SRC/sgbrfs.f(3)

🌸 SRC/sgbrfs.f 🌸

Okay bestie, welcome to the manual page for SRC/sgbrfs.f(3) from the Library Functions Manual. This is the LAPACK banded-system error-bounds routine, and we’re gonna get through every single detail together. 💖

💖 NAME 💖

SRC/sgbrfs.f

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

🔥 Function/Subroutine Documentation 🔥

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

🌟 Purpose 🌟

SGBRFS 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 mission, no cap. 💅

🎀 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 = 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 REAL 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 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 — 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 SGBTRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
• B — B is REAL 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 REAL array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by SGBTRS. 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 REAL array, dimension (3*N).
• IWORK — IWORK is INTEGER 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 202 of file sgbrfs.f.

💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie. Signed off with LAPACK Version 3.12.0 and SRC/sgbrfs.f(3) energy. Byeee 💅✨🫶