1SLA_SYAMV(1)LAPACK routine (version 3.2)                           SLA_SYAMV(1)
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NAME

6       SLA_SYAMV    -    performs   the   matrix-vector   operation     y   :=
7       alpha*abs(A)*abs(x) + beta*abs(y),
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SYNOPSIS

10       SUBROUTINE SLA_SYAMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
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12           IMPLICIT          NONE
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14           REAL              ALPHA, BETA
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16           INTEGER           INCX, INCY, LDA, N, UPLO
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18           REAL              A( LDA, * ), X( * ), Y( * )
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PURPOSE

21       SLA_SYAMV  performs the matrix-vector operation where  alpha  and  beta
22       are scalars, x and y are vectors and A is an n by n symmetric matrix.
23       This  function  is primarily used in calculating error bounds.  To pro‐
24       tect against underflow during evaluation, components in  the  resulting
25       vector  are  perturbed  away  from  zero  by  (N+1) times the underflow
26       threshold.  To prevent unnecessarily large errors  for  block-structure
27       embedded in general matrices,
28       "symbolically" zero components are not perturbed.  A zero entry is con‐
29       sidered "symbolic" if all multiplications involved  in  computing  that
30       entry have at least one zero multiplicand.
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ARGUMENTS

33       UPLO   - INTEGER
34              On  entry,  UPLO specifies whether the upper or lower triangular
35              part of the array A is to  be  referenced  as  follows:  UPLO  =
36              BLAS_UPPER   Only the upper triangular part of A is to be refer‐
37              enced.  UPLO = BLAS_LOWER   Only the lower triangular part of  A
38              is to be referenced.  Unchanged on exit.
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40       N      - INTEGER.
41              On  entry, N specifies the number of columns of the matrix A.  N
42              must be at least zero.  Unchanged on exit.
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44       ALPHA  - REAL            .
45              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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47       A      - REAL             array of DIMENSION ( LDA, n ).
48              Before entry, the leading m by n part of the array A  must  con‐
49              tain the matrix of coefficients.  Unchanged on exit.
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51       LDA    - INTEGER.
52              On  entry, LDA specifies the first dimension of A as declared in
53              the calling (sub) program. LDA must be at least  max(  1,  n  ).
54              Unchanged on exit.
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56       X      - REAL             array of DIMENSION at least
57              (  1  +  (  n  - 1 )*abs( INCX ) ) Before entry, the incremented
58              array X must contain the vector x.  Unchanged on exit.
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60       INCX   - INTEGER.
61              On entry, INCX specifies the increment for the  elements  of  X.
62              INCX must not be zero.  Unchanged on exit.
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64       BETA   - REAL            .
65              On  entry, BETA specifies the scalar beta. When BETA is supplied
66              as zero then Y need not be set on input.  Unchanged on exit.
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68       Y      - REAL             array of DIMENSION at least
69              ( 1 + ( n - 1 )*abs( INCY ) ) Before entry with  BETA  non-zero,
70              the incremented array Y must contain the vector y. On exit, Y is
71              overwritten by the updated vector y.
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73       INCY   - INTEGER.
74              On entry, INCY specifies the increment for the  elements  of  Y.
75              INCY must not be zero.  Unchanged on exit.
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FURTHER DETAILS

78       Level 2 Blas routine.
79       -- Written on 22-October-1986.
80          Jack Dongarra, Argonne National Lab.
81          Jeremy Du Croz, Nag Central Office.
82          Sven Hammarling, Nag Central Office.
83          Richard Hanson, Sandia National Labs.
84       -- Modified for the absolute-value product, April 2006
85          Jason Riedy, UC Berkeley
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89    LAPACK routine (version 3.2) November 2008                    SLA_SYAMV(1)
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