DTBT03(3)

💖 NAME 💖

This is DTBT03(3), bestie — from the Library Functions Manual ✨ — and the NAME line points at this file path:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtbt03.f

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DTBT03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale,
    cnorm, tscal, x, ldx, b, ldb, work, resid)
    DTBT03

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🎀 Function/Subroutine Documentation 🎀

subroutine DTBT03 (character uplo, character trans, character diag, integer
     n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab,
     integer ldab, double precision scale, double precision, dimension( * )
     cnorm, double precision tscal, double precision, dimension( ldx, * ) x,
     integer ldx, double precision, dimension( ldb, * ) b, integer ldb,
     double precision, dimension( * ) work, double precision resid)
     DTBT03

🌸 Purpose

Okay so DTBT03 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. Periodt 💅

🦋 Parameters

• UPLO — UPLO is CHARACTER*1. Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular; = 'L': Lower triangular. 🫶
• TRANS — TRANS is 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 — DIAG is CHARACTER*1. Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular; = 'U': Unit triangular. 💜
• N — N is INTEGER. The order of the matrix A. N >= 0. 🎀
• KD — KD is INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. 🌈
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0. 💖
• AB — AB is DOUBLE PRECISION 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 — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1. 🦋
• SCALE — SCALE is DOUBLE PRECISION. The scaling factor s used in solving the triangular system. 🌸
• CNORM — CNORM is DOUBLE PRECISION array, dimension (N). The 1-norms of the columns of A, not counting the diagonal. 💫
• TSCAL — TSCAL is DOUBLE PRECISION. The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A. 🔥
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations. 👑
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N). 🌟
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations. 💕
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 🧚
• WORK — WORK is DOUBLE PRECISION array, dimension (N). 🍓
• RESID — RESID is DOUBLE PRECISION. 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 dtbt03.f. ✨

🌈 Author

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie 🫶 — LAPACK, Version 3.12.0, and the page path /home/abui...IN/dtbt03.f(3). Keep those residuals tiny and those vibes immaculate 💖✨