--- rpl/lapack/lapack/dlaed1.f 2010/08/06 15:32:25 1.4
+++ rpl/lapack/lapack/dlaed1.f 2012/12/14 12:30:22 1.12
@@ -1,10 +1,172 @@
+*> \brief \b DLAED1 used by sstedc. Computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix. Used when the original matrix is tridiagonal.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLAED1 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
+* INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER CUTPNT, INFO, LDQ, N
+* DOUBLE PRECISION RHO
+* ..
+* .. Array Arguments ..
+* INTEGER INDXQ( * ), IWORK( * )
+* DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLAED1 computes the updated eigensystem of a diagonal
+*> matrix after modification by a rank-one symmetric matrix. This
+*> routine is used only for the eigenproblem which requires all
+*> eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles
+*> the case in which eigenvalues only or eigenvalues and eigenvectors
+*> of a full symmetric matrix (which was reduced to tridiagonal form)
+*> are desired.
+*>
+*> T = Q(in) ( D(in) + RHO * Z*Z**T ) Q**T(in) = Q(out) * D(out) * Q**T(out)
+*>
+*> where Z = Q**T*u, u is a vector of length N with ones in the
+*> CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
+*>
+*> The eigenvectors of the original matrix are stored in Q, and the
+*> eigenvalues are in D. The algorithm consists of three stages:
+*>
+*> The first stage consists of deflating the size of the problem
+*> when there are multiple eigenvalues or if there is a zero in
+*> the Z vector. For each such occurence the dimension of the
+*> secular equation problem is reduced by one. This stage is
+*> performed by the routine DLAED2.
+*>
+*> The second stage consists of calculating the updated
+*> eigenvalues. This is done by finding the roots of the secular
+*> equation via the routine DLAED4 (as called by DLAED3).
+*> This routine also calculates the eigenvectors of the current
+*> problem.
+*>
+*> The final stage consists of computing the updated eigenvectors
+*> directly using the updated eigenvalues. The eigenvectors for
+*> the current problem are multiplied with the eigenvectors from
+*> the overall problem.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The dimension of the symmetric tridiagonal matrix. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*> D is DOUBLE PRECISION array, dimension (N)
+*> On entry, the eigenvalues of the rank-1-perturbed matrix.
+*> On exit, the eigenvalues of the repaired matrix.
+*> \endverbatim
+*>
+*> \param[in,out] Q
+*> \verbatim
+*> Q is DOUBLE PRECISION array, dimension (LDQ,N)
+*> On entry, the eigenvectors of the rank-1-perturbed matrix.
+*> On exit, the eigenvectors of the repaired tridiagonal matrix.
+*> \endverbatim
+*>
+*> \param[in] LDQ
+*> \verbatim
+*> LDQ is INTEGER
+*> The leading dimension of the array Q. LDQ >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] INDXQ
+*> \verbatim
+*> INDXQ is INTEGER array, dimension (N)
+*> On entry, the permutation which separately sorts the two
+*> subproblems in D into ascending order.
+*> On exit, the permutation which will reintegrate the
+*> subproblems back into sorted order,
+*> i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
+*> \endverbatim
+*>
+*> \param[in] RHO
+*> \verbatim
+*> RHO is DOUBLE PRECISION
+*> The subdiagonal entry used to create the rank-1 modification.
+*> \endverbatim
+*>
+*> \param[in] CUTPNT
+*> \verbatim
+*> CUTPNT is INTEGER
+*> The location of the last eigenvalue in the leading sub-matrix.
+*> min(1,N) <= CUTPNT <= N/2.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (4*N + N**2)
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (4*N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit.
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> > 0: if INFO = 1, an eigenvalue did not converge
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date September 2012
+*
+*> \ingroup auxOTHERcomputational
+*
+*> \par Contributors:
+* ==================
+*>
+*> Jeff Rutter, Computer Science Division, University of California
+*> at Berkeley, USA \n
+*> Modified by Francoise Tisseur, University of Tennessee
+*>
+* =====================================================================
SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
$ INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* September 2012
*
* .. Scalar Arguments ..
INTEGER CUTPNT, INFO, LDQ, N
@@ -15,90 +177,6 @@
DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DLAED1 computes the updated eigensystem of a diagonal
-* matrix after modification by a rank-one symmetric matrix. This
-* routine is used only for the eigenproblem which requires all
-* eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles
-* the case in which eigenvalues only or eigenvalues and eigenvectors
-* of a full symmetric matrix (which was reduced to tridiagonal form)
-* are desired.
-*
-* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
-*
-* where Z = Q'u, u is a vector of length N with ones in the
-* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
-*
-* The eigenvectors of the original matrix are stored in Q, and the
-* eigenvalues are in D. The algorithm consists of three stages:
-*
-* The first stage consists of deflating the size of the problem
-* when there are multiple eigenvalues or if there is a zero in
-* the Z vector. For each such occurence the dimension of the
-* secular equation problem is reduced by one. This stage is
-* performed by the routine DLAED2.
-*
-* The second stage consists of calculating the updated
-* eigenvalues. This is done by finding the roots of the secular
-* equation via the routine DLAED4 (as called by DLAED3).
-* This routine also calculates the eigenvectors of the current
-* problem.
-*
-* The final stage consists of computing the updated eigenvectors
-* directly using the updated eigenvalues. The eigenvectors for
-* the current problem are multiplied with the eigenvectors from
-* the overall problem.
-*
-* Arguments
-* =========
-*
-* N (input) INTEGER
-* The dimension of the symmetric tridiagonal matrix. N >= 0.
-*
-* D (input/output) DOUBLE PRECISION array, dimension (N)
-* On entry, the eigenvalues of the rank-1-perturbed matrix.
-* On exit, the eigenvalues of the repaired matrix.
-*
-* Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
-* On entry, the eigenvectors of the rank-1-perturbed matrix.
-* On exit, the eigenvectors of the repaired tridiagonal matrix.
-*
-* LDQ (input) INTEGER
-* The leading dimension of the array Q. LDQ >= max(1,N).
-*
-* INDXQ (input/output) INTEGER array, dimension (N)
-* On entry, the permutation which separately sorts the two
-* subproblems in D into ascending order.
-* On exit, the permutation which will reintegrate the
-* subproblems back into sorted order,
-* i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
-*
-* RHO (input) DOUBLE PRECISION
-* The subdiagonal entry used to create the rank-1 modification.
-*
-* CUTPNT (input) INTEGER
-* The location of the last eigenvalue in the leading sub-matrix.
-* min(1,N) <= CUTPNT <= N/2.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (4*N + N**2)
-*
-* IWORK (workspace) INTEGER array, dimension (4*N)
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* > 0: if INFO = 1, an eigenvalue did not converge
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Jeff Rutter, Computer Science Division, University of California
-* at Berkeley, USA
-* Modified by Francoise Tisseur, University of Tennessee.
-*
* =====================================================================
*
* .. Local Scalars ..