void	f16zcc (Nag_OrderType order, Nag_SideType side, Nag_UploType uplo, Integer m, Integer n, Complex alpha, const Complex a[], Integer pda, const Complex b[], Integer pdb, Complex beta, Complex c[], Integer pdc, NagError *fail)

The function may be called by the names: f16zcc, nag_blast_zhemm or nag_zhemm.

3 Description

f16zcc performs one of the matrix-matrix operations

C \leftarrow α A B + β C or C \leftarrow α B A + β C,

where

A

is a complex Hermitian matrix,

B

and

C

are

m \times n

complex matrices, and

α

and

β

are complex scalars.

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: $side$ – Nag_SideType Input

On entry: specifies whether

B

is operated on from the left or the right.

$side = Nag_LeftSide$: $B$ is pre-multiplied from the left.
$side = Nag_RightSide$: $B$ is post-multiplied from the right.

Constraint:

side = Nag_LeftSide

Nag_RightSide

3: $uplo$ – Nag_UploType Input

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

A

is stored.

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

Constraint:

uplo = Nag_Upper

Nag_Lower

4: $m$ – Integer Input

On entry:

m

, the number of rows of the matrices

B

and

C

; the order of

A

side = Nag_LeftSide

Constraint:

m \geq 0

5: $n$ – Integer Input

On entry:

n

, the number of columns of the matrices

B

and

C

; the order of

A

side = Nag_RightSide

Constraint:

n \geq 0

6: $alpha$ – Complex Input

On entry: the scalar

α

7: $a [\dim]$ – const Complex Input

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

$\max (1, pda \times m)$ when $side = Nag_LeftSide$ ;
$\max (1, pda \times n)$ when $side = Nag_RightSide$ .

On entry: the Hermitian matrix

A

;

A

m \times m

side = Nag_LeftSide

, or

n \times n

side = Nag_RightSide

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]

uplo = Nag_Upper

, the upper triangular part of

A

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

uplo = Nag_Lower

, the lower triangular part of

A

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

8: $pda$ – Integer Input

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

A

in the array a.

Constraints:

if $side = Nag_LeftSide$ , $pda \geq \max (1, m)$ ;
if $side = Nag_RightSide$ , $pda \geq \max (1, n)$ .

9: $b [\dim]$ – const Complex Input

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

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

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

m \times n

matrix

B

10: $pdb$ – Integer Input

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

Constraints:

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

11: $beta$ – Complex Input

On entry: the scalar

β

12: $c [\dim]$ – Complex Input/Output

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

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

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]

On entry: the

m \times n

matrix

C

beta = 0

, c need not be set.

On exit: the updated matrix

C

13: $pdc$ – Integer Input

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

Constraints:

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

14: $fail$ – 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_ENUM_INT_2: On entry, $side = ⟨ value ⟩$ , $m = ⟨ value ⟩$ , $pda = ⟨ value ⟩$ .
Constraint: if $side = Nag_LeftSide$ , $pda \geq \max (1, m)$ .

On entry, $side = ⟨ value ⟩$ , $n = ⟨ value ⟩$ , $pda = ⟨ value ⟩$ .
Constraint: if $side = Nag_RightSide$ , $pda \geq \max (1, n)$ .
NE_INT: On entry, $m = ⟨ value ⟩$ .
Constraint: $m \geq 0$ .

On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .
NE_INT_2: On entry, $pdb = ⟨ value ⟩$ , $m = ⟨ value ⟩$ .
Constraint: $pdb \geq \max (1, m)$ .

On entry, $pdb = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $pdb \geq \max (1, n)$ .

On entry, $pdc = ⟨ value ⟩$ , $m = ⟨ value ⟩$ .
Constraint: $pdc \geq \max (1, m)$ .

On entry, $pdc = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
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.
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

Background information to multithreading can be found in the Multithreading documentation.

f16zcc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

None.

10 Example

This example computes the matrix-matrix product

C = α A B + β C

where

A = (\begin{array}{r} 1.0 + 0.0 i & 1.0 + 2.0 i & - 2.0 + 3.0 i \\ 1.0 - 2.0 i & 2.0 + 0.0 i & 1.0 + 2.0 i \\ - 2.0 - 3.0 i & 1.0 - 2.0 i & 3.0 + 0.0 i \end{array}),

B = (\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 + 1.0 i \end{array}),

C = (\begin{array}{r} - 3.5 - 0.5 i & 1.5 + 2.0 i \\ - 4.5 + 1.5 i & - 2.0 + 3.5 i \\ - 5.5 + 3.5 i & 3.0 - 1.5 i \end{array}),

α = 1.0 + 0.0 i and β = 2.0 + 0.0 i .

f16zc: FL CL CPP AD PY MB

NAG CL Interfacef16zcc (zhemm)

▸▿ 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
f16zcc (zhemm)