Developer Reference for Intel® oneAPI Math Kernel Library for C
?gbmv
Computes a matrix-vector product with a general band matrix.
Syntax
void cblas_sgbmv(const CBLAS_LAYOUT Layout, const CBLAS_TRANSPOSE trans, const MKL_INT m,
const MKL_INT n, const MKL_INT kl, const MKL_INT ku, const float alpha,
const float *a, const MKL_INT lda, const float *x, const MKL_INT incx,
const float beta, float *y, const MKL_INT incy);
void cblas_dgbmv(const CBLAS_LAYOUT Layout, const CBLAS_TRANSPOSE trans, const MKL_INT m,
const MKL_INT n, const MKL_INT kl, const MKL_INT ku, const double alpha,
const double *a, const MKL_INT lda, const double *x, const MKL_INT incx,
const double beta, double *y, const MKL_INT incy);
void cblas_cgbmv(const CBLAS_LAYOUT Layout, const CBLAS_TRANSPOSE trans, const MKL_INT m,
const MKL_INT n, const MKL_INT kl, const MKL_INT ku, const void *alpha,
const void *a, const MKL_INT lda, const void *x, const MKL_INT incx,
const void *beta, void *y, const MKL_INT incy);
void cblas_zgbmv(const CBLAS_LAYOUT Layout, const CBLAS_TRANSPOSE trans, const MKL_INT m,
const MKL_INT n, const MKL_INT kl, const MKL_INT ku, const void *alpha,
const void *a, const MKL_INT lda, const void *x, const MKL_INT incx,
const void *beta, void *y, const MKL_INT incy);Include Files
mkl.h
Description
The ?gbmv routines perform a matrix-vector operation defined as \(y := \alpha\cdot A\cdot x + \beta\cdot y\), or \(y := \alpha\cdot A^{T}\cdot x + \beta\cdot y\), or \(y := \alpha\cdot A^{H}\cdot x + \beta\cdot y\) ,
where:
alpha and beta are scalars,
x and y are vectors,
A is an m -by- n band matrix, with kl sub-diagonals and ku super-diagonals.
Input Parameters
Layout
Specifies whether two-dimensional array storage is row-major ( CblasRowMajor ) or column-major ( CblasColMajor ).
trans
Specifies the operation:
If trans = CblasNoTrans , then \(y := \alpha \cdot A \cdot x + \beta \cdot y\)
If trans = CblasTrans , then \(y := \alpha \cdot A^{T} \cdot x + \beta \cdot y\)
If trans = CblasConjTrans , then \(y := \alpha \cdot A^{H} \cdot x + \beta \cdot y\)
- m
-
Specifies the number of rows of the matrix A. The value of m must be at least zero.
- n
-
Specifies the number of columns of the matrix A. The value of n must be at least zero.
kl
Specifies the number of sub-diagonals of the matrix A. The value of kl must satisfy \(0 \leq \text{kl}\).
ku
Specifies the number of super-diagonals of the matrix A. The value of ku must satisfy \(0 \leq \text{ku}\).
alpha
Specifies the scalar alpha.
a
Array, size lda*n.
Layout = CblasColMajor : Before entry, the leading (kl + ku + 1) by n part of the array a must contain the matrix of coefficients. This matrix must be supplied column-by-column, with the leading diagonal of the matrix in row (ku + 1) of the array, the first super-diagonal starting at position 1 in row (ku - 1) , the first sub-diagonal starting at position 0 in row (ku + 21) , and so on. Elements in the array a that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced.
The following program segment transfers a band matrix from conventional full matrix storage ( matrix , with leading dimension ldm ) to band storage ( a , with leading dimension lda ):
for (j = 0; j < n; j++) {
k = ku - j;
for (i = max(0, j-ku); i < min(m, j+kl+1); i++) {
a[(k+i) + j*lda] = matrix[i + j*ldm];
}
}Layout = CblasRowMajor : Before entry, the leading (kl + ku + 1) by m part of the array a must contain the matrix of coefficients. This matrix must be supplied row-by-row, with the leading diagonal of the matrix in column (kl) of the array, the first super-diagonal starting at position 0 in column (kl + 1) , the first sub-diagonal starting at position 1 in row (kl - 1) , and so on. Elements in the array a that do not correspond to elements in the band matrix (such as the top left kl by kl triangle) are not referenced.
The following program segment transfers a band matrix from row-major full matrix storage ( matrix , with leading dimension ldm ) to band storage ( a , with leading dimension lda ):
for (i = 0; i < m; i++) {
k = kl - i;
for (j = max(0, i-kl); j < min(n, i+ku+1); j++) {
a[(k+j) + i*lda] = matrix[j + i*ldm];
}
}- lda
-
Specifies the leading dimension of a as declared in the calling (sub)program. The value of lda must be at least (kl + ku + 1) .
x
Array, size at least (1 + (n - 1)*abs(incx)) when trans = CblasNoTrans , and at least (1 + (m - 1)*abs(incx)) otherwise. Before entry, the array x must contain the vector x .
- incx
-
Specifies the increment for the elements of x . incx must not be zero.
beta
Specifies the scalar beta. When beta is equal to zero, then y need not be set on input.
y
Array, size at least (1 +(m - 1)*abs(incy)) when trans = CblasNoTrans and at least (1 +(n - 1)*abs(incy)) otherwise. Before entry, the incremented array y must contain the vector y .
- incy
-
Specifies the increment for the elements of y . The value of incy must not be zero.
Output Parameters
- y
-
Buffer holding the updated vector y .
BLAS 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.