TESTING/LIN/ctbt03.f(3)

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TESTING/LIN/ctbt03.f

Hey bestie 💖 welcome to the Library Functions Manual page for TESTING/LIN/ctbt03.f. This is the whole cute-but-serious documentation moment for the ctbt03 subroutine and its CTBT03 label.

NAME

TESTING/LIN/ctbt03.f — that’s the file name, periodt. This is its manual page.

SYNOPSIS

Functions/Subroutines

subroutine ctbt03 (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale,
           cnorm, tscal, x, ldx, b, ldb, work, resid)
           CTBT03

That’s the quick peek: the ctbt03 subroutine signature, followed by 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

Here’s the full signature, exactly as it lives in the docs. Every type, every array dimension, every comma — preserved. 🫶

Purpose

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

UPLO is CHARACTER*1. It specifies whether the matrix A is upper or lower triangular.

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

TRANS

TRANS is CHARACTER*1. It 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

DIAG is CHARACTER*1. It specifies whether or not the matrix A is unit triangular.

  • = 'N': Non-unit triangular
  • = 'U': Unit triangular

N

N is INTEGER. It’s the order of the matrix A. Constraint: N >= 0.

KD

KD is INTEGER. It’s the number of superdiagonals or subdiagonals of the triangular band matrix A. Constraint: KD >= 0.

NRHS

NRHS is INTEGER. It’s the number of right hand sides, i.e., the number of columns of the matrices X and B. Constraint: NRHS >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N). It’s 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. It’s the leading dimension of the array AB. Constraint: LDAB >= KD+1.

SCALE

SCALE is REAL. It’s the scaling factor s used in solving the triangular system.

CNORM

CNORM is REAL array, dimension (N). It holds the 1-norms of the columns of A, not counting the diagonal.

TSCAL

TSCAL is REAL. It’s the scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.

X

X is COMPLEX array, dimension (LDX,NRHS). It holds the computed solution vectors for the system of linear equations.

LDX

LDX is INTEGER. It’s the leading dimension of the array X. Constraint: LDX >= max(1,N).

B

B is COMPLEX array, dimension (LDB,NRHS). It holds the right hand side vectors for the system of linear equations.

LDB

LDB is INTEGER. It’s the leading dimension of the array B. Constraint: LDB >= max(1,N).

WORK

WORK is COMPLEX array, dimension (N).

RESID

RESID is REAL. It’s 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

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