zher2k.f man page

zher2k.f —

Synopsis

Functions/Subroutines

subroutine zher2k (UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHER2K

Function/Subroutine Documentation

subroutine zher2k (characterUPLO, characterTRANS, integerN, integerK, complex*16ALPHA, complex*16, dimension(lda,*)A, integerLDA, complex*16, dimension(ldb,*)B, integerLDB, double precisionBETA, complex*16, dimension(ldc,*)C, integerLDC)

ZHER2K Purpose:

ZHER2K  performs one of the hermitian rank 2k operations

   C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C,

or

   C := alpha*A**H*B + conjg( alpha )*B**H*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

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**H          +
                               conjg( alpha )*B*A**H +
                               beta*C.

    TRANS = 'C' or 'c'    C := alpha*A**H*B          +
                               conjg( alpha )*B**H*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 = 'C' or 'c',  K  specifies  the number of rows of the
 matrices  A and B.  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 ).

B

B is COMPLEX*16 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.

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 ).
 Unchanged on exit.

BETA

BETA is DOUBLE PRECISION .
 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  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

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.

-- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
   Ed Anderson, Cray Research Inc.

Definition at line 199 of file zher2k.f.

Author

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Referenced By

zher2k(3) is an alias of zher2k.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK