CSYRFS(3)

CSYRFS(3) — Library Functions Manual 💅

okay bestie, this is the CSYRFS page from the LAPACK universe, and it's giving “symmetric indefinite solver aftercare” energy. No cap. 🦋

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NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/csyrfs.f

That's the file path, exactly. Iconic. 💖

SYNOPSIS ✨

Functions/Subroutines 🦋

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

CSYRFS — that's the subroutine. 🎀

Function/Subroutine Documentation 🎀

subroutine CSYRFS (character uplo, integer n, integer nrhs, complex,
    dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af,
    integer ldaf, integer, dimension( * ) ipiv, complex, dimension( ldb, * )
    b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real,
    dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * )
    work, real, dimension( * ) rwork, integer info)

CSYRFS again, but now with all the types and dimensions laid out. Slay. 💅

Purpose: 💡

Lowkey the whole point: CSYRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and it provides error bounds and backward error estimates for the solution. That's the tea. 💖

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 COMPLEX 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 COMPLEX 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 CSYTRF.
• LDAF — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CSYTRF.
• B — B is COMPLEX 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 COMPLEX array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by CSYTRS. 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 COMPLEX array, dimension (2*N).
• RWORK — RWORK is REAL 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. Periodt. 💀

Author 👑

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

Definition at line 190 of file csyrfs.f. 💀

Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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Sign-off: LAPACK Version 3.12.0, source path /home/abui...RC/csyrfs.f(3) — bye bestie, go improve that solution 💅✨