# csyr2k.f - Man Page

BLAS/SRC/csyr2k.f

## Synopsis

### Functions/Subroutines

subroutine csyr2k (uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CSYR2K

## Function/Subroutine Documentation

### subroutine csyr2k (character uplo, character trans, integer n, integer k, complex alpha, complex, dimension(lda,*) a, integer lda, complex, dimension(ldb,*) b, integer ldb, complex beta, complex, dimension(ldc,*) c, integer ldc)

CSYR2K

Purpose:

``` CSYR2K  performs one of the symmetric rank 2k operations

C := alpha*A*B**T + alpha*B*A**T + beta*C,

or

C := alpha*A**T*B + alpha*B**T*A + beta*C,

where  alpha and beta  are scalars,  C is an  n by n symmetric matrix
and  A and B  are  n by k  matrices  in the  first  case  and  k by n
matrices 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*B**T + alpha*B*A**T +
beta*C.

TRANS = 'T' or 't'    C := alpha*A**T*B + alpha*B**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  matrices  A and B,  and on  entry  with
TRANS = 'T' or 't',  K  specifies  the number of rows of the
matrices  A and B.  K must be at least zero.```

ALPHA

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

A

```          A is COMPLEX 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 ).```

B

```          B is COMPLEX array, dimension ( LDB, kb ), where kb 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  B  must contain the matrix  B,  otherwise
the leading  k by n  part of the array  B  must contain  the
matrix B.```

LDB

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

BETA

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

C

```          C is COMPLEX 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

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 187 of file csyr2k.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page csyr2k(3) is an alias of csyr2k.f(3).

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