SRC/spprfs.f(3)

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version 3.12.1 · 7 versions
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💖 SRC/spprfs.f(3) — Library Functions Manual 💖

okay so this is the manual page for SRC/spprfs.f(3), and the main character is the spprfs subroutine. It's giving LAPACK refinement energy: packed symmetric positive definite systems get their solution polished, and the error bounds come along for the ride. Buckle up bestie. 🎀

✨ NAME ✨

SRC/spprfs.f — that's the file, and the routine living in it is spprfs. Slay.

✨ SYNOPSIS ✨

✨ Functions/Subroutines ✨

  • subroutine spprfs (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr, work, iwork, info) — SPPRFS.
subroutine spprfs (uplo, n, nrhs, ap, afp, b, ldb, x, ldx, ferr, berr,
    work, iwork, info)

✨ Function/Subroutine Documentation ✨

subroutine spprfs

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

SPPRFS

✨ Purpose ✨

okay so what does SPPRFS actually do? It improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and it provides error bounds and backward error estimates for the solution. That's the whole assignment, no cap. 💅

✨ Parameters ✨

  • UPLO — UPLO is CHARACTER*1. = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. It's literally telling you which triangle of A is packed in there. 🦋
  • 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). This holds 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
  • AFP — AFP is REAL array, dimension (N*(N+1)/2). This is the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF, packed columnwise in a linear array in the same format as A (see AP).
  • 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 SPPTRS. 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), then 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 is almost always a slight overestimate of the true error. Not me being dramatic, that's literally the spec. 😭
  • 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 — the maximum number of steps of iterative refinement. That's the internal dial, iykyk. 🔥

✨ Author ✨

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

Definition at line 169 of file spprfs.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code. Yes, bestie, that's the second Author block — Doxygen really said "and I took that personally." 💀

LAPACK Version 3.12.0 · SRC/spprfs.f(3) — that's the footer energy, mwah! 🫶✨💖

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