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NAME ZHPR2 - perform the hermitian rank 2 operation A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, SYNOPSIS SUBROUTINE ZHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) COMPLEX*16 ALPHA INTEGER INCX, INCY, N CHARACTER*1 UPLO COMPLEX*16 AP( * ), X( * ), Y( * ) PURPOSE ZHPR2 performs the hermitian rank 2 operation where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form. PARAMETERS UPLO - 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. N - INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit. ALPHA - COMPLEX*16 . 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 ele- ments of X. INCX must not be zero. Unchanged on exit. Y - COMPLEX*16 array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. Unchanged on exit. INCY - INTEGER. On entry, INCY specifies the increment for the ele- ments of Y. INCY must not be zero. Unchanged on exit. AP - COMPLEX*16 array of DIMENSION at least ( ( n*( n + 1 ) )/2 ). Before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangu- lar 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. Before 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 ) respec- tively, and so on. On exit, the array AP is overwrit- ten by the lower triangular part of the updated matrix. Note that the imaginary parts of the diago- nal elements need not be set, they are assumed to be zero, and on exit they are set to zero. 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. NAME SYNOPSIS rou- tine zrotg(ca,cb,c,s) sub- ble dou- complex ca,cb,s ble dou- precision c ble dou- precision norm,scale ble dou- complex alpha if (cdabs(ca) .ne. 0.0d0) go to 10 c = 0.0d0 s = (1.0d0,0.0d0) ca = cb go to 20 10 con- tinue scale = cdabs(ca) + cdabs(cb) norm = scale*dsqrt((cdabs(ca/dcmplx(scale,0.0d0)))**2 + * (cdabs(cb/dcmplx(scale,0.0d0)))**2) alpha = ca /cdabs(ca) c = cdabs(ca) / norm s = alpha * dconjg(cb) / norm ca = alpha * norm 20 continue return end PUR- POSE NAME SYNOPSIS rou- tine zscal(n,za,zx,incx) sub- c scales a vec- tor by a con- stant. c jack dongarra, 3/11/78. c modified to correct prob- lem with nega- tive incre- ment, 8/21/90. ble dou- complex za,zx(1) integer i,incx,ix,n if(n.le.0)return if(incx.eq.1)go to 20 c code for incre- ment not equal to 1 ix = 1 if(incx.lt.0)ix = (- n+1)*incx + 1 do 10 i = 1,n zx(ix) = za*zx(ix) ix = ix + incx 10 con- tinue return c code for incre- ment equal to 1 20 do 30 i = 1,n zx(i) = za*zx(i) 30 con- tinue return end PUR- POSE