b?laexc

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

b?laexc

Swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation.

Syntax

call bslaexc ( n , t , ldt , j1 , n1 , n2 , itraf , dtraf , work , info )

call bdlaexc ( n , t , ldt , j1 , n1 , n2 , itraf , dtraf , work , info )

Include Files

mkl_scalapack.h

Description

b?laexc swaps adjacent diagonal blocks T11 and T22 of order 1 or 2 in an upper quasi-triangular matrix T by an orthogonal similarity transformation.

In contrast to the LAPACK routine ?laexc (Swaps adjacent diagonal blocks of a real upper quasi-triangular matrix in Schur canonical form, by an orthogonal similarity transformation.) function ?laexc , the orthogonal transformation matrix Q is not explicitly constructed but represented by parameters contained in the arrays itraf and dtraf . See the description of b?trexc (Reorders the Schur factorization of a general matrix.) for more details.

T must be in Schur canonical form, that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diagonal elements of opposite sign.

Input Parameters

n

INTEGER The order of the matrix T . n ≥ 0.

t

REAL for bslaexc DOUBLE PRECISION for bdlaexc

Array of size ( ldt , n ) .

The upper quasi-triangular matrix T , in Schur canonical form.

ldt

INTEGER The leading dimension of the array t . ldt ≥ max(1, n ).

j1

INTEGER The index of the first row of the first block T11 .

n1

INTEGER The order of the first block T11 . n1 = 0, 1 or 2.

n2

INTEGER The order of the second block T22 . n2 = 0, 1 or 2.

work

REAL for bslaexc DOUBLE PRECISION for bdlaexc (Workspace) array of size n .

OUTPUT Parameters

t: The updated matrix T , in Schur canonical form.

itraf

INTEGER array, length k , where

k = 1, if n1 + n2 = 2; k = 2, if n1 + n2 = 3; k = 4, if n1 + n2 = 4. List of parameters for representing the transformation matrix Q , see b?trexc (Reorders the Schur factorization of a general matrix.) .

dtraf: REAL for bslaexc DOUBLE PRECISION for bdlaexc Array, length k , where k = 2, if n1 + n2 = 2; k = 5, if n1 + n2 = 3; k = 10, if n1 + n2 = 4. List of parameters for representing the transformation matrix Q , see b?trexc (Reorders the Schur factorization of a general matrix.) .
info: INTEGER = 0: successful exit = 1: the transformed matrix T would be too far from Schur form; the blocks are not swapped and T and Q are unchanged.

NOTE:

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

b?laexc

Syntax

Include Files

Description

Input Parameters

OUTPUT Parameters