LAPACK

NAME¶

laeda - laeda: D&C step: z vector

SYNOPSIS¶

Functions¶

subroutine dlaeda (n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z, ztemp, info)
DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense. subroutine slaeda (n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z, ztemp, info)
SLAEDA used by SSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.

Detailed Description¶

Function Documentation¶

subroutine dlaeda (integer n, integer tlvls, integer curlvl, integer curpbm, integer, dimension( * ) prmptr, integer, dimension( * ) perm, integer, dimension( * ) givptr, integer, dimension( 2, * ) givcol, double precision, dimension( 2, * ) givnum, double precision, dimension( * ) q, integer, dimension( * ) qptr, double precision, dimension( * ) z, double precision, dimension( * ) ztemp, integer info)¶

DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.

Purpose:



 DLAEDA computes the Z vector corresponding to the merge step in the


 CURLVLth step of the merge process with TLVLS steps for the CURPBMth


 problem.

Parameters



          N is INTEGER


         The dimension of the symmetric tridiagonal matrix.  N >= 0.

TLVLS



          TLVLS is INTEGER


         The total number of merging levels in the overall divide and


         conquer tree.

CURLVL



          CURLVL is INTEGER


         The current level in the overall merge routine,


         0 <= curlvl <= tlvls.

CURPBM



          CURPBM is INTEGER


         The current problem in the current level in the overall


         merge routine (counting from upper left to lower right).

PRMPTR



          PRMPTR is 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 incidentally the


         size of the full, non-deflated problem.

PERM



          PERM is INTEGER array, dimension (N lg N)


         Contains the permutations (from deflation and sorting) to be


         applied to each eigenblock.

GIVPTR



          GIVPTR is 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



          GIVCOL is INTEGER array, dimension (2, N lg N)


         Each pair of numbers indicates a pair of columns to take place


         in a Givens rotation.

GIVNUM



          GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N)


         Each number indicates the S value to be used in the


         corresponding Givens rotation.



          Q is DOUBLE PRECISION array, dimension (N**2)


         Contains the square eigenblocks from previous levels, the


         starting positions for blocks are given by QPTR.

QPTR



          QPTR is INTEGER array, dimension (N+2)


         Contains a list of pointers which indicate where in Q an


         eigenblock is stored.  SQRT( QPTR(i+1) - QPTR(i) ) indicates


         the size of the block.



          Z is DOUBLE PRECISION array, dimension (N)


         On output this vector contains the updating vector (the last


         row of the first sub-eigenvector matrix and the first row of


         the second sub-eigenvector matrix).

ZTEMP



          ZTEMP is DOUBLE PRECISION array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit.


          < 0:  if INFO = -i, the i-th argument had an illegal value.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

subroutine slaeda (integer n, integer tlvls, integer curlvl, integer curpbm, integer, dimension( * ) prmptr, integer, dimension( * ) perm, integer, dimension( * ) givptr, integer, dimension( 2, * ) givcol, real, dimension( 2, * ) givnum, real, dimension( * ) q, integer, dimension( * ) qptr, real, dimension( * ) z, real, dimension( * ) ztemp, integer info)¶

SLAEDA used by SSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.