SRC/dporfs.f(3)

okay bestie, welcome to SRC/dporfs.f(3) from the Library Functions Manual 🌈 this page is the DPORFS routine’s whole personality, and we are keeping every single detail. no cap.

💖 NAME 💖

SRC/dporfs.f — that’s the name, periodt 💅

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine dporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx,
    ferr, berr, work, iwork, info)
    DPORFS

🦋 Function/Subroutine Documentation 🦋

subroutine dporfs (character uplo, integer n, integer nrhs, double
    precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldaf, * ) af, integer ldaf, 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)
    DPORFS

🎯 Purpose: 🎯

DPORFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite, and it provides error bounds and backward error estimates for the solution. that’s the whole glow-up, bestie 💅

🌸 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 DOUBLE PRECISION array, dimension (LDA,N); the symmetric 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 DOUBLE PRECISION array, dimension (LDAF,N); the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPOTRF. 🧚
• LDAF — LDAF is INTEGER; the leading dimension of the array AF. LDAF >= max(1,N). ⭐
• B — B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS); on entry, the solution matrix X, as computed by DPOTRS. 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 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 — 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 DOUBLE PRECISION 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 181 of file dporfs.f.

💫 Author 💫

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signed with LAPACK Version 3.12.0 energy from SRC/dporfs.f(3) — that’s the footer, bestie, and that’s a wrap 💖✨🎀