b?laexc

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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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 )

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, 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 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.

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.

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.

Parent topic: ScaLAPACK Auxiliary Routines

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b?laexc

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