NAG Library Routine Document

f06vxf (zsgesr)

1
Purpose

f06vxf applies to a complex rectangular matrix a sequence of plane rotations having real cosines and complex sines.

2
Specification

Fortran Interface
Subroutine f06vxf ( side, pivot, direct, m, n, k1, k2, c, s, a, lda)
Integer, Intent (In):: m, n, k1, k2, lda
Real (Kind=nag_wp), Intent (In):: c(*), s(*)
Complex (Kind=nag_wp), Intent (Inout):: a(lda,*)
Character (1), Intent (In):: side, pivot, direct
C Header Interface
#include <nagmk26.h>
void  f06vxf_ (const char *side, const char *pivot, const char *direct, const Integer *m, const Integer *n, const Integer *k1, const Integer *k2, const double c[], const double s[], Complex a[], const Integer *lda, const Charlen length_side, const Charlen length_pivot, const Charlen length_direct)

3
Description

f06vxf performs the transformation
APA   or   AAPH ,  
where A is an m by n complex matrix and P is a real orthogonal matrix, defined as a sequence of real plane rotations, Pk, applied in planes k1 to k2.
The 2 by 2 plane rotation part of Pk is assumed to have the form
ck sk -sk ck  
with ck and sk real.

4
References

None.

5
Arguments

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* – Real (Kind=nag_wp) arrayInput
Note: the dimension of the array c must be at least k2-1.
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 k2-1.
On entry: sk must hold sk, the sine of the rotation Pk, for k=k1,,k2-1.
10:   alda* – 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 f06vxf is called.
Constraint: lda max1,m .

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06vxf is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.