BigDataStatMeth (version 1.0.3)

bdSolve: Solve Linear System AX = B (In-Memory)

Description

Solves the linear system AX = B where A is an N-by-N matrix and X and B are N-by-NRHS matrices. The function automatically detects if A is symmetric and uses the appropriate solver.

Usage

bdSolve(A, B)

Value

Numeric matrix X, the solution to AX = B.

Arguments

A

Numeric matrix. The coefficient matrix (must be square).

B

Numeric matrix. The right-hand side matrix (must have same number of rows as A).

Details

This function provides an efficient implementation for solving linear systems using LAPACK routines. Key features:

• Automatic detection of matrix properties:

  • Checks for matrix symmetry

  • Selects optimal solver based on matrix structure

• Solver selection:

  • Symmetric systems: Uses LAPACK's dsysv routine

  • Non-symmetric systems: Uses LAPACK's dgesv routine

• Performance optimizations:

  • Automatic workspace sizing

  • Efficient memory management

  • Support for multiple right-hand sides

The implementation ensures:

• Robust error handling

• Efficient memory usage

• Numerical stability

• Support for various matrix sizes

References

• Anderson, E. et al. (1999). LAPACK Users' Guide, 3rd Edition. SIAM, Philadelphia.

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

See Also

• bdSolve_hdf5 for solving systems with HDF5-stored matrices

• solve for R's built-in solver

Examples

library(BigDataStatMeth)

# Create test matrices
n <- 500
m <- 500

A <- matrix(runif(n*m), nrow = n, ncol = m)
B <- matrix(runif(n), nrow = n)
AS <- A %*% t(A)  # Create symmetric matrix

# Solve using bdSolve
X <- bdSolve(A, B)

# Compare with R's solve
XR <- solve(A, B)
all.equal(X, XR, check.attributes=FALSE)