NAG FL Interface
f06paf (dgemv)

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1 Purpose

f06paf computes the matrix-vector product for a real general matrix or its transpose.

2 Specification

Fortran Interface
Subroutine f06paf ( trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
Integer, Intent (In) :: m, n, 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) :: trans
C Header Interface
#include <nag.h>
void  f06paf_ (const char *trans, const Integer *m, const Integer *n, 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_trans)
The routine may be called by the names f06paf, nagf_blas_dgemv or its BLAS name dgemv.

3 Description

f06paf performs one of the matrix-vector operations
yαAx + βy ,   or   yαATx + βy ,  
where A is an m×n real matrix, x and y are real vectors, and α and β are real scalars.
If m=0 or n=0, no operation is performed.

4 References

None.

5 Arguments

1: trans Character(1) Input
On entry: specifies the operation to be performed.
trans='N'
yαAx+βy.
trans='T' or 'C'
yαATx+βy.
Constraint: trans='N', 'T' or 'C'.
2: m Integer Input
On entry: m, the number of rows of the matrix A.
Constraint: m0.
3: n Integer Input
On entry: n, the number of columns of the matrix A.
Constraint: n0.
4: alpha Real (Kind=nag_wp) Input
On entry: the scalar α.
5: a(lda,*) Real (Kind=nag_wp) array Input
Note: the second dimension of the array a must be at least n.
On entry: the m×n matrix A.
6: lda Integer Input
On entry: the first dimension of the array a as declared in the (sub)program from which f06paf is called.
Constraint: lda max(1,m) .
7: x(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array x must be at least max(1, 1+ (n-1) ×|incx| ) if trans='N' and at least max(1, 1+ (m-1) ×|incx| ) if trans='T' or 'C'.
On entry: the vector x.
If trans='N',
  • if incx>0, xi must be stored in x(1+(i-1)×incx) , for i=1,2,,n;
  • if incx<0, xi must be stored in x(1-(n-i)×incx) , for i=1,2,,n.
If trans='T' or 'C',
  • if incx>0, xi must be stored in x(1+(i-1)×incx) , for i=1,2,,m;
  • if incx<0, xi must be stored in x(1-(m-i)×incx) , for i=1,2,,m.
8: incx Integer Input
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) array Input/Output
Note: the dimension of the array y must be at least max(1,1+(m-1) ×|incy|) if trans='N' and at least max(1,1+(n-1) ×|incy|) if trans='T' or 'C'.
On entry: the vector y, if beta=0.0, y need not be set.
If trans='N',
  • if incy>0, yi must be stored in y(1+(i-1)×incy) , for i=1,2,,m;
  • if incy<0, yi must be stored in y(1-(m-i)×incy) , for i=1,2,,m.
If trans='T' or 'C',
  • if incy>0, yi must be stored in y(1+(i-1)×incy) , for i=1,2,,n;
  • if incy<0, yi must be stored in y(1-(n-i)×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 Integer Input
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

Background information to multithreading can be found in the Multithreading documentation.
f06paf is not threaded in any implementation.

9 Further Comments

None.

10 Example

None.