NAG Library Function Document

nag_zgemv (f16sac)

void	nag_zgemv (Nag_OrderType order, Nag_TransType trans, Integer m, Integer n, Complex alpha, const Complex a[], Integer pda, const Complex x[], Integer incx, Complex beta, Complex y[], Integer incy, NagError *fail)

3 Description

nag_zgemv (f16sac) performs one of the matrix-vector operations

y \leftarrow α A x + β y, y \leftarrow α A^{T} x + β y or y \leftarrow α A^{H} x + β y

where

A

is an

m

n

complex matrix,

x

and

y

are complex vectors, and

α

and

β

are complex scalars.

m = 0

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 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

Constraint:

order = Nag_RowMajor

Nag_ColMajor

2: $trans$ – Nag_TransTypeInput

On entry: specifies the operation to be performed.

$trans = Nag_NoTrans$: $y \leftarrow α A x + β y$ .
$trans = Nag_Trans$: $y \leftarrow α A^{T} x + β y$ .
$trans = Nag_ConjTrans$: $y \leftarrow α A^{H} x + β y$ .

Constraint:

trans = Nag_NoTrans

Nag_Trans

Nag_ConjTrans

3: $m$ – IntegerInput

On entry:

m

, the number of rows of the matrix

A

Constraint:

m \geq 0

4: $n$ – IntegerInput

On entry:

n

, the number of columns of the matrix

A

Constraint:

n \geq 0

5: $alpha$ – ComplexInput

On entry: the scalar

α

6: $a [\dim]$ – const ComplexInput

Note: the dimension, dim, of the array a must be at least

$\max (1, pda \times n)$ when $order = Nag_ColMajor$ ;
$\max (1, m \times pda)$ when $order = Nag_RowMajor$ .

order = Nag_ColMajor

A_{i j}

is stored in

a [(j - 1) \times pda + i - 1]

order = Nag_RowMajor

A_{i j}

is stored in

a [(i - 1) \times pda + j - 1]

On entry: the

m

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 $order = Nag_ColMajor$ , $pda \geq \max (1, m)$ ;
if $order = Nag_RowMajor$ , $pda \geq n$ .

8: $x [\dim]$ – const ComplexInput

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

9: $incx$ – IntegerInput

On entry: the increment in the subscripts of x between successive elements of

x

Constraint:

incx \neq 0

10: $beta$ – ComplexInput

On entry: the scalar

β

11: $y [\dim]$ – ComplexInput/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

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:

incy \neq 0

13: $fail$ – 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.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT: On entry, $incx = 〈value〉$ .
Constraint: $incx \neq 0$ .

On entry, $incy = 〈value〉$ .
Constraint: $incy \neq 0$ .

On entry, $m = 〈value〉$ .
Constraint: $m \geq 0$ .

On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .
NE_INT_2: On entry, $pda = 〈value〉$ , $m = 〈value〉$ .
Constraint: $pda \geq \max (1, m)$ .

On entry, $pda = 〈value〉$ and $n = 〈value〉$ .
Constraint: $pda \geq n$ .
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.

An unexpected error has been triggered by this function. Please contact NAG.
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)).

8 Parallelism and Performance

Not applicable.

9 Further Comments

None.

10 Example

This example computes the matrix-vector product

y = α A x + β y

where

A = (\begin{array}{r} 1.0 + 1.0 i & 1.0 + 2.0 i \\ 2.0 + 1.0 i & 2.0 + 2.0 i \\ 3.0 + 1.0 i & 3.0 + 2.0 i \end{array}),

x = (\begin{array}{r} 1.0 - 1.0 i \\ 2.0 - 2.0 i \end{array}),

y = (\begin{array}{r} - 3.5 - 0.5 i \\ - 4.5 + 1.5 i \\ - 5.5 + 3.5 i \end{array}),

α = 1.0 + 0.0 i and β = 2.0 + 0.0 i .

NAG Library Function Documentnag_zgemv (f16sac)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG Library Function Document

nag_zgemv (f16sac)