectors of the original matrix are stored in Q, and the
! 53: *> eigenvalues are in D. The algorithm consists of three stages:
! 54: *>
! 55: *> The first stage consists of deflating the size of the problem
! 56: *> when there are multiple eigenvalues or if there is a zero in
! 57: *> the Z vector. For each such occurence the dimension of the
! 58: *> secular equation problem is reduced by one. This stage is
! 59: *> performed by the routine DLAED2.
! 60: *>
! 61: *> The second stage consists of calculating the updated
! 62: *> eigenvalues. This is done by finding the roots of the secular
! 63: *> equation via the routine DLAED4 (as called by DLAED3).
! 64: *> This routine also calculates the eigenvectors of the current
! 65: *> problem.
! 66: *>
! 67: *> The final stage consists of computing the updated eigenvectors
! 68: *> directly using the updated eigenvalues. The eigenvectors for
! 69: *> the current problem are multiplied with the eigenvectors from
! 70: *> the overall problem.
! 71: *> \endverbatim
! 72: *
! 73: * Arguments:
! 74: * ==========
! 75: *
! 76: *> \param[in] N
! 77: *> \verbatim
! 78: *> N is INTEGER
! 79: *> The dimension of the symmetric tridiagonal matrix. N >= 0.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in,out] D
! 83: *> \verbatim
! 84: *> D is DOUBLE PRECISION array, dimension (N)
! 85: *> On entry, the eigenvalues of the rank-1-perturbed matrix.
! 86: *> On exit, the eigenvalues of the repaired matrix.
! 87: *> \endverbatim
! 88: *>
! 89: *> \param[in,out] Q
! 90: *> \verbatim
! 91: *> Q is DOUBLE PRECISION array, dimension (LDQ,N)
! 92: *> On entry, the eigenvectors of the rank-1-perturbed matrix.
! 93: *> On exit, the eigenvectors of the repaired tridiagonal matrix.
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[in] LDQ
! 97: *> \verbatim
! 98: *> LDQ is INTEGER
! 99: *> The leading dimension of the array Q. LDQ >= max(1,N).
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[in,out] INDXQ
! 103: *> \verbatim
! 104: *> INDXQ is INTEGER array, dimension (N)
! 105: *> On entry, the permutation which separately sorts the two
! 106: *> subproblems in D into ascending order.
! 107: *> On exit, the permutation which will reintegrate the
! 108: *> subproblems back into sorted order,
! 109: *> i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
! 110: *> \endverbatim
! 111: *>
! 112: *> \param[in] RHO
! 113: *> \verbatim
! 114: *> RHO is DOUBLE PRECISION
! 115: *> The subdiagonal entry used to create the rank-1 modification.
! 116: *> \endverbatim
! 117: *>
! 118: *> \param[in] CUTPNT
! 119: *> \verbatim
! 120: *> CUTPNT is INTEGER
! 121: *> The location of the last eigenvalue in the leading sub-matrix.
! 122: *> min(1,N) <= CUTPNT <= N/2.
! 123: *> \endverbatim
! 124: *>
! 125: *> \param[out] WORK
! 126: *> \verbatim
! 127: *> WORK is DOUBLE PRECISION array, dimension (4*N + N**2)
! 128: *> \endverbatim
! 129: *>
! 130: *> \param[out] IWORK
! 131: *> \verbatim
! 132: *> IWORK is INTEGER array, dimension (4*N)
! 133: *> \endverbatim
! 134: *>
! 135: *> \param[out] INFO
! 136: *> \verbatim
! 137: *> INFO is INTEGER
! 138: *> = 0: successful exit.
! 139: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 140: *> > 0: if INFO = 1, an eigenvalue did not converge
! 141: *> \endverbatim
! 142: *
! 143: * Authors:
! 144: * ========
! 145: *
! 146: *> \author Univ. of Tennessee
! 147: *> \author Univ. of California Berkeley
! 148: *> \author Univ. of Colorado Denver
! 149: *> \author NAG Ltd.
