F06CHF : NAG Library, Mark 24

NAG Library Routine Document

F06CHF

Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

1 Purpose

F06CHF applies a complex similarity rotation having real cosine and complex sine to a

2

2

complex Hermitian matrix.

2 Specification

3 Description

F06CHF applies a complex similarity rotation, with parameters

c

(real) and

s

(complex), to a given

2

2

complex Hermitian matrix; that is, it performs the operation:

(\begin{matrix} x & y \\ \bar{y} & z \end{matrix}) \leftarrow (\begin{array}{rc} c & \bar{s} \\ - s & c \end{array}) (\begin{matrix} x & y \\ \bar{y} & z \end{matrix}) (\begin{array}{rc} c & - \bar{s} \\ s & c \end{array}),

where

x

and

z

are real.

The parameter X and Z which hold

x

and

z

are declared complex for convenience when using the routine to operate on submatrices of larger Hermitian matrices.

Note that:

(\begin{matrix} z & \bar{y} \\ y & x \end{matrix}) \leftarrow (\begin{array}{rc} c & \bar{w} \\ - w & c \end{array}) (\begin{matrix} z & \bar{y} \\ y & x \end{matrix}) (\begin{array}{rc} c & - \bar{w} \\ w & c \end{array}),

where

w = - \bar{s}

, so to use F06CHF when

y

is the

(2, 1)

element of the matrix, you can make the call

CALL F06CHF(Z, Y, X, C, -CONJG(S))

5 Parameters

1: X – COMPLEX (KIND=nag_wp)Input/Output

On entry: the value

x

, the

(1, 1)

element of the input matrix. The imaginary part of X need not be set; it is assumed to be zero.

On exit: the transformed value

x

. The imaginary part of X is set to zero.

2: Y – COMPLEX (KIND=nag_wp)Input/Output

On entry: the value

y

, the

(1, 2)

element of the input matrix.

On exit: the transformed value

y

3: Z – COMPLEX (KIND=nag_wp)Input/Output

On entry: the value

z

, the

(2, 2)

element of the input matrix. The imaginary part of Z need not be set; it is assumed to be zero.

On exit: the transformed value

z

. The imaginary part of Z is set to zero.

4: C – REAL (KIND=nag_wp)Input

On entry: the value

c

, the cosine of the rotation.

5: S – COMPLEX (KIND=nag_wp)Input

On entry: the value

s

, the sine of the rotation.

NAG Library Routine Document

F06CHF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

NAG Library Routine DocumentF06CHF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

NAG Library Routine Document

F06CHF