SRC/dgbrfs.f(3)

💅 NAME 💅

SRC/dgbrfs.f — okay so bestie, this page is from the Library Functions Manual, and it's giving DGBRFS energy: the routine that improves your computed solution to a banded linear system and serves up error bounds + backward error estimates. 💖

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📜 SYNOPSIS 📜

🧚 Functions/Subroutines 🧚

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

🛠️ Function/Subroutine Documentation 🛠️

here's the full typed-out signature, no cap:

   subroutine dgbrfs (character trans, integer n, integer kl, integer ku,
       integer nrhs, double precision, dimension( ldab, * ) ab, integer ldab,
       double precision, dimension( ldafb, * ) afb, integer ldafb, integer,
       dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer
       ldb, double precision, dimension( ldx, * ) x, integer ldx, double
       precision, dimension( * ) ferr, double precision, dimension( * ) berr,
       double precision, dimension( * ) work, integer, dimension( * ) iwork,
       integer info)
       DGBRFS

🎯 Purpose 🎯

DGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution. literally its whole main-character job 💅

🌸 Parameters 🌸

• TRANS — CHARACTER*1: 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 — INTEGER: 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.
• NRHS — INTEGER: the number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• AB — DOUBLE PRECISION 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 — INTEGER: the leading dimension of the array AB. LDAB >= KL+KU+1.
• AFB — DOUBLE PRECISION array, dimension (LDAFB,N): details of the LU factorization of the band matrix A, as computed by DGBTRF. 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.
• IPIV — INTEGER array, dimension (N): the pivot indices from DGBTRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
• B — DOUBLE PRECISION array, dimension (LDB,NRHS): the right hand side matrix B.
• LDB — INTEGER: the leading dimension of the array B. LDB >= max(1,N).
• X — DOUBLE PRECISION array, dimension (LDX,NRHS): on entry, the solution matrix X, as computed by DGBTRS. On exit, the improved solution matrix X.
• LDX — INTEGER: the leading dimension of the array X. LDX >= max(1,N).
• FERR — DOUBLE PRECISION 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 — DOUBLE PRECISION 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 — DOUBLE PRECISION array, dimension (3*N).
• IWORK — INTEGER array, dimension (N).
• INFO — 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 dgbrfs.f.

🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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💖 that's the whole glow-up, bestie — LAPACK Version 3.12.0, straight from SRC/dgbrfs.f(3). now go get those error bounds, mwah 💋✨