F06ZPF (ZHERK) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

NAG Library Routine Document

F06ZPF (ZHERK)

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy
    9  Example

1  Purpose

F06ZPF (ZHERK) performs one of the Hermitian rank-k update operations
CαAAH+βC  or  CαAHA+βC
where A is a complex matrix, C is an n by n complex Hermitian matrix, and α and β are real scalars.

2  Specification

SUBROUTINE F06ZPF ( UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)
INTEGER  N, K, LDA, LDC
REAL (KIND=nag_wp)  ALPHA, BETA
COMPLEX (KIND=nag_wp)  A(LDA,*), C(LDC,*)
CHARACTER(1)  UPLO, TRANS
The routine may be called by its BLAS name zherk.

3  Description

None.

4  References

None.

5  Parameters

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'
CαAAH+βC.
TRANS='C'
CαAHA+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='T' or '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='T' or 'C'.
Constraint: K0.
5:     ALPHA – REAL (KIND=nag_wp)Input
On entry: the scalar α.
6:     A(LDA,*) – 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='T' or 'C'.
On entry: the matrix A; A is n by k if TRANS='N', or k by n if TRANS='T' or 'C'.
7:     LDA – INTEGERInput
On entry: the first dimension of the array A as declared in the (sub)program from which F06ZPF (ZHERK) is called.
Constraints:
  • if TRANS='N', LDA max1,N ;
  • if TRANS='T' or 'C', LDA max1,K .
8:     BETA – REAL (KIND=nag_wp)Input
On entry: the scalar β.
9:     C(LDC,*) – 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.
10:   LDC – INTEGERInput
On entry: the first dimension of the array C as declared in the (sub)program from which F06ZPF (ZHERK) is called.
Constraint: LDCmax1,N .

6  Error Indicators and Warnings

None.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

None.

F06ZPF (ZHERK) (PDF version)
F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012