/home/abui.../strsyl3.f(3)

🦋 strsyl3.f — Library Functions Manual 🦋

okay so this is /home/abui.../strsyl3.f(3), bestie — a LAPACK page, and honestly? it's giving main character energy 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/strsyl3.f

like, that's the whole name. it's a whole path. yes it's long. no we're not shortening it. 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine STRSYL3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc,
    scale, iwork, liwork, swork, ldswork, info)

STRSYL3 — that's our girl 💖

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✨ Function/Subroutine Documentation ✨

subroutine STRSYL3 (character trana, character tranb, integer isgn, integer
    m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension(
    ldb, * ) b, integer ldb, real, dimension( ldc, * ) c, integer ldc, real
    scale, integer, dimension( * ) iwork, integer liwork, real, dimension(
    ldswork, * ) swork, integer ldswork, integer info)

STRSYL3 — literally the same subroutine, just spelled out with all the types. slay. ✨

🎀 Purpose 🎀

ok so the actual code comment goes like this, no cap:

!>
!>  STRSYL3 solves the real Sylvester matrix equation:
!>
!>     op(A)*X + X*op(B) = scale*C or
!>     op(A)*X - X*op(B) = scale*C,
!>
!>  where op(A) = A or A**T, and  A and B are both upper quasi-
!>  triangular. A is M-by-M and B is N-by-N; the right hand side C and
!>  the solution X are M-by-N; and scale is an output scale factor, set
!>  <= 1 to avoid overflow in X.
!>
!>  A and B 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.
!>
!>  This is the block version of the algorithm.
!>

so basically: it solves the Sylvester matrix equation, in one of two flavours — plus or minus — and it hands you back a scale factor (<= 1) so nothing overflows in X. 🔥 big brain behaviour fr fr.

and the vibe check on the inputs: A and B have to be in Schur canonical form (the thing SHSEQR gives you), i.e. block upper triangular with 1-by-1 and 2-by-2 diagonal blocks, and each 2-by-2 block has equal diagonals with off-diagonals of opposite sign. and yes — this is the block version of the algorithm. iconic. 👑

💜 Parameters 💜

• TRANA — TRANA is CHARACTER*1. it specifies the option op(A):
  • = 'N': op(A) = A (No transpose)
  • = 'T': op(A) = A**T (Transpose)
  • = 'C': op(A) = A**H (Conjugate transpose = Transpose)
• TRANB — TRANB is CHARACTER*1. it specifies the option op(B):
  • = 'N': op(B) = B (No transpose)
  • = 'T': op(B) = B**T (Transpose)
  • = 'C': op(B) = B**H (Conjugate transpose = Transpose)
• ISGN — ISGN is INTEGER. it specifies the sign in the equation:
  • = +1: solve op(A)*X + X*op(B) = scale*C
  • = -1: solve op(A)*X - X*op(B) = scale*C
• M — M is INTEGER. the order of the matrix A, and the number of rows in the matrices X and C. M >= 0.
• N — N is INTEGER. the order of the matrix B, and the number of columns in the matrices X and C. N >= 0.
• A — A is REAL array, dimension (LDA,M). the upper quasi-triangular matrix A, in Schur canonical form. 🌸
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,M).
• B — B is REAL array, dimension (LDB,N). the upper quasi-triangular matrix B, in Schur canonical form. 🌸
• LDB — LDB is INTEGER. the leading dimension of the array B. LDB >= max(1,N).
• C — C is REAL array, dimension (LDC,N).
  • On entry, the M-by-N right hand side matrix C.
  • On exit, C is overwritten by the solution matrix X. ⚠️ like, she's not a backup, she's a glow-up.
• LDC — LDC is INTEGER. the leading dimension of the array C. LDC >= max(1,M)
• SCALE — SCALE is REAL. the scale factor, scale, set <= 1 to avoid overflow in X.
• IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. 👀
• LIWORK — LIWORK is INTEGER (yes, the docs literally say IWORK here, and we're keeping it exactly as written, that's our house style 💀). the dimension of the array IWORK. LIWORK >= ((M + NB - 1) / NB + 1) + ((N + NB - 1) / NB + 1), where NB is the optimal block size.

If LIWORK = -1, then a workspace query is assumed; the routine only calculates the optimal dimension of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued by XERBLA. ✨

• SWORK — SWORK is REAL array, dimension (MAX(2, ROWS), MAX(1,COLS)). On exit, if INFO = 0, SWORK(1) returns the optimal value ROWS and SWORK(2) returns the optimal COLS. 🎀
• LDSWORK — LDSWORK is INTEGER. LDSWORK >= MAX(2,ROWS), where ROWS = ((M + NB - 1) / NB + 1) and NB is the optimal block size.

If LDSWORK = -1, then a workspace query is assumed; the routine only calculates the optimal dimensions of the SWORK matrix, returns these values as the first and second entry of the SWORK matrix, and no error message related LWORK is issued by XERBLA.

ngl the doc says LWORK here even though this parameter is LDSWORK — copying it exactly, character for character. not me fixing upstream docs, that's not my job 🙈

• INFO — INFO is INTEGER:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • = 1: A and B have common or very close eigenvalues; perturbed values were used to solve the equation (but the matrices A and B are unchanged). ⚠️ like — she tweaked the math, not your matrices, so don't panic, but do take the hint.

📌 Definition 📌

Definition at line 178 of file strsyl3.f.

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✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code. 🤖 (not a human, bestie, an auto-generated icon)

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and that's the page!! 💜 LAPACK, Version 3.12.0, dated /home/abui.../strsyl3.f(3) — mwah, go solve some Sylvester equations, you've got this 🫶✨🎀