?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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?laexc

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

Syntax

call slaexc( wantq, n, t, ldt, q, ldq, j1, n1, n2, work, info )

call dlaexc( wantq, n, t, ldt, q, ldq, j1, n1, n2, work, info )

Include Files

mkl.fi

Description

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

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

wantq

LOGICAL.

If wantq = .TRUE., accumulate the transformation in the matrix Q;

If wantq = .FALSE., do not accumulate the transformation.

n

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

t, q

REAL for slaexc

DOUBLE PRECISION for dlaexc

Arrays:

t(ldt,*) contains on entry the upper quasi-triangular matrix T, in Schur canonical form.

The second dimension of t must be at least max(1, n).

q(ldq,*) contains on entry, if wantq = .TRUE., the orthogonal matrix Q. If wantq = .FALSE., q is not referenced. The second dimension of q must be at least max(1, n).

ldt

INTEGER. The leading dimension of t; at least max(1, n).

ldq

INTEGER. The leading dimension of q;

If wantq = .FALSE., then ldq≥ 1.

If wantq = .TRUE., then ldq≥ 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 slaexc;

DOUBLE PRECISION for dlaexc.

Workspace array, DIMENSION (n).

Output Parameters

t

On exit, the updated matrix T, again in Schur canonical form.

q

On exit, if wantq = .TRUE., the updated matrix Q.

info

INTEGER.

If info = 0, the execution is successful.

If info = 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: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?laexc