void	f16pmc (Nag_OrderType order, Nag_ConjType conj, Integer m, Integer n, double alpha, const double x[], Integer incx, const double y[], Integer incy, double beta, double a[], Integer pda, NagError *fail)

The function may be called by the names: f16pmc, nag_blast_dger or nag_dger.

3 Description

f16pmc performs the rank-1 update operation

A \leftarrow α x y^{T} + β A,

where

A

is an

m

n

real matrix,

x

is an

m

element real vector,

y

is an

n

-element real vector, and

α

and

β

are real scalars. If

m

n

is equal to zero or if

β

is equal to one and

α

is equal to zero, this function returns immediately.

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

Nag_ColMajor

2: $conj$ – Nag_ConjType Input

On entry: the argument conj is not referenced if

x

and

y

are real vectors. It is suggested that you set

conj = Nag_NoConj

where the elements

y_{i}

are not conjugated.

Constraint:

conj = Nag_NoConj

3: $m$ – Integer Input

On entry:

m

, the number of rows of the matrix

A

Constraint:

m \geq 0

4: $n$ – Integer Input

On entry:

n

, the number of columns of the matrix

A

Constraint:

n \geq 0

5: $alpha$ – double Input

On entry: the scalar

α

6: $x [\dim]$ – const double Input

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

\max (1, 1 + (n - 1) |incx|)

On entry: the

n

-element vector

x

incx > 0

x_{i}

must be stored in

x [(i - 1) \times incx]

, for

i = 1, 2, \dots, m

incx < 0

x_{i}

must be stored in

x [(m - i) \times |incx|]

, for

i = 1, 2, \dots, m

Intermediate elements of x are not referenced. If

m = 0

, x is not referenced and may be NULL.

7: $incx$ – Integer Input

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

x

Constraint:

incx \neq 0

8: $y [\dim]$ – const double Input

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

\max (1, 1 + (n - 1) |incy|)

On entry: the

n

-element vector

y

incy > 0

y_{i}

must be stored in

y [(i - 1) \times incy]

, for

i = 1, 2, \dots, n

incy < 0

y_{i}

must be stored in

y [(n - i) \times |incy|]

, for

i = 1, 2, \dots, n

Intermediate elements of y are not referenced. If

α = 0.0

n = 0

, y is not referenced and may be NULL.

9: $incy$ – Integer Input

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

y

Constraint:

incy \neq 0

10: $beta$ – double Input

On entry: the scalar

β

11: $a [\dim]$ – double Input/Output

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

On exit: the updated matrix

A

12: $pda$ – Integer Input

On entry: the stride separating row or column elements (depending on the value of order) in the array a.

Constraints:

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

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: $incx \neq 0$ .

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.
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

f16pmc is not threaded in any implementation.

9 Further Comments

The argument conj is not referenced in this case where

x

and

y

are real vectors.

10 Example

Perform rank-1 update of real matrix

A

using vectors

x

and

y

A \leftarrow A - x y^{T},

where

A

is the

3

2

matrix given by

A = (\begin{matrix} 3.0 & 2.0 \\ 3.0 & 4.0 \\ 5.0 & 9.0 \end{matrix}),

x = {(2.0, 3.0, 5.0)}^{T} and y = {(0.0, 1.0, 0.0)}^{T} .

f16pm: FL CL CPP AD

NAG CL Interfacef16pmc (dger)

▸▿ 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 CL Interface
f16pmc (dger)