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

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

10       SUBROUTINE CLA_GBAMV( TRANS, M, N, KL, KU, ALPHA, AB,  LDAB,  X,  INCX,
11                             BETA, Y, INCY )
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13           IMPLICIT          NONE
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15           REAL              ALPHA, BETA
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17           INTEGER           INCX, INCY, LDAB, M, N, KL, KU, TRANS
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19           COMPLEX           AB( LDAB, * ), X( * )
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21           REAL              Y( * )
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PURPOSE

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

38       TRANS  - INTEGER
39              On entry, TRANS specifies the operation to be performed as  fol‐
40              lows:
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42       BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
43                          BLAS_TRANS           y   :=  alpha*abs(A')*abs(x)  +
44                          beta*abs(y)
45                          BLAS_CONJ_TRANS     y  :=   alpha*abs(A')*abs(x)   +
46                          beta*abs(y) Unchanged on exit.
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48       M      - INTEGER
49              On  entry,  M  specifies  the number of rows of the matrix A.  M
50              must be at least zero.  Unchanged on exit.
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52       N      - INTEGER
53              On entry, N specifies the number of columns of the matrix A.   N
54              must be at least zero.  Unchanged on exit.
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56       KL     - INTEGER
57              The number of subdiagonals within the band of A.  KL >= 0.
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59       KU     - INTEGER
60              The number of superdiagonals within the band of A.  KU >= 0.
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62       ALPHA  - REAL
63              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.
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65       A      - REAL             array of DIMENSION ( LDA, n )
66              Before  entry,  the leading m by n part of the array A must con‐
67              tain the matrix of coefficients.  Unchanged on exit.
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69       LDA    - INTEGER
70              On entry, LDA specifies the first dimension of A as declared  in
71              the  calling  (sub)  program.  LDA must be at least max( 1, m ).
72              Unchanged on exit.
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74       X      - REAL             array of DIMENSION at least
75              ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N'  or  'n'  and  at
76              least  (  1  + ( m - 1 )*abs( INCX ) ) otherwise.  Before entry,
77              the incremented array X must contain the vector x.  Unchanged on
78              exit.
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80       INCX   - INTEGER
81              On  entry,  INCX  specifies the increment for the elements of X.
82              INCX must not be zero.  Unchanged on exit.
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84       BETA   - REAL
85              On entry, BETA specifies the scalar beta. When BETA is  supplied
86              as zero then Y need not be set on input.  Unchanged on exit.
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88       Y      - REAL             array of DIMENSION at least
89              (  1  +  (  m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at
90              least ( 1 + ( n - 1 )*abs( INCY )  )  otherwise.   Before  entry
91              with  BETA  non-zero,  the  incremented array Y must contain the
92              vector y. On exit, Y is overwritten by the updated vector y.
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94       INCY   - INTEGER
95              On entry, INCY specifies the increment for the  elements  of  Y.
96              INCY  must  not  be zero.  Unchanged on exit.  Level 2 Blas rou‐
97              tine.
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101    LAPACK routine (version 3.2) November 2008                    CLA_GBAMV(1)