STREXC(3)

okay bestie, welcome to STREXC(3) from the Library Functions Manual — it’s LAPACK’s real Schur reordering glow-up, and we’re gonna get you comfy with it 💖

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/strexc.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

👑 Function/Subroutine Documentation 👑

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 the whole point: 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 (yes, the page says it twice 😭). 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.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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byeee bestie 💖 this was LAPACK Version 3.12.0, source page /home/abui...RC/strexc.f(3), and the footer didn’t list a date — so consider this the timeless edition ✨🫶