CGBRFS(3)

📦 version 3.12.0, in opensuse-leap 16.0

💅 CGBRFS(3) — Library Functions Manual, but make it group-chat

okay bestie, this is the LAPACK page for CGBRFS — yes, the (3) is right there. We're in Library Functions Manual territory, and the whole vibe is: banded matrices, iterative refinement, error bounds. Let's go. 🦋

✨ NAME ✨

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

That's literally the NAME section: the Fortran source file path. Not a typo, not me being lazy — that's what the original page says. 😭

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine CGBRFS (trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv,
    b, ldb, x, ldx, ferr, berr, work, rwork, info)

CGBRFS

🎀 Function/Subroutine Documentation 🎀

subroutine CGBRFS (character trans, integer n, integer kl, integer ku,
    integer nrhs, complex, dimension( ldab, * ) ab, integer ldab, complex,
    dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv,
    complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, *
    ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr,
    complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CGBRFS

💖 Purpose 💖

okay so CGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and it provides error bounds and backward error estimates for the solution. That's the whole purpose. Periodt. ✨

🦋 Parameters 🦋

TRANS

TRANS is CHARACTER*1. It specifies the form of the system of equations:

  • 'N': A * X = B (No transpose)
  • 'T': A**T * X = B (Transpose)
  • 'C': A**H * X = B (Conjugate transpose)

N

N is INTEGER. The order of the matrix A. N >= 0.

KL

KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0.

KU

KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0.

NRHS

NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N). The original band matrix A, stored 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

LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.

AFB

AFB is COMPLEX array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by CGBTRF. 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

LDAFB is INTEGER. The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.

IPIV

IPIV is INTEGER array, dimension (N). The pivot indices from CGBTRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).

B

B is COMPLEX array, dimension (LDB,NRHS). The right hand side matrix B.

LDB

LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).

X

X is COMPLEX array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by CGBTRS. On exit, the improved solution matrix X.

LDX

LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).

FERR

FERR is REAL array, dimension (NRHS). The estimated forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.

BERR

BERR is REAL array, dimension (NRHS). The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).

WORK

WORK is COMPLEX array, dimension (2*N).

RWORK

RWORK is REAL array, dimension (N).

INFO

INFO is INTEGER.

  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

🌈 Internal Parameters 🌈

ITMAX is the maximum number of steps of iterative refinement.

👑 Author 👑

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

Definition at line 203 of file cgbrfs.f.

👑 Author (generated-by-Doxygen edition) 👑

Generated automatically by Doxygen for LAPACK from the source code.

cute sign-off, bestie: that's the whole page. Signed off with 💖 from the footer — LAPACK Version 3.12.0 and /home/abui...RC/cgbrfs.f(3). Go improve those banded systems with your iconic self. 🎀

📦 where this page comes from