SRC/dtrsyl.f(3)

💖 SRC/dtrsyl.f(3) 💖

okay so bestie, welcome to the SRC/dtrsyl.f(3) page from the Library Functions Manual. This is the DTRSYL moment, and yes, it’s giving linear algebra main character energy. 🫶

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✨ NAME ✨

SRC/dtrsyl.f — that’s the name, no cap. The icon of the page is dtrsyl, the real Sylvester equation solver. 💅

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🌸 SYNOPSIS 🌸

🎀 Functions/Subroutines 🎀

• subroutine dtrsyl — DTRSYL, the whole vibe. Signature below, exactly:

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

DTRSYL

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💅 Function/Subroutine Documentation 💅

🧚 subroutine dtrsyl 🧚

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

✨ 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. 🌀

bestie, listen: 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. That’s the requirement, periodt. 💀

🍓 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)

• 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)

• 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 DOUBLE PRECISION array, dimension (LDA,M); the upper quasi-triangular matrix A, in Schur canonical form. 🌈
• LDA — LDA is INTEGER; the leading dimension of the array A. LDA >= max(1,M).
• B — B is DOUBLE PRECISION array, dimension (LDB,N); the upper quasi-triangular matrix B, in Schur canonical form. 🦋
• LDB — LDB is INTEGER; the leading dimension of the array B. LDB >= max(1,N).
• C — C is 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 — 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).

ngl, that INFO = 1 note is important: A and B have common or very close eigenvalues, and 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.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the sign-off, bestie: LAPACK Version 3.12.0, SRC/dtrsyl.f(3) — slay, bye! 💖✨🎀