# zhfrk.f man page

zhfrk.f —

## Synopsis

### Functions/Subroutines

subroutinezhfrk(TRANSR, UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C)ZHFRKperforms a Hermitian rank-k operation for matrix in RFP format.

## Function/Subroutine Documentation

### subroutine zhfrk (characterTRANSR, characterUPLO, characterTRANS, integerN, integerK, double precisionALPHA, complex*16, dimension( lda, * )A, integerLDA, double precisionBETA, complex*16, dimension( * )C)

**ZHFRK** performs a Hermitian rank-k operation for matrix in RFP format.

**Purpose:**

```
Level 3 BLAS like routine for C in RFP Format.
ZHFRK performs one of the Hermitian rank--k operations
C := alpha*A*A**H + beta*C,
or
C := alpha*A**H*A + beta*C,
where alpha and beta are real scalars, C is an n--by--n Hermitian
matrix and A is an n--by--k matrix in the first case and a k--by--n
matrix in the second case.
```

**Parameters:**

*TRANSR*

```
TRANSR is CHARACTER*1
= 'N': The Normal Form of RFP A is stored;
= 'C': The Conjugate-transpose Form of RFP A is stored.
```

*UPLO*

```
UPLO is CHARACTER*1
On entry, UPLO specifies whether the upper or lower
triangular part of the array C is to be referenced as
follows:
UPLO = 'U' or 'u' Only the upper triangular part of C
is to be referenced.
UPLO = 'L' or 'l' Only the lower triangular part of C
is to be referenced.
Unchanged on exit.
```

*TRANS*

```
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*A**H + beta*C.
TRANS = 'C' or 'c' C := alpha*A**H*A + beta*C.
Unchanged on exit.
```

*N*

```
N is INTEGER
On entry, N specifies the order of the matrix C. N must be
at least zero.
Unchanged on exit.
```

*K*

```
K is INTEGER
On entry with TRANS = 'N' or 'n', K specifies the number
of columns of the matrix A, and on entry with
TRANS = 'C' or 'c', K specifies the number of rows of the
matrix A. K must be at least zero.
Unchanged on exit.
```

*ALPHA*

```
ALPHA is DOUBLE PRECISION
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
```

*A*

```
A is COMPLEX*16 array of DIMENSION (LDA,ka)
where KA
is K when TRANS = 'N' or 'n', and is N otherwise. Before
entry with TRANS = 'N' or 'n', the leading N--by--K part of
the array A must contain the matrix A, otherwise the leading
K--by--N part of the array A must contain the matrix A.
Unchanged on exit.
```

*LDA*

```
LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When TRANS = 'N' or 'n'
then LDA must be at least max( 1, n ), otherwise LDA must
be at least max( 1, k ).
Unchanged on exit.
```

*BETA*

```
BETA is DOUBLE PRECISION
On entry, BETA specifies the scalar beta.
Unchanged on exit.
```

*C*

```
C is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the matrix A in RFP Format. RFP Format is
described by TRANSR, UPLO and N. Note that the imaginary
parts of the diagonal elements need not be set, they are
assumed to be zero, and on exit they are set to zero.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 168 of file zhfrk.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zhfrk(3) is an alias of zhfrk.f(3).