laeda(3)

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

              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

              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

              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

Definition at line 164 of file dlaeda.f.

  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.

Purpose:

     SLAEDA 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

              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 REAL array, dimension (2, N lg N)
             Each number indicates the S value to be used in the
             corresponding Givens rotation.

    Q

              Q is REAL 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

              Z is REAL 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 REAL 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

Definition at line 164 of file slaeda.f.

Author

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