Integer, Intent (In)	::	n, k1, k2, lda
Real (Kind=nag_wp), Intent (In)	::	c(*)
Complex (Kind=nag_wp), Intent (In)	::	s(*)
Complex (Kind=nag_wp), Intent (Inout)	::	a(lda,*)
Character (1), Intent (In)	::	uplo, pivot, direct

C Header Interface

#include <nag.h>

void	f06tmf_ (const char uplo, const char pivot, const char direct, const Integer n, const Integer k1, const Integer k2, const double c[], const Complex s[], Complex a[], const Integer *lda, const Charlen length_uplo, const Charlen length_pivot, const Charlen length_direct)

The routine may be called by the names f06tmf or nagf_blas_zhesrc.

3 Description

f06tmf performs the transformation

A \leftarrow P A P^{H}

where

A

is an

n \times n

complex Hermitian matrix, and

P

is a complex unitary matrix defined as a sequence of plane rotations,

P_{k}

, applied in planes

k_{1}

k_{2}

The

2 \times 2

plane rotation part of

P_{k}

is assumed to have the form

(\begin{array}{r} c_{k} & {\bar{s}}_{k} \\ - s_{k} & c_{k} \end{array})

with

c_{k}

real.

4 References

None.

5 Arguments

1: $uplo$ – Character(1) Input

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

A

is stored.

$uplo ='U'$: The upper triangular part of $A$ is stored.
$uplo ='L'$: The lower triangular part of $A$ is stored.

Constraint:

uplo ='U'

'L'

2: $pivot$ – Character(1) Input

On entry: specifies the plane rotated by

P_{k}

$pivot ='V'$ (variable pivot): $P_{k}$ rotates the $(k, k + 1)$ plane.
$pivot ='T'$ (top pivot): $P_{k}$ rotates the $(k_{1}, k + 1)$ plane.
$pivot ='B'$ (bottom pivot): $P_{k}$ rotates the $(k, k_{2})$ plane.

Constraint:

pivot ='V'

'T'

'B'

3: $direct$ – Character(1) Input

On entry: specifies the sequence direction.

$direct ='F'$ (forward sequence): $P = P_{k_{2} - 1} \dots P_{k_{1} + 1} P_{k_{1}}$ .
$direct ='B'$ (backward sequence): $P = P_{k_{1}} P_{k_{1} + 1} \dots P_{k_{2} - 1}$ .

Constraint:

direct ='F'

'B'

4: $n$ – Integer Input

On entry:

n

, the order of the matrix

A

Constraint:

n \geq 0

5: $k1$ – Integer Input

6: $k2$ – Integer Input

On entry: the values

k_{1}

and

k_{2}

k1 < 1

k2 \leq k1

k2 > n

, an immediate return is effected.

7: $c (*)$ – Real (Kind=nag_wp) array Input

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

k2 - 1

On entry:

c (k)

must hold

c_{k}

, the cosine of the rotation

P_{k}

, for

k = k_{1}, \dots, k_{2} - 1

8: $s (*)$ – Complex (Kind=nag_wp) array Input

Note: the dimension of the array s must be at least

k2 - 1

On entry:

s (k)

must hold

s_{k}

, the sine of the rotation

P_{k}

, for

k = k_{1}, \dots, k_{2} - 1

9: $a (lda, *)$ – Complex (Kind=nag_wp) array Input/Output

Note: the second dimension of the array a must be at least

\max (1, n)

On entry: the

n \times n

Hermitian matrix

A

If $uplo ='U'$ , the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
If $uplo ='L'$ , the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.

On exit: the transformed matrix

A

. The imaginary parts of the diagonal elements are set to zero.

10: $lda$ – Integer Input

On entry: the first dimension of the array a as declared in the (sub)program from which f06tmf is called.

Constraint:

lda \geq \max (1, n)

6 Error Indicators and Warnings

None.

7 Accuracy

Not applicable.

8 Parallelism and Performance

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

f06tmf is not threaded in any implementation.

9 Further Comments

None.

10 Example

None.

NAG Library Manual, Mark 30.3

Interfaces: FL CL CPP AD PY MB

NAG FL Interface Introduction

F06 (Blas) Chapter Contents

F06 (Blas) Chapter Introduction

f06tm: FL CL CPP AD PY MB

NAG FL Interfacef06tmf (zhesrc)

▸▿ 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

NAG FL Interface
f06tmf (zhesrc)