DTBT02(3)

📦 version 3.12.0, in opensuse-leap 16.0

🦋 DTBT02(3) 🦋

okay so bestie, this is the Library Functions Manual page for DTBT02(3), and the page path is /home/abui...IN/dtbt02.f(3). It’s giving LAPACK testing-lib energy, and we are going to keep every single technical crumb intact 💅.

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtbt02.f

That’s the exact file path this page names. No cap.

🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine DTBT02 (uplo, trans, diag, n, kd, nrhs, ab, ldab, x, ldx, b,
    ldb, work, resid)
    DTBT02

🎀 Function/Subroutine Documentation 🎀

subroutine DTBT02

subroutine DTBT02 (character uplo, character trans, character diag, integer
    n, integer kd, integer nrhs, double precision, dimension( ldab, * ) ab,
    integer ldab, double precision, dimension( ldx, * ) x, integer ldx,
    double precision, dimension( ldb, * ) b, integer ldb, double precision,
    dimension( * ) work, double precision resid)

DTBT02 is the subroutine name, periodt. The signature above is the full character-for-character cast list.

🧪 Purpose 🧪

DTBT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when A is a triangular band matrix. The test ratio is the maximum over:

norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),

where op(A) = A or A**T, b is the column of B, x is the solution vector, and EPS is the machine epsilon. The norm used is the 1-norm. That’s the whole flex: max over the right-hand sides of that residual ratio.

🔍 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 = B  (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  A**H * X = B  (Conjugate transpose = 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. 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 DOUBLE PRECISION 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. The leading dimension of the array AB. LDAB >= KD+1.

X

X is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N).

RESID

RESID is DOUBLE PRECISION. The maximum over the number of right hand sides of:

norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).

👑 Author 👑

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

Definition at line 152 of file dtbt02.f.

📜 Author 📜

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