zher (l) - Linux Manuals

zher: performs the hermitian rank 1 operation A := alpha*x*conjg( xaq ) + A,

NAME

ZHER - performs the hermitian rank 1 operation A := alpha*x*conjg( xaq ) + A,

SYNOPSIS

SUBROUTINE ZHER(UPLO,N,ALPHA,X,INCX,A,LDA)

    
DOUBLE PRECISION ALPHA

    
INTEGER INCX,LDA,N

    
CHARACTER UPLO

    
DOUBLE COMPLEX A(LDA,*),X(*)

PURPOSE

ZHER performs the hermitian rank 1 operation

where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix.

ARGUMENTS

UPLO - CHARACTER*1.
On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows:

UPLO = aqUaq or aquaq Only the upper triangular part of A is to be referenced.

UPLO = aqLaq or aqlaq Only the lower triangular part of A is to be referenced.

Unchanged on exit.

N - INTEGER.
On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
X - COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. Unchanged on exit.
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
A - COMPLEX*16 array of DIMENSION ( LDA, n ).
Before entry with UPLO = aqUaq or aquaq, the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = aqLaq or aqlaq, the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A 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.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit.

FURTHER DETAILS

Level 2 Blas routine.

-- Written on 22-October-1986.

Jack Dongarra, Argonne National Lab.

Jeremy Du Croz, Nag Central Office.

Sven Hammarling, Nag Central Office.

Richard Hanson, Sandia National Labs.

Pages related to zher

  • zher (3)
  • zher2 (l) - performs the hermitian rank 2 operation A := alpha*x*conjg( yaq ) + conjg( alpha )*y*conjg( xaq ) + A,
  • zher2k (l) - performs one of the hermitian rank 2k operations C := alpha*A*conjg( Baq ) + conjg( alpha )*B*conjg( Aaq ) + beta*C,
  • zherfs (l) - improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution
  • zherfsx (l) - ZHERFSX improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution
  • zherk (l) - performs one of the hermitian rank k operations C := alpha*A*conjg( Aaq ) + beta*C,
  • zhecon (l) - estimates the reciprocal of the condition number of a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF
  • zheequb (l) - computes row and column scalings intended to equilibrate a symmetric matrix A and reduce its condition number (with respect to the two-norm)
  • zheev (l) - computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A
  • zheevd (l) - computes all eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A