NAG CL Interface
f16pac (dgemv)

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1 Purpose

f16pac performs matrix-vector multiplication for a real general matrix.

2 Specification

#include <nag.h>
void  f16pac (Nag_OrderType order, Nag_TransType trans, Integer m, Integer n, double alpha, const double a[], Integer pda, const double x[], Integer incx, double beta, double y[], Integer incy, NagError *fail)
The function may be called by the names: f16pac, nag_blast_dgemv or nag_dgemv.

3 Description

f16pac 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

Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001) Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard University of Tennessee, Knoxville, Tennessee https://www.netlib.org/blas/blast-forum/blas-report.pdf

5 Arguments

1: order Nag_OrderType Input
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.1.3 in the Introduction to the NAG Library CL Interface for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2: trans Nag_TransType Input
On entry: specifies the operation to be performed.
trans=Nag_NoTrans
yαAx+βy.
trans=Nag_Trans or Nag_ConjTrans
yαATx+βy.
Constraint: trans=Nag_NoTrans, Nag_Trans or Nag_ConjTrans.
3: m Integer Input
On entry: m, the number of rows of the matrix A.
Constraint: m0.
4: n Integer Input
On entry: n, the number of columns of the matrix A.
Constraint: n0.
5: alpha double Input
On entry: the scalar α.
6: a[dim] const double Input
Note: the dimension, dim, of the array a must be at least
  • max(1,pda×n) when order=Nag_ColMajor;
  • max(1,m×pda) when order=Nag_RowMajor.
If order=Nag_ColMajor, Aij is stored in a[(j-1)×pda+i-1].
If order=Nag_RowMajor, Aij is stored in a[(i-1)×pda+j-1].
On entry: the m×n matrix A.
7: pda Integer Input
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraints:
  • if order=Nag_ColMajor, pdamax(1,m);
  • if order=Nag_RowMajor, pdan.
8: x[dim] const double Input
Note: the dimension, dim, of the array x must be at least
  • max(1,1+(n-1)|incx|) when trans=Nag_NoTrans;
  • max(1,1+(m-1)|incx|) when trans=Nag_Trans or Nag_ConjTrans.
On entry: the vector x.
If trans=Nag_NoTrans, then x is an n-element vector.
  • If incx>0, xi must be stored in x[(i-1)×incx], for i=1,2,,n.
  • If incx<0, xi must be stored in x[(n-i)×|incx|], for i=1,2,,n.
  • Intermediate elements of x are not referenced. If n=0, x is not referenced and may be NULL.
Otherwise, x is an m-element vector.
  • If incx>0, xi must be stored in x[(i-1)×incx], for i=1,2,,m.
  • If incx<0, xi must be stored in x[(m-i)×|incx|], for i=1,2,,m.
  • Intermediate elements of x are not referenced. If m=0, x is not referenced and may be NULL.
9: incx Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
10: beta double Input
On entry: the scalar β.
11: y[dim] double Input/Output
Note: the dimension, dim, of the array y must be at least
  • max(1,1+(m-1)|incy|) when trans=Nag_NoTrans;
  • max(1,1+(n-1)|incy|) when trans=Nag_Trans or Nag_ConjTrans.
On entry: the vector y. See x for details of storage.
If beta=0, y need not be set.
On exit: the updated vector y.
12: incy Integer Input
On entry: the increment in the subscripts of y between successive elements of y.
Constraint: incy0.
13: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, incx=value.
Constraint: incx0.
On entry, incy=value.
Constraint: incy0.
On entry, m=value.
Constraint: m0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pda=value, m=value.
Constraint: pdamax(1,m).
On entry, pda=value and n=value.
Constraint: pdan.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

The BLAS standard requires accurate implementations which avoid unnecessary over/underflow (see Section 2.7 of Basic Linear Algebra Subprograms Technical (BLAST) Forum (2001)).

8 Parallelism and Performance

f16pac is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example computes the matrix-vector product
y = αAx+βy  
where
A= ( 1.0 2.0 3.0 4.0 5.0 6.0 ) ,  
x = ( -1.0 2.0 ) ,  
y= ( 1.0 2.0 3.0 ) ,  
α=1.5 ​ and ​ β=1.0 .  

10.1 Program Text

Program Text (f16pace.c)

10.2 Program Data

Program Data (f16pace.d)

10.3 Program Results

Program Results (f16pace.r)