slaed1.f File Reference

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Functions/Subroutines
subroutine	slaed1 (N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK, INFO)
	SLAED1 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.

---

Function/Subroutine Documentation

subroutine slaed1	(	integer	N,
		real, dimension( * )	D,
		real, dimension( ldq, * )	Q,
		integer	LDQ,
		integer, dimension( * )	INDXQ,
		real	RHO,
		integer	CUTPNT,
		real, dimension( * )	WORK,
		integer, dimension( * )	IWORK,
		integer	INFO
	)

SLAED1 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.

Download SLAED1 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

 SLAED1 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.  SLAED7 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 SLAED2.

       The second stage consists of calculating the updated
       eigenvalues. This is done by finding the roots of the secular
       equation via the routine SLAED4 (as called by SLAED3).
       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.

Parameters:

[in]	N	N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0.
[in,out]	D	D is REAL array, dimension (N) On entry, the eigenvalues of the rank-1-perturbed matrix. On exit, the eigenvalues of the repaired matrix.
[in,out]	Q	Q is REAL array, dimension (LDQ,N) On entry, the eigenvectors of the rank-1-perturbed matrix. On exit, the eigenvectors of the repaired tridiagonal matrix.
[in]	LDQ	LDQ is INTEGER The leading dimension of the array Q. LDQ >= max(1,N).
[in,out]	INDXQ	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.
[in]	RHO	RHO is REAL The subdiagonal entry used to create the rank-1 modification.
[in]	CUTPNT	CUTPNT is INTEGER The location of the last eigenvalue in the leading sub-matrix. min(1,N) <= CUTPNT <= N/2.
[out]	WORK	WORK is REAL array, dimension (4*N + N**2)
[out]	IWORK	IWORK is INTEGER array, dimension (4*N)
[out]	INFO	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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee

Definition at line 163 of file slaed1.f.

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