SRC/ssprfs.f(3)

💖 SRC/ssprfs.f 💖

okay so bestie, welcome to SRC/ssprfs.f from the Library Functions Manual — this is the LAPACK page for SSPRFS, and it's giving "packed symmetric-indefinite solver gets an extra glow-up pass." ✨

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NAME

SRC/ssprfs.f — that's the name, no cap. 🫶

SYNOPSIS

Functions/Subroutines

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

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

The subroutine is SSPRFS, and yes, she is iconic. 👑

Purpose

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. That's the whole assignment. 💅

Parameters

• UPLO — UPLO is CHARACTER*1. = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. Pick your triangle, bestie. 🎀
• 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.
• AP — AP is 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 — AFP is 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 — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by SSPTRF.
• 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 SSPTRS. 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. That's the "how cooked is my answer" vibe, but mathematically. 😭
• 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 — ITMAX is the maximum number of steps of iterative refinement. That's the secret-sauce counter. 🔥

Author

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

Definition at line 177 of file ssprfs.f.

Yep — this one lives at line 177 of ssprfs.f. 💅

Author

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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Cute sign-off: this is LAPACK Version 3.12.0, page SRC/ssprfs.f(3) — that's the footer's whole story; no separate date is printed here, so I'm not inventing one, bestie. 🫶💖