nag_dsyr2k (f16yrc) : NAG Library, Mark 24

2 Specification

#include <nag.h>

#include <nagf16.h>

void	nag_dsyr2k (Nag_OrderType order, Nag_UploType uplo, Nag_TransType trans, Integer n, Integer k, double alpha, const double a[], Integer pda, const double b[], Integer pdb, double beta, double c[], Integer pdc, NagError *fail)

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: uplo – Nag_UploTypeInput

On entry: specifies whether the upper or lower triangular part of

C

is stored.

$uplo = Nag_Upper$: The upper triangular part of $C$ is stored.
$uplo = Nag_Lower$: The lower triangular part of $C$ is stored.

Constraint:

uplo = Nag_Upper

Nag_Lower

3: trans – Nag_TransTypeInput

On entry: specifies the operation to be performed.

$trans = Nag_NoTrans$: $C \leftarrow α A B^{T} + α B A^{T} + β C$ .
$trans = Nag_Trans$ or $Nag_ConjTrans$: $C \leftarrow α A^{T} B + α B^{T} A + β C$ .

Constraint:

trans = Nag_NoTrans

Nag_Trans

Nag_ConjTrans

4: n – IntegerInput

On entry:

n

, the order of the matrix

C

; the number of rows of

A

and

B

trans = Nag_NoTrans

, or the number of columns of

A

and

B

otherwise.

Constraint:

n \geq 0

5: k – IntegerInput

On entry:

k

, the number of columns of

A

and

B

trans = Nag_NoTrans

, or the number of rows of

A

and

B

otherwise.

Constraint:

k \geq 0

6: alpha – doubleInput

On entry: the scalar

α

7: a[

\dim

] – const doubleInput

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

$\max (1, pda \times k)$ when $trans = Nag_NoTrans$ and $order = Nag_ColMajor$ ;
$\max (1, n \times pda)$ when $trans = Nag_NoTrans$ and $order = Nag_RowMajor$ ;
$\max (1, pda \times n)$ when $trans = Nag_Trans$ or $Nag_ConjTrans$ and $order = Nag_ColMajor$ ;
$\max (1, k \times pda)$ when $trans = Nag_Trans$ or $Nag_ConjTrans$ and $order = Nag_RowMajor$ .

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 matrix

A

;

A

n

k

trans = Nag_NoTrans

, or

k

n

otherwise.

8: 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,
- if $trans = Nag_NoTrans$ , $pda \geq \max (1, n)$ ;
- if $trans = Nag_Trans$ or $Nag_ConjTrans$ , $pda \geq \max (1, k)$ ;
if order=Nag_RowMajor,
- if $trans = Nag_NoTrans$ , $pda \geq \max (1, k)$ ;
- if $trans = Nag_Trans$ or $Nag_ConjTrans$ , $pda \geq \max (1, n)$ .

9: b[

\dim

] – const doubleInput

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

$\max (1, pdb \times k)$ when $trans = Nag_NoTrans$ and $order = Nag_ColMajor$ ;
$\max (1, n \times pdb)$ when $trans = Nag_NoTrans$ and $order = Nag_RowMajor$ ;
$\max (1, pdb \times n)$ when $trans = Nag_Trans$ or $Nag_ConjTrans$ and $order = Nag_ColMajor$ ;
$\max (1, k \times pdb)$ when $trans = Nag_Trans$ or $Nag_ConjTrans$ and $order = Nag_RowMajor$ .

order = Nag_ColMajor

B_{i j}

is stored in

b [(j - 1) \times pdb + i - 1]

order = Nag_RowMajor

B_{i j}

is stored in

b [(i - 1) \times pdb + j - 1]

On entry: the matrix

B

;

B

n

k

trans = Nag_NoTrans

, or

k

n

otherwise.

10: pdb – IntegerInput

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

Constraints:

if order=Nag_ColMajor,
- if $trans = Nag_NoTrans$ , $pdb \geq \max (1, n)$ ;
- if $trans = Nag_Trans$ or $Nag_ConjTrans$ , $pdb \geq \max (1, k)$ ;
if order=Nag_RowMajor,
- if $trans = Nag_NoTrans$ , $pdb \geq \max (1, k)$ ;
- if $trans = Nag_Trans$ or $Nag_ConjTrans$ , $pdb \geq \max (1, n)$ .

