NAG Library Routine Document

f06zrf (zher2k)

1
Purpose

f06zrf (zher2k) performs one of the Hermitian rank-2k update operations
CαABH + α-BAH + βC   or   CαAHB + α-BHA+βC ,  
where A and B are complex matrices, C is an n by n complex Hermitian matrix, α is a complex scalar, and β is a real scalar.

2
Specification

Fortran Interface
Subroutine f06zrf ( uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
Integer, Intent (In):: n, k, lda, ldb, ldc
Real (Kind=nag_wp), Intent (In):: beta
Complex (Kind=nag_wp), Intent (In):: alpha, a(lda,*), b(ldb,*)
Complex (Kind=nag_wp), Intent (Inout):: c(ldc,*)
Character (1), Intent (In):: uplo, trans
C Header Interface
#include <nagmk26.h>
void  f06zrf_ (const char *uplo, const char *trans, const Integer *n, const Integer *k, const Complex *alpha, const Complex a[], const Integer *lda, const Complex b[], const Integer *ldb, const double *beta, Complex c[], const Integer *ldc, const Charlen length_uplo, const Charlen length_trans)
The routine may be called by its BLAS name zher2k.

3
Description

None.

4
References

None.

5
Arguments

1:     uplo – Character(1)Input
On entry: specifies whether the upper or lower triangular part of C is stored.
uplo='U'
The upper triangular part of C is stored.
uplo='L'
The lower triangular part of C is stored.
Constraint: uplo='U' or 'L'.
2:     trans – Character(1)Input
On entry: specifies the operation to be performed.
trans='N'
CαABH+α-BAH+βC.
trans='C'
CαAHB+α-BHA+βC.
Constraint: trans='N' or 'C'.
3:     n – IntegerInput
On entry: n, the order of the matrix C; the number of rows of A if trans='N', or the number of columns of A if trans='C'.
Constraint: n0.
4:     k – IntegerInput
On entry: k, the number of columns of A if trans='N', or the number of rows of A if trans='C'.
Constraint: k0.
5:     alpha – Complex (Kind=nag_wp)Input
On entry: the scalar α.
6:     alda* – Complex (Kind=nag_wp) arrayInput
Note: the second dimension of the array a must be at least max1,k if trans='N' and at least max1,n if trans='C'.
On entry: the matrix A; A is n by k if trans='N', or k by n if trans='C'.
7:     lda – IntegerInput
On entry: the first dimension of the array a as declared in the (sub)program from which f06zrf (zher2k) is called.
Constraints:
  • if trans='N', lda max1,n ;
  • if trans='C', lda max1,k .
8:     bldb* – Complex (Kind=nag_wp) arrayInput
Note: the second dimension of the array b must be at least max1,k if trans='N' and at least max1,n if trans='C'.
On entry: the matrix B; B is n by k if trans='N', or k by n if trans='C'.
9:     ldb – IntegerInput
On entry: the first dimension of the array b as declared in the (sub)program from which f06zrf (zher2k) is called.
Constraints:
  • if trans='N', ldb max1,n ;
  • if trans='C', ldb max1,k .
10:   beta – Real (Kind=nag_wp)Input
On entry: the scalar β.
11:   cldc* – Complex (Kind=nag_wp) arrayInput/Output
Note: the second dimension of the array c must be at least max1,n.
On entry: the n by n Hermitian matrix C.
  • If uplo='U', the upper triangular part of C must be stored and the elements of the array below the diagonal are not referenced.
  • If uplo='L', the lower triangular part of C must be stored and the elements of the array above the diagonal are not referenced.
On exit: the updated matrix C. The imaginary parts of the diagonal elements are set to zero.
12:   ldc – IntegerInput
On entry: the first dimension of the array c as declared in the (sub)program from which f06zrf (zher2k) is called.
Constraint: ldcmax1,n .

6
Error Indicators and Warnings

None.

7
Accuracy

Not applicable.

8
Parallelism and Performance

f06zrf (zher2k) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
f06zrf (zher2k) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9
Further Comments

None.

10
Example

None.