Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

cblas_?trsm_batch

Solves a triangular matrix equation for a group of matrices.

Syntax

void
cblas_strsm_batch
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_SIDE
*Side_Array
,
const
CBLAS_UPLO
*Uplo_Array
,
const
CBLAS_TRANSPOSE
*TransA_Array
,
const
CBLAS_DIAG
*Diag_Array
,
const
MKL_INT
*M_Array
,
const
MKL_INT
*N_Array
,
const
float
*alpha_Array
,
const
float
*
*A_Array
,
const
MKL_INT
*lda_Array
,
float
*
*B_Array
,
const
MKL_INT
*ldb_Array
,
const
MKL_INT
group_count
,
const
MKL_INT
*group_size
);
void
cblas_dtrsm_batch
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_SIDE
*Side_Array
,
const
CBLAS_UPLO
*Uplo_Array
,
const
CBLAS_TRANSPOSE
*Transa_Array
,
const
CBLAS_DIAG
*Diag_Array
,
const
MKL_INT
*M_Array
,
const
MKL_INT
*N_Array
,
const
double
*alpha_Array
,
const
double
*
*A_Array
,
const
MKL_INT
*lda_Array
,
double
*
*B_Array
,
const
MKL_INT
*ldb_Array
,
const
MKL_INT
group_count
,
const
MKL_INT
*group_size
);
void
cblas_ctrsm_batch
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_SIDE
*Side_Array
,
const
CBLAS_UPLO
*Uplo_Array
,
const
CBLAS_TRANSPOSE
*Transa_Array
,
const
CBLAS_DIAG
*Diag_Array
,
const
MKL_INT
*M_Array
,
const
MKL_INT
*N_Array
,
const
void
*alpha_Array
,
const
void
*
*A_Array
,
const
MKL_INT
*lda_Array
,
void
*
*B_Array
,
const
MKL_INT
*ldb_Array
,
const
MKL_INT
group_count
,
const
MKL_INT
*group_size
);
void
cblas_ztrsm_batch
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_SIDE
*Side_Array
,
const
CBLAS_UPLO
*Uplo_Array
,
const
CBLAS_TRANSPOSE
*Transa_Array
,
const
CBLAS_DIAG
*Diag_Array
,
const
MKL_INT
*M_Array
,
const
MKL_INT
*N_Array
,
const
void
*alpha_Array
,
const
void
*
*A_Array
,
const
MKL_INT
*lda_Array
,
void
*
*B_Array
,
const
MKL_INT
*ldb_Array
,
const
MKL_INT
group_count
,
const
MKL_INT
*group_size
);
Include Files
  • mkl.h
Description
The
?trsm_batch
 routines solve a series of matrix equations. They are similar to the
?trsm
 routines except that they operate on groups of matrices which have the same parameters. The
?trsm_batch
 routines process a number of groups at once. 
idx = 0
for i = 0..group_count - 1
    alpha in alpha_array[i]
    for j = 0..group_size[i] - 1
        A and B matrix in a_array[idx] and b_array[idx]
        Solve op(A)*X = alpha*B
          or
        Solve X*op(A) = alpha*B
        idx = idx + 1
    end for
end for
where:
alpha
 is a scalar element of
alpha_array
,
X
 and
B
 are
m
-by-
n
 matrices for
m
 and
n
 which are elements of
m_array
 and
n_array
, respectively,
A
 is a unit, or non-unit, upper or lower triangular matrix,
and
op(
A
)
 is one of
op(
A
) =
A
, or
op(
A
) =
A
T
, or
op(
A
) = conjg(
A
T
)
.
A
 and
B
 represent matrices stored at addresses pointed to by
a_array
 and
b_array
, respectively. There are
total_batch_count
 entries in each of
a_array
 and
b_array
, where
total_batch_count
 is the sum of all the
group_size
 entries.
Input Parameters
Layout
Specifies whether two-dimensional array storage is row-major (
CblasRowMajor
) or column-major (
CblasColMajor
).
side_array
Array of size
group_count
. For group
i
,
0
≤
i
≤
group_count
 - 1
,
side
i
 =
side_array
[
i
]
 specifies whether
op(
A
)
 appears on the left or right of
X
 in the equation:
if
side
i
 =
CblasLeft
, then
op(
A
)*
X
 =
alpha
*
B
;
if
side
i
 =
CblasRight
, then
X
*op(
A
) =
alpha
*
B
.
uplo_array
Array of size
group_count
. For group
i
,
0
≤
i
≤
group_count
 - 1
,
uplo
i
 =
uplo_array
[
i
]
 specifies whether the matrix
A
 is upper or lower triangular:
uplo
i
 =
CblasUpper
if
uplo
i
 =
CblasLower
