SRC/zporfs.f(3)

okay bestie, welcome to the SRC/zporfs.f(3) page — it's the Library Functions Manual entry for SRC/zporfs.f, and the routine is ZPORFS 💖✨

💖 NAME 💖

SRC/zporfs.f

🌈 SYNOPSIS 🌈

🫶 Functions/Subroutines 🫶

• zporfs — the subroutine, bestie; the exact call signature is right below 💅

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

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, copied exactly because code is sacred:

subroutine zporfs (character uplo, integer n, integer nrhs, complex*16,
    dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af,
    integer ldaf, 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)

This routine is ZPORFS — main character energy only. 🫶

🎯 Purpose 🎯

bestie, ZPORFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian positive definite, and it provides error bounds and backward error estimates for the solution. no cap. ✨

💅 Parameters 💅

• UPLO — CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored.
• N — INTEGER, the order of the matrix A. N >= 0.
• NRHS — INTEGER, the number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• A — COMPLEX*16 array, dimension (LDA,N). It's 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 — INTEGER, the leading dimension of the array A. LDA >= max(1,N).
• AF — COMPLEX*16 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 ZPOTRF.
• LDAF — INTEGER, the leading dimension of the array AF. LDAF >= max(1,N).
• B — COMPLEX*16 array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — INTEGER, the leading dimension of the array B. LDB >= max(1,N).
• X — COMPLEX*16 array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by ZPOTRS. 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 — COMPLEX*16 array, dimension (2*N).
• RWORK — DOUBLE PRECISION array, dimension (N).
• INFO — INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.

🔥 Internal Parameters 🔥

• ITMAX — 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 zporfs.f 🧚

fr fr: Definition at line 181 of file zporfs.f.

💜 Author 💜

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