NAG FL Interface
f06tdf (zspr)

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FL Name Style:

FL Specification Language:

1 Purpose

f06tdf performs the symmetric rank-1 update operation
AαxxT + A ,  
where A is an n×n complex symmetric matrix, stored in packed form, x is an n-element complex vector, and α is a complex scalar.

2 Specification

Fortran Interface
Subroutine f06tdf ( uplo, n, alpha, x, incx, ap)
Integer, Intent (In) :: n, incx
Complex (Kind=nag_wp), Intent (In) :: alpha, x(*)
Complex (Kind=nag_wp), Intent (Inout) :: ap(*)
Character (1), Intent (In) :: uplo
C Header Interface
#include <nag.h>
void  f06tdf_ (const char *uplo, const Integer *n, const Complex *alpha, const Complex x[], const Integer *incx, Complex ap[], const Charlen length_uplo)
The routine may be called by the names f06tdf or nagf_blas_zspr.

3 Description


4 References


5 Arguments

1: uplo Character(1) Input
On entry: specifies whether the upper or lower triangular part of A is stored.
The upper triangular part of A is stored.
The lower triangular part of A is stored.
Constraint: uplo='U' or 'L'.
2: n Integer Input
On entry: n, the order of the matrix A.
Constraint: n0.
3: alpha Complex (Kind=nag_wp) Input
On entry: the scalar α.
4: x(*) Complex (Kind=nag_wp) array Input
Note: the dimension of the array x must be at least max(1, 1+(n-1) ×|incx| ) .
On entry: the n-element vector x.
If incx>0, xi must be stored in x(1+(i-1)×incx), for i=1,2,,n.
If incx<0, xi must be stored in x(1-(n-i)×incx), for i=1,2,,n.
Intermediate elements of x are not referenced.
5: incx Integer Input
On entry: the increment in the subscripts of x between successive elements of x.
Constraint: incx0.
6: ap(*) Complex (Kind=nag_wp) array Input/Output
Note: the dimension of the array ap must be at least n× (n+1)/2 .
On entry: the n×n symmetric matrix A, packed by columns.
More precisely,
  • if uplo='U', the upper triangle of A must be stored with element Aij in ap(i+j(j-1)/2) for ij;
  • if uplo='L', the lower triangle of A must be stored with element Aij in ap(i+(2n-j)(j-1)/2) for ij.
On exit: the updated matrix A.

6 Error Indicators and Warnings


7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
f06tdf is not threaded in any implementation.

9 Further Comments


10 Example