SRC/strsyl3.f(3)

📦
version 3.12.1 · 2 versions
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💖 NAME 💖

okay so this is the SRC/strsyl3.f(3) page from the Library Functions Manual, bestie ✨ and the name is literally SRC/strsyl3.f — that's the whole name, no cap 😭💅

✨ SYNOPSIS ✨

🦋 Functions/Subroutines

subroutine strsyl3 (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc,
    scale, iwork, liwork, swork, ldswork, info)

STRSYL3

🎀 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

🌸 Purpose 🌸

okay so STRSYL3 solves the real Sylvester matrix equation, and it's giving main-character math energy 🧚✨:

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. periodt 👑

This is the block version of the algorithm. iconic.

💅 Parameters 💅

  • TRANA — TRANA is CHARACTER*1. 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). slay 💫
  • TRANB — TRANB is CHARACTER*1. 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). yes bestie 💅
  • ISGN — ISGN is INTEGER. 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. choose your fighter ⚔️
  • M — M is INTEGER. The order of the matrix A, and the number of rows in the matrices X and C. M >= 0. no negative row counts, bestie 🙈
  • N — N is INTEGER. The order of the matrix B, and the number of columns in the matrices X and C. N >= 0. same vibe, columns edition 🌈
  • A — A is REAL array, dimension (LDA,M). The upper quasi-triangular matrix A, in Schur canonical form. she's structured ✨
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M). respect the leading dimension 🫶
  • B — B is REAL array, dimension (LDB,N). The upper quasi-triangular matrix B, in Schur canonical form. also structured, also slaying 💅
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). yup yup 💖
  • 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. glow-up moment 🔥
  • LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M). don't forget it bestie 😭
  • SCALE — SCALE is REAL. The scale factor, scale, set <= 1 to avoid overflow in X. safety first, always 💜
  • IWORK — IWORK is INTEGER array, dimension (MAX(1,LIWORK)). On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. cute little integer workspace 🎀
  • LIWORK — the source text here says IWORK is INTEGER, and this parameter is 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. workspace query realness 🫡
  • 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. two little integers doing big things 💫
  • 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. as the source says, bestie 😭💀
  • 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). read the INFO, love her 💖

Definition at line 196 of file strsyl3.f.

👑 Author 👑

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okay that's the whole page, bestie 🫶💖 — this sparkly little sign-off comes from LAPACK, Version 3.12.0, source SRC/strsyl3.f(3); the footer doesn't give a date, so consider this your cute final-boss footer moment periodt ✨🎀🌈

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