SLASY2(3)

🌟 SLASY2(3) — Library Functions Manual 🌟

okay bestie, welcome to SLASY2(3) from the Library Functions Manual. the header literally has /home/abui...RC/slasy2.f(3) on both sides, and it is giving main character energy for a Fortran routine. 💅✨

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💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slasy2.f

that's the file, bestie. that's the whole NAME. iconic. 🎀

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine SLASY2 (ltranl, ltranr, isgn, n1, n2, tl, ldtl, tr, ldtr, b,
    ldb, scale, x, ldx, xnorm, info)

SLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2.

🎀 Function/Subroutine Documentation 🎀

okay so this is the full main-character signature, no cap:

subroutine SLASY2 (logical ltranl, logical ltranr, integer isgn, integer n1,
    integer n2, real, dimension( ldtl, * ) tl, integer ldtl, real,
    dimension( ldtr, * ) tr, integer ldtr, real, dimension( ldb, * ) b,
    integer ldb, real scale, real, dimension( ldx, * ) x, integer ldx, real
    xnorm, integer info)

SLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2.

💅 Purpose 💅

the goal is literally this: SLASY2 solves for the N1 by N2 matrix X, 1 <= N1,N2 <= 2, in

op(TL)*X + ISGN*X*op(TR) = SCALE*B,

where TL is N1 by N1, TR is N2 by N2, B is N1 by N2, and ISGN = 1 or -1. op(T) = T or T**T, where T**T denotes the transpose of T. 🌈

🦋 Parameters 🦋

okay bestie, here is the whole parameter lineup, in order, no skips:

• LTRANL — LTRANL is LOGICAL. On entry, LTRANL specifies the op(TL):
  • = .FALSE., op(TL) = TL,
  • = .TRUE., op(TL) = TL**T.
• LTRANR — LTRANR is LOGICAL. On entry, LTRANR specifies the op(TR):
  • = .FALSE., op(TR) = TR,
  • = .TRUE., op(TR) = TR**T.
• ISGN — ISGN is INTEGER. On entry, ISGN specifies the sign of the equation as described before. ISGN may only be 1 or -1.
• N1 — N1 is INTEGER. On entry, N1 specifies the order of matrix TL. N1 may only be 0, 1 or 2.
• N2 — N2 is INTEGER. On entry, N2 specifies the order of matrix TR. N2 may only be 0, 1 or 2.
• TL — TL is REAL array, dimension (LDTL,2). On entry, TL contains an N1 by N1 matrix.
• LDTL — LDTL is INTEGER. The leading dimension of the matrix TL. LDTL >= max(1,N1).
• TR — TR is REAL array, dimension (LDTR,2). On entry, TR contains an N2 by N2 matrix.
• LDTR — LDTR is INTEGER. The leading dimension of the matrix TR. LDTR >= max(1,N2).
• B — B is REAL array, dimension (LDB,2). On entry, the N1 by N2 matrix B contains the right-hand side of the equation.
• LDB — LDB is INTEGER. The leading dimension of the matrix B. LDB >= max(1,N1).
• SCALE — SCALE is REAL. On exit, SCALE contains the scale factor. SCALE is chosen less than or equal to 1 to prevent the solution overflowing.
• X — X is REAL array, dimension (LDX,2). On exit, X contains the N1 by N2 solution.
• LDX — LDX is INTEGER. The leading dimension of the matrix X. LDX >= max(1,N1).
• XNORM — XNORM is REAL. On exit, XNORM is the infinity-norm of the solution.
• INFO — INFO is INTEGER. On exit, INFO is set to:
  • 0: successful exit.
  • 1: TL and TR have too close eigenvalues, so TL or TR is perturbed to get a nonsingular equation.

NOTE: In the interests of speed, this routine does not check the inputs for errors. 💀

👑 Author 👑

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

Definition at line 172 of file slasy2.f.

🌈 Author 🌈

and the top-level author note is literally: Generated automatically by Doxygen for LAPACK from the source code. 🫶

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