# stbt03.f - Man Page

TESTING/LIN/stbt03.f

## Synopsis

### Functions/Subroutines

subroutine **stbt03** (uplo, trans, diag, n, kd, nrhs, ab, ldab, scale, cnorm, tscal, x, ldx, b, ldb, work, resid)**STBT03**

## Function/Subroutine Documentation

### subroutine stbt03 (character uplo, character trans, character diag, integer n, integer kd, integer nrhs, real, dimension( ldab, * ) ab, integer ldab, real scale, real, dimension( * ) cnorm, real tscal, real, dimension( ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, real resid)

**STBT03**

**Purpose:**

STBT03 computes the residual for the solution to a scaled triangular system of equations A*x = s*b or A'*x = s*b when A is a triangular band matrix. Here A' is the 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 or A' and EPS is the machine epsilon.

**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 operation applied to A. = '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 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 REAL 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*LDAB is INTEGER The leading dimension of the array AB. LDAB >= KD+1.

*SCALE*SCALE is REAL The scaling factor s used in solving the triangular system.

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

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

*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. LDX >= max(1,N).

*B*B is REAL 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 REAL array, dimension (N)

*RESID*RESID is 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 **172** of file **stbt03.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page stbt03(3) is an alias of stbt03.f(3).

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