NAG Library Routine Document

f06qmf (dsysrc)

1
Purpose

f06qmf performs an orthogonal similarity transformation (as a sequence of plane rotations) of a real symmetric matrix.

2
Specification

Fortran Interface
Subroutine f06qmf ( uplo, pivot, direct, n, k1, k2, c, s, a, lda)
Integer, Intent (In):: n, k1, k2, lda
Real (Kind=nag_wp), Intent (In):: c(*), s(*)
Real (Kind=nag_wp), Intent (Inout):: a(lda,*)
Character (1), Intent (In):: uplo, pivot, direct
C Header Interface
#include <nagmk26.h>
void  f06qmf_ (const char *uplo, const char *pivot, const char *direct, const Integer *n, const Integer *k1, const Integer *k2, const double c[], const double s[], double a[], const Integer *lda, const Charlen length_uplo, const Charlen length_pivot, const Charlen length_direct)

3
Description

f06qmf performs the transformation
APAPT  
where A is an n by n real symmetric matrix, and P is a real orthogonal matrix defined as a sequence of 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 .  

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' or 'L'.
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:     n – IntegerInput
On entry: n, the order of the matrix A.
Constraint: n0.
5:     k1 – IntegerInput
6:     k2 – IntegerInput
On entry: the values k1 and k2.
If k1<1 or k2k1 or k2>n, an immediate return is effected.
7:     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.
8:     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.
9:     alda* – Real (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array a must be at least max1,n.
On entry: the n by n symmetric 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.
10:   lda – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06qmf is called.
Constraint: lda max1,n .

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06qmf is not threaded in any implementation.

9
Further Comments

None.

10
Example

None.