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Technical Reference: Base Operating System and Extensions , Volume 2
Performs the Hermitian rank 1
operation.
BLAS Library
(libblas.a)
SUBROUTINE CHPR(UPLO, N, ALPHA,
X, INCX, AP)
REAL ALPHA
INTEGER INCX, N
CHARACTER*1 UPLO
COMPLEX AP(*), X(*)
SUBROUTINE ZHPR(UPLO, N, ALPHA,
X, INCX, AP)
DOUBLE PRECISION ALPHA
INTEGER INCX,N
CHARACTER*1 UPLO
COMPLEX*16 AP(*), X(*)
The CHPR or
ZHPR subroutine performs the Hermitian rank 1 operation:
A := alpha
* x * conjg( x' ) + A
where alpha is a real scalar, x
is an N element vector and A is an N by
N Hermitian matrix, supplied in packed form.
UPLO
 On entry, UPLO specifies whether the upper or lower triangular
part of the matrix A is supplied in the packed array AP
as follows:
 UPLO = 'U'
or 'u'
 The upper triangular part of A is supplied in
AP.
 UPLO = 'L'
or 'l'
 The lower triangular part of A is supplied in
AP.
Unchanged on exit.

N
 On entry, N specifies the order of the matrix
A; N must be at least 0; unchanged on
exit.

ALPHA
 On entry, ALPHA specifies the scalar alpha; unchanged on
exit.

X
 A vector of dimension at least (1 + (N1) *
abs(INCX) ); on entry, the incremented array X must
contain the N element vector x; unchanged on exit.

INCX
 On entry, INCX specifies the increment for the elements of
X; INCX must not be 0; unchanged on
exit.

AP
 A vector of dimension at least ( ( N * (N+1) )/2
); on entry with UPLO = 'U' or 'u', the
array AP must contain the upper triangular part of the Hermitian
matrix packed sequentially, column by column, so that AP(1)
contains A(1,1), AP(2) and AP(3) contain
A(1,2) and A(2,2) respectively, and so on. On exit, the
array AP is overwritten by the upper triangular part of the updated
matrix. On entry with UPLO = 'L' or 'l',
the array AP must contain the lower triangular part of the
Hermitian matrix packed sequentially, column by column, so that
AP(1) contains A(1,1), AP(2) and
AP(3) contain A(2,1) and A(3,1) respectively,
and so on. On exit, the array AP is overwritten by the lower
triangular part of the updated matrix. The imaginary parts of the
diagonal elements need not be set, they are assumed to be 0, and on exit they
are set to 0.

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