TESTING/LIN/dtbt03.f(3)

🌸 NAME 🌸

TESTING/LIN/dtbt03.f — bestie, this whole page is about that file, straight from the Library Functions Manual. It’s giving “tiny subroutine, big residual-checking energy” 💅

🫶 SYNOPSIS 🫶

Functions/Subroutines

   subroutine dtbt03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale,
       cnorm, tscal, x, ldx, b, ldb, work, resid)
       DTBT03

🎀 Function/Subroutine Documentation 🎀

Here’s the full signature, no cap:

   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. That’s the vibe check this routine is doing, fr fr 🦋

🌸 Parameters 🌸

• UPLO — type check: CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — type check: 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 — type check: CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — type check: INTEGER. The order of the matrix A. N >= 0.
• KD — type check: INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• NRHS — type check: INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AB — type check: 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 — type check: INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• SCALE — type check: DOUBLE PRECISION. The scaling factor s used in solving the triangular system.
• CNORM — type check: DOUBLE PRECISION array, dimension (N). The 1-norms of the columns of A, not counting the diagonal.
• TSCAL — type check: DOUBLE PRECISION. The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
• X — type check: DOUBLE PRECISION array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — type check: INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — type check: DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — type check: INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — type check: DOUBLE PRECISION array, dimension (N). Just the work array, bestie — that’s all she wrote. 🫶
• RESID — type check: 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. Auto-generated queen behavior, honestly ⭐

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Okay that’s the whole page, bestie 💅 This one is LAPACK Version 3.12.0, source page TESTING/LIN/dtbt03.f(3). The footer doesn’t print a calendar date, so I’m not inventing one — no cap. Mwah 🫶