DLASY2(3)

okay bestie, welcome to the dlasy2.f(3) page in the Library Functions Manual — it’s LAPACK’s very own DLASY2 subroutine, and she is here to solve the tiny Sylvester matrix equation for matrices of order 1 or 2. 💅✨

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlasy2.f

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

       subroutine DLASY2 (ltranl, ltranr, isgn, n1, n2, tl, ldtl, tr, ldtr, b,
           ldb, scale, x, ldx, xnorm, info)
           DLASY2 solves the Sylvester matrix equation where the matrices are
           of order 1 or 2.

🫶 Function/Subroutine Documentation 🫶

   subroutine DLASY2 (logical ltranl, logical ltranr, integer isgn, integer n1,
       integer n2, double precision, dimension( ldtl, * ) tl, integer ldtl,
       double precision, dimension( ldtr, * ) tr, integer ldtr, double
       precision, dimension( ldb, * ) b, integer ldb, double precision scale,
       double precision, dimension( ldx, * ) x, integer ldx, double precision
       xnorm, integer info)

DLASY2 solves the Sylvester matrix equation where the matrices are of order 1 or 2. periodt.

🌸 Purpose 🌸

okay so DLASY2 solves for the N1 by N2 matrix X, with 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 🎀

• LTRANL — LOGICAL. On entry, LTRANL specifies the op(TL):
  • = .FALSE., op(TL) = TL,
  • = .TRUE., op(TL) = TL**T.
• LTRANR — LOGICAL. On entry, LTRANR specifies the op(TR):
  • = .FALSE., op(TR) = TR,
  • = .TRUE., op(TR) = TR**T.
• ISGN — INTEGER. On entry, ISGN specifies the sign of the equation as described before. ISGN may only be 1 or -1.
• N1 — INTEGER. On entry, N1 specifies the order of matrix TL. N1 may only be 0, 1 or 2.
• N2 — INTEGER. On entry, N2 specifies the order of matrix TR. N2 may only be 0, 1 or 2.
• TL — DOUBLE PRECISION array, dimension (LDTL,2). On entry, TL contains an N1 by N1 matrix.
• LDTL — INTEGER. The leading dimension of the matrix TL. LDTL >= max(1,N1).
• TR — DOUBLE PRECISION array, dimension (LDTR,2). On entry, TR contains an N2 by N2 matrix.
• LDTR — INTEGER. The leading dimension of the matrix TR. LDTR >= max(1,N2).
• B — DOUBLE PRECISION array, dimension (LDB,2). On entry, the N1 by N2 matrix B contains the right-hand side of the equation.
• LDB — INTEGER. The leading dimension of the matrix B. LDB >= max(1,N1).
• SCALE — DOUBLE PRECISION. On exit, SCALE contains the scale factor. SCALE is chosen less than or equal to 1 to prevent the solution overflowing.
• X — DOUBLE PRECISION array, dimension (LDX,2). On exit, X contains the N1 by N2 solution.
• LDX — INTEGER. The leading dimension of the matrix X. LDX >= max(1,N1).
• XNORM — DOUBLE PRECISION. On exit, XNORM is the infinity-norm of the solution.
• INFO — 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. bestie, she said no input validation, we die like legends 😭

👑 Author 👑

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

Definition at line 172 of file dlasy2.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that’s the whole page. The cute little footer says LAPACK Version 3.12.0 and points back to /home/abui...RC/dlasy2.f(3). Go forth and solve your tiny Sylvester situation, slay 💅✨