nag_dgemv (f16pac) (PDF version)
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NAG Library Manual

NAG Library Function Document

nag_dgemv (f16pac)

 Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_dgemv (f16pac) performs matrix-vector multiplication for a real general matrix.

2  Specification

#include <nag.h>
#include <nagf16.h>
void  nag_dgemv (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)

3  Description

nag_dgemv (f16pac) performs one of the matrix-vector operations
yαAx + βy ,   or   yαATx + βy ,  
where A is an m by 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 http://www.netlib.org/blas/blast-forum/blas-report.pdf

5  Arguments

1:     order Nag_OrderTypeInput
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 2.3.1.3 in How to Use the NAG Library and its Documentation for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     trans Nag_TransTypeInput
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 IntegerInput
On entry: m, the number of rows of the matrix A.
Constraint: m0.
4:     n IntegerInput
On entry: n, the number of columns of the matrix A.
Constraint: n0.
5:     alpha doubleInput
On entry: the scalar α.
6:     a[dim] const doubleInput
Note: the dimension, dim, of the array a must be at least
  • max1,pda×n when order=Nag_ColMajor;
  • max1,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 by n matrix A.
7:     pda IntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraints:
  • if order=Nag_ColMajor, pdamax1,m;
  • if order=Nag_RowMajor, pdan.
8:     x[dim] const doubleInput
Note: the dimension, dim, of the array x must be at least
  • max1,1+n-1incx when trans=Nag_NoTrans;
  • max1,1+m-1incx 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 IntegerInput
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
10:   beta doubleInput
On entry: the scalar β.
11:   y[dim] doubleInput/Output
Note: the dimension, dim, of the array y must be at least
  • max1,1+m-1incy when trans=Nag_NoTrans;
  • max1,1+n-1incy 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 IntegerInput
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 2.7 in How to Use the NAG Library and its Documentation).

6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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: pdamax1,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.
An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation 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

nag_dgemv (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)


nag_dgemv (f16pac) (PDF version)
f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2016