SRC/ctrsyl.f(3)

✨ NAME ✨

Library Functions Manual, but make it cute: this whole page is about SRC/ctrsyl.f (a.k.a. SRC/ctrsyl.f(3)), and honestly it's giving complex Sylvester equation solver main character energy. 🫶

📚 SYNOPSIS 📚

Functions/Subroutines

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

CTRSYL — that's the icon, no cap. 💅

🛠️ 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 — yes bestie, same icon, now with the full glow-up signature. ✨

🎯 Purpose

Okay so 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. 🫶

🧸 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 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 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 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.
• 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.
• 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).

👑 Author

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

Definition at line 155 of file ctrsyl.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie — every flag and fact accounted for, periodt. Sign-off vibes: LAPACK Version 3.12.0, SRC/ctrsyl.f(3) 💅✨