Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

cblas_?gemm3m

Computes a scalar-matrix-matrix product using matrix multiplications and adds the result to a scalar-matrix product.

Syntax

void
cblas_cgemm3m
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_TRANSPOSE
transa
,
const
CBLAS_TRANSPOSE
transb
,
const
MKL_INT
m
,
const
MKL_INT
n
,
const
MKL_INT
k
,
const
void
*alpha
,
const
void
*a
,
const
MKL_INT
lda
,
const
void
*b
,
const
MKL_INT
ldb
,
const
void
*beta
,
void
*c
,
const
MKL_INT
ldc
);
void
cblas_zgemm3m
(
const
CBLAS_LAYOUT
Layout
,
const
CBLAS_TRANSPOSE
transa
,
const
CBLAS_TRANSPOSE
transb
,
const
MKL_INT
m
,
const
MKL_INT
n
,
const
MKL_INT
k
,
const
void
*alpha
,
const
void
*a
,
const
MKL_INT
lda
,
const
void
*b
,
const
MKL_INT
ldb
,
const
void
*beta
,
void
*c
,
const
MKL_INT
ldc
);
Include Files
  • mkl.h
Description
The
?gemm3m
 routines perform a matrix-matrix operation with general complex matrices. These routines are similar to the
?gemm
 routines, but they use fewer matrix multiplication operations
(see
Application Notes
 below)
.
The operation is defined as 
C := alpha*op(A)*op(B) + beta*C,
where:
op(
x
)
 is one of
op(
x
) =
x
, or
op(
x
) =
x
'
, or
op(
x
) = conjg(
x
')
,
alpha
 and
beta
 are scalars,
A
,
B
 and
C
 are matrices:
op(
A
)
 is an
m
-by-
k
 matrix,
op(
B
)
 is a
k
-by-
n
 matrix,
C
 is an
m
-by-
n
 matrix.
Input Parameters
Layout
Specifies whether two-dimensional array storage is row-major (
CblasRowMajor
) or column-major (
CblasColMajor
).
transa
Specifies the form of
op(
A
)
used in the matrix multiplication:
if
transa
=
CblasNoTrans
, then
op(
A
) =
A
;
if
transa
=
CblasTrans
, then
op(
A
) =
A
'
;
if
transa
=
CblasConjTrans
, then
op(
A
) = conjg(
A
')
.
transb
Specifies the form of
op(
B
)
 used in the matrix multiplication:
if
transb
=
CblasNoTrans
, then
op(
B
) =
B
;
if
transb
=
CblasTrans
, then
op(
B
) =
B
'
;
if
transb
=
CblasConjTrans
, then
op(
B
) = conjg(
B
')
.
m
Specifies the number of rows of the matrix
op(
A
)
 and of the matrix
C
. The value of
m
 must be at least zero.
n
Specifies the number of columns of the matrix
op(
B
)
 and the number of columns of the matrix
C
.
The value of
n
 must be at least zero.
k
Specifies the number of columns of the matrix
op(
A
)
 and the number of rows of the matrix
op(
B
)
.
The value of
k
 must be at least zero.
alpha
Specifies the scalar
alpha
.
a
transa
=
CblasNoTrans
transa
=
CblasTrans
 or
transa
=
CblasConjTrans
Layout
 =
CblasColMajor
Array, size
lda
*
k
.
Before entry, the leading
m
-by-
k
 part of the array
a
 must contain the matrix
A
.
Array, size
lda
*
m
.
Before entry, the leading
k
-by-
m
 part of the array
a
 must contain the matrix
A
.
Layout
 =
CblasRowMajor
Array, size
lda
*
m
.
Before entry, the leading
k
-by-
m
 part of the array
a
 must contain the matrix
A
.
Array, size
lda
*
k
.
Before entry, the leading
m
-by-
k
 part of the array
a
 must contain the matrix
A
.
lda
Specifies the leading dimension of
a
 as declared in the calling (sub)program.
transa
=
CblasNoTrans
