?laeda

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

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

slaeda dlaeda

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