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.
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.

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)