SRC/cporfs.f(3)

🌸 NAME 🌸

SRC/cporfs.f — that's the name, bestie, no secret subtitle needed. 💅

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine cporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx,
     ferr, berr, work, rwork, info)
     CPORFS

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💖 Function/Subroutine Documentation 💖

okay so here's the full signature, and yes it's a whole lot of arguments, but we're gonna get through it together:

subroutine cporfs (character uplo, integer n, integer nrhs, complex,
     dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,
     integer ldaf, 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)
     CPORFS

🧚 Purpose 🧚

CPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, and provides error bounds and backward error estimates for the solution. literally doing the most helpful math bestie behavior. 🫶

🦋 Parameters 🦋

• UPLO — UPLO is CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
• 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 Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• AF — AF is COMPLEX array, dimension (LDAF,N). The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF.
• LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
• 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 CPOTRS. 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 — 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 🦋

Definition at line 181 of file cporfs.f.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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bye bestie 💖 this page is LAPACK Version 3.12.0, filed as SRC/cporfs.f(3), and the footer says it was generated automatically by Doxygen for LAPACK from the source code. periodt. 🌈✨