LAEXC - 5.2 English - 68552

LAEXC swaps adjacent diagonal blocks of a real upper quasi-triangular

matrix in Schur canonical form, by an orthogonal similarity transformation.

Purpose:

 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.

 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 elemnts equal and its off-diagonal elements of
 opposite sign.

Parameters:

• WANTQ – [in]

  WANTQ is LOGICAL

  = .TRUE. : accumulate the transformation in the matrix Q;

  = .FALSE.: do not accumulate the transformation.

• N – [in]

  N is INTEGER

  The order of the matrix T. N >= 0.

• T – [inout]

  T is REAL array, dimension (LDT,N)

  On entry, the upper quasi-triangular matrix T, in Schur canonical form.

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

• LDT – [in]

  LDT is INTEGER

  The leading dimension of the array T. LDT >= fla_max(1,N).

• Q – [inout]

  Q is REAL array, dimension (LDQ,N)

  On entry, if WANTQ is .TRUE., the orthogonal matrix Q. On exit, if WANTQ is .TRUE., the updated matrix Q.

  If WANTQ is .FALSE., Q is not referenced.

• LDQ – [in]

  LDQ is INTEGER

  The leading dimension of the array Q. LDQ >= 1; and if WANTQ is .TRUE., LDQ >= N.

• J1 – [in]

  J1 is INTEGER

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

• N1 – [in]

  N1 is INTEGER

  The order of the first block T11. N1 = 0, 1 or 2.

• N2 – [in]

  N2 is INTEGER

  The order of the second block T22. N2 = 0, 1 or 2.

• WORK – [out] WORK is REAL array, dimension (N)

• INFO – [out]

  INFO is 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.