la_gbamv#

Functions

void cla_gbamv(
    const INT           trans,
    const INT           m,
    const INT           n,
    const INT           kl,
    const INT           ku,
    const f32           alpha,
    const c64* restrict AB,
    const INT           ldab,
    const c64* restrict X,
    const INT           incx,
    const f32           beta,
          f32* restrict Y,
    const INT           incy
);
void cla_gbamv(const INT trans, const INT m, const INT n, const INT kl, const INT ku, const f32 alpha, const c64 *restrict AB, const INT ldab, const c64 *restrict X, const INT incx, const f32 beta, f32 *restrict Y, const INT incy)#

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

in
trans

Specifies the operation to be performed: CblasNoTrans: y := alpha*abs(A)*abs(x) + beta*abs(y) CblasTrans: y := alpha*abs(A**T)*abs(x) + beta*abs(y) CblasConjTrans: y := alpha*abs(A**T)*abs(x) + beta*abs(y)

in
m

The number of rows of the matrix A. m >= 0.

in
n

The number of columns of the matrix A. n >= 0.

in
kl

The number of subdiagonals within the band of A. kl >= 0.

in
ku

The number of superdiagonals within the band of A. ku >= 0.

in
alpha

The scalar alpha.

in
AB

Complex*16 array, dimension (ldab, n). Before entry, the leading m by n part of the array AB must contain the matrix of coefficients.

in
ldab

The first dimension of AB. ldab >= kl+ku+1.

in
X

Complex*16 array, dimension (1 + (n-1)*abs(incx)) when trans = CblasNoTrans and at least (1 + (m-1)*abs(incx)) otherwise.

in
incx

The increment for the elements of X. incx != 0.

in
beta

The scalar beta.

inout
Y

Single precision array, dimension (1 + (m-1)*abs(incy)) when trans = CblasNoTrans and at least (1 + (n-1)*abs(incy)) otherwise.

in
incy

The increment for the elements of Y. incy != 0.

Functions

void zla_gbamv(
    const INT            trans,
    const INT            m,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const f64            alpha,
    const c128* restrict AB,
    const INT            ldab,
    const c128* restrict X,
    const INT            incx,
    const f64            beta,
          f64*  restrict Y,
    const INT            incy
);
void zla_gbamv(const INT trans, const INT m, const INT n, const INT kl, const INT ku, const f64 alpha, const c128 *restrict AB, const INT ldab, const c128 *restrict X, const INT incx, const f64 beta, f64 *restrict Y, const INT incy)#

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

in
trans

Specifies the operation to be performed: CblasNoTrans: y := alpha*abs(A)*abs(x) + beta*abs(y) CblasTrans: y := alpha*abs(A**T)*abs(x) + beta*abs(y) CblasConjTrans: y := alpha*abs(A**T)*abs(x) + beta*abs(y)

in
m

The number of rows of the matrix A. m >= 0.

in
n

The number of columns of the matrix A. n >= 0.

in
kl

The number of subdiagonals within the band of A. kl >= 0.

in
ku

The number of superdiagonals within the band of A. ku >= 0.

in
alpha

The scalar alpha.

in
AB

Complex*16 array, dimension (ldab, n). Before entry, the leading m by n part of the array AB must contain the matrix of coefficients.

in
ldab

The first dimension of AB. ldab >= kl+ku+1.

in
X

Complex*16 array, dimension (1 + (n-1)*abs(incx)) when trans = CblasNoTrans and at least (1 + (m-1)*abs(incx)) otherwise.

in
incx

The increment for the elements of X. incx != 0.

in
beta

The scalar beta.

inout
Y

Double precision array, dimension (1 + (m-1)*abs(incy)) when trans = CblasNoTrans and at least (1 + (n-1)*abs(incy)) otherwise.

in
incy

The increment for the elements of Y. incy != 0.

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