# NAG FL Interfacef06zcf (zhemm)

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## 1Purpose

f06zcf performs one of the matrix-matrix operations
 $C←αAB + βC or C←αBA + βC ,$
where $A$ is a complex Hermitian matrix, $B$ and $C$ are $m×n$ complex matrices, and $\alpha$ and $\beta$ are complex scalars.

## 2Specification

Fortran Interface
 Subroutine f06zcf ( side, uplo, m, n, a, lda, b, ldb, beta, c, ldc)
 Integer, Intent (In) :: m, n, lda, ldb, ldc Complex (Kind=nag_wp), Intent (In) :: alpha, a(lda,*), b(ldb,*), beta Complex (Kind=nag_wp), Intent (Inout) :: c(ldc,*) Character (1), Intent (In) :: side, uplo
#include <nag.h>
 void f06zcf_ (const char *side, const char *uplo, const Integer *m, const Integer *n, const Complex *alpha, const Complex a[], const Integer *lda, const Complex b[], const Integer *ldb, const Complex *beta, Complex c[], const Integer *ldc, const Charlen length_side, const Charlen length_uplo)
The routine may be called by the names f06zcf, nagf_blas_zhemm or its BLAS name zhemm.

None.

None.

## 5Arguments

1: $\mathbf{side}$Character(1) Input
On entry: specifies whether $B$ is operated on from the left or the right.
${\mathbf{side}}=\text{'L'}$
$B$ is pre-multiplied from the left.
${\mathbf{side}}=\text{'R'}$
$B$ is post-multiplied from the right.
Constraint: ${\mathbf{side}}=\text{'L'}$ or $\text{'R'}$.
2: $\mathbf{uplo}$Character(1) Input
On entry: specifies whether the upper or lower triangular part of $A$ is stored.
${\mathbf{uplo}}=\text{'U'}$
The upper triangular part of $A$ is stored.
${\mathbf{uplo}}=\text{'L'}$
The lower triangular part of $A$ is stored.
Constraint: ${\mathbf{uplo}}=\text{'U'}$ or $\text{'L'}$.
3: $\mathbf{m}$Integer Input
On entry: $m$, the number of rows of the matrices $B$ and $C$; the order of $A$ if ${\mathbf{side}}=\text{'L'}$.
Constraint: ${\mathbf{m}}\ge 0$.
4: $\mathbf{n}$Integer Input
On entry: $n$, the number of columns of the matrices $B$ and $C$; the order of $A$ if ${\mathbf{side}}=\text{'R'}$.
Constraint: ${\mathbf{n}}\ge 0$.
5: $\mathbf{alpha}$Complex (Kind=nag_wp) Input
On entry: the scalar $\alpha$.
6: $\mathbf{a}\left({\mathbf{lda}},*\right)$Complex (Kind=nag_wp) array Input
Note: the second dimension of the array a must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$ if ${\mathbf{side}}=\text{'L'}$ and at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$ if ${\mathbf{side}}=\text{'R'}$.
On entry: the Hermitian matrix $A$; $A$ is $m×m$ if ${\mathbf{side}}=\text{'L'}$, or $n×n$ if ${\mathbf{side}}=\text{'R'}$.
• If ${\mathbf{uplo}}=\text{'U'}$, the upper triangular part of $A$ must be stored and the elements of the array below the diagonal are not referenced.
• If ${\mathbf{uplo}}=\text{'L'}$, the lower triangular part of $A$ must be stored and the elements of the array above the diagonal are not referenced.
7: $\mathbf{lda}$Integer Input
On entry: the first dimension of the array a as declared in the (sub)program from which f06zcf is called.
Constraints:
• if ${\mathbf{side}}=\text{'L'}$, ${\mathbf{lda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$;
• if ${\mathbf{side}}=\text{'R'}$, ${\mathbf{lda}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
8: $\mathbf{b}\left({\mathbf{ldb}},*\right)$Complex (Kind=nag_wp) array Input
Note: the second dimension of the array b must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
On entry: the $m×n$ matrix $B$.
9: $\mathbf{ldb}$Integer Input
On entry: the first dimension of the array b as declared in the (sub)program from which f06zcf is called.
Constraint: ${\mathbf{ldb}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$.
10: $\mathbf{beta}$Complex (Kind=nag_wp) Input
On entry: the scalar $\beta$.
11: $\mathbf{c}\left({\mathbf{ldc}},*\right)$Complex (Kind=nag_wp) array Input/Output
Note: the second dimension of the array c must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{n}}\right)$.
On entry: the $m×n$ matrix $C$.
If ${\mathbf{beta}}=0.0$, c need not be set.
On exit: the updated matrix $C$.
12: $\mathbf{ldc}$Integer Input
On entry: the first dimension of the array c as declared in the (sub)program from which f06zcf is called.
Constraint: ${\mathbf{ldc}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{m}}\right)$.

None.

Not applicable.