# sgbt02.f - Man Page

TESTING/LIN/sgbt02.f

## Synopsis

### Functions/Subroutines

subroutine **sgbt02** (trans, m, n, kl, ku, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)**SGBT02**

## Function/Subroutine Documentation

### subroutine sgbt02 (character trans, integer m, integer n, integer kl, integer ku, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real resid)

**SGBT02**

**Purpose:**

SGBT02 computes the residual for a solution of a banded system of equations op(A)*X = B: RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ), where op(A) = A or A**T, depending on TRANS, and EPS is the machine epsilon. The norm used is the 1-norm.

**Parameters***TRANS*TRANS is CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = 'T': A**T * X = B (Transpose) = 'C': A**H * X = B (Conjugate transpose = Transpose)

*M*M is INTEGER The number of rows of the matrix A. M >= 0.

*N*N is INTEGER The number of columns of the matrix A. N >= 0.

*KL*KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.

*KU*KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.

*NRHS*NRHS is INTEGER The number of columns of B. NRHS >= 0.

*A*A is REAL array, dimension (LDA,N) The original matrix A in band storage, stored in rows 1 to KL+KU+1.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,KL+KU+1).

*X*X is REAL 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. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).

*B*B is REAL array, dimension (LDB,NRHS) On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.

*LDB*LDB is INTEGER The leading dimension of the array B. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).

*RWORK*RWORK is REAL array, dimension (MAX(1,LRWORK)), where LRWORK >= M when TRANS = 'T' or 'C'; otherwise, RWORK is not referenced.

*RESID*RESID is REAL The maximum over the number of right hand sides of norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **147** of file **sgbt02.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sgbt02(3) is an alias of sgbt02.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK