# zsyrk.f man page

zsyrk.f —

## Synopsis

### Functions/Subroutines

subroutinezsyrk(UPLO, TRANS, N, K, ALPHA, A, LDA, BETA, C, LDC)ZSYRK

## Function/Subroutine Documentation

### subroutine zsyrk (characterUPLO, characterTRANS, integerN, integerK, complex*16ALPHA, complex*16, dimension(lda,*)A, integerLDA, complex*16BETA, complex*16, dimension(ldc,*)C, integerLDC)

**ZSYRK Purpose:**

```
ZSYRK performs one of the symmetric rank k operations
C := alpha*A*A**T + beta*C,
or
C := alpha*A**T*A + beta*C,
where alpha and beta are scalars, C is an n by n symmetric matrix
and A is an n by k matrix in the first case and a k by n matrix
in the second case.
```

**Parameters:**

*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.
```

*TRANS*

```
TRANS is CHARACTER*1
On entry, TRANS specifies the operation to be performed as
follows:
TRANS = 'N' or 'n' C := alpha*A*A**T + beta*C.
TRANS = 'T' or 't' C := alpha*A**T*A + beta*C.
```

*N*

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

*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 = 'T' or 't', K specifies the number of rows of the
matrix A. K must be at least zero.
```

*ALPHA*

```
ALPHA is COMPLEX*16
On entry, ALPHA specifies the scalar alpha.
```

*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.
```

*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 ).
```

*BETA*

```
BETA is COMPLEX*16
On entry, BETA specifies the scalar beta.
```

*C*

```
C is COMPLEX*16 array of DIMENSION ( LDC, n ).
Before entry with UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array C must contain the upper
triangular part of the symmetric matrix and the strictly
lower triangular part of C is not referenced. On exit, the
upper triangular part of the array C is overwritten by the
upper triangular part of the updated matrix.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array C must contain the lower
triangular part of the symmetric matrix and the strictly
upper triangular part of C is not referenced. On exit, the
lower triangular part of the array C is overwritten by the
lower triangular part of the updated matrix.
```

*LDC*

```
LDC is INTEGER
On entry, LDC specifies the first dimension of C as declared
in the calling (sub) program. LDC must be at least
max( 1, n ).
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

**Further Details:**

```
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
```

Definition at line 168 of file zsyrk.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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