TESTING/LIN/ctbt05.f(3)

💅 TESTING/LIN/ctbt05.f — Library Functions Manual vibes ✨

Okay bestie, this is the TESTING/LIN/ctbt05.f(3) page from the Library Functions Manual, and it's all about the CTBT05 subroutine. No cap, it's giving error-bound check energy.

💖 NAME

TESTING/LIN/ctbt05.f

🌈 SYNOPSIS

Functions/Subroutines

       subroutine ctbt05 (uplo, trans, diag, n, kd, nrhs, ab, ldab, b, ldb, x,
           ldx, xact, ldxact, ferr, berr, reslts)
           CTBT05

📚 Function/Subroutine Documentation

   subroutine ctbt05 (character uplo, character trans, character diag, integer
       n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer
       ldab, complex, dimension( ldb, * ) b, integer ldb, complex, dimension(
       ldx, * ) x, integer ldx, complex, dimension( ldxact, * ) xact, integer
       ldxact, real, dimension( * ) ferr, real, dimension( * ) berr, real,
       dimension( * ) reslts)
       CTBT05

Purpose 🎯

CTBT05 tests the error bounds from iterative refinement for the computed solution to a system of equations A*X = B, where A is a triangular band matrix. Slay.

RESLTS(1) = test of the error bound
          = norm(X - XACT) / ( norm(X) * FERR )

A large value is returned if this ratio is not less than one.

RESLTS(2) = residual from the iterative refinement routine
          = the maximum of BERR / ( NZ*EPS + (*) ), where
            (*) = NZ*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
            and NZ = max. number of nonzeros in any row of A, plus 1

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 form of the system of equations.
  • = '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 number of rows of the matrices X, B, and XACT, and the order of the matrix A. N >= 0.
• KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
• NRHS — NRHS is INTEGER. The number of columns of the matrices X, B, and XACT. NRHS >= 0.
• AB — AB is COMPLEX 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).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• B — B is COMPLEX 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).
• X — X is COMPLEX array, dimension (LDX,NRHS). The computed solution vectors. Each vector is stored as a column of the matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• XACT — XACT is COMPLEX array, dimension (LDX,NRHS). The exact solution vectors. Each vector is stored as a column of the matrix XACT.
• LDXACT — LDXACT is INTEGER. The leading dimension of the array XACT. LDXACT >= max(1,N).
• FERR — FERR is REAL array, dimension (NRHS). The estimated forward error bounds for each solution vector X. If XTRUE is the true solution, FERR bounds the magnitude of the largest entry in (X - XTRUE) divided by the magnitude of the largest entry in X.
• BERR — BERR is REAL array, dimension (NRHS). The componentwise relative backward error of each solution vector (i.e., the smallest relative change in any entry of A or B that makes X an exact solution).
• RESLTS — RESLTS is REAL array, dimension (2). The maximum over the NRHS solution vectors of the ratios:

RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
RESLTS(2) = BERR / ( NZ*EPS + (*) )

Author 👑

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

Definition 📌

Definition at line 187 of file ctbt05.f.

✨ Author

Generated automatically by Doxygen for LAPACK from the source code.

---

Okay bestie, that's the whole ctbt05 page! 🫶 It was generated automatically by Doxygen for LAPACK from the source code, and it's serving LAPACK Version 3.12.0 for TESTING/LIN/ctbt05.f(3). Bye! 💖