NAG Library Routine Document

f06pkf  (dtbsv)

 Contents

    1  Purpose
    7  Accuracy
    10  Example

1
Purpose

f06pkf (dtbsv) solves a real triangular banded system of equations with a single right hand side.

2
Specification

Fortran Interface
Subroutine f06pkf ( uplo, trans, diag, n, k, a, lda, x, incx)
Integer, Intent (In):: n, k, lda, incx
Real (Kind=nag_wp), Intent (In):: a(lda,*)
Real (Kind=nag_wp), Intent (Inout):: x(*)
Character (1), Intent (In):: uplo, trans, diag
C Header Interface
#include nagmk26.h
void  f06pkf_ ( const char *uplo, const char *trans, const char *diag, const Integer *n, const Integer *k, const double a[], const Integer *lda, double x[], const Integer *incx, const Charlen length_uplo, const Charlen length_trans, const Charlen length_diag)
The routine may be called by its BLAS name dtbsv.

3
Description

f06pkf (dtbsv) performs one of the matrix-vector operations
xA-1x   or   xA-Tx ,  
where A is an n by n real triangular band matrix with k subdiagonals or superdiagonals, and x is an n-element real vector. A-T  denotes AT-1  or equivalently A-1T .
No test for singularity or near-singularity of A is included in this routine. Such tests must be performed before calling this routine.

4
References

None.

5
Arguments

1:     uplo – Character(1)Input
On entry: specifies whether A is upper or lower triangular.
uplo='U'
A is upper triangular.
uplo='L'
A is lower triangular.
Constraint: uplo='U' or 'L'.
2:     trans – Character(1)Input
On entry: specifies the operation to be performed.
trans='N'
xA-1x.
trans='T' or 'C'
xA-Tx.
Constraint: trans='N', 'T' or 'C'.
3:     diag – Character(1)Input
On entry: specifies whether A has nonunit or unit diagonal elements.
diag='N'
The diagonal elements are stored explicitly.
diag='U'
The diagonal elements are assumed to be 1, and are not referenced.
Constraint: diag='N' or 'U'.
4:     n – IntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
5:     k – IntegerInput
On entry: k, the number of subdiagonals or superdiagonals of the matrix A.
Constraint: k0.
6:     alda* – Real (Kind=nag_wp) arrayInput
Note: the second dimension of the array a must be at least n.
On entry: the n by n triangular band matrix A 
The matrix is stored in rows 1 to k+1, more precisely,
  • if uplo='U', the elements of the upper triangle of A within the band must be stored with element Aij in ak+1+i-jj​ for ​max1,j-kij;
  • if uplo='L', the elements of the lower triangle of A within the band must be stored with element Aij in a1+i-jj​ for ​jiminn,j+k.
If diag='U', the diagonal elements of A are assumed to be 1, and are not referenced.
7:     lda – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06pkf (dtbsv) is called.
Constraint: ldak+1.
8:     x* – Real (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array x must be at least max1, 1+n-1 ×incx .
On entry: the n-element vector x.
If incx>0, xi must be stored in x1+i1×incx , for i=1,2,,n.
If incx<0, xi must be stored in x1ni×incx , for i=1,2,,n.
On exit: the updated vector x stored in the array elements used to supply the original vector x.
9:     incx – IntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06pkf (dtbsv) is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.
© The Numerical Algorithms Group Ltd, Oxford, UK. 2017