TESTING/LIN/stbt03.f(3)

🧚 TESTING/LIN/stbt03.f(3) 🧚

from the Library Functions Manual, bestie. This is the stbt03 subroutine page, and we're gonna go through every single thing it does. No skipping, no cap. 💖

✨ NAME ✨

TESTING/LIN/stbt03.f — the file/page for the stbt03 subroutine. That's it, that's the name. 🎀

✨ SYNOPSIS ✨

🌸 Functions/Subroutines 🌸

subroutine stbt03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale,
    cnorm, tscal, x, ldx, b, ldb, work, resid)

STBT03

💅 Function/Subroutine Documentation 💅

🫶 subroutine stbt03 🫶

subroutine stbt03 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer
    ldab, real scale, real, dimension( * ) cnorm, real tscal, real,
    dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer
    ldb, real, dimension( * ) work, real resid)

STBT03

🎯 Purpose 🎯

Okay so STBT03 computes the residual for the solution to a scaled triangular system of equations A*x = s*b or A'*x = s*b when A is a triangular band matrix. Here A' is the transpose of A, s is a scalar, and x and b are N by NRHS matrices. The test ratio is the maximum over the number of right hand sides of:

norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),

where op(A) denotes A or A' and EPS is the machine epsilon. Slay, math. 🔥

🌈 Parameters 🌈

• UPLO — CHARACTER*1. Specifies whether the matrix A is upper or lower triangular: = 'U': Upper triangular; = 'L': Lower triangular. Pick one, bestie. 💅
• TRANS — CHARACTER*1. Specifies the operation applied to A: = 'N': A *x = b (No transpose); = 'T': A'*x = b (Transpose); = 'C': A'*x = b (Conjugate transpose = Transpose).
• DIAG — CHARACTER*1. Specifies whether or not the matrix A is unit triangular: = 'N': Non-unit triangular; = 'U': Unit triangular.
• N — INTEGER. The order of the matrix A. N >= 0.
• KD — INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AB — REAL array, dimension (LDAB,N). The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• SCALE — REAL. The scaling factor s used in solving the triangular system.
• CNORM — REAL array, dimension (N). The 1-norms of the columns of A, not counting the diagonal.
• TSCAL — REAL. The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
• X — REAL array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — REAL array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — REAL array, dimension (N). That's the whole vibe for this one. 🫶
• RESID — REAL. The maximum over the number of right hand sides of norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

👑 Author 👑

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

Definition at line 172 of file stbt03.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

---

That's the whole page, bestie! Source/version vibe: LAPACK Version 3.12.0, and the page is TESTING/LIN/stbt03.f(3). Byeee 💖✨