1ZSPR(1)             LAPACK auxiliary routine (version 3.1)             ZSPR(1)
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NAME

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

9       SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
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11           CHARACTER    UPLO
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13           INTEGER      INCX, N
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15           COMPLEX*16   ALPHA
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17           COMPLEX*16   AP( * ), X( * )
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PURPOSE

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

27       UPLO     (input) CHARACTER*1
28                On entry, UPLO specifies whether the upper or lower triangular
29                part  of  the  matrix  A is supplied in the packed array AP as
30                follows:
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32                UPLO = 'U' or 'u'   The upper triangular part of A is supplied
33                in AP.
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35                UPLO = 'L' or 'l'   The lower triangular part of A is supplied
36                in AP.
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38                Unchanged on exit.
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40       N        (input) INTEGER
41                On entry, N specifies the order of the matrix A.  N must be at
42                least zero.  Unchanged on exit.
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44       ALPHA    (input) COMPLEX*16
45                On  entry,  ALPHA  specifies  the  scalar alpha.  Unchanged on
46                exit.
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48       X        (input) COMPLEX*16 array, dimension at least
49                ( 1 + ( N - 1 )*abs( INCX ) ).  Before entry, the  incremented
50                array  X  must  contain the N- element vector x.  Unchanged on
51                exit.
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53       INCX     (input) INTEGER
54                On entry, INCX specifies the increment for the elements of  X.
55                INCX must not be zero.  Unchanged on exit.
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57       AP       (input/output) COMPLEX*16 array, dimension at least
58                ( ( N*( N + 1 ) )/2 ).  Before entry, with  UPLO = 'U' or 'u',
59                the array AP must contain the upper  triangular  part  of  the
60                symmetric  matrix  packed  sequentially,  column by column, so
61                that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3  )  contain
62                a(  1, 2 ) and a( 2, 2 ) respectively, and so on. On exit, the
63                array AP is overwritten by the upper triangular  part  of  the
64                updated  matrix.   Before  entry,  with UPLO = 'L' or 'l', the
65                array AP must contain the lower triangular part of the symmet‐
66                ric  matrix packed sequentially, column by column, so that AP(
67                1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1  )
68                and  a(  3, 1 ) respectively, and so on. On exit, the array AP
69                is overwritten by the lower triangular  part  of  the  updated
70                matrix.   Note  that  the imaginary parts of the diagonal ele‐
71                ments need not be set, they are assumed to  be  zero,  and  on
72                exit they are set to zero.
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76 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                         ZSPR(1)
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