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

6       ZLA_GEAMV  -  performs  one  of  the  matrix-vector  operations    y :=
7       alpha*abs(A)*abs(x) + beta*abs(y),
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SYNOPSIS

10       SUBROUTINE ZLA_GEAMV ( TRANS, M, N, ALPHA, A, LDA, X,  INCX,  BETA,  Y,
11                            INCY )
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13           IMPLICIT         NONE
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15           DOUBLE           PRECISION ALPHA, BETA
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17           INTEGER          INCX, INCY, LDA, M, N
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19           INTEGER          TRANS
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21           COMPLEX*16       A( LDA, * ), X( * )
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23           DOUBLE           PRECISION Y( * )
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PURPOSE

26       ZLA_GEAMV  performs one of the matrix-vector operations
27          or   y := alpha*abs(A)'*abs(x) + beta*abs(y),
28       where  alpha and beta are scalars, x and y are vectors and A is an m by
29       n matrix.
30       This function is primarily used in calculating error bounds.   To  pro‐
31       tect  against  underflow during evaluation, components in the resulting
32       vector are perturbed away  from  zero  by  (N+1)  times  the  underflow
33       threshold.   To  prevent unnecessarily large errors for block-structure
34       embedded in general matrices,
35       "symbolically" zero components are not perturbed.  A zero entry is con‐
36       sidered  "symbolic"  if  all multiplications involved in computing that
37       entry have at least one zero multiplicand.
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ARGUMENTS

40       TRANS  - INTEGER
41              On entry, TRANS specifies the operation to be performed as  fol‐
42              lows:
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44       BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
45                          BLAS_TRANS           y   :=  alpha*abs(A')*abs(x)  +
46                          beta*abs(y)
47                          BLAS_CONJ_TRANS     y  :=   alpha*abs(A')*abs(x)   +
48                          beta*abs(y) Unchanged on exit.
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50       M      - INTEGER
51              On  entry,  M  specifies  the number of rows of the matrix A.  M
52              must be at least zero.  Unchanged on exit.
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54       N      - INTEGER
55              On entry, N specifies the number of columns of the matrix A.   N
56              must be at least zero.  Unchanged on exit.
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58       ALPHA  - DOUBLE PRECISION
59              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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61       A      - COMPLEX*16         array of DIMENSION ( LDA, n )
62              Before  entry,  the leading m by n part of the array A must con‐
63              tain the matrix of coefficients.  Unchanged on exit.
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65       LDA    - INTEGER
66              On entry, LDA specifies the first dimension of A as declared  in
67              the  calling  (sub)  program.  LDA must be at least max( 1, m ).
68              Unchanged on exit.
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70       X      - COMPLEX*16         array of DIMENSION at least
71              ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N'  or  'n'  and  at
72              least  (  1  + ( m - 1 )*abs( INCX ) ) otherwise.  Before entry,
73              the incremented array X must contain the vector x.  Unchanged on
74              exit.
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76       INCX   - INTEGER
77              On  entry,  INCX  specifies the increment for the elements of X.
78              INCX must not be zero.  Unchanged on exit.
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80       BETA   - DOUBLE PRECISION
81              On entry, BETA specifies the scalar beta. When BETA is  supplied
82              as zero then Y need not be set on input.  Unchanged on exit.
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84       Y      - DOUBLE PRECISION   array of DIMENSION at least
85              (  1  +  (  m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at
86              least ( 1 + ( n - 1 )*abs( INCY )  )  otherwise.   Before  entry
87              with  BETA  non-zero,  the  incremented array Y must contain the
88              vector y. On exit, Y is overwritten by the updated vector y.
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90       INCY   - INTEGER
91              On entry, INCY specifies the increment for the  elements  of  Y.
92              INCY  must  not  be zero.  Unchanged on exit.  Level 2 Blas rou‐
93              tine.
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97    LAPACK routine (version 3.2) November 2008                    ZLA_GEAMV(1)