SRC/strexc.f(3)

💅 SRC/strexc.f 💅

Bestie, this is the Library Functions Manual page for SRC/strexc.f — yes, we folded the manual name right up here because we're cute like that. It's all about strexc, a tiny but iconic reordering subroutine. 🫶✨

✨ NAME ✨

SRC/strexc.f — home of the strexc subroutine, the one that reorders the real Schur factorization. Periodt.

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine strexc (compq, n, t, ldt, q, ldq, ifst, ilst, work, info)
    STREXC

👑 Function/Subroutine Documentation 👑

Here's the full signature, bestie — keep it exactly as it is:

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 🎀

Okay so 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. That's the vibe check for T. 💅

🧚 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. (Yes, it really says “Schur Schur” — we report, we don't edit.)
• 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. That's the whole card, bestie; the actual moving instructions live under ILST.
• 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.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

💌 Cute sign-off: this page is from LAPACK, Version 3.12.0, source page SRC/strexc.f(3) — sending you all the good vibes, bestie. 🎀💖