SRC/stprfs.f(3)

🦋 SRC/stprfs.f(3) — Library Functions Manual 🦋

okay so bestie, this is the page for STPRFS — the LAPACK error-bound and backward-error-estimate girlie for triangular packed linear systems. No cap, she’s here to tell you how good your solve is 💅✨

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🌸 NAME 🌸

SRC/stprfs.f — the file behind the stprfs subroutine. iykyk 🫶

✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine stprfs (uplo, trans, diag, n, nrhs, ap, b, ldb, x, ldx, ferr, berr, work, iwork, info) — STPRFS

🦋 FUNCTION/SUBROUTINE DOCUMENTATION 🦋

💖 subroutine stprfs 💖

subroutine stprfs (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( * ) ap, 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)

STPRFS

🎀 Purpose 🎀

So here’s the tea: STPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. Literally exactly what it says on the tin 💖

The solution matrix X must be computed by STPTRS or some other means before entering this routine.

🫶 And bestie, STPRFS does not do iterative refinement — because doing so cannot improve the backward error. Periodt.

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🌈 Parameters 🌈

• UPLO — is CHARACTER*1
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• TRANS — is CHARACTER*1. Specifies the form of the system of equations:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)
• DIAG — is CHARACTER*1
  • = 'N': A is non-unit triangular;
  • = 'U': A is unit triangular.
• N — is INTEGER. The order of the matrix A. N >= 0.
• NRHS — is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• AP — is REAL array, dimension (N*(N+1)/2). The upper or lower triangular 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.

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

• B — is REAL array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — is REAL array, dimension (LDX,NRHS). The solution matrix X.
• LDX — is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• 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 — 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 — is REAL array, dimension (3*N).
• IWORK — is INTEGER array, dimension (N).
• INFO — is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value

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👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📌 Definition 📌

Definition at line 173 of file stprfs.f.

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🌟 Author (generated) 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole thing, bestie — SRC/stprfs.f(3) from LAPACK Version 3.12.0. The original footer didn’t give me a calendar date to repeat, so I’m not making one up 💅💖✨