trexc(3) Library Functions Manual trexc(3) NAME trexc - trexc: reorder Schur form SYNOPSIS Functions subroutine ctrexc (compq, n, t, ldt, q, ldq, ifst, ilst, info) CTREXC subroutine dtrexc (compq, n, t, ldt, q, ldq, ifst, ilst, work, info) DTREXC subroutine strexc (compq, n, t, ldt, q, ldq, ifst, ilst, work, info) STREXC subroutine ztrexc (compq, n, t, ldt, q, ldq, ifst, ilst, info) ZTREXC Detailed Description Function Documentation subroutine ctrexc (character compq, integer n, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, integer info) CTREXC Purpose: CTREXC reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST. The Schur form T is reordered by a unitary similarity transformation Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by postmultiplying it with Z. Parameters COMPQ COMPQ is CHARACTER*1 = 'V': update the matrix Q of Schur vectors; = 'N': do not update Q. N N is INTEGER The order of the matrix T. N >= 0. If N == 0 arguments ILST and IFST may be any value. T T is COMPLEX array, dimension (LDT,N) On entry, the upper triangular matrix T. On exit, the reordered upper triangular matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). Q Q is COMPLEX array, dimension (LDQ,N) On entry, if COMPQ = 'V', the matrix Q of Schur vectors. On exit, if COMPQ = 'V', Q has been postmultiplied by the unitary transformation matrix Z which reorders T. If COMPQ = 'N', Q is not referenced. LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= 1, and if COMPQ = 'V', LDQ >= max(1,N). IFST IFST is INTEGER ILST ILST is INTEGER Specify the reordering of the diagonal elements of T: The element with row index IFST is moved to row ILST by a sequence of transpositions between adjacent elements. 1 <= IFST <= N; 1 <= ILST <= N. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 125 of file ctrexc.f. subroutine dtrexc (character compq, integer n, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, double precision, dimension( * ) work, integer info) DTREXC Purpose: DTREXC reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST. The real Schur form T is reordered by an orthogonal similarity transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors is updated by postmultiplying it with Z. T must be in Schur canonical form (as returned by DHSEQR), 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. Parameters COMPQ COMPQ is CHARACTER*1 = 'V': update the matrix Q of Schur vectors; = 'N': do not update Q. N N is INTEGER The order of the matrix T. N >= 0. If N == 0 arguments ILST and IFST may be any value. T T is DOUBLE PRECISION array, dimension (LDT,N) On entry, the upper quasi-triangular matrix T, in Schur Schur canonical form. On exit, the reordered upper quasi-triangular matrix, again in Schur canonical form. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). Q Q is DOUBLE PRECISION array, dimension (LDQ,N) On entry, if COMPQ = 'V', the matrix Q of Schur vectors. On exit, if COMPQ = 'V', Q has been postmultiplied by the orthogonal transformation matrix Z which reorders T. If COMPQ = 'N', Q is not referenced. LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= 1, and if COMPQ = 'V', LDQ >= max(1,N). IFST IFST is INTEGER ILST ILST is INTEGER Specify the reordering of the diagonal blocks of T. The block with row index IFST is moved to row ILST, by a sequence of transpositions between adjacent blocks. On exit, if IFST pointed on entry to the second row of a 2-by-2 block, it is changed to point to the first row; ILST always points to the first row of the block in its final position (which may differ from its input value by +1 or -1). 1 <= IFST <= N; 1 <= ILST <= N. WORK WORK is DOUBLE PRECISION array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value = 1: two adjacent blocks were too close to swap (the problem is very ill-conditioned); T may have been partially reordered, and ILST points to the first row of the current position of the block being moved. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 146 of file dtrexc.f. subroutine strexc (character compq, integer n, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, real, dimension( * ) work, integer info) STREXC Purpose: STREXC reorders the real Schur factorization of a real matrix A = Q*T*Q**T, so that the diagonal block of T with row index IFST is moved to row ILST. The real Schur form T is reordered by an orthogonal similarity transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors is updated by postmultiplying it with Z. T must be in Schur canonical form (as returned by SHSEQR), 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. Parameters COMPQ COMPQ is CHARACTER*1 = 'V': update the matrix Q of Schur vectors; = 'N': do not update Q. N N is INTEGER The order of the matrix T. N >= 0. If N == 0 arguments ILST and IFST may be any value. T T is REAL array, dimension (LDT,N) On entry, the upper quasi-triangular matrix T, in Schur Schur canonical form. On exit, the reordered upper quasi-triangular matrix, again in Schur canonical form. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). Q Q is REAL array, dimension (LDQ,N) On entry, if COMPQ = 'V', the matrix Q of Schur vectors. On exit, if COMPQ = 'V', Q has been postmultiplied by the orthogonal transformation matrix Z which reorders T. If COMPQ = 'N', Q is not referenced. LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= 1, and if COMPQ = 'V', LDQ >= max(1,N). IFST IFST is INTEGER ILST ILST is INTEGER Specify the reordering of the diagonal blocks of T. The block with row index IFST is moved to row ILST, by a sequence of transpositions between adjacent blocks. On exit, if IFST pointed on entry to the second row of a 2-by-2 block, it is changed to point to the first row; ILST always points to the first row of the block in its final position (which may differ from its input value by +1 or -1). 1 <= IFST <= N; 1 <= ILST <= N. WORK WORK is REAL array, dimension (N) INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value = 1: two adjacent blocks were too close to swap (the problem is very ill-conditioned); T may have been partially reordered, and ILST points to the first row of the current position of the block being moved. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 146 of file strexc.f. subroutine ztrexc (character compq, integer n, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, integer info) ZTREXC Purpose: ZTREXC reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST. The Schur form T is reordered by a unitary similarity transformation Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by postmultiplying it with Z. Parameters COMPQ COMPQ is CHARACTER*1 = 'V': update the matrix Q of Schur vectors; = 'N': do not update Q. N N is INTEGER The order of the matrix T. N >= 0. If N == 0 arguments ILST and IFST may be any value. T T is COMPLEX*16 array, dimension (LDT,N) On entry, the upper triangular matrix T. On exit, the reordered upper triangular matrix. LDT LDT is INTEGER The leading dimension of the array T. LDT >= max(1,N). Q Q is COMPLEX*16 array, dimension (LDQ,N) On entry, if COMPQ = 'V', the matrix Q of Schur vectors. On exit, if COMPQ = 'V', Q has been postmultiplied by the unitary transformation matrix Z which reorders T. If COMPQ = 'N', Q is not referenced. LDQ LDQ is INTEGER The leading dimension of the array Q. LDQ >= 1, and if COMPQ = 'V', LDQ >= max(1,N). IFST IFST is INTEGER ILST ILST is INTEGER Specify the reordering of the diagonal elements of T: The element with row index IFST is moved to row ILST by a sequence of transpositions between adjacent elements. 1 <= IFST <= N; 1 <= ILST <= N. INFO INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 125 of file ztrexc.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 trexc(3)