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la_gbamv - Man Page

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,
 '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.
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,
 '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.
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,
 '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.
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,
 '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.
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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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK