f16 Chapter Contents
f16 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_dgemv (f16pac)

## 1  Purpose

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

## 2  Specification

 #include #include
 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
 $y←αAx + βy , or y←αATx + βy ,$
where $A$ is an $m$ by $n$ real matrix, $x$ and $y$ are real vectors, and $\alpha$ and $\beta$ 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:    $\mathbf{order}$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 ${\mathbf{order}}=\mathrm{Nag_RowMajor}$. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: ${\mathbf{order}}=\mathrm{Nag_RowMajor}$ or $\mathrm{Nag_ColMajor}$.
2:    $\mathbf{trans}$Nag_TransTypeInput
On entry: specifies the operation to be performed.
${\mathbf{trans}}=\mathrm{Nag_NoTrans}$
$y←\alpha Ax+\beta y$.
${\mathbf{trans}}=\mathrm{Nag_Trans}$ or $\mathrm{Nag_ConjTrans}$
$y←\alpha {A}^{\mathrm{T}}x+\beta y$.
Constraint: ${\mathbf{trans}}=\mathrm{Nag_NoTrans}$, $\mathrm{Nag_Trans}$ or $\mathrm{Nag_ConjTrans}$.
3:    $\mathbf{m}$IntegerInput
On entry: $m$, the number of rows of the matrix $A$.
Constraint: ${\mathbf{m}}\ge 0$.
4:    $\mathbf{n}$IntegerInput
On entry: $n$, the number of columns of the matrix $A$.
Constraint: ${\mathbf{n}}\ge 0$.
5:    $\mathbf{alpha}$doubleInput
On entry: the scalar $\alpha$.
6:    $\mathbf{a}\left[\mathit{dim}\right]$const doubleInput
Note: the dimension, dim, of the array a must be at least
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{pda}}×{\mathbf{n}}\right)$ when ${\mathbf{order}}=\mathrm{Nag_ColMajor}$;
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}×{\mathbf{pda}}\right)$ when ${\mathbf{order}}=\mathrm{Nag_RowMajor}$.
If ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(j-1\right)×{\mathbf{pda}}+i-1\right]$.
If ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${A}_{ij}$ is stored in ${\mathbf{a}}\left[\left(i-1\right)×{\mathbf{pda}}+j-1\right]$.
On entry: the $m$ by $n$ matrix $A$.
7:    $\mathbf{pda}$IntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array a.
Constraints:
• if ${\mathbf{order}}=\mathrm{Nag_ColMajor}$, ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$;
• if ${\mathbf{order}}=\mathrm{Nag_RowMajor}$, ${\mathbf{pda}}\ge {\mathbf{n}}$.
8:    $\mathbf{x}\left[\mathit{dim}\right]$const doubleInput
Note: the dimension, dim, of the array x must be at least
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)\left|{\mathbf{incx}}\right|\right)$ when ${\mathbf{trans}}=\mathrm{Nag_NoTrans}$;
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{m}}-1\right)\left|{\mathbf{incx}}\right|\right)$ when ${\mathbf{trans}}=\mathrm{Nag_Trans}$ or $\mathrm{Nag_ConjTrans}$.
On entry: the vector $x$.
9:    $\mathbf{incx}$IntegerInput
On entry: the increment in the subscripts of x between successive elements of $x$.
Constraint: ${\mathbf{incx}}\ne 0$.
10:  $\mathbf{beta}$doubleInput
On entry: the scalar $\beta$.
11:  $\mathbf{y}\left[\mathit{dim}\right]$doubleInput/Output
Note: the dimension, dim, of the array y must be at least
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{m}}-1\right)\left|{\mathbf{incy}}\right|\right)$ when ${\mathbf{trans}}=\mathrm{Nag_NoTrans}$;
• $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,1+\left({\mathbf{n}}-1\right)\left|{\mathbf{incy}}\right|\right)$ when ${\mathbf{trans}}=\mathrm{Nag_Trans}$ or $\mathrm{Nag_ConjTrans}$.
On entry: the vector $y$.
If ${\mathbf{beta}}=0$, y need not be set.
On exit: the updated vector $y$.
12:  $\mathbf{incy}$IntegerInput
On entry: the increment in the subscripts of y between successive elements of $y$.
Constraint: ${\mathbf{incy}}\ne 0$.
13:  $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{incx}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{incx}}\ne 0$.
On entry, ${\mathbf{incy}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{incy}}\ne 0$.
On entry, ${\mathbf{m}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{m}}\ge 0$.
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
NE_INT_2
On entry, ${\mathbf{pda}}=〈\mathit{\text{value}}〉$, ${\mathbf{m}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{pda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$.
On entry, ${\mathbf{pda}}=〈\mathit{\text{value}}〉$ and ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{pda}}\ge {\mathbf{n}}$.
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.
See Section 3.6.6 in the Essential Introduction for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction 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)).

Not applicable.

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)