LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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zspr.f File Reference

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Functions/Subroutines

subroutine zspr (UPLO, N, ALPHA, X, INCX, AP)
 ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

Function/Subroutine Documentation

subroutine zspr ( character  UPLO,
integer  N,
complex*16  ALPHA,
complex*16, dimension( * )  X,
integer  INCX,
complex*16, dimension( * )  AP 
)

ZSPR performs the symmetrical rank-1 update of a complex symmetric packed matrix.

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Purpose: 
 ZSPR    performs the symmetric rank 1 operation

    A := alpha*x*x**H + A,

 where alpha is a complex scalar, x is an n element vector and A is an
 n by n symmetric matrix, supplied in packed form.
Parameters:
[in]UPLO
          UPLO is CHARACTER*1
           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.
[in]N
          N is INTEGER
           On entry, N specifies the order of the matrix A.
           N must be at least zero.
           Unchanged on exit.
[in]ALPHA
          ALPHA is COMPLEX*16
           On entry, ALPHA specifies the scalar alpha.
           Unchanged on exit.
[in]X
          X is COMPLEX*16 array, dimension at least
           ( 1 + ( N - 1 )*abs( INCX ) ).
           Before entry, the incremented array X must contain the N-
           element vector x.
           Unchanged on exit.
[in]INCX
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X. INCX must not be zero.
           Unchanged on exit.
[in,out]AP
          AP is COMPLEX*16 array, dimension at least
           ( ( N*( N + 1 ) )/2 ).
           Before entry, with  UPLO = 'U' or 'u', the array AP must
           contain the upper triangular part of the symmetric 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.
           Before entry, with UPLO = 'L' or 'l', the array AP must
           contain the lower triangular part of the symmetric 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.
           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.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012

Definition at line 133 of file zspr.f.

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