SRC/dsyrfs.f(3)

🌸 SRC/dsyrfs.f — like, the dsyrfs situation 💅

okay bestie, welcome to the Library Functions Manual entry for SRC/dsyrfs.f — yes it's a Fortran file, yes it's from LAPACK, and yes we're gonna get through this together. grab a snack 🍓

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✨ NAME ✨

SRC/dsyrfs.f — like, that's literally the name, no cap. this is the home of the dsyrfs subroutine and it's giving very "symmetric indefinite systems get error bounds" energy 🦋

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines

• subroutine dsyrfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, iwork, info) — the one, the only, DSYRFS 👑

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💖 Function/Subroutine Documentation 💖

🌈 the subroutine itself

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 — that's the whole title card, iconic, no notes 💀

⭐ 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. !>

so like — you already solved something, and now you want it better, plus you want receipts on how wrong it might still be. that's the whole gig 🫶

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🧚 Parameters (yes, all of them, I would never skip one)

• UPLO — UPLO is CHARACTER*1. it tells you which triangle of A is the one doing the work:
  • = '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 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. (half of it is literally just vibes, it's not read 💀)
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• AF — 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.
• 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 DSYTRF.
• B — B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by DSYTRS. On exit, the improved solution matrix X. ✨ glow-up on exit ✨
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• FERR — 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.
• BERR — 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). lowkey the most useful little number ever 🧮
• WORK — WORK is DOUBLE PRECISION array, dimension (3*N). that's right, three whole N's, bring the big scratch pad.
• 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 🙈

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🦋 Internal Parameters:

!> ITMAX is the maximum number of steps of iterative refinement. !>

that's it, that's the internal one — iterative refinement has a step budget and ITMAX is its name 💅

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👑 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. (so like, don't come for the formatting, a robot did it 🤖)

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okay that's the whole page, you made it, I'm so proud 🥹 this was LAPACK Version 3.12.0 dropping SRC/dsyrfs.f(3) from the Library Functions Manual — mwah, go improve some solutions bestie 💖✨🎀