SLA_GEAMV  performs one of the matrix-vector operations


         y := alpha*abs(A)*abs(x) + beta*abs(y),


    or   y := alpha*abs(A)**T*abs(x) + beta*abs(y),


 where alpha and beta are scalars, x and y are vectors and A is an


 m by n matrix.


 This function is primarily used in calculating error bounds.


 To protect against underflow during evaluation, components in


 the resulting vector are perturbed away from zero by (N+1)


 times the underflow threshold.  To prevent unnecessarily large


 errors for block-structure embedded in general matrices,


 "symbolically" zero components are not perturbed.  A zero


 entry is considered "symbolic" if all multiplications involved


 in computing that entry have at least one zero multiplicand.

TRANS

          TRANS is INTEGER


           On entry, TRANS specifies the operation to be performed as


           follows:


             BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)


             BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)


             BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)


           Unchanged on exit.

M

          M is INTEGER


           On entry, M specifies the number of rows of the matrix A.


           M must be at least zero.


           Unchanged on exit.

N

          N is INTEGER


           On entry, N specifies the number of columns of the matrix A.


           N must be at least zero.


           Unchanged on exit.

ALPHA

          ALPHA is REAL


           On entry, ALPHA specifies the scalar alpha.


           Unchanged on exit.

A

          A is REAL array, dimension ( LDA, n )


           Before entry, the leading m by n part of the array A must


           contain the matrix of coefficients.


           Unchanged on exit.

LDA

          LDA is INTEGER


           On entry, LDA specifies the first dimension of A as declared


           in the calling (sub) program. LDA must be at least


           max( 1, m ).


           Unchanged on exit.

X

          X is REAL array, dimension


           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'


           and at least


           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.


           Before entry, the incremented array X must contain the


           vector x.


           Unchanged on exit.

INCX

          INCX is INTEGER


           On entry, INCX specifies the increment for the elements of


           X. INCX must not be zero.


           Unchanged on exit.

BETA

          BETA is REAL


           On entry, BETA specifies the scalar beta. When BETA is


           supplied as zero then Y need not be set on input.


           Unchanged on exit.

Y

          Y is REAL array,


           dimension at least


           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'


           and at least


           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.


           Before entry with BETA non-zero, the incremented array Y


           must contain the vector y. On exit, Y is overwritten by the


           updated vector y.

INCY

          INCY is INTEGER


           On entry, INCY specifies the increment for the elements of


           Y. INCY must not be zero.


           Unchanged on exit.


  Level 2 Blas routine.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

June 2017