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la_gbamv(3) Library Functions Manual la_gbamv(3)

NAME

la_gbamv - la_gbamv: matrix-vector multiply |A| * |x|, general banded

SYNOPSIS

Functions


subroutine CLA_GBAMV (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)
CLA_GBAMV performs a matrix-vector operation to calculate error bounds. subroutine DLA_GBAMV (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)
DLA_GBAMV performs a matrix-vector operation to calculate error bounds. subroutine SLA_GBAMV (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)
SLA_GBAMV performs a matrix-vector operation to calculate error bounds. subroutine ZLA_GBAMV (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy)
ZLA_GBAMV performs a matrix-vector operation to calculate error bounds.

Detailed Description

Function Documentation

subroutine CLA_GBAMV (integer trans, integer m, integer n, integer kl, integer ku, real alpha, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( * ) x, integer incx, real beta, real, dimension( * ) y, integer incy)

CLA_GBAMV performs a matrix-vector operation to calculate error bounds.

Purpose:

!>
!> CLA_GBAMV  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,
!>  zero components are not perturbed.  A zero
!> entry is considered  if all multiplications involved
!> in computing that entry have at least one zero multiplicand.
!>

Parameters

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.
!>

KL

!>          KL is INTEGER
!>           The number of subdiagonals within the band of A.  KL >= 0.
!>

KU

!>          KU is INTEGER
!>           The number of superdiagonals within the band of A.  KU >= 0.
!>

ALPHA

!>          ALPHA is REAL
!>           On entry, ALPHA specifies the scalar alpha.
!>           Unchanged on exit.
!>

AB

!>          AB is COMPLEX array, dimension (LDAB,n)
!>           Before entry, the leading m by n part of the array AB must
!>           contain the matrix of coefficients.
!>           Unchanged on exit.
!>

LDAB

!>          LDAB is INTEGER
!>           On entry, LDAB specifies the first dimension of AB as declared
!>           in the calling (sub) program. LDAB must be at least
!>           max( 1, m ).
!>           Unchanged on exit.
!>

X

!>          X is COMPLEX 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
!>           ( 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.
!>           If either m or n is zero, then Y not referenced and the function
!>           performs a quick return.
!>

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.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 186 of file cla_gbamv.f.

subroutine DLA_GBAMV (integer trans, integer m, integer n, integer kl, integer ku, double precision alpha, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) x, integer incx, double precision beta, double precision, dimension( * ) y, integer incy)

DLA_GBAMV performs a matrix-vector operation to calculate error bounds.

Purpose:

!>
!> DLA_GBAMV  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,
!>  zero components are not perturbed.  A zero
!> entry is considered  if all multiplications involved
!> in computing that entry have at least one zero multiplicand.
!>

Parameters

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.
!>

KL

!>          KL is INTEGER
!>           The number of subdiagonals within the band of A.  KL >= 0.
!>

KU

!>          KU is INTEGER
!>           The number of superdiagonals within the band of A.  KU >= 0.
!>

ALPHA

!>          ALPHA is DOUBLE PRECISION
!>           On entry, ALPHA specifies the scalar alpha.
!>           Unchanged on exit.
!>

AB

!>          AB is DOUBLE PRECISION array, dimension ( LDAB, n )
!>           Before entry, the leading m by n part of the array AB must
!>           contain the matrix of coefficients.
!>           Unchanged on exit.
!>

LDAB

!>          LDAB is INTEGER
!>           On entry, LDA specifies the first dimension of AB as declared
!>           in the calling (sub) program. LDAB must be at least
!>           max( 1, m ).
!>           Unchanged on exit.
!>

X

!>          X is DOUBLE PRECISION 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 DOUBLE PRECISION
!>           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 DOUBLE PRECISION array, dimension
!>           ( 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.
!>           If either m or n is zero, then Y not referenced and the function
!>           performs a quick return.
!>

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.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 185 of file dla_gbamv.f.

subroutine SLA_GBAMV (integer trans, integer m, integer n, integer kl, integer ku, real alpha, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) x, integer incx, real beta, real, dimension( * ) y, integer incy)

SLA_GBAMV performs a matrix-vector operation to calculate error bounds.

Purpose:

!>
!> SLA_GBAMV  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,
!>  zero components are not perturbed.  A zero
!> entry is considered  if all multiplications involved
!> in computing that entry have at least one zero multiplicand.
!>

Parameters

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.
!>

KL

!>          KL is INTEGER
!>           The number of subdiagonals within the band of A.  KL >= 0.
!>

KU

!>          KU is INTEGER
!>           The number of superdiagonals within the band of A.  KU >= 0.
!>

ALPHA

!>          ALPHA is REAL
!>           On entry, ALPHA specifies the scalar alpha.
!>           Unchanged on exit.
!>

AB

!>          AB is REAL array, dimension ( LDAB, n )
!>           Before entry, the leading m by n part of the array AB must
!>           contain the matrix of coefficients.
!>           Unchanged on exit.
!>

LDAB

!>          LDAB is INTEGER
!>           On entry, LDA specifies the first dimension of AB as declared
!>           in the calling (sub) program. LDAB 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
!>           ( 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.
!>           If either m or n is zero, then Y not referenced and the function
!>           performs a quick return.
!>

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.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 185 of file sla_gbamv.f.

subroutine ZLA_GBAMV (integer trans, integer m, integer n, integer kl, integer ku, double precision alpha, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( * ) x, integer incx, double precision beta, double precision, dimension( * ) y, integer incy)

ZLA_GBAMV performs a matrix-vector operation to calculate error bounds.

Purpose:

!>
!> ZLA_GBAMV  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,
!>  zero components are not perturbed.  A zero
!> entry is considered  if all multiplications involved
!> in computing that entry have at least one zero multiplicand.
!>

Parameters

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.
!>

KL

!>          KL is INTEGER
!>           The number of subdiagonals within the band of A.  KL >= 0.
!>

KU

!>          KU is INTEGER
!>           The number of superdiagonals within the band of A.  KU >= 0.
!>

ALPHA

!>          ALPHA is DOUBLE PRECISION
!>           On entry, ALPHA specifies the scalar alpha.
!>           Unchanged on exit.
!>

AB

!>          AB is COMPLEX*16 array, dimension ( LDAB, n )
!>           Before entry, the leading m by n part of the array AB must
!>           contain the matrix of coefficients.
!>           Unchanged on exit.
!>

LDAB

!>          LDAB is INTEGER
!>           On entry, LDAB specifies the first dimension of AB as declared
!>           in the calling (sub) program. LDAB must be at least
!>           max( 1, m ).
!>           Unchanged on exit.
!>

X

!>          X is COMPLEX*16 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 DOUBLE PRECISION
!>           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 DOUBLE PRECISION array, dimension
!>           ( 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.
!>           If either m or n is zero, then Y not referenced and the function
!>           performs a quick return.
!>

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.
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 186 of file zla_gbamv.f.

Author

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