Computes the inverse of a symmetric positive-definite matrix stored in an HDF5 file using the Cholesky decomposition method. This approach is more efficient and numerically stable than general matrix inversion methods for symmetric positive-definite matrices.
Character string. Path to the HDF5 file containing the input matrix.
group
Character string. Path to the group containing the input dataset.
dataset
Character string. Name of the input dataset to invert.
outdataset
Character string. Name for the output dataset.
outgroup
Character string. Optional output group path. If not provided, results are stored in the input group.
fullMatrix
Logical. If TRUE, stores the complete inverse matrix. If FALSE (default), stores only the lower triangular part to save space.
overwrite
Logical. If TRUE, allows overwriting existing results.
threads
Integer. Number of threads for parallel computation (default = 2).
elementsBlock
Integer. Maximum number of elements to process in each block (default = 1,000,000). For matrices larger than 5000x5000, automatically adjusted to number of rows or columns * 2.
4 Value
List with components:
fn: Character string with the HDF5 filename
ds: Character string with the full dataset path to the inverse Cholesky decomposition A^(-1) result (group/dataset)
5 Details
This function implements an efficient matrix inversion algorithm that leverages the special properties of symmetric positive-definite matrices. Key features: - Uses Cholesky decomposition for improved numerical stability - Block-based computation for large matrices - Optional storage formats (full or triangular) - Parallel processing support - Memory-efficient block algorithm
The algorithm proceeds in two main steps: 1. Compute the Cholesky decomposition A = LL’ 2. Solve the system LL’X = I for X = A^(-1)
Advantages of this method: - More efficient than general matrix inversion - Better numerical stability - Preserves matrix symmetry - Exploits positive-definiteness for efficiency
6 Examples
Code
library(rhdf5)# Create a symmetric positive-definite matrixset.seed(1234)X <-matrix(rnorm(100), 10, 10)A <-crossprod(X) # A = X'X is symmetric positive-definite# Save to HDF5h5createFile("matrix.h5")h5write(A, "matrix.h5", "data/matrix")# Compute inverse using Cholesky decompositionbdInvCholesky_hdf5("matrix.h5", "data", "matrix",outdataset ="inverse",outgroup ="results",fullMatrix =TRUE,threads =4)# Verify the inverseAinv <-h5read("matrix.h5", "results/inverse")max(abs(A %*% Ainv -diag(nrow(A)))) # Should be very small
---title: "bdInvCholesky_hdf5"subtitle: "bdInvCholesky_hdf5"---<span class="category-badge hdf5_algebra">HDF5_ALGEBRA</span>## DescriptionComputes the inverse of a symmetric positive-definite matrix stored in an HDF5 fileusing the Cholesky decomposition method. This approach is more efficient andnumerically stable than general matrix inversion methods for symmetricpositive-definite matrices.## Usage```rbdInvCholesky_hdf5(filename, group, dataset, outdataset, outgroup =NULL, fullMatrix =NULL, overwrite =NULL, threads =2L, elementsBlock =1000000L)```## Arguments::: {.param-table}| Parameter | Description ||-----------|-------------||`filename`| Character string. Path to the HDF5 file containing the input matrix. ||`group`| Character string. Path to the group containing the input dataset. ||`dataset`| Character string. Name of the input dataset to invert. ||`outdataset`| Character string. Name for the output dataset. ||`outgroup`| Character string. Optional output group path. If not provided, results are stored in the input group. ||`fullMatrix`| Logical. If TRUE, stores the complete inverse matrix. If FALSE (default), stores only the lower triangular part to save space. ||`overwrite`| Logical. If TRUE, allows overwriting existing results. ||`threads`| Integer. Number of threads for parallel computation (default = 2). ||`elementsBlock`| Integer. Maximum number of elements to process in each block (default = 1,000,000). For matrices larger than 5000x5000, automatically adjusted to number of rows or columns * 2. |:::## Value::: {.return-value}List with components:- **`fn`**: Character string with the HDF5 filename- **`ds`**: Character string with the full dataset path to the inverse Cholesky decomposition A^(-1) result (group/dataset):::## DetailsThis function implements an efficient matrix inversion algorithm that leveragesthe special properties of symmetric positive-definite matrices. Key features:- Uses Cholesky decomposition for improved numerical stability- Block-based computation for large matrices- Optional storage formats (full or triangular)- Parallel processing support- Memory-efficient block algorithmThe algorithm proceeds in two main steps:1. Compute the Cholesky decomposition A = LL'2. Solve the system LL'X = I for X = A^(-1)Advantages of this method:- More efficient than general matrix inversion- Better numerical stability- Preserves matrix symmetry- Exploits positive-definiteness for efficiency## Examples```{r}#| eval: false#| code-fold: showlibrary(rhdf5)# Create a symmetric positive-definite matrixset.seed(1234)X <-matrix(rnorm(100), 10, 10)A <-crossprod(X) # A = X'X is symmetric positive-definite# Save to HDF5h5createFile("matrix.h5")h5write(A, "matrix.h5", "data/matrix")# Compute inverse using Cholesky decompositionbdInvCholesky_hdf5("matrix.h5", "data", "matrix",outdataset ="inverse",outgroup ="results",fullMatrix =TRUE,threads =4)# Verify the inverseAinv <-h5read("matrix.h5", "results/inverse")max(abs(A %*% Ainv -diag(nrow(A)))) # Should be very small```## See Also::: {.see-also}- [bdCholesky_hdf5](bdCholesky_hdf5.html) for the underlying Cholesky decomposition- [bdSolve_hdf5](bdSolve_hdf5.html) for solving linear systems:::