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

6       SLA_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 SLA_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           REAL             ALPHA, BETA
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17           INTEGER          INCX, INCY, LDA, M, N, TRANS
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19           REAL             A( LDA, * ), X( * ), Y( * )
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PURPOSE

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

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