SRC/dtrexc.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

✨ NAME ✨

SRC/dtrexc.f — bestie, this is the page, and the manual name is Library Functions Manual. It’s all about the DTREXC subroutine, and honestly? Iconic. 🫶

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine dtrexc (compq, n, t, ldt, q, ldq, ifst, ilst, work, info) — DTREXC, the whole point of this page. 💅

💖 Function/Subroutine Documentation 💖

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:

Okay so 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. No cap, that’s the whole mission. ✨

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.
🚨 Bestie, the INFO = 1 case is the messy one: 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. Keep that in mind, fr fr.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 146 of file dtrexc.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

💖 That’s the whole vibe, bestie — page from SRC/dtrexc.f(3), LAPACK Version 3.12.0, and yes, she ate. Periodt. 🎀✨

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