Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

cblas_?sbmv

Computes a matrix-vector product with a symmetric band matrix.

Syntax

void
cblas_ssbmv
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_UPLO
uplo
,
const
MKL_INT
n
,
const
MKL_INT
k
,
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_dsbmv
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_UPLO
uplo
,
const
MKL_INT
n
,
const
MKL_INT
k
,
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
);
Include Files
  • mkl.h
Description
The
?sbmv
routines perform a matrix-vector operation defined as
y
:=
alpha
*
A
*
x
+
beta
*
y
,
where:
alpha
and
beta
are scalars,
x
and
y
are
n
-element vectors,
A
is an
n
-by-
n
symmetric band matrix, with
k
super-diagonals.
Input Parameters
Layout
Specifies whether two-dimensional array storage is row-major (
CblasRowMajor
) or column-major (
CblasColMajor
).
uplo
Specifies whether the upper or lower triangular part of the band matrix
A
is used:
if
uplo
=
CblasUpper
- upper triangular part;
if
uplo
=
CblasLower
- low triangular part.
n
Specifies the order of the matrix
A
. The value of
n
must be at least zero.
k
Specifies the number of super-diagonals of the matrix
A
.
The value of
k
must satisfy
0
k
.
alpha
Specifies the scalar
alpha
.
a
Array, size
lda
*
n
. Before entry with
uplo
=
CblasUpper
, the leading
(
k
+ 1)
by
n
part of the array
a
must contain the upper triangular band part of the symmetric matrix, supplied column-by-column,
with the leading diagonal of the matrix in row
k
of the array, the first super-diagonal starting at position 1 in row
(
k
- 1)
, and so on.
The top left
k
by
k
triangle of the array
a
is not referenced.
The following program segment transfers the upper triangular part of a symmetric 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++) { m = k - j; for (i = max( 0, j - k); i <= j; i++) { a[(m+i) + j*lda] = matrix[i + j*ldm]; } }
Before entry with
uplo
=
CblasLower
, the leading
(
k
+ 1)
by
n
part of the array
a
must contain the lower triangular band part of the symmetric matrix, supplied column-by-column,
with the leading diagonal of the matrix in row 0 of the array, the first sub-diagonal starting at position 0 in row 1
, and so on. The bottom right
k
by
k
triangle of the array
a
is not referenced.
The following program segment transfers the lower triangular part of a symmetric 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++) { m = -j; for (i = j; i < min(n, j + k + 1); i++) { a[(m+i) + j*lda] = matrix[i + j*ldm]; } }
Layout = CblasRowMajor:
Before entry with
uplo
=
CblasUpper
, the leading (
k
+ 1)-by-
n
part of array
a
must contain the upper triangular band part of the symmetric matrix. The matrix must be supplied row-by-row, with the leading diagonal of the matrix in column 0 of the array, the first super-diagonal starting at position 0 in column 1, and so on. The bottom right
k
-by-
k
triangle of array
a
is not referenced.
The following program segment transfers the upper triangular part of a symmetric band matrix from row-major full matrix storage (
matrix
with leading dimension
ldm
) to row-major band storage (
a
, with leading dimension
lda
):
for (i = 0; i < n; i++) { m = -i; for (j = i; j < MIN(n, i+k+1); j++) { a[(m+j) + i*lda] = matrix[j + i*ldm]; } }
Before entry with
uplo
=
CblasLower
, the leading (
k
+ 1)-by-
n
part of array
a
must contain the lower triangular band part of the symmetric matrix, supplied row-by-row, with the leading diagonal of the matrix in column
k
of the array, the first sub-diagonal starting at position 1 in column
k
-1, and so on. The top left
k
-by-
k
triangle of array
a
is not referenced.
The following program segment transfers the lower triangular part of a symmetric row-major band matrix from row-major full matrix storage (
matrix
, with leading dimension
ldm
) to row-major band storage (
a
, with leading dimension
lda
):
for (i = 0; i < n; i++) { m = k - i; for (j = max(0, i-k); j <= i; j++) { a[(m+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
(
k
+ 1)
.
x
Array, size at least
(1 + (
n
- 1)*abs(
incx
))
. Before entry, the incremented array
x
must contain the vector
x
.
incx
Specifies the increment for the elements of
x
.
The value of
incx
must not be zero.
beta
Specifies the scalar
beta
.
y
Array, size at least
(1 + (
n
- 1)*abs(
incy
))
. 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
Overwritten by the updated vector
y
.

Product and Performance Information

1

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