Version: 0.9
Last Updated: 09/09/2020
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cblas_?gemm_batch

Computes

scalar-matrix-matrix products and adds the results to scalar matrix products for groups of

general matrices.

Syntax

void

cblas_sgemm_batch

(

const

CBLAS_LAYOUT

Layout

const

CBLAS_TRANSPOSE*

transa_array

const

CBLAS_TRANSPOSE*

transb_array

const

MKL_INT*

m_array

const

MKL_INT*

n_array

const

MKL_INT*

k_array

const

float*

alpha_array

const

float

**a_array

const

MKL_INT*

lda_array

const

float

**b_array

const

MKL_INT*

ldb_array

const

float*

beta_array

float

**c_array

const

MKL_INT*

ldc_array

const MKL_INT

group_count

const MKL_INT*

group_size

);

void

cblas_dgemm_batch

(

const

CBLAS_LAYOUT

Layout

const

CBLAS_TRANSPOSE*

transa_array

const

CBLAS_TRANSPOSE*

transb_array

const

MKL_INT*

m_array

const

MKL_INT*

n_array

const

MKL_INT*

k_array

const

double*

alpha_array

const

double

**a_array

const

MKL_INT*

lda_array

const

double

**b_array

const

MKL_INT*

ldb_array

const

double*

beta_array

double

**c_array

const

MKL_INT*

ldc_array

const MKL_INT

group_count

const MKL_INT*

group_size

);

void

cblas_cgemm_batch

(

const

CBLAS_LAYOUT

Layout

const

CBLAS_TRANSPOSE*

transa_array

const

CBLAS_TRANSPOSE*

transb_array

const

MKL_INT*

m_array

const

MKL_INT*

n_array

const

MKL_INT*

k_array

const

void

*alpha_array

const

void

**a_array

const

MKL_INT*

lda_array

const

void

**b_array

const

MKL_INT*

ldb_array

const

void

*beta_array

void

**c_array

const

MKL_INT*

ldc_array

const MKL_INT

group_count

const MKL_INT*

group_size

);

void

cblas_zgemm_batch

(

const

CBLAS_LAYOUT

Layout

const

CBLAS_TRANSPOSE*

transa_array

const

CBLAS_TRANSPOSE*

transb_array

const

MKL_INT*

m_array

const

MKL_INT*

n_array

const

MKL_INT*

k_array

const

void

*alpha_array

const

void

**a_array

const

MKL_INT*

lda_array

const

void

**b_array

const

MKL_INT*

ldb_array

const

void

*beta_array

void

**c_array

const

MKL_INT*

ldc_array

const MKL_INT

group_count

const MKL_INT*

group_size

);

Include Files

mkl.h

Description

The

?gemm_batch

routines perform a series of matrix-matrix operations with general matrices. They are similar to the

?gemm

routine counterparts, but the

?gemm_batch

routines perform matrix-matrix operations with groups of matrices

, processing a number of groups at once

. The groups contain matrices with the same parameters.

The operation is defined as

idx = 0
for i = 0..group_count - 1
     alpha and beta in alpha_array[i] and beta_array[i]
     for j = 0..group_size[i] - 1 
          A, B, and C matrix in a_array[idx], b_array[idx], and c_array[idx]
          C := alpha*op(A)*op(B) + beta*C,
          idx = idx + 1
     end for
 end for

where:

op(X)

is one of

op(X) = X

, or

op(X) = X^T

, or

op(X) = X^H

alpha and beta are scalar elements of

alpha_array

and

beta_array

A, B and C are matrices such that for m, n, and k which are elements of

m_array

n_array

, and

k_array

op(A)

is an

-by-k matrix,

op(B)

is a k-by-n matrix,

C is an m-by-n matrix.

A, B, and C represent matrices stored at addresses pointed to by

a_array

b_array

, and

c_array

, respectively. The number of entries in

a_array

b_array

, and

c_array

is total_batch_count = the sum of all of the

group_size

entries.

See also gemm for a detailed description of multiplication for general matrices and ?gemm3m_batch, BLAS-like extension routines for similar matrix-matrix operations.

Error checking is not performed for

oneMKL

Windows* single dynamic libraries for the

?gemm_batch

routines.

Input Parameters

Layout: Specifies whether two-dimensional array storage is row-major (
CblasRowMajor
) or column-major (
CblasColMajor
).
transa_array: Array of size
group_count
. For the group i,
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
, then
op(A) = A^T
;
if
transa_i = CblasConjTrans
, then
op(A) = A^H
.
transb_array: Array of size
group_count
. For the group i,
transb_i =
transb_array
[i]
specifies the form of
op(B_i)
used in the matrix multiplication:
if
transb_i = CblasNoTrans
, then
op(B) = B
;
if
transb_i = CblasTrans
, then
op(B) = B^T
;
if
transb_i = CblasConjTrans
, then
op(B) = B^H
.
m_array: Array of size
group_count
. For the group i, m_i =
m_array
[i]
specifies the number of rows of the matrix
op(A)
and of the matrix C.
The value of each element of
m_array
must be at least zero.
n_array: Array of size
group_count
. For the group i, n_i =
n_array
[i]
specifies the number of columns of the matrix
op(B)
and the number of columns of the matrix C.
The value of each element of
n_array
must be at least zero.
k_array: Array of size
group_count
. For the group i, k_i =
k_array
[i]
specifies the number of columns of the matrix
op(A)
and the number of rows of the matrix
op(B)
.
The value of each element of
k_array
must be at least zero.
alpha_array: Array of size
group_count
. For the group i,
alpha_array
[i]
specifies the scalar alpha_i.
a_array: Array, size total_batch_count, of pointers to arrays used to store A matrices.
lda_array: Array of size
group_count
. For the group i,
lda_i =
lda_array
[i]
specifies the leading dimension of the array storing matrix A as declared in the calling (sub)program.

transa
_i=CblasNoTrans
transa
_i=CblasTrans or
transa
_i=CblasConjTrans

Layout
= CblasColMajor
lda
_i must be at least
max(1,
m
_i)
.
lda
_i must be at least
max(1,
k
_i)

Layout
= CblasRowMajor
lda
_i must be at least
max(1,
k
_i)
lda
_i must be at least
max(1,
m
_i)
.
b_array: Array, size total_batch_count, of pointers to arrays used to store B matrices.
ldb_array: Array of size
group_count
. For the group i,
ldb_i =
ldb_array
[i]
specifies the leading dimension of the array storing matrix B as declared in the calling (sub)program.

transb
_i=CblasNoTrans
transb
_i=CblasTrans or
transb
_i=CblasConjTrans

Layout
= CblasColMajor
ldb
_i must be at least
max(1,
k
_i)
.
ldb
_i must be at least
max(1,
n
_i)
.

Layout
= CblasRowMajor
ldb
_i must be at least
max(1,
n
_i)
.
ldb
_i must be at least
max(1,
k
_i)
.
beta_array: Array of size
group_count
. For the group i,
beta_array
[i]
specifies the scalar beta_i.
When beta_i is equal to zero, then C matrices in group i need not be set on input.
c_array: Array, size total_batch_count, of pointers to arrays used to store C matrices.
ldc_array: Array of size
group_count
. For the group i,
ldc_i =
ldc_array
[i]
specifies the leading dimension of all arrays storing matrix C in group i as declared in the calling (sub)program.
When
Layout
= CblasColMajor
ldc_i must be at least
max(1, m_i)
.
When
Layout
= CblasRowMajor
ldc_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

c_array: Output buffer, overwritten by total_batch_count matrix multiply operations of the form
alpha*op(A)*op(B) + beta*C
.

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cblas_?gemm_batch

Syntax

	transa _i=`CblasNoTrans`	transa _i=`CblasTrans` or transa _i=`CblasConjTrans`
Layout = `CblasColMajor`	lda _i must be at least max(1, m _i) .	lda _i must be at least max(1, k _i)
Layout = `CblasRowMajor`	lda _i must be at least max(1, k _i)	lda _i must be at least max(1, m _i) .

	transb _i=`CblasNoTrans`	transb _i=`CblasTrans` or transb _i=`CblasConjTrans`
Layout = `CblasColMajor`	ldb _i must be at least max(1, k _i) .	ldb _i must be at least max(1, n _i) .
Layout = `CblasRowMajor`	ldb _i must be at least max(1, n _i) .	ldb _i must be at least max(1, k _i) .

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cblas_?gemm_batch

Syntax