TESTING/LIN/stbt02.f(3)

💅 NAME 💅

TESTING/LIN/stbt02.f — okay so this page is from the Library Functions Manual, and it's literally the manual page for the stbt02 subroutine. It's giving linear algebra energy, and we're obsessed. 💖

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✨ SYNOPSIS ✨

Functions/Subroutines — the whole synopsis vibe is:

subroutine stbt02 (uplo, trans, diag, n, kd, nrhs, ab, ldab, x, ldx, b,
    ldb, work, resid)
    STBT02

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🎀 Function/Subroutine Documentation 🎀

subroutine stbt02 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer
    ldab, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, *
    ) b, integer ldb, real, dimension( * ) work, real resid)
    STBT02

🧮 Purpose 🧮

Okay so STBT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when A is a triangular band matrix. The test ratio is the maximum over

norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),

where op(A) = A or A**T, b is the column of B, x is the solution vector, and EPS is the machine epsilon.

The norm used is the 1-norm. Slay. ✨

🎛 Parameters 🎛

• UPLO — CHARACTER*1; specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular; = 'L': Lower triangular.
• TRANS — CHARACTER*1; specifies the operation applied to A. = 'N': A * X = B (No transpose); = 'T': A**T * X = B (Transpose); = 'C': A**H * 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.
• 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).
• RESID — REAL; the maximum over the number of right hand sides of norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).

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👑 Author 👑

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

Definition at line 152 of file stbt02.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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byeee bestie 🫶 the footer info is LAPACK, Version 3.12.0, and TESTING/LIN/stbt02.f(3) — source/version/page id, periodt. 💅✨