# laeda - Man Page

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.

## 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

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

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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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK