ZTRSYL(3)

💜 ZTRSYL(3) — bestie, we're solving the Sylvester equation today

okay so real talk: this page lives in the LAPACK manual, and the file it documents is literally

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

that's the whole NAME section, no notes, she's just a path 💅 and honestly? iconic.

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine ZTRSYL (trana, tranb, isgn, m, n, a, lda, b, ldb, c, ldc, scale, info) — that's our girl, ZTRSYL 🎀

subroutine ZTRSYL (character trana, character tranb, integer isgn, integer
    m, integer n, complex*16, dimension( lda, * ) a, integer lda,
    complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension(
    ldc, * ) c, integer ldc, double precision scale, integer info)

🌸 Function/Subroutine Documentation 🌸

🧚 Purpose

no cap, here's the whole vibe — ZTRSYL 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. 🫶

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💖 Parameters

• TRANA — TRANA is CHARACTER*1. Specifies the option op(A):
  • = 'N': op(A) = A (No transpose)
  • = 'C': op(A) = A**H (Conjugate transpose)
• TRANB — TRANB is CHARACTER*1. Specifies the option op(B):
  • = 'N': op(B) = B (No transpose)
  • = 'C': op(B) = B**H (Conjugate transpose)
• 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
• 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 COMPLEX*16 array, dimension (LDA,M). The upper triangular matrix A. 👑
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• B — B is COMPLEX*16 array, dimension (LDB,N). The upper triangular matrix B. 👑
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• C — C is COMPLEX*16 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. 🦋 (she gets replaced, so don't come crying if your original C is gone)
• LDC — LDC is INTEGER. The leading dimension of the array C. LDC >= max(1,M)
• SCALE — SCALE is DOUBLE PRECISION. The scale factor, scale, set <= 1 to avoid overflow in X. 🔥
• 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).

bestie listen 👀 that INFO = 1 is not an error exactly, but it IS her way of saying "the eigenvalues were uncomfortably close so I fudged the numbers to get it done — your A and B are untouched tho, promise."

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🎀 Author

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

Definition at line 155 of file ztrsyl.f. ⭐

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🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, iykyk 💜 shoutout to the footer: LAPACK, Version 3.12.0, page source /home/abui...RC/ztrsyl.f(3) — mwah, go solve your triangular Sylvester equation, main character 🧚💅