# dsyrk.f - Man Page

BLAS/SRC/dsyrk.f

## Synopsis

### Functions/Subroutines

subroutine dsyrk (uplo, trans, n, k, alpha, a, lda, beta, c, ldc)
DSYRK

## Function/Subroutine Documentation

### subroutine dsyrk (character uplo, character trans, integer n, integer k, double precision alpha, double precision, dimension(lda,*) a, integer lda, double precision beta, double precision, dimension(ldc,*) c, integer ldc)

DSYRK

Purpose:

``` DSYRK  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.

TRANS = 'C' or 'c'   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' or 'C' or 'c',  K  specifies  the  number
of rows of the matrix  A.  K must be at least zero.```

ALPHA

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

A

```          A is DOUBLE PRECISION array, 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 DOUBLE PRECISION.
On entry, BETA specifies the scalar beta.```

C

```          C is DOUBLE PRECISION array, 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.

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 dsyrk.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dsyrk(3) is an alias of dsyrk.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK