CTRSYL(3)

🦋 CTRSYL(3) — Library Functions Manual ✨

ok so picture this: you're deep in some LAPACK source tree at /home/abui...RC/ctrsyl.f(3) and the manual name is literally CTRSYL(3) — that's Library Functions Manual energy, bestie. this is the page for subroutine CTRSYL, and it's giving "math but make it fashion". let's go 💅

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🌸 NAME

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

like. that's the whole NAME section. it's just the file path. iconic of it honestly 🎀

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✨ SYNOPSIS

Functions/Subroutines

subroutine CTRSYL (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc,
    scale, info)

CTRSYL — that's her. that's the subroutine 💖

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👑 Function/Subroutine Documentation

subroutine CTRSYL (character trana, character tranb, integer isgn, integer
    m, integer n, complex, dimension( lda, * ) a, integer lda, complex,
    dimension( ldb, * ) b, integer ldb, complex, dimension( ldc, * ) c,
    integer ldc, real scale, integer info)

CTRSYL. again. hi queen 🫶

💜 Purpose:

ok so this is the moment. CTRSYL solves the complex 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**H, and A and B are both upper 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. no cap, that's the whole vibe check 🔥

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🌈 Parameters

• TRANA — is CHARACTER*1. specifies the option op(A): = 'N': op(A) = A (No transpose) ✨; = 'C': op(A) = A**H (Conjugate transpose) 💫
• TRANB — is CHARACTER*1. specifies the option op(B): = 'N': op(B) = B (No transpose) ✨; = 'C': op(B) = B**H (Conjugate transpose) 💫
• 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 🌸
• M — is INTEGER. the order of the matrix A, and the number of rows in the matrices X and C. M >= 0. periodt 💅
• N — is INTEGER. the order of the matrix B, and the number of columns in the matrices X and C. N >= 0. also periodt 💅
• A — is COMPLEX array, dimension (LDA,M). the upper triangular matrix A. that's her. that's the queen bee 👑
• LDA — is INTEGER. the leading dimension of the array A. LDA >= max(1,M). don't get it wrong bestie 🙈
• B — is COMPLEX array, dimension (LDB,N). the upper triangular matrix B. second main character energy 🦋
• LDB — is INTEGER. the leading dimension of the array B. LDB >= max(1,N). same rule, different letter 🎀
• C — is COMPLEX 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. so she gets replaced, no biggie, glow-up moment 💖
• LDC — is INTEGER. the leading dimension of the array C. LDC >= max(1,M). yes the page really does end that line without a period. we respect the original's choices 🫶
• SCALE — is REAL. the scale factor, scale, set <= 1 to avoid overflow in X. literally keeping X from overflowing, she's a bodyguard 😭
• INFO — is INTEGER:
  • = 0: successful exit 🎉 slay
  • < 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). ngl that's a little spooky but the matrices are fine, she promises 🙈

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🧚 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

shoutout to the whole team, we stan 💜

Definition at line 155 of file ctrsyl.f. not me knowing exactly where she lives 📍

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⭐ Author

Generated automatically by Doxygen for LAPACK from the source code. a robot wrote this page and honestly? she ate 🤖💅

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lowkey reminder: INFO = 1 means perturbed values were used, but the matrices A and B are unchanged — do not come for A and B, they're innocent 🫶

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and that's the whole page!! toodles bestie 💖

LAPACK — Version 3.12.0 · /home/abui...RC/ctrsyl.f(3) · mwah, see u in the man pages 💋🎀