DSYRFS(3)

DSYRFS(3) 💖

okay bestie, welcome to the Library Functions Manual page for DSYRFS(3) — literally the glow-up routine for symmetric indefinite linear systems. No cap, it's giving main character energy. ✨

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsyrfs.f — yup, that's the source file for DSYRFS, bestie. This is the Library Functions Manual entry for DSYRFS(3). 🫶

🌈 SYNOPSIS 🌈

🦋 Functions/Subroutines 🦋

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

💅 Function/Subroutine Documentation 💅

Here's the full signature, character for character, because we respect the code:

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

🎀 Purpose 🎀

DSYRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution. It's literally "I made your solve better and also brought receipts" energy. 💅

🌸 Parameters 🌸

• UPLO — is CHARACTER*1; = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. Choose your fighter. ⭐
• N — is INTEGER; the order of the matrix A. N >= 0.
• NRHS — is INTEGER; the number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• 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. Respect the triangle, bestie. 🫶
• LDA — is INTEGER; the leading dimension of the array A. LDA >= max(1,N).
• AF — is DOUBLE PRECISION array, dimension (LDAF,N); the factored form of the matrix A. AF contains the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by DSYTRF. Iconic factorization behavior. 👑
• LDAF — is INTEGER; the leading dimension of the array AF. LDAF >= max(1,N).
• IPIV — is INTEGER array, dimension (N); details of the interchanges and the block structure of D as determined by DSYTRF.
• B — is DOUBLE PRECISION array, dimension (LDB,NRHS); the right hand side matrix B.
• LDB — is INTEGER; the leading dimension of the array B. LDB >= max(1,N).
• X — is DOUBLE PRECISION array, dimension (LDX,NRHS); on entry, the solution matrix X, as computed by DSYTRS; on exit, the improved solution matrix X. The glow-up happens in place, periodt. 💅
• LDX — is INTEGER; the leading dimension of the array X. LDX >= max(1,N).
• 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. So it's not being shady — it's just cautious. 😭
• 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 — is DOUBLE PRECISION array, dimension (3*N).
• IWORK — is INTEGER array, dimension (N).
• INFO — is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. Bestie, negative INFO means something in the argument list is sus. 👀

🔧 Internal Parameters 🔧

ITMAX is the maximum number of steps of iterative refinement. It's the "one more little tweak" budget, iykyk. ✨

👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 189 of file dsyrfs.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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kisses, LAPACK Version 3.12.0 💖 — source: /home/abui...RC/dsyrfs.f(3) 🎀