dtrexc - reorder 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
SUBROUTINE DTREXC(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO) CHARACTER*1 COMPQ INTEGER N, LDT, LDQ, IFST, ILST, INFO DOUBLE PRECISION T(LDT,*), Q(LDQ,*), WORK(*) SUBROUTINE DTREXC_64(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO) CHARACTER*1 COMPQ INTEGER*8 N, LDT, LDQ, IFST, ILST, INFO DOUBLE PRECISION T(LDT,*), Q(LDQ,*), WORK(*) F95 INTERFACE SUBROUTINE TREXC(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO) CHARACTER(LEN=1) :: COMPQ INTEGER :: N, LDT, LDQ, IFST, ILST, INFO REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: T, Q SUBROUTINE TREXC_64(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO) CHARACTER(LEN=1) :: COMPQ INTEGER(8) :: N, LDT, LDQ, IFST, ILST, INFO REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: T, Q C INTERFACE #include <sunperf.h> void dtrexc(char compq, int n, double *t, int ldt, double *q, int ldq, int *ifst, int *ilst, int *info); void dtrexc_64(char compq, long n, double *t, long ldt, double *q, long ldq, long *ifst, long *ilst, long *info);
Oracle Solaris Studio Performance Library dtrexc(3P) NAME dtrexc - reorder 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 SYNOPSIS SUBROUTINE DTREXC(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO) CHARACTER*1 COMPQ INTEGER N, LDT, LDQ, IFST, ILST, INFO DOUBLE PRECISION T(LDT,*), Q(LDQ,*), WORK(*) SUBROUTINE DTREXC_64(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO) CHARACTER*1 COMPQ INTEGER*8 N, LDT, LDQ, IFST, ILST, INFO DOUBLE PRECISION T(LDT,*), Q(LDQ,*), WORK(*) F95 INTERFACE SUBROUTINE TREXC(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO) CHARACTER(LEN=1) :: COMPQ INTEGER :: N, LDT, LDQ, IFST, ILST, INFO REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: T, Q SUBROUTINE TREXC_64(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO) CHARACTER(LEN=1) :: COMPQ INTEGER(8) :: N, LDT, LDQ, IFST, ILST, INFO REAL(8), DIMENSION(:) :: WORK REAL(8), DIMENSION(:,:) :: T, Q C INTERFACE #include <sunperf.h> void dtrexc(char compq, int n, double *t, int ldt, double *q, int ldq, int *ifst, int *ilst, int *info); void dtrexc_64(char compq, long n, double *t, long ldt, double *q, long ldq, long *ifst, long *ilst, long *info); 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 trans- formation 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-diag- onal elements of opposite sign. ARGUMENTS COMPQ (input) = 'V': update the matrix Q of Schur vectors; = 'N': do not update Q. N (input) The order of the matrix T. N >= 0. T (input/output) On entry, the upper quasi-triangular matrix T, in Schur Schur canonical form. On exit, the reordered upper quasi-triangu- lar matrix, again in Schur canonical form. LDT (input) The leading dimension of the array T. LDT >= max(1,N). Q (input) 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 (input) The leading dimension of the array Q. LDQ >= max(1,N). IFST (input/output) 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 dif- fer from its input value by +1 or -1). 1 <= IFST <= N; 1 <= ILST <= N. ILST (input/output) See the description of IFST. WORK (workspace) dimension(N) INFO (output) = 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. 7 Nov 2015 dtrexc(3P)