NAG Library Routine Document

f06pdf (dsbmv)

1
Purpose

f06pdf (dsbmv) computes the matrix-vector product for a real symmetric band matrix.

2
Specification

Fortran Interface
Subroutine f06pdf ( uplo, n, k, alpha, a, lda, x, incx, beta, y, incy)
Integer, Intent (In):: n, k, lda, incx, incy
Real (Kind=nag_wp), Intent (In):: alpha, a(lda,*), x(*), beta
Real (Kind=nag_wp), Intent (Inout):: y(*)
Character (1), Intent (In):: uplo
C Header Interface
#include <nagmk26.h>
void  f06pdf_ (const char *uplo, const Integer *n, const Integer *k, const double *alpha, const double a[], const Integer *lda, const double x[], const Integer *incx, const double *beta, double y[], const Integer *incy, const Charlen length_uplo)
The routine may be called by its BLAS name dsbmv.

3
Description

f06pdf (dsbmv) performs the matrix-vector operation
yαAx+βy ,  
where A is an n by n real symmetric band matrix with k subdiagonals and k superdiagonals, x and y are n-element real vectors, and α and β are real scalars.

4
References

None.

5
Arguments

1:     uplo – Character(1)Input
On entry: specifies whether the upper or lower triangular part of A is stored.
uplo='U'
The upper triangular part of A is stored.
uplo='L'
The lower triangular part of A is stored.
Constraint: uplo='U' or 'L'.
2:     n – IntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
3:     k – IntegerInput
On entry: k, the number of subdiagonals or superdiagonals of the matrix A.
Constraint: k0.
4:     alpha – Real (Kind=nag_wp)Input
On entry: the scalar α.
5:     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 symmetric 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.
6:     lda – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06pdf (dsbmv) is called.
Constraint: ldak+1.
7:     x* – Real (Kind=nag_wp) arrayInput
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+i-1×incx, for i=1,2,,n.
If incx<0, xi must be stored in x1-n-i×incx, for i=1,2,,n.
Intermediate elements of x are not referenced.
8:     incx – IntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
9:     beta – Real (Kind=nag_wp)Input
On entry: the scalar β.
10:   y* – Real (Kind=nag_wp) arrayInput/Output
Note: the dimension of the array y must be at least max1, 1+n-1 ×incy .
On entry: the n-element vector y, if beta=0.0 y need not be set.
If incy>0, yi must be stored in y1+i1×incy , for i=1,2,,n.
If incy<0, yi must be stored in y1ni×incy , for i=1,2,,n.
On exit: the updated vector y stored in the array elements used to supply the original vector y.
11:   incy – IntegerInput
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06pdf (dsbmv) is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.