Linear Algebra

1 Overview

Linear algebra operations that run in memory (RAM).

2 Functions

2.1 bdQR

Computes the QR decomposition (also called QR factorization) of a matrix A into a product A = QR where Q is an orthogonal matrix and R is an upper triangular matrix. This function operates on in-memory matrices.

2.2 bdSolve

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.

2.3 bdpseudoinv

Computes the Moore-Penrose pseudoinverse of a matrix using SVD decomposition. This implementation handles both square and rectangular matrices, and provides numerically stable results even for singular or near-singular matrices.

2.4 bdCorr_matrix

Compute Pearson or Spearman correlation matrix for matrices that fit in memory. This function automatically detects whether to compute:

2.5 bdCrossprod

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.

2.6 bdScalarwproduct

Multiplies a numeric matrix by a scalar weight , returning . The input must be a base R numeric matrix (or convertible to one).

2.7 bdtCrossprod

Computes matrix transposed cross-products efficiently using block-based algorithms and optional parallel processing. Supports both single-matrix (XX’) and two-matrix (XY’) transposed cross-products.

2.8 bd_wproduct

Compute weighted operations using a diagonal weight from : Inputs may be base numeric matrices .

---
title: "Linear Algebra"
---

## Overview

Linear algebra operations that run in memory (RAM).

## Functions


### [bdQR](bdQR.qmd)

Computes the QR decomposition (also called QR factorization) of a matrix A into 
a product A = QR where Q is an orthogonal matrix and R is an upper triangular matrix.
This function operates on in-memory matrices.


### [bdSolve](bdSolve.qmd)

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.


### [bdpseudoinv](bdpseudoinv.qmd)

Computes the Moore-Penrose pseudoinverse of a matrix using SVD decomposition.
This implementation handles both square and rectangular matrices, and provides
numerically stable results even for singular or near-singular matrices.


### [bdCorr_matrix](bdCorr_matrix.qmd)

Compute Pearson or Spearman correlation matrix for matrices that fit in memory.
This function automatically detects whether to compute:
\itemize{
  \item Single matrix correlation cor(X) - when only matrix X is provided
  \item Cross-correlation cor(X,Y) - when both matrices X and Y are provided
}


### [bdCrossprod](bdCrossprod.qmd)

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.


### [bdScalarwproduct](bdScalarwproduct.qmd)

Multiplies a numeric matrix \code{A} by a scalar weight \code{w},
returning \eqn{w * A}. The input must be a base R numeric matrix (or
convertible to one). 


### [bdtCrossprod](bdtCrossprod.qmd)

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


### [bd_wproduct](bd_wproduct.qmd)

Compute weighted operations using a diagonal weight from \code{w}:
\itemize{
\item \code{"xtwx"}: \eqn{X' diag(w) X}  (row weights; \code{length(w) = nrow(X)})
\item \code{"xwxt"}: \eqn{X diag(w) X'}  (column weights; \code{length(w) = ncol(X)})
\item \code{"xw"}  : \eqn{X diag(w)}     (column scaling; \code{length(w) = ncol(X)})
\item \code{"wx"}  : \eqn{diag(w) X}     (row scaling;    \code{length(w) = nrow(X)})
}
Inputs may be base numeric matrices .