?laeda

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 10/15/2026

Version

Public

?laeda

Used by ?stedc . Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.

Syntax

call slaeda(n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z,
            ztemp, info)

call dlaeda(n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z,
            ztemp, info)

Include Files

mkl.fi

Description

The routine ?laeda computes the Z vector corresponding to the merge step in the curlvl -th step of the merge process with tlvls steps for the curpbm -th problem.

Input Parameters

n: INTEGER . The dimension of the symmetric tridiagonal matrix ( n≥ 0 ).
tlvls: INTEGER . The total number of merging levels in the overall divide and conquer tree.
curlvl: INTEGER . The current level in the overall merge routine, 0 ≤ curlvl ≤ tlvls .
curpbm: INTEGER . The current problem in the current level in the overall merge routine (counting from upper left to lower right).
prmptr , perm , givptr: INTEGER . Arrays, dimension ( n log ₂n ) each. The array prmptr (*) 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. The array perm (*) contains the permutations (from deflation and sorting) to be applied to each eigenblock. The array givptr (*) 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: INTEGER . Array, dimension (2, n log ₂n ). Each pair of numbers indicates a pair of columns to take place in a Givens rotation.
givnum: REAL for slaeda DOUBLE PRECISION for dlaeda . Array, dimension (2, n log ₂n ). Each number indicates the S value to be used in the corresponding Givens rotation.
q: REAL for slaeda DOUBLE PRECISION for dlaeda . Array, dimension ( n² ). Contains the square eigenblocks from previous levels, the starting positions for blocks are given by qptr .
qptr: 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.
ztemp: REAL for slaeda DOUBLE PRECISION for dlaeda . Workspace array, dimension ( n ).

Output Parameters

z: REAL for slaeda DOUBLE PRECISION for dlaeda . Array, dimension ( n ). Contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix).

info

INTEGER .

If info = 0 , the execution is successful.
If info = -i , the i -th parameter had an illegal value.

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laeda

Syntax

Include Files

Description

Input Parameters

Output Parameters