SRC/zgbrfs.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

💅 SRC/zgbrfs.f

okay so this page is from the Library Functions Manual and it's literally the glow-up arc for your banded-matrix solutions ✨

SYNOPSIS 🎀 (Functions/Subroutines)

  • subroutine zgbrfs (trans, n, kl, ku, nrhs, ab, ldab, afb, ldafb, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info) — ZGBRFS, bestie. That's the whole cast list.

🫶 Function/Subroutine Documentation

subroutine zgbrfs (character trans, integer n, integer kl, integer ku,
    integer nrhs, complex*16, dimension( ldab, * ) ab, integer ldab,
    complex*16, dimension( ldafb, * ) afb, integer ldafb, integer,
    dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb,
    complex*16, dimension( ldx, * ) x, integer ldx, double precision,
    dimension( * ) ferr, double precision, dimension( * ) berr, complex*16,
    dimension( * ) work, double precision, dimension( * ) rwork, integer
    info)

ZGBRFS — say it with your chest 💖

🌸 Purpose

ZGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and honestly? It also provides error bounds and backward error estimates for the solution. It's giving responsible friend who double-checks the group project 🫶

✨ Parameters

TRANS

TRANS is CHARACTER*1 — specifies the form of the system of equations, no cap:

= '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*16 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, like this:

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*16 array, dimension (LDAFB,N) — details of the LU factorization of the band matrix A, as computed by ZGBTRF. 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. obsessed with how tidy that is 🧚

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 ZGBTRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).

B

B is COMPLEX*16 array, dimension (LDB,NRHS) — the right hand side matrix B. iconic, no notes.

LDB

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

X

X is COMPLEX*16 array, dimension (LDX,NRHS) — on entry, the solution matrix X, as computed by ZGBTRS. On exit, the improved solution matrix X. main character transformation arc 💅

LDX

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

FERR

FERR is 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. lowkey humble about it too 😌

BERR

BERR is 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

WORK is COMPLEX*16 array, dimension (2*N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

INFO

INFO is INTEGER — the vibe check:

= 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. That's it, that's the whole internal lore. iykyk 🦋

👑 Author

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

Definition at line 203 of file zgbrfs.f.

🌈 Author (yes, again)

Generated automatically by Doxygen for LAPACK from the source code. not a human, just vibes and a parser 💀

fr fr bestie, that's the whole page — every parameter, every bound, every last >= accounted for 🍓

LAPACK · Version 3.12.0 · SRC/zgbrfs.f(3) — mwah, that's a wrap 💜

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