, then the matrix is low triangular.
transa_array
Array of size
group_count
. For group
i
,
0
≤
i
≤
group_count
 - 1
,
transa
i
 =
transa_array
[
i
]
 specifies the form of
op(
A
)
 used in the matrix multiplication:
if
transa
i
=
CblasNoTrans
, then
op(
A
) =
A
;
if
transa
i
=
CblasTrans
;
if
transa
i
=
CblasConjTrans
, then
op(
A
) = conjg(
A
')
.
diag_array
Array of size
group_count
. For group
i
,
0
≤
i
≤
group_count
 - 1
,
diag
i
 =
diag_array
[
i
]
 specifies whether the matrix
A
 is unit triangular:
if
diag
i
 =
CblasUnit
 then the matrix is unit triangular;
if
diag
i
 =
CblasNonUnit
, then the matrix is not unit triangular.
m_array
Array of size
group_count
. For group
i
,
0
≤
i
≤
group_count
 - 1
,
m
i
 =
m_array
[
i
]
 specifies the number of rows of
B
. The value of
m
i
 must be at least zero.
n_array
Array of size
group_count
. For group
i
,
0
≤
i
≤
group_count
 - 1
,
n
i
 =
n_array
[
i
]
 specifies the number of columns of
B
. The value of
n
i
 must be at least zero.
alpha_array
Array of size
group_count
. For group
i
,
0
≤
i
≤
group_count
 - 1
,
alpha_array
[
i
]
 specifies the scalar
alpha
i
.
a_array
Array, size
total_batch_count
, of pointers to arrays used to store
A
 matrices.
For group
i
,
0
≤
i
≤
group_count
 - 1
,
k
 is
m
i
 when
side
i
 =
CblasLeft
 and is
n
i
 when
side
i
 =
CblasRight
 and
a
 is any of the
group_size
[
i
]
 arrays starting with
a_array
[
group_size
[0] +
group_size
[1] + ... +
group_size
(
i
 - 1)]
:
Before entry with
uplo
i
 =
CblasUpper
, the leading
k
 by
k
 upper triangular part of the array
a
 must contain the upper triangular matrix and the strictly lower triangular part of
a
 is not referenced.
Before entry with
uplo
i
 =
CblasLower
 lower triangular part of the array
a
 must contain the lower triangular matrix and the strictly upper triangular part of
a
 is not referenced.
When
diag
i
 =
CblasUnit
, the diagonal elements of
a
 are not referenced either, but are assumed to be unity.
lda_array
Array of size
group_count
. For group
i
,
0
≤
i
≤
group_count
 - 1
,
lda
i
 =
lda_array
[
i
]
 specifies the leading dimension of
a
 as declared in the calling (sub)program. When
side
i
 =
CblasLeft
, then
lda
i
 must be at least
max(1,
m
i
)
, when
side
i
 =
CblasRight
, then
lda
i
 must be at least
max(1,
n
i
)
.
b_array
Array, size
total_batch_count
, of pointers to arrays used to store
B
 matrices.
For group
i
,
0
≤
i
≤
group_count
 - 1
,
b
 is any of the
group_size
[
i
]
 arrays starting with
b_array
[
group_size
[0] +
group_size
[1] + ... +
group_size
(
i
 - 1)]
:
For
Layout
 =
CblasColMajor
: before entry, the leading
m
i
-by-
n
i
 part of the array
b
 must contain the matrix
B
.
For
Layout
 =
CblasRowMajor
: before entry, the leading
n
i
-by-
m
i
 part of the array
b
 must contain the matrix
B
.
ldb_array
Array of size
group_count
. Specifies the leading dimension of
b
 as declared in the calling (sub)program.
When
Layout
 =
CblasColMajor
,
ldb
 must be at least
max(1,
m
)
; otherwise,
ldb
 must be at least
max(1,
n
)
.
Array of size
group_count
. For group
i
,
0
≤
i
≤
group_count
 - 1
,
ldb
i
 =
ldb_array
[
i
]
 specifies the leading dimension of
b
 as declared in the calling (sub)program.
When
Layout
 =
CblasColMajor
,
ldb
i
 must be at least
max(1,
m
i
)
; otherwise,
ldb
i
 must be at least
max(1,
n
i
)
.
group_count
Specifies the number of groups. Must be at least 0.
group_size
Array of size
group_count
. The element
group_size
[
i
]
 specifies the number of matrices in group
i
. Each element in
group_size
 must be at least 0.
Output Parameters
b_array
Overwritten by the solution matrix
X
.