transa
=
CblasTrans
 or
transa
=
CblasConjTrans
Layout
 =
CblasColMajor
lda
 must be at least
max(1,
m
)
.
lda
 must be at least
max(1,
k
)
Layout
 =
CblasRowMajor
lda
 must be at least
max(1,
k
)
lda
 must be at least
max(1,
m
)
.
b
transb
=
CblasNoTrans
transb
=
CblasTrans
 or
transb
=
CblasConjTrans
Layout
 =
CblasColMajor
Array, size
ldb
 by
n
. Before entry, the leading
k
-by-
n
 part of the array
b
 must contain the matrix
B
.
Array, size
ldb
 by
k
. Before entry the leading
n
-by-
k
 part of the array
b
 must contain the matrix
B
.
Layout
 =
CblasRowMajor
Array, size
ldb
 by
k
. Before entry the leading
n
-by-
k
 part of the array
b
 must contain the matrix
B
.
Array, size
ldb
 by
n
. Before entry, the leading
k
-by-
n
 part of the array
b
 must contain the matrix
B
.
ldb
Specifies the leading dimension of
b
 as declared in the calling (sub)program.
transb
=
CblasNoTrans
transb
=
CblasTrans
 or
transb
=
CblasConjTrans
Layout
 =
CblasColMajor
ldb
 must be at least
max(1,
k
)
.
ldb
 must be at least
max(1,
n
)
.
Layout
 =
CblasRowMajor
ldb
 must be at least
max(1,
n
)
.
ldb
 must be at least
max(1,
k
)
.
beta
Specifies the scalar
beta
.
When
beta
 is equal to zero, then
c
 need not be set on input.
c
Layout
 =
CblasColMajor
Array, size
ldc
 by
n
. Before entry, the leading
m
-by-
n
 part of the array
c
 must contain the matrix
C
, except when
beta
 is equal to zero, in which case
c
 need not be set on entry.
Layout
 =
CblasRowMajor
Array, size
ldc
 by
m
. Before entry, the leading
n
-by-
m
 part of the array
c
 must contain the matrix
C
, except when
beta
 is equal to zero, in which case
c
 need not be set on entry.
ldc
Specifies the leading dimension of
c
 as declared in the calling (sub)program.
Layout
 =
CblasColMajor
ldc
 must be at least
max(1,
m
)
.
Layout
 =
CblasRowMajor
ldc
 must be at least
max(1,
n
)
.
Output Parameters
c
Overwritten by the
m
-by-
n
 matrix
(
alpha
*op(
A
)*op(
B
) +
beta
*
C
)
.
Application Notes
These routines perform a complex matrix multiplication by forming the real and imaginary parts of the input matrices. This uses three real matrix multiplications and five real matrix additions instead of the conventional four real matrix multiplications and two real matrix additions. The use of three real matrix multiplications reduces the time spent in matrix operations by 25%, resulting in significant savings in compute time for large matrices.
If the errors in the floating point calculations satisfy the following conditions:
fl
(
x
 op
y
)=(
x
 op
y
)(1+δ),|δ|≤
u
, op=×,/,
fl
(
x
±
y
)=
x
(1+α)±
y
(1+β), |α|,|β|≤
u
then for an
n
-by-
n
 matrix
Ĉ
=
fl
(
C
1
+
i
C
2
)=
fl
((
A
1
+
i
A
2
)(
B
1
+
i
B
2
))=
Ĉ
1
+
i
Ĉ
2
, the following bounds are satisfied:
║
Ĉ
1
-
C
1
║≤ 2(
n
+1)
u
║
A
║
∞
║
B
║
∞
+
O
(
u
2
)
,
║
Ĉ
2
-
C
2
║≤ 4(
n
+4)
u
║
A
║
∞
║
B
║
∞
+
O
(
u
2
)
,
where
║
A
║
∞
=max(║
A
1
║
∞
,║
A
2
║
∞
)
, and
║
B
║
∞
=max(║
B
1
║
∞
,║
B
2
║
∞
)
.
Thus the corresponding matrix multiplications are stable.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.