SLA_GBRPVGRW(3)

🌸 NAME 🌸

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

okay bestie, this page is from the LAPACK Library Functions Manual 💖, and the header shows the path as /home/abui..._gbrpvgrw.f(3) (yes, abbreviated exactly like that, iykyk). The actual NAME line is the full path above. slay.

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✨ SYNOPSIS ✨

   Functions/Subroutines
       real function SLA_GBRPVGRW (n, kl, ku, ncols, ab, ldab, afb, ldafb)
           SLA_GBRPVGRW computes the reciprocal pivot growth factor
           norm(A)/norm(U) for a general banded matrix.

and the full function/subroutine documentation signature is:

   real function SLA_GBRPVGRW (integer n, integer kl, integer ku, integer
       ncols, real, dimension( ldab, * ) ab, integer ldab, real, dimension(
       ldafb, * ) afb, integer ldafb)

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💖 Function/Subroutine Documentation 💖

SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix. periodt 💅

🌸 Purpose 🌸

okay so SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U). The norm is used. If this is much less than 1, the stability of the LU factorization of the (equilibrated) matrix A could be poor 😭. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

🎀 Parameters 🎀

• N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. 💖
• KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0. 🦋
• KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0. ✨
• NCOLS — INTEGER. The number of columns of the matrix A. NCOLS >= 0. 🎀
• AB — REAL array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl). 💅
• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1. 🌈
• AFB — REAL array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. 🔥
• LDAFB — INTEGER. The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. ⭐

👑 Author 👑

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

Definition at line 115 of file sla_gbrpvgrw.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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💖 cute sign-off: this is from LAPACK Version 3.12.0, generated automatically by Doxygen for LAPACK from the source code, and the footer points back to /home/abui..._gbrpvgrw.f(3). That's the whole vibe, bestie 🫶✨