F06TYF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06TYF

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.

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

F06TYF applies to a complex rectangular matrix a sequence of plane rotations having real sines and complex cosines.

2  Specification

SUBROUTINE F06TYF ( SIDE, PIVOT, DIRECT, M, N, K1, K2, C, S, A, LDA)
INTEGER  M, N, K1, K2, LDA
REAL (KIND=nag_wp)  S(*)
COMPLEX (KIND=nag_wp)  C(*), A(LDA,*)
CHARACTER(1)  SIDE, PIVOT, DIRECT

3  Description

F06TYF performs the transformation
APA   or   AAPH ,
where A is an m by n complex matrix and P is a complex unitary matrix, defined as a sequence of complex plane rotations, Pk, with real sines, applied in planes k1 to k2.
The 2 by 2 plane rotation part of Pk is assumed to have the form
c-k sk -sk ck
with sk real.

4  References

None.

5  Parameters

1:     SIDE – CHARACTER(1)Input
On entry: specifies whether A is operated on from the left or the right.
SIDE='L'
A is pre-multiplied from the left.
SIDE='R'
A is post-multiplied from the right.
Constraint: SIDE='L' or 'R'.
2:     PIVOT – CHARACTER(1)Input
On entry: specifies the plane rotated by Pk.
PIVOT='V' (variable pivot)
Pk rotates the k,k+1  plane.
PIVOT='T' (top pivot)
Pk rotates the k1,k+1  plane.
PIVOT='B' (bottom pivot)
Pk rotates the k,k2  plane.
Constraint: PIVOT='V', 'T' or 'B'.
3:     DIRECT – CHARACTER(1)Input
On entry: specifies the sequence direction.
DIRECT='F' (forward sequence)
P=Pk2-1Pk1+1Pk1.
DIRECT='B' (backward sequence)
P=Pk1Pk1+1Pk2-1.
Constraint: DIRECT='F' or 'B'.
4:     M – INTEGERInput
On entry: m, the number of rows of the matrix A.
Constraint: M0.
5:     N – INTEGERInput
On entry: n, the number of columns of the matrix A.
Constraint: N0.
6:     K1 – INTEGERInput
7:     K2 – INTEGERInput
On entry: the values k1 and k2.
If K1<1 or K2K1, or SIDE='L' and K2>M, or SIDE='R' and K2>N, an immediate return is effected.
8:     C(*) – COMPLEX (KIND=nag_wp) arrayInput
Note: the dimension of the array C must be at least K2-K1.
On entry: Ck must hold ck, the cosine of the rotation Pk, for k=k1,,k2-1.
9:     S(*) – REAL (KIND=nag_wp) arrayInput
Note: the dimension of the array S must be at least K2-K1.
On entry: Sk must hold sk, the sine of the rotation Pk, for k=k1,,k2-1.
10:   A(LDA,*) – COMPLEX (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array A must be at least N.
On entry: the m by n matrix A.
On exit: the transformed matrix A.
11:   LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F06TYF is called.
Constraint: LDA max1,M .

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

None.

F06TYF (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012