F06PDF (DSBMV) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06PDF (DSBMV)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

F06PDF (DSBMV) computes the matrix-vector product for a real symmetric band matrix.

2  Specification

SUBROUTINE F06PDF ( UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
INTEGER  N, K, LDA, INCX, INCY
REAL (KIND=nag_wp)  ALPHA, A(LDA,*), X(*), BETA, Y(*)
CHARACTER(1)  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  Parameters

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:     A(LDA,*) – 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  Further Comments

None.

9  Example

None.

F06PDF (DSBMV) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012