bdSolve

bdSolve

LINEAR_ALGEBRA

1 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.

2 Usage

bdSolve(A, B)

3 Arguments

Parameter	Description
`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).

4 Value

Numeric matrix X, the solution to AX = B.

5 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

6 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)

7 See Also

bdSolve_hdf5 for solving systems with HDF5-stored matrices
solve for R’s built-in solver

---
title: "bdSolve"
subtitle: "bdSolve"
---

<span class="category-badge linear_algebra">LINEAR_ALGEBRA</span>

## 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

```r
bdSolve(A, B)
```
## Arguments

::: {.param-table}
| Parameter | Description |
|-----------|-------------|
| `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).  |
:::

## Value

::: {.return-value}
Numeric matrix X, the solution to AX = B.

:::
## 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

## Examples
```{r}
#| eval: false
#| warning: false

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)

```
## See Also

::: {.see-also}
- [bdSolve_hdf5](../hdf5_algebra/bdSolve_hdf5.html) for solving systems with HDF5-stored matrices
- [solve](solve.html) for R's built-in solver

:::