11: beta – doubleInput

On entry: the scalar

β

12: c[

\dim

] – doubleInput/Output

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

\max (1, pdc \times n)

On entry: the

n

n

symmetric matrix

C

order = Nag_ColMajor

C_{i j}

is stored in

c [(j - 1) \times pdc + i - 1]

order = Nag_RowMajor

C_{i j}

is stored in

c [(i - 1) \times pdc + j - 1]

uplo = Nag_Upper

, the upper triangular part of

C

must be stored and the elements of the array below the diagonal are not referenced.

uplo = Nag_Lower

, the lower triangular part of

C

must be stored and the elements of the array above the diagonal are not referenced.

On exit: the updated matrix

C

13: pdc – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) of the matrix

C

in the array c.

Constraint:

pdc \geq \max (1, n)

14: 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_ENUM_INT_2

On entry,

trans = ⟨value⟩

k = ⟨value⟩

pda = ⟨value⟩

.
Constraint: if

trans = Nag_NoTrans

pda \geq \max (1, k)

On entry,

trans = ⟨value⟩

k = ⟨value⟩

pda = ⟨value⟩

.
Constraint: if

trans = Nag_Trans

Nag_ConjTrans

pda \geq \max (1, k)

On entry,

trans = ⟨value⟩

k = ⟨value⟩

pdb = ⟨value⟩

.
Constraint: if

trans = Nag_NoTrans

pdb \geq \max (1, k)

On entry,

trans = ⟨value⟩

k = ⟨value⟩

pdb = ⟨value⟩

.
Constraint: if

trans = Nag_Trans

Nag_ConjTrans

pdb \geq \max (1, k)

On entry,

trans = ⟨value⟩

n = ⟨value⟩

pda = ⟨value⟩

.
Constraint: if

trans = Nag_NoTrans

pda \geq \max (1, n)

On entry,

trans = ⟨value⟩

n = ⟨value⟩

pda = ⟨value⟩

.
Constraint: if

trans = Nag_Trans

Nag_ConjTrans

pda \geq \max (1, n)

On entry,

trans = ⟨value⟩

n = ⟨value⟩

pdb = ⟨value⟩

.
Constraint: if

trans = Nag_NoTrans

pdb \geq \max (1, n)

On entry,

trans = ⟨value⟩

n = ⟨value⟩

pdb = ⟨value⟩

.
Constraint: if

trans = Nag_Trans

Nag_ConjTrans

pdb \geq \max (1, n)

NE_INT

On entry,

k = ⟨value⟩

.
Constraint:

k \geq 0

On entry,

n = ⟨value⟩

.
Constraint:

n \geq 0

NE_INT_2

On entry,

pdc = ⟨value⟩

n = ⟨value⟩

.
Constraint:

pdc \geq \max (1, 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.

10 Example

Perform rank-

2 k

update of real symmetric

4

4

matrix

C

using

4

2

matrices

A

and

B

C = C - A B^{T} - B A^{T}

, where

C = (\begin{matrix} 4.30 & - 3.96 & 0.40 & - 0.27 \\ - 3.96 & - 4.87 & 0.31 & 0.07 \\ 0.40 & 0.31 & - 8.02 & - 5.95 \\ - 0.27 & 0.07 & - 5.95 & 0.12 \end{matrix}),

A = (\begin{matrix} - 3.0 & - 5.0 \\ - 1.0 & 1.0 \\ 2.0 & - 1.0 \\ 1.0 & 1.0 \end{matrix})

and

B = (\begin{matrix} 3.0 & - 2.0 \\ - 1.0 & 1.0 \\ 2.0 & - 1.0 \\ 1.0 & 0.0 \end{matrix}) .

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG Library Function Document

nag_dsyr2k (f16yrc)

+− 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 Documentnag_dsyr2k (f16yrc)

+− 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_dsyr2k (f16yrc)