1ZSPR(1)             LAPACK auxiliary routine (version 3.2)             ZSPR(1)
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NAME

6       ZSPR - performs the symmetric rank 1 operation   A := alpha*x*conjg( x'
7       ) + A,
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SYNOPSIS

10       SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
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12           CHARACTER    UPLO
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14           INTEGER      INCX, N
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16           COMPLEX*16   ALPHA
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18           COMPLEX*16   AP( * ), X( * )
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PURPOSE

21       ZSPR    performs the symmetric rank 1 operation where alpha is  a  com‐
22       plex  scalar,  x  is  an  n element vector and A is an n by n symmetric
23       matrix, supplied in packed form.
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ARGUMENTS

26       UPLO     (input) CHARACTER*1
27                On entry, UPLO specifies whether the upper or lower triangular
28                part  of  the  matrix  A is supplied in the packed array AP as
29                follows: UPLO = 'U' or 'u'   The upper triangular part of A is
30                supplied in AP.  UPLO = 'L' or 'l'   The lower triangular part
31                of A is supplied in AP.  Unchanged on exit.
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33       N        (input) INTEGER
34                On entry, N specifies the order of the matrix A.  N must be at
35                least zero.  Unchanged on exit.
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37       ALPHA    (input) COMPLEX*16
38                On  entry,  ALPHA  specifies  the  scalar alpha.  Unchanged on
39                exit.
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41       X        (input) COMPLEX*16 array, dimension at least
42                ( 1 + ( N - 1 )*abs( INCX ) ).  Before entry, the  incremented
43                array  X  must  contain the N- element vector x.  Unchanged on
44                exit.
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46       INCX     (input) INTEGER
47                On entry, INCX specifies the increment for the elements of  X.
48                INCX must not be zero.  Unchanged on exit.
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50       AP       (input/output) COMPLEX*16 array, dimension at least
51                ( ( N*( N + 1 ) )/2 ).  Before entry, with  UPLO = 'U' or 'u',
52                the array AP must contain the upper  triangular  part  of  the
53                symmetric  matrix  packed  sequentially,  column by column, so
54                that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3  )  contain
55                a(  1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the
56                array AP is overwritten by the upper triangular  part  of  the
57                updated  matrix.   Before  entry,  with UPLO = 'L' or 'l', the
58                array AP must contain the lower triangular part of the symmet‐
59                ric  matrix packed sequentially, column by column, so that AP(
60                1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1  )
61                and  a(  3, 1 ) respectively, and so on. On exit, the array AP
62                is overwritten by the lower triangular  part  of  the  updated
63                matrix.   Note  that  the imaginary parts of the diagonal ele‐
64                ments need not be set, they are assumed to  be  zero,  and  on
65                exit they are set to zero.
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69 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                         ZSPR(1)
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