STPRFS(3)

🌸 NAME

okay so bestie, this is the STPRFS(3) page from the LAPACK Library Functions Manual — section 3, no cap. The NAME section is literally this source-file path:

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

It's giving “the whole page is about this one .f file,” and honestly? Iconic. 💅

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✨ SYNOPSIS

💅 Functions/Subroutines

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

That's the subroutine right there: STPRFS. Periodt.

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🦋 Function/Subroutine Documentation

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)

Subroutine name: STPRFS. We been knew. 🫶

🎯 Purpose

STPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. Triangular packed matrix is the whole vibe here.

The solution matrix X must be computed by STPTRS or some other means before entering this routine. STPRFS does not do iterative refinement because doing so cannot improve the backward error. That's not a suggestion, bestie — that's just how it is.

🌈 Parameters

<pink>UPLO</pink>

UPLO is CHARACTER*1.

• 'U': A is upper triangular;
• 'L': A is lower triangular.

<pink>TRANS</pink>

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)

<pink>DIAG</pink>

DIAG is CHARACTER*1.

• 'N': A is non-unit triangular;
• 'U': A is unit triangular.

<pink>N</pink>

N is INTEGER.

The order of the matrix A. N >= 0.

<pink>NRHS</pink>

NRHS is INTEGER.

The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.

<pink>AP</pink>

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.

<pink>B</pink>

B is REAL array, dimension (LDB,NRHS).

The right hand side matrix B.

<pink>LDB</pink>

LDB is INTEGER.

The leading dimension of the array B. LDB >= max(1,N).

<pink>X</pink>

X is REAL array, dimension (LDX,NRHS).

The solution matrix X.

<pink>LDX</pink>

LDX is INTEGER.

The leading dimension of the array X. LDX >= max(1,N).

<pink>FERR</pink>

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. Almost always a slight overestimate — cute, reliable, a little dramatic. 🙈

<pink>BERR</pink>

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).

<pink>WORK</pink>

WORK is REAL array, dimension (3*N).

<pink>IWORK</pink>

IWORK is INTEGER array, dimension (N).

<pink>INFO</pink>

INFO is INTEGER.

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value

👑 Author

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

📜 Definition at line 173 of file stprfs.f.

🧚 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Source/version/date sign-off: this is LAPACK Version 3.12.0, footer ref /home/abui...RC/stprfs.f(3) — and the date isn't listed in that footer block, so I'm not inventing one, bestie. Byeee 💖🎀🦋