NAG FL Interface
f06qmf (dsysrc)

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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 <nag.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)
The routine may be called by the names f06qmf or nagf_blas_dsysrc.

3 Description

f06qmf performs the transformation
APAPT  
where A is an n×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 2×2 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 Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
5: k1 Integer Input
6: k2 Integer Input
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) array Input
Note: the dimension of the array c must be at least k2-1.
On entry: c(k) must hold ck, the cosine of the rotation Pk, for k=k1,,k2-1.
8: s(*) Real (Kind=nag_wp) array Input
Note: the dimension of the array s must be at least k2-1.
On entry: s(k) must hold sk, the sine of the rotation Pk, for k=k1,,k2-1.
9: a(lda,*) Real (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×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 Integer Input
On entry: the first dimension of the array a as declared in the (sub)program from which f06qmf is called.
Constraint: lda max(1,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.