SRC/cgerfs.f(3)

💖 NAME 💖

SRC/cgerfs.f — hey bestie, this is the page, and we're in the Library Functions Manual. It's giving LAPACK linear algebra, and the star of the show is CGERFS. 🫶

✨ SYNOPSIS ✨

Functions/Subroutines:

       subroutine cgerfs (trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x,
           ldx, ferr, berr, work, rwork, info)
           CGERFS

🫶 FUNCTION/SUBROUTINE DOCUMENTATION 🫶

CGERFS

   subroutine cgerfs (character trans, integer n, integer nrhs, complex,
       dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,
       integer ldaf, 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)
       CGERFS

🎀 Purpose 🎀

Okay so CGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. That's the whole assignment, 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)

N

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

A

A is COMPLEX array, dimension (LDA,N). The original N-by-N matrix A.

LDA

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

AF

AF is COMPLEX array, dimension (LDAF,N). The factors L and U from the factorization A = P*L*U as computed by CGETRF.

LDAF

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

IPIV

IPIV is INTEGER array, dimension (N). The pivot indices from CGETRF; 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 CGETRS. 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), then 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 it 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 184 of file cgerfs.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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Later, bestie 💅 — source/version: LAPACK Version 3.12.0; page: SRC/cgerfs.f(3); date: not listed in the footer, so we're not inventing one. 🎀