BigDataStatMeth (version 2.0.3)

bdCrossprod: Efficient Matrix Cross-Product Computation

Description

Computes matrix cross-products efficiently using block-based algorithms and optional parallel processing. Supports both single-matrix (X'X) and two-matrix (X'Y) cross-products.

Usage

bdCrossprod(
  A,
  B = NULL,
  transposed = NULL,
  block_size = NULL,
  paral = NULL,
  threads = NULL
)

Value

Numeric matrix containing the cross-product result.

Arguments

A

Numeric matrix. First input matrix.

B

Optional numeric matrix. If provided, computes A'B instead of A'A.

transposed

Logical. If TRUE, uses transposed input matrix.

block_size

Integer. Block size for computation. If NULL, uses optimal block size based on matrix dimensions and cache size.

paral

Logical. If TRUE, enables parallel computation.

threads

Integer. Number of threads for parallel computation. If NULL, uses all available threads.

Details

This function implements efficient cross-product computation using block-based algorithms optimized for cache efficiency and memory usage. Key features:

• Operation modes:

  • Single matrix: Computes X'X

  • Two matrices: Computes X'Y

• Performance optimizations:

  • Block-based computation for cache efficiency

  • Parallel processing for large matrices

  • Automatic block size selection

  • Memory-efficient implementation

The function automatically selects optimal computation strategies based on input size and available resources. For large matrices, block-based computation is used to improve cache utilization.

References

• Golub, G. H., & Van Loan, C. F. (2013). Matrix Computations, 4th Edition. Johns Hopkins University Press.

• Kumar, V. et al. (1994). Introduction to Parallel Computing: Design and Analysis of Algorithms. Benjamin/Cummings Publishing Company.

See Also

• bdtCrossprod for transposed cross-product

• bdblockMult for block-based matrix multiplication

Examples

# Single matrix cross-product
n <- 100
p <- 60
X <- matrix(rnorm(n*p), nrow=n, ncol=p)
res <- bdCrossprod(X)

# Verify against base R
all.equal(crossprod(X), res)

# Two-matrix cross-product
n <- 100
p <- 100
Y <- matrix(rnorm(n*p), nrow=n)
res <- bdCrossprod(X, Y)
all.equal(crossprod(X, Y), res)

# Parallel computation
res_par <- bdCrossprod(X, paral = TRUE, threads = 2)