SSPRFS(3)

🌸 NAME 🌸

okay bestie, welcome to the Library Functions Manual — we're looking at the ssprfs.f(3) page and honestly it's giving legendary LAPACK subroutine energy. 💅 The source path is:

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

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine SSPRFS (uplo, n, nrhs, ap, afp, ipiv, b, ldb, x, ldx, ferr,
    berr, work, iwork, info)
    SSPRFS

This subroutine is SSPRFS, and yes she's the main character. 👑

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🎀 Function/Subroutine Documentation 🎀

subroutine SSPRFS (character uplo, integer n, integer nrhs, real, dimension(
    * ) ap, real, dimension( * ) afp, integer, dimension( * ) ipiv, 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)
    SSPRFS

💖 Purpose 💖

okay so SSPRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite and packed, and it provides error bounds and backward error estimates for the solution. no cap, that's the whole glow-up. ✨

🌈 Parameters 🌈

• UPLO — CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. choose your triangle, bestie. 💅
• N — INTEGER. the order of the matrix A. N >= 0.
• NRHS — INTEGER. the number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• AP — REAL array, dimension (N*(N+1)/2). the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. the j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
• AFP — REAL array, dimension (N*(N+1)/2). the factored form of the matrix A. AFP 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 SSPTRF, stored as a packed triangular matrix. 💖
• IPIV — INTEGER array, dimension (N). details of the interchanges and the block structure of D as determined by SSPTRF.
• B — REAL array, dimension (LDB,NRHS). the right hand side matrix B.
• LDB — INTEGER. the leading dimension of the array B. LDB >= max(1,N).
• X — REAL array, dimension (LDX,NRHS). on entry, the solution matrix X, as computed by SSPTRS. on exit, the improved solution matrix X. she enters, she slays, she exits improved. 💅
• LDX — INTEGER. the leading dimension of the array X. LDX >= max(1,N).
• FERR — 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 it's almost always a slight overestimate of the true error. 🫶
• BERR — 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 — REAL array, dimension (3*N).
• IWORK — INTEGER array, dimension (N).
• INFO — INTEGER. = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value. bestie if you see < 0, that's not a vibe. 😭

💜 Internal Parameters 💜

• ITMAX — the maximum number of steps of iterative refinement. that's the limit, periodt. ✨

🌸 Author 🌸

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

Definition at line 177 of file ssprfs.f.

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🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie! huge shoutout to LAPACK Version 3.12.0, source /home/abui...RC/ssprfs.f(3) — the footer didn't hand us a date, so no cap, just love. 💖🎀🦋