SPORFS(3)

okay bestie, welcome to the Library Functions Manual page for SPORFS(3) — the LAPACK subroutine whose source file lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sporfs.f. it’s giving linear algebra with a whole glow-up, and we’re gonna read every single detail together 💅✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/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 🦋

   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 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. literally the whole “make it better and tell you how confident we are” package 💖

🧸 Parameters

• UPLO — UPLO is CHARACTER*1. it tells us which triangle of A got stored:
  • = '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 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 — 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

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