Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

cblas_?hbmv

Computes a matrix-vector product using a Hermitian band matrix.

Syntax

void
cblas_chbmv
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_UPLO
uplo
,
const
MKL_INT
n
,
const
MKL_INT
k
,
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_zhbmv
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_UPLO
uplo
,
const
MKL_INT
n
,
const
MKL_INT
k
,
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
?hbmv
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
Hermitian 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 Hermitian band matrix
A
is used:
If
uplo
=
CblasUpper
, then the upper triangular part of the matrix
A
is used.
If
uplo
=
CblasLower
, then the low triangular part of the matrix
A
is used.
n
Specifies the order of the matrix
A
. The value of
n
must be at least zero.
k
For
uplo
=
CblasUpper
:
Specifies the number of super-diagonals of the matrix
A
.
For
uplo
=
CblasLower
: Specifies the number of sub-diagonals of the matrix
A
.
The value of
k
must satisfy
0
k
.
alpha
Specifies the scalar
alpha
.
a
Array, size
lda
*
n
.
Layout
=
CblasColMajor
:
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 Hermitian matrix. The matrix must be 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 Hermitian 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 Hermitian 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 Hermitian 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 Hermitian 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 Hermitian 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 Hermitian 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 Hermitian 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]; } }
The imaginary parts of the diagonal elements need not be set and are assumed to be zero.
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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804