CTBT03(3)

💅 CTBT03(3) — Library Functions Manual 💅

Welcome to the Library Functions Manual page for ctbt03.f(3)! ✨ This is the documentation for the CTBT03 subroutine, and yes, it's giving major linear algebra energy. 🧮💖

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ctbt03.f

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine CTBT03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale,
    cnorm, tscal, x, ldx, b, ldb, work, resid)
    CTBT03

🎀 Function/Subroutine Documentation 🎀

subroutine CTBT03 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, complex, dimension( ldab, * ) ab, integer
    ldab, real scale, real, dimension( * ) cnorm, real tscal, complex,
    dimension( ldx, * ) x, integer ldx, complex, dimension( ldb, * ) b,
    integer ldb, complex, dimension( * ) work, real resid)
    CTBT03

💖 Purpose 💖

Okay so bestie, CTBT03 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. Here 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. 🔥

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

• LDAB (INTEGER) — The leading dimension of the array AB. LDAB >= KD+1.
• SCALE (REAL) — The scaling factor s used in solving the triangular system.
• CNORM (REAL array, dimension (N)) — The 1-norms of the columns of A, not counting the diagonal.
• TSCAL (REAL) — The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
• X (COMPLEX 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 (COMPLEX 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 (COMPLEX array, dimension (N))
• RESID (REAL) — 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 ctbt03.f. 📍

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code.

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LAPACK Version 3.12.0 — /home/abui...IN/ctbt03.f(3) 💖✨