NAME

cher2k - perform one of the Hermitian rank 2k operations   C := alpha∗A∗conjg( B’ ) + conjg( alpha )∗B∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗B + conjg( alpha )∗conjg( B’ )∗A + beta∗C

SYNOPSIS

SUBROUTINE CHER2K(
UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC )

CHARACTER∗1 UPLO, TRANS

INTEGER N, K, LDA, LDB, LDC

REAL BETA

COMPLEX ALPHA

COMPLEX A( LDA, ∗ ), B( LDB, ∗ ), C( LDC, ∗ )

PURPOSE

CHER2K  performs one of the Hermitian rank 2k operations C := alpha∗A∗conjg( B’ ) + conjg( alpha )∗B∗conjg( A’ ) + beta∗C or C := alpha∗conjg( A’ )∗B + conjg( alpha )∗conjg( B’ )∗A + beta∗C where  alpha and beta  are scalars with  beta  real,  C is an  n by n Hermitian 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   - 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  - CHARACTER∗1. 
On entry,  TRANS  specifies the operation to be performed as follows:
 
TRANS = ’N’ or ’n’    C := alpha∗A∗conjg( B’ )          + conjg( alpha )∗B∗conjg( A’ ) + beta∗C.
 
TRANS = ’C’ or ’c’    C := alpha∗conjg( A’ )∗B          + conjg( alpha )∗conjg( B’ )∗A + beta∗C.
 
Unchanged on exit.

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

K      - 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 = ’C’ or ’c’,  K  specifies  the number of rows of the matrices  A and B.  K must be at least zero. Unchanged on exit.

ALPHA  - COMPLEX         . 
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

A      - COMPLEX          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    - 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.

B      - COMPLEX          array of 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. Unchanged on exit.

LDB    - 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 ). Unchanged on exit.

BETA   - REAL            . 
On entry, BETA specifies the scalar beta. Unchanged on exit.

C      - COMPLEX          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  Hermitian 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  Hermitian 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.
 
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.

LDC    - 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 ). Unchanged on exit.

SunSoft, Inc.  —  Last change: 27 Jun 1995