TESTING/LIN/ztbt03.f(3)

✨ NAME ✨

TESTING/LIN/ztbt03.f — that's the file, bestie, and the manual-header vibe is TESTING/LIN/ztbt03.f(3) / Library Functions Manual. It’s giving “subroutine documentation but make it iconic” 💅.

🌸 SYNOPSIS 🌸

✨ Functions/Subroutines ✨

• subroutine ztbt03 — ZTBT03

subroutine ztbt03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale,
    cnorm, tscal, x, ldx, b, ldb, work, resid)

ZTBT03

💅 Function/Subroutine Documentation 💅

subroutine ztbt03 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, complex*16, dimension( ldab, * ) ab,
    integer ldab, double precision scale, double precision, dimension( * )
    cnorm, double precision tscal, complex*16, dimension( ldx, * ) x,
    integer ldx, complex*16, dimension( ldb, * ) b, integer ldb, complex*16,
    dimension( * ) work, double precision resid)

ZTBT03

🎯 Purpose:

Okay bestie, here’s the whole vibe: ZTBT03 computes the residual for the solution to a scaled triangular system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b when A is a triangular band matrix. Quick glossary moment: A**T denotes the transpose of A, A**H denotes the conjugate 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, A**T, or A**H, and EPS is the machine epsilon. periodt ✨

🔥 Parameters

• UPLO — UPLO is CHARACTER*1. It specifies whether the matrix A is upper or lower triangular. The values are:

= 'U':  Upper triangular
= 'L':  Lower triangular

• TRANS — TRANS is CHARACTER*1. It specifies the operation applied to A. The values are:

= 'N':  A *x = s*b     (No transpose)
= 'T':  A**T *x = s*b  (Transpose)
= 'C':  A**H *x = s*b  (Conjugate transpose)

• DIAG — DIAG is CHARACTER*1. It specifies whether or not the matrix A is unit triangular. The values are:

= '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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 174 of file ztbt03.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, source file TESTING/LIN/ztbt03.f(3). slay and bye 🎀