trexc(3)

📦

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🎀 trexc(3) — reorder Schur form 🎀

okay so this is trexc(3), from the Library Functions Manual, and bestie… it's giving "four subroutines, one very specific job" energy ✨ This whole page is about taking a Schur form and moving one thing somewhere else in it, and honestly? iconic behaviour. Let's get into it 💅

✨ 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 💫

No extra lore here — the page goes straight into documenting the functions themselves, so that's exactly what we're doing too 🎀

👑 Function Documentation 👑

💜 ctrexc — CTREXC

subroutine ctrexc (character compq, integer n, complex, dimension( ldt, * ) t,
     integer ldt, complex, dimension( ldq, * ) q, integer ldq, integer
     ifst, integer ilst, integer info)

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 gets 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. Slay ✨

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. (no thoughts, head empty, it literally does not matter 🙈)
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. (she's not coming to the party 🫶)
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
- These two 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.

🦋 dtrexc — DTREXC

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)

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.

Heads up bestie 📢 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. No substitutions, no "close enough" — the vibe check is strict.

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. (yes, it says Schur twice — the source really did that, and honestly? she ate 😭)
- 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
- These 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). Track that glow-up carefully 💅
- 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. Not a full slay, more of a partial slay 💀

Author: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.

Definition at line 146 of file dtrexc.f.

🌸 strexc — STREXC

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)

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.

Same deal as above, bestie 📢 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. (double Schur again — consistency is key ✨)
- 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
- These 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.

🧚 ztrexc — ZTREXC

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)

Purpose:

…and that's exactly where this half of the page runs out 🫠 the rest of ZTREXC's purpose, parameters, author line and file definition are all waiting for you in part 2 💖

…okay so picking right back up, bestie 💅

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. Fr fr, that's the whole plot.

The Schur form T gets 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. Lowkey elegant, ngl 🦋

✨ Parameters ✨

COMPQ

COMPQ is CHARACTER*1

= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.

Like, do you want the vectors or not, pick a lane bestie 🎀

N

N is INTEGER

The order of the matrix T. N >= 0.

And here's the little get-out-of-jail card: if N == 0, arguments ILST and IFST may be any value. Zero-sized matrix, zero problems, we love a chill edge case 💖

T

T is COMPLEX*16 array, dimension (LDT,N)

On entry, the upper triangular matrix T.

On exit, the reordered upper triangular matrix. She gets a glow-up in place, iconic 💅

LDT

LDT is INTEGER

The leading dimension of the array T. LDT >= max(1,N). Respect the leading dimension or perish, that's the rule 🙈

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. She's simply not invited to the function, no hard feelings 🫶

LDQ

LDQ is INTEGER

The leading dimension of the array Q. LDQ >= 1, and if COMPQ = 'V', LDQ >= max(1,N). Read the condition, bestie — it's conditional for a reason ✨

IFST

IFST is INTEGER

ILST

ILST is INTEGER

These two 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.

Heads up: those bounds are not a suggestion. Step outside 1 to N and INFO will come for you 💀

INFO

INFO is INTEGER

= 0: successful exit 🎉 slay, we ate
< 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.

And that's the whole page, bestie 🫶 this little beauty is from LAPACK Version 3.12.0 — the trexc(3) page — and no, I did not make any of it up, every flag is right where the source code left it. Go reorder some Schur forms, you absolute main character 🌈⭐💜

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms