bdblockMult

LINEAR_ALGEBRA

1 Description

Performs efficient matrix multiplication using block-based algorithms. The function supports various input combinations (matrix-matrix, matrix-vector, vector-vector) and provides options for parallel processing and block-based computation.

2 Usage

bdblockMult(A, B, block_size = NULL, paral = NULL, byBlocks = TRUE, threads = NULL)

3 Arguments

Parameter	Description
`A`	Matrix or vector. First input operand.
`B`	Matrix or vector. Second input operand.
`block_size`	Integer. Block size for computation. If NULL, uses maximum allowed block size.
`paral`	Logical. If TRUE, enables parallel computation. Default is FALSE.
`byBlocks`	Logical. If TRUE (default), forces block-based computation for large matrices. Can be set to FALSE to disable blocking.
`threads`	Integer. Number of threads for parallel computation. If NULL, uses half of available threads or maximum allowed threads.

4 Value

Matrix or vector containing the result of A * B.

5 Details

This function implements block-based matrix multiplication algorithms optimized for cache efficiency and memory usage. Key features: - Input combinations supported: - Matrix-matrix multiplication - Matrix-vector multiplication (both left and right) - Vector-vector multiplication - Performance optimizations: - Block-based computation for cache efficiency - Parallel processing for large matrices - Automatic block size selection - Memory-efficient implementation

The function automatically selects the appropriate multiplication method based on input types and sizes. For large matrices (>2.25e+08 elements), block-based computation is used by default.

6 Examples

\donttest{

# Matrix-matrix multiplication
N <- 2500
M <- 400
nc <- 4

set.seed(555)
mat <- matrix(rnorm(N*M, mean=0, sd=10), N, M)

# Parallel block multiplication
result <- bdblockMult(mat, mat,
                      paral = TRUE,
                      threads = nc)

# Matrix-vector multiplication
vec <- rnorm(M)
result_mv <- bdblockMult(mat, vec,
                         paral = TRUE,
                         threads = nc)
}

7 See Also

bdblockSum for block-based matrix addition
bdblockSubstract for block-based matrix subtraction

--- title: "bdblockMult" subtitle: "bdblockMult" --- <span class="category-badge linear_algebra">LINEAR_ALGEBRA</span> ## Description Performs efficient matrix multiplication using block-based algorithms. The function supports various input combinations (matrix-matrix, matrix-vector, vector-vector) and provides options for parallel processing and block-based computation. ## Usage ```r bdblockMult(A, B, block_size = NULL, paral = NULL, byBlocks = TRUE, threads = NULL) ``` ## Arguments ::: {.param-table} | Parameter | Description | |-----------|-------------| | `A` | Matrix or vector. First input operand. | | `B` | Matrix or vector. Second input operand. | | `block_size` | Integer. Block size for computation. If NULL, uses maximum allowed block size. | | `paral` | Logical. If TRUE, enables parallel computation. Default is FALSE. | | `byBlocks` | Logical. If TRUE (default), forces block-based computation for large matrices. Can be set to FALSE to disable blocking. | | `threads` | Integer. Number of threads for parallel computation. If NULL, uses half of available threads or maximum allowed threads. | ::: ## Value ::: {.return-value} Matrix or vector containing the result of A * B. ::: ## Details This function implements block-based matrix multiplication algorithms optimized for cache efficiency and memory usage. Key features: - Input combinations supported: - Matrix-matrix multiplication - Matrix-vector multiplication (both left and right) - Vector-vector multiplication - Performance optimizations: - Block-based computation for cache efficiency - Parallel processing for large matrices - Automatic block size selection - Memory-efficient implementation The function automatically selects the appropriate multiplication method based on input types and sizes. For large matrices (>2.25e+08 elements), block-based computation is used by default. ## Examples ```{r} #| eval: false #| warning: false \donttest{ # Matrix-matrix multiplication N <- 2500 M <- 400 nc <- 4 set.seed(555) mat <- matrix(rnorm(N*M, mean=0, sd=10), N, M) # Parallel block multiplication result <- bdblockMult(mat, mat, paral = TRUE, threads = nc) # Matrix-vector multiplication vec <- rnorm(M) result_mv <- bdblockMult(mat, vec, paral = TRUE, threads = nc) } ``` ## See Also ::: {.see-also} - [bdblockSum](bdblockSum.html) for block-based matrix addition - [bdblockSubstract](bdblockSubstract.html) for block-based matrix subtraction :::