! 150: *
! 151: *> \date November 2011
! 152: *
! 153: *> \ingroup auxOTHERcomputational
! 154: *
! 155: *> \par Contributors:
! 156: * ==================
! 157: *>
! 158: *> Jeff Rutter, Computer Science Division, University of California
! 159: *> at Berkeley, USA \n
! 160: *> Modified by Francoise Tisseur, University of Tennessee
! 161: *>
! 162: * =====================================================================
1.1 bertrand 163: SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
164: $ INFO )
165: *
1.9 ! bertrand 166: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 167: * -- LAPACK is a software package provided by Univ. of Tennessee, --
168: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 169: * November 2011
1.1 bertrand 170: *
171: * .. Scalar Arguments ..
172: INTEGER CUTPNT, INFO, LDQ, N
173: DOUBLE PRECISION RHO
174: * ..
175: * .. Array Arguments ..
176: INTEGER INDXQ( * ), IWORK( * )
177: DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * )
178: * ..
179: *
180: * =====================================================================
181: *
182: * .. Local Scalars ..
183: INTEGER COLTYP, I, IDLMDA, INDX, INDXC, INDXP, IQ2, IS,
184: $ IW, IZ, K, N1, N2, ZPP1
185: * ..
186: * .. External Subroutines ..
187: EXTERNAL DCOPY, DLAED2, DLAED3, DLAMRG, XERBLA
188: * ..
189: * .. Intrinsic Functions ..
190: INTRINSIC MAX, MIN
191: * ..
192: * .. Executable Statements ..
193: *
194: * Test the input parameters.
195: *
196: INFO = 0
197: *
198: IF( N.LT.0 ) THEN
199: INFO = -1
200: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
201: INFO = -4
202: ELSE IF( MIN( 1, N / 2 ).GT.CUTPNT .OR. ( N / 2 ).LT.CUTPNT ) THEN
203: INFO = -7
204: END IF
205: IF( INFO.NE.0 ) THEN
206: CALL XERBLA( 'DLAED1', -INFO )
207: RETURN
208: END IF
209: *
210: * Quick return if possible
211: *
212: IF( N.EQ.0 )
213: $ RETURN
214: *
215: * The following values are integer pointers which indicate
216: * the portion of the workspace
217: * used by a particular array in DLAED2 and DLAED3.
218: *
219: IZ = 1
220: IDLMDA = IZ + N
221: IW = IDLMDA + N
222: IQ2 = IW + N
223: *
224: INDX = 1
225: INDXC = INDX + N
226: COLTYP = INDXC + N
227: INDXP = COLTYP + N
228: *
229: *
230: * Form the z-vector which consists of the last row of Q_1 and the
231: * first row of Q_2.
232: *
233: CALL DCOPY( CUTPNT, Q( CUTPNT, 1 ), LDQ, WORK( IZ ), 1 )
234: ZPP1 = CUTPNT + 1
235: CALL DCOPY( N-CUTPNT, Q( ZPP1, ZPP1 ), LDQ, WORK( IZ+CUTPNT ), 1 )
236: *
237: * Deflate eigenvalues.
238: *
239: CALL DLAED2( K, N, CUTPNT, D, Q, LDQ, INDXQ, RHO, WORK( IZ ),
240: $ WORK( IDLMDA ), WORK( IW ), WORK( IQ2 ),
241: $ IWORK( INDX ), IWORK( INDXC ), IWORK( INDXP ),
242: $ IWORK( COLTYP ), INFO )
243: *
244: IF( INFO.NE.0 )
245: $ GO TO 20
246: *
247: * Solve Secular Equation.
248: *
249: IF( K.NE.0 ) THEN
250: IS = ( IWORK( COLTYP )+IWORK( COLTYP+1 ) )*CUTPNT +
251: $ ( IWORK( COLTYP+1 )+IWORK( COLTYP+2 ) )*( N-CUTPNT ) + IQ2
252: CALL DLAED3( K, N, CUTPNT, D, Q, LDQ, RHO, WORK( IDLMDA ),
253: $ WORK( IQ2 ), IWORK( INDXC ), IWORK( COLTYP ),
254: $ WORK( IW ), WORK( IS ), INFO )
255: IF( INFO.NE.0 )
256: $ GO TO 20
257: *
258: * Prepare the INDXQ sorting permutation.
259: *
260: N1 = K
261: N2 = N - K
262: CALL DLAMRG( N1, N2, D, 1, -1, INDXQ )
263: ELSE
264: DO 10 I = 1, N
265: INDXQ( I ) = I
266: 10 CONTINUE
267: END IF
268: *
269: 20 CONTINUE
270: RETURN
271: *
272: * End of DLAED1
273: *
274: END
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