SRC/sporfs.f(3)

Manual name: Library Functions Manual — page: SRC/sporfs.f(3). Okay bestie, let’s get into it 💅✨

💖 NAME 💖

SRC/sporfs.f

---

✨ SYNOPSIS ✨

Functions/Subroutines:

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

---

🫶 Function/Subroutine Documentation 🫶

Here’s the full signature, exactly as it’s written, no cap:

       subroutine sporfs (character uplo, integer n, integer nrhs, real, dimension(
           lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf,
           real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x,
           integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real,
           dimension( * ) work, integer, dimension( * ) iwork, integer info)
           SPORFS

Purpose 🌸

SPORFS is literally here to improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite 💖 It also gives you error bounds and backward error estimates for the solution. Iconic behavior, honestly.

Parameters 💖

UPLO

UPLO is CHARACTER*1.

• = 'U': the upper triangle of A is stored.
• = 'L': the 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 REAL 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 REAL 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 SPOTRF.

LDAF

LDAF is INTEGER.

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

B

B is REAL 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 REAL array, dimension (LDX,NRHS).

On entry, the solution matrix X, as computed by SPOTRS. 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 REAL 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 sporfs.f.

Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

---

And that’s the cute little sign-off, bestie: footer says LAPACK Version 3.12.0, source SRC/sporfs.f(3) 🫶💅✨