SUBROUTINE CLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q,
$ LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM,
$ GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK,
$ INFO )
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ,
$ TLVLS
REAL RHO
* ..
* .. Array Arguments ..
INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ),
$ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * )
REAL D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * )
COMPLEX Q( LDQ, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* CLAED7 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 optionally eigenvectors of a dense or banded
* Hermitian matrix that has been reduced to tridiagonal form.
*
* 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 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.
*
* Arguments
* =========
*
* N (input) INTEGER
* The dimension of the symmetric tridiagonal matrix. N >= 0.
*
* CUTPNT (input) INTEGER
* Contains the location of the last eigenvalue in the leading
* sub-matrix. min(1,N) <= CUTPNT <= N.
*
* QSIZ (input) INTEGER
* The dimension of the unitary matrix used to reduce
* the full matrix to tridiagonal form. QSIZ >= N.
*
* TLVLS (input) INTEGER
* The total number of merging levels in the overall divide and
* conquer tree.
*
* CURLVL (input) INTEGER
* The current level in the overall merge routine,
* 0 <= curlvl <= tlvls.
*
* CURPBM (input) INTEGER
* The current problem in the current level in the overall
* merge routine (counting from upper left to lower right).
*
* D (input/output) REAL array, dimension (N)
* On entry, the eigenvalues of the rank-1-perturbed matrix.
* On exit, the eigenvalues of the repaired matrix.
*
* Q (input/output) COMPLEX 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).
*
* RHO (input) REAL
* Contains the subdiagonal element used to create the rank-1
* modification.
*
* INDXQ (output) INTEGER array, dimension (N)
* This contains the permutation which will reintegrate the
* subproblem just solved back into sorted order,
* ie. D( INDXQ( I = 1, N ) ) will be in ascending order.
*
* IWORK (workspace) INTEGER array, dimension (4*N)
*
* RWORK (workspace) REAL array,
* dimension (3*N+2*QSIZ*N)
*
* WORK (workspace) COMPLEX array, dimension (QSIZ*N)
*
* QSTORE (input/output) REAL array, dimension (N**2+1)
* Stores eigenvectors of submatrices encountered during
* divide and conquer, packed together. QPTR points to
* beginning of the submatrices.
*
* QPTR (input/output) INTEGER array, dimension (N+2)
* List of indices pointing to beginning of submatrices stored
* in QSTORE. The submatrices are numbered starting at the
* bottom left of the divide and conquer tree, from left to
* right and bottom to top.
*
* PRMPTR (input) INTEGER array, dimension (N lg N)
* Contains a list of pointers which indicate where in PERM a
* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i)
* indicates the size of the permutation and also the size of
* the full, non-deflated problem.
*
* PERM (input) INTEGER array, dimension (N lg N)
* Contains the permutations (from deflation and sorting) to be
* applied to each eigenblock.
*
* GIVPTR (input) INTEGER array, dimension (N lg N)
* Contains a list of pointers which indicate where in GIVCOL a
* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i)
* indicates the number of Givens rotations.
*
* GIVCOL (input) INTEGER array, dimension (2, N lg N)
* Each pair of numbers indicates a pair of columns to take place
* in a Givens rotation.
*
* GIVNUM (input) REAL array, dimension (2, N lg N)
* Each number indicates the S value to be used in the
* corresponding Givens rotation.
*
* 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
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER COLTYP, CURR, I, IDLMDA, INDX,
$ INDXC, INDXP, IQ, IW, IZ, K, N1, N2, PTR
* ..
* .. External Subroutines ..
EXTERNAL CLACRM, CLAED8, SLAED9, SLAEDA, SLAMRG, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
*
* IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN
* INFO = -1
* ELSE IF( N.LT.0 ) THEN
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN
INFO = -2
ELSE IF( QSIZ.LT.N ) THEN
INFO = -3
ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CLAED7', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* The following values are for bookkeeping purposes only. They are
* integer pointers which indicate the portion of the workspace
* used by a particular array in SLAED2 and SLAED3.
*
IZ = 1
IDLMDA = IZ + N
IW = IDLMDA + N
IQ = IW + N
*
INDX = 1
INDXC = INDX + N
COLTYP = INDXC + N
INDXP = COLTYP + N
*
* Form the z-vector which consists of the last row of Q_1 and the
* first row of Q_2.
*
PTR = 1 + 2**TLVLS
DO 10 I = 1, CURLVL - 1
PTR = PTR + 2**( TLVLS-I )
10 CONTINUE
CURR = PTR + CURPBM
CALL SLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
$ GIVCOL, GIVNUM, QSTORE, QPTR, RWORK( IZ ),
$ RWORK( IZ+N ), INFO )
*
* When solving the final problem, we no longer need the stored data,
* so we will overwrite the data from this level onto the previously
* used storage space.
*
IF( CURLVL.EQ.TLVLS ) THEN
QPTR( CURR ) = 1
PRMPTR( CURR ) = 1
GIVPTR( CURR ) = 1
END IF
*
* Sort and Deflate eigenvalues.
*
CALL CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, RWORK( IZ ),
$ RWORK( IDLMDA ), WORK, QSIZ, RWORK( IW ),
$ IWORK( INDXP ), IWORK( INDX ), INDXQ,
$ PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ),
$ GIVCOL( 1, GIVPTR( CURR ) ),
$ GIVNUM( 1, GIVPTR( CURR ) ), INFO )
PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N
GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR )
*
* Solve Secular Equation.
*
IF( K.NE.0 ) THEN
CALL SLAED9( K, 1, K, N, D, RWORK( IQ ), K, RHO,
$ RWORK( IDLMDA ), RWORK( IW ),
$ QSTORE( QPTR( CURR ) ), K, INFO )
CALL CLACRM( QSIZ, K, WORK, QSIZ, QSTORE( QPTR( CURR ) ), K, Q,
$ LDQ, RWORK( IQ ) )
QPTR( CURR+1 ) = QPTR( CURR ) + K**2
IF( INFO.NE.0 ) THEN
RETURN
END IF
*
* Prepare the INDXQ sorting premutation.
*
N1 = K
N2 = N - K
CALL SLAMRG( N1, N2, D, 1, -1, INDXQ )
ELSE
QPTR( CURR+1 ) = QPTR( CURR )
DO 20 I = 1, N
INDXQ( I ) = I
20 CONTINUE
END IF
*
RETURN
*
* End of CLAED7
*
END