DTRSYL(3)

💅 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtrsyl.f is the source file for this dtrsyl.f(3) LAPACK manual page. That's the whole name section, bestie — it's literally a path, no cap. 🫶

✨ SYNOPSIS

🧚 Functions/Subroutines

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

DTRSYL — yes, that's the main character. 👑

🦋 Function/Subroutine Documentation

Here's the full signature, copied exactly because precision is the vibe:

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

DTRSYL is the function/subroutine we're documenting.

💖 Purpose

Okay so DTRSYL 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 DHSEQR), 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.

🎀 Parameters

• TRANA — 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)
• TRANB — 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)
• ISGN — 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 — INTEGER. The order of the matrix A, and the number of rows in the matrices X and C. M >= 0.
• N — INTEGER. The order of the matrix B, and the number of columns in the matrices X and C. N >= 0.
• A — DOUBLE PRECISION array, dimension (LDA,M). The upper quasi-triangular matrix A, in Schur canonical form.
• LDA — INTEGER. The leading dimension of the array A. LDA >= max(1,M).
• B — DOUBLE PRECISION array, dimension (LDB,N). The upper quasi-triangular matrix B, in Schur canonical form.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• C — DOUBLE PRECISION 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 — INTEGER. The leading dimension of the array C. LDC >= max(1,M)
• SCALE — DOUBLE PRECISION. The scale factor, scale, set <= 1 to avoid overflow in X.
• INFO — 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 162 of file dtrsyl.f.

That's the exact location, bestie: line 162 in dtrsyl.f. 📍

🌸 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole dtrsyl.f(3) moment, bb! Source/version: LAPACK, Version 3.12.0. Page file: /home/abui...RC/dtrsyl.f(3). The original footer doesn't give a date, so I'm not making one up — we stay factual while looking cute. 💅✨🎀