?gemm_batch

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 11/07/2023

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?gemm_batch

Computes scalar-matrix-matrix products and adds the results to scalar matrix products for groups of general matrices.

Syntax

call sgemm_batch(transa_array, transb_array, m_array, n_array, k_array, alpha_array, a_array, lda_array, b_array, ldb_array, beta_array, c_array, ldc_array, group_count, group_size)

call dgemm_batch(transa_array, transb_array, m_array, n_array, k_array, alpha_array, a_array, lda_array, b_array, ldb_array, beta_array, c_array, ldc_array, group_count, group_size)

call cgemm_batch(transa_array, transb_array, m_array, n_array, k_array, alpha_array, a_array, lda_array, b_array, ldb_array, beta_array, c_array, ldc_array, group_count, group_size)

call zgemm_batch(transa_array, transb_array, m_array, n_array, k_array, alpha_array, a_array, lda_array, b_array, ldb_array, beta_array, c_array, ldc_array, group_count, group_size)

call sgemm_batch(a_array, b_array, c_array, m_array, n_array, k_array, group_size [,transa_array][,transb_array] [,alpha_array][,beta_array])

call dgemm_batch(a_array, b_array, c_array, m_array, n_array, k_array, group_size [,transa_array][,transb_array] [,alpha_array][,beta_array])

call cgemm_batch(a_array, b_array, c_array, m_array, n_array, k_array, group_size [,transa_array][,transb_array] [,alpha_array][,beta_array])

call zgemm_batch(a_array, b_array, c_array, m_array, n_array, k_array, group_size [,transa_array][,transb_array] [,alpha_array][,beta_array])

Include Files

mkl.fi, blas.f90

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 = 1
for i = 1..group_count 
     alpha and beta in alpha_array(i) and beta_array(i)
     for j = 1..group_size(i) 
          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 m-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.

NOTE:

Error checking is not performed for oneMKL Windows* single dynamic libraries for the?gemm_batch routines.

Input Parameters

transa_array

CHARACTER*1. 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 = 'N' or 'n', then op(A) = A;

if transa_i = 'T' or 't', then op(A) = A^T;

if transa_i = 'C' or 'c', then op(A) = A^H.

transb_array

CHARACTER*1. 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 = 'N' or 'n', then op(B) = B;

if transb_i = 'T' or 't', then op(B) = B^T;

if transb_i = 'C' or 'c', then op(B) = B^H.

m_array

INTEGER. 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

INTEGER. 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

INTEGER. 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

REAL for sgemm_batch

DOUBLE PRECISION for dgemm_batch

COMPLEX for cgemm_batch

DOUBLE COMPLEX for zgemm_batch

Array of size group_count. For the group i, alpha_array(i) specifies the scalar alpha_i.

a_array

INTEGER*8 for Intel^® 64 architecture

INTEGER*4 for IA-32 architecture

Array, size total_batch_count, of pointers to arrays used to store A matrices.

lda_array

INTEGER. 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.

When transa_i = 'N' or 'n', then lda_i must be at least max(1, m_i), otherwise lda_i must be at least max(1, k_i).

b_array

INTEGER*8 for Intel^® 64 architecture

INTEGER*4 for IA-32 architecture

Array, size total_batch_count, of pointers to arrays used to store B matrices.

ldb_array

INTEGER.

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.

When transb_i = 'N' or 'n', then ldb_i must be at least max(1, k_i), otherwise ldb_i must be at least max(1, n_i).

beta_array

REAL for sgemm_batch

DOUBLE PRECISION for dgemm_batch

COMPLEX for cgemm_batch

DOUBLE COMPLEX for zgemm_batch

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

INTEGER*8 for Intel^® 64 architecture

INTEGER*4 for IA-32 architecture

Array, size total_batch_count, of pointers to arrays used to store C matrices.

ldc_array

INTEGER.

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.

ldc_i must be at least max(1, m_i).

group_count

INTEGER.

Specifies the number of groups. Must be at least 0.

group_size

INTEGER.

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.

BLAS 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see BLAS 95 Interface Conventions.

Specific details for the routine gemm_batch interface are the following:

a_array

Holds pointers to arrays containing matrices A of size (ma,ka) where

ka = k if transa='N',

ka = m otherwise,

ma = m if transa='N',

ma = k otherwise.

b_array

Holds pointers to arrays containing matrices B of size (mb,kb) where

kb = n if transb_array = 'N',

kb = k otherwise,

mb = k if transb_array = 'N',

mb = n otherwise.

c_array

Holds pointers to arrays containing matrices C of size (m,n).

m_array

Array indicating number of rows of matrices op(A) and C for each group.

n_array

Array indicating number of columns of matrices op(B) and C for each group.

k_array

Array indicating number of columns of matrices op(A) and number of rows of matrices op(B) for each group.

group_size

Array indicating number of matrices for each group. Each element in group_size must be at least 0.

transa_array

Array with each element set to one of 'N', 'C', or 'T'.

The default values are 'N'.

transb_array

Array with each element set to one of 'N', 'C', or 'T'.

The default values are 'N'.

alpha_array

Array of alpha values; the default value is 1.

beta_array

Array of beta values; the default value is 0.

Parent topic: BLAS-like Extensions

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?gemm_batch

Syntax

Include Files

Description

Input Parameters

Output Parameters

BLAS 95 Interface Notes